id	sid	tid	token	lemma	pos
ejpam-6593	1	1	european	european	PROPN
ejpam-6593	1	2	journal	journal	PROPN
ejpam-6593	1	3	of	of	ADP
ejpam-6593	1	4	pure	pure	ADJ
ejpam-6593	1	5	and	and	CCONJ
ejpam-6593	1	6	applied	applied	ADJ
ejpam-6593	1	7	mathematics	mathematic	NOUN
ejpam-6593	1	8	2025	2025	NUM
ejpam-6593	1	9	,	,	PUNCT
ejpam-6593	1	10	vol	vol	NOUN
ejpam-6593	1	11	.	.	PROPN
ejpam-6593	1	12	18	18	NUM
ejpam-6593	1	13	,	,	PUNCT
ejpam-6593	1	14	issue	issue	NOUN
ejpam-6593	1	15	3	3	NUM
ejpam-6593	1	16	,	,	PUNCT
ejpam-6593	1	17	article	article	NOUN
ejpam-6593	1	18	number	number	NOUN
ejpam-6593	1	19	6593	6593	NUM
ejpam-6593	1	20	issn	issn	PROPN
ejpam-6593	1	21	1307	1307	NUM
ejpam-6593	1	22	-	-	SYM
ejpam-6593	1	23	5543	5543	NUM
ejpam-6593	1	24	–	–	PUNCT
ejpam-6593	1	25	ejpam.com	ejpam.com	X
ejpam-6593	1	26	published	publish	VERB
ejpam-6593	1	27	by	by	ADP
ejpam-6593	1	28	new	new	PROPN
ejpam-6593	1	29	york	york	PROPN
ejpam-6593	1	30	business	business	PROPN
ejpam-6593	1	31	global	global	PROPN
ejpam-6593	1	32	on	on	ADP
ejpam-6593	1	33	the	the	DET
ejpam-6593	1	34	diophantine	diophantine	NOUN
ejpam-6593	1	35	equation	equation	NOUN
ejpam-6593	1	36	px	px	X
ejpam-6593	1	37	+	+	CCONJ
ejpam-6593	1	38	(	(	PUNCT
ejpam-6593	1	39	p+	p+	PROPN
ejpam-6593	1	40	5k)y	5k)y	NOUN
ejpam-6593	1	41	=	=	SYM
ejpam-6593	1	42	z2	z2	PROPN
ejpam-6593	1	43	merlyn	merlyn	PROPN
ejpam-6593	1	44	c.	c.	PROPN
ejpam-6593	1	45	avenilla1	avenilla1	PROPN
ejpam-6593	1	46	,	,	PUNCT
ejpam-6593	2	1	jerico	jerico	PROPN
ejpam-6593	2	2	b.	b.	PROPN
ejpam-6593	2	3	bacani1,∗	bacani1,∗	PROPN
ejpam-6593	2	4	1	1	NUM
ejpam-6593	2	5	department	department	NOUN
ejpam-6593	2	6	of	of	ADP
ejpam-6593	2	7	mathematics	mathematic	NOUN
ejpam-6593	2	8	and	and	CCONJ
ejpam-6593	2	9	computer	computer	NOUN
ejpam-6593	2	10	science	science	NOUN
ejpam-6593	2	11	,	,	PUNCT
ejpam-6593	2	12	college	college	NOUN
ejpam-6593	2	13	of	of	ADP
ejpam-6593	2	14	science	science	NOUN
ejpam-6593	2	15	,	,	PUNCT
ejpam-6593	2	16	university	university	NOUN
ejpam-6593	2	17	of	of	ADP
ejpam-6593	2	18	the	the	DET
ejpam-6593	2	19	philippines	philippines	PROPN
ejpam-6593	2	20	baguio	baguio	PROPN
ejpam-6593	2	21	,	,	PUNCT
ejpam-6593	2	22	baguio	baguio	PROPN
ejpam-6593	2	23	city	city	PROPN
ejpam-6593	2	24	2600	2600	NUM
ejpam-6593	2	25	,	,	PUNCT
ejpam-6593	2	26	benguet	benguet	PROPN
ejpam-6593	2	27	,	,	PUNCT
ejpam-6593	2	28	philippines	philippine	NOUN
ejpam-6593	2	29	abstract	abstract	ADJ
ejpam-6593	2	30	.	.	PUNCT
ejpam-6593	3	1	with	with	ADP
ejpam-6593	3	2	the	the	DET
ejpam-6593	3	3	use	use	NOUN
ejpam-6593	3	4	of	of	ADP
ejpam-6593	3	5	modular	modular	ADJ
ejpam-6593	3	6	arithmetic	arithmetic	ADJ
ejpam-6593	3	7	and	and	CCONJ
ejpam-6593	3	8	other	other	ADJ
ejpam-6593	3	9	fundamental	fundamental	ADJ
ejpam-6593	3	10	number	number	NOUN
ejpam-6593	3	11	theoretic	theoretic	NOUN
ejpam-6593	3	12	methods	method	NOUN
ejpam-6593	3	13	,	,	PUNCT
ejpam-6593	3	14	as	as	ADV
ejpam-6593	3	15	well	well	ADV
ejpam-6593	3	16	as	as	ADP
ejpam-6593	3	17	the	the	DET
ejpam-6593	3	18	concepts	concept	NOUN
ejpam-6593	3	19	of	of	ADP
ejpam-6593	3	20	the	the	DET
ejpam-6593	3	21	floor	floor	NOUN
ejpam-6593	3	22	function	function	NOUN
ejpam-6593	3	23	and	and	CCONJ
ejpam-6593	3	24	the	the	DET
ejpam-6593	3	25	principle	principle	NOUN
ejpam-6593	3	26	of	of	ADP
ejpam-6593	3	27	mathematical	mathematical	ADJ
ejpam-6593	3	28	induction	induction	NOUN
ejpam-6593	3	29	,	,	PUNCT
ejpam-6593	3	30	this	this	DET
ejpam-6593	3	31	study	study	NOUN
ejpam-6593	3	32	searches	search	VERB
ejpam-6593	3	33	for	for	ADP
ejpam-6593	3	34	possible	possible	ADJ
ejpam-6593	3	35	nonnegative	nonnegative	ADJ
ejpam-6593	3	36	integer	integer	NOUN
ejpam-6593	3	37	solutions	solution	NOUN
ejpam-6593	3	38	of	of	ADP
ejpam-6593	3	39	exponential	exponential	ADJ
ejpam-6593	3	40	diophantine	diophantine	NOUN
ejpam-6593	3	41	equations	equation	NOUN
ejpam-6593	3	42	of	of	ADP
ejpam-6593	3	43	the	the	DET
ejpam-6593	3	44	form	form	NOUN
ejpam-6593	3	45	px	px	X
ejpam-6593	3	46	+	+	CCONJ
ejpam-6593	3	47	(	(	PUNCT
ejpam-6593	3	48	p+	p+	PROPN
ejpam-6593	3	49	5k)y	5k)y	NOUN
ejpam-6593	3	50	=	=	SYM
ejpam-6593	3	51	z2	z2	PROPN
ejpam-6593	3	52	,	,	PUNCT
ejpam-6593	3	53	where	where	SCONJ
ejpam-6593	3	54	k	k	PROPN
ejpam-6593	3	55	∈	∈	PROPN
ejpam-6593	3	56	n.	n.	NOUN
ejpam-6593	3	57	results	result	NOUN
ejpam-6593	3	58	are	be	AUX
ejpam-6593	3	59	obtained	obtain	VERB
ejpam-6593	3	60	for	for	ADP
ejpam-6593	3	61	the	the	DET
ejpam-6593	3	62	following	follow	VERB
ejpam-6593	3	63	cases	case	NOUN
ejpam-6593	3	64	:	:	PUNCT
ejpam-6593	3	65	a	a	X
ejpam-6593	3	66	)	)	PUNCT
ejpam-6593	3	67	when	when	SCONJ
ejpam-6593	3	68	p	p	NOUN
ejpam-6593	3	69	=	=	NOUN
ejpam-6593	3	70	2	2	NUM
ejpam-6593	3	71	;	;	PUNCT
ejpam-6593	3	72	or	or	CCONJ
ejpam-6593	3	73	b	b	X
ejpam-6593	3	74	)	)	PUNCT
ejpam-6593	3	75	when	when	SCONJ
ejpam-6593	3	76	p	p	PROPN
ejpam-6593	3	77	and	and	CCONJ
ejpam-6593	3	78	p+	p+	PROPN
ejpam-6593	3	79	5k	5k	NUM
ejpam-6593	3	80	are	be	AUX
ejpam-6593	3	81	prime	prime	ADJ
ejpam-6593	3	82	pairs	pair	NOUN
ejpam-6593	3	83	.	.	PUNCT
ejpam-6593	4	1	in	in	ADP
ejpam-6593	4	2	addition	addition	NOUN
ejpam-6593	4	3	,	,	PUNCT
ejpam-6593	4	4	the	the	DET
ejpam-6593	4	5	study	study	NOUN
ejpam-6593	4	6	is	be	AUX
ejpam-6593	4	7	limited	limit	VERB
ejpam-6593	4	8	only	only	ADV
ejpam-6593	4	9	to	to	ADP
ejpam-6593	4	10	solutions	solution	NOUN
ejpam-6593	4	11	where	where	SCONJ
ejpam-6593	4	12	x	x	PRON
ejpam-6593	4	13	and	and	CCONJ
ejpam-6593	4	14	y	y	PROPN
ejpam-6593	4	15	are	be	AUX
ejpam-6593	4	16	not	not	PART
ejpam-6593	4	17	both	both	CCONJ
ejpam-6593	4	18	greater	great	ADJ
ejpam-6593	4	19	than	than	ADP
ejpam-6593	4	20	1	1	NUM
ejpam-6593	4	21	.	.	NOUN
ejpam-6593	4	22	2020	2020	NUM
ejpam-6593	4	23	mathematics	mathematic	NOUN
ejpam-6593	4	24	subject	subject	NOUN
ejpam-6593	4	25	classifications	classification	NOUN
ejpam-6593	4	26	:	:	PUNCT
ejpam-6593	4	27	11d61	11d61	NUM
ejpam-6593	4	28	,	,	PUNCT
ejpam-6593	4	29	11d72	11d72	NUM
ejpam-6593	4	30	,	,	PUNCT
ejpam-6593	4	31	11a41	11a41	NUM
ejpam-6593	4	32	key	key	ADJ
ejpam-6593	4	33	words	word	NOUN
ejpam-6593	4	34	and	and	CCONJ
ejpam-6593	4	35	phrases	phrase	NOUN
ejpam-6593	4	36	:	:	PUNCT
ejpam-6593	4	37	exponential	exponential	ADJ
ejpam-6593	4	38	diophantine	diophantine	NOUN
ejpam-6593	4	39	equation	equation	NOUN
ejpam-6593	4	40	,	,	PUNCT
ejpam-6593	4	41	prime	prime	ADJ
ejpam-6593	4	42	pairs	pair	NOUN
ejpam-6593	4	43	,	,	PUNCT
ejpam-6593	4	44	mihăilescu	mihăilescu	PROPN
ejpam-6593	4	45	’s	’s	PART
ejpam-6593	4	46	theorem	theorem	NOUN
ejpam-6593	4	47	1	1	NUM
ejpam-6593	4	48	.	.	NOUN
ejpam-6593	5	1	introduction	introduction	NOUN
ejpam-6593	5	2	a	a	DET
ejpam-6593	5	3	prime	prime	ADJ
ejpam-6593	5	4	number	number	NOUN
ejpam-6593	5	5	is	be	AUX
ejpam-6593	5	6	a	a	DET
ejpam-6593	5	7	natural	natural	ADJ
ejpam-6593	5	8	number	number	NOUN
ejpam-6593	5	9	greater	great	ADJ
ejpam-6593	5	10	than	than	ADP
ejpam-6593	5	11	1	1	NUM
ejpam-6593	5	12	whose	whose	DET
ejpam-6593	5	13	divisors	divisor	NOUN
ejpam-6593	5	14	are	be	AUX
ejpam-6593	5	15	1	1	NUM
ejpam-6593	5	16	and	and	CCONJ
ejpam-6593	5	17	itself	itself	PRON
ejpam-6593	5	18	.	.	PUNCT
ejpam-6593	6	1	the	the	DET
ejpam-6593	6	2	difference	difference	NOUN
ejpam-6593	6	3	between	between	ADP
ejpam-6593	6	4	two	two	NUM
ejpam-6593	6	5	prime	prime	ADJ
ejpam-6593	6	6	numbers	number	NOUN
ejpam-6593	6	7	is	be	AUX
ejpam-6593	6	8	called	call	VERB
ejpam-6593	6	9	prime	prime	ADJ
ejpam-6593	6	10	gap	gap	NOUN
ejpam-6593	6	11	,	,	PUNCT
ejpam-6593	6	12	and	and	CCONJ
ejpam-6593	6	13	the	the	DET
ejpam-6593	6	14	two	two	NUM
ejpam-6593	6	15	prime	prime	ADJ
ejpam-6593	6	16	numbers	number	NOUN
ejpam-6593	6	17	are	be	AUX
ejpam-6593	6	18	called	call	VERB
ejpam-6593	6	19	prime	prime	ADJ
ejpam-6593	6	20	pair	pair	NOUN
ejpam-6593	6	21	.	.	PUNCT
ejpam-6593	7	1	the	the	DET
ejpam-6593	7	2	prime	prime	ADJ
ejpam-6593	7	3	pairs	pair	NOUN
ejpam-6593	7	4	that	that	PRON
ejpam-6593	7	5	have	have	VERB
ejpam-6593	7	6	two	two	NUM
ejpam-6593	7	7	gaps	gap	NOUN
ejpam-6593	7	8	are	be	AUX
ejpam-6593	7	9	called	call	VERB
ejpam-6593	7	10	twin	twin	ADJ
ejpam-6593	7	11	primes	prime	NOUN
ejpam-6593	7	12	,	,	PUNCT
ejpam-6593	7	13	those	those	PRON
ejpam-6593	7	14	with	with	ADP
ejpam-6593	7	15	four	four	NUM
ejpam-6593	7	16	and	and	CCONJ
ejpam-6593	7	17	six	six	NUM
ejpam-6593	7	18	gaps	gap	NOUN
ejpam-6593	7	19	are	be	AUX
ejpam-6593	7	20	called	call	VERB
ejpam-6593	7	21	cousin	cousin	NOUN
ejpam-6593	7	22	primes	prime	NOUN
ejpam-6593	7	23	and	and	CCONJ
ejpam-6593	7	24	sexy	sexy	ADJ
ejpam-6593	7	25	primes	prime	NOUN
ejpam-6593	7	26	,	,	PUNCT
ejpam-6593	7	27	respectively	respectively	ADV
ejpam-6593	7	28	.	.	PUNCT
ejpam-6593	8	1	in	in	ADP
ejpam-6593	8	2	this	this	DET
ejpam-6593	8	3	present	present	ADJ
ejpam-6593	8	4	study	study	NOUN
ejpam-6593	8	5	,	,	PUNCT
ejpam-6593	8	6	we	we	PRON
ejpam-6593	8	7	incorporate	incorporate	VERB
ejpam-6593	8	8	prime	prime	ADJ
ejpam-6593	8	9	bases	basis	NOUN
ejpam-6593	8	10	and	and	CCONJ
ejpam-6593	8	11	prime	prime	ADJ
ejpam-6593	8	12	pairs	pair	NOUN
ejpam-6593	8	13	with	with	ADP
ejpam-6593	8	14	gaps	gap	NOUN
ejpam-6593	8	15	of	of	ADP
ejpam-6593	8	16	multiples	multiple	NOUN
ejpam-6593	8	17	of	of	ADP
ejpam-6593	8	18	five	five	NUM
ejpam-6593	8	19	.	.	PUNCT
ejpam-6593	9	1	they	they	PRON
ejpam-6593	9	2	are	be	AUX
ejpam-6593	9	3	part	part	NOUN
ejpam-6593	9	4	of	of	ADP
ejpam-6593	9	5	the	the	DET
ejpam-6593	9	6	study	study	NOUN
ejpam-6593	9	7	of	of	ADP
ejpam-6593	9	8	exponential	exponential	ADJ
ejpam-6593	9	9	diophantine	diophantine	NOUN
ejpam-6593	9	10	equations	equation	NOUN
ejpam-6593	9	11	.	.	PUNCT
ejpam-6593	10	1	diophantine	diophantine	VERB
ejpam-6593	10	2	equations	equation	NOUN
ejpam-6593	10	3	are	be	AUX
ejpam-6593	10	4	any	any	DET
ejpam-6593	10	5	equations	equation	NOUN
ejpam-6593	10	6	that	that	PRON
ejpam-6593	10	7	seek	seek	VERB
ejpam-6593	10	8	rational	rational	ADJ
ejpam-6593	10	9	solutions	solution	NOUN
ejpam-6593	10	10	,	,	PUNCT
ejpam-6593	10	11	but	but	CCONJ
ejpam-6593	10	12	usually	usually	ADV
ejpam-6593	10	13	integers	integer	NOUN
ejpam-6593	10	14	.	.	PUNCT
ejpam-6593	11	1	these	these	DET
ejpam-6593	11	2	equations	equation	NOUN
ejpam-6593	11	3	are	be	AUX
ejpam-6593	11	4	believed	believe	VERB
ejpam-6593	11	5	to	to	PART
ejpam-6593	11	6	have	have	AUX
ejpam-6593	11	7	been	be	AUX
ejpam-6593	11	8	introduced	introduce	VERB
ejpam-6593	11	9	by	by	ADP
ejpam-6593	11	10	diophantus	diophantus	NOUN
ejpam-6593	11	11	of	of	ADP
ejpam-6593	11	12	alexandria	alexandria	PROPN
ejpam-6593	11	13	.	.	PUNCT
ejpam-6593	12	1	there	there	PRON
ejpam-6593	12	2	are	be	VERB
ejpam-6593	12	3	two	two	NUM
ejpam-6593	12	4	types	type	NOUN
ejpam-6593	12	5	of	of	ADP
ejpam-6593	12	6	diophantine	diophantine	NOUN
ejpam-6593	12	7	equation	equation	NOUN
ejpam-6593	12	8	,	,	PUNCT
ejpam-6593	12	9	namely	namely	ADV
ejpam-6593	12	10	,	,	PUNCT
ejpam-6593	12	11	linear	linear	ADJ
ejpam-6593	12	12	and	and	CCONJ
ejpam-6593	12	13	nonlinear	nonlinear	ADJ
ejpam-6593	12	14	.	.	PUNCT
ejpam-6593	13	1	each	each	DET
ejpam-6593	13	2	type	type	NOUN
ejpam-6593	13	3	could	could	AUX
ejpam-6593	13	4	have	have	VERB
ejpam-6593	13	5	no	no	DET
ejpam-6593	13	6	solution	solution	NOUN
ejpam-6593	13	7	,	,	PUNCT
ejpam-6593	13	8	unique	unique	ADJ
ejpam-6593	13	9	solution	solution	NOUN
ejpam-6593	13	10	,	,	PUNCT
ejpam-6593	13	11	finitely	finitely	ADV
ejpam-6593	13	12	many	many	ADJ
ejpam-6593	13	13	solutions	solution	NOUN
ejpam-6593	13	14	,	,	PUNCT
ejpam-6593	13	15	or	or	CCONJ
ejpam-6593	13	16	infinitely	infinitely	ADV
ejpam-6593	13	17	many	many	ADJ
ejpam-6593	13	18	solutions	solution	NOUN
ejpam-6593	13	19	.	.	PUNCT
ejpam-6593	14	1	the	the	DET
ejpam-6593	14	2	linear	linear	ADJ
ejpam-6593	14	3	diophantine	diophantine	NOUN
ejpam-6593	14	4	equation	equation	NOUN
ejpam-6593	14	5	(	(	PUNCT
ejpam-6593	14	6	lde	lde	X
ejpam-6593	14	7	)	)	PUNCT
ejpam-6593	14	8	is	be	AUX
ejpam-6593	14	9	the	the	DET
ejpam-6593	14	10	famous	famous	ADJ
ejpam-6593	14	11	one	one	NOUN
ejpam-6593	14	12	.	.	PUNCT
ejpam-6593	15	1	in	in	ADP
ejpam-6593	15	2	n	n	PRON
ejpam-6593	15	3	unknowns	unknown	NOUN
ejpam-6593	15	4	,	,	PUNCT
ejpam-6593	15	5	it	it	PRON
ejpam-6593	15	6	is	be	AUX
ejpam-6593	15	7	of	of	ADP
ejpam-6593	15	8	the	the	DET
ejpam-6593	15	9	form	form	NOUN
ejpam-6593	15	10	a1x1	a1x1	NOUN
ejpam-6593	15	11	+	+	NOUN
ejpam-6593	16	1	a2x2	a2x2	NOUN
ejpam-6593	17	1	+	+	CCONJ
ejpam-6593	17	2	.	.	PUNCT
ejpam-6593	17	3	.	.	PUNCT
ejpam-6593	18	1	.+	.+	NOUN
ejpam-6593	18	2	anxn	anxn	NOUN
ejpam-6593	18	3	=	=	SYM
ejpam-6593	18	4	c	c	NOUN
ejpam-6593	18	5	,	,	PUNCT
ejpam-6593	18	6	(	(	PUNCT
ejpam-6593	18	7	1	1	X
ejpam-6593	18	8	)	)	PUNCT
ejpam-6593	18	9	∗corresponding	∗corresponde	VERB
ejpam-6593	18	10	author	author	NOUN
ejpam-6593	18	11	.	.	PUNCT
ejpam-6593	19	1	doi	doi	NOUN
ejpam-6593	19	2	:	:	PUNCT
ejpam-6593	19	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6593	https://doi.org/10.29020/nybg.ejpam.v18i3.6593	NOUN
ejpam-6593	19	4	email	email	NOUN
ejpam-6593	19	5	addresses	address	NOUN
ejpam-6593	19	6	:	:	PUNCT
ejpam-6593	19	7	mcavenilla@up.edu.ph	mcavenilla@up.edu.ph	PROPN
ejpam-6593	19	8	(	(	PUNCT
ejpam-6593	19	9	m.	m.	PROPN
ejpam-6593	19	10	c.	c.	PROPN
ejpam-6593	19	11	avenilla	avenilla	PROPN
ejpam-6593	19	12	)	)	PUNCT
ejpam-6593	19	13	,	,	PUNCT
ejpam-6593	19	14	jbbacani@up.edu.ph	jbbacani@up.edu.ph	PROPN
ejpam-6593	19	15	(	(	PUNCT
ejpam-6593	19	16	j.	j.	PROPN
ejpam-6593	19	17	b.	b.	PROPN
ejpam-6593	19	18	bacani	bacani	PROPN
ejpam-6593	19	19	)	)	PUNCT
ejpam-6593	19	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6593	20	1	1	1	NUM
ejpam-6593	20	2	copyright	copyright	NOUN
ejpam-6593	20	3	:	:	PUNCT
ejpam-6593	20	4	©	©	PROPN
ejpam-6593	20	5	2025	2025	NUM
ejpam-6593	20	6	the	the	DET
ejpam-6593	20	7	author(s	author(s	NOUN
ejpam-6593	20	8	)	)	PUNCT
ejpam-6593	20	9	.	.	PUNCT
ejpam-6593	21	1	(	(	PUNCT
ejpam-6593	21	2	cc	cc	NOUN
ejpam-6593	21	3	by	by	ADP
ejpam-6593	21	4	-	-	PUNCT
ejpam-6593	21	5	nc	nc	PROPN
ejpam-6593	21	6	4.0	4.0	NUM
ejpam-6593	21	7	)	)	PUNCT
ejpam-6593	21	8	m.	m.	NOUN
ejpam-6593	21	9	c.	c.	PROPN
ejpam-6593	21	10	avenilla	avenilla	PROPN
ejpam-6593	21	11	,	,	PUNCT
ejpam-6593	21	12	j.	j.	PROPN
ejpam-6593	21	13	b.	b.	PROPN
ejpam-6593	21	14	bacani	bacani	PROPN
ejpam-6593	21	15	/	/	SYM
ejpam-6593	21	16	eur	eur	PROPN
ejpam-6593	21	17	.	.	PUNCT
ejpam-6593	22	1	j.	j.	PROPN
ejpam-6593	22	2	pure	pure	PROPN
ejpam-6593	22	3	appl	appl	PROPN
ejpam-6593	22	4	.	.	PROPN
ejpam-6593	22	5	math	math	PROPN
ejpam-6593	22	6	,	,	PUNCT
ejpam-6593	22	7	18	18	NUM
ejpam-6593	22	8	(	(	PUNCT
ejpam-6593	22	9	3	3	NUM
ejpam-6593	22	10	)	)	PUNCT
ejpam-6593	22	11	(	(	PUNCT
ejpam-6593	22	12	2025	2025	NUM
ejpam-6593	22	13	)	)	PUNCT
ejpam-6593	22	14	,	,	PUNCT
ejpam-6593	22	15	6593	6593	NUM
ejpam-6593	22	16	2	2	NUM
ejpam-6593	22	17	of	of	ADP
ejpam-6593	22	18	24	24	NUM
ejpam-6593	22	19	where	where	SCONJ
ejpam-6593	22	20	x1	x1	PROPN
ejpam-6593	22	21	,	,	PUNCT
ejpam-6593	22	22	x2	x2	PROPN
ejpam-6593	22	23	,	,	PUNCT
ejpam-6593	22	24	.	.	PUNCT
ejpam-6593	22	25	.	.	PUNCT
ejpam-6593	23	1	.	.	PUNCT
ejpam-6593	24	1	,	,	PUNCT
ejpam-6593	24	2	xn	xn	PROPN
ejpam-6593	24	3	are	be	AUX
ejpam-6593	24	4	the	the	DET
ejpam-6593	24	5	unknowns	unknown	NOUN
ejpam-6593	24	6	,	,	PUNCT
ejpam-6593	24	7	and	and	CCONJ
ejpam-6593	24	8	a1	a1	NOUN
ejpam-6593	24	9	,	,	PUNCT
ejpam-6593	24	10	a2	a2	PROPN
ejpam-6593	24	11	,	,	PUNCT
ejpam-6593	24	12	.	.	PUNCT
ejpam-6593	24	13	.	.	PUNCT
ejpam-6593	25	1	.	.	PUNCT
ejpam-6593	26	1	,	,	PUNCT
ejpam-6593	26	2	an	an	X
ejpam-6593	26	3	,	,	PUNCT
ejpam-6593	26	4	c	c	PROPN
ejpam-6593	26	5	are	be	AUX
ejpam-6593	26	6	fixed	fix	VERB
ejpam-6593	26	7	integers	integer	NOUN
ejpam-6593	26	8	,	,	PUNCT
ejpam-6593	26	9	and	and	CCONJ
ejpam-6593	26	10	not	not	PART
ejpam-6593	26	11	all	all	DET
ejpam-6593	26	12	coefficients	coefficient	NOUN
ejpam-6593	26	13	are	be	AUX
ejpam-6593	26	14	zero	zero	NUM
ejpam-6593	26	15	.	.	PUNCT
ejpam-6593	27	1	the	the	DET
ejpam-6593	27	2	simplest	simple	ADJ
ejpam-6593	27	3	lde	lde	NOUN
ejpam-6593	27	4	is	be	AUX
ejpam-6593	27	5	the	the	DET
ejpam-6593	27	6	one	one	NOUN
ejpam-6593	27	7	with	with	ADP
ejpam-6593	27	8	two	two	NUM
ejpam-6593	27	9	unknowns	unknown	NOUN
ejpam-6593	27	10	,	,	PUNCT
ejpam-6593	27	11	say	say	VERB
ejpam-6593	27	12	x	x	PUNCT
ejpam-6593	27	13	and	and	CCONJ
ejpam-6593	27	14	y.	y.	NOUN
ejpam-6593	27	15	an	an	DET
ejpam-6593	27	16	equation	equation	NOUN
ejpam-6593	27	17	that	that	PRON
ejpam-6593	27	18	is	be	AUX
ejpam-6593	27	19	not	not	PART
ejpam-6593	27	20	of	of	ADP
ejpam-6593	27	21	the	the	DET
ejpam-6593	27	22	form	form	NOUN
ejpam-6593	27	23	(	(	PUNCT
ejpam-6593	27	24	1	1	X
ejpam-6593	27	25	)	)	PUNCT
ejpam-6593	27	26	is	be	AUX
ejpam-6593	27	27	considered	consider	VERB
ejpam-6593	27	28	nonlinear	nonlinear	ADJ
ejpam-6593	27	29	diophantine	diophantine	NOUN
ejpam-6593	27	30	equation	equation	NOUN
ejpam-6593	27	31	(	(	PUNCT
ejpam-6593	27	32	nde	nde	NOUN
ejpam-6593	27	33	)	)	PUNCT
ejpam-6593	27	34	.	.	PUNCT
ejpam-6593	28	1	examples	example	NOUN
ejpam-6593	28	2	of	of	ADP
ejpam-6593	28	3	this	this	DET
ejpam-6593	28	4	type	type	NOUN
ejpam-6593	28	5	include	include	VERB
ejpam-6593	28	6	the	the	DET
ejpam-6593	28	7	pythagorean	pythagorean	PROPN
ejpam-6593	28	8	equation	equation	NOUN
ejpam-6593	28	9	(	(	PUNCT
ejpam-6593	28	10	in	in	ADP
ejpam-6593	28	11	3	3	NUM
ejpam-6593	28	12	unknowns	unknown	NOUN
ejpam-6593	28	13	)	)	PUNCT
ejpam-6593	28	14	x2	x2	PROPN
ejpam-6593	29	1	+	+	CCONJ
ejpam-6593	29	2	y2	y2	NOUN
ejpam-6593	29	3	=	=	SYM
ejpam-6593	29	4	z2	z2	PROPN
ejpam-6593	29	5	,	,	PUNCT
ejpam-6593	29	6	pell	pell	ADJ
ejpam-6593	29	7	equation	equation	NOUN
ejpam-6593	29	8	(	(	PUNCT
ejpam-6593	29	9	in	in	ADP
ejpam-6593	29	10	2	2	NUM
ejpam-6593	29	11	unknowns	unknown	NOUN
ejpam-6593	29	12	)	)	PUNCT
ejpam-6593	29	13	x2	x2	PROPN
ejpam-6593	30	1	−	−	PROPN
ejpam-6593	30	2	dy2	dy2	PROPN
ejpam-6593	30	3	=	=	SYM
ejpam-6593	30	4	1	1	NUM
ejpam-6593	30	5	,	,	PUNCT
ejpam-6593	30	6	nagell	nagell	ADJ
ejpam-6593	30	7	-	-	PUNCT
ejpam-6593	30	8	ljunggren	ljunggren	NOUN
ejpam-6593	30	9	equation	equation	NOUN
ejpam-6593	30	10	(	(	PUNCT
ejpam-6593	30	11	in	in	ADP
ejpam-6593	30	12	4	4	NUM
ejpam-6593	30	13	unknowns	unknown	NOUN
ejpam-6593	30	14	)	)	PUNCT
ejpam-6593	30	15	xn	xn	PUNCT
ejpam-6593	31	1	−	−	PROPN
ejpam-6593	31	2	1	1	NUM
ejpam-6593	31	3	x−	x−	PROPN
ejpam-6593	31	4	1	1	NUM
ejpam-6593	31	5	=	=	SYM
ejpam-6593	31	6	yq	yq	PROPN
ejpam-6593	31	7	,	,	PUNCT
ejpam-6593	31	8	and	and	CCONJ
ejpam-6593	31	9	the	the	DET
ejpam-6593	31	10	catalan	catalan	NOUN
ejpam-6593	31	11	equation	equation	NOUN
ejpam-6593	31	12	(	(	PUNCT
ejpam-6593	31	13	in	in	ADP
ejpam-6593	31	14	4	4	NUM
ejpam-6593	31	15	unknowns	unknown	NOUN
ejpam-6593	31	16	)	)	PUNCT
ejpam-6593	31	17	ax	ax	NOUN
ejpam-6593	31	18	−	−	NOUN
ejpam-6593	31	19	by	by	ADP
ejpam-6593	31	20	=	=	PROPN
ejpam-6593	31	21	1	1	X
ejpam-6593	31	22	.	.	PUNCT
ejpam-6593	32	1	the	the	DET
ejpam-6593	32	2	last	last	ADJ
ejpam-6593	32	3	equation	equation	NOUN
ejpam-6593	32	4	is	be	AUX
ejpam-6593	32	5	also	also	ADV
ejpam-6593	32	6	known	know	VERB
ejpam-6593	32	7	as	as	ADP
ejpam-6593	32	8	an	an	DET
ejpam-6593	32	9	exponential	exponential	ADJ
ejpam-6593	32	10	diophantine	diophantine	NOUN
ejpam-6593	32	11	equation	equation	NOUN
ejpam-6593	32	12	(	(	PUNCT
ejpam-6593	32	13	ede	ede	PROPN
ejpam-6593	32	14	)	)	PUNCT
ejpam-6593	32	15	.	.	PUNCT
ejpam-6593	33	1	it	it	PRON
ejpam-6593	33	2	is	be	AUX
ejpam-6593	33	3	an	an	DET
ejpam-6593	33	4	equation	equation	NOUN
ejpam-6593	33	5	that	that	PRON
ejpam-6593	33	6	involves	involve	VERB
ejpam-6593	33	7	variable	variable	ADJ
ejpam-6593	33	8	exponents	exponent	NOUN
ejpam-6593	33	9	.	.	PUNCT
ejpam-6593	34	1	in	in	ADP
ejpam-6593	34	2	the	the	DET
ejpam-6593	34	3	past	past	ADJ
ejpam-6593	34	4	few	few	ADJ
ejpam-6593	34	5	years	year	NOUN
ejpam-6593	34	6	,	,	PUNCT
ejpam-6593	34	7	many	many	ADJ
ejpam-6593	34	8	researchers	researcher	NOUN
ejpam-6593	34	9	have	have	AUX
ejpam-6593	34	10	studied	study	VERB
ejpam-6593	34	11	edes	ede	NOUN
ejpam-6593	34	12	of	of	ADP
ejpam-6593	34	13	the	the	DET
ejpam-6593	34	14	form	form	NOUN
ejpam-6593	34	15	px	px	X
ejpam-6593	34	16	+	+	CCONJ
ejpam-6593	34	17	qy	qy	NOUN
ejpam-6593	34	18	=	=	PROPN
ejpam-6593	34	19	z2	z2	PROPN
ejpam-6593	34	20	(	(	PUNCT
ejpam-6593	34	21	2	2	NUM
ejpam-6593	34	22	)	)	PUNCT
ejpam-6593	34	23	for	for	ADP
ejpam-6593	34	24	various	various	ADJ
ejpam-6593	34	25	fixed	fix	VERB
ejpam-6593	34	26	values	value	NOUN
ejpam-6593	34	27	of	of	ADP
ejpam-6593	34	28	p	p	NOUN
ejpam-6593	34	29	and	and	CCONJ
ejpam-6593	34	30	q.	q.	NOUN
ejpam-6593	34	31	in	in	ADP
ejpam-6593	34	32	2011	2011	NUM
ejpam-6593	34	33	,	,	PUNCT
ejpam-6593	34	34	singta	singta	VERB
ejpam-6593	34	35	et	et	PROPN
ejpam-6593	34	36	al	al	PROPN
ejpam-6593	34	37	.	.	PUNCT
ejpam-6593	35	1	[	[	X
ejpam-6593	35	2	1	1	X
ejpam-6593	35	3	]	]	PUNCT
ejpam-6593	35	4	proved	prove	VERB
ejpam-6593	35	5	that	that	SCONJ
ejpam-6593	35	6	there	there	PRON
ejpam-6593	35	7	are	be	VERB
ejpam-6593	35	8	no	no	DET
ejpam-6593	35	9	solutions	solution	NOUN
ejpam-6593	35	10	in	in	ADP
ejpam-6593	35	11	the	the	DET
ejpam-6593	35	12	set	set	PROPN
ejpam-6593	35	13	n0	n0	NOUN
ejpam-6593	35	14	of	of	ADP
ejpam-6593	35	15	non	non	ADJ
ejpam-6593	35	16	-	-	ADJ
ejpam-6593	35	17	negative	negative	ADJ
ejpam-6593	35	18	integers	integer	NOUN
ejpam-6593	35	19	when	when	SCONJ
ejpam-6593	35	20	p	p	NOUN
ejpam-6593	35	21	=	=	NOUN
ejpam-6593	35	22	4	4	NUM
ejpam-6593	35	23	and	and	CCONJ
ejpam-6593	35	24	q	q	NOUN
ejpam-6593	35	25	=	=	SYM
ejpam-6593	35	26	7	7	NUM
ejpam-6593	35	27	or	or	CCONJ
ejpam-6593	35	28	11	11	NUM
ejpam-6593	35	29	.	.	PUNCT
ejpam-6593	36	1	in	in	ADP
ejpam-6593	36	2	2012	2012	NUM
ejpam-6593	36	3	,	,	PUNCT
ejpam-6593	36	4	sroysang	sroysang	X
ejpam-6593	37	1	[	[	X
ejpam-6593	37	2	2	2	NUM
ejpam-6593	37	3	]	]	PUNCT
ejpam-6593	37	4	showed	show	VERB
ejpam-6593	37	5	that	that	SCONJ
ejpam-6593	37	6	(	(	PUNCT
ejpam-6593	37	7	1	1	NUM
ejpam-6593	37	8	,	,	PUNCT
ejpam-6593	37	9	0	0	NUM
ejpam-6593	37	10	,	,	PUNCT
ejpam-6593	37	11	2	2	NUM
ejpam-6593	37	12	)	)	PUNCT
ejpam-6593	37	13	is	be	AUX
ejpam-6593	37	14	the	the	DET
ejpam-6593	37	15	only	only	ADJ
ejpam-6593	37	16	solution	solution	NOUN
ejpam-6593	37	17	in	in	ADP
ejpam-6593	37	18	n0	n0	NUM
ejpam-6593	37	19	for	for	ADP
ejpam-6593	37	20	the	the	DET
ejpam-6593	37	21	case	case	NOUN
ejpam-6593	37	22	p	p	X
ejpam-6593	37	23	=	=	NOUN
ejpam-6593	37	24	3	3	NUM
ejpam-6593	37	25	and	and	CCONJ
ejpam-6593	37	26	q	q	NOUN
ejpam-6593	37	27	=	=	NOUN
ejpam-6593	37	28	5	5	X
ejpam-6593	37	29	.	.	PUNCT
ejpam-6593	38	1	in	in	ADP
ejpam-6593	38	2	the	the	DET
ejpam-6593	38	3	same	same	ADJ
ejpam-6593	38	4	year	year	NOUN
ejpam-6593	38	5	,	,	PUNCT
ejpam-6593	38	6	he	he	PRON
ejpam-6593	38	7	also	also	ADV
ejpam-6593	38	8	established	establish	VERB
ejpam-6593	38	9	in	in	ADP
ejpam-6593	38	10	[	[	X
ejpam-6593	38	11	3	3	X
ejpam-6593	38	12	]	]	PUNCT
ejpam-6593	38	13	that	that	SCONJ
ejpam-6593	38	14	(	(	PUNCT
ejpam-6593	38	15	1	1	NUM
ejpam-6593	38	16	,	,	PUNCT
ejpam-6593	38	17	0	0	NUM
ejpam-6593	38	18	,	,	PUNCT
ejpam-6593	38	19	3	3	NUM
ejpam-6593	38	20	)	)	PUNCT
ejpam-6593	38	21	is	be	AUX
ejpam-6593	38	22	the	the	DET
ejpam-6593	38	23	only	only	ADJ
ejpam-6593	38	24	solution	solution	NOUN
ejpam-6593	38	25	in	in	ADP
ejpam-6593	38	26	n0	n0	NOUN
ejpam-6593	38	27	when	when	SCONJ
ejpam-6593	38	28	p	p	PROPN
ejpam-6593	38	29	=	=	NOUN
ejpam-6593	38	30	8	8	NUM
ejpam-6593	38	31	and	and	CCONJ
ejpam-6593	38	32	q	q	NOUN
ejpam-6593	38	33	=	=	NOUN
ejpam-6593	38	34	19	19	NUM
ejpam-6593	38	35	,	,	PUNCT
ejpam-6593	38	36	and	and	CCONJ
ejpam-6593	38	37	posed	pose	VERB
ejpam-6593	38	38	an	an	DET
ejpam-6593	38	39	open	open	ADJ
ejpam-6593	38	40	problem	problem	NOUN
ejpam-6593	38	41	for	for	ADP
ejpam-6593	38	42	the	the	DET
ejpam-6593	38	43	case	case	NOUN
ejpam-6593	38	44	q	q	X
ejpam-6593	39	1	=	=	SYM
ejpam-6593	39	2	17	17	NUM
ejpam-6593	39	3	.	.	PUNCT
ejpam-6593	40	1	this	this	DET
ejpam-6593	40	2	problem	problem	NOUN
ejpam-6593	40	3	was	be	AUX
ejpam-6593	40	4	later	later	ADV
ejpam-6593	40	5	addressed	address	VERB
ejpam-6593	40	6	by	by	ADP
ejpam-6593	40	7	rabago	rabago	PROPN
ejpam-6593	40	8	[	[	X
ejpam-6593	40	9	4	4	NUM
ejpam-6593	40	10	]	]	PUNCT
ejpam-6593	40	11	,	,	PUNCT
ejpam-6593	40	12	who	who	PRON
ejpam-6593	40	13	demonstrated	demonstrate	VERB
ejpam-6593	40	14	that	that	SCONJ
ejpam-6593	40	15	(	(	PUNCT
ejpam-6593	40	16	2	2	X
ejpam-6593	40	17	)	)	PUNCT
ejpam-6593	40	18	has	have	VERB
ejpam-6593	40	19	only	only	ADV
ejpam-6593	40	20	finitely	finitely	ADV
ejpam-6593	40	21	many	many	ADJ
ejpam-6593	40	22	non	non	ADJ
ejpam-6593	40	23	-	-	ADJ
ejpam-6593	40	24	negative	negative	ADJ
ejpam-6593	40	25	integer	integer	NOUN
ejpam-6593	40	26	solutions	solution	NOUN
ejpam-6593	40	27	when	when	SCONJ
ejpam-6593	40	28	p	p	PROPN
ejpam-6593	40	29	=	=	NOUN
ejpam-6593	40	30	8	8	NUM
ejpam-6593	40	31	and	and	CCONJ
ejpam-6593	40	32	q	q	ADJ
ejpam-6593	40	33	=	=	SYM
ejpam-6593	40	34	17	17	NUM
ejpam-6593	40	35	,	,	PUNCT
ejpam-6593	40	36	namely	namely	ADV
ejpam-6593	40	37	,	,	PUNCT
ejpam-6593	40	38	(	(	PUNCT
ejpam-6593	40	39	1	1	NUM
ejpam-6593	40	40	,	,	PUNCT
ejpam-6593	40	41	0	0	NUM
ejpam-6593	40	42	,	,	PUNCT
ejpam-6593	40	43	3	3	NUM
ejpam-6593	40	44	)	)	PUNCT
ejpam-6593	40	45	,	,	PUNCT
ejpam-6593	40	46	(	(	PUNCT
ejpam-6593	40	47	1	1	NUM
ejpam-6593	40	48	,	,	PUNCT
ejpam-6593	40	49	1	1	NUM
ejpam-6593	40	50	,	,	PUNCT
ejpam-6593	40	51	5	5	NUM
ejpam-6593	40	52	)	)	PUNCT
ejpam-6593	40	53	,	,	PUNCT
ejpam-6593	40	54	(	(	PUNCT
ejpam-6593	40	55	2	2	NUM
ejpam-6593	40	56	,	,	PUNCT
ejpam-6593	40	57	1	1	NUM
ejpam-6593	40	58	,	,	PUNCT
ejpam-6593	40	59	9	9	NUM
ejpam-6593	40	60	)	)	PUNCT
ejpam-6593	40	61	,	,	PUNCT
ejpam-6593	40	62	and	and	CCONJ
ejpam-6593	40	63	(	(	PUNCT
ejpam-6593	40	64	3	3	NUM
ejpam-6593	40	65	,	,	PUNCT
ejpam-6593	40	66	1	1	NUM
ejpam-6593	40	67	,	,	PUNCT
ejpam-6593	40	68	23	23	NUM
ejpam-6593	40	69	)	)	PUNCT
ejpam-6593	40	70	.	.	PUNCT
ejpam-6593	41	1	a	a	DET
ejpam-6593	41	2	year	year	NOUN
ejpam-6593	41	3	later	later	ADV
ejpam-6593	41	4	,	,	PUNCT
ejpam-6593	41	5	sroysang	sroysang	X
ejpam-6593	42	1	[	[	X
ejpam-6593	42	2	5	5	NUM
ejpam-6593	42	3	]	]	PUNCT
ejpam-6593	42	4	examined	examine	VERB
ejpam-6593	42	5	the	the	DET
ejpam-6593	42	6	same	same	ADJ
ejpam-6593	42	7	class	class	NOUN
ejpam-6593	42	8	of	of	ADP
ejpam-6593	42	9	edes	ede	NOUN
ejpam-6593	42	10	with	with	ADP
ejpam-6593	42	11	p	p	NOUN
ejpam-6593	42	12	=	=	SYM
ejpam-6593	42	13	5	5	NUM
ejpam-6593	42	14	and	and	CCONJ
ejpam-6593	42	15	q	q	NOUN
ejpam-6593	42	16	=	=	NOUN
ejpam-6593	42	17	7	7	NUM
ejpam-6593	42	18	,	,	PUNCT
ejpam-6593	42	19	but	but	CCONJ
ejpam-6593	42	20	found	find	VERB
ejpam-6593	42	21	no	no	DET
ejpam-6593	42	22	solutions	solution	NOUN
ejpam-6593	42	23	in	in	ADP
ejpam-6593	42	24	n0	n0	PROPN
ejpam-6593	42	25	.	.	PUNCT
ejpam-6593	43	1	in	in	ADP
ejpam-6593	43	2	2013	2013	NUM
ejpam-6593	43	3	,	,	PUNCT
ejpam-6593	43	4	chotchaisthit	chotchaisthit	VERB
ejpam-6593	44	1	[	[	X
ejpam-6593	44	2	6	6	NUM
ejpam-6593	44	3	]	]	PUNCT
ejpam-6593	44	4	studied	study	VERB
ejpam-6593	44	5	the	the	DET
ejpam-6593	44	6	case	case	NOUN
ejpam-6593	44	7	where	where	SCONJ
ejpam-6593	44	8	p	p	NOUN
ejpam-6593	44	9	and	and	CCONJ
ejpam-6593	44	10	q	q	NOUN
ejpam-6593	44	11	are	be	AUX
ejpam-6593	44	12	two	two	NUM
ejpam-6593	44	13	consecutive	consecutive	ADJ
ejpam-6593	44	14	integers	integer	NOUN
ejpam-6593	44	15	,	,	PUNCT
ejpam-6593	44	16	but	but	CCONJ
ejpam-6593	44	17	p	p	NOUN
ejpam-6593	44	18	must	must	AUX
ejpam-6593	44	19	be	be	AUX
ejpam-6593	44	20	a	a	DET
ejpam-6593	44	21	mersenne	mersenne	NOUN
ejpam-6593	44	22	prime	prime	NOUN
ejpam-6593	44	23	.	.	PUNCT
ejpam-6593	45	1	other	other	ADJ
ejpam-6593	45	2	diophantine	diophantine	NOUN
ejpam-6593	45	3	equations	equation	NOUN
ejpam-6593	45	4	that	that	PRON
ejpam-6593	45	5	involve	involve	VERB
ejpam-6593	45	6	bases	basis	NOUN
ejpam-6593	45	7	of	of	ADP
ejpam-6593	45	8	primes	prime	NOUN
ejpam-6593	45	9	and	and	CCONJ
ejpam-6593	45	10	mersenne	mersenne	NOUN
ejpam-6593	45	11	primes	prime	NOUN
ejpam-6593	45	12	are	be	AUX
ejpam-6593	45	13	found	find	VERB
ejpam-6593	45	14	in	in	ADP
ejpam-6593	45	15	the	the	DET
ejpam-6593	45	16	works	work	NOUN
ejpam-6593	45	17	of	of	ADP
ejpam-6593	45	18	gayo	gayo	NOUN
ejpam-6593	45	19	,	,	PUNCT
ejpam-6593	45	20	mina	mina	ADJ
ejpam-6593	45	21	and	and	CCONJ
ejpam-6593	45	22	bacani	bacani	PROPN
ejpam-6593	45	23	(	(	PUNCT
ejpam-6593	45	24	cf	cf	NOUN
ejpam-6593	45	25	.	.	PUNCT
ejpam-6593	46	1	[	[	X
ejpam-6593	46	2	7–11	7–11	NOUN
ejpam-6593	46	3	]	]	X
ejpam-6593	46	4	)	)	PUNCT
ejpam-6593	46	5	.	.	PUNCT
ejpam-6593	47	1	most	most	ADJ
ejpam-6593	47	2	of	of	ADP
ejpam-6593	47	3	these	these	DET
ejpam-6593	47	4	studies	study	NOUN
ejpam-6593	47	5	utilize	utilize	VERB
ejpam-6593	47	6	mihăilescu	mihăilescu	PROPN
ejpam-6593	47	7	’s	’s	PART
ejpam-6593	47	8	theorem	theorem	NOUN
ejpam-6593	47	9	(	(	PUNCT
ejpam-6593	47	10	known	know	VERB
ejpam-6593	47	11	originally	originally	ADV
ejpam-6593	47	12	as	as	ADP
ejpam-6593	47	13	catalan	catalan	NOUN
ejpam-6593	47	14	’s	’s	PART
ejpam-6593	47	15	conjecture	conjecture	NOUN
ejpam-6593	47	16	)	)	PUNCT
ejpam-6593	47	17	.	.	PUNCT
ejpam-6593	48	1	basically	basically	ADV
ejpam-6593	48	2	,	,	PUNCT
ejpam-6593	48	3	this	this	PRON
ejpam-6593	48	4	theorem	theorem	VERB
ejpam-6593	48	5	states	state	NOUN
ejpam-6593	48	6	that	that	SCONJ
ejpam-6593	48	7	the	the	DET
ejpam-6593	48	8	only	only	ADJ
ejpam-6593	48	9	solution	solution	NOUN
ejpam-6593	48	10	to	to	ADP
ejpam-6593	48	11	the	the	DET
ejpam-6593	48	12	diophantine	diophantine	NOUN
ejpam-6593	48	13	equation	equation	NOUN
ejpam-6593	48	14	px	px	ADP
ejpam-6593	48	15	−	−	PROPN
ejpam-6593	48	16	qy	qy	NOUN
ejpam-6593	48	17	=	=	SYM
ejpam-6593	48	18	1	1	NUM
ejpam-6593	48	19	is	be	AUX
ejpam-6593	48	20	(	(	PUNCT
ejpam-6593	48	21	p	p	X
ejpam-6593	48	22	,	,	PUNCT
ejpam-6593	48	23	q	q	ADJ
ejpam-6593	48	24	,	,	PUNCT
ejpam-6593	48	25	x	x	NOUN
ejpam-6593	48	26	,	,	PUNCT
ejpam-6593	48	27	y	y	NOUN
ejpam-6593	48	28	)	)	PUNCT
ejpam-6593	48	29	=	=	PUNCT
ejpam-6593	48	30	(	(	PUNCT
ejpam-6593	48	31	3	3	NUM
ejpam-6593	48	32	,	,	PUNCT
ejpam-6593	48	33	2	2	NUM
ejpam-6593	48	34	,	,	PUNCT
ejpam-6593	48	35	2	2	NUM
ejpam-6593	48	36	,	,	PUNCT
ejpam-6593	48	37	3	3	NUM
ejpam-6593	48	38	)	)	PUNCT
ejpam-6593	48	39	,	,	PUNCT
ejpam-6593	48	40	with	with	ADP
ejpam-6593	48	41	the	the	DET
ejpam-6593	48	42	assumption	assumption	NOUN
ejpam-6593	48	43	that	that	SCONJ
ejpam-6593	48	44	all	all	DET
ejpam-6593	48	45	variables	variable	NOUN
ejpam-6593	48	46	have	have	AUX
ejpam-6593	48	47	values	value	NOUN
ejpam-6593	48	48	greater	great	ADJ
ejpam-6593	48	49	than	than	ADP
ejpam-6593	48	50	1	1	NUM
ejpam-6593	48	51	[	[	X
ejpam-6593	48	52	12	12	NUM
ejpam-6593	48	53	]	]	PUNCT
ejpam-6593	48	54	.	.	PUNCT
ejpam-6593	49	1	it	it	PRON
ejpam-6593	49	2	is	be	AUX
ejpam-6593	49	3	also	also	ADV
ejpam-6593	49	4	observed	observe	VERB
ejpam-6593	49	5	that	that	SCONJ
ejpam-6593	49	6	the	the	DET
ejpam-6593	49	7	ede	ede	PROPN
ejpam-6593	49	8	(	(	PUNCT
ejpam-6593	49	9	2	2	NUM
ejpam-6593	49	10	)	)	PUNCT
ejpam-6593	49	11	has	have	AUX
ejpam-6593	49	12	been	be	AUX
ejpam-6593	49	13	studied	study	VERB
ejpam-6593	49	14	for	for	ADP
ejpam-6593	49	15	specific	specific	ADJ
ejpam-6593	49	16	prime	prime	ADJ
ejpam-6593	49	17	pairs	pair	NOUN
ejpam-6593	49	18	(	(	PUNCT
ejpam-6593	49	19	p	p	X
ejpam-6593	49	20	,	,	PUNCT
ejpam-6593	49	21	q	q	NOUN
ejpam-6593	49	22	)	)	PUNCT
ejpam-6593	49	23	.	.	PUNCT
ejpam-6593	50	1	some	some	DET
ejpam-6593	50	2	examples	example	NOUN
ejpam-6593	50	3	are	be	AUX
ejpam-6593	50	4	found	find	VERB
ejpam-6593	50	5	in	in	ADP
ejpam-6593	50	6	gupta	gupta	PROPN
ejpam-6593	50	7	’s	’s	PART
ejpam-6593	50	8	and	and	CCONJ
ejpam-6593	50	9	sroysang	sroysang	PROPN
ejpam-6593	50	10	’s	’s	PART
ejpam-6593	50	11	papers	paper	NOUN
ejpam-6593	50	12	[	[	X
ejpam-6593	50	13	2	2	NUM
ejpam-6593	50	14	,	,	PUNCT
ejpam-6593	50	15	5	5	NUM
ejpam-6593	50	16	,	,	PUNCT
ejpam-6593	50	17	13	13	NUM
ejpam-6593	50	18	]	]	PUNCT
ejpam-6593	50	19	.	.	PUNCT
ejpam-6593	51	1	in	in	ADP
ejpam-6593	51	2	2015	2015	NUM
ejpam-6593	51	3	,	,	PUNCT
ejpam-6593	51	4	bacani	bacani	NOUN
ejpam-6593	51	5	and	and	CCONJ
ejpam-6593	51	6	rabago	rabago	VERB
ejpam-6593	52	1	[	[	X
ejpam-6593	52	2	14	14	NUM
ejpam-6593	52	3	]	]	PUNCT
ejpam-6593	52	4	investigated	investigate	VERB
ejpam-6593	52	5	the	the	DET
ejpam-6593	52	6	case	case	NOUN
ejpam-6593	52	7	where	where	SCONJ
ejpam-6593	52	8	p	p	NOUN
ejpam-6593	52	9	and	and	CCONJ
ejpam-6593	52	10	q	q	NOUN
ejpam-6593	52	11	are	be	AUX
ejpam-6593	52	12	twin	twin	ADJ
ejpam-6593	52	13	primes	prime	NOUN
ejpam-6593	52	14	.	.	PUNCT
ejpam-6593	53	1	in	in	ADP
ejpam-6593	53	2	2018	2018	NUM
ejpam-6593	53	3	,	,	PUNCT
ejpam-6593	53	4	burshtein	burshtein	ADV
ejpam-6593	53	5	(	(	PUNCT
ejpam-6593	53	6	[	[	X
ejpam-6593	53	7	15	15	NUM
ejpam-6593	53	8	]	]	PUNCT
ejpam-6593	53	9	,	,	PUNCT
ejpam-6593	53	10	[	[	X
ejpam-6593	53	11	16	16	NUM
ejpam-6593	53	12	]	]	PUNCT
ejpam-6593	53	13	)	)	PUNCT
ejpam-6593	53	14	published	publish	VERB
ejpam-6593	53	15	two	two	NUM
ejpam-6593	53	16	articles	article	NOUN
ejpam-6593	53	17	,	,	PUNCT
ejpam-6593	53	18	namely	namely	ADV
ejpam-6593	53	19	,	,	PUNCT
ejpam-6593	53	20	when	when	SCONJ
ejpam-6593	53	21	p	p	NOUN
ejpam-6593	53	22	and	and	CCONJ
ejpam-6593	53	23	q	q	NOUN
ejpam-6593	53	24	are	be	AUX
ejpam-6593	53	25	cousin	cousin	NOUN
ejpam-6593	53	26	primes	prime	NOUN
ejpam-6593	53	27	and	and	CCONJ
ejpam-6593	53	28	when	when	SCONJ
ejpam-6593	53	29	they	they	PRON
ejpam-6593	53	30	are	be	AUX
ejpam-6593	53	31	sexy	sexy	ADJ
ejpam-6593	53	32	primes	prime	NOUN
ejpam-6593	53	33	with	with	ADP
ejpam-6593	53	34	the	the	DET
ejpam-6593	53	35	condition	condition	NOUN
ejpam-6593	53	36	that	that	SCONJ
ejpam-6593	53	37	x	x	X
ejpam-6593	54	1	+	+	NUM
ejpam-6593	54	2	y	y	NOUN
ejpam-6593	54	3	=	=	SYM
ejpam-6593	54	4	2	2	NUM
ejpam-6593	54	5	,	,	PUNCT
ejpam-6593	54	6	3	3	NUM
ejpam-6593	54	7	,	,	PUNCT
ejpam-6593	54	8	4	4	NUM
ejpam-6593	54	9	.	.	PUNCT
ejpam-6593	55	1	in	in	ADP
ejpam-6593	55	2	the	the	DET
ejpam-6593	55	3	same	same	ADJ
ejpam-6593	55	4	year	year	NOUN
ejpam-6593	55	5	,	,	PUNCT
ejpam-6593	55	6	neres	nere	VERB
ejpam-6593	55	7	[	[	X
ejpam-6593	55	8	17	17	NUM
ejpam-6593	55	9	]	]	PUNCT
ejpam-6593	55	10	proved	prove	VERB
ejpam-6593	55	11	the	the	DET
ejpam-6593	55	12	solvability	solvability	NOUN
ejpam-6593	55	13	of	of	ADP
ejpam-6593	55	14	(	(	PUNCT
ejpam-6593	55	15	2	2	NUM
ejpam-6593	55	16	)	)	PUNCT
ejpam-6593	55	17	when	when	SCONJ
ejpam-6593	55	18	p	p	NOUN
ejpam-6593	55	19	and	and	CCONJ
ejpam-6593	55	20	q	q	NOUN
ejpam-6593	55	21	have	have	VERB
ejpam-6593	55	22	a	a	DET
ejpam-6593	55	23	prime	prime	ADJ
ejpam-6593	55	24	gap	gap	NOUN
ejpam-6593	55	25	of	of	ADP
ejpam-6593	55	26	8	8	NUM
ejpam-6593	55	27	,	,	PUNCT
ejpam-6593	55	28	and	and	CCONJ
ejpam-6593	56	1	p	p	X
ejpam-6593	56	2	>	>	X
ejpam-6593	56	3	3	3	X
ejpam-6593	56	4	.	.	PUNCT
ejpam-6593	56	5	recently	recently	ADV
ejpam-6593	56	6	,	,	PUNCT
ejpam-6593	56	7	tadee	tadee	PROPN
ejpam-6593	56	8	[	[	X
ejpam-6593	56	9	18	18	NUM
ejpam-6593	56	10	]	]	PUNCT
ejpam-6593	56	11	studied	study	VERB
ejpam-6593	56	12	the	the	DET
ejpam-6593	56	13	case	case	NOUN
ejpam-6593	56	14	where	where	SCONJ
ejpam-6593	56	15	the	the	DET
ejpam-6593	56	16	prime	prime	ADJ
ejpam-6593	56	17	gap	gap	NOUN
ejpam-6593	56	18	is	be	AUX
ejpam-6593	56	19	14	14	NUM
ejpam-6593	56	20	.	.	PUNCT
ejpam-6593	57	1	a	a	DET
ejpam-6593	57	2	more	more	ADV
ejpam-6593	57	3	interesting	interesting	ADJ
ejpam-6593	57	4	case	case	NOUN
ejpam-6593	57	5	was	be	AUX
ejpam-6593	57	6	what	what	PRON
ejpam-6593	57	7	mina	mina	ADJ
ejpam-6593	57	8	and	and	CCONJ
ejpam-6593	57	9	bacani	bacani	NOUN
ejpam-6593	57	10	[	[	X
ejpam-6593	57	11	19	19	NUM
ejpam-6593	57	12	]	]	PUNCT
ejpam-6593	57	13	published	publish	VERB
ejpam-6593	57	14	in	in	ADP
ejpam-6593	57	15	2021	2021	NUM
ejpam-6593	57	16	,	,	PUNCT
ejpam-6593	57	17	where	where	SCONJ
ejpam-6593	57	18	they	they	PRON
ejpam-6593	57	19	studied	study	VERB
ejpam-6593	57	20	the	the	DET
ejpam-6593	57	21	case	case	NOUN
ejpam-6593	57	22	where	where	SCONJ
ejpam-6593	57	23	p	p	NOUN
ejpam-6593	57	24	and	and	CCONJ
ejpam-6593	57	25	q	q	NOUN
ejpam-6593	57	26	have	have	VERB
ejpam-6593	57	27	prime	prime	ADJ
ejpam-6593	57	28	gaps	gap	NOUN
ejpam-6593	57	29	of	of	ADP
ejpam-6593	57	30	multiples	multiple	NOUN
ejpam-6593	57	31	of	of	ADP
ejpam-6593	57	32	four	four	NUM
ejpam-6593	57	33	.	.	PUNCT
ejpam-6593	58	1	in	in	ADP
ejpam-6593	58	2	2022	2022	NUM
ejpam-6593	58	3	,	,	PUNCT
ejpam-6593	58	4	orosram	orosram	NOUN
ejpam-6593	58	5	,	,	PUNCT
ejpam-6593	58	6	et	et	PROPN
ejpam-6593	58	7	al	al	PROPN
ejpam-6593	58	8	.	.	PUNCT
ejpam-6593	59	1	[	[	X
ejpam-6593	59	2	20	20	NUM
ejpam-6593	59	3	]	]	PUNCT
ejpam-6593	59	4	also	also	ADV
ejpam-6593	59	5	studied	study	VERB
ejpam-6593	59	6	the	the	DET
ejpam-6593	59	7	same	same	ADJ
ejpam-6593	59	8	prime	prime	ADJ
ejpam-6593	59	9	pairs	pair	NOUN
ejpam-6593	59	10	with	with	ADP
ejpam-6593	59	11	an	an	DET
ejpam-6593	59	12	additional	additional	ADJ
ejpam-6593	59	13	constraint	constraint	NOUN
ejpam-6593	59	14	that	that	PRON
ejpam-6593	59	15	p	p	PRON
ejpam-6593	59	16	≡	≡	PROPN
ejpam-6593	59	17	7	7	NUM
ejpam-6593	59	18	(	(	PUNCT
ejpam-6593	59	19	mod	mod	PROPN
ejpam-6593	59	20	12	12	NUM
ejpam-6593	59	21	)	)	PUNCT
ejpam-6593	59	22	.	.	PUNCT
ejpam-6593	60	1	motivated	motivate	VERB
ejpam-6593	60	2	by	by	ADP
ejpam-6593	60	3	the	the	DET
ejpam-6593	60	4	papers	paper	NOUN
ejpam-6593	60	5	mentioned	mention	VERB
ejpam-6593	60	6	above	above	ADV
ejpam-6593	60	7	,	,	PUNCT
ejpam-6593	60	8	the	the	DET
ejpam-6593	60	9	present	present	ADJ
ejpam-6593	60	10	study	study	NOUN
ejpam-6593	60	11	searches	search	NOUN
ejpam-6593	60	12	for	for	ADP
ejpam-6593	60	13	nonnegative	nonnegative	ADJ
ejpam-6593	60	14	integer	integer	NOUN
ejpam-6593	60	15	solutions	solution	NOUN
ejpam-6593	60	16	of	of	ADP
ejpam-6593	60	17	the	the	DET
ejpam-6593	60	18	diophantine	diophantine	NOUN
ejpam-6593	60	19	equation	equation	NOUN
ejpam-6593	60	20	of	of	ADP
ejpam-6593	60	21	the	the	DET
ejpam-6593	60	22	form	form	NOUN
ejpam-6593	60	23	px	px	X
ejpam-6593	60	24	+	+	CCONJ
ejpam-6593	60	25	(	(	PUNCT
ejpam-6593	60	26	p+	p+	PROPN
ejpam-6593	60	27	5k)y	5k)y	NOUN
ejpam-6593	60	28	=	=	SYM
ejpam-6593	60	29	z2	z2	PROPN
ejpam-6593	60	30	,	,	PUNCT
ejpam-6593	60	31	(	(	PUNCT
ejpam-6593	60	32	3	3	X
ejpam-6593	60	33	)	)	PUNCT
ejpam-6593	60	34	where	where	SCONJ
ejpam-6593	60	35	k	k	PROPN
ejpam-6593	60	36	∈	∈	PROPN
ejpam-6593	60	37	n	n	CCONJ
ejpam-6593	60	38	,	,	PUNCT
ejpam-6593	60	39	and	and	CCONJ
ejpam-6593	60	40	p	p	NOUN
ejpam-6593	60	41	satisfies	satisfy	VERB
ejpam-6593	60	42	any	any	PRON
ejpam-6593	60	43	of	of	ADP
ejpam-6593	60	44	the	the	DET
ejpam-6593	60	45	following	follow	VERB
ejpam-6593	60	46	conditions	condition	NOUN
ejpam-6593	60	47	:	:	PUNCT
ejpam-6593	60	48	m.	m.	PROPN
ejpam-6593	60	49	c.	c.	PROPN
ejpam-6593	60	50	avenilla	avenilla	PROPN
ejpam-6593	60	51	,	,	PUNCT
ejpam-6593	60	52	j.	j.	PROPN
ejpam-6593	60	53	b.	b.	PROPN
ejpam-6593	60	54	bacani	bacani	PROPN
ejpam-6593	60	55	/	/	SYM
ejpam-6593	60	56	eur	eur	PROPN
ejpam-6593	60	57	.	.	PUNCT
ejpam-6593	61	1	j.	j.	PROPN
ejpam-6593	61	2	pure	pure	PROPN
ejpam-6593	61	3	appl	appl	PROPN
ejpam-6593	61	4	.	.	PROPN
ejpam-6593	61	5	math	math	PROPN
ejpam-6593	61	6	,	,	PUNCT
ejpam-6593	61	7	18	18	NUM
ejpam-6593	61	8	(	(	PUNCT
ejpam-6593	61	9	3	3	NUM
ejpam-6593	61	10	)	)	PUNCT
ejpam-6593	61	11	(	(	PUNCT
ejpam-6593	61	12	2025	2025	NUM
ejpam-6593	61	13	)	)	PUNCT
ejpam-6593	61	14	,	,	PUNCT
ejpam-6593	61	15	6593	6593	NUM
ejpam-6593	61	16	3	3	NUM
ejpam-6593	61	17	of	of	ADP
ejpam-6593	61	18	24	24	NUM
ejpam-6593	61	19	a	a	NOUN
ejpam-6593	61	20	)	)	PUNCT
ejpam-6593	61	21	p	p	NOUN
ejpam-6593	61	22	=	=	NOUN
ejpam-6593	61	23	2	2	NUM
ejpam-6593	61	24	;	;	PUNCT
ejpam-6593	61	25	or	or	CCONJ
ejpam-6593	61	26	b	b	X
ejpam-6593	61	27	)	)	PUNCT
ejpam-6593	61	28	p	p	NOUN
ejpam-6593	61	29	and	and	CCONJ
ejpam-6593	61	30	p+	p+	PROPN
ejpam-6593	61	31	5k	5k	NUM
ejpam-6593	61	32	are	be	AUX
ejpam-6593	61	33	prime	prime	ADJ
ejpam-6593	61	34	pairs	pair	NOUN
ejpam-6593	61	35	.	.	PUNCT
ejpam-6593	62	1	the	the	DET
ejpam-6593	62	2	principle	principle	NOUN
ejpam-6593	62	3	of	of	ADP
ejpam-6593	62	4	mathematical	mathematical	ADJ
ejpam-6593	62	5	induction	induction	NOUN
ejpam-6593	62	6	is	be	AUX
ejpam-6593	62	7	also	also	ADV
ejpam-6593	62	8	used	use	VERB
ejpam-6593	62	9	in	in	ADP
ejpam-6593	62	10	this	this	DET
ejpam-6593	62	11	study	study	NOUN
ejpam-6593	62	12	,	,	PUNCT
ejpam-6593	62	13	as	as	ADV
ejpam-6593	62	14	well	well	ADV
ejpam-6593	62	15	as	as	ADP
ejpam-6593	62	16	the	the	DET
ejpam-6593	62	17	concept	concept	NOUN
ejpam-6593	62	18	of	of	ADP
ejpam-6593	62	19	floor	floor	NOUN
ejpam-6593	62	20	function	function	NOUN
ejpam-6593	62	21	,	,	PUNCT
ejpam-6593	62	22	which	which	PRON
ejpam-6593	62	23	is	be	AUX
ejpam-6593	62	24	usually	usually	ADV
ejpam-6593	62	25	not	not	PART
ejpam-6593	62	26	seen	see	VERB
ejpam-6593	62	27	in	in	ADP
ejpam-6593	62	28	related	related	ADJ
ejpam-6593	62	29	literature	literature	NOUN
ejpam-6593	62	30	.	.	PUNCT
ejpam-6593	63	1	furthermore	furthermore	ADV
ejpam-6593	63	2	,	,	PUNCT
ejpam-6593	63	3	the	the	DET
ejpam-6593	63	4	results	result	NOUN
ejpam-6593	63	5	presented	present	VERB
ejpam-6593	63	6	here	here	ADV
ejpam-6593	63	7	extend	extend	VERB
ejpam-6593	63	8	those	those	PRON
ejpam-6593	63	9	of	of	ADP
ejpam-6593	63	10	dokchan	dokchan	NOUN
ejpam-6593	63	11	and	and	CCONJ
ejpam-6593	63	12	panngam	panngam	ADV
ejpam-6593	64	1	[	[	X
ejpam-6593	64	2	21	21	NUM
ejpam-6593	64	3	]	]	X
ejpam-6593	64	4	,	,	PUNCT
ejpam-6593	64	5	who	who	PRON
ejpam-6593	64	6	investigated	investigate	VERB
ejpam-6593	64	7	the	the	DET
ejpam-6593	64	8	same	same	ADJ
ejpam-6593	64	9	equation	equation	NOUN
ejpam-6593	64	10	under	under	ADP
ejpam-6593	64	11	the	the	DET
ejpam-6593	64	12	condition	condition	NOUN
ejpam-6593	64	13	p	p	X
ejpam-6593	64	14	≡	≡	PROPN
ejpam-6593	64	15	1	1	NUM
ejpam-6593	64	16	(	(	PUNCT
ejpam-6593	64	17	mod	mod	NOUN
ejpam-6593	64	18	5	5	NUM
ejpam-6593	64	19	)	)	PUNCT
ejpam-6593	64	20	and	and	CCONJ
ejpam-6593	64	21	sought	seek	VERB
ejpam-6593	64	22	solutions	solution	NOUN
ejpam-6593	64	23	in	in	ADP
ejpam-6593	64	24	n.	n.	PROPN
ejpam-6593	64	25	2	2	NUM
ejpam-6593	64	26	.	.	PUNCT
ejpam-6593	64	27	main	main	ADJ
ejpam-6593	64	28	results	result	NOUN
ejpam-6593	64	29	the	the	DET
ejpam-6593	64	30	results	result	NOUN
ejpam-6593	64	31	are	be	AUX
ejpam-6593	64	32	divided	divide	VERB
ejpam-6593	64	33	into	into	ADP
ejpam-6593	64	34	two	two	NUM
ejpam-6593	64	35	parts	part	NOUN
ejpam-6593	64	36	.	.	PUNCT
ejpam-6593	65	1	first	first	ADV
ejpam-6593	65	2	,	,	PUNCT
ejpam-6593	65	3	we	we	PRON
ejpam-6593	65	4	present	present	VERB
ejpam-6593	65	5	interesting	interesting	ADJ
ejpam-6593	65	6	results	result	NOUN
ejpam-6593	65	7	for	for	ADP
ejpam-6593	65	8	the	the	DET
ejpam-6593	65	9	case	case	NOUN
ejpam-6593	65	10	p	p	X
ejpam-6593	66	1	=	=	NOUN
ejpam-6593	67	1	2	2	X
ejpam-6593	67	2	.	.	PUNCT
ejpam-6593	68	1	next	next	ADV
ejpam-6593	68	2	,	,	PUNCT
ejpam-6593	68	3	we	we	PRON
ejpam-6593	68	4	discuss	discuss	VERB
ejpam-6593	68	5	the	the	DET
ejpam-6593	68	6	solutions	solution	NOUN
ejpam-6593	68	7	of	of	ADP
ejpam-6593	68	8	the	the	DET
ejpam-6593	68	9	equation	equation	NOUN
ejpam-6593	68	10	when	when	SCONJ
ejpam-6593	68	11	p	p	PROPN
ejpam-6593	68	12	and	and	CCONJ
ejpam-6593	68	13	p+	p+	PROPN
ejpam-6593	68	14	5k	5k	NUM
ejpam-6593	68	15	are	be	AUX
ejpam-6593	68	16	prime	prime	ADJ
ejpam-6593	68	17	pairs	pair	NOUN
ejpam-6593	68	18	.	.	PUNCT
ejpam-6593	69	1	2.1	2.1	NUM
ejpam-6593	69	2	.	.	PUNCT
ejpam-6593	70	1	on	on	ADP
ejpam-6593	70	2	the	the	DET
ejpam-6593	70	3	diophantine	diophantine	NOUN
ejpam-6593	70	4	equation	equation	NOUN
ejpam-6593	70	5	2x	2x	NUM
ejpam-6593	70	6	+	+	CCONJ
ejpam-6593	70	7	(	(	PUNCT
ejpam-6593	70	8	2	2	NUM
ejpam-6593	70	9	+	+	NUM
ejpam-6593	70	10	5k)y	5k)y	NUM
ejpam-6593	70	11	=	=	SYM
ejpam-6593	70	12	z2	z2	PROPN
ejpam-6593	70	13	this	this	DET
ejpam-6593	70	14	subsection	subsection	NOUN
ejpam-6593	70	15	talks	talk	NOUN
ejpam-6593	70	16	about	about	ADP
ejpam-6593	70	17	the	the	DET
ejpam-6593	70	18	diophantine	diophantine	NOUN
ejpam-6593	70	19	equation	equation	NOUN
ejpam-6593	70	20	(	(	PUNCT
ejpam-6593	70	21	3	3	NUM
ejpam-6593	70	22	)	)	PUNCT
ejpam-6593	70	23	,	,	PUNCT
ejpam-6593	70	24	where	where	SCONJ
ejpam-6593	70	25	p	p	NOUN
ejpam-6593	70	26	=	=	NOUN
ejpam-6593	70	27	2	2	NUM
ejpam-6593	70	28	,	,	PUNCT
ejpam-6593	70	29	that	that	ADV
ejpam-6593	70	30	is	is	ADV
ejpam-6593	70	31	,	,	PUNCT
ejpam-6593	70	32	2x	2x	NUM
ejpam-6593	70	33	+	+	CCONJ
ejpam-6593	70	34	(	(	PUNCT
ejpam-6593	70	35	2	2	NUM
ejpam-6593	70	36	+	+	NUM
ejpam-6593	70	37	5k)y	5k)y	NOUN
ejpam-6593	70	38	=	=	SYM
ejpam-6593	70	39	z2	z2	PROPN
ejpam-6593	70	40	.	.	PUNCT
ejpam-6593	71	1	(	(	PUNCT
ejpam-6593	71	2	4	4	X
ejpam-6593	71	3	)	)	PUNCT
ejpam-6593	71	4	it	it	PRON
ejpam-6593	71	5	is	be	AUX
ejpam-6593	71	6	further	far	ADV
ejpam-6593	71	7	divided	divide	VERB
ejpam-6593	71	8	into	into	ADP
ejpam-6593	71	9	two	two	NUM
ejpam-6593	71	10	parts	part	NOUN
ejpam-6593	71	11	.	.	PUNCT
ejpam-6593	72	1	the	the	DET
ejpam-6593	72	2	first	first	ADJ
ejpam-6593	72	3	part	part	NOUN
ejpam-6593	72	4	discusses	discuss	VERB
ejpam-6593	72	5	the	the	DET
ejpam-6593	72	6	case	case	NOUN
ejpam-6593	72	7	when	when	SCONJ
ejpam-6593	72	8	y	y	PROPN
ejpam-6593	72	9	=	=	SYM
ejpam-6593	72	10	1	1	NUM
ejpam-6593	72	11	,	,	PUNCT
ejpam-6593	72	12	and	and	CCONJ
ejpam-6593	72	13	the	the	DET
ejpam-6593	72	14	second	second	ADJ
ejpam-6593	72	15	part	part	NOUN
ejpam-6593	72	16	contains	contain	VERB
ejpam-6593	72	17	all	all	DET
ejpam-6593	72	18	other	other	ADJ
ejpam-6593	72	19	claims	claim	NOUN
ejpam-6593	72	20	when	when	SCONJ
ejpam-6593	72	21	y	y	PROPN
ejpam-6593	72	22	̸=	̸=	PROPN
ejpam-6593	72	23	1	1	NUM
ejpam-6593	72	24	.	.	PUNCT
ejpam-6593	73	1	2.1.1	2.1.1	NUM
ejpam-6593	73	2	.	.	PUNCT
ejpam-6593	74	1	part	part	NOUN
ejpam-6593	75	1	i	i	PRON
ejpam-6593	75	2	:	:	PUNCT
ejpam-6593	75	3	the	the	DET
ejpam-6593	75	4	case	case	NOUN
ejpam-6593	75	5	where	where	SCONJ
ejpam-6593	75	6	y	y	PROPN
ejpam-6593	75	7	=	=	NOUN
ejpam-6593	75	8	1	1	X
ejpam-6593	75	9	.	.	PUNCT
ejpam-6593	75	10	consider	consider	VERB
ejpam-6593	75	11	the	the	DET
ejpam-6593	75	12	equation	equation	NOUN
ejpam-6593	75	13	2x	2x	NUM
ejpam-6593	76	1	+	+	CCONJ
ejpam-6593	76	2	(	(	PUNCT
ejpam-6593	76	3	2	2	NUM
ejpam-6593	76	4	+	+	NUM
ejpam-6593	76	5	5k	5k	NUM
ejpam-6593	76	6	)	)	PUNCT
ejpam-6593	76	7	=	=	SYM
ejpam-6593	76	8	z2	z2	PROPN
ejpam-6593	76	9	.	.	PUNCT
ejpam-6593	77	1	(	(	PUNCT
ejpam-6593	77	2	5	5	NUM
ejpam-6593	77	3	)	)	PUNCT
ejpam-6593	77	4	for	for	ADP
ejpam-6593	77	5	this	this	DET
ejpam-6593	77	6	case	case	NOUN
ejpam-6593	77	7	,	,	PUNCT
ejpam-6593	77	8	the	the	DET
ejpam-6593	77	9	following	follow	VERB
ejpam-6593	77	10	variables	variable	NOUN
ejpam-6593	77	11	will	will	AUX
ejpam-6593	77	12	be	be	AUX
ejpam-6593	77	13	used	use	VERB
ejpam-6593	77	14	:	:	PUNCT
ejpam-6593	77	15	variable	variable	ADJ
ejpam-6593	77	16	meaning	mean	VERB
ejpam-6593	77	17	xn	xn	PROPN
ejpam-6593	77	18	the	the	DET
ejpam-6593	77	19	value	value	NOUN
ejpam-6593	77	20	of	of	ADP
ejpam-6593	77	21	x	x	PUNCT
ejpam-6593	77	22	at	at	ADP
ejpam-6593	77	23	a	a	DET
ejpam-6593	77	24	specific	specific	ADJ
ejpam-6593	77	25	value	value	NOUN
ejpam-6593	77	26	of	of	ADP
ejpam-6593	77	27	n	n	PRON
ejpam-6593	77	28	∈	∈	PROPN
ejpam-6593	77	29	n0	n0	PROPN
ejpam-6593	77	30	z(0,xn	z(0,xn	PROPN
ejpam-6593	77	31	)	)	PUNCT
ejpam-6593	77	32	the	the	DET
ejpam-6593	77	33	first	first	ADJ
ejpam-6593	77	34	value	value	NOUN
ejpam-6593	77	35	of	of	ADP
ejpam-6593	77	36	z	z	NOUN
ejpam-6593	77	37	at	at	ADP
ejpam-6593	77	38	a	a	DET
ejpam-6593	77	39	specific	specific	ADJ
ejpam-6593	77	40	value	value	NOUN
ejpam-6593	77	41	of	of	ADP
ejpam-6593	77	42	xn	xn	PROPN
ejpam-6593	77	43	z(m	z(m	PROPN
ejpam-6593	77	44	,	,	PUNCT
ejpam-6593	77	45	xn	xn	NUM
ejpam-6593	77	46	)	)	PUNCT
ejpam-6593	77	47	the	the	DET
ejpam-6593	77	48	(	(	PUNCT
ejpam-6593	77	49	m+	m+	NUM
ejpam-6593	77	50	1)st	1)st	NUM
ejpam-6593	77	51	value	value	NOUN
ejpam-6593	77	52	of	of	ADP
ejpam-6593	77	53	z	z	NOUN
ejpam-6593	77	54	at	at	ADP
ejpam-6593	77	55	a	a	DET
ejpam-6593	77	56	specific	specific	ADJ
ejpam-6593	77	57	value	value	NOUN
ejpam-6593	77	58	of	of	ADP
ejpam-6593	77	59	xn	xn	PROPN
ejpam-6593	77	60	k(0,xn	k(0,xn	PROPN
ejpam-6593	77	61	)	)	PUNCT
ejpam-6593	77	62	the	the	DET
ejpam-6593	77	63	first	first	ADJ
ejpam-6593	77	64	value	value	NOUN
ejpam-6593	77	65	of	of	ADP
ejpam-6593	77	66	k	k	PROPN
ejpam-6593	77	67	at	at	ADP
ejpam-6593	77	68	a	a	DET
ejpam-6593	77	69	specific	specific	ADJ
ejpam-6593	77	70	value	value	NOUN
ejpam-6593	77	71	of	of	ADP
ejpam-6593	77	72	xn	xn	PROPN
ejpam-6593	77	73	k(1,xn	k(1,xn	PROPN
ejpam-6593	77	74	)	)	PUNCT
ejpam-6593	77	75	the	the	DET
ejpam-6593	77	76	second	second	ADJ
ejpam-6593	77	77	value	value	NOUN
ejpam-6593	77	78	of	of	ADP
ejpam-6593	77	79	k	k	PROPN
ejpam-6593	77	80	at	at	ADP
ejpam-6593	77	81	a	a	DET
ejpam-6593	77	82	specific	specific	ADJ
ejpam-6593	77	83	value	value	NOUN
ejpam-6593	77	84	of	of	ADP
ejpam-6593	77	85	xn	xn	PROPN
ejpam-6593	77	86	αxn	αxn	PROPN
ejpam-6593	77	87	the	the	DET
ejpam-6593	77	88	difference	difference	NOUN
ejpam-6593	77	89	between	between	ADP
ejpam-6593	77	90	the	the	DET
ejpam-6593	77	91	first	first	ADJ
ejpam-6593	77	92	and	and	CCONJ
ejpam-6593	77	93	second	second	ADJ
ejpam-6593	77	94	value	value	NOUN
ejpam-6593	77	95	of	of	ADP
ejpam-6593	77	96	k	k	PROPN
ejpam-6593	77	97	at	at	ADP
ejpam-6593	77	98	a	a	DET
ejpam-6593	77	99	specific	specific	ADJ
ejpam-6593	77	100	value	value	NOUN
ejpam-6593	77	101	of	of	ADP
ejpam-6593	77	102	xn	xn	PROPN
ejpam-6593	77	103	k(m	k(m	PROPN
ejpam-6593	77	104	,	,	PUNCT
ejpam-6593	77	105	xn	xn	PROPN
ejpam-6593	77	106	)	)	PUNCT
ejpam-6593	78	1	the	the	DET
ejpam-6593	78	2	(	(	PUNCT
ejpam-6593	78	3	m+	m+	NUM
ejpam-6593	78	4	1)st	1)st	NUM
ejpam-6593	78	5	value	value	NOUN
ejpam-6593	78	6	of	of	ADP
ejpam-6593	78	7	k	k	PROPN
ejpam-6593	78	8	at	at	ADP
ejpam-6593	78	9	a	a	DET
ejpam-6593	78	10	specific	specific	ADJ
ejpam-6593	78	11	value	value	NOUN
ejpam-6593	78	12	of	of	ADP
ejpam-6593	78	13	xn	xn	PROPN
ejpam-6593	78	14	table	table	NOUN
ejpam-6593	78	15	1	1	NUM
ejpam-6593	78	16	:	:	PUNCT
ejpam-6593	78	17	variables	variable	NOUN
ejpam-6593	78	18	considered	consider	VERB
ejpam-6593	78	19	in	in	ADP
ejpam-6593	78	20	solving	solve	VERB
ejpam-6593	78	21	2x	2x	NUM
ejpam-6593	78	22	+	+	CCONJ
ejpam-6593	78	23	(	(	PUNCT
ejpam-6593	78	24	2	2	NUM
ejpam-6593	78	25	+	+	NUM
ejpam-6593	78	26	5k	5k	NUM
ejpam-6593	78	27	)	)	PUNCT
ejpam-6593	78	28	=	=	SYM
ejpam-6593	78	29	z2	z2	NOUN
ejpam-6593	78	30	we	we	PRON
ejpam-6593	78	31	derive	derive	VERB
ejpam-6593	78	32	k(0,xn	k(0,xn	PROPN
ejpam-6593	78	33	)	)	PUNCT
ejpam-6593	78	34	and	and	CCONJ
ejpam-6593	78	35	k(m	k(m	PROPN
ejpam-6593	78	36	,	,	PUNCT
ejpam-6593	78	37	xn	xn	PROPN
ejpam-6593	78	38	)	)	PUNCT
ejpam-6593	78	39	from	from	ADP
ejpam-6593	78	40	(	(	PUNCT
ejpam-6593	78	41	5	5	NUM
ejpam-6593	78	42	)	)	PUNCT
ejpam-6593	78	43	,	,	PUNCT
ejpam-6593	78	44	and	and	CCONJ
ejpam-6593	78	45	define	define	VERB
ejpam-6593	78	46	αxn	αxn	NOUN
ejpam-6593	78	47	as	as	ADP
ejpam-6593	78	48	the	the	DET
ejpam-6593	78	49	difference	difference	NOUN
ejpam-6593	78	50	of	of	ADP
ejpam-6593	78	51	k(0,xn	k(0,xn	PROPN
ejpam-6593	78	52	)	)	PUNCT
ejpam-6593	78	53	and	and	CCONJ
ejpam-6593	78	54	k(1,xn	k(1,xn	PROPN
ejpam-6593	78	55	):	):	PUNCT
ejpam-6593	78	56	k(0,xn	k(0,xn	PROPN
ejpam-6593	78	57	)	)	PUNCT
ejpam-6593	78	58	=	=	SYM
ejpam-6593	78	59	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	78	60	)	)	PUNCT
ejpam-6593	79	1	−	−	NOUN
ejpam-6593	80	1	2xn	2xn	ADJ
ejpam-6593	80	2	−	−	NOUN
ejpam-6593	80	3	2	2	NUM
ejpam-6593	80	4	5	5	NUM
ejpam-6593	80	5	,	,	PUNCT
ejpam-6593	80	6	(	(	PUNCT
ejpam-6593	80	7	6a	6a	NOUN
ejpam-6593	80	8	)	)	PUNCT
ejpam-6593	80	9	m.	m.	NOUN
ejpam-6593	80	10	c.	c.	PROPN
ejpam-6593	80	11	avenilla	avenilla	PROPN
ejpam-6593	80	12	,	,	PUNCT
ejpam-6593	80	13	j.	j.	PROPN
ejpam-6593	80	14	b.	b.	PROPN
ejpam-6593	80	15	bacani	bacani	PROPN
ejpam-6593	80	16	/	/	SYM
ejpam-6593	80	17	eur	eur	PROPN
ejpam-6593	80	18	.	.	PUNCT
ejpam-6593	81	1	j.	j.	PROPN
ejpam-6593	81	2	pure	pure	PROPN
ejpam-6593	81	3	appl	appl	PROPN
ejpam-6593	81	4	.	.	PROPN
ejpam-6593	81	5	math	math	PROPN
ejpam-6593	81	6	,	,	PUNCT
ejpam-6593	81	7	18	18	NUM
ejpam-6593	81	8	(	(	PUNCT
ejpam-6593	81	9	3	3	NUM
ejpam-6593	81	10	)	)	PUNCT
ejpam-6593	81	11	(	(	PUNCT
ejpam-6593	81	12	2025	2025	NUM
ejpam-6593	81	13	)	)	PUNCT
ejpam-6593	81	14	,	,	PUNCT
ejpam-6593	81	15	6593	6593	NUM
ejpam-6593	81	16	4	4	NUM
ejpam-6593	81	17	of	of	ADP
ejpam-6593	81	18	24	24	NUM
ejpam-6593	81	19	k(m	k(m	PROPN
ejpam-6593	81	20	,	,	PUNCT
ejpam-6593	81	21	xn	xn	PROPN
ejpam-6593	81	22	)	)	PUNCT
ejpam-6593	81	23	=	=	PUNCT
ejpam-6593	82	1	z2(m	z2(m	NUM
ejpam-6593	82	2	,	,	PUNCT
ejpam-6593	82	3	xn	xn	PROPN
ejpam-6593	82	4	)	)	PUNCT
ejpam-6593	82	5	−	−	ADP
ejpam-6593	83	1	2xn	2xn	ADJ
ejpam-6593	83	2	−	−	NOUN
ejpam-6593	83	3	2	2	NUM
ejpam-6593	83	4	5	5	NUM
ejpam-6593	83	5	,	,	PUNCT
ejpam-6593	83	6	(	(	PUNCT
ejpam-6593	83	7	6b	6b	NOUN
ejpam-6593	83	8	)	)	PUNCT
ejpam-6593	83	9	αxn	αxn	PROPN
ejpam-6593	83	10	=	=	SYM
ejpam-6593	83	11	k(1,xn	k(1,xn	PROPN
ejpam-6593	83	12	)	)	PUNCT
ejpam-6593	84	1	−	−	PROPN
ejpam-6593	84	2	k(0,xn	k(0,xn	PROPN
ejpam-6593	84	3	)	)	PUNCT
ejpam-6593	84	4	.	.	PUNCT
ejpam-6593	85	1	(	(	PUNCT
ejpam-6593	85	2	6c	6c	NOUN
ejpam-6593	85	3	)	)	PUNCT
ejpam-6593	85	4	here	here	ADV
ejpam-6593	85	5	,	,	PUNCT
ejpam-6593	85	6	m	m	PROPN
ejpam-6593	85	7	∈	∈	NOUN
ejpam-6593	85	8	n.	n.	NOUN
ejpam-6593	85	9	we	we	PRON
ejpam-6593	85	10	begin	begin	VERB
ejpam-6593	85	11	the	the	DET
ejpam-6593	85	12	discussion	discussion	NOUN
ejpam-6593	85	13	with	with	ADP
ejpam-6593	85	14	the	the	DET
ejpam-6593	85	15	following	follow	VERB
ejpam-6593	85	16	lemmas	lemmas	NOUN
ejpam-6593	85	17	.	.	PUNCT
ejpam-6593	86	1	lemma	lemma	PROPN
ejpam-6593	86	2	1	1	NUM
ejpam-6593	86	3	.	.	PUNCT
ejpam-6593	86	4	suppose	suppose	VERB
ejpam-6593	86	5	the	the	DET
ejpam-6593	86	6	exponential	exponential	ADJ
ejpam-6593	86	7	diophantine	diophantine	NOUN
ejpam-6593	86	8	equation	equation	NOUN
ejpam-6593	86	9	(	(	PUNCT
ejpam-6593	86	10	5	5	NUM
ejpam-6593	86	11	)	)	PUNCT
ejpam-6593	86	12	has	have	VERB
ejpam-6593	86	13	a	a	DET
ejpam-6593	86	14	solution	solution	NOUN
ejpam-6593	86	15	.	.	PUNCT
ejpam-6593	87	1	then	then	ADV
ejpam-6593	87	2	,	,	PUNCT
ejpam-6593	87	3	x	x	PROPN
ejpam-6593	87	4	≡	≡	PROPN
ejpam-6593	87	5	1	1	NUM
ejpam-6593	87	6	(	(	PUNCT
ejpam-6593	87	7	mod	mod	NOUN
ejpam-6593	87	8	4	4	X
ejpam-6593	87	9	)	)	PUNCT
ejpam-6593	87	10	if	if	SCONJ
ejpam-6593	87	11	and	and	CCONJ
ejpam-6593	87	12	only	only	ADV
ejpam-6593	87	13	if	if	SCONJ
ejpam-6593	87	14	z	z	PROPN
ejpam-6593	87	15	≡	≡	PROPN
ejpam-6593	87	16	2	2	NUM
ejpam-6593	87	17	(	(	PUNCT
ejpam-6593	87	18	mod	mod	NOUN
ejpam-6593	87	19	5	5	NUM
ejpam-6593	87	20	)	)	PUNCT
ejpam-6593	87	21	or	or	CCONJ
ejpam-6593	87	22	z	z	PROPN
ejpam-6593	87	23	≡	≡	PROPN
ejpam-6593	87	24	3	3	NUM
ejpam-6593	87	25	(	(	PUNCT
ejpam-6593	87	26	mod	mod	NOUN
ejpam-6593	87	27	5	5	NUM
ejpam-6593	87	28	)	)	PUNCT
ejpam-6593	87	29	.	.	PUNCT
ejpam-6593	88	1	proof	proof	NOUN
ejpam-6593	88	2	.	.	PUNCT
ejpam-6593	89	1	let	let	VERB
ejpam-6593	89	2	x	x	SYM
ejpam-6593	89	3	≡	≡	PROPN
ejpam-6593	89	4	1	1	NUM
ejpam-6593	89	5	(	(	PUNCT
ejpam-6593	89	6	mod	mod	NOUN
ejpam-6593	89	7	4	4	NUM
ejpam-6593	89	8	)	)	PUNCT
ejpam-6593	89	9	in	in	ADP
ejpam-6593	89	10	the	the	DET
ejpam-6593	89	11	exponential	exponential	ADJ
ejpam-6593	89	12	diophantine	diophantine	NOUN
ejpam-6593	89	13	equation	equation	NOUN
ejpam-6593	89	14	(	(	PUNCT
ejpam-6593	89	15	5	5	NUM
ejpam-6593	89	16	)	)	PUNCT
ejpam-6593	89	17	.	.	PUNCT
ejpam-6593	90	1	this	this	PRON
ejpam-6593	90	2	means	mean	VERB
ejpam-6593	90	3	that	that	SCONJ
ejpam-6593	90	4	2x	2x	NUM
ejpam-6593	90	5	≡	≡	PROPN
ejpam-6593	90	6	2	2	NUM
ejpam-6593	90	7	(	(	PUNCT
ejpam-6593	90	8	mod	mod	NOUN
ejpam-6593	90	9	5	5	NUM
ejpam-6593	90	10	)	)	PUNCT
ejpam-6593	90	11	and	and	CCONJ
ejpam-6593	90	12	2	2	NUM
ejpam-6593	90	13	+	+	NUM
ejpam-6593	90	14	5k	5k	NUM
ejpam-6593	90	15	≡	≡	PROPN
ejpam-6593	90	16	2	2	NUM
ejpam-6593	90	17	(	(	PUNCT
ejpam-6593	90	18	mod	mod	NOUN
ejpam-6593	90	19	5	5	NUM
ejpam-6593	90	20	)	)	PUNCT
ejpam-6593	90	21	for	for	ADP
ejpam-6593	90	22	all	all	DET
ejpam-6593	90	23	k	k	PROPN
ejpam-6593	90	24	∈	∈	PROPN
ejpam-6593	90	25	n.	n.	PROPN
ejpam-6593	90	26	thus	thus	ADV
ejpam-6593	90	27	,	,	PUNCT
ejpam-6593	90	28	z2	z2	PROPN
ejpam-6593	90	29	≡	≡	PROPN
ejpam-6593	90	30	2x	2x	NUM
ejpam-6593	90	31	+	+	CCONJ
ejpam-6593	90	32	(	(	PUNCT
ejpam-6593	90	33	2	2	NUM
ejpam-6593	90	34	+	+	NUM
ejpam-6593	90	35	5k	5k	NUM
ejpam-6593	90	36	)	)	PUNCT
ejpam-6593	90	37	≡	≡	PROPN
ejpam-6593	90	38	4	4	NUM
ejpam-6593	90	39	(	(	PUNCT
ejpam-6593	90	40	mod	mod	NOUN
ejpam-6593	90	41	5	5	NUM
ejpam-6593	90	42	)	)	PUNCT
ejpam-6593	90	43	.	.	PUNCT
ejpam-6593	91	1	we	we	PRON
ejpam-6593	91	2	claim	claim	VERB
ejpam-6593	91	3	that	that	SCONJ
ejpam-6593	91	4	z	z	NOUN
ejpam-6593	91	5	≡	≡	PROPN
ejpam-6593	91	6	2	2	NUM
ejpam-6593	91	7	(	(	PUNCT
ejpam-6593	91	8	mod	mod	NOUN
ejpam-6593	91	9	5	5	NUM
ejpam-6593	91	10	)	)	PUNCT
ejpam-6593	91	11	or	or	CCONJ
ejpam-6593	91	12	z	z	PROPN
ejpam-6593	91	13	≡	≡	PROPN
ejpam-6593	91	14	3	3	NUM
ejpam-6593	91	15	(	(	PUNCT
ejpam-6593	91	16	mod	mod	NOUN
ejpam-6593	91	17	5	5	NUM
ejpam-6593	91	18	)	)	PUNCT
ejpam-6593	91	19	.	.	PUNCT
ejpam-6593	92	1	suppose	suppose	VERB
ejpam-6593	92	2	on	on	ADP
ejpam-6593	92	3	the	the	DET
ejpam-6593	92	4	contrary	contrary	NOUN
ejpam-6593	93	1	that	that	PRON
ejpam-6593	93	2	z	z	NOUN
ejpam-6593	93	3	≡	≡	PROPN
ejpam-6593	93	4	0	0	PUNCT
ejpam-6593	94	1	(	(	PUNCT
ejpam-6593	94	2	mod	mod	PROPN
ejpam-6593	94	3	5	5	NUM
ejpam-6593	94	4	)	)	PUNCT
ejpam-6593	94	5	,	,	PUNCT
ejpam-6593	94	6	z	z	PROPN
ejpam-6593	94	7	≡	≡	PROPN
ejpam-6593	94	8	1	1	NUM
ejpam-6593	94	9	(	(	PUNCT
ejpam-6593	94	10	mod	mod	NOUN
ejpam-6593	94	11	5	5	NUM
ejpam-6593	94	12	)	)	PUNCT
ejpam-6593	94	13	,	,	PUNCT
ejpam-6593	94	14	or	or	CCONJ
ejpam-6593	94	15	z	z	PROPN
ejpam-6593	94	16	≡	≡	PROPN
ejpam-6593	94	17	4	4	NUM
ejpam-6593	94	18	(	(	PUNCT
ejpam-6593	94	19	mod	mod	NOUN
ejpam-6593	94	20	5	5	NUM
ejpam-6593	94	21	)	)	PUNCT
ejpam-6593	94	22	.	.	PUNCT
ejpam-6593	95	1	then	then	ADV
ejpam-6593	95	2	,	,	PUNCT
ejpam-6593	95	3	z2	z2	PROPN
ejpam-6593	95	4	≡	≡	PROPN
ejpam-6593	95	5	0	0	PUNCT
ejpam-6593	96	1	(	(	PUNCT
ejpam-6593	96	2	mod	mod	PROPN
ejpam-6593	96	3	5	5	NUM
ejpam-6593	96	4	)	)	PUNCT
ejpam-6593	96	5	,	,	PUNCT
ejpam-6593	96	6	z2	z2	PROPN
ejpam-6593	96	7	≡	≡	PROPN
ejpam-6593	96	8	1	1	NUM
ejpam-6593	96	9	(	(	PUNCT
ejpam-6593	96	10	mod	mod	NOUN
ejpam-6593	96	11	5	5	NUM
ejpam-6593	96	12	)	)	PUNCT
ejpam-6593	96	13	,	,	PUNCT
ejpam-6593	96	14	or	or	CCONJ
ejpam-6593	96	15	z2	z2	PROPN
ejpam-6593	96	16	≡	≡	PROPN
ejpam-6593	96	17	1	1	NUM
ejpam-6593	96	18	(	(	PUNCT
ejpam-6593	96	19	mod	mod	NOUN
ejpam-6593	96	20	5	5	NUM
ejpam-6593	96	21	)	)	PUNCT
ejpam-6593	96	22	,	,	PUNCT
ejpam-6593	96	23	respectively	respectively	ADV
ejpam-6593	96	24	.	.	PUNCT
ejpam-6593	97	1	however	however	ADV
ejpam-6593	97	2	,	,	PUNCT
ejpam-6593	97	3	any	any	PRON
ejpam-6593	97	4	of	of	ADP
ejpam-6593	97	5	these	these	PRON
ejpam-6593	97	6	is	be	AUX
ejpam-6593	97	7	impossible	impossible	ADJ
ejpam-6593	97	8	since	since	SCONJ
ejpam-6593	97	9	we	we	PRON
ejpam-6593	97	10	already	already	ADV
ejpam-6593	97	11	established	establish	VERB
ejpam-6593	97	12	that	that	SCONJ
ejpam-6593	97	13	z2	z2	PROPN
ejpam-6593	97	14	≡	≡	PROPN
ejpam-6593	97	15	4	4	NUM
ejpam-6593	97	16	(	(	PUNCT
ejpam-6593	97	17	mod	mod	NOUN
ejpam-6593	97	18	5	5	NUM
ejpam-6593	97	19	)	)	PUNCT
ejpam-6593	97	20	.	.	PUNCT
ejpam-6593	98	1	this	this	PRON
ejpam-6593	98	2	implies	imply	VERB
ejpam-6593	98	3	that	that	SCONJ
ejpam-6593	98	4	z	z	PROPN
ejpam-6593	98	5	≡	≡	PROPN
ejpam-6593	98	6	2	2	NUM
ejpam-6593	98	7	(	(	PUNCT
ejpam-6593	98	8	mod	mod	NOUN
ejpam-6593	98	9	5	5	NUM
ejpam-6593	98	10	)	)	PUNCT
ejpam-6593	98	11	or	or	CCONJ
ejpam-6593	98	12	z	z	PROPN
ejpam-6593	98	13	≡	≡	PROPN
ejpam-6593	98	14	3	3	NUM
ejpam-6593	98	15	(	(	PUNCT
ejpam-6593	98	16	mod	mod	NOUN
ejpam-6593	98	17	5	5	NUM
ejpam-6593	98	18	)	)	PUNCT
ejpam-6593	98	19	.	.	PUNCT
ejpam-6593	99	1	now	now	ADV
ejpam-6593	99	2	,	,	PUNCT
ejpam-6593	99	3	let	let	VERB
ejpam-6593	99	4	z	z	PROPN
ejpam-6593	99	5	≡	≡	PROPN
ejpam-6593	99	6	2	2	NUM
ejpam-6593	99	7	(	(	PUNCT
ejpam-6593	99	8	mod	mod	NOUN
ejpam-6593	99	9	5	5	NUM
ejpam-6593	99	10	)	)	PUNCT
ejpam-6593	99	11	or	or	CCONJ
ejpam-6593	99	12	z	z	PROPN
ejpam-6593	99	13	≡	≡	PROPN
ejpam-6593	99	14	3	3	NUM
ejpam-6593	99	15	(	(	PUNCT
ejpam-6593	99	16	mod	mod	NOUN
ejpam-6593	99	17	5	5	NUM
ejpam-6593	99	18	)	)	PUNCT
ejpam-6593	99	19	in	in	ADP
ejpam-6593	99	20	equation	equation	NOUN
ejpam-6593	99	21	(	(	PUNCT
ejpam-6593	99	22	5	5	NUM
ejpam-6593	99	23	)	)	PUNCT
ejpam-6593	99	24	.	.	PUNCT
ejpam-6593	100	1	then	then	ADV
ejpam-6593	100	2	,	,	PUNCT
ejpam-6593	100	3	z2	z2	PROPN
ejpam-6593	100	4	≡	≡	PROPN
ejpam-6593	100	5	4	4	NUM
ejpam-6593	100	6	(	(	PUNCT
ejpam-6593	100	7	mod	mod	NOUN
ejpam-6593	100	8	5	5	NUM
ejpam-6593	100	9	)	)	PUNCT
ejpam-6593	100	10	.	.	PUNCT
ejpam-6593	101	1	assume	assume	VERB
ejpam-6593	101	2	the	the	DET
ejpam-6593	101	3	contrary	contrary	NOUN
ejpam-6593	101	4	that	that	SCONJ
ejpam-6593	101	5	x	x	SYM
ejpam-6593	101	6	̸≡	̸≡	PROPN
ejpam-6593	101	7	1	1	NUM
ejpam-6593	101	8	(	(	PUNCT
ejpam-6593	101	9	mod	mod	NOUN
ejpam-6593	101	10	4	4	NUM
ejpam-6593	101	11	)	)	PUNCT
ejpam-6593	101	12	.	.	PUNCT
ejpam-6593	102	1	we	we	PRON
ejpam-6593	102	2	first	first	ADV
ejpam-6593	102	3	consider	consider	VERB
ejpam-6593	102	4	x	x	SYM
ejpam-6593	102	5	≡	≡	PROPN
ejpam-6593	102	6	2	2	NUM
ejpam-6593	102	7	(	(	PUNCT
ejpam-6593	102	8	mod	mod	NOUN
ejpam-6593	102	9	4	4	NUM
ejpam-6593	102	10	)	)	PUNCT
ejpam-6593	102	11	.	.	PUNCT
ejpam-6593	103	1	then	then	ADV
ejpam-6593	103	2	,	,	PUNCT
ejpam-6593	103	3	2x	2x	NUM
ejpam-6593	103	4	≡	≡	PROPN
ejpam-6593	103	5	4	4	NUM
ejpam-6593	103	6	(	(	PUNCT
ejpam-6593	103	7	mod	mod	NOUN
ejpam-6593	103	8	5	5	NUM
ejpam-6593	103	9	)	)	PUNCT
ejpam-6593	103	10	and	and	CCONJ
ejpam-6593	103	11	the	the	DET
ejpam-6593	103	12	equation	equation	NOUN
ejpam-6593	103	13	2x	2x	NUM
ejpam-6593	103	14	+	+	CCONJ
ejpam-6593	103	15	(	(	PUNCT
ejpam-6593	103	16	2	2	NUM
ejpam-6593	103	17	+	+	NUM
ejpam-6593	103	18	5k	5k	NUM
ejpam-6593	103	19	)	)	PUNCT
ejpam-6593	103	20	≡	≡	PROPN
ejpam-6593	103	21	4	4	NUM
ejpam-6593	104	1	+	+	SYM
ejpam-6593	104	2	2	2	NUM
ejpam-6593	104	3	≡	≡	PROPN
ejpam-6593	104	4	1	1	NUM
ejpam-6593	104	5	(	(	PUNCT
ejpam-6593	104	6	mod	mod	NOUN
ejpam-6593	104	7	5	5	NUM
ejpam-6593	104	8	)	)	PUNCT
ejpam-6593	104	9	.	.	PUNCT
ejpam-6593	105	1	next	next	ADV
ejpam-6593	105	2	,	,	PUNCT
ejpam-6593	105	3	we	we	PRON
ejpam-6593	105	4	let	let	VERB
ejpam-6593	105	5	x	x	SYM
ejpam-6593	105	6	≡	≡	PROPN
ejpam-6593	105	7	3	3	NUM
ejpam-6593	105	8	(	(	PUNCT
ejpam-6593	105	9	mod	mod	NOUN
ejpam-6593	105	10	4	4	NUM
ejpam-6593	105	11	)	)	PUNCT
ejpam-6593	105	12	.	.	PUNCT
ejpam-6593	106	1	consequently	consequently	ADV
ejpam-6593	106	2	,	,	PUNCT
ejpam-6593	106	3	2x	2x	NUM
ejpam-6593	106	4	≡	≡	PROPN
ejpam-6593	106	5	3	3	NUM
ejpam-6593	106	6	(	(	PUNCT
ejpam-6593	106	7	mod	mod	NOUN
ejpam-6593	106	8	5	5	NUM
ejpam-6593	106	9	)	)	PUNCT
ejpam-6593	106	10	and	and	CCONJ
ejpam-6593	106	11	2x	2x	NUM
ejpam-6593	106	12	+	+	CCONJ
ejpam-6593	106	13	(	(	PUNCT
ejpam-6593	106	14	2	2	NUM
ejpam-6593	106	15	+	+	NUM
ejpam-6593	106	16	5k	5k	NUM
ejpam-6593	106	17	)	)	PUNCT
ejpam-6593	106	18	≡	≡	PROPN
ejpam-6593	106	19	3	3	NUM
ejpam-6593	107	1	+	+	SYM
ejpam-6593	107	2	2	2	NUM
ejpam-6593	107	3	≡	≡	PROPN
ejpam-6593	107	4	0	0	PUNCT
ejpam-6593	107	5	(	(	PUNCT
ejpam-6593	107	6	mod	mod	PROPN
ejpam-6593	107	7	5	5	NUM
ejpam-6593	107	8	)	)	PUNCT
ejpam-6593	107	9	.	.	PUNCT
ejpam-6593	108	1	lastly	lastly	ADV
ejpam-6593	108	2	,	,	PUNCT
ejpam-6593	108	3	we	we	PRON
ejpam-6593	108	4	take	take	VERB
ejpam-6593	108	5	x	x	PUNCT
ejpam-6593	108	6	≡	≡	PROPN
ejpam-6593	108	7	0	0	PUNCT
ejpam-6593	109	1	(	(	PUNCT
ejpam-6593	109	2	mod	mod	PROPN
ejpam-6593	109	3	4	4	NUM
ejpam-6593	109	4	)	)	PUNCT
ejpam-6593	109	5	.	.	PUNCT
ejpam-6593	110	1	then	then	ADV
ejpam-6593	110	2	,	,	PUNCT
ejpam-6593	110	3	2x	2x	NUM
ejpam-6593	110	4	≡	≡	PROPN
ejpam-6593	110	5	1	1	NUM
ejpam-6593	110	6	(	(	PUNCT
ejpam-6593	110	7	mod	mod	NOUN
ejpam-6593	110	8	5	5	NUM
ejpam-6593	110	9	)	)	PUNCT
ejpam-6593	110	10	and	and	CCONJ
ejpam-6593	110	11	2x	2x	NUM
ejpam-6593	110	12	+	+	CCONJ
ejpam-6593	110	13	(	(	PUNCT
ejpam-6593	110	14	2	2	NUM
ejpam-6593	110	15	+	+	NUM
ejpam-6593	110	16	5k	5k	NUM
ejpam-6593	110	17	)	)	PUNCT
ejpam-6593	110	18	≡	≡	PROPN
ejpam-6593	110	19	1	1	NUM
ejpam-6593	111	1	+	+	SYM
ejpam-6593	111	2	2	2	NUM
ejpam-6593	111	3	≡	≡	PROPN
ejpam-6593	111	4	3	3	NUM
ejpam-6593	111	5	(	(	PUNCT
ejpam-6593	111	6	mod	mod	NOUN
ejpam-6593	111	7	5	5	NUM
ejpam-6593	111	8	)	)	PUNCT
ejpam-6593	111	9	.	.	PUNCT
ejpam-6593	112	1	for	for	ADP
ejpam-6593	112	2	all	all	DET
ejpam-6593	112	3	these	these	DET
ejpam-6593	112	4	cases	case	NOUN
ejpam-6593	112	5	,	,	PUNCT
ejpam-6593	112	6	we	we	PRON
ejpam-6593	112	7	have	have	VERB
ejpam-6593	112	8	2x	2x	NUM
ejpam-6593	112	9	+	+	CCONJ
ejpam-6593	112	10	(	(	PUNCT
ejpam-6593	112	11	2	2	NUM
ejpam-6593	112	12	+	+	NUM
ejpam-6593	112	13	5k	5k	NUM
ejpam-6593	112	14	)	)	PUNCT
ejpam-6593	112	15	̸≡	̸≡	PROPN
ejpam-6593	112	16	z2	z2	PROPN
ejpam-6593	112	17	(	(	PUNCT
ejpam-6593	112	18	mod	mod	PROPN
ejpam-6593	112	19	5	5	NUM
ejpam-6593	112	20	)	)	PUNCT
ejpam-6593	112	21	.	.	PUNCT
ejpam-6593	113	1	hence	hence	ADV
ejpam-6593	113	2	,	,	PUNCT
ejpam-6593	113	3	x	x	PRON
ejpam-6593	113	4	must	must	AUX
ejpam-6593	113	5	be	be	AUX
ejpam-6593	113	6	congruent	congruent	ADJ
ejpam-6593	113	7	to	to	ADP
ejpam-6593	113	8	1	1	NUM
ejpam-6593	113	9	(	(	PUNCT
ejpam-6593	113	10	mod	mod	NOUN
ejpam-6593	113	11	4	4	NUM
ejpam-6593	113	12	)	)	PUNCT
ejpam-6593	113	13	.	.	PUNCT
ejpam-6593	114	1	therefore	therefore	ADV
ejpam-6593	114	2	,	,	PUNCT
ejpam-6593	114	3	the	the	DET
ejpam-6593	114	4	equation	equation	NOUN
ejpam-6593	114	5	2x	2x	NUM
ejpam-6593	114	6	+	+	CCONJ
ejpam-6593	114	7	(	(	PUNCT
ejpam-6593	114	8	2	2	NUM
ejpam-6593	114	9	+	+	NUM
ejpam-6593	114	10	5k	5k	NUM
ejpam-6593	114	11	)	)	PUNCT
ejpam-6593	114	12	=	=	SYM
ejpam-6593	114	13	z2	z2	PROPN
ejpam-6593	114	14	has	have	VERB
ejpam-6593	114	15	a	a	DET
ejpam-6593	114	16	solution	solution	NOUN
ejpam-6593	114	17	when	when	SCONJ
ejpam-6593	114	18	x	x	SYM
ejpam-6593	114	19	≡	≡	PROPN
ejpam-6593	114	20	1	1	NUM
ejpam-6593	114	21	(	(	PUNCT
ejpam-6593	114	22	mod	mod	NOUN
ejpam-6593	114	23	4	4	X
ejpam-6593	114	24	)	)	PUNCT
ejpam-6593	114	25	if	if	SCONJ
ejpam-6593	114	26	and	and	CCONJ
ejpam-6593	114	27	only	only	ADV
ejpam-6593	114	28	if	if	SCONJ
ejpam-6593	114	29	z	z	PROPN
ejpam-6593	114	30	≡	≡	PROPN
ejpam-6593	114	31	2	2	NUM
ejpam-6593	114	32	(	(	PUNCT
ejpam-6593	114	33	mod	mod	NOUN
ejpam-6593	114	34	5	5	NUM
ejpam-6593	114	35	)	)	PUNCT
ejpam-6593	114	36	or	or	CCONJ
ejpam-6593	114	37	z	z	PROPN
ejpam-6593	114	38	≡	≡	PROPN
ejpam-6593	114	39	3	3	NUM
ejpam-6593	114	40	(	(	PUNCT
ejpam-6593	114	41	mod	mod	NOUN
ejpam-6593	114	42	5	5	NUM
ejpam-6593	114	43	)	)	PUNCT
ejpam-6593	114	44	.	.	PUNCT
ejpam-6593	115	1	from	from	ADP
ejpam-6593	115	2	equation	equation	NOUN
ejpam-6593	115	3	(	(	PUNCT
ejpam-6593	115	4	5	5	NUM
ejpam-6593	115	5	)	)	PUNCT
ejpam-6593	115	6	,	,	PUNCT
ejpam-6593	115	7	we	we	PRON
ejpam-6593	115	8	can	can	AUX
ejpam-6593	115	9	first	first	ADV
ejpam-6593	115	10	look	look	VERB
ejpam-6593	115	11	at	at	ADP
ejpam-6593	115	12	the	the	DET
ejpam-6593	115	13	smallest	small	ADJ
ejpam-6593	115	14	possible	possible	ADJ
ejpam-6593	115	15	value	value	NOUN
ejpam-6593	115	16	of	of	ADP
ejpam-6593	115	17	z	z	NOUN
ejpam-6593	115	18	and	and	CCONJ
ejpam-6593	115	19	then	then	ADV
ejpam-6593	115	20	add	add	VERB
ejpam-6593	115	21	a	a	DET
ejpam-6593	115	22	multiple	multiple	NOUN
ejpam-6593	115	23	of	of	ADP
ejpam-6593	115	24	five	five	NUM
ejpam-6593	115	25	to	to	PART
ejpam-6593	115	26	get	get	VERB
ejpam-6593	115	27	the	the	DET
ejpam-6593	115	28	other	other	ADJ
ejpam-6593	115	29	values	value	NOUN
ejpam-6593	115	30	of	of	ADP
ejpam-6593	115	31	z.	z.	PROPN
ejpam-6593	115	32	to	to	PART
ejpam-6593	115	33	get	get	VERB
ejpam-6593	115	34	the	the	DET
ejpam-6593	115	35	smallest	small	ADJ
ejpam-6593	115	36	number	number	NOUN
ejpam-6593	115	37	of	of	ADP
ejpam-6593	115	38	possible	possible	ADJ
ejpam-6593	115	39	conditions	condition	NOUN
ejpam-6593	115	40	for	for	ADP
ejpam-6593	115	41	z(0,xn	z(0,xn	PROPN
ejpam-6593	115	42	)	)	PUNCT
ejpam-6593	115	43	,	,	PUNCT
ejpam-6593	115	44	we	we	PRON
ejpam-6593	115	45	use	use	VERB
ejpam-6593	115	46	⌊√	⌊√	PROPN
ejpam-6593	115	47	2x	2x	NUM
ejpam-6593	115	48	⌋	⌋	NOUN
ejpam-6593	115	49	because	because	SCONJ
ejpam-6593	115	50	√	√	ADJ
ejpam-6593	115	51	2x	2x	NUM
ejpam-6593	115	52	will	will	AUX
ejpam-6593	115	53	never	never	ADV
ejpam-6593	115	54	be	be	AUX
ejpam-6593	115	55	an	an	DET
ejpam-6593	115	56	integer	integer	NOUN
ejpam-6593	115	57	since	since	SCONJ
ejpam-6593	115	58	x	x	PROPN
ejpam-6593	115	59	≡	≡	PROPN
ejpam-6593	115	60	1	1	NUM
ejpam-6593	115	61	(	(	PUNCT
ejpam-6593	115	62	mod	mod	NOUN
ejpam-6593	115	63	4	4	NUM
ejpam-6593	115	64	)	)	PUNCT
ejpam-6593	115	65	.	.	PUNCT
ejpam-6593	116	1	as	as	ADP
ejpam-6593	116	2	a	a	DET
ejpam-6593	116	3	result	result	NOUN
ejpam-6593	116	4	,	,	PUNCT
ejpam-6593	116	5	we	we	PRON
ejpam-6593	116	6	obtain	obtain	VERB
ejpam-6593	116	7	the	the	DET
ejpam-6593	116	8	following	follow	VERB
ejpam-6593	116	9	formulas	formula	NOUN
ejpam-6593	116	10	:	:	PUNCT
ejpam-6593	116	11	x	x	X
ejpam-6593	116	12	:	:	PUNCT
ejpam-6593	116	13	=	=	SYM
ejpam-6593	116	14	xn	xn	PUNCT
ejpam-6593	116	15	=	=	SYM
ejpam-6593	116	16	1	1	NUM
ejpam-6593	116	17	+	+	NUM
ejpam-6593	116	18	4n	4n	X
ejpam-6593	116	19	(	(	PUNCT
ejpam-6593	116	20	7a	7a	NUM
ejpam-6593	116	21	)	)	PUNCT
ejpam-6593	116	22	z(0,xn	z(0,xn	PROPN
ejpam-6593	116	23	)	)	PUNCT
ejpam-6593	117	1	=	=	PUNCT
ejpam-6593	117	2			NUM
ejpam-6593	117	3	⌊√	⌊√	NOUN
ejpam-6593	117	4	2xn	2xn	ADJ
ejpam-6593	117	5	⌋	⌋	NOUN
ejpam-6593	118	1	+	+	CCONJ
ejpam-6593	118	2	6	6	NUM
ejpam-6593	118	3	if	if	SCONJ
ejpam-6593	118	4	x	x	NOUN
ejpam-6593	118	5	=	=	SYM
ejpam-6593	118	6	1,⌊√	1,⌊√	NUM
ejpam-6593	118	7	2xn	2xn	ADJ
ejpam-6593	118	8	⌋	⌋	NOUN
ejpam-6593	119	1	+	+	CCONJ
ejpam-6593	119	2	1	1	NUM
ejpam-6593	119	3	if	if	SCONJ
ejpam-6593	119	4	⌊√	⌊√	PROPN
ejpam-6593	119	5	2xn	2xn	ADJ
ejpam-6593	119	6	⌋	⌋	NOUN
ejpam-6593	119	7	≡	≡	PROPN
ejpam-6593	119	8	1	1	NUM
ejpam-6593	119	9	(	(	PUNCT
ejpam-6593	119	10	mod	mod	NOUN
ejpam-6593	119	11	5),⌊√	5),⌊√	NUM
ejpam-6593	119	12	2xn	2xn	ADJ
ejpam-6593	119	13	⌋	⌋	NOUN
ejpam-6593	119	14	+	+	CCONJ
ejpam-6593	119	15	5	5	NUM
ejpam-6593	119	16	if	if	SCONJ
ejpam-6593	119	17	⌊√	⌊√	PROPN
ejpam-6593	119	18	2xn	2xn	ADJ
ejpam-6593	119	19	⌋	⌋	NOUN
ejpam-6593	119	20	≡	≡	PROPN
ejpam-6593	119	21	2	2	NUM
ejpam-6593	119	22	(	(	PUNCT
ejpam-6593	119	23	mod	mod	NOUN
ejpam-6593	119	24	5),⌊√	5),⌊√	NUM
ejpam-6593	119	25	2xn	2xn	ADJ
ejpam-6593	119	26	⌋	⌋	NOUN
ejpam-6593	120	1	+	+	CCONJ
ejpam-6593	120	2	4	4	NUM
ejpam-6593	120	3	if	if	SCONJ
ejpam-6593	120	4	⌊√	⌊√	PROPN
ejpam-6593	120	5	2xn	2xn	ADJ
ejpam-6593	120	6	⌋	⌋	NOUN
ejpam-6593	120	7	≡	≡	PROPN
ejpam-6593	120	8	3	3	NUM
ejpam-6593	120	9	(	(	PUNCT
ejpam-6593	120	10	mod	mod	PROPN
ejpam-6593	120	11	5),⌊√	5),⌊√	NUM
ejpam-6593	120	12	2xn	2xn	ADJ
ejpam-6593	120	13	⌋	⌋	NOUN
ejpam-6593	121	1	+	+	CCONJ
ejpam-6593	121	2	3	3	NUM
ejpam-6593	121	3	if	if	SCONJ
ejpam-6593	121	4	⌊√	⌊√	PROPN
ejpam-6593	121	5	2xn	2xn	ADJ
ejpam-6593	121	6	⌋	⌋	NOUN
ejpam-6593	121	7	≡	≡	PROPN
ejpam-6593	121	8	4	4	NUM
ejpam-6593	121	9	(	(	PUNCT
ejpam-6593	121	10	mod	mod	NOUN
ejpam-6593	121	11	5),⌊√	5),⌊√	NUM
ejpam-6593	121	12	2xn	2xn	ADJ
ejpam-6593	121	13	⌋	⌋	NOUN
ejpam-6593	122	1	+	+	CCONJ
ejpam-6593	122	2	2	2	NUM
ejpam-6593	122	3	if	if	SCONJ
ejpam-6593	122	4	⌊√	⌊√	PROPN
ejpam-6593	122	5	2xn	2xn	ADJ
ejpam-6593	122	6	⌋	⌋	NOUN
ejpam-6593	122	7	≡	≡	PROPN
ejpam-6593	122	8	0	0	PUNCT
ejpam-6593	123	1	(	(	PUNCT
ejpam-6593	123	2	mod	mod	PROPN
ejpam-6593	123	3	5	5	NUM
ejpam-6593	123	4	)	)	PUNCT
ejpam-6593	123	5	,	,	PUNCT
ejpam-6593	123	6	(	(	PUNCT
ejpam-6593	123	7	7b	7b	NOUN
ejpam-6593	123	8	)	)	PUNCT
ejpam-6593	123	9	m.	m.	NOUN
ejpam-6593	123	10	c.	c.	PROPN
ejpam-6593	123	11	avenilla	avenilla	PROPN
ejpam-6593	123	12	,	,	PUNCT
ejpam-6593	123	13	j.	j.	PROPN
ejpam-6593	123	14	b.	b.	PROPN
ejpam-6593	123	15	bacani	bacani	PROPN
ejpam-6593	123	16	/	/	SYM
ejpam-6593	123	17	eur	eur	PROPN
ejpam-6593	123	18	.	.	PUNCT
ejpam-6593	124	1	j.	j.	PROPN
ejpam-6593	124	2	pure	pure	PROPN
ejpam-6593	124	3	appl	appl	PROPN
ejpam-6593	124	4	.	.	PROPN
ejpam-6593	124	5	math	math	PROPN
ejpam-6593	124	6	,	,	PUNCT
ejpam-6593	124	7	18	18	NUM
ejpam-6593	124	8	(	(	PUNCT
ejpam-6593	124	9	3	3	NUM
ejpam-6593	124	10	)	)	PUNCT
ejpam-6593	124	11	(	(	PUNCT
ejpam-6593	124	12	2025	2025	NUM
ejpam-6593	124	13	)	)	PUNCT
ejpam-6593	124	14	,	,	PUNCT
ejpam-6593	124	15	6593	6593	NUM
ejpam-6593	124	16	5	5	NUM
ejpam-6593	124	17	of	of	ADP
ejpam-6593	124	18	24	24	NUM
ejpam-6593	124	19	or	or	CCONJ
ejpam-6593	124	20	z(0,xn	z(0,xn	PROPN
ejpam-6593	124	21	)	)	PUNCT
ejpam-6593	124	22	=	=	SYM
ejpam-6593	125	1			NUM
ejpam-6593	125	2	⌊√	⌊√	PROPN
ejpam-6593	125	3	2xn	2xn	ADJ
ejpam-6593	125	4	⌋	⌋	NOUN
ejpam-6593	126	1	+	+	CCONJ
ejpam-6593	126	2	2	2	NUM
ejpam-6593	126	3	if	if	SCONJ
ejpam-6593	126	4	⌊√	⌊√	PROPN
ejpam-6593	126	5	2xn	2xn	ADJ
ejpam-6593	126	6	⌋	⌋	NOUN
ejpam-6593	126	7	≡	≡	PROPN
ejpam-6593	126	8	1	1	NUM
ejpam-6593	126	9	(	(	PUNCT
ejpam-6593	126	10	mod	mod	NOUN
ejpam-6593	126	11	5),⌊√	5),⌊√	NUM
ejpam-6593	126	12	2xn	2xn	ADJ
ejpam-6593	126	13	⌋	⌋	NOUN
ejpam-6593	127	1	+	+	CCONJ
ejpam-6593	127	2	1	1	NUM
ejpam-6593	127	3	if	if	SCONJ
ejpam-6593	127	4	⌊√	⌊√	PROPN
ejpam-6593	127	5	2xn	2xn	ADJ
ejpam-6593	127	6	⌋	⌋	NOUN
ejpam-6593	127	7	≡	≡	PROPN
ejpam-6593	127	8	2	2	NUM
ejpam-6593	127	9	(	(	PUNCT
ejpam-6593	127	10	mod	mod	NOUN
ejpam-6593	127	11	5),⌊√	5),⌊√	NUM
ejpam-6593	127	12	2xn	2xn	ADJ
ejpam-6593	127	13	⌋	⌋	NOUN
ejpam-6593	128	1	+	+	CCONJ
ejpam-6593	128	2	5	5	NUM
ejpam-6593	128	3	if	if	SCONJ
ejpam-6593	128	4	⌊√	⌊√	PROPN
ejpam-6593	128	5	2xn	2xn	ADJ
ejpam-6593	128	6	⌋	⌋	NOUN
ejpam-6593	128	7	≡	≡	PROPN
ejpam-6593	128	8	3	3	NUM
ejpam-6593	128	9	(	(	PUNCT
ejpam-6593	128	10	mod	mod	PROPN
ejpam-6593	128	11	5),⌊√	5),⌊√	NUM
ejpam-6593	128	12	2xn	2xn	ADJ
ejpam-6593	128	13	⌋	⌋	NOUN
ejpam-6593	129	1	+	+	CCONJ
ejpam-6593	129	2	4	4	NUM
ejpam-6593	129	3	if	if	SCONJ
ejpam-6593	129	4	⌊√	⌊√	PROPN
ejpam-6593	129	5	2xn	2xn	ADJ
ejpam-6593	129	6	⌋	⌋	NOUN
ejpam-6593	129	7	≡	≡	PROPN
ejpam-6593	129	8	4	4	NUM
ejpam-6593	129	9	(	(	PUNCT
ejpam-6593	129	10	mod	mod	NOUN
ejpam-6593	129	11	5),⌊√	5),⌊√	NUM
ejpam-6593	129	12	2xn	2xn	ADJ
ejpam-6593	129	13	⌋	⌋	NOUN
ejpam-6593	129	14	+	+	CCONJ
ejpam-6593	129	15	3	3	NUM
ejpam-6593	129	16	if	if	SCONJ
ejpam-6593	129	17	⌊√	⌊√	PROPN
ejpam-6593	129	18	2xn	2xn	ADJ
ejpam-6593	129	19	⌋	⌋	NOUN
ejpam-6593	129	20	≡	≡	PROPN
ejpam-6593	129	21	0	0	PUNCT
ejpam-6593	130	1	(	(	PUNCT
ejpam-6593	130	2	mod	mod	PROPN
ejpam-6593	130	3	5	5	NUM
ejpam-6593	130	4	)	)	PUNCT
ejpam-6593	130	5	,	,	PUNCT
ejpam-6593	130	6	(	(	PUNCT
ejpam-6593	130	7	7c	7c	NOUN
ejpam-6593	130	8	)	)	PUNCT
ejpam-6593	130	9	z(m	z(m	PROPN
ejpam-6593	130	10	,	,	PUNCT
ejpam-6593	130	11	xn	xn	NUM
ejpam-6593	130	12	)	)	PUNCT
ejpam-6593	130	13	=	=	SYM
ejpam-6593	130	14	z(0,xn	z(0,xn	PROPN
ejpam-6593	130	15	)	)	PUNCT
ejpam-6593	131	1	+	+	CCONJ
ejpam-6593	131	2	5	5	NUM
ejpam-6593	131	3	m	m	NOUN
ejpam-6593	131	4	,	,	PUNCT
ejpam-6593	131	5	(	(	PUNCT
ejpam-6593	131	6	7d	7d	NUM
ejpam-6593	131	7	)	)	PUNCT
ejpam-6593	131	8	where	where	SCONJ
ejpam-6593	131	9	n	n	X
ejpam-6593	131	10	∈	∈	PROPN
ejpam-6593	131	11	n0	n0	PROPN
ejpam-6593	131	12	and	and	CCONJ
ejpam-6593	131	13	m	m	PROPN
ejpam-6593	131	14	∈	∈	PROPN
ejpam-6593	131	15	n.	n.	NOUN
ejpam-6593	131	16	the	the	DET
ejpam-6593	131	17	five	five	NUM
ejpam-6593	131	18	-	-	PUNCT
ejpam-6593	131	19	tuple	tuple	NOUN
ejpam-6593	131	20	(	(	PUNCT
ejpam-6593	131	21	p	p	X
ejpam-6593	131	22	,	,	PUNCT
ejpam-6593	131	23	k	k	NOUN
ejpam-6593	131	24	,	,	PUNCT
ejpam-6593	131	25	x	x	X
ejpam-6593	131	26	,	,	PUNCT
ejpam-6593	131	27	y	y	PROPN
ejpam-6593	131	28	,	,	PUNCT
ejpam-6593	131	29	z	z	NOUN
ejpam-6593	131	30	)	)	PUNCT
ejpam-6593	131	31	=	=	SYM
ejpam-6593	131	32	(	(	PUNCT
ejpam-6593	131	33	2	2	NUM
ejpam-6593	131	34	,	,	PUNCT
ejpam-6593	131	35	k(m	k(m	PROPN
ejpam-6593	131	36	,	,	PUNCT
ejpam-6593	131	37	xn	xn	PROPN
ejpam-6593	131	38	)	)	PUNCT
ejpam-6593	131	39	,	,	PUNCT
ejpam-6593	131	40	xn	xn	PROPN
ejpam-6593	131	41	,	,	PUNCT
ejpam-6593	131	42	1	1	NUM
ejpam-6593	131	43	,	,	PUNCT
ejpam-6593	131	44	z(m	z(m	PROPN
ejpam-6593	131	45	,	,	PUNCT
ejpam-6593	131	46	xn	xn	NUM
ejpam-6593	131	47	)	)	PUNCT
ejpam-6593	131	48	)	)	PUNCT
ejpam-6593	131	49	is	be	AUX
ejpam-6593	131	50	a	a	DET
ejpam-6593	131	51	solution	solution	NOUN
ejpam-6593	131	52	of	of	ADP
ejpam-6593	131	53	(	(	PUNCT
ejpam-6593	131	54	3	3	NUM
ejpam-6593	131	55	)	)	PUNCT
ejpam-6593	131	56	.	.	PUNCT
ejpam-6593	132	1	as	as	ADP
ejpam-6593	132	2	an	an	DET
ejpam-6593	132	3	example	example	NOUN
ejpam-6593	132	4	,	,	PUNCT
ejpam-6593	132	5	we	we	PRON
ejpam-6593	132	6	use	use	VERB
ejpam-6593	132	7	our	our	PRON
ejpam-6593	132	8	equations	equation	NOUN
ejpam-6593	132	9	when	when	SCONJ
ejpam-6593	132	10	x	x	X
ejpam-6593	132	11	=	=	PUNCT
ejpam-6593	132	12	xn	xn	PUNCT
ejpam-6593	132	13	=	=	SYM
ejpam-6593	132	14	1	1	NUM
ejpam-6593	132	15	+	+	CCONJ
ejpam-6593	132	16	4n	4n	NOUN
ejpam-6593	132	17	and	and	CCONJ
ejpam-6593	132	18	z	z	PROPN
ejpam-6593	132	19	≡	≡	PROPN
ejpam-6593	132	20	2	2	NUM
ejpam-6593	132	21	(	(	PUNCT
ejpam-6593	132	22	mod	mod	NOUN
ejpam-6593	132	23	5	5	NUM
ejpam-6593	132	24	)	)	PUNCT
ejpam-6593	132	25	.	.	PUNCT
ejpam-6593	133	1	if	if	SCONJ
ejpam-6593	133	2	n	n	NOUN
ejpam-6593	133	3	=	=	SYM
ejpam-6593	133	4	0	0	NUM
ejpam-6593	133	5	,	,	PUNCT
ejpam-6593	133	6	we	we	PRON
ejpam-6593	133	7	have	have	VERB
ejpam-6593	133	8	x	x	X
ejpam-6593	133	9	=	=	SYM
ejpam-6593	133	10	1	1	NUM
ejpam-6593	133	11	,	,	PUNCT
ejpam-6593	133	12	z(0,1	z(0,1	NOUN
ejpam-6593	133	13	)	)	PUNCT
ejpam-6593	133	14	=	=	SYM
ejpam-6593	133	15	7	7	NUM
ejpam-6593	133	16	,	,	PUNCT
ejpam-6593	133	17	and	and	CCONJ
ejpam-6593	133	18	z(1,1	z(1,1	NUM
ejpam-6593	133	19	)	)	PUNCT
ejpam-6593	133	20	=	=	NOUN
ejpam-6593	134	1	12	12	NUM
ejpam-6593	134	2	from	from	ADP
ejpam-6593	134	3	(	(	PUNCT
ejpam-6593	134	4	7a	7a	NUM
ejpam-6593	134	5	)	)	PUNCT
ejpam-6593	134	6	,	,	PUNCT
ejpam-6593	134	7	(	(	PUNCT
ejpam-6593	134	8	7b	7b	NOUN
ejpam-6593	134	9	)	)	PUNCT
ejpam-6593	134	10	,	,	PUNCT
ejpam-6593	134	11	and	and	CCONJ
ejpam-6593	134	12	(	(	PUNCT
ejpam-6593	134	13	7d	7d	NUM
ejpam-6593	134	14	)	)	PUNCT
ejpam-6593	134	15	,	,	PUNCT
ejpam-6593	134	16	respectively	respectively	ADV
ejpam-6593	134	17	.	.	PUNCT
ejpam-6593	135	1	note	note	VERB
ejpam-6593	135	2	that	that	SCONJ
ejpam-6593	135	3	when	when	SCONJ
ejpam-6593	135	4	x	x	X
ejpam-6593	135	5	=	=	SYM
ejpam-6593	135	6	x0	x0	PROPN
ejpam-6593	135	7	=	=	SYM
ejpam-6593	135	8	1	1	NUM
ejpam-6593	135	9	and	and	CCONJ
ejpam-6593	135	10	z	z	NOUN
ejpam-6593	135	11	is	be	AUX
ejpam-6593	135	12	congruent	congruent	ADJ
ejpam-6593	135	13	to	to	ADP
ejpam-6593	135	14	2	2	NUM
ejpam-6593	135	15	(	(	PUNCT
ejpam-6593	135	16	mod	mod	PROPN
ejpam-6593	135	17	5	5	NUM
ejpam-6593	135	18	)	)	PUNCT
ejpam-6593	135	19	,	,	PUNCT
ejpam-6593	135	20	the	the	DET
ejpam-6593	135	21	smallest	small	ADJ
ejpam-6593	135	22	value	value	NOUN
ejpam-6593	135	23	of	of	ADP
ejpam-6593	135	24	z	z	NOUN
ejpam-6593	135	25	is	be	AUX
ejpam-6593	135	26	⌊	⌊	VERB
ejpam-6593	135	27	√	√	NUM
ejpam-6593	135	28	2x0⌋	2x0⌋	NUM
ejpam-6593	136	1	+	+	CCONJ
ejpam-6593	136	2	6	6	NUM
ejpam-6593	136	3	because	because	SCONJ
ejpam-6593	136	4	we	we	PRON
ejpam-6593	136	5	must	must	AUX
ejpam-6593	136	6	have	have	VERB
ejpam-6593	136	7	k	k	X
ejpam-6593	136	8	>	>	X
ejpam-6593	137	1	0	0	X
ejpam-6593	137	2	.	.	PUNCT
ejpam-6593	138	1	from	from	ADP
ejpam-6593	138	2	(	(	PUNCT
ejpam-6593	138	3	6a	6a	NOUN
ejpam-6593	138	4	)	)	PUNCT
ejpam-6593	138	5	and	and	CCONJ
ejpam-6593	138	6	(	(	PUNCT
ejpam-6593	138	7	6b	6b	NOUN
ejpam-6593	138	8	)	)	PUNCT
ejpam-6593	138	9	,	,	PUNCT
ejpam-6593	138	10	we	we	PRON
ejpam-6593	138	11	have	have	VERB
ejpam-6593	138	12	that	that	DET
ejpam-6593	138	13	k(0,1	k(0,1	NOUN
ejpam-6593	138	14	)	)	PUNCT
ejpam-6593	138	15	=	=	SYM
ejpam-6593	138	16	9	9	NUM
ejpam-6593	138	17	and	and	CCONJ
ejpam-6593	138	18	k(1,1	k(1,1	NOUN
ejpam-6593	138	19	)	)	PUNCT
ejpam-6593	138	20	=	=	SYM
ejpam-6593	138	21	28	28	NUM
ejpam-6593	138	22	.	.	PUNCT
ejpam-6593	139	1	thus	thus	ADV
ejpam-6593	139	2	,	,	PUNCT
ejpam-6593	139	3	the	the	DET
ejpam-6593	139	4	first	first	ADJ
ejpam-6593	139	5	two	two	NUM
ejpam-6593	139	6	solutions	solution	NOUN
ejpam-6593	139	7	when	when	SCONJ
ejpam-6593	139	8	x	x	PROPN
ejpam-6593	139	9	=	=	SYM
ejpam-6593	139	10	1	1	NUM
ejpam-6593	139	11	and	and	CCONJ
ejpam-6593	139	12	z	z	PROPN
ejpam-6593	139	13	≡	≡	PROPN
ejpam-6593	139	14	2	2	NUM
ejpam-6593	139	15	(	(	PUNCT
ejpam-6593	139	16	mod	mod	NOUN
ejpam-6593	139	17	5	5	NUM
ejpam-6593	139	18	)	)	PUNCT
ejpam-6593	139	19	are	be	AUX
ejpam-6593	139	20	(	(	PUNCT
ejpam-6593	139	21	p	p	X
ejpam-6593	139	22	,	,	PUNCT
ejpam-6593	139	23	k	k	NOUN
ejpam-6593	139	24	,	,	PUNCT
ejpam-6593	139	25	x	x	X
ejpam-6593	139	26	,	,	PUNCT
ejpam-6593	139	27	y	y	PROPN
ejpam-6593	139	28	,	,	PUNCT
ejpam-6593	139	29	z	z	NOUN
ejpam-6593	139	30	)	)	PUNCT
ejpam-6593	139	31	=	=	SYM
ejpam-6593	139	32	(	(	PUNCT
ejpam-6593	139	33	2	2	NUM
ejpam-6593	139	34	,	,	PUNCT
ejpam-6593	139	35	9	9	NUM
ejpam-6593	139	36	,	,	PUNCT
ejpam-6593	139	37	1	1	NUM
ejpam-6593	139	38	,	,	PUNCT
ejpam-6593	139	39	1	1	NUM
ejpam-6593	139	40	,	,	PUNCT
ejpam-6593	139	41	7	7	NUM
ejpam-6593	139	42	)	)	PUNCT
ejpam-6593	139	43	and	and	CCONJ
ejpam-6593	139	44	(	(	PUNCT
ejpam-6593	139	45	2	2	NUM
ejpam-6593	139	46	,	,	PUNCT
ejpam-6593	139	47	28	28	NUM
ejpam-6593	139	48	,	,	PUNCT
ejpam-6593	139	49	1	1	NUM
ejpam-6593	139	50	,	,	PUNCT
ejpam-6593	139	51	1	1	NUM
ejpam-6593	139	52	,	,	PUNCT
ejpam-6593	139	53	12	12	NUM
ejpam-6593	139	54	)	)	PUNCT
ejpam-6593	139	55	.	.	PUNCT
ejpam-6593	140	1	when	when	SCONJ
ejpam-6593	140	2	z	z	PROPN
ejpam-6593	140	3	≡	≡	PROPN
ejpam-6593	140	4	3	3	NUM
ejpam-6593	140	5	(	(	PUNCT
ejpam-6593	140	6	mod	mod	NOUN
ejpam-6593	140	7	5	5	NUM
ejpam-6593	140	8	)	)	PUNCT
ejpam-6593	140	9	,	,	PUNCT
ejpam-6593	140	10	we	we	PRON
ejpam-6593	140	11	have	have	VERB
ejpam-6593	140	12	x	x	X
ejpam-6593	140	13	=	=	SYM
ejpam-6593	140	14	1	1	NUM
ejpam-6593	140	15	,	,	PUNCT
ejpam-6593	140	16	z(0,1	z(0,1	NOUN
ejpam-6593	140	17	)	)	PUNCT
ejpam-6593	140	18	=	=	SYM
ejpam-6593	140	19	3	3	NUM
ejpam-6593	140	20	,	,	PUNCT
ejpam-6593	140	21	and	and	CCONJ
ejpam-6593	140	22	z(1,1	z(1,1	NUM
ejpam-6593	140	23	)	)	PUNCT
ejpam-6593	140	24	=	=	SYM
ejpam-6593	140	25	8	8	NUM
ejpam-6593	140	26	from	from	ADP
ejpam-6593	140	27	(	(	PUNCT
ejpam-6593	140	28	7a	7a	NUM
ejpam-6593	140	29	)	)	PUNCT
ejpam-6593	140	30	,	,	PUNCT
ejpam-6593	140	31	(	(	PUNCT
ejpam-6593	140	32	7c	7c	NOUN
ejpam-6593	140	33	)	)	PUNCT
ejpam-6593	140	34	,	,	PUNCT
ejpam-6593	140	35	and	and	CCONJ
ejpam-6593	140	36	(	(	PUNCT
ejpam-6593	140	37	7d	7d	NUM
ejpam-6593	140	38	)	)	PUNCT
ejpam-6593	140	39	,	,	PUNCT
ejpam-6593	140	40	respectively	respectively	ADV
ejpam-6593	140	41	,	,	PUNCT
ejpam-6593	140	42	for	for	ADP
ejpam-6593	140	43	n	n	NOUN
ejpam-6593	140	44	=	=	SYM
ejpam-6593	140	45	0	0	NUM
ejpam-6593	140	46	.	.	PUNCT
ejpam-6593	141	1	we	we	PRON
ejpam-6593	141	2	also	also	ADV
ejpam-6593	141	3	have	have	VERB
ejpam-6593	141	4	k(0,1	k(0,1	NOUN
ejpam-6593	141	5	)	)	PUNCT
ejpam-6593	141	6	=	=	SYM
ejpam-6593	141	7	1	1	NUM
ejpam-6593	141	8	and	and	CCONJ
ejpam-6593	141	9	k(1,1	k(1,1	NOUN
ejpam-6593	141	10	)	)	PUNCT
ejpam-6593	141	11	=	=	NOUN
ejpam-6593	141	12	12	12	NUM
ejpam-6593	141	13	from	from	ADP
ejpam-6593	141	14	(	(	PUNCT
ejpam-6593	141	15	6a	6a	NOUN
ejpam-6593	141	16	)	)	PUNCT
ejpam-6593	141	17	and	and	CCONJ
ejpam-6593	141	18	(	(	PUNCT
ejpam-6593	141	19	6b	6b	NOUN
ejpam-6593	141	20	)	)	PUNCT
ejpam-6593	141	21	.	.	PUNCT
ejpam-6593	142	1	thus	thus	ADV
ejpam-6593	142	2	,	,	PUNCT
ejpam-6593	142	3	the	the	DET
ejpam-6593	142	4	first	first	ADJ
ejpam-6593	142	5	two	two	NUM
ejpam-6593	142	6	solutions	solution	NOUN
ejpam-6593	142	7	when	when	SCONJ
ejpam-6593	142	8	x	x	PROPN
ejpam-6593	142	9	=	=	SYM
ejpam-6593	142	10	1	1	NUM
ejpam-6593	142	11	and	and	CCONJ
ejpam-6593	142	12	z	z	PROPN
ejpam-6593	142	13	≡	≡	PROPN
ejpam-6593	142	14	3	3	NUM
ejpam-6593	142	15	(	(	PUNCT
ejpam-6593	142	16	mod	mod	NOUN
ejpam-6593	142	17	5	5	NUM
ejpam-6593	142	18	)	)	PUNCT
ejpam-6593	142	19	are	be	AUX
ejpam-6593	142	20	(	(	PUNCT
ejpam-6593	142	21	p	p	X
ejpam-6593	142	22	,	,	PUNCT
ejpam-6593	142	23	k	k	NOUN
ejpam-6593	142	24	,	,	PUNCT
ejpam-6593	142	25	x	x	X
ejpam-6593	142	26	,	,	PUNCT
ejpam-6593	142	27	y	y	PROPN
ejpam-6593	142	28	,	,	PUNCT
ejpam-6593	142	29	z	z	NOUN
ejpam-6593	142	30	)	)	PUNCT
ejpam-6593	142	31	=	=	SYM
ejpam-6593	142	32	(	(	PUNCT
ejpam-6593	142	33	2	2	NUM
ejpam-6593	142	34	,	,	PUNCT
ejpam-6593	142	35	1	1	NUM
ejpam-6593	142	36	,	,	PUNCT
ejpam-6593	142	37	1	1	NUM
ejpam-6593	142	38	,	,	PUNCT
ejpam-6593	142	39	1	1	NUM
ejpam-6593	142	40	,	,	PUNCT
ejpam-6593	142	41	3	3	NUM
ejpam-6593	142	42	)	)	PUNCT
ejpam-6593	142	43	and	and	CCONJ
ejpam-6593	142	44	(	(	PUNCT
ejpam-6593	142	45	2	2	NUM
ejpam-6593	142	46	,	,	PUNCT
ejpam-6593	142	47	12	12	NUM
ejpam-6593	142	48	,	,	PUNCT
ejpam-6593	142	49	1	1	NUM
ejpam-6593	142	50	,	,	PUNCT
ejpam-6593	142	51	1	1	NUM
ejpam-6593	142	52	,	,	PUNCT
ejpam-6593	142	53	8)	8)	NUM
ejpam-6593	142	54	.	.	PUNCT
ejpam-6593	143	1	lemma	lemma	PROPN
ejpam-6593	143	2	2	2	X
ejpam-6593	143	3	.	.	PUNCT
ejpam-6593	143	4	suppose	suppose	VERB
ejpam-6593	143	5	the	the	DET
ejpam-6593	143	6	exponential	exponential	ADJ
ejpam-6593	143	7	diophantine	diophantine	NOUN
ejpam-6593	143	8	equation	equation	NOUN
ejpam-6593	143	9	(	(	PUNCT
ejpam-6593	143	10	5	5	NUM
ejpam-6593	143	11	)	)	PUNCT
ejpam-6593	143	12	has	have	VERB
ejpam-6593	143	13	a	a	DET
ejpam-6593	143	14	solution	solution	NOUN
ejpam-6593	143	15	.	.	PUNCT
ejpam-6593	144	1	then	then	ADV
ejpam-6593	144	2	,	,	PUNCT
ejpam-6593	144	3	x	x	PROPN
ejpam-6593	144	4	≡	≡	PROPN
ejpam-6593	144	5	2	2	NUM
ejpam-6593	144	6	(	(	PUNCT
ejpam-6593	144	7	mod	mod	NOUN
ejpam-6593	144	8	4	4	X
ejpam-6593	144	9	)	)	PUNCT
ejpam-6593	144	10	if	if	SCONJ
ejpam-6593	144	11	and	and	CCONJ
ejpam-6593	144	12	only	only	ADV
ejpam-6593	144	13	if	if	SCONJ
ejpam-6593	144	14	z	z	PROPN
ejpam-6593	144	15	≡	≡	PROPN
ejpam-6593	144	16	1	1	NUM
ejpam-6593	144	17	(	(	PUNCT
ejpam-6593	144	18	mod	mod	NOUN
ejpam-6593	144	19	5	5	NUM
ejpam-6593	144	20	)	)	PUNCT
ejpam-6593	144	21	or	or	CCONJ
ejpam-6593	144	22	z	z	PROPN
ejpam-6593	144	23	≡	≡	PROPN
ejpam-6593	144	24	4	4	NUM
ejpam-6593	144	25	(	(	PUNCT
ejpam-6593	144	26	mod	mod	NOUN
ejpam-6593	144	27	5	5	NUM
ejpam-6593	144	28	)	)	PUNCT
ejpam-6593	144	29	.	.	PUNCT
ejpam-6593	145	1	proof	proof	NOUN
ejpam-6593	145	2	.	.	PUNCT
ejpam-6593	146	1	consider	consider	VERB
ejpam-6593	146	2	the	the	DET
ejpam-6593	146	3	diophantine	diophantine	NOUN
ejpam-6593	146	4	equation	equation	NOUN
ejpam-6593	146	5	(	(	PUNCT
ejpam-6593	146	6	5	5	NUM
ejpam-6593	146	7	)	)	PUNCT
ejpam-6593	146	8	.	.	PUNCT
ejpam-6593	147	1	let	let	VERB
ejpam-6593	147	2	x	x	SYM
ejpam-6593	147	3	≡	≡	PROPN
ejpam-6593	147	4	2	2	NUM
ejpam-6593	147	5	(	(	PUNCT
ejpam-6593	147	6	mod	mod	NOUN
ejpam-6593	147	7	4	4	NUM
ejpam-6593	147	8	)	)	PUNCT
ejpam-6593	147	9	.	.	PUNCT
ejpam-6593	148	1	this	this	PRON
ejpam-6593	148	2	means	mean	VERB
ejpam-6593	148	3	that	that	SCONJ
ejpam-6593	148	4	2x	2x	NUM
ejpam-6593	148	5	≡	≡	PROPN
ejpam-6593	148	6	4	4	NUM
ejpam-6593	148	7	(	(	PUNCT
ejpam-6593	148	8	mod	mod	NOUN
ejpam-6593	148	9	5	5	NUM
ejpam-6593	148	10	)	)	PUNCT
ejpam-6593	148	11	and	and	CCONJ
ejpam-6593	148	12	2	2	NUM
ejpam-6593	148	13	+	+	NUM
ejpam-6593	148	14	5k	5k	NUM
ejpam-6593	148	15	≡	≡	PROPN
ejpam-6593	148	16	2	2	NUM
ejpam-6593	148	17	(	(	PUNCT
ejpam-6593	148	18	mod	mod	NOUN
ejpam-6593	148	19	5	5	NUM
ejpam-6593	148	20	)	)	PUNCT
ejpam-6593	148	21	for	for	ADP
ejpam-6593	148	22	all	all	DET
ejpam-6593	148	23	k	k	PROPN
ejpam-6593	148	24	∈	∈	PROPN
ejpam-6593	148	25	n.	n.	PROPN
ejpam-6593	148	26	thus	thus	ADV
ejpam-6593	148	27	,	,	PUNCT
ejpam-6593	148	28	2x	2x	NUM
ejpam-6593	148	29	+	+	CCONJ
ejpam-6593	148	30	(	(	PUNCT
ejpam-6593	148	31	2	2	NUM
ejpam-6593	148	32	+	+	NUM
ejpam-6593	148	33	5k	5k	NUM
ejpam-6593	148	34	)	)	PUNCT
ejpam-6593	148	35	≡	≡	PROPN
ejpam-6593	148	36	1	1	NUM
ejpam-6593	148	37	(	(	PUNCT
ejpam-6593	148	38	mod	mod	NOUN
ejpam-6593	148	39	5	5	NUM
ejpam-6593	148	40	)	)	PUNCT
ejpam-6593	148	41	≡	≡	PROPN
ejpam-6593	148	42	z2	z2	PROPN
ejpam-6593	148	43	.	.	PUNCT
ejpam-6593	149	1	we	we	PRON
ejpam-6593	149	2	claim	claim	VERB
ejpam-6593	149	3	that	that	SCONJ
ejpam-6593	149	4	z	z	PROPN
ejpam-6593	149	5	≡	≡	PROPN
ejpam-6593	149	6	1	1	NUM
ejpam-6593	149	7	(	(	PUNCT
ejpam-6593	149	8	mod	mod	NOUN
ejpam-6593	149	9	5	5	NUM
ejpam-6593	149	10	)	)	PUNCT
ejpam-6593	149	11	or	or	CCONJ
ejpam-6593	149	12	z	z	PROPN
ejpam-6593	149	13	≡	≡	PROPN
ejpam-6593	149	14	4	4	NUM
ejpam-6593	149	15	(	(	PUNCT
ejpam-6593	149	16	mod	mod	NOUN
ejpam-6593	149	17	5	5	NUM
ejpam-6593	149	18	)	)	PUNCT
ejpam-6593	149	19	.	.	PUNCT
ejpam-6593	150	1	suppose	suppose	VERB
ejpam-6593	150	2	otherwise	otherwise	ADV
ejpam-6593	150	3	that	that	SCONJ
ejpam-6593	150	4	z	z	PROPN
ejpam-6593	150	5	≡	≡	PROPN
ejpam-6593	150	6	0	0	PUNCT
ejpam-6593	151	1	(	(	PUNCT
ejpam-6593	151	2	mod	mod	PROPN
ejpam-6593	151	3	5	5	NUM
ejpam-6593	151	4	)	)	PUNCT
ejpam-6593	151	5	,	,	PUNCT
ejpam-6593	151	6	z	z	PROPN
ejpam-6593	151	7	≡	≡	PROPN
ejpam-6593	151	8	2	2	NUM
ejpam-6593	151	9	(	(	PUNCT
ejpam-6593	151	10	mod	mod	NOUN
ejpam-6593	151	11	5	5	NUM
ejpam-6593	151	12	)	)	PUNCT
ejpam-6593	151	13	,	,	PUNCT
ejpam-6593	151	14	or	or	CCONJ
ejpam-6593	151	15	z	z	PROPN
ejpam-6593	151	16	≡	≡	PROPN
ejpam-6593	151	17	3	3	NUM
ejpam-6593	151	18	(	(	PUNCT
ejpam-6593	151	19	mod	mod	NOUN
ejpam-6593	151	20	5	5	NUM
ejpam-6593	151	21	)	)	PUNCT
ejpam-6593	151	22	.	.	PUNCT
ejpam-6593	152	1	then	then	ADV
ejpam-6593	152	2	,	,	PUNCT
ejpam-6593	152	3	we	we	PRON
ejpam-6593	152	4	have	have	VERB
ejpam-6593	152	5	z2	z2	PROPN
ejpam-6593	152	6	≡	≡	PROPN
ejpam-6593	152	7	0	0	PUNCT
ejpam-6593	153	1	(	(	PUNCT
ejpam-6593	153	2	mod	mod	PROPN
ejpam-6593	153	3	5	5	NUM
ejpam-6593	153	4	)	)	PUNCT
ejpam-6593	153	5	,	,	PUNCT
ejpam-6593	153	6	z2	z2	PROPN
ejpam-6593	153	7	≡	≡	PROPN
ejpam-6593	153	8	4	4	NUM
ejpam-6593	153	9	(	(	PUNCT
ejpam-6593	153	10	mod	mod	NOUN
ejpam-6593	153	11	5	5	NUM
ejpam-6593	153	12	)	)	PUNCT
ejpam-6593	153	13	,	,	PUNCT
ejpam-6593	153	14	or	or	CCONJ
ejpam-6593	153	15	z2	z2	PROPN
ejpam-6593	153	16	≡	≡	PROPN
ejpam-6593	153	17	4	4	NUM
ejpam-6593	153	18	(	(	PUNCT
ejpam-6593	153	19	mod	mod	NOUN
ejpam-6593	153	20	5	5	NUM
ejpam-6593	153	21	)	)	PUNCT
ejpam-6593	153	22	,	,	PUNCT
ejpam-6593	153	23	respectively	respectively	ADV
ejpam-6593	153	24	.	.	PUNCT
ejpam-6593	154	1	any	any	PRON
ejpam-6593	154	2	of	of	ADP
ejpam-6593	154	3	these	these	PRON
ejpam-6593	154	4	is	be	AUX
ejpam-6593	154	5	a	a	DET
ejpam-6593	154	6	contradiction	contradiction	NOUN
ejpam-6593	154	7	since	since	SCONJ
ejpam-6593	154	8	we	we	PRON
ejpam-6593	154	9	already	already	ADV
ejpam-6593	154	10	established	establish	VERB
ejpam-6593	154	11	that	that	SCONJ
ejpam-6593	154	12	z2	z2	PROPN
ejpam-6593	154	13	≡	≡	PROPN
ejpam-6593	154	14	1	1	NUM
ejpam-6593	154	15	(	(	PUNCT
ejpam-6593	154	16	mod	mod	NOUN
ejpam-6593	154	17	5	5	NUM
ejpam-6593	154	18	)	)	PUNCT
ejpam-6593	154	19	.	.	PUNCT
ejpam-6593	155	1	now	now	ADV
ejpam-6593	155	2	,	,	PUNCT
ejpam-6593	155	3	let	let	VERB
ejpam-6593	155	4	z	z	PROPN
ejpam-6593	155	5	≡	≡	PROPN
ejpam-6593	155	6	1	1	NUM
ejpam-6593	155	7	(	(	PUNCT
ejpam-6593	155	8	mod	mod	NOUN
ejpam-6593	155	9	5	5	NUM
ejpam-6593	155	10	)	)	PUNCT
ejpam-6593	155	11	or	or	CCONJ
ejpam-6593	155	12	z	z	PROPN
ejpam-6593	155	13	≡	≡	PROPN
ejpam-6593	155	14	4	4	NUM
ejpam-6593	155	15	(	(	PUNCT
ejpam-6593	155	16	mod	mod	NOUN
ejpam-6593	155	17	5	5	NUM
ejpam-6593	155	18	)	)	PUNCT
ejpam-6593	155	19	.	.	PUNCT
ejpam-6593	156	1	then	then	ADV
ejpam-6593	156	2	,	,	PUNCT
ejpam-6593	156	3	both	both	PRON
ejpam-6593	156	4	will	will	AUX
ejpam-6593	156	5	give	give	VERB
ejpam-6593	156	6	z2	z2	PROPN
ejpam-6593	156	7	≡	≡	PROPN
ejpam-6593	156	8	1	1	NUM
ejpam-6593	156	9	(	(	PUNCT
ejpam-6593	156	10	mod	mod	NOUN
ejpam-6593	156	11	5	5	NUM
ejpam-6593	156	12	)	)	PUNCT
ejpam-6593	156	13	.	.	PUNCT
ejpam-6593	157	1	thus	thus	ADV
ejpam-6593	157	2	,	,	PUNCT
ejpam-6593	157	3	when	when	SCONJ
ejpam-6593	157	4	x	x	X
ejpam-6593	157	5	≡	≡	PROPN
ejpam-6593	157	6	2	2	NUM
ejpam-6593	157	7	(	(	PUNCT
ejpam-6593	157	8	mod	mod	NOUN
ejpam-6593	157	9	4	4	NUM
ejpam-6593	157	10	)	)	PUNCT
ejpam-6593	157	11	,	,	PUNCT
ejpam-6593	157	12	(	(	PUNCT
ejpam-6593	157	13	5	5	X
ejpam-6593	157	14	)	)	PUNCT
ejpam-6593	157	15	only	only	ADV
ejpam-6593	157	16	has	have	VERB
ejpam-6593	157	17	a	a	DET
ejpam-6593	157	18	solution	solution	NOUN
ejpam-6593	157	19	when	when	SCONJ
ejpam-6593	157	20	z	z	PROPN
ejpam-6593	157	21	≡	≡	PROPN
ejpam-6593	157	22	1	1	NUM
ejpam-6593	157	23	(	(	PUNCT
ejpam-6593	157	24	mod	mod	NOUN
ejpam-6593	157	25	5	5	NUM
ejpam-6593	157	26	)	)	PUNCT
ejpam-6593	157	27	or	or	CCONJ
ejpam-6593	157	28	z	z	PROPN
ejpam-6593	157	29	≡	≡	PROPN
ejpam-6593	157	30	4	4	NUM
ejpam-6593	157	31	(	(	PUNCT
ejpam-6593	157	32	mod	mod	NOUN
ejpam-6593	157	33	5	5	NUM
ejpam-6593	157	34	)	)	PUNCT
ejpam-6593	157	35	.	.	PUNCT
ejpam-6593	158	1	now	now	ADV
ejpam-6593	158	2	,	,	PUNCT
ejpam-6593	158	3	let	let	VERB
ejpam-6593	158	4	z	z	PROPN
ejpam-6593	158	5	≡	≡	PROPN
ejpam-6593	158	6	1	1	NUM
ejpam-6593	158	7	(	(	PUNCT
ejpam-6593	158	8	mod	mod	NOUN
ejpam-6593	158	9	5	5	NUM
ejpam-6593	158	10	)	)	PUNCT
ejpam-6593	158	11	or	or	CCONJ
ejpam-6593	158	12	z	z	PROPN
ejpam-6593	158	13	≡	≡	PROPN
ejpam-6593	158	14	4	4	NUM
ejpam-6593	158	15	(	(	PUNCT
ejpam-6593	158	16	mod	mod	NOUN
ejpam-6593	158	17	5	5	NUM
ejpam-6593	158	18	)	)	PUNCT
ejpam-6593	158	19	in	in	ADP
ejpam-6593	158	20	(	(	PUNCT
ejpam-6593	158	21	5	5	NUM
ejpam-6593	158	22	)	)	PUNCT
ejpam-6593	158	23	.	.	PUNCT
ejpam-6593	159	1	then	then	ADV
ejpam-6593	159	2	,	,	PUNCT
ejpam-6593	159	3	z2	z2	PROPN
ejpam-6593	159	4	≡	≡	PROPN
ejpam-6593	159	5	1	1	NUM
ejpam-6593	159	6	(	(	PUNCT
ejpam-6593	159	7	mod	mod	NOUN
ejpam-6593	159	8	5	5	NUM
ejpam-6593	159	9	)	)	PUNCT
ejpam-6593	159	10	.	.	PUNCT
ejpam-6593	160	1	assume	assume	VERB
ejpam-6593	160	2	the	the	DET
ejpam-6593	160	3	contrary	contrary	NOUN
ejpam-6593	160	4	that	that	SCONJ
ejpam-6593	160	5	x	x	SYM
ejpam-6593	160	6	̸≡	̸≡	PROPN
ejpam-6593	160	7	2	2	NUM
ejpam-6593	160	8	(	(	PUNCT
ejpam-6593	160	9	mod	mod	NOUN
ejpam-6593	160	10	4	4	NUM
ejpam-6593	160	11	)	)	PUNCT
ejpam-6593	160	12	.	.	PUNCT
ejpam-6593	161	1	if	if	SCONJ
ejpam-6593	161	2	x	x	SYM
ejpam-6593	161	3	≡	≡	PROPN
ejpam-6593	161	4	1	1	NUM
ejpam-6593	161	5	(	(	PUNCT
ejpam-6593	161	6	mod	mod	NOUN
ejpam-6593	161	7	4	4	NUM
ejpam-6593	161	8	)	)	PUNCT
ejpam-6593	161	9	,	,	PUNCT
ejpam-6593	161	10	then	then	ADV
ejpam-6593	161	11	2x	2x	NUM
ejpam-6593	161	12	≡	≡	PROPN
ejpam-6593	161	13	2	2	NUM
ejpam-6593	161	14	(	(	PUNCT
ejpam-6593	161	15	mod	mod	NOUN
ejpam-6593	161	16	5	5	NUM
ejpam-6593	161	17	)	)	PUNCT
ejpam-6593	161	18	and	and	CCONJ
ejpam-6593	161	19	2x+(2	2x+(2	NUM
ejpam-6593	161	20	+	+	NOUN
ejpam-6593	161	21	5k	5k	NUM
ejpam-6593	161	22	)	)	PUNCT
ejpam-6593	161	23	≡	≡	PROPN
ejpam-6593	161	24	4	4	NUM
ejpam-6593	161	25	(	(	PUNCT
ejpam-6593	161	26	mod	mod	NOUN
ejpam-6593	161	27	5	5	NUM
ejpam-6593	161	28	)	)	PUNCT
ejpam-6593	161	29	.	.	PUNCT
ejpam-6593	162	1	if	if	SCONJ
ejpam-6593	162	2	x	x	SYM
ejpam-6593	162	3	≡	≡	PROPN
ejpam-6593	162	4	3	3	NUM
ejpam-6593	162	5	(	(	PUNCT
ejpam-6593	162	6	mod	mod	NOUN
ejpam-6593	162	7	4	4	NUM
ejpam-6593	162	8	)	)	PUNCT
ejpam-6593	162	9	,	,	PUNCT
ejpam-6593	162	10	then	then	ADV
ejpam-6593	162	11	2x	2x	NUM
ejpam-6593	162	12	≡	≡	PROPN
ejpam-6593	162	13	3	3	NUM
ejpam-6593	162	14	(	(	PUNCT
ejpam-6593	162	15	mod	mod	NOUN
ejpam-6593	162	16	5	5	NUM
ejpam-6593	162	17	)	)	PUNCT
ejpam-6593	162	18	and	and	CCONJ
ejpam-6593	162	19	2x	2x	NUM
ejpam-6593	162	20	+	+	CCONJ
ejpam-6593	162	21	(	(	PUNCT
ejpam-6593	162	22	2	2	NUM
ejpam-6593	162	23	+	+	NUM
ejpam-6593	162	24	5k	5k	NUM
ejpam-6593	162	25	)	)	PUNCT
ejpam-6593	162	26	≡	≡	PROPN
ejpam-6593	162	27	0	0	PUNCT
ejpam-6593	162	28	(	(	PUNCT
ejpam-6593	162	29	mod	mod	PROPN
ejpam-6593	162	30	5	5	NUM
ejpam-6593	162	31	)	)	PUNCT
ejpam-6593	162	32	.	.	PUNCT
ejpam-6593	163	1	lastly	lastly	ADV
ejpam-6593	163	2	,	,	PUNCT
ejpam-6593	163	3	if	if	SCONJ
ejpam-6593	163	4	x	x	SYM
ejpam-6593	163	5	≡	≡	PROPN
ejpam-6593	163	6	0	0	PUNCT
ejpam-6593	163	7	(	(	PUNCT
ejpam-6593	163	8	mod	mod	PROPN
ejpam-6593	163	9	4	4	NUM
ejpam-6593	163	10	)	)	PUNCT
ejpam-6593	163	11	,	,	PUNCT
ejpam-6593	163	12	then	then	ADV
ejpam-6593	163	13	2x	2x	NUM
ejpam-6593	163	14	≡	≡	PROPN
ejpam-6593	163	15	1	1	NUM
ejpam-6593	163	16	(	(	PUNCT
ejpam-6593	163	17	mod	mod	NOUN
ejpam-6593	163	18	5	5	NUM
ejpam-6593	163	19	)	)	PUNCT
ejpam-6593	163	20	and	and	CCONJ
ejpam-6593	163	21	2x	2x	NUM
ejpam-6593	163	22	+	+	CCONJ
ejpam-6593	163	23	(	(	PUNCT
ejpam-6593	163	24	2	2	NUM
ejpam-6593	163	25	+	+	NUM
ejpam-6593	163	26	5k	5k	NUM
ejpam-6593	163	27	)	)	PUNCT
ejpam-6593	163	28	≡	≡	PROPN
ejpam-6593	163	29	3	3	NUM
ejpam-6593	163	30	(	(	PUNCT
ejpam-6593	163	31	mod	mod	NOUN
ejpam-6593	163	32	5	5	NUM
ejpam-6593	163	33	)	)	PUNCT
ejpam-6593	163	34	.	.	PUNCT
ejpam-6593	164	1	in	in	ADP
ejpam-6593	164	2	any	any	DET
ejpam-6593	164	3	case	case	NOUN
ejpam-6593	164	4	,	,	PUNCT
ejpam-6593	164	5	we	we	PRON
ejpam-6593	164	6	have	have	VERB
ejpam-6593	164	7	2x	2x	NUM
ejpam-6593	164	8	+	+	CCONJ
ejpam-6593	164	9	(	(	PUNCT
ejpam-6593	164	10	2	2	NUM
ejpam-6593	164	11	+	+	NUM
ejpam-6593	164	12	5k	5k	NUM
ejpam-6593	164	13	)	)	PUNCT
ejpam-6593	164	14	̸≡	̸≡	PROPN
ejpam-6593	164	15	z2	z2	PROPN
ejpam-6593	164	16	.	.	PUNCT
ejpam-6593	165	1	hence	hence	ADV
ejpam-6593	165	2	,	,	PUNCT
ejpam-6593	165	3	when	when	SCONJ
ejpam-6593	165	4	z	z	PROPN
ejpam-6593	165	5	≡	≡	PROPN
ejpam-6593	165	6	1	1	NUM
ejpam-6593	165	7	(	(	PUNCT
ejpam-6593	165	8	mod	mod	NOUN
ejpam-6593	165	9	5	5	NUM
ejpam-6593	165	10	)	)	PUNCT
ejpam-6593	165	11	or	or	CCONJ
ejpam-6593	165	12	z	z	PROPN
ejpam-6593	165	13	≡	≡	PROPN
ejpam-6593	165	14	4	4	NUM
ejpam-6593	165	15	(	(	PUNCT
ejpam-6593	165	16	mod	mod	NOUN
ejpam-6593	165	17	5	5	NUM
ejpam-6593	165	18	)	)	PUNCT
ejpam-6593	165	19	,	,	PUNCT
ejpam-6593	165	20	(	(	PUNCT
ejpam-6593	165	21	5	5	X
ejpam-6593	165	22	)	)	PUNCT
ejpam-6593	165	23	only	only	ADV
ejpam-6593	165	24	has	have	VERB
ejpam-6593	165	25	a	a	DET
ejpam-6593	165	26	solution	solution	NOUN
ejpam-6593	165	27	when	when	SCONJ
ejpam-6593	165	28	x	x	SYM
ejpam-6593	165	29	≡	≡	PROPN
ejpam-6593	165	30	2	2	NUM
ejpam-6593	165	31	(	(	PUNCT
ejpam-6593	165	32	mod	mod	NOUN
ejpam-6593	165	33	4	4	NUM
ejpam-6593	165	34	)	)	PUNCT
ejpam-6593	165	35	.	.	PUNCT
ejpam-6593	166	1	therefore	therefore	ADV
ejpam-6593	166	2	,	,	PUNCT
ejpam-6593	166	3	the	the	DET
ejpam-6593	166	4	equation	equation	NOUN
ejpam-6593	166	5	2x	2x	NUM
ejpam-6593	166	6	+	+	CCONJ
ejpam-6593	166	7	(	(	PUNCT
ejpam-6593	166	8	2	2	NUM
ejpam-6593	166	9	+	+	NUM
ejpam-6593	166	10	5k	5k	NUM
ejpam-6593	166	11	)	)	PUNCT
ejpam-6593	166	12	=	=	SYM
ejpam-6593	166	13	z2	z2	PROPN
ejpam-6593	166	14	has	have	VERB
ejpam-6593	166	15	a	a	DET
ejpam-6593	166	16	solution	solution	NOUN
ejpam-6593	166	17	when	when	SCONJ
ejpam-6593	166	18	x	x	SYM
ejpam-6593	166	19	≡	≡	PROPN
ejpam-6593	166	20	2	2	NUM
ejpam-6593	166	21	(	(	PUNCT
ejpam-6593	166	22	mod	mod	NOUN
ejpam-6593	166	23	4	4	X
ejpam-6593	166	24	)	)	PUNCT
ejpam-6593	166	25	if	if	SCONJ
ejpam-6593	166	26	and	and	CCONJ
ejpam-6593	166	27	only	only	ADV
ejpam-6593	166	28	if	if	SCONJ
ejpam-6593	166	29	z	z	PROPN
ejpam-6593	166	30	≡	≡	PROPN
ejpam-6593	166	31	1	1	NUM
ejpam-6593	166	32	(	(	PUNCT
ejpam-6593	166	33	mod	mod	NOUN
ejpam-6593	166	34	5	5	NUM
ejpam-6593	166	35	)	)	PUNCT
ejpam-6593	166	36	or	or	CCONJ
ejpam-6593	166	37	z	z	PROPN
ejpam-6593	166	38	≡	≡	PROPN
ejpam-6593	166	39	4	4	NUM
ejpam-6593	166	40	(	(	PUNCT
ejpam-6593	166	41	mod	mod	NOUN
ejpam-6593	166	42	5	5	NUM
ejpam-6593	166	43	)	)	PUNCT
ejpam-6593	166	44	.	.	PUNCT
ejpam-6593	167	1	we	we	PRON
ejpam-6593	167	2	note	note	VERB
ejpam-6593	167	3	that	that	SCONJ
ejpam-6593	167	4	for	for	ADP
ejpam-6593	167	5	this	this	DET
ejpam-6593	167	6	case	case	NOUN
ejpam-6593	167	7	,	,	PUNCT
ejpam-6593	167	8	√	√	PROPN
ejpam-6593	167	9	2x	2x	NUM
ejpam-6593	167	10	is	be	AUX
ejpam-6593	167	11	always	always	ADV
ejpam-6593	167	12	an	an	DET
ejpam-6593	167	13	integer	integer	NOUN
ejpam-6593	167	14	.	.	PUNCT
ejpam-6593	168	1	to	to	PART
ejpam-6593	168	2	reduce	reduce	VERB
ejpam-6593	168	3	the	the	DET
ejpam-6593	168	4	number	number	NOUN
ejpam-6593	168	5	of	of	ADP
ejpam-6593	168	6	possible	possible	ADJ
ejpam-6593	168	7	conditions	condition	NOUN
ejpam-6593	168	8	to	to	PART
ejpam-6593	168	9	be	be	AUX
ejpam-6593	168	10	considered	consider	VERB
ejpam-6593	168	11	for	for	ADP
ejpam-6593	168	12	the	the	DET
ejpam-6593	168	13	smallest	small	ADJ
ejpam-6593	168	14	possible	possible	ADJ
ejpam-6593	168	15	value	value	NOUN
ejpam-6593	168	16	of	of	ADP
ejpam-6593	168	17	z	z	PROPN
ejpam-6593	168	18	,	,	PUNCT
ejpam-6593	168	19	we	we	PRON
ejpam-6593	168	20	use	use	VERB
ejpam-6593	168	21	√	√	NOUN
ejpam-6593	168	22	2x	2x	NUM
ejpam-6593	168	23	.	.	PUNCT
ejpam-6593	169	1	with	with	ADP
ejpam-6593	169	2	this	this	PRON
ejpam-6593	169	3	,	,	PUNCT
ejpam-6593	169	4	m.	m.	PROPN
ejpam-6593	169	5	c.	c.	PROPN
ejpam-6593	169	6	avenilla	avenilla	PROPN
ejpam-6593	169	7	,	,	PUNCT
ejpam-6593	169	8	j.	j.	PROPN
ejpam-6593	169	9	b.	b.	PROPN
ejpam-6593	169	10	bacani	bacani	PROPN
ejpam-6593	169	11	/	/	SYM
ejpam-6593	169	12	eur	eur	PROPN
ejpam-6593	169	13	.	.	PUNCT
ejpam-6593	170	1	j.	j.	PROPN
ejpam-6593	170	2	pure	pure	PROPN
ejpam-6593	170	3	appl	appl	PROPN
ejpam-6593	170	4	.	.	PROPN
ejpam-6593	170	5	math	math	PROPN
ejpam-6593	170	6	,	,	PUNCT
ejpam-6593	170	7	18	18	NUM
ejpam-6593	170	8	(	(	PUNCT
ejpam-6593	170	9	3	3	NUM
ejpam-6593	170	10	)	)	PUNCT
ejpam-6593	170	11	(	(	PUNCT
ejpam-6593	170	12	2025	2025	NUM
ejpam-6593	170	13	)	)	PUNCT
ejpam-6593	170	14	,	,	PUNCT
ejpam-6593	170	15	6593	6593	NUM
ejpam-6593	170	16	6	6	NUM
ejpam-6593	170	17	of	of	ADP
ejpam-6593	170	18	24	24	NUM
ejpam-6593	170	19	we	we	PRON
ejpam-6593	170	20	have	have	VERB
ejpam-6593	170	21	the	the	DET
ejpam-6593	170	22	following	follow	VERB
ejpam-6593	170	23	formulas	formula	NOUN
ejpam-6593	170	24	.	.	PUNCT
ejpam-6593	171	1	x	x	X
ejpam-6593	171	2	:	:	PUNCT
ejpam-6593	171	3	=	=	SYM
ejpam-6593	171	4	xn	xn	PUNCT
ejpam-6593	171	5	=	=	SYM
ejpam-6593	171	6	2	2	NUM
ejpam-6593	171	7	+	+	NUM
ejpam-6593	171	8	4n	4n	X
ejpam-6593	171	9	(	(	PUNCT
ejpam-6593	171	10	8a	8a	NUM
ejpam-6593	171	11	)	)	PUNCT
ejpam-6593	171	12	z(0,xn	z(0,xn	PROPN
ejpam-6593	171	13	)	)	PUNCT
ejpam-6593	172	1	=	=	PRON
ejpam-6593	172	2	{	{	PUNCT
ejpam-6593	173	1	√	√	NUM
ejpam-6593	173	2	2xn	2xn	ADJ
ejpam-6593	174	1	+	+	CCONJ
ejpam-6593	174	2	4	4	NUM
ejpam-6593	174	3	if	if	SCONJ
ejpam-6593	174	4	n	n	PRON
ejpam-6593	174	5	is	be	AUX
ejpam-6593	174	6	even,√	even,√	NOUN
ejpam-6593	174	7	2xn	2xn	ADJ
ejpam-6593	175	1	+	+	CCONJ
ejpam-6593	175	2	3	3	NUM
ejpam-6593	175	3	if	if	SCONJ
ejpam-6593	175	4	n	n	NOUN
ejpam-6593	175	5	is	be	AUX
ejpam-6593	175	6	odd	odd	ADJ
ejpam-6593	175	7	,	,	PUNCT
ejpam-6593	175	8	(	(	PUNCT
ejpam-6593	175	9	8b	8b	NUM
ejpam-6593	175	10	)	)	PUNCT
ejpam-6593	175	11	or	or	CCONJ
ejpam-6593	175	12	z(0,xn	z(0,xn	PROPN
ejpam-6593	175	13	)	)	PUNCT
ejpam-6593	176	1	=	=	PRON
ejpam-6593	176	2	{	{	PUNCT
ejpam-6593	177	1	√	√	NUM
ejpam-6593	177	2	2xn	2xn	ADJ
ejpam-6593	178	1	+	+	CCONJ
ejpam-6593	178	2	2	2	NUM
ejpam-6593	178	3	if	if	SCONJ
ejpam-6593	178	4	n	n	PRON
ejpam-6593	178	5	is	be	AUX
ejpam-6593	178	6	even,√	even,√	NOUN
ejpam-6593	179	1	2xn	2xn	ADJ
ejpam-6593	180	1	+	+	CCONJ
ejpam-6593	180	2	1	1	NUM
ejpam-6593	180	3	if	if	SCONJ
ejpam-6593	180	4	n	n	PRON
ejpam-6593	180	5	is	be	AUX
ejpam-6593	180	6	odd	odd	ADJ
ejpam-6593	180	7	,	,	PUNCT
ejpam-6593	180	8	(	(	PUNCT
ejpam-6593	180	9	8c	8c	X
ejpam-6593	180	10	)	)	PUNCT
ejpam-6593	180	11	z(m	z(m	NOUN
ejpam-6593	180	12	,	,	PUNCT
ejpam-6593	180	13	xn	xn	NUM
ejpam-6593	180	14	)	)	PUNCT
ejpam-6593	180	15	=	=	SYM
ejpam-6593	180	16	z(0,xn	z(0,xn	PROPN
ejpam-6593	180	17	)	)	PUNCT
ejpam-6593	181	1	+	+	CCONJ
ejpam-6593	181	2	5	5	NUM
ejpam-6593	181	3	m	m	NOUN
ejpam-6593	181	4	,	,	PUNCT
ejpam-6593	181	5	(	(	PUNCT
ejpam-6593	181	6	8d	8d	NOUN
ejpam-6593	181	7	)	)	PUNCT
ejpam-6593	181	8	where	where	SCONJ
ejpam-6593	181	9	n	n	X
ejpam-6593	181	10	∈	∈	PROPN
ejpam-6593	181	11	n0	n0	PROPN
ejpam-6593	181	12	and	and	CCONJ
ejpam-6593	181	13	m	m	PROPN
ejpam-6593	181	14	∈	∈	PROPN
ejpam-6593	181	15	n.	n.	NOUN
ejpam-6593	181	16	the	the	DET
ejpam-6593	181	17	five	five	NUM
ejpam-6593	181	18	-	-	PUNCT
ejpam-6593	181	19	tuple	tuple	NOUN
ejpam-6593	181	20	(	(	PUNCT
ejpam-6593	181	21	p	p	X
ejpam-6593	181	22	,	,	PUNCT
ejpam-6593	181	23	k	k	NOUN
ejpam-6593	181	24	,	,	PUNCT
ejpam-6593	181	25	x	x	X
ejpam-6593	181	26	,	,	PUNCT
ejpam-6593	181	27	y	y	PROPN
ejpam-6593	181	28	,	,	PUNCT
ejpam-6593	181	29	z	z	NOUN
ejpam-6593	181	30	)	)	PUNCT
ejpam-6593	181	31	=	=	SYM
ejpam-6593	181	32	(	(	PUNCT
ejpam-6593	181	33	2	2	NUM
ejpam-6593	181	34	,	,	PUNCT
ejpam-6593	181	35	k(m	k(m	PROPN
ejpam-6593	181	36	,	,	PUNCT
ejpam-6593	181	37	xn	xn	PROPN
ejpam-6593	181	38	)	)	PUNCT
ejpam-6593	181	39	,	,	PUNCT
ejpam-6593	181	40	xn	xn	PROPN
ejpam-6593	181	41	,	,	PUNCT
ejpam-6593	181	42	1	1	NUM
ejpam-6593	181	43	,	,	PUNCT
ejpam-6593	181	44	z(m	z(m	PROPN
ejpam-6593	181	45	,	,	PUNCT
ejpam-6593	181	46	xn	xn	NUM
ejpam-6593	181	47	)	)	PUNCT
ejpam-6593	181	48	)	)	PUNCT
ejpam-6593	181	49	is	be	AUX
ejpam-6593	181	50	a	a	DET
ejpam-6593	181	51	solution	solution	NOUN
ejpam-6593	181	52	of	of	ADP
ejpam-6593	181	53	(	(	PUNCT
ejpam-6593	181	54	3	3	NUM
ejpam-6593	181	55	)	)	PUNCT
ejpam-6593	181	56	.	.	PUNCT
ejpam-6593	182	1	as	as	ADP
ejpam-6593	182	2	an	an	DET
ejpam-6593	182	3	example	example	NOUN
ejpam-6593	182	4	,	,	PUNCT
ejpam-6593	182	5	we	we	PRON
ejpam-6593	182	6	use	use	VERB
ejpam-6593	182	7	our	our	PRON
ejpam-6593	182	8	equations	equation	NOUN
ejpam-6593	182	9	when	when	SCONJ
ejpam-6593	182	10	x	x	X
ejpam-6593	182	11	=	=	PUNCT
ejpam-6593	182	12	xn	xn	PUNCT
ejpam-6593	182	13	=	=	SYM
ejpam-6593	182	14	2	2	NUM
ejpam-6593	182	15	+	+	CCONJ
ejpam-6593	182	16	4n	4n	NOUN
ejpam-6593	182	17	and	and	CCONJ
ejpam-6593	182	18	z	z	PROPN
ejpam-6593	182	19	≡	≡	PROPN
ejpam-6593	182	20	1	1	NUM
ejpam-6593	182	21	(	(	PUNCT
ejpam-6593	182	22	mod	mod	NOUN
ejpam-6593	182	23	4	4	NUM
ejpam-6593	182	24	)	)	PUNCT
ejpam-6593	182	25	.	.	PUNCT
ejpam-6593	183	1	if	if	SCONJ
ejpam-6593	183	2	n	n	NOUN
ejpam-6593	183	3	=	=	SYM
ejpam-6593	183	4	0	0	NUM
ejpam-6593	183	5	,	,	PUNCT
ejpam-6593	183	6	we	we	PRON
ejpam-6593	183	7	have	have	VERB
ejpam-6593	183	8	x	x	X
ejpam-6593	183	9	=	=	SYM
ejpam-6593	183	10	2	2	NUM
ejpam-6593	183	11	,	,	PUNCT
ejpam-6593	183	12	z(0,2	z(0,2	NOUN
ejpam-6593	183	13	)	)	PUNCT
ejpam-6593	183	14	=	=	SYM
ejpam-6593	183	15	6	6	NUM
ejpam-6593	183	16	,	,	PUNCT
ejpam-6593	183	17	and	and	CCONJ
ejpam-6593	183	18	z(1,2	z(1,2	NUM
ejpam-6593	183	19	)	)	PUNCT
ejpam-6593	183	20	=	=	SYM
ejpam-6593	183	21	11	11	NUM
ejpam-6593	183	22	from	from	ADP
ejpam-6593	183	23	(	(	PUNCT
ejpam-6593	183	24	8a	8a	NUM
ejpam-6593	183	25	)	)	PUNCT
ejpam-6593	183	26	,	,	PUNCT
ejpam-6593	183	27	(	(	PUNCT
ejpam-6593	183	28	8b	8b	NUM
ejpam-6593	183	29	)	)	PUNCT
ejpam-6593	183	30	,	,	PUNCT
ejpam-6593	183	31	and	and	CCONJ
ejpam-6593	183	32	(	(	PUNCT
ejpam-6593	183	33	8d	8d	NUM
ejpam-6593	183	34	)	)	PUNCT
ejpam-6593	183	35	,	,	PUNCT
ejpam-6593	183	36	respectively	respectively	ADV
ejpam-6593	183	37	.	.	PUNCT
ejpam-6593	184	1	from	from	ADP
ejpam-6593	184	2	(	(	PUNCT
ejpam-6593	184	3	6a	6a	NOUN
ejpam-6593	184	4	)	)	PUNCT
ejpam-6593	184	5	and	and	CCONJ
ejpam-6593	184	6	(	(	PUNCT
ejpam-6593	184	7	6b	6b	NOUN
ejpam-6593	184	8	)	)	PUNCT
ejpam-6593	184	9	,	,	PUNCT
ejpam-6593	184	10	we	we	PRON
ejpam-6593	184	11	have	have	VERB
ejpam-6593	184	12	that	that	DET
ejpam-6593	184	13	k(0,2	k(0,2	NOUN
ejpam-6593	184	14	)	)	PUNCT
ejpam-6593	184	15	=	=	SYM
ejpam-6593	184	16	6	6	NUM
ejpam-6593	184	17	and	and	CCONJ
ejpam-6593	184	18	k(1,2	k(1,2	NOUN
ejpam-6593	184	19	)	)	PUNCT
ejpam-6593	184	20	=	=	SYM
ejpam-6593	184	21	23	23	NUM
ejpam-6593	184	22	.	.	PUNCT
ejpam-6593	185	1	thus	thus	ADV
ejpam-6593	185	2	,	,	PUNCT
ejpam-6593	185	3	the	the	DET
ejpam-6593	185	4	first	first	ADJ
ejpam-6593	185	5	two	two	NUM
ejpam-6593	185	6	solutions	solution	NOUN
ejpam-6593	185	7	when	when	SCONJ
ejpam-6593	185	8	x	x	PROPN
ejpam-6593	185	9	=	=	SYM
ejpam-6593	185	10	2	2	NUM
ejpam-6593	185	11	and	and	CCONJ
ejpam-6593	185	12	z	z	PROPN
ejpam-6593	185	13	≡	≡	PROPN
ejpam-6593	185	14	1	1	NUM
ejpam-6593	185	15	(	(	PUNCT
ejpam-6593	185	16	mod	mod	NOUN
ejpam-6593	185	17	5	5	NUM
ejpam-6593	185	18	)	)	PUNCT
ejpam-6593	185	19	are	be	AUX
ejpam-6593	185	20	(	(	PUNCT
ejpam-6593	185	21	p	p	X
ejpam-6593	185	22	,	,	PUNCT
ejpam-6593	185	23	k	k	NOUN
ejpam-6593	185	24	,	,	PUNCT
ejpam-6593	185	25	x	x	X
ejpam-6593	185	26	,	,	PUNCT
ejpam-6593	185	27	y	y	PROPN
ejpam-6593	185	28	,	,	PUNCT
ejpam-6593	185	29	z	z	NOUN
ejpam-6593	185	30	)	)	PUNCT
ejpam-6593	185	31	=	=	SYM
ejpam-6593	185	32	(	(	PUNCT
ejpam-6593	185	33	2	2	NUM
ejpam-6593	185	34	,	,	PUNCT
ejpam-6593	185	35	6	6	NUM
ejpam-6593	185	36	,	,	PUNCT
ejpam-6593	185	37	2	2	NUM
ejpam-6593	185	38	,	,	PUNCT
ejpam-6593	185	39	1	1	NUM
ejpam-6593	185	40	,	,	PUNCT
ejpam-6593	185	41	6	6	NUM
ejpam-6593	185	42	)	)	PUNCT
ejpam-6593	185	43	and	and	CCONJ
ejpam-6593	185	44	(	(	PUNCT
ejpam-6593	185	45	2	2	NUM
ejpam-6593	185	46	,	,	PUNCT
ejpam-6593	185	47	23	23	NUM
ejpam-6593	185	48	,	,	PUNCT
ejpam-6593	185	49	2	2	NUM
ejpam-6593	185	50	,	,	PUNCT
ejpam-6593	185	51	1	1	NUM
ejpam-6593	185	52	,	,	PUNCT
ejpam-6593	185	53	11	11	NUM
ejpam-6593	185	54	)	)	PUNCT
ejpam-6593	185	55	.	.	PUNCT
ejpam-6593	186	1	when	when	SCONJ
ejpam-6593	186	2	z	z	PROPN
ejpam-6593	186	3	≡	≡	PROPN
ejpam-6593	186	4	4	4	NUM
ejpam-6593	186	5	(	(	PUNCT
ejpam-6593	186	6	mod	mod	NOUN
ejpam-6593	186	7	5	5	NUM
ejpam-6593	186	8	)	)	PUNCT
ejpam-6593	186	9	,	,	PUNCT
ejpam-6593	186	10	we	we	PRON
ejpam-6593	186	11	have	have	VERB
ejpam-6593	186	12	x	x	X
ejpam-6593	186	13	=	=	SYM
ejpam-6593	186	14	2	2	NUM
ejpam-6593	186	15	,	,	PUNCT
ejpam-6593	186	16	z(0,2	z(0,2	NOUN
ejpam-6593	186	17	)	)	PUNCT
ejpam-6593	186	18	=	=	SYM
ejpam-6593	186	19	4	4	NUM
ejpam-6593	186	20	,	,	PUNCT
ejpam-6593	186	21	and	and	CCONJ
ejpam-6593	186	22	z(1,2	z(1,2	NUM
ejpam-6593	186	23	)	)	PUNCT
ejpam-6593	186	24	=	=	SYM
ejpam-6593	187	1	9	9	NUM
ejpam-6593	187	2	from	from	ADP
ejpam-6593	187	3	(	(	PUNCT
ejpam-6593	187	4	8a	8a	NUM
ejpam-6593	187	5	)	)	PUNCT
ejpam-6593	187	6	,	,	PUNCT
ejpam-6593	187	7	(	(	PUNCT
ejpam-6593	187	8	8c	8c	NUM
ejpam-6593	187	9	)	)	PUNCT
ejpam-6593	187	10	,	,	PUNCT
ejpam-6593	187	11	and	and	CCONJ
ejpam-6593	187	12	(	(	PUNCT
ejpam-6593	187	13	8d	8d	NUM
ejpam-6593	187	14	)	)	PUNCT
ejpam-6593	187	15	,	,	PUNCT
ejpam-6593	187	16	respectively	respectively	ADV
ejpam-6593	187	17	,	,	PUNCT
ejpam-6593	187	18	for	for	ADP
ejpam-6593	187	19	n	n	NOUN
ejpam-6593	187	20	=	=	SYM
ejpam-6593	187	21	0	0	NUM
ejpam-6593	187	22	.	.	PUNCT
ejpam-6593	188	1	we	we	PRON
ejpam-6593	188	2	also	also	ADV
ejpam-6593	188	3	have	have	VERB
ejpam-6593	188	4	k(0,2	k(0,2	NOUN
ejpam-6593	188	5	)	)	PUNCT
ejpam-6593	188	6	=	=	SYM
ejpam-6593	188	7	2	2	NUM
ejpam-6593	188	8	and	and	CCONJ
ejpam-6593	188	9	k(1,2	k(1,2	NOUN
ejpam-6593	188	10	)	)	PUNCT
ejpam-6593	188	11	=	=	SYM
ejpam-6593	188	12	15	15	NUM
ejpam-6593	188	13	from	from	ADP
ejpam-6593	188	14	(	(	PUNCT
ejpam-6593	188	15	6a	6a	NOUN
ejpam-6593	188	16	)	)	PUNCT
ejpam-6593	188	17	and	and	CCONJ
ejpam-6593	188	18	(	(	PUNCT
ejpam-6593	188	19	6b	6b	NOUN
ejpam-6593	188	20	)	)	PUNCT
ejpam-6593	188	21	.	.	PUNCT
ejpam-6593	189	1	thus	thus	ADV
ejpam-6593	189	2	,	,	PUNCT
ejpam-6593	189	3	the	the	DET
ejpam-6593	189	4	first	first	ADJ
ejpam-6593	189	5	two	two	NUM
ejpam-6593	189	6	solutions	solution	NOUN
ejpam-6593	189	7	when	when	SCONJ
ejpam-6593	189	8	x	x	PROPN
ejpam-6593	189	9	=	=	SYM
ejpam-6593	189	10	2	2	NUM
ejpam-6593	189	11	and	and	CCONJ
ejpam-6593	189	12	z	z	PROPN
ejpam-6593	189	13	≡	≡	PROPN
ejpam-6593	189	14	4	4	NUM
ejpam-6593	189	15	(	(	PUNCT
ejpam-6593	189	16	mod	mod	NOUN
ejpam-6593	189	17	5	5	NUM
ejpam-6593	189	18	)	)	PUNCT
ejpam-6593	189	19	are	be	AUX
ejpam-6593	189	20	(	(	PUNCT
ejpam-6593	189	21	p	p	X
ejpam-6593	189	22	,	,	PUNCT
ejpam-6593	189	23	k	k	NOUN
ejpam-6593	189	24	,	,	PUNCT
ejpam-6593	189	25	x	x	X
ejpam-6593	189	26	,	,	PUNCT
ejpam-6593	189	27	y	y	PROPN
ejpam-6593	189	28	,	,	PUNCT
ejpam-6593	189	29	z	z	NOUN
ejpam-6593	189	30	)	)	PUNCT
ejpam-6593	189	31	=	=	SYM
ejpam-6593	189	32	(	(	PUNCT
ejpam-6593	189	33	2	2	NUM
ejpam-6593	189	34	,	,	PUNCT
ejpam-6593	189	35	2	2	NUM
ejpam-6593	189	36	,	,	PUNCT
ejpam-6593	189	37	2	2	NUM
ejpam-6593	189	38	,	,	PUNCT
ejpam-6593	189	39	1	1	NUM
ejpam-6593	189	40	,	,	PUNCT
ejpam-6593	189	41	4	4	NUM
ejpam-6593	189	42	)	)	PUNCT
ejpam-6593	189	43	and	and	CCONJ
ejpam-6593	189	44	(	(	PUNCT
ejpam-6593	189	45	2	2	NUM
ejpam-6593	189	46	,	,	PUNCT
ejpam-6593	189	47	15	15	NUM
ejpam-6593	189	48	,	,	PUNCT
ejpam-6593	189	49	2	2	NUM
ejpam-6593	189	50	,	,	PUNCT
ejpam-6593	189	51	1	1	NUM
ejpam-6593	189	52	,	,	PUNCT
ejpam-6593	189	53	9	9	NUM
ejpam-6593	189	54	)	)	PUNCT
ejpam-6593	189	55	.	.	PUNCT
ejpam-6593	190	1	lemma	lemma	PROPN
ejpam-6593	190	2	3	3	X
ejpam-6593	190	3	.	.	PUNCT
ejpam-6593	190	4	suppose	suppose	VERB
ejpam-6593	190	5	the	the	DET
ejpam-6593	190	6	exponential	exponential	ADJ
ejpam-6593	190	7	diophantine	diophantine	NOUN
ejpam-6593	190	8	equation	equation	NOUN
ejpam-6593	190	9	(	(	PUNCT
ejpam-6593	190	10	5	5	NUM
ejpam-6593	190	11	)	)	PUNCT
ejpam-6593	190	12	has	have	VERB
ejpam-6593	190	13	a	a	DET
ejpam-6593	190	14	solution	solution	NOUN
ejpam-6593	190	15	.	.	PUNCT
ejpam-6593	191	1	then	then	ADV
ejpam-6593	191	2	,	,	PUNCT
ejpam-6593	191	3	x	x	PROPN
ejpam-6593	191	4	≡	≡	PROPN
ejpam-6593	191	5	3	3	NUM
ejpam-6593	191	6	(	(	PUNCT
ejpam-6593	191	7	mod	mod	NOUN
ejpam-6593	191	8	4	4	X
ejpam-6593	191	9	)	)	PUNCT
ejpam-6593	191	10	if	if	SCONJ
ejpam-6593	191	11	and	and	CCONJ
ejpam-6593	191	12	only	only	ADV
ejpam-6593	191	13	if	if	SCONJ
ejpam-6593	191	14	z	z	PROPN
ejpam-6593	191	15	≡	≡	PROPN
ejpam-6593	191	16	0	0	PUNCT
ejpam-6593	191	17	(	(	PUNCT
ejpam-6593	191	18	mod	mod	PROPN
ejpam-6593	191	19	5	5	NUM
ejpam-6593	191	20	)	)	PUNCT
ejpam-6593	191	21	.	.	PUNCT
ejpam-6593	192	1	the	the	DET
ejpam-6593	192	2	proof	proof	NOUN
ejpam-6593	192	3	is	be	AUX
ejpam-6593	192	4	omitted	omit	VERB
ejpam-6593	192	5	as	as	SCONJ
ejpam-6593	192	6	it	it	PRON
ejpam-6593	192	7	follows	follow	VERB
ejpam-6593	192	8	the	the	DET
ejpam-6593	192	9	same	same	ADJ
ejpam-6593	192	10	reasoning	reasoning	NOUN
ejpam-6593	192	11	as	as	ADP
ejpam-6593	192	12	in	in	ADP
ejpam-6593	192	13	the	the	DET
ejpam-6593	192	14	proof	proof	NOUN
ejpam-6593	192	15	of	of	ADP
ejpam-6593	192	16	lemma	lemma	PROPN
ejpam-6593	192	17	1	1	NUM
ejpam-6593	192	18	.	.	NOUN
ejpam-6593	192	19	similar	similar	ADJ
ejpam-6593	192	20	to	to	ADP
ejpam-6593	192	21	the	the	DET
ejpam-6593	192	22	case	case	NOUN
ejpam-6593	192	23	when	when	SCONJ
ejpam-6593	192	24	x	x	PRON
ejpam-6593	192	25	≡	≡	PROPN
ejpam-6593	192	26	1	1	NUM
ejpam-6593	192	27	(	(	PUNCT
ejpam-6593	192	28	mod	mod	NOUN
ejpam-6593	192	29	4	4	NUM
ejpam-6593	192	30	)	)	PUNCT
ejpam-6593	192	31	,	,	PUNCT
ejpam-6593	192	32	we	we	PRON
ejpam-6593	192	33	use	use	VERB
ejpam-6593	192	34	⌊√	⌊√	PROPN
ejpam-6593	192	35	2x	2x	NUM
ejpam-6593	192	36	⌋	⌋	NOUN
ejpam-6593	192	37	because	because	SCONJ
ejpam-6593	192	38	√	√	ADJ
ejpam-6593	192	39	2x	2x	NUM
ejpam-6593	192	40	will	will	AUX
ejpam-6593	192	41	never	never	ADV
ejpam-6593	192	42	be	be	AUX
ejpam-6593	192	43	an	an	DET
ejpam-6593	192	44	integer	integer	NOUN
ejpam-6593	192	45	since	since	SCONJ
ejpam-6593	192	46	x	x	PROPN
ejpam-6593	192	47	≡	≡	PROPN
ejpam-6593	192	48	3	3	NUM
ejpam-6593	192	49	(	(	PUNCT
ejpam-6593	192	50	mod	mod	NOUN
ejpam-6593	192	51	4	4	NUM
ejpam-6593	192	52	)	)	PUNCT
ejpam-6593	192	53	.	.	PUNCT
ejpam-6593	193	1	thus	thus	ADV
ejpam-6593	193	2	,	,	PUNCT
ejpam-6593	193	3	we	we	PRON
ejpam-6593	193	4	will	will	AUX
ejpam-6593	193	5	have	have	VERB
ejpam-6593	193	6	the	the	DET
ejpam-6593	193	7	smallest	small	ADJ
ejpam-6593	193	8	number	number	NOUN
ejpam-6593	193	9	of	of	ADP
ejpam-6593	193	10	possible	possible	ADJ
ejpam-6593	193	11	condition	condition	NOUN
ejpam-6593	193	12	for	for	ADP
ejpam-6593	193	13	z(0,xn	z(0,xn	PROPN
ejpam-6593	193	14	)	)	PUNCT
ejpam-6593	193	15	.	.	PUNCT
ejpam-6593	194	1	hence	hence	ADV
ejpam-6593	194	2	,	,	PUNCT
ejpam-6593	194	3	we	we	PRON
ejpam-6593	194	4	have	have	VERB
ejpam-6593	194	5	these	these	DET
ejpam-6593	194	6	formulas	formula	NOUN
ejpam-6593	194	7	:	:	PUNCT
ejpam-6593	194	8	x	x	SYM
ejpam-6593	194	9	=	=	PUNCT
ejpam-6593	194	10	xn	xn	PUNCT
ejpam-6593	194	11	=	=	SYM
ejpam-6593	194	12	3	3	NUM
ejpam-6593	194	13	+	+	CCONJ
ejpam-6593	194	14	4n	4n	NOUN
ejpam-6593	194	15	,	,	PUNCT
ejpam-6593	194	16	(	(	PUNCT
ejpam-6593	194	17	9a	9a	NOUN
ejpam-6593	194	18	)	)	PUNCT
ejpam-6593	194	19	z(0,xn	z(0,xn	PROPN
ejpam-6593	194	20	)	)	PUNCT
ejpam-6593	195	1	=	=	SYM
ejpam-6593	195	2			NUM
ejpam-6593	196	1	⌊√	⌊√	PROPN
ejpam-6593	196	2	2xn	2xn	ADJ
ejpam-6593	196	3	⌋	⌋	NOUN
ejpam-6593	197	1	+	+	CCONJ
ejpam-6593	197	2	4	4	NUM
ejpam-6593	197	3	if	if	SCONJ
ejpam-6593	197	4	⌊√	⌊√	PROPN
ejpam-6593	197	5	2xn	2xn	ADJ
ejpam-6593	197	6	⌋	⌋	NOUN
ejpam-6593	197	7	≡	≡	PROPN
ejpam-6593	197	8	1	1	NUM
ejpam-6593	197	9	(	(	PUNCT
ejpam-6593	197	10	mod	mod	NOUN
ejpam-6593	197	11	5),⌊√	5),⌊√	NUM
ejpam-6593	197	12	2xn	2xn	ADJ
ejpam-6593	197	13	⌋	⌋	NOUN
ejpam-6593	198	1	+	+	CCONJ
ejpam-6593	198	2	3	3	NUM
ejpam-6593	198	3	if	if	SCONJ
ejpam-6593	198	4	⌊√	⌊√	PROPN
ejpam-6593	198	5	2xn	2xn	ADJ
ejpam-6593	198	6	⌋	⌋	NOUN
ejpam-6593	198	7	≡	≡	PROPN
ejpam-6593	198	8	2	2	NUM
ejpam-6593	198	9	(	(	PUNCT
ejpam-6593	198	10	mod	mod	NOUN
ejpam-6593	198	11	5),⌊√	5),⌊√	NUM
ejpam-6593	198	12	2xn	2xn	ADJ
ejpam-6593	198	13	⌋	⌋	NOUN
ejpam-6593	199	1	+	+	CCONJ
ejpam-6593	199	2	2	2	NUM
ejpam-6593	199	3	if	if	SCONJ
ejpam-6593	199	4	⌊√	⌊√	PROPN
ejpam-6593	199	5	2xn	2xn	ADJ
ejpam-6593	199	6	⌋	⌋	NOUN
ejpam-6593	199	7	≡	≡	PROPN
ejpam-6593	199	8	3	3	NUM
ejpam-6593	199	9	(	(	PUNCT
ejpam-6593	199	10	mod	mod	PROPN
ejpam-6593	199	11	5),⌊√	5),⌊√	NUM
ejpam-6593	199	12	2xn	2xn	ADJ
ejpam-6593	199	13	⌋	⌋	NOUN
ejpam-6593	200	1	+	+	CCONJ
ejpam-6593	200	2	1	1	NUM
ejpam-6593	200	3	if	if	SCONJ
ejpam-6593	200	4	⌊√	⌊√	PROPN
ejpam-6593	200	5	2xn	2xn	ADJ
ejpam-6593	200	6	⌋	⌋	NOUN
ejpam-6593	200	7	≡	≡	PROPN
ejpam-6593	200	8	4	4	NUM
ejpam-6593	200	9	(	(	PUNCT
ejpam-6593	200	10	mod	mod	NOUN
ejpam-6593	200	11	5),⌊√	5),⌊√	NUM
ejpam-6593	200	12	2xn	2xn	ADJ
ejpam-6593	200	13	⌋	⌋	NOUN
ejpam-6593	200	14	+	+	CCONJ
ejpam-6593	200	15	5	5	NUM
ejpam-6593	200	16	if	if	SCONJ
ejpam-6593	200	17	⌊√	⌊√	PROPN
ejpam-6593	200	18	2xn	2xn	ADJ
ejpam-6593	200	19	⌋	⌋	NOUN
ejpam-6593	200	20	≡	≡	PROPN
ejpam-6593	200	21	0	0	PUNCT
ejpam-6593	201	1	(	(	PUNCT
ejpam-6593	201	2	mod	mod	PROPN
ejpam-6593	201	3	5	5	NUM
ejpam-6593	201	4	)	)	PUNCT
ejpam-6593	201	5	,	,	PUNCT
ejpam-6593	201	6	(	(	PUNCT
ejpam-6593	201	7	9b	9b	NOUN
ejpam-6593	201	8	)	)	PUNCT
ejpam-6593	201	9	z(m	z(m	PROPN
ejpam-6593	201	10	,	,	PUNCT
ejpam-6593	201	11	xn	xn	NUM
ejpam-6593	201	12	)	)	PUNCT
ejpam-6593	201	13	=	=	SYM
ejpam-6593	201	14	z(0,xn	z(0,xn	PROPN
ejpam-6593	201	15	)	)	PUNCT
ejpam-6593	202	1	+	+	CCONJ
ejpam-6593	202	2	5	5	NUM
ejpam-6593	202	3	m	m	NOUN
ejpam-6593	202	4	,	,	PUNCT
ejpam-6593	202	5	(	(	PUNCT
ejpam-6593	202	6	9c	9c	NOUN
ejpam-6593	202	7	)	)	PUNCT
ejpam-6593	202	8	where	where	SCONJ
ejpam-6593	202	9	n	n	X
ejpam-6593	202	10	∈	∈	PROPN
ejpam-6593	202	11	n0	n0	PROPN
ejpam-6593	202	12	and	and	CCONJ
ejpam-6593	202	13	m	m	PROPN
ejpam-6593	202	14	∈	∈	PROPN
ejpam-6593	202	15	n.	n.	NOUN
ejpam-6593	202	16	the	the	DET
ejpam-6593	202	17	five	five	NUM
ejpam-6593	202	18	-	-	PUNCT
ejpam-6593	202	19	tuple	tuple	NOUN
ejpam-6593	202	20	(	(	PUNCT
ejpam-6593	202	21	p	p	X
ejpam-6593	202	22	,	,	PUNCT
ejpam-6593	202	23	k	k	NOUN
ejpam-6593	202	24	,	,	PUNCT
ejpam-6593	202	25	x	x	X
ejpam-6593	202	26	,	,	PUNCT
ejpam-6593	202	27	y	y	PROPN
ejpam-6593	202	28	,	,	PUNCT
ejpam-6593	202	29	z	z	NOUN
ejpam-6593	202	30	)	)	PUNCT
ejpam-6593	202	31	=	=	SYM
ejpam-6593	202	32	(	(	PUNCT
ejpam-6593	202	33	2	2	NUM
ejpam-6593	202	34	,	,	PUNCT
ejpam-6593	202	35	k(m	k(m	PROPN
ejpam-6593	202	36	,	,	PUNCT
ejpam-6593	202	37	xn	xn	PROPN
ejpam-6593	202	38	)	)	PUNCT
ejpam-6593	202	39	,	,	PUNCT
ejpam-6593	202	40	xn	xn	PROPN
ejpam-6593	202	41	,	,	PUNCT
ejpam-6593	202	42	1	1	NUM
ejpam-6593	202	43	,	,	PUNCT
ejpam-6593	202	44	z(m	z(m	PROPN
ejpam-6593	202	45	,	,	PUNCT
ejpam-6593	202	46	xn	xn	NUM
ejpam-6593	202	47	)	)	PUNCT
ejpam-6593	202	48	)	)	PUNCT
ejpam-6593	202	49	is	be	AUX
ejpam-6593	202	50	a	a	DET
ejpam-6593	202	51	solution	solution	NOUN
ejpam-6593	202	52	of	of	ADP
ejpam-6593	202	53	(	(	PUNCT
ejpam-6593	202	54	5	5	NUM
ejpam-6593	202	55	)	)	PUNCT
ejpam-6593	202	56	.	.	PUNCT
ejpam-6593	203	1	as	as	ADP
ejpam-6593	203	2	an	an	DET
ejpam-6593	203	3	example	example	NOUN
ejpam-6593	203	4	,	,	PUNCT
ejpam-6593	203	5	if	if	SCONJ
ejpam-6593	203	6	n	n	ADV
ejpam-6593	203	7	=	=	SYM
ejpam-6593	203	8	0	0	NUM
ejpam-6593	203	9	in	in	ADP
ejpam-6593	203	10	x	x	X
ejpam-6593	203	11	=	=	PUNCT
ejpam-6593	203	12	xn	xn	PUNCT
ejpam-6593	203	13	=	=	SYM
ejpam-6593	203	14	3	3	NUM
ejpam-6593	203	15	+	+	CCONJ
ejpam-6593	203	16	4n	4n	NOUN
ejpam-6593	203	17	,	,	PUNCT
ejpam-6593	203	18	we	we	PRON
ejpam-6593	203	19	have	have	VERB
ejpam-6593	203	20	x	x	NOUN
ejpam-6593	203	21	=	=	SYM
ejpam-6593	203	22	3	3	NUM
ejpam-6593	203	23	,	,	PUNCT
ejpam-6593	203	24	z(0,3	z(0,3	NUM
ejpam-6593	203	25	)	)	PUNCT
ejpam-6593	203	26	=	=	SYM
ejpam-6593	203	27	5	5	NUM
ejpam-6593	203	28	,	,	PUNCT
ejpam-6593	203	29	and	and	CCONJ
ejpam-6593	203	30	z(1,3	z(1,3	NOUN
ejpam-6593	203	31	)	)	PUNCT
ejpam-6593	203	32	=	=	SYM
ejpam-6593	204	1	10	10	NUM
ejpam-6593	204	2	from	from	ADP
ejpam-6593	204	3	(	(	PUNCT
ejpam-6593	204	4	9a	9a	NOUN
ejpam-6593	204	5	)	)	PUNCT
ejpam-6593	204	6	,	,	PUNCT
ejpam-6593	204	7	(	(	PUNCT
ejpam-6593	204	8	9b	9b	NOUN
ejpam-6593	204	9	)	)	PUNCT
ejpam-6593	204	10	,	,	PUNCT
ejpam-6593	204	11	and	and	CCONJ
ejpam-6593	204	12	(	(	PUNCT
ejpam-6593	204	13	9c	9c	NUM
ejpam-6593	204	14	)	)	PUNCT
ejpam-6593	204	15	,	,	PUNCT
ejpam-6593	204	16	respectively	respectively	ADV
ejpam-6593	204	17	.	.	PUNCT
ejpam-6593	205	1	from	from	ADP
ejpam-6593	205	2	(	(	PUNCT
ejpam-6593	205	3	6a	6a	NOUN
ejpam-6593	205	4	)	)	PUNCT
ejpam-6593	205	5	and	and	CCONJ
ejpam-6593	205	6	(	(	PUNCT
ejpam-6593	205	7	6b	6b	NOUN
ejpam-6593	205	8	)	)	PUNCT
ejpam-6593	205	9	,	,	PUNCT
ejpam-6593	205	10	we	we	PRON
ejpam-6593	205	11	have	have	VERB
ejpam-6593	205	12	that	that	DET
ejpam-6593	205	13	m.	m.	NOUN
ejpam-6593	205	14	c.	c.	PROPN
ejpam-6593	205	15	avenilla	avenilla	PROPN
ejpam-6593	205	16	,	,	PUNCT
ejpam-6593	205	17	j.	j.	PROPN
ejpam-6593	205	18	b.	b.	PROPN
ejpam-6593	205	19	bacani	bacani	PROPN
ejpam-6593	205	20	/	/	SYM
ejpam-6593	205	21	eur	eur	PROPN
ejpam-6593	205	22	.	.	PUNCT
ejpam-6593	206	1	j.	j.	PROPN
ejpam-6593	206	2	pure	pure	PROPN
ejpam-6593	206	3	appl	appl	PROPN
ejpam-6593	206	4	.	.	PROPN
ejpam-6593	206	5	math	math	PROPN
ejpam-6593	206	6	,	,	PUNCT
ejpam-6593	206	7	18	18	NUM
ejpam-6593	206	8	(	(	PUNCT
ejpam-6593	206	9	3	3	NUM
ejpam-6593	206	10	)	)	PUNCT
ejpam-6593	206	11	(	(	PUNCT
ejpam-6593	206	12	2025	2025	NUM
ejpam-6593	206	13	)	)	PUNCT
ejpam-6593	206	14	,	,	PUNCT
ejpam-6593	206	15	6593	6593	NUM
ejpam-6593	206	16	7	7	NUM
ejpam-6593	206	17	of	of	ADP
ejpam-6593	206	18	24	24	NUM
ejpam-6593	206	19	k(0,3	k(0,3	NOUN
ejpam-6593	206	20	)	)	PUNCT
ejpam-6593	206	21	=	=	SYM
ejpam-6593	206	22	3	3	NUM
ejpam-6593	206	23	and	and	CCONJ
ejpam-6593	206	24	k(1,3	k(1,3	PROPN
ejpam-6593	206	25	)	)	PUNCT
ejpam-6593	206	26	=	=	SYM
ejpam-6593	206	27	18	18	NUM
ejpam-6593	206	28	.	.	PUNCT
ejpam-6593	207	1	thus	thus	ADV
ejpam-6593	207	2	,	,	PUNCT
ejpam-6593	207	3	the	the	DET
ejpam-6593	207	4	first	first	ADJ
ejpam-6593	207	5	two	two	NUM
ejpam-6593	207	6	solutions	solution	NOUN
ejpam-6593	207	7	when	when	SCONJ
ejpam-6593	207	8	x	x	PROPN
ejpam-6593	207	9	=	=	SYM
ejpam-6593	207	10	3	3	NUM
ejpam-6593	207	11	and	and	CCONJ
ejpam-6593	207	12	z	z	PROPN
ejpam-6593	207	13	≡	≡	PROPN
ejpam-6593	207	14	0	0	PUNCT
ejpam-6593	208	1	(	(	PUNCT
ejpam-6593	208	2	mod	mod	NOUN
ejpam-6593	208	3	5	5	NUM
ejpam-6593	208	4	)	)	PUNCT
ejpam-6593	208	5	are	be	AUX
ejpam-6593	208	6	(	(	PUNCT
ejpam-6593	208	7	p	p	X
ejpam-6593	208	8	,	,	PUNCT
ejpam-6593	208	9	k	k	NOUN
ejpam-6593	208	10	,	,	PUNCT
ejpam-6593	208	11	x	x	X
ejpam-6593	208	12	,	,	PUNCT
ejpam-6593	208	13	y	y	PROPN
ejpam-6593	208	14	,	,	PUNCT
ejpam-6593	208	15	z	z	NOUN
ejpam-6593	208	16	)	)	PUNCT
ejpam-6593	208	17	=	=	SYM
ejpam-6593	208	18	(	(	PUNCT
ejpam-6593	208	19	2	2	NUM
ejpam-6593	208	20	,	,	PUNCT
ejpam-6593	208	21	3	3	NUM
ejpam-6593	208	22	,	,	PUNCT
ejpam-6593	208	23	3	3	NUM
ejpam-6593	208	24	,	,	PUNCT
ejpam-6593	208	25	1	1	NUM
ejpam-6593	208	26	,	,	PUNCT
ejpam-6593	208	27	5	5	NUM
ejpam-6593	208	28	)	)	PUNCT
ejpam-6593	208	29	and	and	CCONJ
ejpam-6593	208	30	(	(	PUNCT
ejpam-6593	208	31	2	2	NUM
ejpam-6593	208	32	,	,	PUNCT
ejpam-6593	208	33	18	18	NUM
ejpam-6593	208	34	,	,	PUNCT
ejpam-6593	208	35	3	3	NUM
ejpam-6593	208	36	,	,	PUNCT
ejpam-6593	208	37	1	1	NUM
ejpam-6593	208	38	,	,	PUNCT
ejpam-6593	208	39	10	10	NUM
ejpam-6593	208	40	)	)	PUNCT
ejpam-6593	208	41	.	.	PUNCT
ejpam-6593	209	1	for	for	ADP
ejpam-6593	209	2	these	these	DET
ejpam-6593	209	3	values	value	NOUN
ejpam-6593	209	4	of	of	ADP
ejpam-6593	209	5	xn	xn	PROPN
ejpam-6593	209	6	,	,	PUNCT
ejpam-6593	209	7	we	we	PRON
ejpam-6593	209	8	provide	provide	VERB
ejpam-6593	209	9	an	an	DET
ejpam-6593	209	10	easier	easy	ADJ
ejpam-6593	209	11	way	way	NOUN
ejpam-6593	209	12	to	to	PART
ejpam-6593	209	13	solve	solve	VERB
ejpam-6593	209	14	for	for	ADP
ejpam-6593	209	15	k(m	k(m	PROPN
ejpam-6593	209	16	,	,	PUNCT
ejpam-6593	209	17	xn	xn	PROPN
ejpam-6593	209	18	)	)	PUNCT
ejpam-6593	209	19	by	by	ADP
ejpam-6593	209	20	using	use	VERB
ejpam-6593	209	21	the	the	DET
ejpam-6593	209	22	next	next	ADJ
ejpam-6593	209	23	theorem	theorem	PROPN
ejpam-6593	209	24	.	.	PUNCT
ejpam-6593	209	25	theorem	theorem	NOUN
ejpam-6593	209	26	1	1	NUM
ejpam-6593	209	27	.	.	PUNCT
ejpam-6593	209	28	suppose	suppose	VERB
ejpam-6593	209	29	the	the	DET
ejpam-6593	209	30	exponential	exponential	ADJ
ejpam-6593	209	31	diophantine	diophantine	NOUN
ejpam-6593	209	32	equation	equation	NOUN
ejpam-6593	209	33	(	(	PUNCT
ejpam-6593	209	34	5	5	NUM
ejpam-6593	209	35	)	)	PUNCT
ejpam-6593	209	36	,	,	PUNCT
ejpam-6593	209	37	where	where	SCONJ
ejpam-6593	209	38	x	x	ADP
ejpam-6593	209	39	=	=	PUNCT
ejpam-6593	209	40	xn	xn	PUNCT
ejpam-6593	209	41	=	=	SYM
ejpam-6593	209	42	1	1	NUM
ejpam-6593	209	43	+	+	CCONJ
ejpam-6593	209	44	4n	4n	NOUN
ejpam-6593	209	45	,	,	PUNCT
ejpam-6593	209	46	x	x	SYM
ejpam-6593	209	47	=	=	PUNCT
ejpam-6593	209	48	xn	xn	PUNCT
ejpam-6593	209	49	=	=	SYM
ejpam-6593	209	50	2	2	NUM
ejpam-6593	209	51	+	+	CCONJ
ejpam-6593	209	52	4n	4n	NOUN
ejpam-6593	209	53	,	,	PUNCT
ejpam-6593	209	54	or	or	CCONJ
ejpam-6593	209	55	x	x	SYM
ejpam-6593	209	56	=	=	SYM
ejpam-6593	209	57	xn	xn	PUNCT
ejpam-6593	209	58	=	=	SYM
ejpam-6593	209	59	3	3	NUM
ejpam-6593	209	60	+	+	CCONJ
ejpam-6593	209	61	4n	4n	NOUN
ejpam-6593	209	62	,	,	PUNCT
ejpam-6593	209	63	for	for	ADP
ejpam-6593	209	64	n	n	DET
ejpam-6593	209	65	∈	∈	PROPN
ejpam-6593	209	66	n0	n0	NOUN
ejpam-6593	209	67	,	,	PUNCT
ejpam-6593	209	68	has	have	VERB
ejpam-6593	209	69	a	a	DET
ejpam-6593	209	70	solution	solution	NOUN
ejpam-6593	209	71	.	.	PUNCT
ejpam-6593	210	1	then	then	ADV
ejpam-6593	210	2	,	,	PUNCT
ejpam-6593	210	3	k(m	k(m	PROPN
ejpam-6593	210	4	,	,	PUNCT
ejpam-6593	210	5	xn	xn	PROPN
ejpam-6593	210	6	)	)	PUNCT
ejpam-6593	210	7	=	=	SYM
ejpam-6593	210	8	k(0,xn	k(0,xn	PROPN
ejpam-6593	210	9	)	)	PUNCT
ejpam-6593	211	1	+	+	CCONJ
ejpam-6593	211	2	m−1∑	m−1∑	PROPN
ejpam-6593	211	3	i=0	i=0	PROPN
ejpam-6593	211	4	(	(	PUNCT
ejpam-6593	211	5	αxn	αxn	PROPN
ejpam-6593	211	6	+	+	SYM
ejpam-6593	211	7	10i	10i	NOUN
ejpam-6593	211	8	)	)	PUNCT
ejpam-6593	211	9	,	,	PUNCT
ejpam-6593	211	10	(	(	PUNCT
ejpam-6593	211	11	10	10	NUM
ejpam-6593	211	12	)	)	PUNCT
ejpam-6593	211	13	where	where	SCONJ
ejpam-6593	211	14	m	m	PROPN
ejpam-6593	211	15	∈	∈	PROPN
ejpam-6593	211	16	n.	n.	NOUN
ejpam-6593	211	17	proof	proof	NOUN
ejpam-6593	211	18	.	.	PUNCT
ejpam-6593	212	1	consider	consider	VERB
ejpam-6593	212	2	the	the	DET
ejpam-6593	212	3	diophantine	diophantine	NOUN
ejpam-6593	212	4	equation	equation	NOUN
ejpam-6593	212	5	2x	2x	NUM
ejpam-6593	212	6	+	+	CCONJ
ejpam-6593	212	7	(	(	PUNCT
ejpam-6593	212	8	2	2	NUM
ejpam-6593	212	9	+	+	NUM
ejpam-6593	212	10	5k	5k	NUM
ejpam-6593	212	11	)	)	PUNCT
ejpam-6593	213	1	=	=	SYM
ejpam-6593	213	2	z2	z2	PROPN
ejpam-6593	213	3	,	,	PUNCT
ejpam-6593	213	4	where	where	SCONJ
ejpam-6593	213	5	x	x	ADP
ejpam-6593	213	6	=	=	PUNCT
ejpam-6593	213	7	xn	xn	PUNCT
ejpam-6593	214	1	=	=	SYM
ejpam-6593	214	2	1	1	NUM
ejpam-6593	214	3	+	+	NUM
ejpam-6593	214	4	4n	4n	NOUN
ejpam-6593	214	5	,	,	PUNCT
ejpam-6593	214	6	x	x	SYM
ejpam-6593	214	7	=	=	PUNCT
ejpam-6593	214	8	xn	xn	PUNCT
ejpam-6593	214	9	=	=	SYM
ejpam-6593	214	10	2	2	NUM
ejpam-6593	214	11	+	+	CCONJ
ejpam-6593	214	12	4n	4n	NOUN
ejpam-6593	214	13	,	,	PUNCT
ejpam-6593	214	14	or	or	CCONJ
ejpam-6593	214	15	x	x	SYM
ejpam-6593	214	16	=	=	SYM
ejpam-6593	214	17	xn	xn	PUNCT
ejpam-6593	214	18	=	=	SYM
ejpam-6593	214	19	3	3	NUM
ejpam-6593	214	20	+	+	CCONJ
ejpam-6593	214	21	4n	4n	NOUN
ejpam-6593	214	22	,	,	PUNCT
ejpam-6593	214	23	for	for	ADP
ejpam-6593	214	24	n	n	DET
ejpam-6593	214	25	∈	∈	PROPN
ejpam-6593	214	26	n0	n0	PROPN
ejpam-6593	214	27	.	.	PUNCT
ejpam-6593	215	1	we	we	PRON
ejpam-6593	215	2	prove	prove	VERB
ejpam-6593	215	3	using	use	VERB
ejpam-6593	215	4	the	the	DET
ejpam-6593	215	5	principle	principle	NOUN
ejpam-6593	215	6	of	of	ADP
ejpam-6593	215	7	mathematical	mathematical	ADJ
ejpam-6593	215	8	induction	induction	NOUN
ejpam-6593	215	9	on	on	ADP
ejpam-6593	215	10	m	m	PROPN
ejpam-6593	215	11	that	that	SCONJ
ejpam-6593	215	12	k(m	k(m	PROPN
ejpam-6593	215	13	,	,	PUNCT
ejpam-6593	215	14	xn	xn	PROPN
ejpam-6593	215	15	)	)	PUNCT
ejpam-6593	215	16	=	=	SYM
ejpam-6593	215	17	k(0,xn	k(0,xn	PROPN
ejpam-6593	215	18	)	)	PUNCT
ejpam-6593	216	1	+	+	CCONJ
ejpam-6593	216	2	m−1∑	m−1∑	PROPN
ejpam-6593	216	3	i=0	i=0	PROPN
ejpam-6593	216	4	(	(	PUNCT
ejpam-6593	216	5	αxn	αxn	PROPN
ejpam-6593	216	6	+	+	SYM
ejpam-6593	216	7	10i	10i	NOUN
ejpam-6593	216	8	)	)	PUNCT
ejpam-6593	216	9	,	,	PUNCT
ejpam-6593	216	10	where	where	SCONJ
ejpam-6593	216	11	m	m	PROPN
ejpam-6593	216	12	∈	∈	PROPN
ejpam-6593	216	13	n.	n.	NOUN
ejpam-6593	216	14	firstly	firstly	ADV
ejpam-6593	216	15	,	,	PUNCT
ejpam-6593	216	16	for	for	ADP
ejpam-6593	216	17	m	m	PROPN
ejpam-6593	216	18	=	=	SYM
ejpam-6593	216	19	1	1	NUM
ejpam-6593	216	20	,	,	PUNCT
ejpam-6593	216	21	and	and	CCONJ
ejpam-6593	216	22	by	by	ADP
ejpam-6593	216	23	using	use	VERB
ejpam-6593	216	24	the	the	DET
ejpam-6593	216	25	definition	definition	NOUN
ejpam-6593	216	26	of	of	ADP
ejpam-6593	216	27	αxn	αxn	PROPN
ejpam-6593	216	28	in	in	ADP
ejpam-6593	216	29	(	(	PUNCT
ejpam-6593	216	30	6c	6c	NOUN
ejpam-6593	216	31	)	)	PUNCT
ejpam-6593	216	32	,	,	PUNCT
ejpam-6593	216	33	we	we	PRON
ejpam-6593	216	34	have	have	VERB
ejpam-6593	216	35	:	:	PUNCT
ejpam-6593	216	36	k(1,xn	k(1,xn	PROPN
ejpam-6593	216	37	)	)	PUNCT
ejpam-6593	217	1	=	=	SYM
ejpam-6593	217	2	k(0,xn	k(0,xn	PROPN
ejpam-6593	217	3	)	)	PUNCT
ejpam-6593	218	1	+	+	NUM
ejpam-6593	218	2	αxn	αxn	NOUN
ejpam-6593	218	3	.	.	PUNCT
ejpam-6593	219	1	thus	thus	ADV
ejpam-6593	219	2	,	,	PUNCT
ejpam-6593	219	3	equation	equation	NOUN
ejpam-6593	219	4	(	(	PUNCT
ejpam-6593	219	5	10	10	NUM
ejpam-6593	219	6	)	)	PUNCT
ejpam-6593	219	7	is	be	AUX
ejpam-6593	219	8	satisfied	satisfied	ADJ
ejpam-6593	219	9	when	when	SCONJ
ejpam-6593	219	10	m	m	VERB
ejpam-6593	219	11	=	=	NOUN
ejpam-6593	219	12	1	1	X
ejpam-6593	219	13	.	.	PUNCT
ejpam-6593	220	1	we	we	PRON
ejpam-6593	220	2	now	now	ADV
ejpam-6593	220	3	assume	assume	VERB
ejpam-6593	220	4	that	that	SCONJ
ejpam-6593	220	5	equation	equation	NOUN
ejpam-6593	220	6	(	(	PUNCT
ejpam-6593	220	7	10	10	NUM
ejpam-6593	220	8	)	)	PUNCT
ejpam-6593	220	9	is	be	AUX
ejpam-6593	220	10	true	true	ADJ
ejpam-6593	220	11	for	for	ADP
ejpam-6593	220	12	m	m	PROPN
ejpam-6593	220	13	=	=	SYM
ejpam-6593	220	14	a	a	PROPN
ejpam-6593	220	15	,	,	PUNCT
ejpam-6593	220	16	that	that	ADV
ejpam-6593	220	17	is	is	ADV
ejpam-6593	220	18	,	,	PUNCT
ejpam-6593	220	19	k(a	k(a	PROPN
ejpam-6593	220	20	,	,	PUNCT
ejpam-6593	220	21	xn	xn	NUM
ejpam-6593	220	22	)	)	PUNCT
ejpam-6593	221	1	=	=	SYM
ejpam-6593	221	2	k(0,xn	k(0,xn	PROPN
ejpam-6593	221	3	)	)	PUNCT
ejpam-6593	222	1	+	+	CCONJ
ejpam-6593	222	2	a−1∑	a−1∑	PRON
ejpam-6593	222	3	i=0	i=0	PROPN
ejpam-6593	222	4	(	(	PUNCT
ejpam-6593	222	5	αxn	αxn	PROPN
ejpam-6593	222	6	+	+	SYM
ejpam-6593	222	7	10i	10i	NOUN
ejpam-6593	222	8	)	)	PUNCT
ejpam-6593	222	9	.	.	PUNCT
ejpam-6593	223	1	we	we	PRON
ejpam-6593	223	2	need	need	VERB
ejpam-6593	223	3	to	to	PART
ejpam-6593	223	4	show	show	VERB
ejpam-6593	223	5	that	that	SCONJ
ejpam-6593	223	6	it	it	PRON
ejpam-6593	223	7	is	be	AUX
ejpam-6593	223	8	also	also	ADV
ejpam-6593	223	9	true	true	ADJ
ejpam-6593	223	10	for	for	ADP
ejpam-6593	223	11	m	m	PROPN
ejpam-6593	223	12	=	=	SYM
ejpam-6593	223	13	a+	a+	PUNCT
ejpam-6593	223	14	1	1	X
ejpam-6593	223	15	.	.	PUNCT
ejpam-6593	223	16	by	by	ADP
ejpam-6593	223	17	using	use	VERB
ejpam-6593	223	18	(	(	PUNCT
ejpam-6593	223	19	6b	6b	NUM
ejpam-6593	223	20	)	)	PUNCT
ejpam-6593	223	21	,	,	PUNCT
ejpam-6593	223	22	we	we	PRON
ejpam-6593	223	23	have	have	VERB
ejpam-6593	223	24	the	the	DET
ejpam-6593	223	25	following	follow	VERB
ejpam-6593	223	26	simplification	simplification	NOUN
ejpam-6593	223	27	:	:	PUNCT
ejpam-6593	223	28	k(a	k(a	NOUN
ejpam-6593	223	29	,	,	PUNCT
ejpam-6593	223	30	xn	xn	PUNCT
ejpam-6593	223	31	)	)	PUNCT
ejpam-6593	224	1	+	+	CCONJ
ejpam-6593	224	2	(	(	PUNCT
ejpam-6593	224	3	αxn	αxn	PROPN
ejpam-6593	224	4	+	+	SYM
ejpam-6593	224	5	10a	10a	NOUN
ejpam-6593	224	6	)	)	PUNCT
ejpam-6593	224	7	=	=	SYM
ejpam-6593	224	8	(	(	PUNCT
ejpam-6593	224	9	k(0,xn	k(0,xn	PROPN
ejpam-6593	224	10	)	)	PUNCT
ejpam-6593	225	1	+	+	CCONJ
ejpam-6593	225	2	a−1∑	a−1∑	PRON
ejpam-6593	225	3	i=0	i=0	PROPN
ejpam-6593	225	4	(	(	PUNCT
ejpam-6593	225	5	αxn	αxn	PROPN
ejpam-6593	225	6	+	+	SYM
ejpam-6593	225	7	10i	10i	NOUN
ejpam-6593	225	8	)	)	PUNCT
ejpam-6593	225	9	)	)	PUNCT
ejpam-6593	226	1	+	+	CCONJ
ejpam-6593	226	2	(	(	PUNCT
ejpam-6593	226	3	αxn	αxn	PROPN
ejpam-6593	226	4	+	+	SYM
ejpam-6593	226	5	10a	10a	NOUN
ejpam-6593	226	6	)	)	PUNCT
ejpam-6593	226	7	,	,	PUNCT
ejpam-6593	226	8	z2(a	z2(a	PROPN
ejpam-6593	226	9	,	,	PUNCT
ejpam-6593	226	10	xn	xn	PROPN
ejpam-6593	226	11	)	)	PUNCT
ejpam-6593	226	12	−	−	ADP
ejpam-6593	227	1	2xn	2xn	ADJ
ejpam-6593	227	2	−	−	NUM
ejpam-6593	227	3	2	2	NUM
ejpam-6593	227	4	5	5	NUM
ejpam-6593	227	5	+	+	CCONJ
ejpam-6593	227	6	αxn	αxn	ADJ
ejpam-6593	227	7	+	+	SYM
ejpam-6593	227	8	10a	10a	NOUN
ejpam-6593	227	9	=	=	SYM
ejpam-6593	227	10	k(0,xn	k(0,xn	PROPN
ejpam-6593	227	11	)	)	PUNCT
ejpam-6593	228	1	+	+	CCONJ
ejpam-6593	228	2	a∑	a∑	PROPN
ejpam-6593	228	3	i=0	i=0	PROPN
ejpam-6593	228	4	(	(	PUNCT
ejpam-6593	228	5	αxn	αxn	PROPN
ejpam-6593	228	6	+	+	SYM
ejpam-6593	228	7	10i	10i	NOUN
ejpam-6593	228	8	)	)	PUNCT
ejpam-6593	228	9	.	.	PUNCT
ejpam-6593	229	1	thus	thus	ADV
ejpam-6593	229	2	,	,	PUNCT
ejpam-6593	229	3	we	we	PRON
ejpam-6593	229	4	obtain	obtain	VERB
ejpam-6593	229	5	z2(a	z2(a	NOUN
ejpam-6593	229	6	,	,	PUNCT
ejpam-6593	229	7	xn	xn	PROPN
ejpam-6593	229	8	)	)	PUNCT
ejpam-6593	230	1	−	−	ADP
ejpam-6593	230	2	2xn	2xn	ADJ
ejpam-6593	231	1	−	−	NOUN
ejpam-6593	231	2	2	2	NUM
ejpam-6593	231	3	+	+	CCONJ
ejpam-6593	231	4	5αxn	5αxn	NUM
ejpam-6593	231	5	+	+	NUM
ejpam-6593	231	6	50a	50a	NOUN
ejpam-6593	231	7	5	5	NUM
ejpam-6593	231	8	=	=	SYM
ejpam-6593	231	9	k(0,xn	k(0,xn	PROPN
ejpam-6593	231	10	)	)	PUNCT
ejpam-6593	232	1	+	+	CCONJ
ejpam-6593	232	2	a∑	a∑	PROPN
ejpam-6593	232	3	i=0	i=0	PROPN
ejpam-6593	232	4	(	(	PUNCT
ejpam-6593	232	5	αxn	αxn	PROPN
ejpam-6593	232	6	+	+	SYM
ejpam-6593	232	7	10i	10i	NOUN
ejpam-6593	232	8	)	)	PUNCT
ejpam-6593	232	9	.	.	PUNCT
ejpam-6593	233	1	(	(	PUNCT
ejpam-6593	233	2	11	11	NUM
ejpam-6593	233	3	)	)	PUNCT
ejpam-6593	233	4	m.	m.	NOUN
ejpam-6593	233	5	c.	c.	PROPN
ejpam-6593	233	6	avenilla	avenilla	PROPN
ejpam-6593	233	7	,	,	PUNCT
ejpam-6593	233	8	j.	j.	PROPN
ejpam-6593	233	9	b.	b.	PROPN
ejpam-6593	233	10	bacani	bacani	PROPN
ejpam-6593	233	11	/	/	SYM
ejpam-6593	233	12	eur	eur	PROPN
ejpam-6593	233	13	.	.	PUNCT
ejpam-6593	234	1	j.	j.	PROPN
ejpam-6593	234	2	pure	pure	PROPN
ejpam-6593	234	3	appl	appl	PROPN
ejpam-6593	234	4	.	.	PROPN
ejpam-6593	234	5	math	math	PROPN
ejpam-6593	234	6	,	,	PUNCT
ejpam-6593	234	7	18	18	NUM
ejpam-6593	234	8	(	(	PUNCT
ejpam-6593	234	9	3	3	NUM
ejpam-6593	234	10	)	)	PUNCT
ejpam-6593	234	11	(	(	PUNCT
ejpam-6593	234	12	2025	2025	NUM
ejpam-6593	234	13	)	)	PUNCT
ejpam-6593	234	14	,	,	PUNCT
ejpam-6593	234	15	6593	6593	NUM
ejpam-6593	234	16	8	8	NUM
ejpam-6593	234	17	of	of	ADP
ejpam-6593	234	18	24	24	NUM
ejpam-6593	234	19	by	by	ADP
ejpam-6593	234	20	definition	definition	NOUN
ejpam-6593	234	21	,	,	PUNCT
ejpam-6593	234	22	αxn	αxn	PROPN
ejpam-6593	234	23	=	=	SYM
ejpam-6593	234	24	k(1,xn	k(1,xn	PROPN
ejpam-6593	234	25	)	)	PUNCT
ejpam-6593	234	26	−	−	PROPN
ejpam-6593	235	1	k(0,xn	k(0,xn	PROPN
ejpam-6593	235	2	)	)	PUNCT
ejpam-6593	235	3	.	.	PUNCT
ejpam-6593	236	1	using	use	VERB
ejpam-6593	236	2	(	(	PUNCT
ejpam-6593	236	3	6b	6b	NUM
ejpam-6593	236	4	)	)	PUNCT
ejpam-6593	236	5	and	and	CCONJ
ejpam-6593	236	6	(	(	PUNCT
ejpam-6593	236	7	6a	6a	NOUN
ejpam-6593	236	8	)	)	PUNCT
ejpam-6593	236	9	,	,	PUNCT
ejpam-6593	236	10	we	we	PRON
ejpam-6593	236	11	get	get	VERB
ejpam-6593	236	12	αxn	αxn	ADJ
ejpam-6593	236	13	=	=	SYM
ejpam-6593	236	14	z2(1,xn	z2(1,xn	PROPN
ejpam-6593	236	15	)	)	PUNCT
ejpam-6593	237	1	−	−	NOUN
ejpam-6593	237	2	2xn	2xn	ADJ
ejpam-6593	238	1	−	−	NOUN
ejpam-6593	238	2	2	2	NUM
ejpam-6593	238	3	5	5	NUM
ejpam-6593	238	4	−	−	PROPN
ejpam-6593	238	5	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	238	6	)	)	PUNCT
ejpam-6593	239	1	−	−	X
ejpam-6593	240	1	2xn	2xn	ADJ
ejpam-6593	240	2	−	−	NUM
ejpam-6593	240	3	2	2	NUM
ejpam-6593	240	4	5	5	NUM
ejpam-6593	240	5	=	=	SYM
ejpam-6593	240	6	z2(1,xn	z2(1,xn	PROPN
ejpam-6593	240	7	)	)	PUNCT
ejpam-6593	240	8	−	−	PROPN
ejpam-6593	240	9	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	240	10	)	)	PUNCT
ejpam-6593	240	11	5	5	NUM
ejpam-6593	240	12	.	.	PUNCT
ejpam-6593	241	1	also	also	ADV
ejpam-6593	241	2	,	,	PUNCT
ejpam-6593	241	3	recalling	recall	VERB
ejpam-6593	241	4	that	that	SCONJ
ejpam-6593	241	5	z(m	z(m	PROPN
ejpam-6593	241	6	,	,	PUNCT
ejpam-6593	241	7	xn	xn	NUM
ejpam-6593	241	8	)	)	PUNCT
ejpam-6593	241	9	=	=	SYM
ejpam-6593	241	10	z(0,xn	z(0,xn	PROPN
ejpam-6593	241	11	)	)	PUNCT
ejpam-6593	242	1	+	+	CCONJ
ejpam-6593	242	2	5	5	NUM
ejpam-6593	242	3	m	m	VERB
ejpam-6593	242	4	from	from	ADP
ejpam-6593	242	5	(	(	PUNCT
ejpam-6593	242	6	7d	7d	NUM
ejpam-6593	242	7	)	)	PUNCT
ejpam-6593	242	8	,	,	PUNCT
ejpam-6593	242	9	(	(	PUNCT
ejpam-6593	242	10	8d	8d	NUM
ejpam-6593	242	11	)	)	PUNCT
ejpam-6593	242	12	,	,	PUNCT
ejpam-6593	242	13	and	and	CCONJ
ejpam-6593	242	14	(	(	PUNCT
ejpam-6593	242	15	9c	9c	NUM
ejpam-6593	242	16	)	)	PUNCT
ejpam-6593	242	17	,	,	PUNCT
ejpam-6593	242	18	we	we	PRON
ejpam-6593	242	19	have	have	VERB
ejpam-6593	242	20	z(1,xn	z(1,xn	PROPN
ejpam-6593	242	21	)	)	PUNCT
ejpam-6593	243	1	=	=	SYM
ejpam-6593	243	2	z(0,xn	z(0,xn	PROPN
ejpam-6593	243	3	)	)	PUNCT
ejpam-6593	244	1	+	+	CCONJ
ejpam-6593	244	2	5	5	NUM
ejpam-6593	244	3	and	and	CCONJ
ejpam-6593	244	4	z(a	z(a	NOUN
ejpam-6593	244	5	,	,	PUNCT
ejpam-6593	244	6	xn	xn	NUM
ejpam-6593	244	7	)	)	PUNCT
ejpam-6593	244	8	=	=	SYM
ejpam-6593	244	9	z(0,xn	z(0,xn	PROPN
ejpam-6593	244	10	)	)	PUNCT
ejpam-6593	245	1	+	+	CCONJ
ejpam-6593	245	2	5a	5a	NUM
ejpam-6593	245	3	.	.	PUNCT
ejpam-6593	246	1	hence	hence	ADV
ejpam-6593	246	2	,	,	PUNCT
ejpam-6593	246	3	we	we	PRON
ejpam-6593	246	4	can	can	AUX
ejpam-6593	246	5	simplify	simplify	VERB
ejpam-6593	246	6	the	the	DET
ejpam-6593	246	7	expression	expression	NOUN
ejpam-6593	246	8	as	as	SCONJ
ejpam-6593	246	9	follows	follow	VERB
ejpam-6593	246	10	:	:	PUNCT
ejpam-6593	246	11	z2(a	z2(a	NOUN
ejpam-6593	246	12	,	,	PUNCT
ejpam-6593	246	13	xn	xn	PROPN
ejpam-6593	246	14	)	)	PUNCT
ejpam-6593	247	1	−	−	ADP
ejpam-6593	247	2	2xn	2xn	ADJ
ejpam-6593	248	1	−	−	NOUN
ejpam-6593	248	2	2	2	NUM
ejpam-6593	248	3	+	+	CCONJ
ejpam-6593	248	4	5αxn	5αxn	NUM
ejpam-6593	248	5	+	+	NUM
ejpam-6593	248	6	50a	50a	NOUN
ejpam-6593	248	7	5	5	NUM
ejpam-6593	248	8	=	=	SYM
ejpam-6593	248	9	z2(a	z2(a	PROPN
ejpam-6593	248	10	,	,	PUNCT
ejpam-6593	248	11	xn	xn	PROPN
ejpam-6593	248	12	)	)	PUNCT
ejpam-6593	248	13	−	−	ADP
ejpam-6593	249	1	2xn	2xn	ADJ
ejpam-6593	249	2	−	−	NOUN
ejpam-6593	249	3	2	2	NUM
ejpam-6593	249	4	+	+	SYM
ejpam-6593	249	5	z2(1,xn	z2(1,xn	NUM
ejpam-6593	249	6	)	)	PUNCT
ejpam-6593	249	7	−	−	PROPN
ejpam-6593	249	8	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	249	9	)	)	PUNCT
ejpam-6593	250	1	+	+	NUM
ejpam-6593	250	2	50a	50a	NOUN
ejpam-6593	250	3	5	5	NUM
ejpam-6593	250	4	=	=	SYM
ejpam-6593	250	5	z2(a	z2(a	PROPN
ejpam-6593	250	6	,	,	PUNCT
ejpam-6593	250	7	xn	xn	PROPN
ejpam-6593	250	8	)	)	PUNCT
ejpam-6593	250	9	+	+	NUM
ejpam-6593	250	10	z2(1,xn	z2(1,xn	NUM
ejpam-6593	250	11	)	)	PUNCT
ejpam-6593	250	12	−	−	PROPN
ejpam-6593	250	13	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	250	14	)	)	PUNCT
ejpam-6593	250	15	+	+	NUM
ejpam-6593	250	16	50a−	50a−	NUM
ejpam-6593	250	17	2xn	2xn	NOUN
ejpam-6593	250	18	−	−	NOUN
ejpam-6593	250	19	2	2	NUM
ejpam-6593	250	20	5	5	NUM
ejpam-6593	250	21	=	=	SYM
ejpam-6593	250	22	z2(a	z2(a	PROPN
ejpam-6593	250	23	,	,	PUNCT
ejpam-6593	250	24	xn	xn	PROPN
ejpam-6593	250	25	)	)	PUNCT
ejpam-6593	251	1	+	+	CCONJ
ejpam-6593	251	2	(	(	PUNCT
ejpam-6593	251	3	z(0,xn	z(0,xn	PROPN
ejpam-6593	251	4	)	)	PUNCT
ejpam-6593	252	1	+	+	CCONJ
ejpam-6593	252	2	5)2	5)2	NUM
ejpam-6593	252	3	−	−	PROPN
ejpam-6593	252	4	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	252	5	)	)	PUNCT
ejpam-6593	253	1	+	+	NUM
ejpam-6593	253	2	50a−	50a−	NUM
ejpam-6593	253	3	2xn	2xn	NOUN
ejpam-6593	253	4	−	−	NOUN
ejpam-6593	253	5	2	2	NUM
ejpam-6593	253	6	5	5	NUM
ejpam-6593	253	7	=	=	SYM
ejpam-6593	253	8	z2(a	z2(a	PROPN
ejpam-6593	253	9	,	,	PUNCT
ejpam-6593	253	10	xn	xn	PROPN
ejpam-6593	253	11	)	)	PUNCT
ejpam-6593	254	1	+	+	CCONJ
ejpam-6593	254	2	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	254	3	)	)	PUNCT
ejpam-6593	254	4	+	+	CCONJ
ejpam-6593	254	5	10z(0,xn	10z(0,xn	NUM
ejpam-6593	254	6	)	)	PUNCT
ejpam-6593	255	1	+	+	NUM
ejpam-6593	255	2	25−	25−	NUM
ejpam-6593	255	3	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	255	4	)	)	PUNCT
ejpam-6593	256	1	+	+	NUM
ejpam-6593	256	2	50a−	50a−	NUM
ejpam-6593	256	3	2xn	2xn	NOUN
ejpam-6593	256	4	−	−	NOUN
ejpam-6593	256	5	2	2	NUM
ejpam-6593	256	6	5	5	NUM
ejpam-6593	256	7	=	=	SYM
ejpam-6593	256	8	z2(a	z2(a	PROPN
ejpam-6593	256	9	,	,	PUNCT
ejpam-6593	256	10	xn	xn	PROPN
ejpam-6593	256	11	)	)	PUNCT
ejpam-6593	257	1	+	+	CCONJ
ejpam-6593	257	2	10z(0,xn	10z(0,xn	NUM
ejpam-6593	257	3	)	)	PUNCT
ejpam-6593	258	1	+	+	NUM
ejpam-6593	258	2	50a+	50a+	NUM
ejpam-6593	258	3	25−	25−	NUM
ejpam-6593	258	4	2xn	2xn	NOUN
ejpam-6593	258	5	−	−	ADP
ejpam-6593	258	6	2	2	NUM
ejpam-6593	258	7	5	5	NUM
ejpam-6593	258	8	=	=	SYM
ejpam-6593	258	9	z2(a	z2(a	PROPN
ejpam-6593	258	10	,	,	PUNCT
ejpam-6593	258	11	xn	xn	PROPN
ejpam-6593	258	12	)	)	PUNCT
ejpam-6593	258	13	+	+	NUM
ejpam-6593	258	14	10(z(0,xn	10(z(0,xn	NUM
ejpam-6593	258	15	)	)	PUNCT
ejpam-6593	259	1	+	+	CCONJ
ejpam-6593	259	2	5a	5a	NUM
ejpam-6593	259	3	)	)	PUNCT
ejpam-6593	259	4	+	+	NUM
ejpam-6593	259	5	25−	25−	NUM
ejpam-6593	259	6	2xn	2xn	ADJ
ejpam-6593	259	7	−	−	NUM
ejpam-6593	259	8	2	2	NUM
ejpam-6593	259	9	5	5	NUM
ejpam-6593	259	10	=	=	SYM
ejpam-6593	259	11	z2(a	z2(a	PROPN
ejpam-6593	259	12	,	,	PUNCT
ejpam-6593	259	13	xn	xn	PROPN
ejpam-6593	259	14	)	)	PUNCT
ejpam-6593	260	1	+	+	CCONJ
ejpam-6593	260	2	10z(a	10z(a	NUM
ejpam-6593	260	3	,	,	PUNCT
ejpam-6593	260	4	xn	xn	PUNCT
ejpam-6593	260	5	)	)	PUNCT
ejpam-6593	261	1	+	+	NUM
ejpam-6593	262	1	25−	25−	NUM
ejpam-6593	262	2	2xn	2xn	NOUN
ejpam-6593	262	3	−	−	NUM
ejpam-6593	262	4	2	2	NUM
ejpam-6593	262	5	5	5	NUM
ejpam-6593	262	6	=	=	SYM
ejpam-6593	262	7	(	(	PUNCT
ejpam-6593	262	8	z(a	z(a	PROPN
ejpam-6593	262	9	,	,	PUNCT
ejpam-6593	262	10	xn	xn	PUNCT
ejpam-6593	262	11	)	)	PUNCT
ejpam-6593	263	1	+	+	CCONJ
ejpam-6593	263	2	5)2	5)2	NUM
ejpam-6593	263	3	−	−	NOUN
ejpam-6593	263	4	2xn	2xn	NOUN
ejpam-6593	263	5	−	−	NUM
ejpam-6593	263	6	2	2	NUM
ejpam-6593	263	7	5	5	NUM
ejpam-6593	263	8	=	=	SYM
ejpam-6593	263	9	z2(a+1,xn	z2(a+1,xn	PROPN
ejpam-6593	263	10	)	)	PUNCT
ejpam-6593	263	11	−	−	PROPN
ejpam-6593	264	1	2xn	2xn	ADJ
ejpam-6593	264	2	−	−	NUM
ejpam-6593	264	3	2	2	NUM
ejpam-6593	264	4	5	5	NUM
ejpam-6593	264	5	=	=	SYM
ejpam-6593	264	6	k(a+1,xn	k(a+1,xn	PROPN
ejpam-6593	264	7	)	)	PUNCT
ejpam-6593	264	8	.	.	PUNCT
ejpam-6593	265	1	in	in	ADP
ejpam-6593	265	2	the	the	DET
ejpam-6593	265	3	manipulations	manipulation	NOUN
ejpam-6593	265	4	,	,	PUNCT
ejpam-6593	265	5	we	we	PRON
ejpam-6593	265	6	have	have	AUX
ejpam-6593	265	7	used	use	VERB
ejpam-6593	265	8	the	the	DET
ejpam-6593	265	9	fact	fact	NOUN
ejpam-6593	265	10	that	that	SCONJ
ejpam-6593	265	11	z(a+1,xn	z(a+1,xn	PROPN
ejpam-6593	265	12	)	)	PUNCT
ejpam-6593	266	1	=	=	SYM
ejpam-6593	266	2	z(0,xn	z(0,xn	PROPN
ejpam-6593	266	3	)	)	PUNCT
ejpam-6593	267	1	+	+	CCONJ
ejpam-6593	268	1	5(a	5(a	NUM
ejpam-6593	268	2	+	+	NUM
ejpam-6593	268	3	1	1	NUM
ejpam-6593	268	4	)	)	PUNCT
ejpam-6593	268	5	=	=	SYM
ejpam-6593	268	6	z(0,xn	z(0,xn	PROPN
ejpam-6593	268	7	)	)	PUNCT
ejpam-6593	269	1	+	+	CCONJ
ejpam-6593	269	2	5a	5a	NUM
ejpam-6593	269	3	+	+	CCONJ
ejpam-6593	269	4	5	5	NUM
ejpam-6593	269	5	=	=	SYM
ejpam-6593	269	6	z(a	z(a	NOUN
ejpam-6593	269	7	,	,	PUNCT
ejpam-6593	269	8	xn	xn	PUNCT
ejpam-6593	269	9	)	)	PUNCT
ejpam-6593	269	10	+	+	CCONJ
ejpam-6593	269	11	5	5	NUM
ejpam-6593	269	12	,	,	PUNCT
ejpam-6593	269	13	and	and	CCONJ
ejpam-6593	269	14	the	the	DET
ejpam-6593	269	15	definition	definition	NOUN
ejpam-6593	269	16	of	of	ADP
ejpam-6593	269	17	k(m	k(m	PROPN
ejpam-6593	269	18	,	,	PUNCT
ejpam-6593	269	19	xn	xn	PROPN
ejpam-6593	269	20	)	)	PUNCT
ejpam-6593	269	21	.	.	PUNCT
ejpam-6593	270	1	thus	thus	ADV
ejpam-6593	270	2	,	,	PUNCT
ejpam-6593	270	3	(	(	PUNCT
ejpam-6593	270	4	11	11	NUM
ejpam-6593	270	5	)	)	PUNCT
ejpam-6593	270	6	can	can	AUX
ejpam-6593	270	7	be	be	AUX
ejpam-6593	270	8	written	write	VERB
ejpam-6593	270	9	as	as	ADP
ejpam-6593	270	10	k(a+1,xn	k(a+1,xn	PROPN
ejpam-6593	270	11	)	)	PUNCT
ejpam-6593	271	1	=	=	SYM
ejpam-6593	271	2	k(0,xn	k(0,xn	PROPN
ejpam-6593	271	3	)	)	PUNCT
ejpam-6593	272	1	+	+	CCONJ
ejpam-6593	272	2	a∑	a∑	PROPN
ejpam-6593	272	3	i=0	i=0	PROPN
ejpam-6593	272	4	(	(	PUNCT
ejpam-6593	272	5	αxn	αxn	PROPN
ejpam-6593	272	6	+	+	SYM
ejpam-6593	272	7	10i	10i	NOUN
ejpam-6593	272	8	)	)	PUNCT
ejpam-6593	272	9	,	,	PUNCT
ejpam-6593	272	10	showing	show	VERB
ejpam-6593	272	11	that	that	DET
ejpam-6593	272	12	equation	equation	NOUN
ejpam-6593	272	13	(	(	PUNCT
ejpam-6593	272	14	10	10	NUM
ejpam-6593	272	15	)	)	PUNCT
ejpam-6593	272	16	is	be	AUX
ejpam-6593	272	17	also	also	ADV
ejpam-6593	272	18	true	true	ADJ
ejpam-6593	272	19	for	for	ADP
ejpam-6593	272	20	m	m	PROPN
ejpam-6593	272	21	=	=	SYM
ejpam-6593	272	22	a	a	DET
ejpam-6593	272	23	+	+	NUM
ejpam-6593	272	24	1	1	NUM
ejpam-6593	272	25	.	.	PUNCT
ejpam-6593	273	1	therefore	therefore	ADV
ejpam-6593	273	2	,	,	PUNCT
ejpam-6593	273	3	(	(	PUNCT
ejpam-6593	273	4	10	10	NUM
ejpam-6593	273	5	)	)	PUNCT
ejpam-6593	273	6	is	be	AUX
ejpam-6593	273	7	true	true	ADJ
ejpam-6593	273	8	for	for	ADP
ejpam-6593	273	9	any	any	PRON
ejpam-6593	273	10	x	x	SYM
ejpam-6593	273	11	=	=	PUNCT
ejpam-6593	273	12	xn	xn	PUNCT
ejpam-6593	274	1	=	=	SYM
ejpam-6593	274	2	1	1	NUM
ejpam-6593	274	3	+	+	CCONJ
ejpam-6593	274	4	4n	4n	NOUN
ejpam-6593	274	5	,	,	PUNCT
ejpam-6593	274	6	x	x	SYM
ejpam-6593	274	7	=	=	PUNCT
ejpam-6593	274	8	xn	xn	PUNCT
ejpam-6593	275	1	=	=	SYM
ejpam-6593	275	2	2	2	NUM
ejpam-6593	275	3	+	+	CCONJ
ejpam-6593	275	4	4n	4n	NOUN
ejpam-6593	275	5	,	,	PUNCT
ejpam-6593	275	6	or	or	CCONJ
ejpam-6593	275	7	x	x	SYM
ejpam-6593	276	1	=	=	SYM
ejpam-6593	276	2	xn	xn	PUNCT
ejpam-6593	276	3	=	=	SYM
ejpam-6593	276	4	3	3	NUM
ejpam-6593	276	5	+	+	CCONJ
ejpam-6593	276	6	4n	4n	NOUN
ejpam-6593	276	7	,	,	PUNCT
ejpam-6593	276	8	where	where	SCONJ
ejpam-6593	276	9	n	n	X
ejpam-6593	276	10	∈	∈	PROPN
ejpam-6593	276	11	n0	n0	PROPN
ejpam-6593	276	12	.	.	PUNCT
ejpam-6593	277	1	the	the	DET
ejpam-6593	277	2	next	next	ADJ
ejpam-6593	277	3	remark	remark	NOUN
ejpam-6593	277	4	follows	follow	VERB
ejpam-6593	277	5	directly	directly	ADV
ejpam-6593	277	6	from	from	ADP
ejpam-6593	277	7	theorem	theorem	ADJ
ejpam-6593	277	8	1	1	NUM
ejpam-6593	277	9	.	.	NOUN
ejpam-6593	277	10	remark	remark	NOUN
ejpam-6593	277	11	1	1	NUM
ejpam-6593	277	12	.	.	PUNCT
ejpam-6593	277	13	consider	consider	VERB
ejpam-6593	277	14	the	the	DET
ejpam-6593	277	15	exponential	exponential	ADJ
ejpam-6593	277	16	diophantine	diophantine	NOUN
ejpam-6593	277	17	equation	equation	NOUN
ejpam-6593	277	18	2x	2x	NUM
ejpam-6593	278	1	+	+	CCONJ
ejpam-6593	278	2	(	(	PUNCT
ejpam-6593	278	3	2	2	NUM
ejpam-6593	278	4	+	+	NUM
ejpam-6593	278	5	5k	5k	NUM
ejpam-6593	278	6	)	)	PUNCT
ejpam-6593	279	1	=	=	SYM
ejpam-6593	279	2	z2	z2	PROPN
ejpam-6593	279	3	,	,	PUNCT
ejpam-6593	279	4	where	where	SCONJ
ejpam-6593	279	5	x	x	ADP
ejpam-6593	279	6	=	=	PUNCT
ejpam-6593	279	7	xn	xn	PUNCT
ejpam-6593	280	1	=	=	SYM
ejpam-6593	280	2	1	1	NUM
ejpam-6593	280	3	+	+	CCONJ
ejpam-6593	280	4	4n	4n	NOUN
ejpam-6593	280	5	,	,	PUNCT
ejpam-6593	280	6	x	x	SYM
ejpam-6593	280	7	=	=	PUNCT
ejpam-6593	280	8	xn	xn	PUNCT
ejpam-6593	281	1	=	=	SYM
ejpam-6593	281	2	2	2	NUM
ejpam-6593	281	3	+	+	CCONJ
ejpam-6593	281	4	4n	4n	NOUN
ejpam-6593	281	5	,	,	PUNCT
ejpam-6593	281	6	or	or	CCONJ
ejpam-6593	281	7	x	x	SYM
ejpam-6593	282	1	=	=	SYM
ejpam-6593	282	2	xn	xn	PUNCT
ejpam-6593	282	3	=	=	SYM
ejpam-6593	282	4	3	3	NUM
ejpam-6593	282	5	+	+	CCONJ
ejpam-6593	282	6	4n	4n	NOUN
ejpam-6593	282	7	,	,	PUNCT
ejpam-6593	282	8	for	for	ADP
ejpam-6593	282	9	n	n	DET
ejpam-6593	282	10	∈	∈	PROPN
ejpam-6593	282	11	n0	n0	PROPN
ejpam-6593	282	12	.	.	PUNCT
ejpam-6593	283	1	then	then	ADV
ejpam-6593	283	2	,	,	PUNCT
ejpam-6593	283	3	k(m	k(m	PROPN
ejpam-6593	283	4	,	,	PUNCT
ejpam-6593	283	5	xn	xn	PROPN
ejpam-6593	283	6	)	)	PUNCT
ejpam-6593	283	7	=	=	SYM
ejpam-6593	283	8	k(m−1,xn	k(m−1,xn	PROPN
ejpam-6593	283	9	)	)	PUNCT
ejpam-6593	284	1	+	+	CCONJ
ejpam-6593	284	2	αxn	αxn	X
ejpam-6593	284	3	+	+	SYM
ejpam-6593	284	4	10(m−	10(m−	PROPN
ejpam-6593	284	5	1	1	NUM
ejpam-6593	284	6	)	)	PUNCT
ejpam-6593	284	7	.	.	PUNCT
ejpam-6593	285	1	m.	m.	PROPN
ejpam-6593	285	2	c.	c.	PROPN
ejpam-6593	285	3	avenilla	avenilla	PROPN
ejpam-6593	285	4	,	,	PUNCT
ejpam-6593	285	5	j.	j.	PROPN
ejpam-6593	285	6	b.	b.	PROPN
ejpam-6593	285	7	bacani	bacani	PROPN
ejpam-6593	285	8	/	/	SYM
ejpam-6593	285	9	eur	eur	PROPN
ejpam-6593	285	10	.	.	PUNCT
ejpam-6593	286	1	j.	j.	PROPN
ejpam-6593	286	2	pure	pure	PROPN
ejpam-6593	286	3	appl	appl	PROPN
ejpam-6593	286	4	.	.	PROPN
ejpam-6593	286	5	math	math	PROPN
ejpam-6593	286	6	,	,	PUNCT
ejpam-6593	286	7	18	18	NUM
ejpam-6593	286	8	(	(	PUNCT
ejpam-6593	286	9	3	3	NUM
ejpam-6593	286	10	)	)	PUNCT
ejpam-6593	286	11	(	(	PUNCT
ejpam-6593	286	12	2025	2025	NUM
ejpam-6593	286	13	)	)	PUNCT
ejpam-6593	286	14	,	,	PUNCT
ejpam-6593	286	15	6593	6593	NUM
ejpam-6593	286	16	9	9	NUM
ejpam-6593	286	17	of	of	ADP
ejpam-6593	286	18	24	24	NUM
ejpam-6593	286	19	given	give	VERB
ejpam-6593	286	20	below	below	ADV
ejpam-6593	286	21	are	be	AUX
ejpam-6593	286	22	tables	table	NOUN
ejpam-6593	286	23	containing	contain	VERB
ejpam-6593	286	24	the	the	DET
ejpam-6593	286	25	first	first	ADJ
ejpam-6593	286	26	five	five	NUM
ejpam-6593	286	27	solutions	solution	NOUN
ejpam-6593	286	28	of	of	ADP
ejpam-6593	286	29	equation	equation	NOUN
ejpam-6593	286	30	(	(	PUNCT
ejpam-6593	286	31	5	5	NUM
ejpam-6593	286	32	)	)	PUNCT
ejpam-6593	286	33	,	,	PUNCT
ejpam-6593	286	34	where	where	SCONJ
ejpam-6593	286	35	x	x	X
ejpam-6593	286	36	≡	≡	PROPN
ejpam-6593	286	37	1	1	NUM
ejpam-6593	286	38	,	,	PUNCT
ejpam-6593	286	39	2	2	NUM
ejpam-6593	286	40	or	or	CCONJ
ejpam-6593	286	41	3	3	NUM
ejpam-6593	286	42	(	(	PUNCT
ejpam-6593	286	43	mod	mod	NOUN
ejpam-6593	286	44	4	4	NUM
ejpam-6593	286	45	)	)	PUNCT
ejpam-6593	286	46	.	.	PUNCT
ejpam-6593	287	1	the	the	DET
ejpam-6593	287	2	expression	expression	NOUN
ejpam-6593	287	3	for	for	ADP
ejpam-6593	287	4	k(m	k(m	PROPN
ejpam-6593	287	5	,	,	PUNCT
ejpam-6593	287	6	xn	xn	PROPN
ejpam-6593	287	7	)	)	PUNCT
ejpam-6593	287	8	is	be	AUX
ejpam-6593	287	9	obtained	obtain	VERB
ejpam-6593	287	10	by	by	ADP
ejpam-6593	287	11	applying	apply	VERB
ejpam-6593	287	12	either	either	CCONJ
ejpam-6593	287	13	(	(	PUNCT
ejpam-6593	287	14	6b	6b	NOUN
ejpam-6593	287	15	)	)	PUNCT
ejpam-6593	287	16	,	,	PUNCT
ejpam-6593	287	17	theorem	theorem	VERB
ejpam-6593	287	18	1	1	NUM
ejpam-6593	287	19	,	,	PUNCT
ejpam-6593	287	20	or	or	CCONJ
ejpam-6593	287	21	remark	remark	NOUN
ejpam-6593	287	22	1	1	NUM
ejpam-6593	287	23	.	.	PUNCT
ejpam-6593	288	1	if	if	SCONJ
ejpam-6593	288	2	n	n	NOUN
ejpam-6593	288	3	=	=	SYM
ejpam-6593	288	4	0	0	NUM
ejpam-6593	288	5	in	in	ADP
ejpam-6593	288	6	x	x	X
ejpam-6593	288	7	=	=	PUNCT
ejpam-6593	288	8	xn	xn	PUNCT
ejpam-6593	288	9	=	=	SYM
ejpam-6593	288	10	1	1	NUM
ejpam-6593	289	1	+	+	CCONJ
ejpam-6593	289	2	4n	4n	NOUN
ejpam-6593	289	3	,	,	PUNCT
ejpam-6593	289	4	then	then	ADV
ejpam-6593	289	5	we	we	PRON
ejpam-6593	289	6	have	have	VERB
ejpam-6593	289	7	x	x	X
ejpam-6593	289	8	=	=	SYM
ejpam-6593	289	9	1	1	NUM
ejpam-6593	289	10	,	,	PUNCT
ejpam-6593	289	11	and	and	CCONJ
ejpam-6593	289	12	tables	table	NOUN
ejpam-6593	289	13	2	2	NUM
ejpam-6593	289	14	and	and	CCONJ
ejpam-6593	289	15	3	3	NUM
ejpam-6593	289	16	present	present	VERB
ejpam-6593	289	17	some	some	DET
ejpam-6593	289	18	solutions	solution	NOUN
ejpam-6593	289	19	where	where	SCONJ
ejpam-6593	289	20	z	z	NOUN
ejpam-6593	289	21	≡	≡	PROPN
ejpam-6593	289	22	2	2	NUM
ejpam-6593	289	23	(	(	PUNCT
ejpam-6593	289	24	mod	mod	NOUN
ejpam-6593	289	25	5	5	NUM
ejpam-6593	289	26	)	)	PUNCT
ejpam-6593	289	27	or	or	CCONJ
ejpam-6593	289	28	z	z	PROPN
ejpam-6593	289	29	≡	≡	PROPN
ejpam-6593	289	30	3	3	NUM
ejpam-6593	289	31	(	(	PUNCT
ejpam-6593	289	32	mod	mod	NOUN
ejpam-6593	289	33	5	5	NUM
ejpam-6593	289	34	)	)	PUNCT
ejpam-6593	289	35	.	.	PUNCT
ejpam-6593	290	1	for	for	ADP
ejpam-6593	290	2	z	z	PROPN
ejpam-6593	290	3	≡	≡	PROPN
ejpam-6593	290	4	2	2	NUM
ejpam-6593	290	5	(	(	PUNCT
ejpam-6593	290	6	mod	mod	NOUN
ejpam-6593	290	7	5	5	NUM
ejpam-6593	290	8	)	)	PUNCT
ejpam-6593	290	9	,	,	PUNCT
ejpam-6593	290	10	we	we	PRON
ejpam-6593	290	11	have	have	VERB
ejpam-6593	290	12	the	the	DET
ejpam-6593	290	13	following	follow	VERB
ejpam-6593	290	14	:	:	PUNCT
ejpam-6593	290	15	z(0,1	z(0,1	X
ejpam-6593	290	16	)	)	PUNCT
ejpam-6593	290	17	=	=	SYM
ejpam-6593	290	18	7	7	NUM
ejpam-6593	290	19	,	,	PUNCT
ejpam-6593	290	20	z(1,1	z(1,1	NUM
ejpam-6593	290	21	)	)	PUNCT
ejpam-6593	290	22	=	=	SYM
ejpam-6593	290	23	12	12	NUM
ejpam-6593	290	24	,	,	PUNCT
ejpam-6593	290	25	k(0,1	k(0,1	NOUN
ejpam-6593	290	26	)	)	PUNCT
ejpam-6593	290	27	=	=	SYM
ejpam-6593	290	28	9	9	NUM
ejpam-6593	290	29	,	,	PUNCT
ejpam-6593	290	30	k(1,1	k(1,1	NOUN
ejpam-6593	290	31	)	)	PUNCT
ejpam-6593	290	32	=	=	SYM
ejpam-6593	290	33	28	28	NUM
ejpam-6593	290	34	,	,	PUNCT
ejpam-6593	290	35	α1	α1	PROPN
ejpam-6593	290	36	=	=	SYM
ejpam-6593	290	37	19	19	NUM
ejpam-6593	290	38	.	.	PUNCT
ejpam-6593	291	1	for	for	ADP
ejpam-6593	291	2	z	z	PROPN
ejpam-6593	291	3	≡	≡	PROPN
ejpam-6593	291	4	3	3	NUM
ejpam-6593	291	5	(	(	PUNCT
ejpam-6593	291	6	mod	mod	NOUN
ejpam-6593	291	7	5	5	NUM
ejpam-6593	291	8	)	)	PUNCT
ejpam-6593	291	9	,	,	PUNCT
ejpam-6593	291	10	we	we	PRON
ejpam-6593	291	11	have	have	VERB
ejpam-6593	291	12	z(0,1	z(0,1	NOUN
ejpam-6593	291	13	)	)	PUNCT
ejpam-6593	291	14	=	=	SYM
ejpam-6593	292	1	3	3	NUM
ejpam-6593	292	2	,	,	PUNCT
ejpam-6593	292	3	z(1,1	z(1,1	NUM
ejpam-6593	292	4	)	)	PUNCT
ejpam-6593	292	5	=	=	SYM
ejpam-6593	292	6	8	8	NUM
ejpam-6593	292	7	,	,	PUNCT
ejpam-6593	292	8	k(0,1	k(0,1	NOUN
ejpam-6593	292	9	)	)	PUNCT
ejpam-6593	292	10	=	=	SYM
ejpam-6593	292	11	1	1	NUM
ejpam-6593	292	12	,	,	PUNCT
ejpam-6593	292	13	k(1,1	k(1,1	NOUN
ejpam-6593	292	14	)	)	PUNCT
ejpam-6593	292	15	=	=	SYM
ejpam-6593	292	16	12	12	NUM
ejpam-6593	292	17	,	,	PUNCT
ejpam-6593	292	18	α1	α1	PROPN
ejpam-6593	292	19	=	=	SYM
ejpam-6593	292	20	11	11	NUM
ejpam-6593	292	21	.	.	PUNCT
ejpam-6593	293	1	m	m	VERB
ejpam-6593	294	1	k	k	NOUN
ejpam-6593	294	2	z	z	NOUN
ejpam-6593	294	3	equation	equation	NOUN
ejpam-6593	294	4	solution	solution	NOUN
ejpam-6593	294	5	(	(	PUNCT
ejpam-6593	294	6	p	p	X
ejpam-6593	294	7	,	,	PUNCT
ejpam-6593	294	8	k	k	NOUN
ejpam-6593	294	9	,	,	PUNCT
ejpam-6593	294	10	x	x	X
ejpam-6593	294	11	,	,	PUNCT
ejpam-6593	294	12	y	y	PROPN
ejpam-6593	294	13	,	,	PUNCT
ejpam-6593	294	14	z	z	NOUN
ejpam-6593	294	15	)	)	PUNCT
ejpam-6593	294	16	9	9	NUM
ejpam-6593	294	17	7	7	NUM
ejpam-6593	294	18	2	2	NUM
ejpam-6593	294	19	+	+	CCONJ
ejpam-6593	294	20	(	(	PUNCT
ejpam-6593	294	21	2	2	NUM
ejpam-6593	294	22	+	+	SYM
ejpam-6593	294	23	5(9	5(9	NUM
ejpam-6593	294	24	)	)	PUNCT
ejpam-6593	294	25	)	)	PUNCT
ejpam-6593	295	1	=	=	SYM
ejpam-6593	295	2	72	72	NUM
ejpam-6593	295	3	(	(	PUNCT
ejpam-6593	295	4	2	2	NUM
ejpam-6593	295	5	,	,	PUNCT
ejpam-6593	295	6	9	9	NUM
ejpam-6593	295	7	,	,	PUNCT
ejpam-6593	295	8	1	1	NUM
ejpam-6593	295	9	,	,	PUNCT
ejpam-6593	295	10	1	1	NUM
ejpam-6593	295	11	,	,	PUNCT
ejpam-6593	295	12	7	7	NUM
ejpam-6593	295	13	)	)	PUNCT
ejpam-6593	295	14	1	1	NUM
ejpam-6593	295	15	28	28	NUM
ejpam-6593	295	16	12	12	NUM
ejpam-6593	295	17	2	2	NUM
ejpam-6593	295	18	+	+	CCONJ
ejpam-6593	295	19	(	(	PUNCT
ejpam-6593	295	20	2	2	NUM
ejpam-6593	295	21	+	+	NUM
ejpam-6593	295	22	5(28	5(28	NUM
ejpam-6593	295	23	)	)	PUNCT
ejpam-6593	295	24	)	)	PUNCT
ejpam-6593	296	1	=	=	SYM
ejpam-6593	296	2	122	122	NUM
ejpam-6593	296	3	(	(	PUNCT
ejpam-6593	296	4	2	2	NUM
ejpam-6593	296	5	,	,	PUNCT
ejpam-6593	296	6	28	28	NUM
ejpam-6593	296	7	,	,	PUNCT
ejpam-6593	296	8	1	1	NUM
ejpam-6593	296	9	,	,	PUNCT
ejpam-6593	296	10	1	1	NUM
ejpam-6593	296	11	,	,	PUNCT
ejpam-6593	296	12	12	12	NUM
ejpam-6593	296	13	)	)	PUNCT
ejpam-6593	296	14	2	2	NUM
ejpam-6593	296	15	57	57	NUM
ejpam-6593	296	16	17	17	NUM
ejpam-6593	296	17	2	2	NUM
ejpam-6593	296	18	+	+	CCONJ
ejpam-6593	296	19	(	(	PUNCT
ejpam-6593	296	20	2	2	NUM
ejpam-6593	296	21	+	+	NUM
ejpam-6593	296	22	5(57	5(57	NUM
ejpam-6593	296	23	)	)	PUNCT
ejpam-6593	296	24	)	)	PUNCT
ejpam-6593	297	1	=	=	SYM
ejpam-6593	297	2	172	172	NUM
ejpam-6593	297	3	(	(	PUNCT
ejpam-6593	297	4	2	2	NUM
ejpam-6593	297	5	,	,	PUNCT
ejpam-6593	297	6	57	57	NUM
ejpam-6593	297	7	,	,	PUNCT
ejpam-6593	297	8	1	1	NUM
ejpam-6593	297	9	,	,	PUNCT
ejpam-6593	297	10	1	1	NUM
ejpam-6593	297	11	,	,	PUNCT
ejpam-6593	297	12	17	17	NUM
ejpam-6593	297	13	)	)	PUNCT
ejpam-6593	297	14	3	3	NUM
ejpam-6593	297	15	96	96	NUM
ejpam-6593	297	16	22	22	NUM
ejpam-6593	297	17	2	2	NUM
ejpam-6593	297	18	+	+	CCONJ
ejpam-6593	297	19	(	(	PUNCT
ejpam-6593	297	20	2	2	NUM
ejpam-6593	297	21	+	+	SYM
ejpam-6593	297	22	5(96	5(96	NUM
ejpam-6593	297	23	)	)	PUNCT
ejpam-6593	297	24	)	)	PUNCT
ejpam-6593	298	1	=	=	SYM
ejpam-6593	298	2	222	222	NUM
ejpam-6593	298	3	(	(	PUNCT
ejpam-6593	298	4	2	2	NUM
ejpam-6593	298	5	,	,	PUNCT
ejpam-6593	298	6	96	96	NUM
ejpam-6593	298	7	,	,	PUNCT
ejpam-6593	298	8	1	1	NUM
ejpam-6593	298	9	,	,	PUNCT
ejpam-6593	298	10	1	1	NUM
ejpam-6593	298	11	,	,	PUNCT
ejpam-6593	298	12	22	22	NUM
ejpam-6593	298	13	)	)	PUNCT
ejpam-6593	298	14	4	4	NUM
ejpam-6593	298	15	145	145	NUM
ejpam-6593	298	16	27	27	NUM
ejpam-6593	298	17	2	2	NUM
ejpam-6593	298	18	+	+	CCONJ
ejpam-6593	298	19	(	(	PUNCT
ejpam-6593	298	20	2	2	NUM
ejpam-6593	298	21	+	+	SYM
ejpam-6593	298	22	5(145	5(145	NUM
ejpam-6593	298	23	)	)	PUNCT
ejpam-6593	298	24	)	)	PUNCT
ejpam-6593	299	1	=	=	SYM
ejpam-6593	299	2	272	272	NUM
ejpam-6593	299	3	(	(	PUNCT
ejpam-6593	299	4	2	2	NUM
ejpam-6593	299	5	,	,	PUNCT
ejpam-6593	299	6	145	145	NUM
ejpam-6593	299	7	,	,	PUNCT
ejpam-6593	299	8	1	1	NUM
ejpam-6593	299	9	,	,	PUNCT
ejpam-6593	299	10	1	1	NUM
ejpam-6593	299	11	,	,	PUNCT
ejpam-6593	299	12	27	27	NUM
ejpam-6593	299	13	)	)	PUNCT
ejpam-6593	299	14	table	table	NOUN
ejpam-6593	299	15	2	2	NUM
ejpam-6593	299	16	:	:	PUNCT
ejpam-6593	299	17	some	some	DET
ejpam-6593	299	18	solutions	solution	NOUN
ejpam-6593	299	19	of	of	ADP
ejpam-6593	299	20	(	(	PUNCT
ejpam-6593	299	21	5	5	NUM
ejpam-6593	299	22	)	)	PUNCT
ejpam-6593	299	23	with	with	ADP
ejpam-6593	299	24	x	x	SYM
ejpam-6593	300	1	=	=	SYM
ejpam-6593	300	2	1	1	NUM
ejpam-6593	300	3	,	,	PUNCT
ejpam-6593	300	4	y	y	NOUN
ejpam-6593	300	5	=	=	SYM
ejpam-6593	300	6	1	1	NUM
ejpam-6593	300	7	and	and	CCONJ
ejpam-6593	300	8	z	z	PROPN
ejpam-6593	300	9	≡	≡	PROPN
ejpam-6593	300	10	2	2	NUM
ejpam-6593	300	11	(	(	PUNCT
ejpam-6593	300	12	mod	mod	NOUN
ejpam-6593	300	13	5	5	NUM
ejpam-6593	300	14	)	)	PUNCT
ejpam-6593	300	15	m	m	VERB
ejpam-6593	300	16	k	k	NOUN
ejpam-6593	300	17	z	z	NOUN
ejpam-6593	300	18	equation	equation	NOUN
ejpam-6593	300	19	solution	solution	NOUN
ejpam-6593	300	20	(	(	PUNCT
ejpam-6593	300	21	p	p	X
ejpam-6593	300	22	,	,	PUNCT
ejpam-6593	300	23	k	k	NOUN
ejpam-6593	300	24	,	,	PUNCT
ejpam-6593	300	25	x	x	X
ejpam-6593	300	26	,	,	PUNCT
ejpam-6593	300	27	y	y	PROPN
ejpam-6593	300	28	,	,	PUNCT
ejpam-6593	300	29	z	z	NOUN
ejpam-6593	300	30	)	)	PUNCT
ejpam-6593	300	31	1	1	NUM
ejpam-6593	300	32	3	3	NUM
ejpam-6593	300	33	2	2	NUM
ejpam-6593	300	34	+	+	CCONJ
ejpam-6593	300	35	(	(	PUNCT
ejpam-6593	300	36	2	2	NUM
ejpam-6593	300	37	+	+	NUM
ejpam-6593	300	38	5(1	5(1	NUM
ejpam-6593	300	39	)	)	PUNCT
ejpam-6593	300	40	)	)	PUNCT
ejpam-6593	301	1	=	=	SYM
ejpam-6593	301	2	32	32	NUM
ejpam-6593	301	3	(	(	PUNCT
ejpam-6593	301	4	2	2	NUM
ejpam-6593	301	5	,	,	PUNCT
ejpam-6593	301	6	1	1	NUM
ejpam-6593	301	7	,	,	PUNCT
ejpam-6593	301	8	1	1	NUM
ejpam-6593	301	9	,	,	PUNCT
ejpam-6593	301	10	1	1	NUM
ejpam-6593	301	11	,	,	PUNCT
ejpam-6593	301	12	3	3	X
ejpam-6593	301	13	)	)	PUNCT
ejpam-6593	301	14	1	1	NUM
ejpam-6593	301	15	12	12	NUM
ejpam-6593	301	16	8	8	NUM
ejpam-6593	301	17	2	2	NUM
ejpam-6593	301	18	+	+	CCONJ
ejpam-6593	301	19	(	(	PUNCT
ejpam-6593	301	20	2	2	NUM
ejpam-6593	301	21	+	+	NUM
ejpam-6593	301	22	5(12	5(12	NUM
ejpam-6593	301	23	)	)	PUNCT
ejpam-6593	301	24	)	)	PUNCT
ejpam-6593	302	1	=	=	SYM
ejpam-6593	302	2	82	82	NUM
ejpam-6593	302	3	(	(	PUNCT
ejpam-6593	302	4	2	2	NUM
ejpam-6593	302	5	,	,	PUNCT
ejpam-6593	302	6	12	12	NUM
ejpam-6593	302	7	,	,	PUNCT
ejpam-6593	302	8	1	1	NUM
ejpam-6593	302	9	,	,	PUNCT
ejpam-6593	302	10	1	1	NUM
ejpam-6593	302	11	,	,	PUNCT
ejpam-6593	302	12	8)	8)	NUM
ejpam-6593	302	13	2	2	NUM
ejpam-6593	302	14	33	33	NUM
ejpam-6593	302	15	13	13	NUM
ejpam-6593	302	16	2	2	NUM
ejpam-6593	302	17	+	+	CCONJ
ejpam-6593	302	18	(	(	PUNCT
ejpam-6593	302	19	2	2	NUM
ejpam-6593	302	20	+	+	NUM
ejpam-6593	302	21	5(33	5(33	NUM
ejpam-6593	302	22	)	)	PUNCT
ejpam-6593	302	23	)	)	PUNCT
ejpam-6593	303	1	=	=	SYM
ejpam-6593	303	2	132	132	NUM
ejpam-6593	303	3	(	(	PUNCT
ejpam-6593	303	4	2	2	NUM
ejpam-6593	303	5	,	,	PUNCT
ejpam-6593	303	6	33	33	NUM
ejpam-6593	303	7	,	,	PUNCT
ejpam-6593	303	8	1	1	NUM
ejpam-6593	303	9	,	,	PUNCT
ejpam-6593	303	10	1	1	NUM
ejpam-6593	303	11	,	,	PUNCT
ejpam-6593	303	12	13	13	NUM
ejpam-6593	303	13	)	)	PUNCT
ejpam-6593	303	14	3	3	NUM
ejpam-6593	303	15	64	64	NUM
ejpam-6593	303	16	18	18	NUM
ejpam-6593	303	17	2	2	NUM
ejpam-6593	303	18	+	+	CCONJ
ejpam-6593	303	19	(	(	PUNCT
ejpam-6593	303	20	2	2	NUM
ejpam-6593	303	21	+	+	NUM
ejpam-6593	303	22	5(64	5(64	NUM
ejpam-6593	303	23	)	)	PUNCT
ejpam-6593	303	24	)	)	PUNCT
ejpam-6593	304	1	=	=	SYM
ejpam-6593	304	2	182	182	NUM
ejpam-6593	304	3	(	(	PUNCT
ejpam-6593	304	4	2	2	NUM
ejpam-6593	304	5	,	,	PUNCT
ejpam-6593	304	6	64	64	NUM
ejpam-6593	304	7	,	,	PUNCT
ejpam-6593	304	8	1	1	NUM
ejpam-6593	304	9	,	,	PUNCT
ejpam-6593	304	10	1	1	NUM
ejpam-6593	304	11	,	,	PUNCT
ejpam-6593	304	12	18	18	NUM
ejpam-6593	304	13	)	)	PUNCT
ejpam-6593	304	14	4	4	NUM
ejpam-6593	304	15	105	105	NUM
ejpam-6593	304	16	23	23	NUM
ejpam-6593	304	17	2	2	NUM
ejpam-6593	304	18	+	+	CCONJ
ejpam-6593	304	19	(	(	PUNCT
ejpam-6593	304	20	2	2	NUM
ejpam-6593	304	21	+	+	NUM
ejpam-6593	304	22	5(105	5(105	NUM
ejpam-6593	304	23	)	)	PUNCT
ejpam-6593	304	24	)	)	PUNCT
ejpam-6593	305	1	=	=	SYM
ejpam-6593	305	2	232	232	NUM
ejpam-6593	305	3	(	(	PUNCT
ejpam-6593	305	4	2	2	NUM
ejpam-6593	305	5	,	,	PUNCT
ejpam-6593	305	6	105	105	NUM
ejpam-6593	305	7	,	,	PUNCT
ejpam-6593	305	8	1	1	NUM
ejpam-6593	305	9	,	,	PUNCT
ejpam-6593	305	10	1	1	NUM
ejpam-6593	305	11	,	,	PUNCT
ejpam-6593	305	12	23	23	NUM
ejpam-6593	305	13	)	)	PUNCT
ejpam-6593	305	14	table	table	NOUN
ejpam-6593	305	15	3	3	NUM
ejpam-6593	305	16	:	:	PUNCT
ejpam-6593	305	17	some	some	DET
ejpam-6593	305	18	solutions	solution	NOUN
ejpam-6593	305	19	of	of	ADP
ejpam-6593	305	20	(	(	PUNCT
ejpam-6593	305	21	5	5	NUM
ejpam-6593	305	22	)	)	PUNCT
ejpam-6593	305	23	with	with	ADP
ejpam-6593	305	24	x	x	SYM
ejpam-6593	306	1	=	=	SYM
ejpam-6593	306	2	1	1	NUM
ejpam-6593	306	3	,	,	PUNCT
ejpam-6593	306	4	y	y	NOUN
ejpam-6593	306	5	=	=	SYM
ejpam-6593	306	6	1	1	NUM
ejpam-6593	306	7	and	and	CCONJ
ejpam-6593	306	8	z	z	PROPN
ejpam-6593	306	9	≡	≡	PROPN
ejpam-6593	306	10	3	3	NUM
ejpam-6593	306	11	(	(	PUNCT
ejpam-6593	306	12	mod	mod	NOUN
ejpam-6593	306	13	5	5	NUM
ejpam-6593	306	14	)	)	PUNCT
ejpam-6593	306	15	if	if	SCONJ
ejpam-6593	306	16	n	n	NOUN
ejpam-6593	306	17	=	=	SYM
ejpam-6593	306	18	1	1	NUM
ejpam-6593	306	19	in	in	ADP
ejpam-6593	306	20	x	x	X
ejpam-6593	306	21	=	=	PUNCT
ejpam-6593	306	22	xn	xn	PUNCT
ejpam-6593	307	1	=	=	SYM
ejpam-6593	307	2	1	1	NUM
ejpam-6593	307	3	+	+	CCONJ
ejpam-6593	307	4	4n	4n	NOUN
ejpam-6593	307	5	,	,	PUNCT
ejpam-6593	307	6	we	we	PRON
ejpam-6593	307	7	get	get	VERB
ejpam-6593	307	8	x	x	X
ejpam-6593	307	9	=	=	SYM
ejpam-6593	307	10	5	5	NUM
ejpam-6593	307	11	,	,	PUNCT
ejpam-6593	307	12	and	and	CCONJ
ejpam-6593	307	13	tables	table	NOUN
ejpam-6593	307	14	4	4	NUM
ejpam-6593	307	15	and	and	CCONJ
ejpam-6593	307	16	5	5	NUM
ejpam-6593	307	17	present	present	VERB
ejpam-6593	307	18	some	some	DET
ejpam-6593	307	19	solutions	solution	NOUN
ejpam-6593	307	20	where	where	SCONJ
ejpam-6593	307	21	z	z	NOUN
ejpam-6593	307	22	≡	≡	PROPN
ejpam-6593	307	23	2	2	NUM
ejpam-6593	307	24	(	(	PUNCT
ejpam-6593	307	25	mod	mod	NOUN
ejpam-6593	307	26	5	5	NUM
ejpam-6593	307	27	)	)	PUNCT
ejpam-6593	307	28	or	or	CCONJ
ejpam-6593	307	29	z	z	PROPN
ejpam-6593	307	30	≡	≡	PROPN
ejpam-6593	307	31	3	3	NUM
ejpam-6593	307	32	(	(	PUNCT
ejpam-6593	307	33	mod	mod	NOUN
ejpam-6593	307	34	5	5	NUM
ejpam-6593	307	35	)	)	PUNCT
ejpam-6593	307	36	.	.	PUNCT
ejpam-6593	308	1	for	for	ADP
ejpam-6593	308	2	z	z	PROPN
ejpam-6593	308	3	≡	≡	PROPN
ejpam-6593	308	4	2	2	NUM
ejpam-6593	308	5	(	(	PUNCT
ejpam-6593	308	6	mod	mod	NOUN
ejpam-6593	308	7	5	5	NUM
ejpam-6593	308	8	)	)	PUNCT
ejpam-6593	308	9	,	,	PUNCT
ejpam-6593	308	10	we	we	PRON
ejpam-6593	308	11	have	have	VERB
ejpam-6593	308	12	z(0,5	z(0,5	NUM
ejpam-6593	308	13	)	)	PUNCT
ejpam-6593	308	14	=	=	SYM
ejpam-6593	308	15	7	7	NUM
ejpam-6593	308	16	,	,	PUNCT
ejpam-6593	308	17	z(1,5	z(1,5	PROPN
ejpam-6593	308	18	)	)	PUNCT
ejpam-6593	308	19	=	=	SYM
ejpam-6593	308	20	12	12	NUM
ejpam-6593	308	21	,	,	PUNCT
ejpam-6593	308	22	k(0,5	k(0,5	NOUN
ejpam-6593	308	23	)	)	PUNCT
ejpam-6593	308	24	=	=	SYM
ejpam-6593	309	1	3	3	NUM
ejpam-6593	309	2	,	,	PUNCT
ejpam-6593	309	3	k(1,5	k(1,5	NOUN
ejpam-6593	309	4	)	)	PUNCT
ejpam-6593	309	5	=	=	SYM
ejpam-6593	309	6	22	22	NUM
ejpam-6593	309	7	,	,	PUNCT
ejpam-6593	309	8	and	and	CCONJ
ejpam-6593	309	9	α5	α5	NOUN
ejpam-6593	309	10	=	=	SYM
ejpam-6593	309	11	19	19	NUM
ejpam-6593	309	12	.	.	PUNCT
ejpam-6593	310	1	for	for	ADP
ejpam-6593	310	2	z	z	PROPN
ejpam-6593	310	3	≡	≡	PROPN
ejpam-6593	310	4	3	3	NUM
ejpam-6593	310	5	(	(	PUNCT
ejpam-6593	310	6	mod	mod	NOUN
ejpam-6593	310	7	5	5	NUM
ejpam-6593	310	8	)	)	PUNCT
ejpam-6593	310	9	,	,	PUNCT
ejpam-6593	310	10	we	we	PRON
ejpam-6593	310	11	have	have	VERB
ejpam-6593	310	12	z(0,5	z(0,5	NUM
ejpam-6593	310	13	)	)	PUNCT
ejpam-6593	310	14	=	=	SYM
ejpam-6593	310	15	8	8	NUM
ejpam-6593	310	16	,	,	PUNCT
ejpam-6593	310	17	z(1,5	z(1,5	PROPN
ejpam-6593	310	18	)	)	PUNCT
ejpam-6593	310	19	=	=	SYM
ejpam-6593	310	20	13	13	NUM
ejpam-6593	310	21	,	,	PUNCT
ejpam-6593	310	22	k(0,5	k(0,5	NOUN
ejpam-6593	310	23	)	)	PUNCT
ejpam-6593	310	24	=	=	SYM
ejpam-6593	310	25	6	6	NUM
ejpam-6593	310	26	,	,	PUNCT
ejpam-6593	310	27	k(1,5	k(1,5	NOUN
ejpam-6593	310	28	)	)	PUNCT
ejpam-6593	310	29	=	=	NUM
ejpam-6593	310	30	27	27	NUM
ejpam-6593	310	31	,	,	PUNCT
ejpam-6593	310	32	and	and	CCONJ
ejpam-6593	310	33	α5	α5	NOUN
ejpam-6593	310	34	=	=	SYM
ejpam-6593	310	35	21	21	NUM
ejpam-6593	310	36	.	.	PUNCT
ejpam-6593	310	37	m.	m.	PROPN
ejpam-6593	310	38	c.	c.	PROPN
ejpam-6593	310	39	avenilla	avenilla	PROPN
ejpam-6593	310	40	,	,	PUNCT
ejpam-6593	310	41	j.	j.	PROPN
ejpam-6593	310	42	b.	b.	PROPN
ejpam-6593	310	43	bacani	bacani	PROPN
ejpam-6593	310	44	/	/	SYM
ejpam-6593	310	45	eur	eur	PROPN
ejpam-6593	310	46	.	.	PUNCT
ejpam-6593	311	1	j.	j.	PROPN
ejpam-6593	311	2	pure	pure	PROPN
ejpam-6593	311	3	appl	appl	PROPN
ejpam-6593	311	4	.	.	PROPN
ejpam-6593	311	5	math	math	PROPN
ejpam-6593	311	6	,	,	PUNCT
ejpam-6593	311	7	18	18	NUM
ejpam-6593	311	8	(	(	PUNCT
ejpam-6593	311	9	3	3	NUM
ejpam-6593	311	10	)	)	PUNCT
ejpam-6593	311	11	(	(	PUNCT
ejpam-6593	311	12	2025	2025	NUM
ejpam-6593	311	13	)	)	PUNCT
ejpam-6593	311	14	,	,	PUNCT
ejpam-6593	311	15	6593	6593	NUM
ejpam-6593	311	16	10	10	NUM
ejpam-6593	311	17	of	of	ADP
ejpam-6593	311	18	24	24	NUM
ejpam-6593	311	19	m	m	PROPN
ejpam-6593	311	20	k	k	NOUN
ejpam-6593	311	21	z	z	NOUN
ejpam-6593	311	22	equation	equation	NOUN
ejpam-6593	311	23	solution	solution	NOUN
ejpam-6593	311	24	(	(	PUNCT
ejpam-6593	311	25	p	p	X
ejpam-6593	311	26	,	,	PUNCT
ejpam-6593	311	27	k	k	NOUN
ejpam-6593	311	28	,	,	PUNCT
ejpam-6593	311	29	x	x	X
ejpam-6593	311	30	,	,	PUNCT
ejpam-6593	311	31	y	y	PROPN
ejpam-6593	311	32	,	,	PUNCT
ejpam-6593	311	33	z	z	NOUN
ejpam-6593	311	34	)	)	PUNCT
ejpam-6593	311	35	3	3	NUM
ejpam-6593	311	36	7	7	NUM
ejpam-6593	311	37	25	25	NUM
ejpam-6593	311	38	+	+	CCONJ
ejpam-6593	311	39	(	(	PUNCT
ejpam-6593	311	40	2	2	NUM
ejpam-6593	311	41	+	+	NUM
ejpam-6593	311	42	5(3	5(3	NUM
ejpam-6593	311	43	)	)	PUNCT
ejpam-6593	311	44	)	)	PUNCT
ejpam-6593	312	1	=	=	SYM
ejpam-6593	312	2	72	72	NUM
ejpam-6593	312	3	(	(	PUNCT
ejpam-6593	312	4	2	2	NUM
ejpam-6593	312	5	,	,	PUNCT
ejpam-6593	312	6	3	3	NUM
ejpam-6593	312	7	,	,	PUNCT
ejpam-6593	312	8	5	5	NUM
ejpam-6593	312	9	,	,	PUNCT
ejpam-6593	312	10	1	1	NUM
ejpam-6593	312	11	,	,	PUNCT
ejpam-6593	312	12	7	7	NUM
ejpam-6593	312	13	)	)	SYM
ejpam-6593	312	14	1	1	NUM
ejpam-6593	312	15	22	22	NUM
ejpam-6593	312	16	12	12	NUM
ejpam-6593	312	17	25	25	NUM
ejpam-6593	312	18	+	+	CCONJ
ejpam-6593	312	19	(	(	PUNCT
ejpam-6593	312	20	2	2	NUM
ejpam-6593	312	21	+	+	SYM
ejpam-6593	312	22	5(22	5(22	NUM
ejpam-6593	312	23	)	)	PUNCT
ejpam-6593	312	24	)	)	PUNCT
ejpam-6593	313	1	=	=	SYM
ejpam-6593	313	2	122	122	NUM
ejpam-6593	313	3	(	(	PUNCT
ejpam-6593	313	4	2	2	NUM
ejpam-6593	313	5	,	,	PUNCT
ejpam-6593	313	6	22	22	NUM
ejpam-6593	313	7	,	,	PUNCT
ejpam-6593	313	8	5	5	NUM
ejpam-6593	313	9	,	,	PUNCT
ejpam-6593	313	10	1	1	NUM
ejpam-6593	313	11	,	,	PUNCT
ejpam-6593	313	12	12	12	NUM
ejpam-6593	313	13	)	)	PUNCT
ejpam-6593	313	14	2	2	NUM
ejpam-6593	313	15	51	51	NUM
ejpam-6593	313	16	17	17	NUM
ejpam-6593	313	17	25	25	NUM
ejpam-6593	313	18	+	+	CCONJ
ejpam-6593	313	19	(	(	PUNCT
ejpam-6593	313	20	2	2	NUM
ejpam-6593	313	21	+	+	NUM
ejpam-6593	313	22	5(51	5(51	NUM
ejpam-6593	313	23	)	)	PUNCT
ejpam-6593	313	24	)	)	PUNCT
ejpam-6593	314	1	=	=	SYM
ejpam-6593	314	2	172	172	NUM
ejpam-6593	314	3	(	(	PUNCT
ejpam-6593	314	4	2	2	NUM
ejpam-6593	314	5	,	,	PUNCT
ejpam-6593	314	6	51	51	NUM
ejpam-6593	314	7	,	,	PUNCT
ejpam-6593	314	8	5	5	NUM
ejpam-6593	314	9	,	,	PUNCT
ejpam-6593	314	10	1	1	NUM
ejpam-6593	314	11	,	,	PUNCT
ejpam-6593	314	12	17	17	NUM
ejpam-6593	314	13	)	)	PUNCT
ejpam-6593	314	14	3	3	NUM
ejpam-6593	314	15	90	90	NUM
ejpam-6593	314	16	22	22	NUM
ejpam-6593	314	17	25	25	NUM
ejpam-6593	314	18	+	+	CCONJ
ejpam-6593	314	19	(	(	PUNCT
ejpam-6593	314	20	2	2	NUM
ejpam-6593	314	21	+	+	SYM
ejpam-6593	314	22	5(90	5(90	NUM
ejpam-6593	314	23	)	)	PUNCT
ejpam-6593	314	24	)	)	PUNCT
ejpam-6593	315	1	=	=	SYM
ejpam-6593	315	2	222	222	NUM
ejpam-6593	315	3	(	(	PUNCT
ejpam-6593	315	4	2	2	NUM
ejpam-6593	315	5	,	,	PUNCT
ejpam-6593	315	6	90	90	NUM
ejpam-6593	315	7	,	,	PUNCT
ejpam-6593	315	8	5	5	NUM
ejpam-6593	315	9	,	,	PUNCT
ejpam-6593	315	10	1	1	NUM
ejpam-6593	315	11	,	,	PUNCT
ejpam-6593	315	12	22	22	NUM
ejpam-6593	315	13	)	)	PUNCT
ejpam-6593	315	14	4	4	NUM
ejpam-6593	315	15	139	139	NUM
ejpam-6593	315	16	27	27	NUM
ejpam-6593	315	17	25	25	NUM
ejpam-6593	315	18	+	+	CCONJ
ejpam-6593	315	19	(	(	PUNCT
ejpam-6593	315	20	2	2	NUM
ejpam-6593	315	21	+	+	NUM
ejpam-6593	315	22	5(139	5(139	NUM
ejpam-6593	315	23	)	)	PUNCT
ejpam-6593	315	24	)	)	PUNCT
ejpam-6593	316	1	=	=	SYM
ejpam-6593	316	2	272	272	NUM
ejpam-6593	316	3	(	(	PUNCT
ejpam-6593	316	4	2	2	NUM
ejpam-6593	316	5	,	,	PUNCT
ejpam-6593	316	6	139	139	NUM
ejpam-6593	316	7	,	,	PUNCT
ejpam-6593	316	8	5	5	NUM
ejpam-6593	316	9	,	,	PUNCT
ejpam-6593	316	10	1	1	NUM
ejpam-6593	316	11	,	,	PUNCT
ejpam-6593	316	12	27	27	NUM
ejpam-6593	316	13	)	)	PUNCT
ejpam-6593	316	14	table	table	NOUN
ejpam-6593	316	15	4	4	NUM
ejpam-6593	316	16	:	:	PUNCT
ejpam-6593	316	17	some	some	DET
ejpam-6593	316	18	solutions	solution	NOUN
ejpam-6593	316	19	of	of	ADP
ejpam-6593	316	20	(	(	PUNCT
ejpam-6593	316	21	5	5	NUM
ejpam-6593	316	22	)	)	PUNCT
ejpam-6593	316	23	with	with	ADP
ejpam-6593	316	24	x	x	SYM
ejpam-6593	316	25	=	=	SYM
ejpam-6593	316	26	5	5	NUM
ejpam-6593	316	27	,	,	PUNCT
ejpam-6593	316	28	y	y	NOUN
ejpam-6593	316	29	=	=	SYM
ejpam-6593	316	30	1	1	NUM
ejpam-6593	316	31	and	and	CCONJ
ejpam-6593	316	32	z	z	PROPN
ejpam-6593	316	33	≡	≡	PROPN
ejpam-6593	316	34	2	2	NUM
ejpam-6593	316	35	(	(	PUNCT
ejpam-6593	316	36	mod	mod	NOUN
ejpam-6593	316	37	5	5	NUM
ejpam-6593	316	38	)	)	PUNCT
ejpam-6593	316	39	m	m	VERB
ejpam-6593	316	40	k	k	NOUN
ejpam-6593	316	41	z	z	NOUN
ejpam-6593	316	42	equation	equation	NOUN
ejpam-6593	316	43	solution	solution	NOUN
ejpam-6593	316	44	(	(	PUNCT
ejpam-6593	316	45	p	p	X
ejpam-6593	316	46	,	,	PUNCT
ejpam-6593	316	47	k	k	NOUN
ejpam-6593	316	48	,	,	PUNCT
ejpam-6593	316	49	x	x	X
ejpam-6593	316	50	,	,	PUNCT
ejpam-6593	316	51	y	y	PROPN
ejpam-6593	316	52	,	,	PUNCT
ejpam-6593	316	53	z	z	NOUN
ejpam-6593	316	54	)	)	PUNCT
ejpam-6593	316	55	6	6	NUM
ejpam-6593	316	56	8	8	NUM
ejpam-6593	316	57	25	25	NUM
ejpam-6593	316	58	+	+	CCONJ
ejpam-6593	316	59	(	(	PUNCT
ejpam-6593	316	60	2	2	NUM
ejpam-6593	316	61	+	+	NUM
ejpam-6593	316	62	5(6	5(6	NUM
ejpam-6593	316	63	)	)	PUNCT
ejpam-6593	316	64	)	)	PUNCT
ejpam-6593	317	1	=	=	SYM
ejpam-6593	317	2	82	82	NUM
ejpam-6593	317	3	(	(	PUNCT
ejpam-6593	317	4	2	2	NUM
ejpam-6593	317	5	,	,	PUNCT
ejpam-6593	317	6	6	6	NUM
ejpam-6593	317	7	,	,	PUNCT
ejpam-6593	317	8	5	5	NUM
ejpam-6593	317	9	,	,	PUNCT
ejpam-6593	317	10	1	1	NUM
ejpam-6593	317	11	,	,	PUNCT
ejpam-6593	317	12	8)	8)	NUM
ejpam-6593	317	13	1	1	NUM
ejpam-6593	317	14	27	27	NUM
ejpam-6593	317	15	13	13	NUM
ejpam-6593	317	16	25	25	NUM
ejpam-6593	317	17	+	+	CCONJ
ejpam-6593	317	18	(	(	PUNCT
ejpam-6593	317	19	2	2	NUM
ejpam-6593	317	20	+	+	NUM
ejpam-6593	317	21	5(27	5(27	NUM
ejpam-6593	317	22	)	)	PUNCT
ejpam-6593	317	23	)	)	PUNCT
ejpam-6593	318	1	=	=	SYM
ejpam-6593	318	2	132	132	NUM
ejpam-6593	318	3	(	(	PUNCT
ejpam-6593	318	4	2	2	NUM
ejpam-6593	318	5	,	,	PUNCT
ejpam-6593	318	6	27	27	NUM
ejpam-6593	318	7	,	,	PUNCT
ejpam-6593	318	8	5	5	NUM
ejpam-6593	318	9	,	,	PUNCT
ejpam-6593	318	10	1	1	NUM
ejpam-6593	318	11	,	,	PUNCT
ejpam-6593	318	12	13	13	NUM
ejpam-6593	318	13	)	)	PUNCT
ejpam-6593	318	14	2	2	NUM
ejpam-6593	318	15	58	58	NUM
ejpam-6593	318	16	18	18	NUM
ejpam-6593	318	17	25	25	NUM
ejpam-6593	318	18	+	+	CCONJ
ejpam-6593	318	19	(	(	PUNCT
ejpam-6593	318	20	2	2	NUM
ejpam-6593	318	21	+	+	SYM
ejpam-6593	318	22	5(58	5(58	NUM
ejpam-6593	318	23	)	)	PUNCT
ejpam-6593	318	24	)	)	PUNCT
ejpam-6593	319	1	=	=	SYM
ejpam-6593	319	2	182	182	NUM
ejpam-6593	319	3	(	(	PUNCT
ejpam-6593	319	4	2	2	NUM
ejpam-6593	319	5	,	,	PUNCT
ejpam-6593	319	6	58	58	NUM
ejpam-6593	319	7	,	,	PUNCT
ejpam-6593	319	8	5	5	NUM
ejpam-6593	319	9	,	,	PUNCT
ejpam-6593	319	10	1	1	NUM
ejpam-6593	319	11	,	,	PUNCT
ejpam-6593	319	12	18	18	NUM
ejpam-6593	319	13	)	)	PUNCT
ejpam-6593	319	14	3	3	NUM
ejpam-6593	319	15	99	99	NUM
ejpam-6593	319	16	23	23	NUM
ejpam-6593	319	17	25	25	NUM
ejpam-6593	319	18	+	+	CCONJ
ejpam-6593	319	19	(	(	PUNCT
ejpam-6593	319	20	2	2	NUM
ejpam-6593	319	21	+	+	NOUN
ejpam-6593	319	22	5(99	5(99	NUM
ejpam-6593	319	23	)	)	PUNCT
ejpam-6593	319	24	)	)	PUNCT
ejpam-6593	320	1	=	=	SYM
ejpam-6593	320	2	232	232	NUM
ejpam-6593	320	3	(	(	PUNCT
ejpam-6593	320	4	2	2	NUM
ejpam-6593	320	5	,	,	PUNCT
ejpam-6593	320	6	99	99	NUM
ejpam-6593	320	7	,	,	PUNCT
ejpam-6593	320	8	5	5	NUM
ejpam-6593	320	9	,	,	PUNCT
ejpam-6593	320	10	1	1	NUM
ejpam-6593	320	11	,	,	PUNCT
ejpam-6593	320	12	23	23	NUM
ejpam-6593	320	13	)	)	PUNCT
ejpam-6593	320	14	4	4	NUM
ejpam-6593	320	15	150	150	NUM
ejpam-6593	320	16	28	28	NUM
ejpam-6593	320	17	25	25	NUM
ejpam-6593	320	18	+	+	CCONJ
ejpam-6593	320	19	(	(	PUNCT
ejpam-6593	320	20	2	2	NUM
ejpam-6593	320	21	+	+	NUM
ejpam-6593	320	22	5(150	5(150	NUM
ejpam-6593	320	23	)	)	PUNCT
ejpam-6593	320	24	)	)	PUNCT
ejpam-6593	321	1	=	=	SYM
ejpam-6593	321	2	282	282	NUM
ejpam-6593	321	3	(	(	PUNCT
ejpam-6593	321	4	2	2	NUM
ejpam-6593	321	5	,	,	PUNCT
ejpam-6593	321	6	150	150	NUM
ejpam-6593	321	7	,	,	PUNCT
ejpam-6593	321	8	5	5	NUM
ejpam-6593	321	9	,	,	PUNCT
ejpam-6593	321	10	1	1	NUM
ejpam-6593	321	11	,	,	PUNCT
ejpam-6593	321	12	28	28	NUM
ejpam-6593	321	13	)	)	PUNCT
ejpam-6593	321	14	table	table	NOUN
ejpam-6593	321	15	5	5	NUM
ejpam-6593	321	16	:	:	PUNCT
ejpam-6593	321	17	some	some	DET
ejpam-6593	321	18	solutions	solution	NOUN
ejpam-6593	321	19	of	of	ADP
ejpam-6593	321	20	(	(	PUNCT
ejpam-6593	321	21	5	5	NUM
ejpam-6593	321	22	)	)	PUNCT
ejpam-6593	321	23	with	with	ADP
ejpam-6593	321	24	x	x	SYM
ejpam-6593	321	25	=	=	SYM
ejpam-6593	321	26	5	5	NUM
ejpam-6593	321	27	,	,	PUNCT
ejpam-6593	321	28	y	y	NOUN
ejpam-6593	321	29	=	=	SYM
ejpam-6593	321	30	1	1	NUM
ejpam-6593	321	31	and	and	CCONJ
ejpam-6593	321	32	z	z	PROPN
ejpam-6593	321	33	≡	≡	PROPN
ejpam-6593	321	34	3	3	NUM
ejpam-6593	321	35	(	(	PUNCT
ejpam-6593	321	36	mod	mod	NOUN
ejpam-6593	321	37	5	5	NUM
ejpam-6593	321	38	)	)	PUNCT
ejpam-6593	321	39	if	if	SCONJ
ejpam-6593	321	40	n	n	NOUN
ejpam-6593	321	41	=	=	SYM
ejpam-6593	321	42	0	0	NUM
ejpam-6593	321	43	in	in	ADP
ejpam-6593	321	44	x	x	X
ejpam-6593	321	45	=	=	PUNCT
ejpam-6593	321	46	xn	xn	PUNCT
ejpam-6593	321	47	=	=	SYM
ejpam-6593	322	1	2	2	NUM
ejpam-6593	322	2	+	+	NOUN
ejpam-6593	322	3	4n	4n	NOUN
ejpam-6593	322	4	,	,	PUNCT
ejpam-6593	322	5	we	we	PRON
ejpam-6593	322	6	get	get	VERB
ejpam-6593	322	7	x	x	X
ejpam-6593	322	8	=	=	SYM
ejpam-6593	322	9	2	2	NUM
ejpam-6593	322	10	,	,	PUNCT
ejpam-6593	322	11	and	and	CCONJ
ejpam-6593	322	12	we	we	PRON
ejpam-6593	322	13	have	have	VERB
ejpam-6593	322	14	tables	table	NOUN
ejpam-6593	322	15	6	6	NUM
ejpam-6593	322	16	7	7	NUM
ejpam-6593	322	17	below	below	ADP
ejpam-6593	322	18	that	that	DET
ejpam-6593	322	19	present	present	VERB
ejpam-6593	322	20	some	some	DET
ejpam-6593	322	21	solutions	solution	NOUN
ejpam-6593	322	22	where	where	SCONJ
ejpam-6593	322	23	z	z	NOUN
ejpam-6593	322	24	≡	≡	PROPN
ejpam-6593	322	25	1	1	NUM
ejpam-6593	322	26	(	(	PUNCT
ejpam-6593	322	27	mod	mod	NOUN
ejpam-6593	322	28	5	5	NUM
ejpam-6593	322	29	)	)	PUNCT
ejpam-6593	322	30	or	or	CCONJ
ejpam-6593	322	31	z	z	PROPN
ejpam-6593	322	32	≡	≡	PROPN
ejpam-6593	322	33	4	4	NUM
ejpam-6593	322	34	(	(	PUNCT
ejpam-6593	322	35	mod	mod	NOUN
ejpam-6593	322	36	5	5	NUM
ejpam-6593	322	37	)	)	PUNCT
ejpam-6593	322	38	.	.	PUNCT
ejpam-6593	323	1	m	m	VERB
ejpam-6593	324	1	k	k	NOUN
ejpam-6593	324	2	z	z	NOUN
ejpam-6593	324	3	equation	equation	NOUN
ejpam-6593	324	4	solution	solution	NOUN
ejpam-6593	324	5	(	(	PUNCT
ejpam-6593	324	6	p	p	X
ejpam-6593	324	7	,	,	PUNCT
ejpam-6593	324	8	k	k	NOUN
ejpam-6593	324	9	,	,	PUNCT
ejpam-6593	324	10	x	x	X
ejpam-6593	324	11	,	,	PUNCT
ejpam-6593	324	12	y	y	PROPN
ejpam-6593	324	13	,	,	PUNCT
ejpam-6593	324	14	z	z	NOUN
ejpam-6593	324	15	)	)	PUNCT
ejpam-6593	324	16	6	6	NUM
ejpam-6593	324	17	6	6	NUM
ejpam-6593	324	18	22	22	NUM
ejpam-6593	324	19	+	+	CCONJ
ejpam-6593	324	20	(	(	PUNCT
ejpam-6593	324	21	2	2	NUM
ejpam-6593	324	22	+	+	NUM
ejpam-6593	324	23	5(6	5(6	NUM
ejpam-6593	324	24	)	)	PUNCT
ejpam-6593	324	25	)	)	PUNCT
ejpam-6593	325	1	=	=	SYM
ejpam-6593	326	1	62	62	NUM
ejpam-6593	326	2	(	(	PUNCT
ejpam-6593	326	3	2	2	NUM
ejpam-6593	326	4	,	,	PUNCT
ejpam-6593	326	5	6	6	NUM
ejpam-6593	326	6	,	,	PUNCT
ejpam-6593	326	7	2	2	NUM
ejpam-6593	326	8	,	,	PUNCT
ejpam-6593	326	9	1	1	NUM
ejpam-6593	326	10	,	,	PUNCT
ejpam-6593	326	11	6	6	NUM
ejpam-6593	326	12	)	)	PUNCT
ejpam-6593	326	13	1	1	NUM
ejpam-6593	326	14	23	23	NUM
ejpam-6593	326	15	11	11	NUM
ejpam-6593	326	16	22	22	NUM
ejpam-6593	326	17	+	+	CCONJ
ejpam-6593	326	18	(	(	PUNCT
ejpam-6593	326	19	2	2	NUM
ejpam-6593	326	20	+	+	NUM
ejpam-6593	326	21	5(23	5(23	NUM
ejpam-6593	326	22	)	)	PUNCT
ejpam-6593	326	23	)	)	PUNCT
ejpam-6593	327	1	=	=	SYM
ejpam-6593	327	2	112	112	NUM
ejpam-6593	327	3	(	(	PUNCT
ejpam-6593	327	4	2	2	NUM
ejpam-6593	327	5	,	,	PUNCT
ejpam-6593	327	6	23	23	NUM
ejpam-6593	327	7	,	,	PUNCT
ejpam-6593	327	8	2	2	NUM
ejpam-6593	327	9	,	,	PUNCT
ejpam-6593	327	10	1	1	NUM
ejpam-6593	327	11	,	,	PUNCT
ejpam-6593	327	12	11	11	NUM
ejpam-6593	327	13	)	)	PUNCT
ejpam-6593	327	14	2	2	NUM
ejpam-6593	327	15	50	50	NUM
ejpam-6593	327	16	16	16	NUM
ejpam-6593	327	17	22	22	NUM
ejpam-6593	328	1	+	+	CCONJ
ejpam-6593	328	2	(	(	PUNCT
ejpam-6593	328	3	2	2	NUM
ejpam-6593	328	4	+	+	NUM
ejpam-6593	328	5	5(50	5(50	NUM
ejpam-6593	328	6	)	)	PUNCT
ejpam-6593	328	7	)	)	PUNCT
ejpam-6593	329	1	=	=	SYM
ejpam-6593	329	2	162	162	NUM
ejpam-6593	329	3	(	(	PUNCT
ejpam-6593	329	4	2	2	NUM
ejpam-6593	329	5	,	,	PUNCT
ejpam-6593	329	6	50	50	NUM
ejpam-6593	329	7	,	,	PUNCT
ejpam-6593	329	8	2	2	NUM
ejpam-6593	329	9	,	,	PUNCT
ejpam-6593	329	10	1	1	NUM
ejpam-6593	329	11	,	,	PUNCT
ejpam-6593	329	12	16	16	NUM
ejpam-6593	329	13	)	)	PUNCT
ejpam-6593	329	14	3	3	NUM
ejpam-6593	329	15	87	87	NUM
ejpam-6593	329	16	21	21	NUM
ejpam-6593	329	17	22	22	NUM
ejpam-6593	329	18	+	+	CCONJ
ejpam-6593	329	19	(	(	PUNCT
ejpam-6593	329	20	2	2	NUM
ejpam-6593	329	21	+	+	NUM
ejpam-6593	329	22	5(87	5(87	NUM
ejpam-6593	329	23	)	)	PUNCT
ejpam-6593	329	24	)	)	PUNCT
ejpam-6593	330	1	=	=	SYM
ejpam-6593	330	2	212	212	NUM
ejpam-6593	330	3	(	(	PUNCT
ejpam-6593	330	4	2	2	NUM
ejpam-6593	330	5	,	,	PUNCT
ejpam-6593	330	6	87	87	NUM
ejpam-6593	330	7	,	,	PUNCT
ejpam-6593	330	8	2	2	NUM
ejpam-6593	330	9	,	,	PUNCT
ejpam-6593	330	10	1	1	NUM
ejpam-6593	330	11	,	,	PUNCT
ejpam-6593	330	12	21	21	NUM
ejpam-6593	330	13	)	)	PUNCT
ejpam-6593	331	1	4	4	NUM
ejpam-6593	331	2	134	134	NUM
ejpam-6593	331	3	26	26	NUM
ejpam-6593	331	4	22	22	NUM
ejpam-6593	331	5	+	+	CCONJ
ejpam-6593	331	6	(	(	PUNCT
ejpam-6593	331	7	2	2	NUM
ejpam-6593	331	8	+	+	NUM
ejpam-6593	331	9	5(134	5(134	NUM
ejpam-6593	331	10	)	)	PUNCT
ejpam-6593	331	11	)	)	PUNCT
ejpam-6593	332	1	=	=	SYM
ejpam-6593	332	2	262	262	NUM
ejpam-6593	332	3	(	(	PUNCT
ejpam-6593	332	4	2	2	NUM
ejpam-6593	332	5	,	,	PUNCT
ejpam-6593	332	6	134	134	NUM
ejpam-6593	332	7	,	,	PUNCT
ejpam-6593	332	8	2	2	NUM
ejpam-6593	332	9	,	,	PUNCT
ejpam-6593	332	10	1	1	NUM
ejpam-6593	332	11	,	,	PUNCT
ejpam-6593	332	12	26	26	NUM
ejpam-6593	332	13	)	)	PUNCT
ejpam-6593	332	14	table	table	NOUN
ejpam-6593	332	15	6	6	NUM
ejpam-6593	332	16	:	:	PUNCT
ejpam-6593	332	17	some	some	DET
ejpam-6593	332	18	solutions	solution	NOUN
ejpam-6593	332	19	of	of	ADP
ejpam-6593	332	20	(	(	PUNCT
ejpam-6593	332	21	5	5	NUM
ejpam-6593	332	22	)	)	PUNCT
ejpam-6593	332	23	with	with	ADP
ejpam-6593	332	24	x	x	SYM
ejpam-6593	332	25	=	=	SYM
ejpam-6593	332	26	2	2	NUM
ejpam-6593	332	27	,	,	PUNCT
ejpam-6593	332	28	y	y	NOUN
ejpam-6593	332	29	=	=	SYM
ejpam-6593	332	30	1	1	NUM
ejpam-6593	332	31	and	and	CCONJ
ejpam-6593	332	32	z	z	PROPN
ejpam-6593	332	33	≡	≡	PROPN
ejpam-6593	332	34	1	1	NUM
ejpam-6593	332	35	(	(	PUNCT
ejpam-6593	332	36	mod	mod	NOUN
ejpam-6593	332	37	5	5	NUM
ejpam-6593	332	38	)	)	PUNCT
ejpam-6593	332	39	m	m	VERB
ejpam-6593	332	40	k	k	NOUN
ejpam-6593	332	41	z	z	NOUN
ejpam-6593	332	42	equation	equation	NOUN
ejpam-6593	332	43	solution	solution	NOUN
ejpam-6593	332	44	(	(	PUNCT
ejpam-6593	332	45	p	p	X
ejpam-6593	332	46	,	,	PUNCT
ejpam-6593	332	47	k	k	NOUN
ejpam-6593	332	48	,	,	PUNCT
ejpam-6593	332	49	x	x	X
ejpam-6593	332	50	,	,	PUNCT
ejpam-6593	332	51	y	y	PROPN
ejpam-6593	332	52	,	,	PUNCT
ejpam-6593	332	53	z	z	NOUN
ejpam-6593	332	54	)	)	PUNCT
ejpam-6593	332	55	2	2	NUM
ejpam-6593	332	56	4	4	NUM
ejpam-6593	332	57	22	22	NUM
ejpam-6593	332	58	+	+	CCONJ
ejpam-6593	332	59	(	(	PUNCT
ejpam-6593	332	60	2	2	NUM
ejpam-6593	332	61	+	+	NUM
ejpam-6593	332	62	5(2	5(2	NUM
ejpam-6593	332	63	)	)	PUNCT
ejpam-6593	332	64	)	)	PUNCT
ejpam-6593	333	1	=	=	SYM
ejpam-6593	333	2	42	42	NUM
ejpam-6593	333	3	(	(	PUNCT
ejpam-6593	333	4	2	2	NUM
ejpam-6593	333	5	,	,	PUNCT
ejpam-6593	333	6	2	2	NUM
ejpam-6593	333	7	,	,	PUNCT
ejpam-6593	333	8	2	2	NUM
ejpam-6593	333	9	,	,	PUNCT
ejpam-6593	333	10	1	1	NUM
ejpam-6593	333	11	,	,	PUNCT
ejpam-6593	333	12	4	4	NUM
ejpam-6593	333	13	)	)	PUNCT
ejpam-6593	333	14	1	1	NUM
ejpam-6593	333	15	15	15	NUM
ejpam-6593	333	16	9	9	NUM
ejpam-6593	333	17	22	22	NUM
ejpam-6593	333	18	+	+	CCONJ
ejpam-6593	333	19	(	(	PUNCT
ejpam-6593	333	20	2	2	NUM
ejpam-6593	333	21	+	+	NUM
ejpam-6593	333	22	5(15	5(15	NUM
ejpam-6593	333	23	)	)	PUNCT
ejpam-6593	333	24	)	)	PUNCT
ejpam-6593	334	1	=	=	SYM
ejpam-6593	334	2	92	92	NUM
ejpam-6593	334	3	(	(	PUNCT
ejpam-6593	334	4	2	2	NUM
ejpam-6593	334	5	,	,	PUNCT
ejpam-6593	334	6	15	15	NUM
ejpam-6593	334	7	,	,	PUNCT
ejpam-6593	334	8	2	2	NUM
ejpam-6593	334	9	,	,	PUNCT
ejpam-6593	334	10	1	1	NUM
ejpam-6593	334	11	,	,	PUNCT
ejpam-6593	334	12	9	9	NUM
ejpam-6593	334	13	)	)	PUNCT
ejpam-6593	334	14	2	2	NUM
ejpam-6593	334	15	38	38	NUM
ejpam-6593	334	16	14	14	NUM
ejpam-6593	334	17	22	22	NUM
ejpam-6593	334	18	+	+	CCONJ
ejpam-6593	334	19	(	(	PUNCT
ejpam-6593	334	20	2	2	NUM
ejpam-6593	334	21	+	+	NUM
ejpam-6593	334	22	5(38	5(38	NUM
ejpam-6593	334	23	)	)	PUNCT
ejpam-6593	334	24	)	)	PUNCT
ejpam-6593	335	1	=	=	SYM
ejpam-6593	335	2	142	142	NUM
ejpam-6593	335	3	(	(	PUNCT
ejpam-6593	335	4	2	2	NUM
ejpam-6593	335	5	,	,	PUNCT
ejpam-6593	335	6	38	38	NUM
ejpam-6593	335	7	,	,	PUNCT
ejpam-6593	335	8	2	2	NUM
ejpam-6593	335	9	,	,	PUNCT
ejpam-6593	335	10	1	1	NUM
ejpam-6593	335	11	,	,	PUNCT
ejpam-6593	335	12	14	14	NUM
ejpam-6593	335	13	)	)	PUNCT
ejpam-6593	335	14	3	3	NUM
ejpam-6593	335	15	71	71	NUM
ejpam-6593	335	16	19	19	NUM
ejpam-6593	335	17	22	22	NUM
ejpam-6593	335	18	+	+	CCONJ
ejpam-6593	335	19	(	(	PUNCT
ejpam-6593	335	20	2	2	NUM
ejpam-6593	335	21	+	+	NUM
ejpam-6593	335	22	5(71	5(71	NUM
ejpam-6593	335	23	)	)	PUNCT
ejpam-6593	335	24	)	)	PUNCT
ejpam-6593	336	1	=	=	SYM
ejpam-6593	336	2	192	192	NUM
ejpam-6593	336	3	(	(	PUNCT
ejpam-6593	336	4	2	2	NUM
ejpam-6593	336	5	,	,	PUNCT
ejpam-6593	336	6	71	71	NUM
ejpam-6593	336	7	,	,	PUNCT
ejpam-6593	336	8	2	2	NUM
ejpam-6593	336	9	,	,	PUNCT
ejpam-6593	336	10	1	1	NUM
ejpam-6593	336	11	,	,	PUNCT
ejpam-6593	336	12	19	19	NUM
ejpam-6593	336	13	)	)	PUNCT
ejpam-6593	336	14	4	4	NUM
ejpam-6593	336	15	114	114	NUM
ejpam-6593	336	16	24	24	NUM
ejpam-6593	336	17	22	22	NUM
ejpam-6593	336	18	+	+	CCONJ
ejpam-6593	336	19	(	(	PUNCT
ejpam-6593	336	20	2	2	NUM
ejpam-6593	336	21	+	+	NUM
ejpam-6593	336	22	5(114	5(114	NUM
ejpam-6593	336	23	)	)	PUNCT
ejpam-6593	336	24	)	)	PUNCT
ejpam-6593	337	1	=	=	SYM
ejpam-6593	337	2	242	242	NUM
ejpam-6593	337	3	(	(	PUNCT
ejpam-6593	337	4	2	2	NUM
ejpam-6593	337	5	,	,	PUNCT
ejpam-6593	337	6	114	114	NUM
ejpam-6593	337	7	,	,	PUNCT
ejpam-6593	337	8	2	2	NUM
ejpam-6593	337	9	,	,	PUNCT
ejpam-6593	337	10	1	1	NUM
ejpam-6593	337	11	,	,	PUNCT
ejpam-6593	337	12	24	24	NUM
ejpam-6593	337	13	)	)	PUNCT
ejpam-6593	337	14	table	table	NOUN
ejpam-6593	337	15	7	7	NUM
ejpam-6593	337	16	:	:	PUNCT
ejpam-6593	337	17	some	some	DET
ejpam-6593	337	18	solutions	solution	NOUN
ejpam-6593	337	19	of	of	ADP
ejpam-6593	337	20	(	(	PUNCT
ejpam-6593	337	21	5	5	NUM
ejpam-6593	337	22	)	)	PUNCT
ejpam-6593	337	23	with	with	ADP
ejpam-6593	337	24	x	x	SYM
ejpam-6593	337	25	=	=	SYM
ejpam-6593	337	26	2	2	NUM
ejpam-6593	337	27	,	,	PUNCT
ejpam-6593	337	28	y	y	NOUN
ejpam-6593	337	29	=	=	SYM
ejpam-6593	337	30	1	1	NUM
ejpam-6593	337	31	and	and	CCONJ
ejpam-6593	337	32	z	z	PROPN
ejpam-6593	337	33	≡	≡	PROPN
ejpam-6593	337	34	4	4	NUM
ejpam-6593	337	35	(	(	PUNCT
ejpam-6593	337	36	mod	mod	NOUN
ejpam-6593	337	37	5	5	NUM
ejpam-6593	337	38	)	)	PUNCT
ejpam-6593	337	39	if	if	SCONJ
ejpam-6593	337	40	n	n	NOUN
ejpam-6593	337	41	=	=	SYM
ejpam-6593	337	42	1	1	NUM
ejpam-6593	337	43	in	in	ADP
ejpam-6593	337	44	x	x	X
ejpam-6593	337	45	=	=	PUNCT
ejpam-6593	337	46	xn	xn	PUNCT
ejpam-6593	337	47	=	=	SYM
ejpam-6593	337	48	2	2	NUM
ejpam-6593	337	49	+	+	NUM
ejpam-6593	337	50	4n	4n	NOUN
ejpam-6593	337	51	,	,	PUNCT
ejpam-6593	337	52	we	we	PRON
ejpam-6593	337	53	get	get	VERB
ejpam-6593	337	54	x	x	X
ejpam-6593	337	55	=	=	SYM
ejpam-6593	337	56	6	6	NUM
ejpam-6593	337	57	and	and	CCONJ
ejpam-6593	337	58	tables	table	NOUN
ejpam-6593	337	59	8	8	NUM
ejpam-6593	337	60	9	9	NUM
ejpam-6593	337	61	show	show	VERB
ejpam-6593	337	62	some	some	DET
ejpam-6593	337	63	solutions	solution	NOUN
ejpam-6593	337	64	where	where	SCONJ
ejpam-6593	337	65	z	z	NOUN
ejpam-6593	337	66	≡	≡	PROPN
ejpam-6593	337	67	1	1	NUM
ejpam-6593	337	68	(	(	PUNCT
ejpam-6593	337	69	mod	mod	NOUN
ejpam-6593	337	70	5	5	NUM
ejpam-6593	337	71	)	)	PUNCT
ejpam-6593	337	72	or	or	CCONJ
ejpam-6593	337	73	z	z	PROPN
ejpam-6593	337	74	≡	≡	PROPN
ejpam-6593	337	75	4	4	NUM
ejpam-6593	337	76	(	(	PUNCT
ejpam-6593	337	77	mod	mod	NOUN
ejpam-6593	337	78	5	5	NUM
ejpam-6593	337	79	)	)	PUNCT
ejpam-6593	337	80	.	.	PUNCT
ejpam-6593	338	1	m	m	VERB
ejpam-6593	339	1	k	k	NOUN
ejpam-6593	339	2	z	z	NOUN
ejpam-6593	339	3	equation	equation	NOUN
ejpam-6593	339	4	solution	solution	NOUN
ejpam-6593	339	5	(	(	PUNCT
ejpam-6593	339	6	p	p	X
ejpam-6593	339	7	,	,	PUNCT
ejpam-6593	339	8	k	k	NOUN
ejpam-6593	339	9	,	,	PUNCT
ejpam-6593	339	10	x	x	X
ejpam-6593	339	11	,	,	PUNCT
ejpam-6593	339	12	y	y	PROPN
ejpam-6593	339	13	,	,	PUNCT
ejpam-6593	339	14	z	z	NOUN
ejpam-6593	339	15	)	)	PUNCT
ejpam-6593	339	16	3	3	NUM
ejpam-6593	339	17	9	9	NUM
ejpam-6593	339	18	26	26	NUM
ejpam-6593	339	19	+	+	CCONJ
ejpam-6593	339	20	(	(	PUNCT
ejpam-6593	339	21	2	2	NUM
ejpam-6593	339	22	+	+	NUM
ejpam-6593	339	23	5(3	5(3	NUM
ejpam-6593	339	24	)	)	PUNCT
ejpam-6593	339	25	)	)	PUNCT
ejpam-6593	340	1	=	=	SYM
ejpam-6593	341	1	92	92	NUM
ejpam-6593	341	2	(	(	PUNCT
ejpam-6593	341	3	2	2	NUM
ejpam-6593	341	4	,	,	PUNCT
ejpam-6593	341	5	3	3	NUM
ejpam-6593	341	6	,	,	PUNCT
ejpam-6593	341	7	6	6	NUM
ejpam-6593	341	8	,	,	PUNCT
ejpam-6593	341	9	1	1	NUM
ejpam-6593	341	10	,	,	PUNCT
ejpam-6593	341	11	9	9	NUM
ejpam-6593	341	12	)	)	PUNCT
ejpam-6593	341	13	1	1	NUM
ejpam-6593	341	14	26	26	NUM
ejpam-6593	341	15	14	14	NUM
ejpam-6593	341	16	26	26	NUM
ejpam-6593	342	1	+	+	CCONJ
ejpam-6593	342	2	(	(	PUNCT
ejpam-6593	342	3	2	2	NUM
ejpam-6593	342	4	+	+	NUM
ejpam-6593	342	5	5(26	5(26	NUM
ejpam-6593	342	6	)	)	PUNCT
ejpam-6593	342	7	)	)	PUNCT
ejpam-6593	343	1	=	=	SYM
ejpam-6593	343	2	142	142	NUM
ejpam-6593	343	3	(	(	PUNCT
ejpam-6593	343	4	2	2	NUM
ejpam-6593	343	5	,	,	PUNCT
ejpam-6593	343	6	26	26	NUM
ejpam-6593	343	7	,	,	PUNCT
ejpam-6593	343	8	6	6	NUM
ejpam-6593	343	9	,	,	PUNCT
ejpam-6593	343	10	1	1	NUM
ejpam-6593	343	11	,	,	PUNCT
ejpam-6593	343	12	14	14	NUM
ejpam-6593	343	13	)	)	PUNCT
ejpam-6593	343	14	2	2	NUM
ejpam-6593	343	15	59	59	NUM
ejpam-6593	343	16	19	19	NUM
ejpam-6593	343	17	26	26	NUM
ejpam-6593	343	18	+	+	CCONJ
ejpam-6593	343	19	(	(	PUNCT
ejpam-6593	343	20	2	2	NUM
ejpam-6593	343	21	+	+	NUM
ejpam-6593	343	22	5(59	5(59	NUM
ejpam-6593	343	23	)	)	PUNCT
ejpam-6593	343	24	)	)	PUNCT
ejpam-6593	344	1	=	=	SYM
ejpam-6593	344	2	192	192	NUM
ejpam-6593	344	3	(	(	PUNCT
ejpam-6593	344	4	2	2	NUM
ejpam-6593	344	5	,	,	PUNCT
ejpam-6593	344	6	59	59	NUM
ejpam-6593	344	7	,	,	PUNCT
ejpam-6593	344	8	6	6	NUM
ejpam-6593	344	9	,	,	PUNCT
ejpam-6593	344	10	1	1	NUM
ejpam-6593	344	11	,	,	PUNCT
ejpam-6593	344	12	19	19	NUM
ejpam-6593	344	13	)	)	PUNCT
ejpam-6593	344	14	3	3	NUM
ejpam-6593	344	15	102	102	NUM
ejpam-6593	344	16	24	24	NUM
ejpam-6593	344	17	26	26	NUM
ejpam-6593	345	1	+	+	CCONJ
ejpam-6593	345	2	(	(	PUNCT
ejpam-6593	345	3	2	2	NUM
ejpam-6593	345	4	+	+	NUM
ejpam-6593	345	5	5(102	5(102	NUM
ejpam-6593	345	6	)	)	PUNCT
ejpam-6593	345	7	)	)	PUNCT
ejpam-6593	346	1	=	=	SYM
ejpam-6593	346	2	242	242	NUM
ejpam-6593	346	3	(	(	PUNCT
ejpam-6593	346	4	2	2	NUM
ejpam-6593	346	5	,	,	PUNCT
ejpam-6593	346	6	102	102	NUM
ejpam-6593	346	7	,	,	PUNCT
ejpam-6593	346	8	6	6	NUM
ejpam-6593	346	9	,	,	PUNCT
ejpam-6593	346	10	1	1	NUM
ejpam-6593	346	11	,	,	PUNCT
ejpam-6593	346	12	24	24	NUM
ejpam-6593	346	13	)	)	PUNCT
ejpam-6593	346	14	4	4	NUM
ejpam-6593	346	15	155	155	NUM
ejpam-6593	346	16	29	29	NUM
ejpam-6593	346	17	26	26	NUM
ejpam-6593	346	18	+	+	CCONJ
ejpam-6593	346	19	(	(	PUNCT
ejpam-6593	346	20	2	2	NUM
ejpam-6593	346	21	+	+	NUM
ejpam-6593	346	22	5(155	5(155	NUM
ejpam-6593	346	23	)	)	PUNCT
ejpam-6593	346	24	)	)	PUNCT
ejpam-6593	347	1	=	=	PUNCT
ejpam-6593	347	2	292	292	NUM
ejpam-6593	347	3	(	(	PUNCT
ejpam-6593	347	4	2	2	NUM
ejpam-6593	347	5	,	,	PUNCT
ejpam-6593	347	6	155	155	NUM
ejpam-6593	347	7	,	,	PUNCT
ejpam-6593	347	8	6	6	NUM
ejpam-6593	347	9	,	,	PUNCT
ejpam-6593	347	10	1	1	NUM
ejpam-6593	347	11	,	,	PUNCT
ejpam-6593	347	12	29	29	NUM
ejpam-6593	347	13	)	)	PUNCT
ejpam-6593	347	14	table	table	NOUN
ejpam-6593	347	15	9	9	NUM
ejpam-6593	347	16	:	:	PUNCT
ejpam-6593	347	17	some	some	DET
ejpam-6593	347	18	solutions	solution	NOUN
ejpam-6593	347	19	of	of	ADP
ejpam-6593	347	20	(	(	PUNCT
ejpam-6593	347	21	5	5	NUM
ejpam-6593	347	22	)	)	PUNCT
ejpam-6593	347	23	with	with	ADP
ejpam-6593	347	24	x	x	SYM
ejpam-6593	348	1	=	=	SYM
ejpam-6593	348	2	6	6	NUM
ejpam-6593	348	3	,	,	PUNCT
ejpam-6593	348	4	y	y	PROPN
ejpam-6593	348	5	=	=	SYM
ejpam-6593	348	6	1	1	NUM
ejpam-6593	348	7	and	and	CCONJ
ejpam-6593	348	8	z	z	PROPN
ejpam-6593	348	9	≡	≡	PROPN
ejpam-6593	348	10	4	4	NUM
ejpam-6593	348	11	(	(	PUNCT
ejpam-6593	348	12	mod	mod	NOUN
ejpam-6593	348	13	5	5	NUM
ejpam-6593	348	14	)	)	PUNCT
ejpam-6593	348	15	m.	m.	NOUN
ejpam-6593	348	16	c.	c.	PROPN
ejpam-6593	348	17	avenilla	avenilla	PROPN
ejpam-6593	348	18	,	,	PUNCT
ejpam-6593	348	19	j.	j.	PROPN
ejpam-6593	348	20	b.	b.	PROPN
ejpam-6593	348	21	bacani	bacani	PROPN
ejpam-6593	348	22	/	/	SYM
ejpam-6593	348	23	eur	eur	PROPN
ejpam-6593	348	24	.	.	PUNCT
ejpam-6593	349	1	j.	j.	PROPN
ejpam-6593	349	2	pure	pure	PROPN
ejpam-6593	349	3	appl	appl	PROPN
ejpam-6593	349	4	.	.	PROPN
ejpam-6593	349	5	math	math	PROPN
ejpam-6593	349	6	,	,	PUNCT
ejpam-6593	349	7	18	18	NUM
ejpam-6593	349	8	(	(	PUNCT
ejpam-6593	349	9	3	3	NUM
ejpam-6593	349	10	)	)	PUNCT
ejpam-6593	349	11	(	(	PUNCT
ejpam-6593	349	12	2025	2025	NUM
ejpam-6593	349	13	)	)	PUNCT
ejpam-6593	349	14	,	,	PUNCT
ejpam-6593	349	15	6593	6593	NUM
ejpam-6593	349	16	11	11	NUM
ejpam-6593	349	17	of	of	ADP
ejpam-6593	349	18	24	24	NUM
ejpam-6593	349	19	m	m	NOUN
ejpam-6593	349	20	k	k	NOUN
ejpam-6593	349	21	z	z	NOUN
ejpam-6593	349	22	equation	equation	NOUN
ejpam-6593	349	23	solution	solution	NOUN
ejpam-6593	349	24	(	(	PUNCT
ejpam-6593	349	25	p	p	X
ejpam-6593	349	26	,	,	PUNCT
ejpam-6593	349	27	k	k	NOUN
ejpam-6593	349	28	,	,	PUNCT
ejpam-6593	349	29	x	x	X
ejpam-6593	349	30	,	,	PUNCT
ejpam-6593	349	31	y	y	PROPN
ejpam-6593	349	32	,	,	PUNCT
ejpam-6593	349	33	z	z	NOUN
ejpam-6593	349	34	)	)	PUNCT
ejpam-6593	349	35	11	11	NUM
ejpam-6593	349	36	11	11	NUM
ejpam-6593	349	37	26	26	NUM
ejpam-6593	349	38	+	+	CCONJ
ejpam-6593	349	39	(	(	PUNCT
ejpam-6593	349	40	2	2	NUM
ejpam-6593	349	41	+	+	NUM
ejpam-6593	349	42	5(11	5(11	NUM
ejpam-6593	349	43	)	)	PUNCT
ejpam-6593	349	44	)	)	PUNCT
ejpam-6593	350	1	=	=	SYM
ejpam-6593	350	2	112	112	NUM
ejpam-6593	350	3	(	(	PUNCT
ejpam-6593	350	4	2	2	NUM
ejpam-6593	350	5	,	,	PUNCT
ejpam-6593	350	6	11	11	NUM
ejpam-6593	350	7	,	,	PUNCT
ejpam-6593	350	8	6	6	NUM
ejpam-6593	350	9	,	,	PUNCT
ejpam-6593	350	10	1	1	NUM
ejpam-6593	350	11	,	,	PUNCT
ejpam-6593	350	12	11	11	NUM
ejpam-6593	350	13	)	)	PUNCT
ejpam-6593	350	14	1	1	NUM
ejpam-6593	350	15	38	38	NUM
ejpam-6593	350	16	16	16	NUM
ejpam-6593	350	17	26	26	NUM
ejpam-6593	350	18	+	+	CCONJ
ejpam-6593	350	19	(	(	PUNCT
ejpam-6593	350	20	2	2	NUM
ejpam-6593	350	21	+	+	NUM
ejpam-6593	350	22	5(38	5(38	NUM
ejpam-6593	350	23	)	)	PUNCT
ejpam-6593	350	24	)	)	PUNCT
ejpam-6593	351	1	=	=	SYM
ejpam-6593	351	2	162	162	NUM
ejpam-6593	351	3	(	(	PUNCT
ejpam-6593	351	4	2	2	NUM
ejpam-6593	351	5	,	,	PUNCT
ejpam-6593	351	6	38	38	NUM
ejpam-6593	351	7	,	,	PUNCT
ejpam-6593	351	8	6	6	NUM
ejpam-6593	351	9	,	,	PUNCT
ejpam-6593	351	10	1	1	NUM
ejpam-6593	351	11	,	,	PUNCT
ejpam-6593	351	12	16	16	NUM
ejpam-6593	351	13	)	)	PUNCT
ejpam-6593	351	14	2	2	NUM
ejpam-6593	351	15	75	75	NUM
ejpam-6593	351	16	21	21	NUM
ejpam-6593	351	17	26	26	NUM
ejpam-6593	351	18	+	+	CCONJ
ejpam-6593	351	19	(	(	PUNCT
ejpam-6593	351	20	2	2	NUM
ejpam-6593	351	21	+	+	NUM
ejpam-6593	351	22	5(75	5(75	NUM
ejpam-6593	351	23	)	)	PUNCT
ejpam-6593	351	24	)	)	PUNCT
ejpam-6593	352	1	=	=	SYM
ejpam-6593	352	2	212	212	NUM
ejpam-6593	352	3	(	(	PUNCT
ejpam-6593	352	4	2	2	NUM
ejpam-6593	352	5	,	,	PUNCT
ejpam-6593	352	6	75	75	NUM
ejpam-6593	352	7	,	,	PUNCT
ejpam-6593	352	8	6	6	NUM
ejpam-6593	352	9	,	,	PUNCT
ejpam-6593	352	10	1	1	NUM
ejpam-6593	352	11	,	,	PUNCT
ejpam-6593	352	12	21	21	NUM
ejpam-6593	352	13	)	)	PUNCT
ejpam-6593	352	14	3	3	NUM
ejpam-6593	352	15	122	122	NUM
ejpam-6593	352	16	26	26	NUM
ejpam-6593	352	17	26	26	NUM
ejpam-6593	352	18	+	+	CCONJ
ejpam-6593	352	19	(	(	PUNCT
ejpam-6593	352	20	2	2	NUM
ejpam-6593	352	21	+	+	SYM
ejpam-6593	352	22	5(122	5(122	NUM
ejpam-6593	352	23	)	)	PUNCT
ejpam-6593	352	24	)	)	PUNCT
ejpam-6593	353	1	=	=	SYM
ejpam-6593	353	2	262	262	NUM
ejpam-6593	353	3	(	(	PUNCT
ejpam-6593	353	4	2	2	NUM
ejpam-6593	353	5	,	,	PUNCT
ejpam-6593	353	6	122	122	NUM
ejpam-6593	353	7	,	,	PUNCT
ejpam-6593	353	8	6	6	NUM
ejpam-6593	353	9	,	,	PUNCT
ejpam-6593	353	10	1	1	NUM
ejpam-6593	353	11	,	,	PUNCT
ejpam-6593	353	12	26	26	NUM
ejpam-6593	353	13	)	)	PUNCT
ejpam-6593	353	14	4	4	NUM
ejpam-6593	353	15	179	179	NUM
ejpam-6593	353	16	31	31	NUM
ejpam-6593	353	17	26	26	NUM
ejpam-6593	353	18	+	+	CCONJ
ejpam-6593	353	19	(	(	PUNCT
ejpam-6593	353	20	2	2	NUM
ejpam-6593	353	21	+	+	NUM
ejpam-6593	353	22	5(179	5(179	NUM
ejpam-6593	353	23	)	)	PUNCT
ejpam-6593	353	24	)	)	PUNCT
ejpam-6593	354	1	=	=	SYM
ejpam-6593	354	2	312	312	NUM
ejpam-6593	354	3	(	(	PUNCT
ejpam-6593	354	4	2	2	NUM
ejpam-6593	354	5	,	,	PUNCT
ejpam-6593	354	6	179	179	NUM
ejpam-6593	354	7	,	,	PUNCT
ejpam-6593	354	8	6	6	NUM
ejpam-6593	354	9	,	,	PUNCT
ejpam-6593	354	10	1	1	NUM
ejpam-6593	354	11	,	,	PUNCT
ejpam-6593	354	12	31	31	NUM
ejpam-6593	354	13	)	)	PUNCT
ejpam-6593	354	14	table	table	NOUN
ejpam-6593	354	15	8	8	NUM
ejpam-6593	354	16	:	:	PUNCT
ejpam-6593	354	17	some	some	DET
ejpam-6593	354	18	solutions	solution	NOUN
ejpam-6593	354	19	of	of	ADP
ejpam-6593	354	20	(	(	PUNCT
ejpam-6593	354	21	5	5	NUM
ejpam-6593	354	22	)	)	PUNCT
ejpam-6593	354	23	with	with	ADP
ejpam-6593	354	24	x	x	SYM
ejpam-6593	355	1	=	=	SYM
ejpam-6593	355	2	6	6	NUM
ejpam-6593	355	3	,	,	PUNCT
ejpam-6593	355	4	y	y	PROPN
ejpam-6593	355	5	=	=	SYM
ejpam-6593	355	6	1	1	NUM
ejpam-6593	355	7	and	and	CCONJ
ejpam-6593	355	8	z	z	PROPN
ejpam-6593	355	9	≡	≡	PROPN
ejpam-6593	355	10	1	1	NUM
ejpam-6593	355	11	(	(	PUNCT
ejpam-6593	355	12	mod	mod	NOUN
ejpam-6593	355	13	5	5	NUM
ejpam-6593	355	14	)	)	PUNCT
ejpam-6593	355	15	if	if	SCONJ
ejpam-6593	355	16	n	n	NOUN
ejpam-6593	355	17	=	=	SYM
ejpam-6593	355	18	0	0	NUM
ejpam-6593	355	19	,	,	PUNCT
ejpam-6593	355	20	1	1	NUM
ejpam-6593	355	21	in	in	ADP
ejpam-6593	355	22	x	x	X
ejpam-6593	355	23	=	=	PUNCT
ejpam-6593	355	24	xn	xn	PUNCT
ejpam-6593	356	1	=	=	SYM
ejpam-6593	356	2	3	3	NUM
ejpam-6593	356	3	+	+	CCONJ
ejpam-6593	356	4	4n	4n	NOUN
ejpam-6593	356	5	,	,	PUNCT
ejpam-6593	356	6	we	we	PRON
ejpam-6593	356	7	get	get	VERB
ejpam-6593	356	8	x	x	X
ejpam-6593	356	9	=	=	SYM
ejpam-6593	356	10	3	3	NUM
ejpam-6593	356	11	,	,	PUNCT
ejpam-6593	356	12	7	7	NUM
ejpam-6593	356	13	,	,	PUNCT
ejpam-6593	356	14	respectively	respectively	ADV
ejpam-6593	356	15	,	,	PUNCT
ejpam-6593	356	16	and	and	CCONJ
ejpam-6593	356	17	tables	table	VERB
ejpam-6593	356	18	10	10	NUM
ejpam-6593	356	19	11	11	NUM
ejpam-6593	356	20	show	show	VERB
ejpam-6593	356	21	some	some	DET
ejpam-6593	356	22	solutions	solution	NOUN
ejpam-6593	356	23	wherein	wherein	SCONJ
ejpam-6593	356	24	z	z	PROPN
ejpam-6593	356	25	≡	≡	PROPN
ejpam-6593	356	26	0	0	PUNCT
ejpam-6593	357	1	(	(	PUNCT
ejpam-6593	357	2	mod	mod	PROPN
ejpam-6593	357	3	5	5	NUM
ejpam-6593	357	4	)	)	PUNCT
ejpam-6593	357	5	.	.	PUNCT
ejpam-6593	358	1	m	m	VERB
ejpam-6593	359	1	k	k	NOUN
ejpam-6593	359	2	z	z	NOUN
ejpam-6593	359	3	equation	equation	NOUN
ejpam-6593	359	4	solution	solution	NOUN
ejpam-6593	359	5	(	(	PUNCT
ejpam-6593	359	6	p	p	X
ejpam-6593	359	7	,	,	PUNCT
ejpam-6593	359	8	k	k	NOUN
ejpam-6593	359	9	,	,	PUNCT
ejpam-6593	359	10	x	x	X
ejpam-6593	359	11	,	,	PUNCT
ejpam-6593	359	12	y	y	PROPN
ejpam-6593	359	13	,	,	PUNCT
ejpam-6593	359	14	z	z	NOUN
ejpam-6593	359	15	)	)	PUNCT
ejpam-6593	359	16	3	3	NUM
ejpam-6593	359	17	5	5	NUM
ejpam-6593	359	18	23	23	NUM
ejpam-6593	359	19	+	+	CCONJ
ejpam-6593	359	20	(	(	PUNCT
ejpam-6593	359	21	2	2	NUM
ejpam-6593	359	22	+	+	NUM
ejpam-6593	359	23	5(3	5(3	NUM
ejpam-6593	359	24	)	)	PUNCT
ejpam-6593	359	25	)	)	PUNCT
ejpam-6593	360	1	=	=	SYM
ejpam-6593	360	2	52	52	NUM
ejpam-6593	360	3	(	(	PUNCT
ejpam-6593	360	4	2	2	NUM
ejpam-6593	360	5	,	,	PUNCT
ejpam-6593	360	6	3	3	NUM
ejpam-6593	360	7	,	,	PUNCT
ejpam-6593	360	8	3	3	NUM
ejpam-6593	360	9	,	,	PUNCT
ejpam-6593	360	10	1	1	NUM
ejpam-6593	360	11	,	,	PUNCT
ejpam-6593	360	12	5	5	NUM
ejpam-6593	360	13	)	)	PUNCT
ejpam-6593	360	14	1	1	NUM
ejpam-6593	360	15	18	18	NUM
ejpam-6593	360	16	10	10	NUM
ejpam-6593	360	17	23	23	NUM
ejpam-6593	360	18	+	+	CCONJ
ejpam-6593	360	19	(	(	PUNCT
ejpam-6593	360	20	2	2	NUM
ejpam-6593	360	21	+	+	NUM
ejpam-6593	360	22	5(18	5(18	NUM
ejpam-6593	360	23	)	)	PUNCT
ejpam-6593	360	24	)	)	PUNCT
ejpam-6593	361	1	=	=	SYM
ejpam-6593	361	2	102	102	NUM
ejpam-6593	361	3	(	(	PUNCT
ejpam-6593	361	4	2	2	NUM
ejpam-6593	361	5	,	,	PUNCT
ejpam-6593	361	6	18	18	NUM
ejpam-6593	361	7	,	,	PUNCT
ejpam-6593	361	8	3	3	NUM
ejpam-6593	361	9	,	,	PUNCT
ejpam-6593	361	10	1	1	NUM
ejpam-6593	361	11	,	,	PUNCT
ejpam-6593	361	12	10	10	NUM
ejpam-6593	361	13	)	)	PUNCT
ejpam-6593	361	14	2	2	NUM
ejpam-6593	361	15	43	43	NUM
ejpam-6593	361	16	15	15	NUM
ejpam-6593	361	17	23	23	NUM
ejpam-6593	361	18	+	+	CCONJ
ejpam-6593	361	19	(	(	PUNCT
ejpam-6593	361	20	2	2	NUM
ejpam-6593	361	21	+	+	NUM
ejpam-6593	361	22	5(43	5(43	NUM
ejpam-6593	361	23	)	)	PUNCT
ejpam-6593	361	24	)	)	PUNCT
ejpam-6593	362	1	=	=	SYM
ejpam-6593	362	2	152	152	NUM
ejpam-6593	362	3	(	(	PUNCT
ejpam-6593	362	4	2	2	NUM
ejpam-6593	362	5	,	,	PUNCT
ejpam-6593	362	6	43	43	NUM
ejpam-6593	362	7	,	,	PUNCT
ejpam-6593	362	8	3	3	NUM
ejpam-6593	362	9	,	,	PUNCT
ejpam-6593	362	10	1	1	NUM
ejpam-6593	362	11	,	,	PUNCT
ejpam-6593	362	12	15	15	NUM
ejpam-6593	362	13	)	)	PUNCT
ejpam-6593	362	14	3	3	NUM
ejpam-6593	362	15	78	78	NUM
ejpam-6593	362	16	20	20	NUM
ejpam-6593	362	17	23	23	NUM
ejpam-6593	362	18	+	+	CCONJ
ejpam-6593	362	19	(	(	PUNCT
ejpam-6593	362	20	2	2	NUM
ejpam-6593	362	21	+	+	NUM
ejpam-6593	362	22	5(78	5(78	NUM
ejpam-6593	362	23	)	)	PUNCT
ejpam-6593	362	24	)	)	PUNCT
ejpam-6593	363	1	=	=	SYM
ejpam-6593	364	1	202	202	NUM
ejpam-6593	364	2	(	(	PUNCT
ejpam-6593	364	3	2	2	NUM
ejpam-6593	364	4	,	,	PUNCT
ejpam-6593	364	5	78	78	NUM
ejpam-6593	364	6	,	,	PUNCT
ejpam-6593	364	7	3	3	NUM
ejpam-6593	364	8	,	,	PUNCT
ejpam-6593	364	9	1	1	NUM
ejpam-6593	364	10	,	,	PUNCT
ejpam-6593	364	11	20	20	NUM
ejpam-6593	364	12	)	)	PUNCT
ejpam-6593	364	13	4	4	NUM
ejpam-6593	364	14	123	123	NUM
ejpam-6593	364	15	25	25	NUM
ejpam-6593	364	16	23	23	NUM
ejpam-6593	364	17	+	+	CCONJ
ejpam-6593	364	18	(	(	PUNCT
ejpam-6593	364	19	2	2	NUM
ejpam-6593	364	20	+	+	NUM
ejpam-6593	364	21	5(123	5(123	NUM
ejpam-6593	364	22	)	)	PUNCT
ejpam-6593	364	23	)	)	PUNCT
ejpam-6593	365	1	=	=	PUNCT
ejpam-6593	365	2	252	252	NUM
ejpam-6593	365	3	(	(	PUNCT
ejpam-6593	365	4	2	2	NUM
ejpam-6593	365	5	,	,	PUNCT
ejpam-6593	365	6	123	123	NUM
ejpam-6593	365	7	,	,	PUNCT
ejpam-6593	365	8	3	3	NUM
ejpam-6593	365	9	,	,	PUNCT
ejpam-6593	365	10	1	1	NUM
ejpam-6593	365	11	,	,	PUNCT
ejpam-6593	365	12	25	25	NUM
ejpam-6593	365	13	)	)	PUNCT
ejpam-6593	365	14	table	table	NOUN
ejpam-6593	365	15	10	10	NUM
ejpam-6593	365	16	:	:	PUNCT
ejpam-6593	365	17	some	some	DET
ejpam-6593	365	18	solutions	solution	NOUN
ejpam-6593	365	19	of	of	ADP
ejpam-6593	365	20	(	(	PUNCT
ejpam-6593	365	21	5	5	NUM
ejpam-6593	365	22	)	)	PUNCT
ejpam-6593	365	23	with	with	ADP
ejpam-6593	365	24	x	x	X
ejpam-6593	366	1	=	=	SYM
ejpam-6593	366	2	3	3	NUM
ejpam-6593	366	3	,	,	PUNCT
ejpam-6593	366	4	y	y	PROPN
ejpam-6593	366	5	=	=	SYM
ejpam-6593	366	6	1	1	NUM
ejpam-6593	366	7	and	and	CCONJ
ejpam-6593	366	8	z	z	PROPN
ejpam-6593	366	9	≡	≡	PROPN
ejpam-6593	366	10	0	0	PUNCT
ejpam-6593	367	1	(	(	PUNCT
ejpam-6593	367	2	mod	mod	NOUN
ejpam-6593	367	3	5	5	NUM
ejpam-6593	367	4	)	)	PUNCT
ejpam-6593	367	5	m	m	VERB
ejpam-6593	367	6	k	k	NOUN
ejpam-6593	367	7	z	z	NOUN
ejpam-6593	367	8	equation	equation	NOUN
ejpam-6593	367	9	solution	solution	NOUN
ejpam-6593	367	10	(	(	PUNCT
ejpam-6593	367	11	p	p	X
ejpam-6593	367	12	,	,	PUNCT
ejpam-6593	367	13	k	k	NOUN
ejpam-6593	367	14	,	,	PUNCT
ejpam-6593	367	15	x	x	X
ejpam-6593	367	16	,	,	PUNCT
ejpam-6593	367	17	y	y	PROPN
ejpam-6593	367	18	,	,	PUNCT
ejpam-6593	367	19	z	z	NOUN
ejpam-6593	367	20	)	)	PUNCT
ejpam-6593	367	21	19	19	NUM
ejpam-6593	367	22	15	15	NUM
ejpam-6593	367	23	27	27	NUM
ejpam-6593	367	24	+	+	CCONJ
ejpam-6593	367	25	(	(	PUNCT
ejpam-6593	367	26	2	2	NUM
ejpam-6593	367	27	+	+	NUM
ejpam-6593	367	28	5(19	5(19	NUM
ejpam-6593	367	29	)	)	PUNCT
ejpam-6593	367	30	)	)	PUNCT
ejpam-6593	368	1	=	=	SYM
ejpam-6593	368	2	152	152	NUM
ejpam-6593	368	3	(	(	PUNCT
ejpam-6593	368	4	2	2	NUM
ejpam-6593	368	5	,	,	PUNCT
ejpam-6593	368	6	19	19	NUM
ejpam-6593	368	7	,	,	PUNCT
ejpam-6593	368	8	7	7	NUM
ejpam-6593	368	9	,	,	PUNCT
ejpam-6593	368	10	1	1	NUM
ejpam-6593	368	11	,	,	PUNCT
ejpam-6593	368	12	15	15	NUM
ejpam-6593	368	13	)	)	PUNCT
ejpam-6593	368	14	1	1	NUM
ejpam-6593	368	15	54	54	NUM
ejpam-6593	368	16	20	20	NUM
ejpam-6593	368	17	27	27	NUM
ejpam-6593	368	18	+	+	CCONJ
ejpam-6593	368	19	(	(	PUNCT
ejpam-6593	368	20	2	2	NUM
ejpam-6593	368	21	+	+	NUM
ejpam-6593	368	22	5(54	5(54	NUM
ejpam-6593	368	23	)	)	PUNCT
ejpam-6593	368	24	)	)	PUNCT
ejpam-6593	369	1	=	=	SYM
ejpam-6593	370	1	202	202	NUM
ejpam-6593	370	2	(	(	PUNCT
ejpam-6593	370	3	2	2	NUM
ejpam-6593	370	4	,	,	PUNCT
ejpam-6593	370	5	54	54	NUM
ejpam-6593	370	6	,	,	PUNCT
ejpam-6593	370	7	7	7	NUM
ejpam-6593	370	8	,	,	PUNCT
ejpam-6593	370	9	1	1	NUM
ejpam-6593	370	10	,	,	PUNCT
ejpam-6593	370	11	20	20	NUM
ejpam-6593	370	12	)	)	PUNCT
ejpam-6593	370	13	2	2	NUM
ejpam-6593	370	14	99	99	NUM
ejpam-6593	370	15	25	25	NUM
ejpam-6593	370	16	27	27	NUM
ejpam-6593	370	17	+	+	CCONJ
ejpam-6593	370	18	(	(	PUNCT
ejpam-6593	370	19	2	2	NUM
ejpam-6593	370	20	+	+	NOUN
ejpam-6593	370	21	5(99	5(99	NUM
ejpam-6593	370	22	)	)	PUNCT
ejpam-6593	370	23	)	)	PUNCT
ejpam-6593	371	1	=	=	PUNCT
ejpam-6593	371	2	252	252	NUM
ejpam-6593	371	3	(	(	PUNCT
ejpam-6593	371	4	2	2	NUM
ejpam-6593	371	5	,	,	PUNCT
ejpam-6593	371	6	99	99	NUM
ejpam-6593	371	7	,	,	PUNCT
ejpam-6593	371	8	7	7	NUM
ejpam-6593	371	9	,	,	PUNCT
ejpam-6593	371	10	1	1	NUM
ejpam-6593	371	11	,	,	PUNCT
ejpam-6593	371	12	25	25	NUM
ejpam-6593	371	13	)	)	PUNCT
ejpam-6593	371	14	3	3	NUM
ejpam-6593	371	15	154	154	NUM
ejpam-6593	371	16	30	30	NUM
ejpam-6593	371	17	27	27	NUM
ejpam-6593	371	18	+	+	CCONJ
ejpam-6593	371	19	(	(	PUNCT
ejpam-6593	371	20	2	2	NUM
ejpam-6593	371	21	+	+	NUM
ejpam-6593	371	22	5(154	5(154	NUM
ejpam-6593	371	23	)	)	PUNCT
ejpam-6593	371	24	)	)	PUNCT
ejpam-6593	372	1	=	=	SYM
ejpam-6593	372	2	302	302	NUM
ejpam-6593	372	3	(	(	PUNCT
ejpam-6593	372	4	2	2	NUM
ejpam-6593	372	5	,	,	PUNCT
ejpam-6593	372	6	154	154	NUM
ejpam-6593	372	7	,	,	PUNCT
ejpam-6593	372	8	7	7	NUM
ejpam-6593	372	9	,	,	PUNCT
ejpam-6593	372	10	1	1	NUM
ejpam-6593	372	11	,	,	PUNCT
ejpam-6593	372	12	30	30	NUM
ejpam-6593	372	13	)	)	PUNCT
ejpam-6593	372	14	4	4	NUM
ejpam-6593	372	15	219	219	NUM
ejpam-6593	372	16	35	35	NUM
ejpam-6593	372	17	27	27	NUM
ejpam-6593	372	18	+	+	CCONJ
ejpam-6593	372	19	(	(	PUNCT
ejpam-6593	372	20	2	2	NUM
ejpam-6593	372	21	+	+	SYM
ejpam-6593	372	22	5(219	5(219	NUM
ejpam-6593	372	23	)	)	PUNCT
ejpam-6593	372	24	)	)	PUNCT
ejpam-6593	373	1	=	=	SYM
ejpam-6593	373	2	352	352	NUM
ejpam-6593	373	3	(	(	PUNCT
ejpam-6593	373	4	2	2	NUM
ejpam-6593	373	5	,	,	PUNCT
ejpam-6593	373	6	219	219	NUM
ejpam-6593	373	7	,	,	PUNCT
ejpam-6593	373	8	7	7	NUM
ejpam-6593	373	9	,	,	PUNCT
ejpam-6593	373	10	1	1	NUM
ejpam-6593	373	11	,	,	PUNCT
ejpam-6593	373	12	35	35	NUM
ejpam-6593	373	13	)	)	PUNCT
ejpam-6593	373	14	table	table	NOUN
ejpam-6593	373	15	11	11	NUM
ejpam-6593	373	16	:	:	PUNCT
ejpam-6593	373	17	some	some	DET
ejpam-6593	373	18	solutions	solution	NOUN
ejpam-6593	373	19	of	of	ADP
ejpam-6593	373	20	(	(	PUNCT
ejpam-6593	373	21	5	5	NUM
ejpam-6593	373	22	)	)	PUNCT
ejpam-6593	373	23	with	with	ADP
ejpam-6593	373	24	x	x	X
ejpam-6593	374	1	=	=	SYM
ejpam-6593	374	2	7	7	NUM
ejpam-6593	374	3	,	,	PUNCT
ejpam-6593	374	4	y	y	NOUN
ejpam-6593	374	5	=	=	SYM
ejpam-6593	374	6	1	1	NUM
ejpam-6593	374	7	and	and	CCONJ
ejpam-6593	374	8	z	z	PROPN
ejpam-6593	374	9	≡	≡	PROPN
ejpam-6593	374	10	0	0	PUNCT
ejpam-6593	375	1	(	(	PUNCT
ejpam-6593	375	2	mod	mod	NOUN
ejpam-6593	375	3	5	5	NUM
ejpam-6593	375	4	)	)	PUNCT
ejpam-6593	375	5	the	the	DET
ejpam-6593	375	6	last	last	ADJ
ejpam-6593	375	7	result	result	NOUN
ejpam-6593	375	8	for	for	ADP
ejpam-6593	375	9	this	this	DET
ejpam-6593	375	10	subsection	subsection	NOUN
ejpam-6593	375	11	discusses	discuss	VERB
ejpam-6593	375	12	the	the	DET
ejpam-6593	375	13	case	case	NOUN
ejpam-6593	375	14	when	when	SCONJ
ejpam-6593	375	15	x	x	X
ejpam-6593	375	16	≡	≡	PROPN
ejpam-6593	375	17	0	0	PUNCT
ejpam-6593	375	18	(	(	PUNCT
ejpam-6593	375	19	mod	mod	PROPN
ejpam-6593	375	20	4	4	NUM
ejpam-6593	375	21	)	)	PUNCT
ejpam-6593	375	22	.	.	PUNCT
ejpam-6593	376	1	theorem	theorem	NOUN
ejpam-6593	376	2	2	2	NUM
ejpam-6593	376	3	.	.	PUNCT
ejpam-6593	377	1	the	the	DET
ejpam-6593	377	2	exponential	exponential	ADJ
ejpam-6593	377	3	diophantine	diophantine	NOUN
ejpam-6593	377	4	equation	equation	NOUN
ejpam-6593	377	5	2x	2x	NUM
ejpam-6593	377	6	+	+	CCONJ
ejpam-6593	377	7	(	(	PUNCT
ejpam-6593	377	8	2	2	NUM
ejpam-6593	377	9	+	+	NUM
ejpam-6593	377	10	5k	5k	NUM
ejpam-6593	377	11	)	)	PUNCT
ejpam-6593	377	12	=	=	SYM
ejpam-6593	377	13	z2	z2	PROPN
ejpam-6593	377	14	has	have	VERB
ejpam-6593	377	15	no	no	DET
ejpam-6593	377	16	solution	solution	NOUN
ejpam-6593	377	17	if	if	SCONJ
ejpam-6593	377	18	x	x	SYM
ejpam-6593	377	19	≡	≡	PROPN
ejpam-6593	377	20	0	0	PUNCT
ejpam-6593	377	21	(	(	PUNCT
ejpam-6593	377	22	mod	mod	PROPN
ejpam-6593	377	23	4	4	NUM
ejpam-6593	377	24	)	)	PUNCT
ejpam-6593	377	25	.	.	PUNCT
ejpam-6593	378	1	proof	proof	NOUN
ejpam-6593	378	2	.	.	PUNCT
ejpam-6593	379	1	consider	consider	VERB
ejpam-6593	379	2	the	the	DET
ejpam-6593	379	3	diophantine	diophantine	NOUN
ejpam-6593	379	4	equation	equation	NOUN
ejpam-6593	379	5	2x	2x	NUM
ejpam-6593	380	1	+	+	CCONJ
ejpam-6593	380	2	(	(	PUNCT
ejpam-6593	380	3	2	2	NUM
ejpam-6593	380	4	+	+	NUM
ejpam-6593	380	5	5k	5k	NUM
ejpam-6593	380	6	)	)	PUNCT
ejpam-6593	381	1	=	=	SYM
ejpam-6593	381	2	z2	z2	PROPN
ejpam-6593	381	3	,	,	PUNCT
ejpam-6593	381	4	where	where	SCONJ
ejpam-6593	381	5	x	x	X
ejpam-6593	381	6	≡	≡	PROPN
ejpam-6593	381	7	0	0	PUNCT
ejpam-6593	382	1	(	(	PUNCT
ejpam-6593	382	2	mod	mod	PROPN
ejpam-6593	382	3	4	4	NUM
ejpam-6593	382	4	)	)	PUNCT
ejpam-6593	382	5	.	.	PUNCT
ejpam-6593	383	1	then	then	ADV
ejpam-6593	383	2	,	,	PUNCT
ejpam-6593	383	3	2x	2x	NUM
ejpam-6593	383	4	≡	≡	PROPN
ejpam-6593	383	5	1	1	NUM
ejpam-6593	383	6	(	(	PUNCT
ejpam-6593	383	7	mod	mod	NOUN
ejpam-6593	383	8	5	5	NUM
ejpam-6593	383	9	)	)	PUNCT
ejpam-6593	383	10	.	.	PUNCT
ejpam-6593	384	1	hence	hence	ADV
ejpam-6593	384	2	,	,	PUNCT
ejpam-6593	384	3	2x	2x	NUM
ejpam-6593	384	4	+	+	CCONJ
ejpam-6593	384	5	(	(	PUNCT
ejpam-6593	384	6	2	2	NUM
ejpam-6593	384	7	+	+	NUM
ejpam-6593	384	8	5k	5k	NUM
ejpam-6593	384	9	)	)	PUNCT
ejpam-6593	384	10	≡	≡	PROPN
ejpam-6593	384	11	1	1	NUM
ejpam-6593	385	1	+	+	SYM
ejpam-6593	385	2	2	2	NUM
ejpam-6593	385	3	≡	≡	PROPN
ejpam-6593	385	4	3	3	NUM
ejpam-6593	385	5	(	(	PUNCT
ejpam-6593	385	6	mod	mod	NOUN
ejpam-6593	385	7	5	5	NUM
ejpam-6593	385	8	)	)	PUNCT
ejpam-6593	385	9	.	.	PUNCT
ejpam-6593	386	1	on	on	ADP
ejpam-6593	386	2	the	the	DET
ejpam-6593	386	3	other	other	ADJ
ejpam-6593	386	4	hand	hand	NOUN
ejpam-6593	386	5	,	,	PUNCT
ejpam-6593	386	6	z2	z2	PROPN
ejpam-6593	386	7	≡	≡	PROPN
ejpam-6593	386	8	0	0	NUM
ejpam-6593	386	9	,	,	PUNCT
ejpam-6593	386	10	1	1	NUM
ejpam-6593	386	11	,	,	PUNCT
ejpam-6593	386	12	or	or	CCONJ
ejpam-6593	386	13	4	4	NUM
ejpam-6593	386	14	(	(	PUNCT
ejpam-6593	386	15	mod	mod	NOUN
ejpam-6593	386	16	5	5	NUM
ejpam-6593	386	17	)	)	PUNCT
ejpam-6593	386	18	.	.	PUNCT
ejpam-6593	387	1	thus	thus	ADV
ejpam-6593	387	2	,	,	PUNCT
ejpam-6593	387	3	the	the	DET
ejpam-6593	387	4	equation	equation	NOUN
ejpam-6593	387	5	can	can	AUX
ejpam-6593	387	6	never	never	ADV
ejpam-6593	387	7	be	be	AUX
ejpam-6593	387	8	true	true	ADJ
ejpam-6593	387	9	whenever	whenever	SCONJ
ejpam-6593	387	10	x	x	SYM
ejpam-6593	387	11	≡	≡	PROPN
ejpam-6593	387	12	0	0	PUNCT
ejpam-6593	388	1	(	(	PUNCT
ejpam-6593	388	2	mod	mod	PROPN
ejpam-6593	388	3	4	4	NUM
ejpam-6593	388	4	)	)	PUNCT
ejpam-6593	388	5	.	.	PUNCT
ejpam-6593	389	1	2.1.2	2.1.2	X
ejpam-6593	389	2	.	.	PROPN
ejpam-6593	389	3	part	part	PROPN
ejpam-6593	389	4	ii	ii	PROPN
ejpam-6593	389	5	:	:	PUNCT
ejpam-6593	389	6	2x	2x	NUM
ejpam-6593	389	7	+	+	CCONJ
ejpam-6593	389	8	(	(	PUNCT
ejpam-6593	389	9	2	2	NUM
ejpam-6593	389	10	+	+	NUM
ejpam-6593	389	11	5k)y	5k)y	NOUN
ejpam-6593	389	12	=	=	SYM
ejpam-6593	389	13	z2	z2	PROPN
ejpam-6593	389	14	,	,	PUNCT
ejpam-6593	389	15	where	where	SCONJ
ejpam-6593	389	16	y	y	PROPN
ejpam-6593	389	17	̸=	̸=	PROPN
ejpam-6593	389	18	1	1	NUM
ejpam-6593	389	19	.	.	PUNCT
ejpam-6593	390	1	for	for	ADP
ejpam-6593	390	2	this	this	DET
ejpam-6593	390	3	part	part	NOUN
ejpam-6593	390	4	,	,	PUNCT
ejpam-6593	390	5	we	we	PRON
ejpam-6593	390	6	study	study	VERB
ejpam-6593	390	7	2x	2x	NUM
ejpam-6593	390	8	+	+	CCONJ
ejpam-6593	390	9	(	(	PUNCT
ejpam-6593	390	10	2	2	NUM
ejpam-6593	390	11	+	+	NUM
ejpam-6593	390	12	5k)y	5k)y	NOUN
ejpam-6593	390	13	=	=	SYM
ejpam-6593	390	14	z2	z2	PROPN
ejpam-6593	390	15	,	,	PUNCT
ejpam-6593	390	16	(	(	PUNCT
ejpam-6593	390	17	12	12	NUM
ejpam-6593	390	18	)	)	PUNCT
ejpam-6593	390	19	where	where	SCONJ
ejpam-6593	390	20	y	y	PROPN
ejpam-6593	390	21	̸=	̸=	PROPN
ejpam-6593	390	22	1	1	NUM
ejpam-6593	390	23	.	.	PUNCT
ejpam-6593	391	1	the	the	DET
ejpam-6593	391	2	discussion	discussion	NOUN
ejpam-6593	391	3	begins	begin	VERB
ejpam-6593	391	4	with	with	ADP
ejpam-6593	391	5	the	the	DET
ejpam-6593	391	6	case	case	NOUN
ejpam-6593	391	7	where	where	SCONJ
ejpam-6593	391	8	x	x	SYM
ejpam-6593	391	9	=	=	SYM
ejpam-6593	391	10	0	0	NUM
ejpam-6593	391	11	or	or	CCONJ
ejpam-6593	391	12	y	y	PROPN
ejpam-6593	391	13	=	=	SYM
ejpam-6593	391	14	0	0	PROPN
ejpam-6593	391	15	,	,	PUNCT
ejpam-6593	391	16	followed	follow	VERB
ejpam-6593	391	17	by	by	ADP
ejpam-6593	391	18	a	a	DET
ejpam-6593	391	19	claim	claim	NOUN
ejpam-6593	391	20	when	when	SCONJ
ejpam-6593	391	21	min	min	PROPN
ejpam-6593	391	22	(	(	PUNCT
ejpam-6593	391	23	x	x	PROPN
ejpam-6593	391	24	,	,	PUNCT
ejpam-6593	391	25	y	y	PROPN
ejpam-6593	391	26	)	)	PUNCT
ejpam-6593	391	27	>	>	X
ejpam-6593	391	28	1	1	X
ejpam-6593	391	29	.	.	PUNCT
ejpam-6593	391	30	m.	m.	PROPN
ejpam-6593	391	31	c.	c.	PROPN
ejpam-6593	391	32	avenilla	avenilla	PROPN
ejpam-6593	391	33	,	,	PUNCT
ejpam-6593	391	34	j.	j.	PROPN
ejpam-6593	391	35	b.	b.	PROPN
ejpam-6593	391	36	bacani	bacani	PROPN
ejpam-6593	391	37	/	/	SYM
ejpam-6593	391	38	eur	eur	PROPN
ejpam-6593	391	39	.	.	PUNCT
ejpam-6593	392	1	j.	j.	PROPN
ejpam-6593	392	2	pure	pure	PROPN
ejpam-6593	392	3	appl	appl	PROPN
ejpam-6593	392	4	.	.	PROPN
ejpam-6593	392	5	math	math	PROPN
ejpam-6593	392	6	,	,	PUNCT
ejpam-6593	392	7	18	18	NUM
ejpam-6593	392	8	(	(	PUNCT
ejpam-6593	392	9	3	3	NUM
ejpam-6593	392	10	)	)	PUNCT
ejpam-6593	392	11	(	(	PUNCT
ejpam-6593	392	12	2025	2025	NUM
ejpam-6593	392	13	)	)	PUNCT
ejpam-6593	392	14	,	,	PUNCT
ejpam-6593	392	15	6593	6593	NUM
ejpam-6593	392	16	12	12	NUM
ejpam-6593	392	17	of	of	ADP
ejpam-6593	392	18	24	24	NUM
ejpam-6593	392	19	theorem	theorem	NOUN
ejpam-6593	392	20	3	3	X
ejpam-6593	392	21	.	.	PUNCT
ejpam-6593	392	22	consider	consider	VERB
ejpam-6593	392	23	the	the	DET
ejpam-6593	392	24	diophantine	diophantine	NOUN
ejpam-6593	392	25	equation	equation	NOUN
ejpam-6593	392	26	(	(	PUNCT
ejpam-6593	392	27	12	12	NUM
ejpam-6593	392	28	)	)	PUNCT
ejpam-6593	392	29	.	.	PUNCT
ejpam-6593	393	1	let	let	VERB
ejpam-6593	393	2	y	y	NOUN
ejpam-6593	393	3	=	=	SYM
ejpam-6593	393	4	0	0	PROPN
ejpam-6593	393	5	.	.	PUNCT
ejpam-6593	394	1	then	then	ADV
ejpam-6593	394	2	,	,	PUNCT
ejpam-6593	394	3	(	(	PUNCT
ejpam-6593	394	4	12	12	NUM
ejpam-6593	394	5	)	)	PUNCT
ejpam-6593	394	6	has	have	VERB
ejpam-6593	394	7	a	a	DET
ejpam-6593	394	8	solution	solution	NOUN
ejpam-6593	394	9	only	only	ADV
ejpam-6593	394	10	when	when	SCONJ
ejpam-6593	394	11	x	x	X
ejpam-6593	394	12	=	=	SYM
ejpam-6593	394	13	3	3	X
ejpam-6593	394	14	.	.	PUNCT
ejpam-6593	394	15	consequently	consequently	ADV
ejpam-6593	394	16	,	,	PUNCT
ejpam-6593	394	17	(	(	PUNCT
ejpam-6593	394	18	p	p	X
ejpam-6593	394	19	,	,	PUNCT
ejpam-6593	394	20	k	k	NOUN
ejpam-6593	394	21	,	,	PUNCT
ejpam-6593	394	22	x	x	X
ejpam-6593	394	23	,	,	PUNCT
ejpam-6593	394	24	y	y	PROPN
ejpam-6593	394	25	,	,	PUNCT
ejpam-6593	394	26	z	z	NOUN
ejpam-6593	394	27	)	)	PUNCT
ejpam-6593	394	28	=	=	SYM
ejpam-6593	394	29	(	(	PUNCT
ejpam-6593	394	30	2	2	NUM
ejpam-6593	394	31	,	,	PUNCT
ejpam-6593	394	32	k	k	NOUN
ejpam-6593	394	33	,	,	PUNCT
ejpam-6593	394	34	3	3	NUM
ejpam-6593	394	35	,	,	PUNCT
ejpam-6593	394	36	0	0	NUM
ejpam-6593	394	37	,	,	PUNCT
ejpam-6593	394	38	3	3	NUM
ejpam-6593	394	39	)	)	PUNCT
ejpam-6593	394	40	is	be	AUX
ejpam-6593	394	41	a	a	DET
ejpam-6593	394	42	solution	solution	NOUN
ejpam-6593	394	43	for	for	ADP
ejpam-6593	394	44	all	all	DET
ejpam-6593	394	45	k	k	PROPN
ejpam-6593	394	46	∈	∈	PROPN
ejpam-6593	394	47	n.	n.	NOUN
ejpam-6593	394	48	on	on	ADP
ejpam-6593	394	49	the	the	DET
ejpam-6593	394	50	other	other	ADJ
ejpam-6593	394	51	hand	hand	NOUN
ejpam-6593	394	52	,	,	PUNCT
ejpam-6593	394	53	(	(	PUNCT
ejpam-6593	394	54	12	12	NUM
ejpam-6593	394	55	)	)	PUNCT
ejpam-6593	394	56	has	have	VERB
ejpam-6593	394	57	no	no	DET
ejpam-6593	394	58	solution	solution	NOUN
ejpam-6593	394	59	when	when	SCONJ
ejpam-6593	394	60	x	x	X
ejpam-6593	395	1	=	=	NOUN
ejpam-6593	395	2	0	0	X
ejpam-6593	395	3	.	.	PUNCT
ejpam-6593	396	1	proof	proof	NOUN
ejpam-6593	396	2	.	.	PUNCT
ejpam-6593	397	1	case	case	NOUN
ejpam-6593	397	2	1	1	X
ejpam-6593	397	3	.	.	PUNCT
ejpam-6593	398	1	let	let	VERB
ejpam-6593	398	2	y	y	NOUN
ejpam-6593	398	3	=	=	NOUN
ejpam-6593	398	4	0	0	PROPN
ejpam-6593	399	1	in	in	ADP
ejpam-6593	399	2	(	(	PUNCT
ejpam-6593	399	3	12	12	NUM
ejpam-6593	399	4	)	)	PUNCT
ejpam-6593	399	5	.	.	PUNCT
ejpam-6593	400	1	then	then	ADV
ejpam-6593	400	2	,	,	PUNCT
ejpam-6593	400	3	for	for	ADP
ejpam-6593	400	4	all	all	DET
ejpam-6593	400	5	k	k	PROPN
ejpam-6593	400	6	∈	∈	PROPN
ejpam-6593	400	7	n	n	CCONJ
ejpam-6593	400	8	,	,	PUNCT
ejpam-6593	400	9	(	(	PUNCT
ejpam-6593	400	10	2	2	NUM
ejpam-6593	400	11	+	+	NUM
ejpam-6593	400	12	5k)y	5k)y	NUM
ejpam-6593	400	13	=	=	SYM
ejpam-6593	400	14	1	1	X
ejpam-6593	400	15	.	.	X
ejpam-6593	400	16	we	we	PRON
ejpam-6593	400	17	can	can	AUX
ejpam-6593	400	18	express	express	VERB
ejpam-6593	400	19	(	(	PUNCT
ejpam-6593	400	20	12	12	NUM
ejpam-6593	400	21	)	)	PUNCT
ejpam-6593	400	22	as	as	ADP
ejpam-6593	400	23	2x+1	2x+1	PROPN
ejpam-6593	400	24	=	=	SYM
ejpam-6593	400	25	z2	z2	PROPN
ejpam-6593	400	26	,	,	PUNCT
ejpam-6593	400	27	or	or	CCONJ
ejpam-6593	400	28	equivalently	equivalently	ADV
ejpam-6593	400	29	,	,	PUNCT
ejpam-6593	400	30	z2−	z2−	NOUN
ejpam-6593	400	31	2x	2x	NUM
ejpam-6593	400	32	=	=	SYM
ejpam-6593	400	33	1	1	X
ejpam-6593	400	34	.	.	PUNCT
ejpam-6593	401	1	if	if	SCONJ
ejpam-6593	401	2	z	z	NOUN
ejpam-6593	401	3	=	=	SYM
ejpam-6593	401	4	0	0	NUM
ejpam-6593	401	5	or	or	CCONJ
ejpam-6593	401	6	z	z	NOUN
ejpam-6593	401	7	=	=	SYM
ejpam-6593	401	8	1	1	NUM
ejpam-6593	401	9	,	,	PUNCT
ejpam-6593	401	10	it	it	PRON
ejpam-6593	401	11	is	be	AUX
ejpam-6593	401	12	obvious	obvious	ADJ
ejpam-6593	401	13	that	that	SCONJ
ejpam-6593	401	14	it	it	PRON
ejpam-6593	401	15	has	have	VERB
ejpam-6593	401	16	no	no	DET
ejpam-6593	401	17	solution	solution	NOUN
ejpam-6593	401	18	.	.	PUNCT
ejpam-6593	402	1	however	however	ADV
ejpam-6593	402	2	,	,	PUNCT
ejpam-6593	402	3	if	if	SCONJ
ejpam-6593	402	4	z	z	PROPN
ejpam-6593	402	5	>	>	X
ejpam-6593	402	6	1	1	NUM
ejpam-6593	402	7	,	,	PUNCT
ejpam-6593	402	8	then	then	ADV
ejpam-6593	402	9	this	this	PRON
ejpam-6593	402	10	makes	make	VERB
ejpam-6593	402	11	it	it	PRON
ejpam-6593	402	12	a	a	DET
ejpam-6593	402	13	catalan	catalan	NOUN
ejpam-6593	402	14	equation	equation	NOUN
ejpam-6593	402	15	,	,	PUNCT
ejpam-6593	402	16	so	so	SCONJ
ejpam-6593	402	17	it	it	PRON
ejpam-6593	402	18	has	have	VERB
ejpam-6593	402	19	a	a	DET
ejpam-6593	402	20	unique	unique	ADJ
ejpam-6593	402	21	solution	solution	NOUN
ejpam-6593	402	22	.	.	PUNCT
ejpam-6593	403	1	hence	hence	ADV
ejpam-6593	403	2	,	,	PUNCT
ejpam-6593	403	3	(	(	PUNCT
ejpam-6593	403	4	p	p	X
ejpam-6593	403	5	,	,	PUNCT
ejpam-6593	403	6	k	k	NOUN
ejpam-6593	403	7	,	,	PUNCT
ejpam-6593	403	8	x	x	X
ejpam-6593	403	9	,	,	PUNCT
ejpam-6593	403	10	y	y	PROPN
ejpam-6593	403	11	,	,	PUNCT
ejpam-6593	403	12	z	z	NOUN
ejpam-6593	403	13	)	)	PUNCT
ejpam-6593	403	14	=	=	SYM
ejpam-6593	403	15	(	(	PUNCT
ejpam-6593	403	16	2	2	NUM
ejpam-6593	403	17	,	,	PUNCT
ejpam-6593	403	18	k	k	NOUN
ejpam-6593	403	19	,	,	PUNCT
ejpam-6593	403	20	3	3	NUM
ejpam-6593	403	21	,	,	PUNCT
ejpam-6593	403	22	0	0	NUM
ejpam-6593	403	23	,	,	PUNCT
ejpam-6593	403	24	3	3	NUM
ejpam-6593	403	25	)	)	PUNCT
ejpam-6593	403	26	is	be	AUX
ejpam-6593	403	27	a	a	DET
ejpam-6593	403	28	solution	solution	NOUN
ejpam-6593	403	29	of	of	ADP
ejpam-6593	403	30	(	(	PUNCT
ejpam-6593	403	31	12	12	NUM
ejpam-6593	403	32	)	)	PUNCT
ejpam-6593	403	33	.	.	PUNCT
ejpam-6593	404	1	therefore	therefore	ADV
ejpam-6593	404	2	,	,	PUNCT
ejpam-6593	404	3	if	if	SCONJ
ejpam-6593	404	4	y	y	PROPN
ejpam-6593	404	5	=	=	SYM
ejpam-6593	404	6	0	0	PROPN
ejpam-6593	404	7	,	,	PUNCT
ejpam-6593	404	8	(	(	PUNCT
ejpam-6593	404	9	12	12	NUM
ejpam-6593	404	10	)	)	PUNCT
ejpam-6593	404	11	has	have	VERB
ejpam-6593	404	12	a	a	DET
ejpam-6593	404	13	solution	solution	NOUN
ejpam-6593	404	14	only	only	ADV
ejpam-6593	404	15	if	if	SCONJ
ejpam-6593	404	16	x	x	PROPN
ejpam-6593	404	17	=	=	PUNCT
ejpam-6593	404	18	z	z	NOUN
ejpam-6593	404	19	=	=	SYM
ejpam-6593	404	20	3	3	NUM
ejpam-6593	404	21	for	for	ADP
ejpam-6593	404	22	all	all	DET
ejpam-6593	404	23	k	k	PROPN
ejpam-6593	404	24	∈	∈	PROPN
ejpam-6593	404	25	n.	n.	NOUN
ejpam-6593	404	26	case	case	NOUN
ejpam-6593	405	1	2	2	X
ejpam-6593	405	2	.	.	PUNCT
ejpam-6593	405	3	let	let	VERB
ejpam-6593	405	4	x	x	PUNCT
ejpam-6593	405	5	=	=	SYM
ejpam-6593	405	6	0	0	NUM
ejpam-6593	405	7	in	in	ADP
ejpam-6593	405	8	(	(	PUNCT
ejpam-6593	405	9	12	12	NUM
ejpam-6593	405	10	)	)	PUNCT
ejpam-6593	405	11	.	.	PUNCT
ejpam-6593	406	1	then	then	ADV
ejpam-6593	406	2	,	,	PUNCT
ejpam-6593	406	3	equation	equation	NOUN
ejpam-6593	406	4	(	(	PUNCT
ejpam-6593	406	5	12	12	NUM
ejpam-6593	406	6	)	)	PUNCT
ejpam-6593	406	7	will	will	AUX
ejpam-6593	406	8	be	be	AUX
ejpam-6593	406	9	equivalent	equivalent	ADJ
ejpam-6593	406	10	to	to	ADP
ejpam-6593	406	11	z2−(2	z2−(2	PROPN
ejpam-6593	406	12	+	+	PROPN
ejpam-6593	406	13	5k)y	5k)y	NOUN
ejpam-6593	406	14	=	=	SYM
ejpam-6593	406	15	1	1	X
ejpam-6593	406	16	.	.	PUNCT
ejpam-6593	407	1	by	by	ADP
ejpam-6593	407	2	mihailescu	mihailescu	PROPN
ejpam-6593	407	3	’s	’s	PART
ejpam-6593	407	4	theorem	theorem	PROPN
ejpam-6593	407	5	,	,	PUNCT
ejpam-6593	407	6	this	this	PRON
ejpam-6593	407	7	will	will	AUX
ejpam-6593	407	8	only	only	ADV
ejpam-6593	407	9	have	have	VERB
ejpam-6593	407	10	a	a	DET
ejpam-6593	407	11	solution	solution	NOUN
ejpam-6593	407	12	when	when	SCONJ
ejpam-6593	407	13	z	z	NOUN
ejpam-6593	407	14	=	=	SYM
ejpam-6593	407	15	3	3	NUM
ejpam-6593	407	16	,	,	PUNCT
ejpam-6593	407	17	y	y	PROPN
ejpam-6593	407	18	=	=	SYM
ejpam-6593	407	19	3	3	NUM
ejpam-6593	407	20	and	and	CCONJ
ejpam-6593	407	21	k	k	NOUN
ejpam-6593	407	22	=	=	NOUN
ejpam-6593	408	1	0	0	X
ejpam-6593	408	2	.	.	PUNCT
ejpam-6593	409	1	however	however	ADV
ejpam-6593	409	2	,	,	PUNCT
ejpam-6593	409	3	we	we	PRON
ejpam-6593	409	4	choose	choose	VERB
ejpam-6593	409	5	k	k	PROPN
ejpam-6593	409	6	∈	∈	PROPN
ejpam-6593	409	7	n	n	NOUN
ejpam-6593	410	1	and	and	CCONJ
ejpam-6593	410	2	so	so	ADV
ejpam-6593	410	3	it	it	PRON
ejpam-6593	410	4	is	be	AUX
ejpam-6593	410	5	impossible	impossible	ADJ
ejpam-6593	410	6	for	for	SCONJ
ejpam-6593	410	7	k	k	PROPN
ejpam-6593	410	8	=	=	SYM
ejpam-6593	410	9	0	0	PROPN
ejpam-6593	410	10	to	to	PART
ejpam-6593	410	11	happen	happen	VERB
ejpam-6593	410	12	.	.	PUNCT
ejpam-6593	411	1	therefore	therefore	ADV
ejpam-6593	411	2	,	,	PUNCT
ejpam-6593	411	3	(	(	PUNCT
ejpam-6593	411	4	12	12	NUM
ejpam-6593	411	5	)	)	PUNCT
ejpam-6593	411	6	has	have	VERB
ejpam-6593	411	7	no	no	DET
ejpam-6593	411	8	solution	solution	NOUN
ejpam-6593	411	9	if	if	SCONJ
ejpam-6593	411	10	x	x	PROPN
ejpam-6593	411	11	=	=	SYM
ejpam-6593	411	12	0	0	X
ejpam-6593	411	13	.	.	PUNCT
ejpam-6593	411	14	solutions	solution	NOUN
ejpam-6593	411	15	wherein	wherein	ADJ
ejpam-6593	411	16	min	min	PROPN
ejpam-6593	411	17	(	(	PUNCT
ejpam-6593	411	18	x	x	NOUN
ejpam-6593	411	19	,	,	PUNCT
ejpam-6593	411	20	y	y	PROPN
ejpam-6593	411	21	)	)	PUNCT
ejpam-6593	411	22	>	>	X
ejpam-6593	411	23	1	1	NUM
ejpam-6593	411	24	remains	remain	VERB
ejpam-6593	411	25	an	an	DET
ejpam-6593	411	26	open	open	ADJ
ejpam-6593	411	27	problem	problem	NOUN
ejpam-6593	411	28	.	.	PUNCT
ejpam-6593	412	1	below	below	ADV
ejpam-6593	412	2	is	be	AUX
ejpam-6593	412	3	a	a	DET
ejpam-6593	412	4	claim	claim	NOUN
ejpam-6593	412	5	that	that	PRON
ejpam-6593	412	6	has	have	AUX
ejpam-6593	412	7	been	be	AUX
ejpam-6593	412	8	verified	verify	VERB
ejpam-6593	412	9	numerically	numerically	ADV
ejpam-6593	412	10	but	but	CCONJ
ejpam-6593	412	11	has	have	AUX
ejpam-6593	412	12	not	not	PART
ejpam-6593	412	13	been	be	AUX
ejpam-6593	412	14	proven	prove	VERB
ejpam-6593	412	15	rigorously	rigorously	ADV
ejpam-6593	412	16	.	.	PUNCT
ejpam-6593	413	1	conjecture	conjecture	NOUN
ejpam-6593	413	2	1	1	NUM
ejpam-6593	413	3	.	.	PUNCT
ejpam-6593	414	1	let	let	VERB
ejpam-6593	414	2	k	k	PROPN
ejpam-6593	414	3	≤	≤	NUM
ejpam-6593	414	4	5000	5000	NUM
ejpam-6593	414	5	and	and	CCONJ
ejpam-6593	414	6	x	x	SYM
ejpam-6593	414	7	≤	≤	NOUN
ejpam-6593	414	8	50	50	NUM
ejpam-6593	414	9	.	.	PUNCT
ejpam-6593	415	1	if	if	SCONJ
ejpam-6593	415	2	y	y	PROPN
ejpam-6593	415	3	=	=	SYM
ejpam-6593	415	4	2	2	NUM
ejpam-6593	415	5	,	,	PUNCT
ejpam-6593	415	6	then	then	ADV
ejpam-6593	415	7	equation	equation	NOUN
ejpam-6593	415	8	(	(	PUNCT
ejpam-6593	415	9	12	12	NUM
ejpam-6593	415	10	)	)	PUNCT
ejpam-6593	415	11	has	have	VERB
ejpam-6593	415	12	21	21	NUM
ejpam-6593	415	13	solutions	solution	NOUN
ejpam-6593	415	14	,	,	PUNCT
ejpam-6593	415	15	and	and	CCONJ
ejpam-6593	415	16	if	if	SCONJ
ejpam-6593	415	17	y	y	PROPN
ejpam-6593	415	18	=	=	NOUN
ejpam-6593	415	19	3	3	NUM
ejpam-6593	415	20	then	then	ADV
ejpam-6593	415	21	(	(	PUNCT
ejpam-6593	415	22	12	12	NUM
ejpam-6593	415	23	)	)	PUNCT
ejpam-6593	415	24	has	have	VERB
ejpam-6593	415	25	9	9	NUM
ejpam-6593	415	26	solutions	solution	NOUN
ejpam-6593	415	27	.	.	PUNCT
ejpam-6593	416	1	tables	table	NOUN
ejpam-6593	416	2	12	12	NUM
ejpam-6593	416	3	and	and	CCONJ
ejpam-6593	416	4	13	13	NUM
ejpam-6593	416	5	are	be	AUX
ejpam-6593	416	6	given	give	VERB
ejpam-6593	416	7	below	below	ADV
ejpam-6593	416	8	to	to	PART
ejpam-6593	416	9	illustrate	illustrate	VERB
ejpam-6593	416	10	the	the	DET
ejpam-6593	416	11	list	list	NOUN
ejpam-6593	416	12	of	of	ADP
ejpam-6593	416	13	solutions	solution	NOUN
ejpam-6593	416	14	when	when	SCONJ
ejpam-6593	416	15	y	y	PROPN
ejpam-6593	416	16	=	=	SYM
ejpam-6593	416	17	2	2	NUM
ejpam-6593	416	18	and	and	CCONJ
ejpam-6593	416	19	y	y	NOUN
ejpam-6593	416	20	=	=	SYM
ejpam-6593	416	21	3	3	NUM
ejpam-6593	416	22	,	,	PUNCT
ejpam-6593	416	23	respectively	respectively	ADV
ejpam-6593	416	24	.	.	PUNCT
ejpam-6593	417	1	m.	m.	PROPN
ejpam-6593	417	2	c.	c.	PROPN
ejpam-6593	417	3	avenilla	avenilla	PROPN
ejpam-6593	417	4	,	,	PUNCT
ejpam-6593	417	5	j.	j.	PROPN
ejpam-6593	417	6	b.	b.	PROPN
ejpam-6593	417	7	bacani	bacani	PROPN
ejpam-6593	417	8	/	/	SYM
ejpam-6593	417	9	eur	eur	PROPN
ejpam-6593	417	10	.	.	PUNCT
ejpam-6593	418	1	j.	j.	PROPN
ejpam-6593	418	2	pure	pure	PROPN
ejpam-6593	418	3	appl	appl	PROPN
ejpam-6593	418	4	.	.	PROPN
ejpam-6593	418	5	math	math	PROPN
ejpam-6593	418	6	,	,	PUNCT
ejpam-6593	418	7	18	18	NUM
ejpam-6593	418	8	(	(	PUNCT
ejpam-6593	418	9	3	3	NUM
ejpam-6593	418	10	)	)	PUNCT
ejpam-6593	418	11	(	(	PUNCT
ejpam-6593	418	12	2025	2025	NUM
ejpam-6593	418	13	)	)	PUNCT
ejpam-6593	418	14	,	,	PUNCT
ejpam-6593	418	15	6593	6593	NUM
ejpam-6593	418	16	13	13	NUM
ejpam-6593	418	17	of	of	ADP
ejpam-6593	418	18	24	24	NUM
ejpam-6593	418	19	k	k	PROPN
ejpam-6593	418	20	z	z	NOUN
ejpam-6593	418	21	equation	equation	NOUN
ejpam-6593	418	22	solution	solution	NOUN
ejpam-6593	418	23	(	(	PUNCT
ejpam-6593	418	24	p	p	X
ejpam-6593	418	25	,	,	PUNCT
ejpam-6593	418	26	k	k	NOUN
ejpam-6593	418	27	,	,	PUNCT
ejpam-6593	418	28	x	x	X
ejpam-6593	418	29	,	,	PUNCT
ejpam-6593	418	30	y	y	PROPN
ejpam-6593	418	31	,	,	PUNCT
ejpam-6593	418	32	z	z	NOUN
ejpam-6593	418	33	)	)	PUNCT
ejpam-6593	418	34	1	1	NUM
ejpam-6593	418	35	9	9	NUM
ejpam-6593	418	36	25	25	NUM
ejpam-6593	418	37	+	+	CCONJ
ejpam-6593	418	38	(	(	PUNCT
ejpam-6593	418	39	2	2	NUM
ejpam-6593	418	40	+	+	NUM
ejpam-6593	418	41	5(1))2	5(1))2	NUM
ejpam-6593	418	42	=	=	SYM
ejpam-6593	418	43	92	92	NUM
ejpam-6593	418	44	(	(	PUNCT
ejpam-6593	418	45	2	2	NUM
ejpam-6593	418	46	,	,	PUNCT
ejpam-6593	418	47	1	1	NUM
ejpam-6593	418	48	,	,	PUNCT
ejpam-6593	418	49	5	5	NUM
ejpam-6593	418	50	,	,	PUNCT
ejpam-6593	418	51	2	2	NUM
ejpam-6593	418	52	,	,	PUNCT
ejpam-6593	418	53	9	9	NUM
ejpam-6593	418	54	)	)	SYM
ejpam-6593	418	55	2	2	NUM
ejpam-6593	418	56	20	20	NUM
ejpam-6593	418	57	28	28	NUM
ejpam-6593	418	58	+	+	CCONJ
ejpam-6593	418	59	(	(	PUNCT
ejpam-6593	418	60	2	2	NUM
ejpam-6593	418	61	+	+	NUM
ejpam-6593	418	62	5(2))2	5(2))2	NUM
ejpam-6593	418	63	=	=	SYM
ejpam-6593	418	64	202	202	NUM
ejpam-6593	418	65	(	(	PUNCT
ejpam-6593	418	66	2	2	NUM
ejpam-6593	418	67	,	,	PUNCT
ejpam-6593	418	68	2	2	NUM
ejpam-6593	418	69	,	,	PUNCT
ejpam-6593	418	70	8	8	NUM
ejpam-6593	418	71	,	,	PUNCT
ejpam-6593	418	72	2	2	NUM
ejpam-6593	418	73	,	,	PUNCT
ejpam-6593	418	74	20	20	NUM
ejpam-6593	418	75	)	)	PUNCT
ejpam-6593	418	76	12	12	NUM
ejpam-6593	418	77	66	66	NUM
ejpam-6593	418	78	29	29	NUM
ejpam-6593	418	79	+	+	CCONJ
ejpam-6593	418	80	(	(	PUNCT
ejpam-6593	418	81	2	2	NUM
ejpam-6593	418	82	+	+	NUM
ejpam-6593	418	83	5(12))2	5(12))2	NOUN
ejpam-6593	418	84	=	=	SYM
ejpam-6593	418	85	662	662	NUM
ejpam-6593	418	86	(	(	PUNCT
ejpam-6593	418	87	2	2	NUM
ejpam-6593	418	88	,	,	PUNCT
ejpam-6593	418	89	12	12	NUM
ejpam-6593	418	90	,	,	PUNCT
ejpam-6593	418	91	9	9	NUM
ejpam-6593	418	92	,	,	PUNCT
ejpam-6593	418	93	2	2	NUM
ejpam-6593	418	94	,	,	PUNCT
ejpam-6593	418	95	66	66	NUM
ejpam-6593	418	96	)	)	PUNCT
ejpam-6593	418	97	25	25	NUM
ejpam-6593	418	98	129	129	NUM
ejpam-6593	418	99	29	29	NUM
ejpam-6593	418	100	+	+	CCONJ
ejpam-6593	418	101	(	(	PUNCT
ejpam-6593	418	102	2	2	NUM
ejpam-6593	418	103	+	+	NUM
ejpam-6593	418	104	5(25))2	5(25))2	NOUN
ejpam-6593	418	105	=	=	SYM
ejpam-6593	418	106	1292	1292	NUM
ejpam-6593	418	107	(	(	PUNCT
ejpam-6593	418	108	2	2	NUM
ejpam-6593	418	109	,	,	PUNCT
ejpam-6593	418	110	25	25	NUM
ejpam-6593	418	111	,	,	PUNCT
ejpam-6593	418	112	9	9	NUM
ejpam-6593	418	113	,	,	PUNCT
ejpam-6593	418	114	2	2	NUM
ejpam-6593	418	115	,	,	PUNCT
ejpam-6593	418	116	129	129	NUM
ejpam-6593	418	117	)	)	PUNCT
ejpam-6593	418	118	50	50	NUM
ejpam-6593	418	119	260	260	NUM
ejpam-6593	418	120	212	212	NUM
ejpam-6593	418	121	+	+	CCONJ
ejpam-6593	418	122	(	(	PUNCT
ejpam-6593	418	123	2	2	NUM
ejpam-6593	418	124	+	+	NUM
ejpam-6593	418	125	5(50))2	5(50))2	NUM
ejpam-6593	418	126	=	=	SYM
ejpam-6593	418	127	2602	2602	NUM
ejpam-6593	418	128	(	(	PUNCT
ejpam-6593	418	129	2	2	NUM
ejpam-6593	418	130	,	,	PUNCT
ejpam-6593	418	131	50	50	NUM
ejpam-6593	418	132	,	,	PUNCT
ejpam-6593	418	133	12	12	NUM
ejpam-6593	418	134	,	,	PUNCT
ejpam-6593	418	135	2	2	NUM
ejpam-6593	418	136	,	,	PUNCT
ejpam-6593	418	137	260	260	NUM
ejpam-6593	418	138	)	)	PUNCT
ejpam-6593	418	139	6	6	NUM
ejpam-6593	418	140	96	96	NUM
ejpam-6593	418	141	213	213	NUM
ejpam-6593	418	142	+	+	CCONJ
ejpam-6593	418	143	(	(	PUNCT
ejpam-6593	418	144	2	2	NUM
ejpam-6593	418	145	+	+	NUM
ejpam-6593	418	146	5(6))2	5(6))2	NUM
ejpam-6593	418	147	=	=	SYM
ejpam-6593	418	148	962	962	NUM
ejpam-6593	418	149	(	(	PUNCT
ejpam-6593	418	150	2	2	NUM
ejpam-6593	418	151	,	,	PUNCT
ejpam-6593	418	152	6	6	NUM
ejpam-6593	418	153	,	,	PUNCT
ejpam-6593	418	154	13	13	NUM
ejpam-6593	418	155	,	,	PUNCT
ejpam-6593	418	156	2	2	NUM
ejpam-6593	418	157	,	,	PUNCT
ejpam-6593	418	158	96	96	NUM
ejpam-6593	418	159	)	)	PUNCT
ejpam-6593	418	160	22	22	NUM
ejpam-6593	418	161	144	144	NUM
ejpam-6593	418	162	213	213	NUM
ejpam-6593	418	163	+	+	CCONJ
ejpam-6593	418	164	(	(	PUNCT
ejpam-6593	418	165	2	2	NUM
ejpam-6593	418	166	+	+	NUM
ejpam-6593	418	167	5(22))2	5(22))2	NUM
ejpam-6593	418	168	=	=	SYM
ejpam-6593	418	169	1442	1442	NUM
ejpam-6593	418	170	(	(	PUNCT
ejpam-6593	418	171	2	2	NUM
ejpam-6593	418	172	,	,	PUNCT
ejpam-6593	418	173	22	22	NUM
ejpam-6593	418	174	,	,	PUNCT
ejpam-6593	418	175	13	13	NUM
ejpam-6593	418	176	,	,	PUNCT
ejpam-6593	418	177	2	2	NUM
ejpam-6593	418	178	,	,	PUNCT
ejpam-6593	418	179	144	144	NUM
ejpam-6593	418	180	)	)	PUNCT
ejpam-6593	418	181	204	204	NUM
ejpam-6593	418	182	1026	1026	NUM
ejpam-6593	418	183	213	213	NUM
ejpam-6593	418	184	+	+	CCONJ
ejpam-6593	418	185	(	(	PUNCT
ejpam-6593	418	186	2	2	NUM
ejpam-6593	418	187	+	+	NUM
ejpam-6593	419	1	5(204))2	5(204))2	NUM
ejpam-6593	419	2	=	=	SYM
ejpam-6593	419	3	10262	10262	NUM
ejpam-6593	419	4	(	(	PUNCT
ejpam-6593	419	5	2	2	NUM
ejpam-6593	419	6	,	,	PUNCT
ejpam-6593	419	7	204	204	NUM
ejpam-6593	419	8	,	,	PUNCT
ejpam-6593	419	9	13	13	NUM
ejpam-6593	419	10	,	,	PUNCT
ejpam-6593	419	11	2	2	NUM
ejpam-6593	419	12	,	,	PUNCT
ejpam-6593	419	13	1026	1026	NUM
ejpam-6593	419	14	)	)	PUNCT
ejpam-6593	419	15	409	409	NUM
ejpam-6593	419	16	2049	2049	NUM
ejpam-6593	419	17	213	213	NUM
ejpam-6593	419	18	+	+	CCONJ
ejpam-6593	419	19	(	(	PUNCT
ejpam-6593	419	20	2	2	NUM
ejpam-6593	419	21	+	+	NUM
ejpam-6593	419	22	5(409))2	5(409))2	NUM
ejpam-6593	419	23	=	=	SYM
ejpam-6593	419	24	20492	20492	NUM
ejpam-6593	419	25	(	(	PUNCT
ejpam-6593	419	26	2	2	NUM
ejpam-6593	419	27	,	,	PUNCT
ejpam-6593	419	28	409	409	NUM
ejpam-6593	419	29	,	,	PUNCT
ejpam-6593	419	30	13	13	NUM
ejpam-6593	419	31	,	,	PUNCT
ejpam-6593	419	32	2	2	NUM
ejpam-6593	419	33	,	,	PUNCT
ejpam-6593	419	34	2049	2049	NUM
ejpam-6593	419	35	)	)	PUNCT
ejpam-6593	419	36	38	38	NUM
ejpam-6593	419	37	320	320	NUM
ejpam-6593	419	38	216	216	NUM
ejpam-6593	419	39	+	+	CCONJ
ejpam-6593	419	40	(	(	PUNCT
ejpam-6593	419	41	2	2	NUM
ejpam-6593	419	42	+	+	NUM
ejpam-6593	419	43	5(38))2	5(38))2	NUM
ejpam-6593	419	44	=	=	SYM
ejpam-6593	419	45	3202	3202	NUM
ejpam-6593	419	46	(	(	PUNCT
ejpam-6593	419	47	2	2	NUM
ejpam-6593	419	48	,	,	PUNCT
ejpam-6593	419	49	38	38	NUM
ejpam-6593	419	50	,	,	PUNCT
ejpam-6593	419	51	16	16	NUM
ejpam-6593	419	52	,	,	PUNCT
ejpam-6593	419	53	2	2	NUM
ejpam-6593	419	54	,	,	PUNCT
ejpam-6593	419	55	320	320	NUM
ejpam-6593	419	56	)	)	PUNCT
ejpam-6593	419	57	818	818	NUM
ejpam-6593	419	58	4100	4100	NUM
ejpam-6593	419	59	216	216	NUM
ejpam-6593	419	60	+	+	CCONJ
ejpam-6593	419	61	(	(	PUNCT
ejpam-6593	419	62	2	2	NUM
ejpam-6593	419	63	+	+	NUM
ejpam-6593	419	64	5(818))2	5(818))2	NUM
ejpam-6593	419	65	=	=	SYM
ejpam-6593	419	66	41002	41002	NUM
ejpam-6593	419	67	(	(	PUNCT
ejpam-6593	419	68	2	2	NUM
ejpam-6593	419	69	,	,	PUNCT
ejpam-6593	419	70	818	818	NUM
ejpam-6593	419	71	,	,	PUNCT
ejpam-6593	419	72	16	16	NUM
ejpam-6593	419	73	,	,	PUNCT
ejpam-6593	419	74	2	2	NUM
ejpam-6593	419	75	,	,	PUNCT
ejpam-6593	419	76	4100	4100	NUM
ejpam-6593	419	77	)	)	PUNCT
ejpam-6593	419	78	198	198	NUM
ejpam-6593	419	79	1056	1056	NUM
ejpam-6593	419	80	217	217	NUM
ejpam-6593	420	1	+	+	CCONJ
ejpam-6593	420	2	(	(	PUNCT
ejpam-6593	420	3	2	2	NUM
ejpam-6593	420	4	+	+	NUM
ejpam-6593	420	5	5(198))2	5(198))2	NUM
ejpam-6593	420	6	=	=	SYM
ejpam-6593	420	7	10562	10562	NUM
ejpam-6593	420	8	(	(	PUNCT
ejpam-6593	420	9	2	2	NUM
ejpam-6593	420	10	,	,	PUNCT
ejpam-6593	420	11	198	198	NUM
ejpam-6593	420	12	,	,	PUNCT
ejpam-6593	420	13	17	17	NUM
ejpam-6593	420	14	,	,	PUNCT
ejpam-6593	420	15	2	2	NUM
ejpam-6593	420	16	,	,	PUNCT
ejpam-6593	420	17	1056	1056	NUM
ejpam-6593	420	18	)	)	PUNCT
ejpam-6593	420	19	406	406	NUM
ejpam-6593	420	20	2064	2064	NUM
ejpam-6593	420	21	217	217	NUM
ejpam-6593	420	22	+	+	CCONJ
ejpam-6593	420	23	(	(	PUNCT
ejpam-6593	420	24	2	2	NUM
ejpam-6593	420	25	+	+	SYM
ejpam-6593	420	26	5(406))2	5(406))2	NUM
ejpam-6593	420	27	=	=	SYM
ejpam-6593	420	28	20642	20642	NUM
ejpam-6593	420	29	(	(	PUNCT
ejpam-6593	420	30	2	2	NUM
ejpam-6593	420	31	,	,	PUNCT
ejpam-6593	420	32	406	406	NUM
ejpam-6593	420	33	,	,	PUNCT
ejpam-6593	420	34	17	17	NUM
ejpam-6593	420	35	,	,	PUNCT
ejpam-6593	420	36	2	2	NUM
ejpam-6593	420	37	,	,	PUNCT
ejpam-6593	420	38	2064	2064	NUM
ejpam-6593	420	39	)	)	PUNCT
ejpam-6593	420	40	3276	3276	NUM
ejpam-6593	420	41	16386	16386	NUM
ejpam-6593	420	42	217	217	NUM
ejpam-6593	420	43	+	+	CCONJ
ejpam-6593	420	44	(	(	PUNCT
ejpam-6593	420	45	2	2	NUM
ejpam-6593	420	46	+	+	SYM
ejpam-6593	420	47	5(3276))2	5(3276))2	NUM
ejpam-6593	420	48	=	=	SYM
ejpam-6593	420	49	163862	163862	NUM
ejpam-6593	420	50	(	(	PUNCT
ejpam-6593	420	51	2	2	NUM
ejpam-6593	420	52	,	,	PUNCT
ejpam-6593	420	53	3276	3276	NUM
ejpam-6593	420	54	,	,	PUNCT
ejpam-6593	420	55	17	17	NUM
ejpam-6593	420	56	,	,	PUNCT
ejpam-6593	420	57	2	2	NUM
ejpam-6593	420	58	,	,	PUNCT
ejpam-6593	420	59	16386	16386	NUM
ejpam-6593	420	60	)	)	PUNCT
ejpam-6593	420	61	806	806	NUM
ejpam-6593	420	62	4160	4160	NUM
ejpam-6593	420	63	220	220	NUM
ejpam-6593	420	64	+	+	CCONJ
ejpam-6593	420	65	(	(	PUNCT
ejpam-6593	420	66	2	2	NUM
ejpam-6593	420	67	+	+	NUM
ejpam-6593	420	68	5(806))2	5(806))2	NUM
ejpam-6593	420	69	=	=	SYM
ejpam-6593	420	70	41602	41602	NUM
ejpam-6593	420	71	(	(	PUNCT
ejpam-6593	420	72	2	2	NUM
ejpam-6593	420	73	,	,	PUNCT
ejpam-6593	420	74	806	806	NUM
ejpam-6593	420	75	,	,	PUNCT
ejpam-6593	420	76	20	20	NUM
ejpam-6593	420	77	,	,	PUNCT
ejpam-6593	420	78	2	2	NUM
ejpam-6593	420	79	,	,	PUNCT
ejpam-6593	420	80	4160	4160	NUM
ejpam-6593	420	81	)	)	PUNCT
ejpam-6593	420	82	102	102	NUM
ejpam-6593	420	83	1536	1536	NUM
ejpam-6593	420	84	221	221	NUM
ejpam-6593	420	85	+	+	CCONJ
ejpam-6593	420	86	(	(	PUNCT
ejpam-6593	420	87	2	2	NUM
ejpam-6593	420	88	+	+	NUM
ejpam-6593	420	89	5(102))2	5(102))2	NUM
ejpam-6593	420	90	=	=	SYM
ejpam-6593	420	91	15362	15362	NUM
ejpam-6593	420	92	(	(	PUNCT
ejpam-6593	420	93	2	2	NUM
ejpam-6593	420	94	,	,	PUNCT
ejpam-6593	420	95	102	102	NUM
ejpam-6593	420	96	,	,	PUNCT
ejpam-6593	420	97	21	21	NUM
ejpam-6593	420	98	,	,	PUNCT
ejpam-6593	420	99	2	2	NUM
ejpam-6593	420	100	,	,	PUNCT
ejpam-6593	420	101	1536	1536	NUM
ejpam-6593	420	102	)	)	PUNCT
ejpam-6593	420	103	358	358	NUM
ejpam-6593	420	104	2304	2304	NUM
ejpam-6593	420	105	221	221	NUM
ejpam-6593	420	106	+	+	CCONJ
ejpam-6593	420	107	(	(	PUNCT
ejpam-6593	420	108	2	2	NUM
ejpam-6593	420	109	+	+	NUM
ejpam-6593	420	110	5(358))2	5(358))2	NUM
ejpam-6593	420	111	=	=	SYM
ejpam-6593	420	112	23042	23042	NUM
ejpam-6593	420	113	(	(	PUNCT
ejpam-6593	420	114	2	2	NUM
ejpam-6593	420	115	,	,	PUNCT
ejpam-6593	420	116	358	358	NUM
ejpam-6593	420	117	,	,	PUNCT
ejpam-6593	420	118	21	21	NUM
ejpam-6593	420	119	,	,	PUNCT
ejpam-6593	420	120	2	2	NUM
ejpam-6593	420	121	,	,	PUNCT
ejpam-6593	420	122	2304	2304	NUM
ejpam-6593	420	123	)	)	PUNCT
ejpam-6593	420	124	3270	3270	NUM
ejpam-6593	420	125	16416	16416	NUM
ejpam-6593	420	126	221	221	NUM
ejpam-6593	420	127	+	+	CCONJ
ejpam-6593	420	128	(	(	PUNCT
ejpam-6593	420	129	2	2	NUM
ejpam-6593	420	130	+	+	NUM
ejpam-6593	420	131	5(3270))2	5(3270))2	NOUN
ejpam-6593	420	132	=	=	SYM
ejpam-6593	420	133	164162	164162	NUM
ejpam-6593	420	134	(	(	PUNCT
ejpam-6593	420	135	2	2	NUM
ejpam-6593	420	136	,	,	PUNCT
ejpam-6593	420	137	3270	3270	NUM
ejpam-6593	420	138	,	,	PUNCT
ejpam-6593	420	139	21	21	NUM
ejpam-6593	420	140	,	,	PUNCT
ejpam-6593	420	141	2	2	NUM
ejpam-6593	420	142	,	,	PUNCT
ejpam-6593	420	143	16416	16416	NUM
ejpam-6593	420	144	)	)	PUNCT
ejpam-6593	420	145	614	614	NUM
ejpam-6593	420	146	5120	5120	NUM
ejpam-6593	420	147	224	224	NUM
ejpam-6593	420	148	+	+	CCONJ
ejpam-6593	420	149	(	(	PUNCT
ejpam-6593	420	150	2	2	NUM
ejpam-6593	420	151	+	+	NUM
ejpam-6593	420	152	5(614))2	5(614))2	NUM
ejpam-6593	420	153	=	=	SYM
ejpam-6593	420	154	51202	51202	NUM
ejpam-6593	420	155	(	(	PUNCT
ejpam-6593	420	156	2	2	NUM
ejpam-6593	420	157	,	,	PUNCT
ejpam-6593	420	158	614	614	NUM
ejpam-6593	420	159	,	,	PUNCT
ejpam-6593	420	160	24	24	NUM
ejpam-6593	420	161	,	,	PUNCT
ejpam-6593	420	162	2	2	NUM
ejpam-6593	420	163	,	,	PUNCT
ejpam-6593	420	164	5120	5120	NUM
ejpam-6593	420	165	)	)	PUNCT
ejpam-6593	420	166	3174	3174	NUM
ejpam-6593	420	167	16896	16896	NUM
ejpam-6593	420	168	225	225	NUM
ejpam-6593	421	1	+	+	CCONJ
ejpam-6593	421	2	(	(	PUNCT
ejpam-6593	421	3	2	2	NUM
ejpam-6593	421	4	+	+	NUM
ejpam-6593	421	5	5(3174))2	5(3174))2	NUM
ejpam-6593	421	6	=	=	SYM
ejpam-6593	421	7	168962	168962	NUM
ejpam-6593	421	8	(	(	PUNCT
ejpam-6593	421	9	2	2	NUM
ejpam-6593	421	10	,	,	PUNCT
ejpam-6593	421	11	3174	3174	NUM
ejpam-6593	421	12	,	,	PUNCT
ejpam-6593	421	13	25	25	NUM
ejpam-6593	421	14	,	,	PUNCT
ejpam-6593	421	15	2	2	NUM
ejpam-6593	421	16	,	,	PUNCT
ejpam-6593	421	17	16896	16896	NUM
ejpam-6593	421	18	)	)	PUNCT
ejpam-6593	421	19	1638	1638	NUM
ejpam-6593	421	20	24576	24576	NUM
ejpam-6593	421	21	229	229	NUM
ejpam-6593	422	1	+	+	CCONJ
ejpam-6593	422	2	(	(	PUNCT
ejpam-6593	422	3	2	2	NUM
ejpam-6593	422	4	+	+	NUM
ejpam-6593	422	5	5(1638))2	5(1638))2	NUM
ejpam-6593	422	6	=	=	SYM
ejpam-6593	422	7	245762	245762	NUM
ejpam-6593	422	8	(	(	PUNCT
ejpam-6593	422	9	2	2	NUM
ejpam-6593	422	10	,	,	PUNCT
ejpam-6593	422	11	1638	1638	NUM
ejpam-6593	422	12	,	,	PUNCT
ejpam-6593	422	13	29	29	NUM
ejpam-6593	422	14	,	,	PUNCT
ejpam-6593	422	15	2	2	NUM
ejpam-6593	422	16	,	,	PUNCT
ejpam-6593	422	17	24576	24576	NUM
ejpam-6593	422	18	)	)	PUNCT
ejpam-6593	422	19	table	table	NOUN
ejpam-6593	422	20	12	12	NUM
ejpam-6593	422	21	:	:	PUNCT
ejpam-6593	422	22	solutions	solution	NOUN
ejpam-6593	422	23	of	of	ADP
ejpam-6593	422	24	2x	2x	NUM
ejpam-6593	422	25	+	+	CCONJ
ejpam-6593	422	26	(	(	PUNCT
ejpam-6593	422	27	2	2	NUM
ejpam-6593	422	28	+	+	NUM
ejpam-6593	422	29	5k)y	5k)y	NOUN
ejpam-6593	422	30	=	=	SYM
ejpam-6593	422	31	z2	z2	PROPN
ejpam-6593	422	32	when	when	SCONJ
ejpam-6593	422	33	y	y	PROPN
ejpam-6593	422	34	=	=	SYM
ejpam-6593	422	35	2	2	NUM
ejpam-6593	422	36	k	k	NOUN
ejpam-6593	422	37	z	z	NOUN
ejpam-6593	422	38	equation	equation	NOUN
ejpam-6593	422	39	solution	solution	NOUN
ejpam-6593	422	40	(	(	PUNCT
ejpam-6593	422	41	p	p	X
ejpam-6593	422	42	,	,	PUNCT
ejpam-6593	422	43	k	k	NOUN
ejpam-6593	422	44	,	,	PUNCT
ejpam-6593	422	45	x	x	X
ejpam-6593	422	46	,	,	PUNCT
ejpam-6593	422	47	y	y	PROPN
ejpam-6593	422	48	,	,	PUNCT
ejpam-6593	422	49	z	z	NOUN
ejpam-6593	422	50	)	)	PUNCT
ejpam-6593	422	51	3	3	NUM
ejpam-6593	422	52	71	71	NUM
ejpam-6593	422	53	27	27	NUM
ejpam-6593	422	54	+	+	CCONJ
ejpam-6593	422	55	(	(	PUNCT
ejpam-6593	422	56	2	2	NUM
ejpam-6593	422	57	+	+	NUM
ejpam-6593	422	58	5(3))3	5(3))3	NUM
ejpam-6593	422	59	=	=	SYM
ejpam-6593	422	60	712	712	NUM
ejpam-6593	422	61	(	(	PUNCT
ejpam-6593	422	62	2	2	NUM
ejpam-6593	422	63	,	,	PUNCT
ejpam-6593	422	64	3	3	NUM
ejpam-6593	422	65	,	,	PUNCT
ejpam-6593	422	66	7	7	NUM
ejpam-6593	422	67	,	,	PUNCT
ejpam-6593	422	68	3	3	NUM
ejpam-6593	422	69	,	,	PUNCT
ejpam-6593	422	70	71	71	NUM
ejpam-6593	422	71	)	)	PUNCT
ejpam-6593	422	72	6	6	NUM
ejpam-6593	422	73	192	192	NUM
ejpam-6593	422	74	212	212	NUM
ejpam-6593	422	75	+	+	CCONJ
ejpam-6593	422	76	(	(	PUNCT
ejpam-6593	422	77	2	2	NUM
ejpam-6593	422	78	+	+	NUM
ejpam-6593	422	79	5(6))3	5(6))3	NUM
ejpam-6593	422	80	=	=	SYM
ejpam-6593	422	81	1922	1922	NUM
ejpam-6593	422	82	(	(	PUNCT
ejpam-6593	422	83	2	2	NUM
ejpam-6593	422	84	,	,	PUNCT
ejpam-6593	422	85	6	6	NUM
ejpam-6593	422	86	,	,	PUNCT
ejpam-6593	422	87	12	12	NUM
ejpam-6593	422	88	,	,	PUNCT
ejpam-6593	422	89	3	3	NUM
ejpam-6593	422	90	,	,	PUNCT
ejpam-6593	422	91	192	192	NUM
ejpam-6593	422	92	)	)	PUNCT
ejpam-6593	422	93	6	6	NUM
ejpam-6593	422	94	256	256	NUM
ejpam-6593	422	95	215	215	NUM
ejpam-6593	422	96	+	+	CCONJ
ejpam-6593	422	97	(	(	PUNCT
ejpam-6593	422	98	2	2	NUM
ejpam-6593	422	99	+	+	NUM
ejpam-6593	422	100	5(6))3	5(6))3	NUM
ejpam-6593	422	101	=	=	SYM
ejpam-6593	422	102	2562	2562	NUM
ejpam-6593	422	103	(	(	PUNCT
ejpam-6593	422	104	2	2	NUM
ejpam-6593	422	105	,	,	PUNCT
ejpam-6593	422	106	6	6	NUM
ejpam-6593	422	107	,	,	PUNCT
ejpam-6593	422	108	15	15	NUM
ejpam-6593	422	109	,	,	PUNCT
ejpam-6593	422	110	3	3	NUM
ejpam-6593	422	111	,	,	PUNCT
ejpam-6593	422	112	256	256	NUM
ejpam-6593	422	113	)	)	PUNCT
ejpam-6593	422	114	54	54	NUM
ejpam-6593	422	115	4544	4544	NUM
ejpam-6593	422	116	219	219	NUM
ejpam-6593	423	1	+	+	CCONJ
ejpam-6593	423	2	(	(	PUNCT
ejpam-6593	423	3	2	2	NUM
ejpam-6593	423	4	+	+	NUM
ejpam-6593	423	5	5(54))3	5(54))3	NUM
ejpam-6593	423	6	=	=	SYM
ejpam-6593	423	7	45442	45442	NUM
ejpam-6593	423	8	(	(	PUNCT
ejpam-6593	423	9	2	2	NUM
ejpam-6593	423	10	,	,	PUNCT
ejpam-6593	423	11	54	54	NUM
ejpam-6593	423	12	,	,	PUNCT
ejpam-6593	423	13	19	19	NUM
ejpam-6593	423	14	,	,	PUNCT
ejpam-6593	423	15	3	3	NUM
ejpam-6593	423	16	,	,	PUNCT
ejpam-6593	423	17	4544	4544	NUM
ejpam-6593	423	18	)	)	PUNCT
ejpam-6593	423	19	102	102	NUM
ejpam-6593	423	20	12288	12288	NUM
ejpam-6593	423	21	224	224	NUM
ejpam-6593	423	22	+	+	CCONJ
ejpam-6593	423	23	(	(	PUNCT
ejpam-6593	423	24	2	2	NUM
ejpam-6593	423	25	+	+	SYM
ejpam-6593	423	26	5(102))3	5(102))3	NUM
ejpam-6593	423	27	=	=	SYM
ejpam-6593	423	28	122882	122882	NUM
ejpam-6593	423	29	(	(	PUNCT
ejpam-6593	423	30	2	2	NUM
ejpam-6593	423	31	,	,	PUNCT
ejpam-6593	423	32	102	102	NUM
ejpam-6593	423	33	,	,	PUNCT
ejpam-6593	423	34	24	24	NUM
ejpam-6593	423	35	,	,	PUNCT
ejpam-6593	423	36	3	3	NUM
ejpam-6593	423	37	,	,	PUNCT
ejpam-6593	423	38	12288	12288	NUM
ejpam-6593	423	39	)	)	PUNCT
ejpam-6593	423	40	102	102	NUM
ejpam-6593	423	41	16384	16384	NUM
ejpam-6593	423	42	227	227	NUM
ejpam-6593	424	1	+	+	CCONJ
ejpam-6593	424	2	(	(	PUNCT
ejpam-6593	424	3	2	2	NUM
ejpam-6593	424	4	+	+	SYM
ejpam-6593	424	5	5(102))3	5(102))3	NUM
ejpam-6593	424	6	=	=	SYM
ejpam-6593	424	7	163842	163842	NUM
ejpam-6593	424	8	(	(	PUNCT
ejpam-6593	424	9	2	2	NUM
ejpam-6593	424	10	,	,	PUNCT
ejpam-6593	424	11	102	102	NUM
ejpam-6593	424	12	,	,	PUNCT
ejpam-6593	424	13	27	27	NUM
ejpam-6593	424	14	,	,	PUNCT
ejpam-6593	424	15	3	3	NUM
ejpam-6593	424	16	,	,	PUNCT
ejpam-6593	424	17	16384	16384	NUM
ejpam-6593	424	18	)	)	PUNCT
ejpam-6593	424	19	870	870	NUM
ejpam-6593	424	20	290816	290816	NUM
ejpam-6593	424	21	231	231	NUM
ejpam-6593	424	22	+	+	CCONJ
ejpam-6593	424	23	(	(	PUNCT
ejpam-6593	424	24	2	2	NUM
ejpam-6593	424	25	+	+	SYM
ejpam-6593	424	26	5(870))3	5(870))3	NUM
ejpam-6593	424	27	=	=	SYM
ejpam-6593	424	28	2908162	2908162	NUM
ejpam-6593	424	29	(	(	PUNCT
ejpam-6593	424	30	2	2	NUM
ejpam-6593	424	31	,	,	PUNCT
ejpam-6593	424	32	870	870	NUM
ejpam-6593	424	33	,	,	PUNCT
ejpam-6593	424	34	31	31	NUM
ejpam-6593	424	35	,	,	PUNCT
ejpam-6593	424	36	3	3	NUM
ejpam-6593	424	37	,	,	PUNCT
ejpam-6593	424	38	290816	290816	NUM
ejpam-6593	424	39	)	)	PUNCT
ejpam-6593	424	40	1638	1638	NUM
ejpam-6593	424	41	786432	786432	NUM
ejpam-6593	424	42	236	236	NUM
ejpam-6593	424	43	+	+	CCONJ
ejpam-6593	424	44	(	(	PUNCT
ejpam-6593	424	45	2	2	NUM
ejpam-6593	424	46	+	+	NUM
ejpam-6593	424	47	5(1638))3	5(1638))3	X
ejpam-6593	424	48	=	=	SYM
ejpam-6593	424	49	7864322	7864322	NUM
ejpam-6593	424	50	(	(	PUNCT
ejpam-6593	424	51	2	2	NUM
ejpam-6593	424	52	,	,	PUNCT
ejpam-6593	424	53	1638	1638	NUM
ejpam-6593	424	54	,	,	PUNCT
ejpam-6593	424	55	36	36	NUM
ejpam-6593	424	56	,	,	PUNCT
ejpam-6593	424	57	3	3	NUM
ejpam-6593	424	58	,	,	PUNCT
ejpam-6593	424	59	786432	786432	NUM
ejpam-6593	424	60	)	)	PUNCT
ejpam-6593	424	61	1638	1638	NUM
ejpam-6593	424	62	1048576	1048576	NUM
ejpam-6593	424	63	239	239	NUM
ejpam-6593	424	64	+	+	CCONJ
ejpam-6593	424	65	(	(	PUNCT
ejpam-6593	424	66	2	2	NUM
ejpam-6593	424	67	+	+	NUM
ejpam-6593	424	68	5(1638))3	5(1638))3	NOUN
ejpam-6593	424	69	=	=	SYM
ejpam-6593	424	70	10485762	10485762	NUM
ejpam-6593	424	71	(	(	PUNCT
ejpam-6593	424	72	2	2	NUM
ejpam-6593	424	73	,	,	PUNCT
ejpam-6593	424	74	1638	1638	NUM
ejpam-6593	424	75	,	,	PUNCT
ejpam-6593	424	76	39	39	NUM
ejpam-6593	424	77	,	,	PUNCT
ejpam-6593	424	78	3	3	NUM
ejpam-6593	424	79	,	,	PUNCT
ejpam-6593	424	80	1048576	1048576	NUM
ejpam-6593	424	81	)	)	PUNCT
ejpam-6593	424	82	table	table	NOUN
ejpam-6593	424	83	13	13	NUM
ejpam-6593	424	84	:	:	PUNCT
ejpam-6593	424	85	solutions	solution	NOUN
ejpam-6593	424	86	of	of	ADP
ejpam-6593	424	87	2x	2x	NUM
ejpam-6593	424	88	+	+	CCONJ
ejpam-6593	424	89	(	(	PUNCT
ejpam-6593	424	90	2	2	NUM
ejpam-6593	424	91	+	+	NUM
ejpam-6593	424	92	5k)y	5k)y	NOUN
ejpam-6593	424	93	=	=	SYM
ejpam-6593	424	94	z2	z2	PROPN
ejpam-6593	424	95	when	when	SCONJ
ejpam-6593	424	96	y	y	PROPN
ejpam-6593	424	97	=	=	PROPN
ejpam-6593	424	98	3	3	NUM
ejpam-6593	424	99	2.2	2.2	NUM
ejpam-6593	424	100	.	.	PUNCT
ejpam-6593	425	1	on	on	ADP
ejpam-6593	425	2	the	the	DET
ejpam-6593	425	3	diophantine	diophantine	NOUN
ejpam-6593	425	4	equation	equation	NOUN
ejpam-6593	425	5	px	px	X
ejpam-6593	425	6	+	+	CCONJ
ejpam-6593	425	7	(	(	PUNCT
ejpam-6593	425	8	p+	p+	PROPN
ejpam-6593	425	9	5k)y	5k)y	NOUN
ejpam-6593	425	10	=	=	SYM
ejpam-6593	425	11	z2	z2	PROPN
ejpam-6593	425	12	for	for	ADP
ejpam-6593	425	13	prime	prime	ADJ
ejpam-6593	425	14	pairs	pair	NOUN
ejpam-6593	425	15	p	p	NOUN
ejpam-6593	425	16	and	and	CCONJ
ejpam-6593	425	17	p+	p+	PROPN
ejpam-6593	425	18	5k	5k	NUM
ejpam-6593	425	19	this	this	DET
ejpam-6593	425	20	subsection	subsection	NOUN
ejpam-6593	425	21	discusses	discuss	VERB
ejpam-6593	425	22	some	some	DET
ejpam-6593	425	23	findings	finding	NOUN
ejpam-6593	425	24	regarding	regard	VERB
ejpam-6593	425	25	solutions	solution	NOUN
ejpam-6593	425	26	of	of	ADP
ejpam-6593	425	27	(	(	PUNCT
ejpam-6593	425	28	3	3	NUM
ejpam-6593	425	29	)	)	PUNCT
ejpam-6593	425	30	,	,	PUNCT
ejpam-6593	425	31	where	where	SCONJ
ejpam-6593	425	32	p	p	PROPN
ejpam-6593	425	33	and	and	CCONJ
ejpam-6593	425	34	p+	p+	PROPN
ejpam-6593	425	35	5k	5k	NUM
ejpam-6593	425	36	are	be	AUX
ejpam-6593	425	37	prime	prime	ADJ
ejpam-6593	425	38	pairs	pair	NOUN
ejpam-6593	425	39	.	.	PUNCT
ejpam-6593	426	1	this	this	PRON
ejpam-6593	426	2	is	be	AUX
ejpam-6593	426	3	further	far	ADV
ejpam-6593	426	4	divided	divide	VERB
ejpam-6593	426	5	into	into	ADP
ejpam-6593	426	6	two	two	NUM
ejpam-6593	426	7	sub	sub	NOUN
ejpam-6593	426	8	-	-	NOUN
ejpam-6593	426	9	cases	case	NOUN
ejpam-6593	426	10	based	base	VERB
ejpam-6593	426	11	on	on	ADP
ejpam-6593	426	12	the	the	DET
ejpam-6593	426	13	parity	parity	NOUN
ejpam-6593	426	14	of	of	ADP
ejpam-6593	426	15	k	k	NOUN
ejpam-6593	426	16	;	;	PUNCT
ejpam-6593	426	17	that	that	PRON
ejpam-6593	426	18	is	is	ADV
ejpam-6593	426	19	,	,	PUNCT
ejpam-6593	426	20	when	when	SCONJ
ejpam-6593	426	21	k	k	PROPN
ejpam-6593	426	22	is	be	AUX
ejpam-6593	426	23	odd	odd	ADJ
ejpam-6593	426	24	,	,	PUNCT
ejpam-6593	426	25	and	and	CCONJ
ejpam-6593	426	26	when	when	SCONJ
ejpam-6593	426	27	k	k	PROPN
ejpam-6593	426	28	is	be	AUX
ejpam-6593	426	29	even	even	ADV
ejpam-6593	426	30	.	.	PUNCT
ejpam-6593	427	1	m.	m.	PROPN
ejpam-6593	427	2	c.	c.	PROPN
ejpam-6593	427	3	avenilla	avenilla	PROPN
ejpam-6593	427	4	,	,	PUNCT
ejpam-6593	427	5	j.	j.	PROPN
ejpam-6593	427	6	b.	b.	PROPN
ejpam-6593	427	7	bacani	bacani	PROPN
ejpam-6593	427	8	/	/	SYM
ejpam-6593	427	9	eur	eur	PROPN
ejpam-6593	427	10	.	.	PUNCT
ejpam-6593	428	1	j.	j.	PROPN
ejpam-6593	428	2	pure	pure	PROPN
ejpam-6593	428	3	appl	appl	PROPN
ejpam-6593	428	4	.	.	PROPN
ejpam-6593	428	5	math	math	PROPN
ejpam-6593	428	6	,	,	PUNCT
ejpam-6593	428	7	18	18	NUM
ejpam-6593	428	8	(	(	PUNCT
ejpam-6593	428	9	3	3	NUM
ejpam-6593	428	10	)	)	PUNCT
ejpam-6593	428	11	(	(	PUNCT
ejpam-6593	428	12	2025	2025	NUM
ejpam-6593	428	13	)	)	PUNCT
ejpam-6593	428	14	,	,	PUNCT
ejpam-6593	428	15	6593	6593	NUM
ejpam-6593	428	16	14	14	NUM
ejpam-6593	428	17	of	of	ADP
ejpam-6593	428	18	24	24	NUM
ejpam-6593	428	19	2.2.1	2.2.1	NUM
ejpam-6593	428	20	.	.	PUNCT
ejpam-6593	429	1	sub	sub	NOUN
ejpam-6593	429	2	-	-	NOUN
ejpam-6593	429	3	case	case	NOUN
ejpam-6593	429	4	i	i	PRON
ejpam-6593	429	5	:	:	PUNCT
ejpam-6593	429	6	k	k	PROPN
ejpam-6593	429	7	is	be	AUX
ejpam-6593	429	8	odd	odd	ADJ
ejpam-6593	429	9	.	.	PUNCT
ejpam-6593	430	1	the	the	DET
ejpam-6593	430	2	case	case	NOUN
ejpam-6593	430	3	where	where	SCONJ
ejpam-6593	430	4	p	p	NOUN
ejpam-6593	430	5	=	=	SYM
ejpam-6593	430	6	2	2	NUM
ejpam-6593	430	7	falls	fall	VERB
ejpam-6593	430	8	in	in	ADP
ejpam-6593	430	9	this	this	DET
ejpam-6593	430	10	sub	sub	NOUN
ejpam-6593	430	11	-	-	NOUN
ejpam-6593	430	12	case	case	NOUN
ejpam-6593	430	13	.	.	PUNCT
ejpam-6593	431	1	some	some	DET
ejpam-6593	431	2	results	result	NOUN
ejpam-6593	431	3	have	have	AUX
ejpam-6593	431	4	already	already	ADV
ejpam-6593	431	5	been	be	AUX
ejpam-6593	431	6	discussed	discuss	VERB
ejpam-6593	431	7	in	in	ADP
ejpam-6593	431	8	section	section	NOUN
ejpam-6593	431	9	2.1	2.1	NUM
ejpam-6593	431	10	.	.	PUNCT
ejpam-6593	432	1	additionally	additionally	ADV
ejpam-6593	432	2	,	,	PUNCT
ejpam-6593	432	3	using	use	VERB
ejpam-6593	432	4	similar	similar	ADJ
ejpam-6593	432	5	arguments	argument	NOUN
ejpam-6593	432	6	as	as	ADP
ejpam-6593	432	7	in	in	ADP
ejpam-6593	432	8	proving	prove	VERB
ejpam-6593	432	9	claims	claim	NOUN
ejpam-6593	432	10	in	in	ADP
ejpam-6593	432	11	that	that	DET
ejpam-6593	432	12	section	section	NOUN
ejpam-6593	432	13	,	,	PUNCT
ejpam-6593	432	14	we	we	PRON
ejpam-6593	432	15	obtain	obtain	VERB
ejpam-6593	432	16	the	the	DET
ejpam-6593	432	17	results	result	NOUN
ejpam-6593	432	18	below	below	ADV
ejpam-6593	432	19	.	.	PUNCT
ejpam-6593	433	1	we	we	PRON
ejpam-6593	433	2	note	note	VERB
ejpam-6593	433	3	that	that	SCONJ
ejpam-6593	433	4	in	in	ADP
ejpam-6593	433	5	the	the	DET
ejpam-6593	433	6	diophantine	diophantine	NOUN
ejpam-6593	433	7	equation	equation	NOUN
ejpam-6593	433	8	px	px	X
ejpam-6593	433	9	+	+	PROPN
ejpam-6593	433	10	(	(	PUNCT
ejpam-6593	433	11	p+5k)y	p+5k)y	NOUN
ejpam-6593	433	12	=	=	SYM
ejpam-6593	433	13	z2	z2	PROPN
ejpam-6593	433	14	,	,	PUNCT
ejpam-6593	433	15	where	where	SCONJ
ejpam-6593	433	16	p	p	NOUN
ejpam-6593	433	17	and	and	CCONJ
ejpam-6593	433	18	p+5k	p+5k	PROPN
ejpam-6593	433	19	are	be	AUX
ejpam-6593	433	20	prime	prime	ADJ
ejpam-6593	433	21	pairs	pair	NOUN
ejpam-6593	433	22	and	and	CCONJ
ejpam-6593	433	23	k	k	PROPN
ejpam-6593	433	24	is	be	AUX
ejpam-6593	433	25	odd	odd	ADJ
ejpam-6593	433	26	,	,	PUNCT
ejpam-6593	433	27	the	the	DET
ejpam-6593	433	28	prime	prime	ADJ
ejpam-6593	433	29	gap	gap	NOUN
ejpam-6593	433	30	5k	5k	NUM
ejpam-6593	433	31	is	be	AUX
ejpam-6593	433	32	also	also	ADV
ejpam-6593	433	33	odd	odd	ADJ
ejpam-6593	433	34	.	.	PUNCT
ejpam-6593	434	1	it	it	PRON
ejpam-6593	434	2	is	be	AUX
ejpam-6593	434	3	clear	clear	ADJ
ejpam-6593	434	4	that	that	SCONJ
ejpam-6593	434	5	p	p	PRON
ejpam-6593	434	6	+	+	NOUN
ejpam-6593	434	7	5k	5k	NUM
ejpam-6593	434	8	must	must	AUX
ejpam-6593	434	9	be	be	AUX
ejpam-6593	434	10	odd	odd	ADJ
ejpam-6593	434	11	to	to	PART
ejpam-6593	434	12	be	be	AUX
ejpam-6593	434	13	prime	prime	ADJ
ejpam-6593	434	14	and	and	CCONJ
ejpam-6593	434	15	for	for	SCONJ
ejpam-6593	434	16	it	it	PRON
ejpam-6593	434	17	to	to	PART
ejpam-6593	434	18	have	have	VERB
ejpam-6593	434	19	a	a	DET
ejpam-6593	434	20	prime	prime	ADJ
ejpam-6593	434	21	gap	gap	NOUN
ejpam-6593	434	22	of	of	ADP
ejpam-6593	434	23	an	an	DET
ejpam-6593	434	24	odd	odd	ADJ
ejpam-6593	434	25	number	number	NOUN
ejpam-6593	434	26	,	,	PUNCT
ejpam-6593	434	27	p	p	NOUN
ejpam-6593	434	28	must	must	AUX
ejpam-6593	434	29	be	be	AUX
ejpam-6593	434	30	even	even	ADV
ejpam-6593	434	31	,	,	PUNCT
ejpam-6593	434	32	that	that	ADV
ejpam-6593	434	33	is	is	ADV
ejpam-6593	434	34	,	,	PUNCT
ejpam-6593	434	35	p	p	X
ejpam-6593	434	36	=	=	NOUN
ejpam-6593	434	37	2	2	NUM
ejpam-6593	434	38	.	.	PUNCT
ejpam-6593	435	1	hence	hence	ADV
ejpam-6593	435	2	,	,	PUNCT
ejpam-6593	435	3	some	some	PRON
ejpam-6593	435	4	of	of	ADP
ejpam-6593	435	5	the	the	DET
ejpam-6593	435	6	solutions	solution	NOUN
ejpam-6593	435	7	were	be	AUX
ejpam-6593	435	8	already	already	ADV
ejpam-6593	435	9	included	include	VERB
ejpam-6593	435	10	in	in	ADP
ejpam-6593	435	11	section	section	NOUN
ejpam-6593	435	12	2.1	2.1	NUM
ejpam-6593	435	13	.	.	PUNCT
ejpam-6593	436	1	let	let	VERB
ejpam-6593	436	2	us	we	PRON
ejpam-6593	436	3	start	start	VERB
ejpam-6593	436	4	with	with	ADP
ejpam-6593	436	5	the	the	DET
ejpam-6593	436	6	discussion	discussion	NOUN
ejpam-6593	436	7	of	of	ADP
ejpam-6593	436	8	solutions	solution	NOUN
ejpam-6593	436	9	when	when	SCONJ
ejpam-6593	436	10	x	x	PRON
ejpam-6593	436	11	is	be	AUX
ejpam-6593	436	12	odd	odd	ADJ
ejpam-6593	436	13	.	.	PUNCT
ejpam-6593	437	1	that	that	PRON
ejpam-6593	437	2	is	be	AUX
ejpam-6593	437	3	,	,	PUNCT
ejpam-6593	437	4	x	x	SYM
ejpam-6593	437	5	≡	≡	PROPN
ejpam-6593	437	6	1	1	NUM
ejpam-6593	437	7	(	(	PUNCT
ejpam-6593	437	8	mod	mod	NOUN
ejpam-6593	437	9	4	4	NUM
ejpam-6593	437	10	)	)	PUNCT
ejpam-6593	437	11	and	and	CCONJ
ejpam-6593	437	12	x	x	SYM
ejpam-6593	437	13	≡	≡	PROPN
ejpam-6593	437	14	3	3	NUM
ejpam-6593	437	15	(	(	PUNCT
ejpam-6593	437	16	mod	mod	NOUN
ejpam-6593	437	17	4	4	NUM
ejpam-6593	437	18	)	)	PUNCT
ejpam-6593	437	19	.	.	PUNCT
ejpam-6593	438	1	note	note	VERB
ejpam-6593	438	2	that	that	SCONJ
ejpam-6593	438	3	unlike	unlike	ADP
ejpam-6593	438	4	the	the	DET
ejpam-6593	438	5	previous	previous	ADJ
ejpam-6593	438	6	section	section	NOUN
ejpam-6593	438	7	that	that	PRON
ejpam-6593	438	8	uses	use	VERB
ejpam-6593	438	9	modulo	modulo	NOUN
ejpam-6593	438	10	5	5	NUM
ejpam-6593	438	11	for	for	ADP
ejpam-6593	438	12	z	z	PROPN
ejpam-6593	438	13	,	,	PUNCT
ejpam-6593	438	14	this	this	DET
ejpam-6593	438	15	subsection	subsection	NOUN
ejpam-6593	438	16	uses	use	VERB
ejpam-6593	438	17	modulo	modulo	PART
ejpam-6593	438	18	10	10	NUM
ejpam-6593	438	19	.	.	PUNCT
ejpam-6593	439	1	we	we	PRON
ejpam-6593	439	2	start	start	VERB
ejpam-6593	439	3	the	the	DET
ejpam-6593	439	4	discussion	discussion	NOUN
ejpam-6593	439	5	with	with	ADP
ejpam-6593	439	6	the	the	DET
ejpam-6593	439	7	following	follow	VERB
ejpam-6593	439	8	lemmas	lemmas	NOUN
ejpam-6593	439	9	.	.	PUNCT
ejpam-6593	440	1	lemma	lemma	PROPN
ejpam-6593	440	2	4	4	X
ejpam-6593	440	3	.	.	PUNCT
ejpam-6593	441	1	let	let	VERB
ejpam-6593	441	2	k	k	PRON
ejpam-6593	441	3	be	be	AUX
ejpam-6593	441	4	an	an	DET
ejpam-6593	441	5	odd	odd	ADJ
ejpam-6593	441	6	integer	integer	NOUN
ejpam-6593	441	7	.	.	PUNCT
ejpam-6593	442	1	suppose	suppose	VERB
ejpam-6593	442	2	the	the	DET
ejpam-6593	442	3	diophantine	diophantine	NOUN
ejpam-6593	442	4	equation	equation	NOUN
ejpam-6593	442	5	(	(	PUNCT
ejpam-6593	442	6	5	5	NUM
ejpam-6593	442	7	)	)	PUNCT
ejpam-6593	442	8	has	have	VERB
ejpam-6593	442	9	a	a	DET
ejpam-6593	442	10	solution	solution	NOUN
ejpam-6593	442	11	.	.	PUNCT
ejpam-6593	443	1	then	then	ADV
ejpam-6593	443	2	,	,	PUNCT
ejpam-6593	443	3	x	x	PROPN
ejpam-6593	443	4	≡	≡	PROPN
ejpam-6593	443	5	1	1	NUM
ejpam-6593	443	6	(	(	PUNCT
ejpam-6593	443	7	mod	mod	NOUN
ejpam-6593	443	8	4	4	X
ejpam-6593	443	9	)	)	PUNCT
ejpam-6593	443	10	if	if	SCONJ
ejpam-6593	443	11	and	and	CCONJ
ejpam-6593	443	12	only	only	ADV
ejpam-6593	443	13	if	if	SCONJ
ejpam-6593	443	14	z	z	PROPN
ejpam-6593	443	15	≡	≡	PROPN
ejpam-6593	443	16	3	3	NUM
ejpam-6593	443	17	(	(	PUNCT
ejpam-6593	443	18	mod	mod	PROPN
ejpam-6593	443	19	10	10	NUM
ejpam-6593	443	20	)	)	PUNCT
ejpam-6593	443	21	or	or	CCONJ
ejpam-6593	443	22	z	z	PROPN
ejpam-6593	443	23	≡	≡	PROPN
ejpam-6593	443	24	7	7	NUM
ejpam-6593	443	25	(	(	PUNCT
ejpam-6593	443	26	mod	mod	PROPN
ejpam-6593	443	27	10	10	NUM
ejpam-6593	443	28	)	)	PUNCT
ejpam-6593	443	29	.	.	PUNCT
ejpam-6593	444	1	proof	proof	NOUN
ejpam-6593	444	2	.	.	PUNCT
ejpam-6593	445	1	consider	consider	VERB
ejpam-6593	445	2	equation	equation	NOUN
ejpam-6593	445	3	(	(	PUNCT
ejpam-6593	445	4	5	5	NUM
ejpam-6593	445	5	)	)	PUNCT
ejpam-6593	445	6	and	and	CCONJ
ejpam-6593	445	7	let	let	VERB
ejpam-6593	445	8	x	x	SYM
ejpam-6593	445	9	≡	≡	PROPN
ejpam-6593	445	10	1	1	NUM
ejpam-6593	445	11	(	(	PUNCT
ejpam-6593	445	12	mod	mod	NOUN
ejpam-6593	445	13	4	4	NUM
ejpam-6593	445	14	)	)	PUNCT
ejpam-6593	445	15	and	and	CCONJ
ejpam-6593	445	16	k	k	PROPN
ejpam-6593	445	17	be	be	AUX
ejpam-6593	445	18	odd	odd	ADJ
ejpam-6593	445	19	.	.	PUNCT
ejpam-6593	446	1	this	this	PRON
ejpam-6593	446	2	means	mean	VERB
ejpam-6593	446	3	that	that	SCONJ
ejpam-6593	446	4	2x	2x	NUM
ejpam-6593	446	5	+	+	CCONJ
ejpam-6593	446	6	(	(	PUNCT
ejpam-6593	446	7	2	2	NUM
ejpam-6593	446	8	+	+	NUM
ejpam-6593	446	9	5k	5k	NUM
ejpam-6593	446	10	)	)	PUNCT
ejpam-6593	446	11	≡	≡	PROPN
ejpam-6593	446	12	2	2	NUM
ejpam-6593	447	1	+	+	CCONJ
ejpam-6593	447	2	7	7	NUM
ejpam-6593	447	3	≡	≡	PROPN
ejpam-6593	447	4	9	9	NUM
ejpam-6593	447	5	(	(	PUNCT
ejpam-6593	447	6	mod	mod	PROPN
ejpam-6593	447	7	10	10	NUM
ejpam-6593	447	8	)	)	PUNCT
ejpam-6593	447	9	≡	≡	PROPN
ejpam-6593	447	10	z2	z2	PROPN
ejpam-6593	447	11	.	.	PUNCT
ejpam-6593	448	1	it	it	PRON
ejpam-6593	448	2	follows	follow	VERB
ejpam-6593	448	3	that	that	SCONJ
ejpam-6593	448	4	z2	z2	PROPN
ejpam-6593	448	5	must	must	AUX
ejpam-6593	448	6	be	be	AUX
ejpam-6593	448	7	odd	odd	ADJ
ejpam-6593	448	8	and	and	CCONJ
ejpam-6593	448	9	that	that	SCONJ
ejpam-6593	448	10	z	z	PROPN
ejpam-6593	448	11	is	be	AUX
ejpam-6593	448	12	odd	odd	ADJ
ejpam-6593	448	13	too	too	ADV
ejpam-6593	448	14	.	.	PUNCT
ejpam-6593	449	1	we	we	PRON
ejpam-6593	449	2	claim	claim	VERB
ejpam-6593	449	3	that	that	SCONJ
ejpam-6593	449	4	z	z	PROPN
ejpam-6593	449	5	≡	≡	PROPN
ejpam-6593	449	6	3	3	NUM
ejpam-6593	449	7	(	(	PUNCT
ejpam-6593	449	8	mod	mod	PROPN
ejpam-6593	449	9	10	10	NUM
ejpam-6593	449	10	)	)	PUNCT
ejpam-6593	449	11	or	or	CCONJ
ejpam-6593	449	12	z	z	PROPN
ejpam-6593	449	13	≡	≡	PROPN
ejpam-6593	449	14	7	7	NUM
ejpam-6593	449	15	(	(	PUNCT
ejpam-6593	449	16	mod	mod	PROPN
ejpam-6593	449	17	10	10	NUM
ejpam-6593	449	18	)	)	PUNCT
ejpam-6593	449	19	.	.	PUNCT
ejpam-6593	450	1	suppose	suppose	VERB
ejpam-6593	450	2	on	on	ADP
ejpam-6593	450	3	the	the	DET
ejpam-6593	450	4	contrary	contrary	NOUN
ejpam-6593	450	5	that	that	PRON
ejpam-6593	450	6	z	z	AUX
ejpam-6593	450	7	≡	≡	PROPN
ejpam-6593	450	8	1	1	NUM
ejpam-6593	450	9	,	,	PUNCT
ejpam-6593	450	10	5	5	NUM
ejpam-6593	450	11	or	or	CCONJ
ejpam-6593	450	12	9	9	NUM
ejpam-6593	450	13	(	(	PUNCT
ejpam-6593	450	14	mod	mod	PROPN
ejpam-6593	450	15	10	10	NUM
ejpam-6593	450	16	)	)	PUNCT
ejpam-6593	450	17	.	.	PUNCT
ejpam-6593	451	1	if	if	SCONJ
ejpam-6593	451	2	z	z	PROPN
ejpam-6593	451	3	≡	≡	PROPN
ejpam-6593	451	4	1	1	NUM
ejpam-6593	451	5	,	,	PUNCT
ejpam-6593	451	6	9	9	NUM
ejpam-6593	451	7	(	(	PUNCT
ejpam-6593	451	8	mod	mod	PROPN
ejpam-6593	451	9	10	10	NUM
ejpam-6593	451	10	)	)	PUNCT
ejpam-6593	451	11	,	,	PUNCT
ejpam-6593	451	12	then	then	ADV
ejpam-6593	451	13	z2	z2	PROPN
ejpam-6593	451	14	≡	≡	PROPN
ejpam-6593	451	15	1	1	NUM
ejpam-6593	451	16	(	(	PUNCT
ejpam-6593	451	17	mod	mod	PROPN
ejpam-6593	451	18	10	10	NUM
ejpam-6593	451	19	)	)	PUNCT
ejpam-6593	451	20	.	.	PUNCT
ejpam-6593	452	1	if	if	SCONJ
ejpam-6593	452	2	z	z	PROPN
ejpam-6593	452	3	≡	≡	PROPN
ejpam-6593	452	4	5	5	NUM
ejpam-6593	452	5	(	(	PUNCT
ejpam-6593	452	6	mod	mod	PROPN
ejpam-6593	452	7	10	10	NUM
ejpam-6593	452	8	)	)	PUNCT
ejpam-6593	452	9	,	,	PUNCT
ejpam-6593	452	10	then	then	ADV
ejpam-6593	452	11	z2	z2	PROPN
ejpam-6593	452	12	≡	≡	PROPN
ejpam-6593	452	13	5	5	NUM
ejpam-6593	452	14	(	(	PUNCT
ejpam-6593	452	15	mod	mod	PROPN
ejpam-6593	452	16	10	10	NUM
ejpam-6593	452	17	)	)	PUNCT
ejpam-6593	452	18	.	.	PUNCT
ejpam-6593	453	1	any	any	PRON
ejpam-6593	453	2	of	of	ADP
ejpam-6593	453	3	these	these	PRON
ejpam-6593	453	4	is	be	AUX
ejpam-6593	453	5	a	a	DET
ejpam-6593	453	6	contradiction	contradiction	NOUN
ejpam-6593	453	7	since	since	SCONJ
ejpam-6593	453	8	we	we	PRON
ejpam-6593	453	9	established	establish	VERB
ejpam-6593	453	10	that	that	SCONJ
ejpam-6593	453	11	z2	z2	PROPN
ejpam-6593	453	12	≡	≡	PROPN
ejpam-6593	453	13	9	9	NUM
ejpam-6593	453	14	(	(	PUNCT
ejpam-6593	453	15	mod	mod	PROPN
ejpam-6593	453	16	10	10	NUM
ejpam-6593	453	17	)	)	PUNCT
ejpam-6593	453	18	.	.	PUNCT
ejpam-6593	454	1	now	now	ADV
ejpam-6593	454	2	,	,	PUNCT
ejpam-6593	454	3	if	if	SCONJ
ejpam-6593	454	4	z	z	PROPN
ejpam-6593	454	5	≡	≡	PROPN
ejpam-6593	454	6	3	3	NUM
ejpam-6593	454	7	,	,	PUNCT
ejpam-6593	454	8	7	7	NUM
ejpam-6593	454	9	(	(	PUNCT
ejpam-6593	454	10	mod	mod	PROPN
ejpam-6593	454	11	10	10	NUM
ejpam-6593	454	12	)	)	PUNCT
ejpam-6593	454	13	,	,	PUNCT
ejpam-6593	454	14	then	then	ADV
ejpam-6593	454	15	z2	z2	PROPN
ejpam-6593	454	16	≡	≡	PROPN
ejpam-6593	454	17	9	9	NUM
ejpam-6593	454	18	(	(	PUNCT
ejpam-6593	454	19	mod	mod	PROPN
ejpam-6593	454	20	10	10	NUM
ejpam-6593	454	21	)	)	PUNCT
ejpam-6593	454	22	.	.	PUNCT
ejpam-6593	455	1	hence	hence	ADV
ejpam-6593	455	2	,	,	PUNCT
ejpam-6593	455	3	when	when	SCONJ
ejpam-6593	455	4	x	x	X
ejpam-6593	455	5	≡	≡	PROPN
ejpam-6593	455	6	1	1	NUM
ejpam-6593	455	7	(	(	PUNCT
ejpam-6593	455	8	mod	mod	NOUN
ejpam-6593	455	9	4	4	NUM
ejpam-6593	455	10	)	)	PUNCT
ejpam-6593	455	11	,	,	PUNCT
ejpam-6593	455	12	(	(	PUNCT
ejpam-6593	455	13	5	5	X
ejpam-6593	455	14	)	)	PUNCT
ejpam-6593	455	15	only	only	ADV
ejpam-6593	455	16	has	have	VERB
ejpam-6593	455	17	a	a	DET
ejpam-6593	455	18	solution	solution	NOUN
ejpam-6593	455	19	when	when	SCONJ
ejpam-6593	455	20	z	z	PROPN
ejpam-6593	455	21	≡	≡	PROPN
ejpam-6593	455	22	3	3	NUM
ejpam-6593	455	23	(	(	PUNCT
ejpam-6593	455	24	mod	mod	PROPN
ejpam-6593	455	25	10	10	NUM
ejpam-6593	455	26	)	)	PUNCT
ejpam-6593	455	27	or	or	CCONJ
ejpam-6593	455	28	z	z	PROPN
ejpam-6593	455	29	≡	≡	PROPN
ejpam-6593	455	30	7	7	NUM
ejpam-6593	455	31	(	(	PUNCT
ejpam-6593	455	32	mod	mod	PROPN
ejpam-6593	455	33	10	10	NUM
ejpam-6593	455	34	)	)	PUNCT
ejpam-6593	455	35	.	.	PUNCT
ejpam-6593	456	1	now	now	ADV
ejpam-6593	456	2	,	,	PUNCT
ejpam-6593	456	3	let	let	VERB
ejpam-6593	456	4	z	z	PROPN
ejpam-6593	456	5	≡	≡	PROPN
ejpam-6593	456	6	3	3	NUM
ejpam-6593	456	7	(	(	PUNCT
ejpam-6593	456	8	mod	mod	PROPN
ejpam-6593	456	9	10	10	NUM
ejpam-6593	456	10	)	)	PUNCT
ejpam-6593	456	11	or	or	CCONJ
ejpam-6593	456	12	z	z	PROPN
ejpam-6593	456	13	≡	≡	PROPN
ejpam-6593	456	14	7	7	NUM
ejpam-6593	456	15	(	(	PUNCT
ejpam-6593	456	16	mod	mod	PROPN
ejpam-6593	456	17	10	10	NUM
ejpam-6593	456	18	)	)	PUNCT
ejpam-6593	456	19	in	in	ADP
ejpam-6593	456	20	(	(	PUNCT
ejpam-6593	456	21	5	5	NUM
ejpam-6593	456	22	)	)	PUNCT
ejpam-6593	456	23	,	,	PUNCT
ejpam-6593	456	24	where	where	SCONJ
ejpam-6593	456	25	k	k	PROPN
ejpam-6593	456	26	is	be	AUX
ejpam-6593	456	27	odd	odd	ADJ
ejpam-6593	456	28	.	.	PUNCT
ejpam-6593	457	1	then	then	ADV
ejpam-6593	457	2	,	,	PUNCT
ejpam-6593	457	3	z2	z2	PROPN
ejpam-6593	457	4	≡	≡	PROPN
ejpam-6593	457	5	9	9	NUM
ejpam-6593	457	6	(	(	PUNCT
ejpam-6593	457	7	mod	mod	PROPN
ejpam-6593	457	8	10	10	NUM
ejpam-6593	457	9	)	)	PUNCT
ejpam-6593	457	10	.	.	PUNCT
ejpam-6593	458	1	suppose	suppose	VERB
ejpam-6593	458	2	on	on	ADP
ejpam-6593	458	3	the	the	DET
ejpam-6593	458	4	contrary	contrary	NOUN
ejpam-6593	459	1	that	that	SCONJ
ejpam-6593	459	2	x	x	SYM
ejpam-6593	459	3	≡	≡	PROPN
ejpam-6593	459	4	2	2	NUM
ejpam-6593	459	5	,	,	PUNCT
ejpam-6593	459	6	3	3	NUM
ejpam-6593	459	7	,	,	PUNCT
ejpam-6593	459	8	0	0	NUM
ejpam-6593	459	9	(	(	PUNCT
ejpam-6593	459	10	mod	mod	PROPN
ejpam-6593	459	11	4	4	NUM
ejpam-6593	459	12	)	)	PUNCT
ejpam-6593	459	13	,	,	PUNCT
ejpam-6593	459	14	then	then	ADV
ejpam-6593	459	15	2x	2x	NUM
ejpam-6593	459	16	≡	≡	PROPN
ejpam-6593	459	17	4	4	NUM
ejpam-6593	459	18	,	,	PUNCT
ejpam-6593	459	19	8	8	NUM
ejpam-6593	459	20	,	,	PUNCT
ejpam-6593	459	21	6	6	NUM
ejpam-6593	459	22	(	(	PUNCT
ejpam-6593	459	23	mod	mod	PROPN
ejpam-6593	459	24	10	10	NUM
ejpam-6593	459	25	)	)	PUNCT
ejpam-6593	459	26	,	,	PUNCT
ejpam-6593	459	27	respectively	respectively	ADV
ejpam-6593	459	28	.	.	PUNCT
ejpam-6593	460	1	hence	hence	ADV
ejpam-6593	460	2	,	,	PUNCT
ejpam-6593	460	3	we	we	PRON
ejpam-6593	460	4	will	will	AUX
ejpam-6593	460	5	have	have	VERB
ejpam-6593	460	6	2x	2x	NUM
ejpam-6593	460	7	+	+	CCONJ
ejpam-6593	460	8	(	(	PUNCT
ejpam-6593	460	9	2	2	NUM
ejpam-6593	460	10	+	+	NUM
ejpam-6593	460	11	5k	5k	NUM
ejpam-6593	460	12	)	)	PUNCT
ejpam-6593	460	13	≡	≡	PROPN
ejpam-6593	460	14	1	1	NUM
ejpam-6593	460	15	,	,	PUNCT
ejpam-6593	460	16	5	5	NUM
ejpam-6593	460	17	,	,	PUNCT
ejpam-6593	460	18	3	3	NUM
ejpam-6593	460	19	(	(	PUNCT
ejpam-6593	460	20	mod	mod	PROPN
ejpam-6593	460	21	10	10	NUM
ejpam-6593	460	22	)	)	PUNCT
ejpam-6593	460	23	,	,	PUNCT
ejpam-6593	460	24	respectively	respectively	ADV
ejpam-6593	460	25	.	.	PUNCT
ejpam-6593	461	1	this	this	PRON
ejpam-6593	461	2	will	will	AUX
ejpam-6593	461	3	be	be	AUX
ejpam-6593	461	4	a	a	DET
ejpam-6593	461	5	contradiction	contradiction	NOUN
ejpam-6593	461	6	from	from	ADP
ejpam-6593	461	7	the	the	DET
ejpam-6593	461	8	assumption	assumption	NOUN
ejpam-6593	461	9	that	that	SCONJ
ejpam-6593	461	10	z2	z2	PROPN
ejpam-6593	461	11	≡	≡	PROPN
ejpam-6593	461	12	9	9	NUM
ejpam-6593	461	13	(	(	PUNCT
ejpam-6593	461	14	mod	mod	PROPN
ejpam-6593	461	15	10	10	NUM
ejpam-6593	461	16	)	)	PUNCT
ejpam-6593	461	17	.	.	PUNCT
ejpam-6593	462	1	thus	thus	ADV
ejpam-6593	462	2	,	,	PUNCT
ejpam-6593	462	3	if	if	SCONJ
ejpam-6593	462	4	z	z	PROPN
ejpam-6593	462	5	≡	≡	PROPN
ejpam-6593	462	6	3	3	NUM
ejpam-6593	462	7	(	(	PUNCT
ejpam-6593	462	8	mod	mod	PROPN
ejpam-6593	462	9	10	10	NUM
ejpam-6593	462	10	)	)	PUNCT
ejpam-6593	462	11	or	or	CCONJ
ejpam-6593	462	12	z	z	PROPN
ejpam-6593	462	13	≡	≡	PROPN
ejpam-6593	462	14	7	7	NUM
ejpam-6593	462	15	(	(	PUNCT
ejpam-6593	462	16	mod	mod	PROPN
ejpam-6593	462	17	10	10	NUM
ejpam-6593	462	18	)	)	PUNCT
ejpam-6593	462	19	,	,	PUNCT
ejpam-6593	462	20	(	(	PUNCT
ejpam-6593	462	21	5	5	X
ejpam-6593	462	22	)	)	PUNCT
ejpam-6593	462	23	only	only	ADV
ejpam-6593	462	24	has	have	VERB
ejpam-6593	462	25	a	a	DET
ejpam-6593	462	26	solution	solution	NOUN
ejpam-6593	462	27	when	when	SCONJ
ejpam-6593	462	28	x	x	SYM
ejpam-6593	462	29	≡	≡	PROPN
ejpam-6593	462	30	1	1	NUM
ejpam-6593	462	31	(	(	PUNCT
ejpam-6593	462	32	mod	mod	NOUN
ejpam-6593	462	33	4	4	NUM
ejpam-6593	462	34	)	)	PUNCT
ejpam-6593	462	35	.	.	PUNCT
ejpam-6593	463	1	therefore	therefore	ADV
ejpam-6593	463	2	,	,	PUNCT
ejpam-6593	463	3	the	the	DET
ejpam-6593	463	4	equation	equation	NOUN
ejpam-6593	463	5	2x	2x	NUM
ejpam-6593	463	6	+	+	CCONJ
ejpam-6593	463	7	(	(	PUNCT
ejpam-6593	463	8	2	2	NUM
ejpam-6593	463	9	+	+	NUM
ejpam-6593	463	10	5k	5k	NUM
ejpam-6593	463	11	)	)	PUNCT
ejpam-6593	463	12	=	=	SYM
ejpam-6593	463	13	z2	z2	NOUN
ejpam-6593	463	14	where	where	SCONJ
ejpam-6593	463	15	2	2	NUM
ejpam-6593	463	16	and	and	CCONJ
ejpam-6593	463	17	2	2	NUM
ejpam-6593	463	18	+	+	NUM
ejpam-6593	463	19	5k	5k	NUM
ejpam-6593	463	20	are	be	AUX
ejpam-6593	463	21	prime	prime	ADJ
ejpam-6593	463	22	pairs	pair	NOUN
ejpam-6593	463	23	and	and	CCONJ
ejpam-6593	463	24	k	k	PROPN
ejpam-6593	463	25	is	be	AUX
ejpam-6593	463	26	odd	odd	ADJ
ejpam-6593	463	27	,	,	PUNCT
ejpam-6593	463	28	has	have	AUX
ejpam-6593	463	29	a	a	DET
ejpam-6593	463	30	solution	solution	NOUN
ejpam-6593	463	31	when	when	SCONJ
ejpam-6593	463	32	x	x	SYM
ejpam-6593	463	33	≡	≡	PROPN
ejpam-6593	463	34	1	1	NUM
ejpam-6593	463	35	(	(	PUNCT
ejpam-6593	463	36	mod	mod	NOUN
ejpam-6593	463	37	4	4	X
ejpam-6593	463	38	)	)	PUNCT
ejpam-6593	463	39	if	if	SCONJ
ejpam-6593	463	40	and	and	CCONJ
ejpam-6593	463	41	only	only	ADV
ejpam-6593	463	42	if	if	SCONJ
ejpam-6593	463	43	z	z	PROPN
ejpam-6593	463	44	≡	≡	PROPN
ejpam-6593	463	45	3	3	NUM
ejpam-6593	463	46	(	(	PUNCT
ejpam-6593	463	47	mod	mod	PROPN
ejpam-6593	463	48	10	10	NUM
ejpam-6593	463	49	)	)	PUNCT
ejpam-6593	463	50	or	or	CCONJ
ejpam-6593	463	51	z	z	PROPN
ejpam-6593	463	52	≡	≡	PROPN
ejpam-6593	463	53	7	7	NUM
ejpam-6593	463	54	(	(	PUNCT
ejpam-6593	463	55	mod	mod	PROPN
ejpam-6593	463	56	10	10	NUM
ejpam-6593	463	57	)	)	PUNCT
ejpam-6593	463	58	.	.	PUNCT
ejpam-6593	464	1	using	use	VERB
ejpam-6593	464	2	this	this	DET
ejpam-6593	464	3	result	result	NOUN
ejpam-6593	464	4	,	,	PUNCT
ejpam-6593	464	5	the	the	DET
ejpam-6593	464	6	first	first	ADJ
ejpam-6593	464	7	two	two	NUM
ejpam-6593	464	8	solutions	solution	NOUN
ejpam-6593	464	9	when	when	SCONJ
ejpam-6593	464	10	x	x	PROPN
ejpam-6593	464	11	=	=	SYM
ejpam-6593	464	12	1	1	NUM
ejpam-6593	464	13	and	and	CCONJ
ejpam-6593	464	14	z	z	PROPN
ejpam-6593	464	15	≡	≡	PROPN
ejpam-6593	464	16	3	3	NUM
ejpam-6593	464	17	(	(	PUNCT
ejpam-6593	464	18	mod	mod	PROPN
ejpam-6593	464	19	10	10	NUM
ejpam-6593	464	20	)	)	PUNCT
ejpam-6593	464	21	are	be	AUX
ejpam-6593	464	22	(	(	PUNCT
ejpam-6593	464	23	p	p	X
ejpam-6593	464	24	,	,	PUNCT
ejpam-6593	464	25	k	k	NOUN
ejpam-6593	464	26	,	,	PUNCT
ejpam-6593	464	27	x	x	X
ejpam-6593	464	28	,	,	PUNCT
ejpam-6593	464	29	y	y	PROPN
ejpam-6593	464	30	,	,	PUNCT
ejpam-6593	464	31	z	z	NOUN
ejpam-6593	464	32	)	)	PUNCT
ejpam-6593	465	1	=	=	SYM
ejpam-6593	465	2	(	(	PUNCT
ejpam-6593	465	3	2	2	NUM
ejpam-6593	465	4	,	,	PUNCT
ejpam-6593	465	5	1	1	NUM
ejpam-6593	465	6	,	,	PUNCT
ejpam-6593	465	7	1	1	NUM
ejpam-6593	465	8	,	,	PUNCT
ejpam-6593	465	9	1	1	NUM
ejpam-6593	465	10	,	,	PUNCT
ejpam-6593	465	11	3	3	NUM
ejpam-6593	465	12	)	)	PUNCT
ejpam-6593	465	13	and	and	CCONJ
ejpam-6593	465	14	(	(	PUNCT
ejpam-6593	465	15	2	2	NUM
ejpam-6593	465	16	,	,	PUNCT
ejpam-6593	465	17	33	33	NUM
ejpam-6593	465	18	,	,	PUNCT
ejpam-6593	465	19	1	1	NUM
ejpam-6593	465	20	,	,	PUNCT
ejpam-6593	465	21	1	1	NUM
ejpam-6593	465	22	,	,	PUNCT
ejpam-6593	465	23	13	13	NUM
ejpam-6593	465	24	)	)	PUNCT
ejpam-6593	465	25	.	.	PUNCT
ejpam-6593	466	1	on	on	ADP
ejpam-6593	466	2	the	the	DET
ejpam-6593	466	3	other	other	ADJ
ejpam-6593	466	4	hand	hand	NOUN
ejpam-6593	466	5	,	,	PUNCT
ejpam-6593	466	6	the	the	DET
ejpam-6593	466	7	first	first	ADJ
ejpam-6593	466	8	solution	solution	NOUN
ejpam-6593	466	9	when	when	SCONJ
ejpam-6593	466	10	x	x	PROPN
ejpam-6593	466	11	=	=	SYM
ejpam-6593	466	12	1	1	NUM
ejpam-6593	466	13	and	and	CCONJ
ejpam-6593	466	14	z	z	PROPN
ejpam-6593	466	15	≡	≡	PROPN
ejpam-6593	466	16	7	7	NUM
ejpam-6593	466	17	(	(	PUNCT
ejpam-6593	466	18	mod	mod	PROPN
ejpam-6593	466	19	10	10	NUM
ejpam-6593	466	20	)	)	PUNCT
ejpam-6593	466	21	is	be	AUX
ejpam-6593	466	22	(	(	PUNCT
ejpam-6593	466	23	p	p	X
ejpam-6593	466	24	,	,	PUNCT
ejpam-6593	466	25	k	k	NOUN
ejpam-6593	466	26	,	,	PUNCT
ejpam-6593	466	27	x	x	X
ejpam-6593	466	28	,	,	PUNCT
ejpam-6593	466	29	y	y	PROPN
ejpam-6593	466	30	,	,	PUNCT
ejpam-6593	466	31	z	z	NOUN
ejpam-6593	466	32	)	)	PUNCT
ejpam-6593	466	33	=	=	SYM
ejpam-6593	466	34	(	(	PUNCT
ejpam-6593	466	35	2	2	NUM
ejpam-6593	466	36	,	,	PUNCT
ejpam-6593	466	37	9	9	NUM
ejpam-6593	466	38	,	,	PUNCT
ejpam-6593	466	39	1	1	NUM
ejpam-6593	466	40	,	,	PUNCT
ejpam-6593	466	41	1	1	NUM
ejpam-6593	466	42	,	,	PUNCT
ejpam-6593	466	43	7	7	NUM
ejpam-6593	466	44	)	)	PUNCT
ejpam-6593	466	45	.	.	PUNCT
ejpam-6593	467	1	lemma	lemma	PROPN
ejpam-6593	467	2	5	5	X
ejpam-6593	467	3	.	.	PUNCT
ejpam-6593	468	1	let	let	VERB
ejpam-6593	468	2	k	k	PRON
ejpam-6593	468	3	be	be	AUX
ejpam-6593	468	4	an	an	DET
ejpam-6593	468	5	odd	odd	ADJ
ejpam-6593	468	6	integer	integer	NOUN
ejpam-6593	468	7	.	.	PUNCT
ejpam-6593	469	1	suppose	suppose	VERB
ejpam-6593	469	2	the	the	DET
ejpam-6593	469	3	diophantine	diophantine	NOUN
ejpam-6593	469	4	equation	equation	NOUN
ejpam-6593	469	5	(	(	PUNCT
ejpam-6593	469	6	5	5	NUM
ejpam-6593	469	7	)	)	PUNCT
ejpam-6593	469	8	has	have	VERB
ejpam-6593	469	9	a	a	DET
ejpam-6593	469	10	solution	solution	NOUN
ejpam-6593	469	11	.	.	PUNCT
ejpam-6593	470	1	then	then	ADV
ejpam-6593	470	2	,	,	PUNCT
ejpam-6593	470	3	x	x	PROPN
ejpam-6593	470	4	≡	≡	PROPN
ejpam-6593	470	5	3	3	NUM
ejpam-6593	470	6	(	(	PUNCT
ejpam-6593	470	7	mod	mod	NOUN
ejpam-6593	470	8	4	4	X
ejpam-6593	470	9	)	)	PUNCT
ejpam-6593	470	10	if	if	SCONJ
ejpam-6593	470	11	and	and	CCONJ
ejpam-6593	470	12	only	only	ADV
ejpam-6593	470	13	if	if	SCONJ
ejpam-6593	470	14	z	z	PROPN
ejpam-6593	470	15	≡	≡	PROPN
ejpam-6593	470	16	5	5	NUM
ejpam-6593	470	17	(	(	PUNCT
ejpam-6593	470	18	mod	mod	PROPN
ejpam-6593	470	19	10	10	NUM
ejpam-6593	470	20	)	)	PUNCT
ejpam-6593	470	21	.	.	PUNCT
ejpam-6593	471	1	proof	proof	NOUN
ejpam-6593	471	2	.	.	PUNCT
ejpam-6593	472	1	let	let	VERB
ejpam-6593	472	2	x	x	SYM
ejpam-6593	472	3	≡	≡	PROPN
ejpam-6593	472	4	3	3	NUM
ejpam-6593	472	5	(	(	PUNCT
ejpam-6593	472	6	mod	mod	NOUN
ejpam-6593	472	7	4	4	NUM
ejpam-6593	472	8	)	)	PUNCT
ejpam-6593	472	9	in	in	ADP
ejpam-6593	472	10	(	(	PUNCT
ejpam-6593	472	11	5	5	NUM
ejpam-6593	472	12	)	)	PUNCT
ejpam-6593	472	13	,	,	PUNCT
ejpam-6593	472	14	where	where	SCONJ
ejpam-6593	472	15	p	p	NOUN
ejpam-6593	472	16	=	=	NOUN
ejpam-6593	472	17	2	2	NUM
ejpam-6593	472	18	and	and	CCONJ
ejpam-6593	472	19	p+5k	p+5k	PROPN
ejpam-6593	472	20	are	be	AUX
ejpam-6593	472	21	prime	prime	ADJ
ejpam-6593	472	22	pairs	pair	NOUN
ejpam-6593	472	23	and	and	CCONJ
ejpam-6593	472	24	k	k	PROPN
ejpam-6593	472	25	is	be	AUX
ejpam-6593	472	26	odd	odd	ADJ
ejpam-6593	472	27	.	.	PUNCT
ejpam-6593	473	1	this	this	PRON
ejpam-6593	473	2	means	mean	VERB
ejpam-6593	473	3	that	that	SCONJ
ejpam-6593	473	4	2x+(2	2x+(2	NUM
ejpam-6593	473	5	+	+	SYM
ejpam-6593	473	6	5k	5k	NUM
ejpam-6593	473	7	)	)	PUNCT
ejpam-6593	473	8	≡	≡	PROPN
ejpam-6593	473	9	8	8	NUM
ejpam-6593	473	10	+	+	SYM
ejpam-6593	473	11	7	7	NUM
ejpam-6593	473	12	≡	≡	PROPN
ejpam-6593	473	13	5	5	NUM
ejpam-6593	473	14	(	(	PUNCT
ejpam-6593	473	15	mod	mod	PROPN
ejpam-6593	473	16	10	10	NUM
ejpam-6593	473	17	)	)	PUNCT
ejpam-6593	473	18	≡	≡	PROPN
ejpam-6593	473	19	z2	z2	PROPN
ejpam-6593	473	20	.	.	PUNCT
ejpam-6593	474	1	then	then	ADV
ejpam-6593	474	2	,	,	PUNCT
ejpam-6593	474	3	z2	z2	PROPN
ejpam-6593	474	4	is	be	AUX
ejpam-6593	474	5	odd	odd	ADJ
ejpam-6593	474	6	and	and	CCONJ
ejpam-6593	474	7	z	z	NOUN
ejpam-6593	474	8	must	must	AUX
ejpam-6593	474	9	be	be	AUX
ejpam-6593	474	10	odd	odd	ADJ
ejpam-6593	474	11	too	too	ADV
ejpam-6593	474	12	.	.	PUNCT
ejpam-6593	475	1	we	we	PRON
ejpam-6593	475	2	claim	claim	VERB
ejpam-6593	475	3	that	that	SCONJ
ejpam-6593	475	4	z	z	PROPN
ejpam-6593	475	5	≡	≡	PROPN
ejpam-6593	475	6	5	5	NUM
ejpam-6593	475	7	(	(	PUNCT
ejpam-6593	475	8	mod	mod	PROPN
ejpam-6593	475	9	10	10	NUM
ejpam-6593	475	10	)	)	PUNCT
ejpam-6593	475	11	.	.	PUNCT
ejpam-6593	476	1	suppose	suppose	VERB
ejpam-6593	476	2	on	on	ADP
ejpam-6593	476	3	the	the	DET
ejpam-6593	476	4	contrary	contrary	NOUN
ejpam-6593	476	5	that	that	SCONJ
ejpam-6593	476	6	z	z	NOUN
ejpam-6593	476	7	̸≡	̸≡	VERB
ejpam-6593	476	8	5	5	NUM
ejpam-6593	476	9	(	(	PUNCT
ejpam-6593	476	10	mod	mod	PROPN
ejpam-6593	476	11	10	10	NUM
ejpam-6593	476	12	)	)	PUNCT
ejpam-6593	476	13	.	.	PUNCT
ejpam-6593	477	1	if	if	SCONJ
ejpam-6593	477	2	z	z	PROPN
ejpam-6593	477	3	≡	≡	PROPN
ejpam-6593	477	4	1	1	NUM
ejpam-6593	477	5	,	,	PUNCT
ejpam-6593	477	6	9	9	NUM
ejpam-6593	477	7	(	(	PUNCT
ejpam-6593	477	8	mod	mod	PROPN
ejpam-6593	477	9	10	10	NUM
ejpam-6593	477	10	)	)	PUNCT
ejpam-6593	477	11	,	,	PUNCT
ejpam-6593	477	12	then	then	ADV
ejpam-6593	477	13	z2	z2	PROPN
ejpam-6593	477	14	≡	≡	PROPN
ejpam-6593	477	15	1	1	NUM
ejpam-6593	477	16	(	(	PUNCT
ejpam-6593	477	17	mod	mod	PROPN
ejpam-6593	477	18	10	10	NUM
ejpam-6593	477	19	)	)	PUNCT
ejpam-6593	477	20	.	.	PUNCT
ejpam-6593	478	1	if	if	SCONJ
ejpam-6593	478	2	z	z	PROPN
ejpam-6593	478	3	≡	≡	PROPN
ejpam-6593	478	4	3	3	NUM
ejpam-6593	478	5	,	,	PUNCT
ejpam-6593	478	6	7	7	NUM
ejpam-6593	478	7	(	(	PUNCT
ejpam-6593	478	8	mod	mod	PROPN
ejpam-6593	478	9	10	10	NUM
ejpam-6593	478	10	)	)	PUNCT
ejpam-6593	478	11	,	,	PUNCT
ejpam-6593	478	12	then	then	ADV
ejpam-6593	478	13	z2	z2	PROPN
ejpam-6593	478	14	≡	≡	PROPN
ejpam-6593	478	15	1	1	NUM
ejpam-6593	478	16	(	(	PUNCT
ejpam-6593	478	17	mod	mod	PROPN
ejpam-6593	478	18	10	10	NUM
ejpam-6593	478	19	)	)	PUNCT
ejpam-6593	478	20	.	.	PUNCT
ejpam-6593	479	1	any	any	PRON
ejpam-6593	479	2	of	of	ADP
ejpam-6593	479	3	these	these	PRON
ejpam-6593	479	4	is	be	AUX
ejpam-6593	479	5	a	a	DET
ejpam-6593	479	6	contradiction	contradiction	NOUN
ejpam-6593	479	7	since	since	SCONJ
ejpam-6593	479	8	we	we	PRON
ejpam-6593	479	9	established	establish	VERB
ejpam-6593	479	10	that	that	SCONJ
ejpam-6593	479	11	z2	z2	PROPN
ejpam-6593	479	12	≡	≡	PROPN
ejpam-6593	479	13	5	5	NUM
ejpam-6593	479	14	(	(	PUNCT
ejpam-6593	479	15	mod	mod	PROPN
ejpam-6593	479	16	10	10	NUM
ejpam-6593	479	17	)	)	PUNCT
ejpam-6593	479	18	.	.	PUNCT
ejpam-6593	480	1	now	now	ADV
ejpam-6593	480	2	,	,	PUNCT
ejpam-6593	480	3	if	if	SCONJ
ejpam-6593	480	4	z	z	PROPN
ejpam-6593	480	5	≡	≡	PROPN
ejpam-6593	480	6	5	5	NUM
ejpam-6593	480	7	(	(	PUNCT
ejpam-6593	480	8	mod	mod	PROPN
ejpam-6593	480	9	10	10	NUM
ejpam-6593	480	10	)	)	PUNCT
ejpam-6593	480	11	,	,	PUNCT
ejpam-6593	480	12	then	then	ADV
ejpam-6593	480	13	z2	z2	PROPN
ejpam-6593	480	14	≡	≡	PROPN
ejpam-6593	480	15	5	5	NUM
ejpam-6593	480	16	(	(	PUNCT
ejpam-6593	480	17	mod	mod	PROPN
ejpam-6593	480	18	10	10	NUM
ejpam-6593	480	19	)	)	PUNCT
ejpam-6593	480	20	.	.	PUNCT
ejpam-6593	481	1	hence	hence	ADV
ejpam-6593	481	2	,	,	PUNCT
ejpam-6593	481	3	when	when	SCONJ
ejpam-6593	481	4	x	x	X
ejpam-6593	481	5	≡	≡	PROPN
ejpam-6593	481	6	3	3	NUM
ejpam-6593	481	7	(	(	PUNCT
ejpam-6593	481	8	mod	mod	NOUN
ejpam-6593	481	9	4	4	NUM
ejpam-6593	481	10	)	)	PUNCT
ejpam-6593	481	11	,	,	PUNCT
ejpam-6593	481	12	(	(	PUNCT
ejpam-6593	481	13	5	5	X
ejpam-6593	481	14	)	)	PUNCT
ejpam-6593	481	15	only	only	ADV
ejpam-6593	481	16	has	have	VERB
ejpam-6593	481	17	a	a	DET
ejpam-6593	481	18	solution	solution	NOUN
ejpam-6593	481	19	when	when	SCONJ
ejpam-6593	481	20	z	z	PROPN
ejpam-6593	481	21	≡	≡	PROPN
ejpam-6593	481	22	5	5	NUM
ejpam-6593	481	23	(	(	PUNCT
ejpam-6593	481	24	mod	mod	PROPN
ejpam-6593	481	25	10	10	NUM
ejpam-6593	481	26	)	)	PUNCT
ejpam-6593	481	27	.	.	PUNCT
ejpam-6593	482	1	m.	m.	PROPN
ejpam-6593	482	2	c.	c.	PROPN
ejpam-6593	482	3	avenilla	avenilla	PROPN
ejpam-6593	482	4	,	,	PUNCT
ejpam-6593	482	5	j.	j.	PROPN
ejpam-6593	482	6	b.	b.	PROPN
ejpam-6593	482	7	bacani	bacani	PROPN
ejpam-6593	482	8	/	/	SYM
ejpam-6593	482	9	eur	eur	PROPN
ejpam-6593	482	10	.	.	PUNCT
ejpam-6593	483	1	j.	j.	PROPN
ejpam-6593	483	2	pure	pure	PROPN
ejpam-6593	483	3	appl	appl	PROPN
ejpam-6593	483	4	.	.	PROPN
ejpam-6593	483	5	math	math	PROPN
ejpam-6593	483	6	,	,	PUNCT
ejpam-6593	483	7	18	18	NUM
ejpam-6593	483	8	(	(	PUNCT
ejpam-6593	483	9	3	3	NUM
ejpam-6593	483	10	)	)	PUNCT
ejpam-6593	483	11	(	(	PUNCT
ejpam-6593	483	12	2025	2025	NUM
ejpam-6593	483	13	)	)	PUNCT
ejpam-6593	483	14	,	,	PUNCT
ejpam-6593	483	15	6593	6593	NUM
ejpam-6593	483	16	15	15	NUM
ejpam-6593	483	17	of	of	ADP
ejpam-6593	483	18	24	24	NUM
ejpam-6593	483	19	now	now	ADV
ejpam-6593	483	20	,	,	PUNCT
ejpam-6593	483	21	let	let	VERB
ejpam-6593	483	22	z	z	PROPN
ejpam-6593	483	23	≡	≡	PROPN
ejpam-6593	483	24	5	5	NUM
ejpam-6593	483	25	(	(	PUNCT
ejpam-6593	483	26	mod	mod	PROPN
ejpam-6593	483	27	10	10	NUM
ejpam-6593	483	28	)	)	PUNCT
ejpam-6593	483	29	.	.	PUNCT
ejpam-6593	484	1	then	then	ADV
ejpam-6593	484	2	,	,	PUNCT
ejpam-6593	484	3	z2	z2	PROPN
ejpam-6593	484	4	≡	≡	PROPN
ejpam-6593	484	5	5	5	NUM
ejpam-6593	484	6	(	(	PUNCT
ejpam-6593	484	7	mod	mod	PROPN
ejpam-6593	484	8	10	10	NUM
ejpam-6593	484	9	)	)	PUNCT
ejpam-6593	484	10	.	.	PUNCT
ejpam-6593	484	11	suppose	suppose	VERB
ejpam-6593	484	12	on	on	ADP
ejpam-6593	484	13	the	the	DET
ejpam-6593	484	14	contrary	contrary	NOUN
ejpam-6593	484	15	that	that	SCONJ
ejpam-6593	484	16	x	x	SYM
ejpam-6593	484	17	≡	≡	PROPN
ejpam-6593	484	18	1	1	NUM
ejpam-6593	484	19	,	,	PUNCT
ejpam-6593	484	20	2	2	NUM
ejpam-6593	484	21	,	,	PUNCT
ejpam-6593	484	22	0	0	NUM
ejpam-6593	484	23	(	(	PUNCT
ejpam-6593	484	24	mod	mod	PROPN
ejpam-6593	484	25	4	4	NUM
ejpam-6593	484	26	)	)	PUNCT
ejpam-6593	484	27	,	,	PUNCT
ejpam-6593	484	28	then	then	ADV
ejpam-6593	484	29	2x	2x	NUM
ejpam-6593	484	30	≡	≡	PROPN
ejpam-6593	484	31	2	2	NUM
ejpam-6593	484	32	,	,	PUNCT
ejpam-6593	484	33	4	4	NUM
ejpam-6593	484	34	,	,	PUNCT
ejpam-6593	484	35	6	6	NUM
ejpam-6593	484	36	(	(	PUNCT
ejpam-6593	484	37	mod	mod	PROPN
ejpam-6593	484	38	10	10	NUM
ejpam-6593	484	39	)	)	PUNCT
ejpam-6593	484	40	,	,	PUNCT
ejpam-6593	484	41	respectively	respectively	ADV
ejpam-6593	484	42	.	.	PUNCT
ejpam-6593	485	1	thus	thus	ADV
ejpam-6593	485	2	,	,	PUNCT
ejpam-6593	485	3	we	we	PRON
ejpam-6593	485	4	will	will	AUX
ejpam-6593	485	5	have	have	VERB
ejpam-6593	485	6	equation	equation	NOUN
ejpam-6593	485	7	(	(	PUNCT
ejpam-6593	485	8	5	5	NUM
ejpam-6593	485	9	)	)	PUNCT
ejpam-6593	485	10	as	as	ADP
ejpam-6593	485	11	2x	2x	NUM
ejpam-6593	485	12	+	+	CCONJ
ejpam-6593	485	13	(	(	PUNCT
ejpam-6593	485	14	2	2	NUM
ejpam-6593	485	15	+	+	NUM
ejpam-6593	485	16	5k)y	5k)y	NUM
ejpam-6593	485	17	≡	≡	PROPN
ejpam-6593	485	18	9	9	NUM
ejpam-6593	485	19	,	,	PUNCT
ejpam-6593	485	20	1	1	NUM
ejpam-6593	485	21	,	,	PUNCT
ejpam-6593	485	22	3	3	NUM
ejpam-6593	485	23	(	(	PUNCT
ejpam-6593	485	24	mod	mod	PROPN
ejpam-6593	485	25	10	10	NUM
ejpam-6593	485	26	)	)	PUNCT
ejpam-6593	485	27	≡	≡	PROPN
ejpam-6593	485	28	z2	z2	PROPN
ejpam-6593	485	29	,	,	PUNCT
ejpam-6593	485	30	respectively	respectively	ADV
ejpam-6593	485	31	.	.	PUNCT
ejpam-6593	486	1	this	this	PRON
ejpam-6593	486	2	will	will	AUX
ejpam-6593	486	3	be	be	AUX
ejpam-6593	486	4	a	a	DET
ejpam-6593	486	5	contradiction	contradiction	NOUN
ejpam-6593	486	6	from	from	ADP
ejpam-6593	486	7	the	the	DET
ejpam-6593	486	8	assumption	assumption	NOUN
ejpam-6593	486	9	that	that	SCONJ
ejpam-6593	486	10	z2	z2	PROPN
ejpam-6593	486	11	≡	≡	PROPN
ejpam-6593	486	12	5	5	NUM
ejpam-6593	486	13	(	(	PUNCT
ejpam-6593	486	14	mod	mod	PROPN
ejpam-6593	486	15	10	10	NUM
ejpam-6593	486	16	)	)	PUNCT
ejpam-6593	486	17	.	.	PUNCT
ejpam-6593	487	1	hence	hence	ADV
ejpam-6593	487	2	,	,	PUNCT
ejpam-6593	487	3	if	if	SCONJ
ejpam-6593	487	4	z	z	PROPN
ejpam-6593	487	5	≡	≡	PROPN
ejpam-6593	487	6	5	5	NUM
ejpam-6593	487	7	(	(	PUNCT
ejpam-6593	487	8	mod	mod	PROPN
ejpam-6593	487	9	10	10	NUM
ejpam-6593	487	10	)	)	PUNCT
ejpam-6593	487	11	,	,	PUNCT
ejpam-6593	487	12	(	(	PUNCT
ejpam-6593	487	13	5	5	X
ejpam-6593	487	14	)	)	PUNCT
ejpam-6593	487	15	only	only	ADV
ejpam-6593	487	16	has	have	VERB
ejpam-6593	487	17	a	a	DET
ejpam-6593	487	18	solution	solution	NOUN
ejpam-6593	487	19	when	when	SCONJ
ejpam-6593	487	20	x	x	X
ejpam-6593	487	21	≡	≡	PROPN
ejpam-6593	487	22	3	3	NUM
ejpam-6593	487	23	(	(	PUNCT
ejpam-6593	487	24	mod	mod	NOUN
ejpam-6593	487	25	4	4	NUM
ejpam-6593	487	26	)	)	PUNCT
ejpam-6593	487	27	.	.	PUNCT
ejpam-6593	488	1	therefore	therefore	ADV
ejpam-6593	488	2	,	,	PUNCT
ejpam-6593	488	3	the	the	DET
ejpam-6593	488	4	equation	equation	NOUN
ejpam-6593	488	5	2x	2x	NUM
ejpam-6593	488	6	+	+	CCONJ
ejpam-6593	488	7	(	(	PUNCT
ejpam-6593	488	8	2	2	NUM
ejpam-6593	488	9	+	+	NUM
ejpam-6593	488	10	5k	5k	NUM
ejpam-6593	488	11	)	)	PUNCT
ejpam-6593	488	12	=	=	SYM
ejpam-6593	488	13	z2	z2	PROPN
ejpam-6593	488	14	,	,	PUNCT
ejpam-6593	488	15	where	where	SCONJ
ejpam-6593	488	16	p	p	NOUN
ejpam-6593	488	17	=	=	NOUN
ejpam-6593	488	18	2	2	NUM
ejpam-6593	488	19	and	and	CCONJ
ejpam-6593	488	20	p	p	NOUN
ejpam-6593	489	1	+	+	NOUN
ejpam-6593	489	2	5k	5k	NUM
ejpam-6593	489	3	are	be	AUX
ejpam-6593	489	4	prime	prime	ADJ
ejpam-6593	489	5	pairs	pair	NOUN
ejpam-6593	489	6	and	and	CCONJ
ejpam-6593	489	7	k	k	PROPN
ejpam-6593	489	8	is	be	AUX
ejpam-6593	489	9	odd	odd	ADJ
ejpam-6593	489	10	,	,	PUNCT
ejpam-6593	489	11	only	only	ADV
ejpam-6593	489	12	has	have	VERB
ejpam-6593	489	13	a	a	DET
ejpam-6593	489	14	solution	solution	NOUN
ejpam-6593	489	15	when	when	SCONJ
ejpam-6593	489	16	x	x	X
ejpam-6593	489	17	≡	≡	PROPN
ejpam-6593	489	18	3	3	NUM
ejpam-6593	489	19	(	(	PUNCT
ejpam-6593	489	20	mod	mod	NOUN
ejpam-6593	489	21	4	4	X
ejpam-6593	489	22	)	)	PUNCT
ejpam-6593	489	23	if	if	SCONJ
ejpam-6593	489	24	and	and	CCONJ
ejpam-6593	489	25	only	only	ADV
ejpam-6593	489	26	if	if	SCONJ
ejpam-6593	489	27	z	z	PROPN
ejpam-6593	489	28	≡	≡	PROPN
ejpam-6593	489	29	5	5	NUM
ejpam-6593	489	30	(	(	PUNCT
ejpam-6593	489	31	mod	mod	PROPN
ejpam-6593	489	32	10	10	NUM
ejpam-6593	489	33	)	)	PUNCT
ejpam-6593	489	34	.	.	PUNCT
ejpam-6593	490	1	one	one	PRON
ejpam-6593	490	2	can	can	AUX
ejpam-6593	490	3	verify	verify	VERB
ejpam-6593	490	4	that	that	SCONJ
ejpam-6593	490	5	the	the	DET
ejpam-6593	490	6	first	first	ADJ
ejpam-6593	490	7	solution	solution	NOUN
ejpam-6593	490	8	when	when	SCONJ
ejpam-6593	490	9	x	x	PROPN
ejpam-6593	490	10	=	=	SYM
ejpam-6593	490	11	3	3	NUM
ejpam-6593	490	12	and	and	CCONJ
ejpam-6593	490	13	z	z	PROPN
ejpam-6593	490	14	≡	≡	PROPN
ejpam-6593	490	15	5	5	NUM
ejpam-6593	490	16	(	(	PUNCT
ejpam-6593	490	17	mod	mod	PROPN
ejpam-6593	490	18	10	10	NUM
ejpam-6593	490	19	)	)	PUNCT
ejpam-6593	490	20	is	be	AUX
ejpam-6593	490	21	(	(	PUNCT
ejpam-6593	490	22	p	p	X
ejpam-6593	490	23	,	,	PUNCT
ejpam-6593	490	24	k	k	NOUN
ejpam-6593	490	25	,	,	PUNCT
ejpam-6593	490	26	x	x	X
ejpam-6593	490	27	,	,	PUNCT
ejpam-6593	490	28	y	y	PROPN
ejpam-6593	490	29	,	,	PUNCT
ejpam-6593	490	30	z	z	NOUN
ejpam-6593	490	31	)	)	PUNCT
ejpam-6593	490	32	=	=	SYM
ejpam-6593	490	33	(	(	PUNCT
ejpam-6593	490	34	2	2	NUM
ejpam-6593	490	35	,	,	PUNCT
ejpam-6593	490	36	3	3	NUM
ejpam-6593	490	37	,	,	PUNCT
ejpam-6593	490	38	3	3	NUM
ejpam-6593	490	39	,	,	PUNCT
ejpam-6593	490	40	1	1	NUM
ejpam-6593	490	41	,	,	PUNCT
ejpam-6593	490	42	5	5	NUM
ejpam-6593	490	43	)	)	PUNCT
ejpam-6593	490	44	.	.	PUNCT
ejpam-6593	491	1	for	for	ADP
ejpam-6593	491	2	values	value	NOUN
ejpam-6593	491	3	of	of	ADP
ejpam-6593	491	4	xn	xn	PROPN
ejpam-6593	491	5	that	that	PRON
ejpam-6593	491	6	are	be	AUX
ejpam-6593	491	7	either	either	CCONJ
ejpam-6593	491	8	in	in	ADP
ejpam-6593	491	9	the	the	DET
ejpam-6593	491	10	form	form	NOUN
ejpam-6593	491	11	1	1	NUM
ejpam-6593	491	12	+	+	CCONJ
ejpam-6593	491	13	4n	4n	NOUN
ejpam-6593	491	14	or	or	CCONJ
ejpam-6593	491	15	3	3	NUM
ejpam-6593	491	16	+	+	CCONJ
ejpam-6593	491	17	4n	4n	NOUN
ejpam-6593	491	18	,	,	PUNCT
ejpam-6593	491	19	an	an	DET
ejpam-6593	491	20	easier	easy	ADJ
ejpam-6593	491	21	way	way	NOUN
ejpam-6593	491	22	to	to	PART
ejpam-6593	491	23	solve	solve	VERB
ejpam-6593	491	24	for	for	ADP
ejpam-6593	491	25	k(m	k(m	PROPN
ejpam-6593	491	26	,	,	PUNCT
ejpam-6593	491	27	xn	xn	PROPN
ejpam-6593	491	28	)	)	PUNCT
ejpam-6593	491	29	is	be	AUX
ejpam-6593	491	30	given	give	VERB
ejpam-6593	491	31	by	by	ADP
ejpam-6593	491	32	the	the	DET
ejpam-6593	491	33	next	next	ADJ
ejpam-6593	491	34	theorem	theorem	NOUN
ejpam-6593	491	35	,	,	PUNCT
ejpam-6593	491	36	which	which	PRON
ejpam-6593	491	37	can	can	AUX
ejpam-6593	491	38	be	be	AUX
ejpam-6593	491	39	proven	prove	VERB
ejpam-6593	491	40	by	by	ADP
ejpam-6593	491	41	induction	induction	NOUN
ejpam-6593	491	42	.	.	PUNCT
ejpam-6593	492	1	theorem	theorem	ADJ
ejpam-6593	492	2	4	4	NUM
ejpam-6593	492	3	.	.	PUNCT
ejpam-6593	492	4	suppose	suppose	VERB
ejpam-6593	492	5	the	the	DET
ejpam-6593	492	6	exponential	exponential	ADJ
ejpam-6593	492	7	diophantine	diophantine	NOUN
ejpam-6593	492	8	equation	equation	NOUN
ejpam-6593	492	9	(	(	PUNCT
ejpam-6593	492	10	5	5	NUM
ejpam-6593	492	11	)	)	PUNCT
ejpam-6593	492	12	,	,	PUNCT
ejpam-6593	492	13	where	where	SCONJ
ejpam-6593	492	14	x	x	ADP
ejpam-6593	492	15	=	=	PUNCT
ejpam-6593	492	16	xn	xn	PUNCT
ejpam-6593	492	17	=	=	SYM
ejpam-6593	492	18	1	1	NUM
ejpam-6593	492	19	+	+	CCONJ
ejpam-6593	492	20	4n	4n	NOUN
ejpam-6593	492	21	or	or	CCONJ
ejpam-6593	492	22	x	x	SYM
ejpam-6593	492	23	=	=	PUNCT
ejpam-6593	492	24	xn	xn	PUNCT
ejpam-6593	492	25	=	=	SYM
ejpam-6593	492	26	3	3	NUM
ejpam-6593	492	27	+	+	CCONJ
ejpam-6593	492	28	4n	4n	NOUN
ejpam-6593	492	29	,	,	PUNCT
ejpam-6593	492	30	n	n	PROPN
ejpam-6593	492	31	∈	∈	PROPN
ejpam-6593	492	32	n0	n0	NOUN
ejpam-6593	492	33	,	,	PUNCT
ejpam-6593	492	34	has	have	VERB
ejpam-6593	492	35	a	a	DET
ejpam-6593	492	36	solution	solution	NOUN
ejpam-6593	492	37	.	.	PUNCT
ejpam-6593	493	1	then	then	ADV
ejpam-6593	493	2	,	,	PUNCT
ejpam-6593	493	3	k(m	k(m	PROPN
ejpam-6593	493	4	,	,	PUNCT
ejpam-6593	493	5	xn	xn	PROPN
ejpam-6593	493	6	)	)	PUNCT
ejpam-6593	493	7	=	=	SYM
ejpam-6593	493	8	k(0,xn	k(0,xn	PROPN
ejpam-6593	493	9	)	)	PUNCT
ejpam-6593	494	1	+	+	CCONJ
ejpam-6593	494	2	m−1∑	m−1∑	PROPN
ejpam-6593	494	3	i=0	i=0	PROPN
ejpam-6593	494	4	(	(	PUNCT
ejpam-6593	494	5	αxn	αxn	PROPN
ejpam-6593	494	6	+	+	SYM
ejpam-6593	494	7	40i	40i	NOUN
ejpam-6593	494	8	)	)	PUNCT
ejpam-6593	494	9	,	,	PUNCT
ejpam-6593	494	10	(	(	PUNCT
ejpam-6593	494	11	13	13	NUM
ejpam-6593	494	12	)	)	PUNCT
ejpam-6593	494	13	where	where	SCONJ
ejpam-6593	494	14	m	m	PROPN
ejpam-6593	494	15	∈	∈	PROPN
ejpam-6593	494	16	n.	n.	NOUN
ejpam-6593	494	17	proof	proof	NOUN
ejpam-6593	494	18	.	.	PUNCT
ejpam-6593	495	1	consider	consider	VERB
ejpam-6593	495	2	the	the	DET
ejpam-6593	495	3	diophantine	diophantine	NOUN
ejpam-6593	495	4	equation	equation	NOUN
ejpam-6593	495	5	2x	2x	NUM
ejpam-6593	495	6	+	+	CCONJ
ejpam-6593	495	7	(	(	PUNCT
ejpam-6593	495	8	2	2	NUM
ejpam-6593	495	9	+	+	NUM
ejpam-6593	495	10	5k	5k	NUM
ejpam-6593	495	11	)	)	PUNCT
ejpam-6593	496	1	=	=	SYM
ejpam-6593	496	2	z2	z2	PROPN
ejpam-6593	496	3	,	,	PUNCT
ejpam-6593	496	4	where	where	SCONJ
ejpam-6593	496	5	x	x	X
ejpam-6593	496	6	:	:	PUNCT
ejpam-6593	496	7	=	=	SYM
ejpam-6593	496	8	xn	xn	PUNCT
ejpam-6593	496	9	=	=	SYM
ejpam-6593	497	1	1	1	NUM
ejpam-6593	497	2	+	+	NUM
ejpam-6593	497	3	4n	4n	NOUN
ejpam-6593	497	4	or	or	CCONJ
ejpam-6593	497	5	x	x	SYM
ejpam-6593	497	6	:	:	PUNCT
ejpam-6593	497	7	=	=	SYM
ejpam-6593	497	8	xn	xn	PUNCT
ejpam-6593	497	9	=	=	SYM
ejpam-6593	497	10	3	3	NUM
ejpam-6593	497	11	+	+	CCONJ
ejpam-6593	497	12	4n	4n	NOUN
ejpam-6593	497	13	,	,	PUNCT
ejpam-6593	497	14	n	n	PROPN
ejpam-6593	497	15	∈	∈	PROPN
ejpam-6593	497	16	n0	n0	PROPN
ejpam-6593	497	17	.	.	PUNCT
ejpam-6593	498	1	we	we	PRON
ejpam-6593	498	2	prove	prove	VERB
ejpam-6593	498	3	by	by	ADP
ejpam-6593	498	4	induction	induction	NOUN
ejpam-6593	498	5	on	on	ADP
ejpam-6593	498	6	m	m	PROPN
ejpam-6593	498	7	that	that	SCONJ
ejpam-6593	498	8	k(m	k(m	PROPN
ejpam-6593	498	9	,	,	PUNCT
ejpam-6593	498	10	xn	xn	PROPN
ejpam-6593	498	11	)	)	PUNCT
ejpam-6593	498	12	=	=	SYM
ejpam-6593	498	13	k(0,xn	k(0,xn	PROPN
ejpam-6593	498	14	)	)	PUNCT
ejpam-6593	499	1	+	+	CCONJ
ejpam-6593	499	2	m−1∑	m−1∑	PROPN
ejpam-6593	499	3	i=0	i=0	PROPN
ejpam-6593	499	4	(	(	PUNCT
ejpam-6593	499	5	αxn	αxn	PROPN
ejpam-6593	499	6	+	+	SYM
ejpam-6593	499	7	40i	40i	NOUN
ejpam-6593	499	8	)	)	PUNCT
ejpam-6593	499	9	,	,	PUNCT
ejpam-6593	499	10	where	where	SCONJ
ejpam-6593	499	11	m	m	PROPN
ejpam-6593	499	12	∈	∈	PROPN
ejpam-6593	499	13	n.	n.	NOUN
ejpam-6593	499	14	we	we	PRON
ejpam-6593	499	15	first	first	ADV
ejpam-6593	499	16	note	note	VERB
ejpam-6593	499	17	that	that	SCONJ
ejpam-6593	499	18	by	by	ADP
ejpam-6593	499	19	using	use	VERB
ejpam-6593	499	20	the	the	DET
ejpam-6593	499	21	definition	definition	NOUN
ejpam-6593	499	22	of	of	ADP
ejpam-6593	499	23	αxn	αxn	NOUN
ejpam-6593	499	24	,	,	PUNCT
ejpam-6593	499	25	equation	equation	NOUN
ejpam-6593	499	26	(	(	PUNCT
ejpam-6593	499	27	13	13	NUM
ejpam-6593	499	28	)	)	PUNCT
ejpam-6593	499	29	is	be	AUX
ejpam-6593	499	30	satisfied	satisfied	ADJ
ejpam-6593	499	31	when	when	SCONJ
ejpam-6593	499	32	m	m	VERB
ejpam-6593	499	33	=	=	SYM
ejpam-6593	499	34	1	1	NUM
ejpam-6593	499	35	,	,	PUNCT
ejpam-6593	499	36	as	as	SCONJ
ejpam-6593	499	37	seen	see	VERB
ejpam-6593	499	38	below	below	ADV
ejpam-6593	499	39	:	:	PUNCT
ejpam-6593	499	40	k(1,xn	k(1,xn	PROPN
ejpam-6593	499	41	)	)	PUNCT
ejpam-6593	500	1	=	=	SYM
ejpam-6593	500	2	k(0,xn	k(0,xn	PROPN
ejpam-6593	500	3	)	)	PUNCT
ejpam-6593	501	1	+	+	NUM
ejpam-6593	501	2	αxn	αxn	VERB
ejpam-6593	501	3	.	.	PUNCT
ejpam-6593	502	1	we	we	PRON
ejpam-6593	502	2	now	now	ADV
ejpam-6593	502	3	assume	assume	VERB
ejpam-6593	502	4	that	that	SCONJ
ejpam-6593	502	5	equation	equation	NOUN
ejpam-6593	502	6	(	(	PUNCT
ejpam-6593	502	7	13	13	NUM
ejpam-6593	502	8	)	)	PUNCT
ejpam-6593	502	9	is	be	AUX
ejpam-6593	502	10	true	true	ADJ
ejpam-6593	502	11	for	for	ADP
ejpam-6593	502	12	m	m	PROPN
ejpam-6593	502	13	=	=	SYM
ejpam-6593	502	14	a	a	PROPN
ejpam-6593	502	15	,	,	PUNCT
ejpam-6593	502	16	that	that	ADV
ejpam-6593	502	17	is	is	ADV
ejpam-6593	502	18	,	,	PUNCT
ejpam-6593	502	19	k(a	k(a	PROPN
ejpam-6593	502	20	,	,	PUNCT
ejpam-6593	502	21	xn	xn	NUM
ejpam-6593	502	22	)	)	PUNCT
ejpam-6593	503	1	=	=	SYM
ejpam-6593	503	2	k(0,xn	k(0,xn	PROPN
ejpam-6593	503	3	)	)	PUNCT
ejpam-6593	504	1	+	+	CCONJ
ejpam-6593	504	2	a−1∑	a−1∑	PRON
ejpam-6593	504	3	i=0	i=0	PROPN
ejpam-6593	504	4	(	(	PUNCT
ejpam-6593	504	5	αxn	αxn	PROPN
ejpam-6593	504	6	+	+	CCONJ
ejpam-6593	504	7	40i	40i	NOUN
ejpam-6593	504	8	)	)	PUNCT
ejpam-6593	504	9	.	.	PUNCT
ejpam-6593	505	1	by	by	ADP
ejpam-6593	505	2	recalling	recall	VERB
ejpam-6593	505	3	that	that	SCONJ
ejpam-6593	505	4	k(a	k(a	PROPN
ejpam-6593	505	5	,	,	PUNCT
ejpam-6593	505	6	xn	xn	X
ejpam-6593	505	7	)	)	PUNCT
ejpam-6593	505	8	=	=	SYM
ejpam-6593	505	9	z2	z2	PROPN
ejpam-6593	505	10	(	(	PUNCT
ejpam-6593	505	11	a	a	PRON
ejpam-6593	505	12	,	,	PUNCT
ejpam-6593	505	13	xn	xn	PROPN
ejpam-6593	505	14	)	)	PUNCT
ejpam-6593	505	15	−2xn−2	−2xn−2	ADP
ejpam-6593	505	16	5	5	NUM
ejpam-6593	505	17	,	,	PUNCT
ejpam-6593	505	18	we	we	PRON
ejpam-6593	505	19	get	get	VERB
ejpam-6593	505	20	k(a	k(a	NOUN
ejpam-6593	505	21	,	,	PUNCT
ejpam-6593	505	22	xn	xn	PUNCT
ejpam-6593	505	23	)	)	PUNCT
ejpam-6593	506	1	+	+	CCONJ
ejpam-6593	506	2	(	(	PUNCT
ejpam-6593	506	3	αxn	αxn	PROPN
ejpam-6593	506	4	+	+	SYM
ejpam-6593	506	5	40a	40a	NUM
ejpam-6593	506	6	)	)	PUNCT
ejpam-6593	506	7	=	=	SYM
ejpam-6593	506	8	(	(	PUNCT
ejpam-6593	506	9	k(0,xn	k(0,xn	PROPN
ejpam-6593	506	10	)	)	PUNCT
ejpam-6593	507	1	+	+	CCONJ
ejpam-6593	507	2	a−1∑	a−1∑	PRON
ejpam-6593	507	3	i=0	i=0	PROPN
ejpam-6593	507	4	(	(	PUNCT
ejpam-6593	507	5	αxn	αxn	NOUN
ejpam-6593	507	6	+	+	SYM
ejpam-6593	507	7	40i	40i	NOUN
ejpam-6593	507	8	)	)	PUNCT
ejpam-6593	507	9	)	)	PUNCT
ejpam-6593	508	1	+	+	CCONJ
ejpam-6593	508	2	(	(	PUNCT
ejpam-6593	508	3	αxn	αxn	PROPN
ejpam-6593	508	4	+	+	SYM
ejpam-6593	508	5	40a	40a	NUM
ejpam-6593	508	6	)	)	PUNCT
ejpam-6593	508	7	,	,	PUNCT
ejpam-6593	508	8	z2(a	z2(a	PROPN
ejpam-6593	508	9	,	,	PUNCT
ejpam-6593	508	10	xn	xn	PROPN
ejpam-6593	508	11	)	)	PUNCT
ejpam-6593	509	1	−	−	ADP
ejpam-6593	509	2	2xn	2xn	ADJ
ejpam-6593	509	3	−	−	NUM
ejpam-6593	509	4	2	2	NUM
ejpam-6593	509	5	5	5	NUM
ejpam-6593	509	6	+	+	CCONJ
ejpam-6593	509	7	αxn	αxn	ADJ
ejpam-6593	509	8	+	+	SYM
ejpam-6593	509	9	40a	40a	NUM
ejpam-6593	509	10	=	=	SYM
ejpam-6593	509	11	k(0,xn	k(0,xn	PROPN
ejpam-6593	509	12	)	)	PUNCT
ejpam-6593	510	1	+	+	CCONJ
ejpam-6593	510	2	a∑	a∑	PROPN
ejpam-6593	510	3	i=0	i=0	PROPN
ejpam-6593	510	4	(	(	PUNCT
ejpam-6593	510	5	αxn	αxn	PROPN
ejpam-6593	510	6	+	+	SYM
ejpam-6593	510	7	40i	40i	NOUN
ejpam-6593	510	8	)	)	PUNCT
ejpam-6593	510	9	.	.	PUNCT
ejpam-6593	511	1	m.	m.	PROPN
ejpam-6593	511	2	c.	c.	PROPN
ejpam-6593	511	3	avenilla	avenilla	PROPN
ejpam-6593	511	4	,	,	PUNCT
ejpam-6593	511	5	j.	j.	PROPN
ejpam-6593	511	6	b.	b.	PROPN
ejpam-6593	511	7	bacani	bacani	PROPN
ejpam-6593	511	8	/	/	SYM
ejpam-6593	511	9	eur	eur	PROPN
ejpam-6593	511	10	.	.	PUNCT
ejpam-6593	512	1	j.	j.	PROPN
ejpam-6593	512	2	pure	pure	PROPN
ejpam-6593	512	3	appl	appl	PROPN
ejpam-6593	512	4	.	.	PROPN
ejpam-6593	512	5	math	math	PROPN
ejpam-6593	512	6	,	,	PUNCT
ejpam-6593	512	7	18	18	NUM
ejpam-6593	512	8	(	(	PUNCT
ejpam-6593	512	9	3	3	NUM
ejpam-6593	512	10	)	)	PUNCT
ejpam-6593	512	11	(	(	PUNCT
ejpam-6593	512	12	2025	2025	NUM
ejpam-6593	512	13	)	)	PUNCT
ejpam-6593	512	14	,	,	PUNCT
ejpam-6593	512	15	6593	6593	NUM
ejpam-6593	512	16	16	16	NUM
ejpam-6593	512	17	of	of	ADP
ejpam-6593	512	18	24	24	NUM
ejpam-6593	512	19	thus	thus	ADV
ejpam-6593	512	20	,	,	PUNCT
ejpam-6593	512	21	we	we	PRON
ejpam-6593	512	22	have	have	AUX
ejpam-6593	512	23	z2(a	z2(a	NOUN
ejpam-6593	512	24	,	,	PUNCT
ejpam-6593	512	25	xn	xn	PROPN
ejpam-6593	512	26	)	)	PUNCT
ejpam-6593	513	1	−	−	ADP
ejpam-6593	513	2	2xn	2xn	ADJ
ejpam-6593	514	1	−	−	NOUN
ejpam-6593	514	2	2	2	NUM
ejpam-6593	515	1	+	+	NUM
ejpam-6593	515	2	5αxn	5αxn	NUM
ejpam-6593	515	3	+	+	NUM
ejpam-6593	515	4	200a	200a	NUM
ejpam-6593	515	5	5	5	NUM
ejpam-6593	515	6	=	=	SYM
ejpam-6593	515	7	k(0,xn	k(0,xn	PROPN
ejpam-6593	515	8	)	)	PUNCT
ejpam-6593	516	1	+	+	CCONJ
ejpam-6593	516	2	a∑	a∑	PROPN
ejpam-6593	516	3	i=0	i=0	PROPN
ejpam-6593	516	4	(	(	PUNCT
ejpam-6593	516	5	αxn	αxn	PROPN
ejpam-6593	516	6	+	+	SYM
ejpam-6593	516	7	40i	40i	NOUN
ejpam-6593	516	8	)	)	PUNCT
ejpam-6593	516	9	.	.	PUNCT
ejpam-6593	517	1	(	(	PUNCT
ejpam-6593	517	2	14	14	NUM
ejpam-6593	517	3	)	)	PUNCT
ejpam-6593	517	4	note	note	NOUN
ejpam-6593	517	5	that	that	SCONJ
ejpam-6593	517	6	αxn	αxn	NOUN
ejpam-6593	517	7	can	can	AUX
ejpam-6593	517	8	also	also	ADV
ejpam-6593	517	9	be	be	AUX
ejpam-6593	517	10	written	write	VERB
ejpam-6593	517	11	as	as	SCONJ
ejpam-6593	517	12	follows	follow	VERB
ejpam-6593	517	13	:	:	PUNCT
ejpam-6593	517	14	αxn	αxn	PROPN
ejpam-6593	517	15	=	=	SYM
ejpam-6593	517	16	z2(1,xn	z2(1,xn	PROPN
ejpam-6593	517	17	)	)	PUNCT
ejpam-6593	517	18	−	−	NOUN
ejpam-6593	518	1	2xn	2xn	ADJ
ejpam-6593	518	2	−	−	NOUN
ejpam-6593	518	3	2	2	NUM
ejpam-6593	518	4	5	5	NUM
ejpam-6593	518	5	−	−	PROPN
ejpam-6593	518	6	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	518	7	)	)	PUNCT
ejpam-6593	519	1	−	−	X
ejpam-6593	520	1	2xn	2xn	ADJ
ejpam-6593	520	2	−	−	NUM
ejpam-6593	520	3	2	2	NUM
ejpam-6593	520	4	5	5	NUM
ejpam-6593	520	5	=	=	SYM
ejpam-6593	520	6	z2(1,xn	z2(1,xn	PROPN
ejpam-6593	520	7	)	)	PUNCT
ejpam-6593	520	8	−	−	PROPN
ejpam-6593	520	9	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	520	10	)	)	PUNCT
ejpam-6593	520	11	5	5	NUM
ejpam-6593	520	12	.	.	PUNCT
ejpam-6593	521	1	this	this	PRON
ejpam-6593	521	2	,	,	PUNCT
ejpam-6593	521	3	together	together	ADV
ejpam-6593	521	4	with	with	ADP
ejpam-6593	521	5	the	the	DET
ejpam-6593	521	6	equations	equation	NOUN
ejpam-6593	521	7	z(1,xn	z(1,xn	PROPN
ejpam-6593	521	8	)	)	PUNCT
ejpam-6593	522	1	=	=	SYM
ejpam-6593	522	2	z(0,xn	z(0,xn	PROPN
ejpam-6593	522	3	)	)	PUNCT
ejpam-6593	523	1	+	+	CCONJ
ejpam-6593	523	2	10	10	NUM
ejpam-6593	523	3	and	and	CCONJ
ejpam-6593	523	4	z(a	z(a	NOUN
ejpam-6593	523	5	,	,	PUNCT
ejpam-6593	523	6	xn	xn	NUM
ejpam-6593	523	7	)	)	PUNCT
ejpam-6593	524	1	=	=	SYM
ejpam-6593	524	2	z(0,xn	z(0,xn	PROPN
ejpam-6593	524	3	)	)	PUNCT
ejpam-6593	525	1	+	+	NUM
ejpam-6593	525	2	10a	10a	NOUN
ejpam-6593	525	3	,	,	PUNCT
ejpam-6593	525	4	will	will	AUX
ejpam-6593	525	5	lead	lead	VERB
ejpam-6593	525	6	us	we	PRON
ejpam-6593	525	7	to	to	ADP
ejpam-6593	525	8	the	the	DET
ejpam-6593	525	9	following	follow	VERB
ejpam-6593	525	10	simplification	simplification	NOUN
ejpam-6593	525	11	:	:	PUNCT
ejpam-6593	525	12	z2(a	z2(a	NOUN
ejpam-6593	525	13	,	,	PUNCT
ejpam-6593	525	14	xn	xn	PROPN
ejpam-6593	525	15	)	)	PUNCT
ejpam-6593	526	1	−	−	ADP
ejpam-6593	526	2	2xn	2xn	ADJ
ejpam-6593	527	1	−	−	NOUN
ejpam-6593	527	2	2	2	NUM
ejpam-6593	528	1	+	+	NUM
ejpam-6593	528	2	5αxn	5αxn	NUM
ejpam-6593	528	3	+	+	NUM
ejpam-6593	528	4	200a	200a	NUM
ejpam-6593	528	5	5	5	NUM
ejpam-6593	528	6	=	=	SYM
ejpam-6593	528	7	z2(a	z2(a	PROPN
ejpam-6593	528	8	,	,	PUNCT
ejpam-6593	528	9	xn	xn	PROPN
ejpam-6593	528	10	)	)	PUNCT
ejpam-6593	529	1	−	−	ADP
ejpam-6593	529	2	2xn	2xn	ADJ
ejpam-6593	529	3	−	−	NOUN
ejpam-6593	529	4	2	2	NUM
ejpam-6593	529	5	+	+	SYM
ejpam-6593	529	6	z2(1,xn	z2(1,xn	NUM
ejpam-6593	529	7	)	)	PUNCT
ejpam-6593	529	8	−	−	PROPN
ejpam-6593	529	9	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	529	10	)	)	PUNCT
ejpam-6593	530	1	+	+	CCONJ
ejpam-6593	530	2	200a	200a	NUM
ejpam-6593	530	3	5	5	NUM
ejpam-6593	530	4	=	=	SYM
ejpam-6593	530	5	z2(a	z2(a	PROPN
ejpam-6593	530	6	,	,	PUNCT
ejpam-6593	530	7	xn	xn	PROPN
ejpam-6593	530	8	)	)	PUNCT
ejpam-6593	530	9	+	+	NUM
ejpam-6593	530	10	z2(1,xn	z2(1,xn	NUM
ejpam-6593	530	11	)	)	PUNCT
ejpam-6593	530	12	−	−	PROPN
ejpam-6593	530	13	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	530	14	)	)	PUNCT
ejpam-6593	531	1	+	+	CCONJ
ejpam-6593	531	2	200a−	200a−	NUM
ejpam-6593	531	3	2xn	2xn	NOUN
ejpam-6593	531	4	−	−	ADP
ejpam-6593	531	5	2	2	NUM
ejpam-6593	531	6	5	5	NUM
ejpam-6593	531	7	=	=	SYM
ejpam-6593	531	8	z2(a	z2(a	PROPN
ejpam-6593	531	9	,	,	PUNCT
ejpam-6593	531	10	xn	xn	PROPN
ejpam-6593	531	11	)	)	PUNCT
ejpam-6593	532	1	+	+	CCONJ
ejpam-6593	532	2	(	(	PUNCT
ejpam-6593	532	3	z(0,xn	z(0,xn	PROPN
ejpam-6593	532	4	)	)	PUNCT
ejpam-6593	533	1	+	+	CCONJ
ejpam-6593	533	2	10)2	10)2	NUM
ejpam-6593	533	3	−	−	PROPN
ejpam-6593	533	4	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	533	5	)	)	PUNCT
ejpam-6593	534	1	+	+	CCONJ
ejpam-6593	534	2	200a−	200a−	NUM
ejpam-6593	534	3	2xn	2xn	NOUN
ejpam-6593	534	4	−	−	ADP
ejpam-6593	534	5	2	2	NUM
ejpam-6593	534	6	5	5	NUM
ejpam-6593	534	7	=	=	SYM
ejpam-6593	534	8	z2(a	z2(a	PROPN
ejpam-6593	534	9	,	,	PUNCT
ejpam-6593	534	10	xn	xn	PROPN
ejpam-6593	534	11	)	)	PUNCT
ejpam-6593	535	1	+	+	CCONJ
ejpam-6593	535	2	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	535	3	)	)	PUNCT
ejpam-6593	535	4	+	+	CCONJ
ejpam-6593	535	5	20z(0,xn	20z(0,xn	NUM
ejpam-6593	535	6	)	)	PUNCT
ejpam-6593	536	1	+	+	CCONJ
ejpam-6593	536	2	100−	100−	PROPN
ejpam-6593	536	3	z2(0,xn	z2(0,xn	PROPN
ejpam-6593	536	4	)	)	PUNCT
ejpam-6593	537	1	+	+	CCONJ
ejpam-6593	537	2	200a−	200a−	NUM
ejpam-6593	537	3	2xn	2xn	NOUN
ejpam-6593	537	4	−	−	ADP
ejpam-6593	537	5	2	2	NUM
ejpam-6593	537	6	5	5	NUM
ejpam-6593	537	7	=	=	SYM
ejpam-6593	537	8	z2(a	z2(a	PROPN
ejpam-6593	537	9	,	,	PUNCT
ejpam-6593	537	10	xn	xn	PROPN
ejpam-6593	537	11	)	)	PUNCT
ejpam-6593	538	1	+	+	CCONJ
ejpam-6593	538	2	20z(0,xn	20z(0,xn	NUM
ejpam-6593	538	3	)	)	PUNCT
ejpam-6593	539	1	+	+	CCONJ
ejpam-6593	539	2	200a+	200a+	NUM
ejpam-6593	539	3	100−	100−	NUM
ejpam-6593	539	4	2xn	2xn	ADJ
ejpam-6593	539	5	−	−	NUM
ejpam-6593	539	6	2	2	NUM
ejpam-6593	539	7	5	5	NUM
ejpam-6593	539	8	=	=	SYM
ejpam-6593	539	9	z2(a	z2(a	PROPN
ejpam-6593	539	10	,	,	PUNCT
ejpam-6593	539	11	xn	xn	PROPN
ejpam-6593	539	12	)	)	PUNCT
ejpam-6593	539	13	+	+	NUM
ejpam-6593	539	14	20(z(0,xn	20(z(0,xn	NUM
ejpam-6593	539	15	)	)	PUNCT
ejpam-6593	540	1	+	+	NUM
ejpam-6593	540	2	10a	10a	NOUN
ejpam-6593	540	3	)	)	PUNCT
ejpam-6593	541	1	+	+	CCONJ
ejpam-6593	542	1	100−	100−	NUM
ejpam-6593	542	2	2xn	2xn	NOUN
ejpam-6593	542	3	−	−	NOUN
ejpam-6593	542	4	2	2	NUM
ejpam-6593	542	5	5	5	NUM
ejpam-6593	542	6	=	=	SYM
ejpam-6593	542	7	z2(a	z2(a	PROPN
ejpam-6593	542	8	,	,	PUNCT
ejpam-6593	542	9	xn	xn	PROPN
ejpam-6593	542	10	)	)	PUNCT
ejpam-6593	543	1	+	+	CCONJ
ejpam-6593	543	2	20z(a	20z(a	NUM
ejpam-6593	543	3	,	,	PUNCT
ejpam-6593	543	4	xn	xn	PUNCT
ejpam-6593	543	5	)	)	PUNCT
ejpam-6593	544	1	+	+	CCONJ
ejpam-6593	544	2	100−	100−	NUM
ejpam-6593	544	3	2xn	2xn	NOUN
ejpam-6593	544	4	−	−	NOUN
ejpam-6593	544	5	2	2	NUM
ejpam-6593	544	6	5	5	NUM
ejpam-6593	544	7	=	=	SYM
ejpam-6593	544	8	(	(	PUNCT
ejpam-6593	544	9	z(a	z(a	PROPN
ejpam-6593	544	10	,	,	PUNCT
ejpam-6593	544	11	xn	xn	PUNCT
ejpam-6593	544	12	)	)	PUNCT
ejpam-6593	545	1	+	+	CCONJ
ejpam-6593	545	2	10)2	10)2	NUM
ejpam-6593	545	3	−	−	NOUN
ejpam-6593	545	4	2xn	2xn	ADJ
ejpam-6593	545	5	−	−	PROPN
ejpam-6593	545	6	2	2	NUM
ejpam-6593	545	7	5	5	NUM
ejpam-6593	545	8	.	.	PUNCT
ejpam-6593	546	1	since	since	SCONJ
ejpam-6593	546	2	z(a+1,xn	z(a+1,xn	PROPN
ejpam-6593	546	3	)	)	PUNCT
ejpam-6593	546	4	=	=	SYM
ejpam-6593	546	5	z(0,xn	z(0,xn	PROPN
ejpam-6593	546	6	)	)	PUNCT
ejpam-6593	547	1	+	+	NUM
ejpam-6593	547	2	10(a+	10(a+	NOUN
ejpam-6593	547	3	1	1	NUM
ejpam-6593	547	4	)	)	PUNCT
ejpam-6593	548	1	=	=	SYM
ejpam-6593	548	2	z(0,xn	z(0,xn	PROPN
ejpam-6593	548	3	)	)	PUNCT
ejpam-6593	549	1	+	+	NUM
ejpam-6593	549	2	10a+	10a+	NUM
ejpam-6593	549	3	10	10	NUM
ejpam-6593	549	4	=	=	SYM
ejpam-6593	549	5	z(a	z(a	PROPN
ejpam-6593	549	6	,	,	PUNCT
ejpam-6593	549	7	xn	xn	PUNCT
ejpam-6593	549	8	)	)	PUNCT
ejpam-6593	549	9	+	+	CCONJ
ejpam-6593	549	10	10	10	NUM
ejpam-6593	549	11	,	,	PUNCT
ejpam-6593	549	12	and	and	CCONJ
ejpam-6593	549	13	by	by	ADP
ejpam-6593	549	14	definition	definition	NOUN
ejpam-6593	549	15	of	of	ADP
ejpam-6593	549	16	k(m	k(m	PROPN
ejpam-6593	549	17	,	,	PUNCT
ejpam-6593	549	18	xn	xn	PROPN
ejpam-6593	549	19	)	)	PUNCT
ejpam-6593	549	20	,	,	PUNCT
ejpam-6593	549	21	we	we	PRON
ejpam-6593	549	22	have	have	VERB
ejpam-6593	549	23	z2(a	z2(a	NOUN
ejpam-6593	549	24	,	,	PUNCT
ejpam-6593	549	25	xn	xn	PROPN
ejpam-6593	549	26	)	)	PUNCT
ejpam-6593	550	1	−	−	ADP
ejpam-6593	550	2	2xn	2xn	ADJ
ejpam-6593	551	1	−	−	NOUN
ejpam-6593	551	2	2	2	NUM
ejpam-6593	552	1	+	+	NUM
ejpam-6593	552	2	5αxn	5αxn	NUM
ejpam-6593	552	3	+	+	NUM
ejpam-6593	552	4	200a	200a	NUM
ejpam-6593	552	5	5	5	NUM
ejpam-6593	552	6	=	=	SYM
ejpam-6593	552	7	z2(a+1,xn	z2(a+1,xn	PROPN
ejpam-6593	552	8	)	)	PUNCT
ejpam-6593	552	9	−	−	PROPN
ejpam-6593	553	1	2xn	2xn	ADJ
ejpam-6593	553	2	−	−	NUM
ejpam-6593	553	3	2	2	NUM
ejpam-6593	553	4	5	5	NUM
ejpam-6593	553	5	=	=	SYM
ejpam-6593	553	6	k(a+1,xn	k(a+1,xn	PROPN
ejpam-6593	553	7	)	)	PUNCT
ejpam-6593	553	8	.	.	PUNCT
ejpam-6593	554	1	hence	hence	ADV
ejpam-6593	554	2	,	,	PUNCT
ejpam-6593	554	3	k(a+1,xn	k(a+1,xn	PROPN
ejpam-6593	554	4	)	)	PUNCT
ejpam-6593	554	5	=	=	SYM
ejpam-6593	554	6	k(0,xn	k(0,xn	PROPN
ejpam-6593	554	7	)	)	PUNCT
ejpam-6593	555	1	+	+	CCONJ
ejpam-6593	555	2	a∑	a∑	PROPN
ejpam-6593	555	3	i=0	i=0	PROPN
ejpam-6593	555	4	(	(	PUNCT
ejpam-6593	555	5	αxn	αxn	PROPN
ejpam-6593	555	6	+	+	SYM
ejpam-6593	555	7	40i	40i	NOUN
ejpam-6593	555	8	)	)	PUNCT
ejpam-6593	555	9	,	,	PUNCT
ejpam-6593	555	10	m.	m.	PROPN
ejpam-6593	555	11	c.	c.	PROPN
ejpam-6593	555	12	avenilla	avenilla	PROPN
ejpam-6593	555	13	,	,	PUNCT
ejpam-6593	555	14	j.	j.	PROPN
ejpam-6593	555	15	b.	b.	PROPN
ejpam-6593	555	16	bacani	bacani	PROPN
ejpam-6593	555	17	/	/	SYM
ejpam-6593	555	18	eur	eur	PROPN
ejpam-6593	555	19	.	.	PUNCT
ejpam-6593	556	1	j.	j.	PROPN
ejpam-6593	556	2	pure	pure	PROPN
ejpam-6593	556	3	appl	appl	PROPN
ejpam-6593	556	4	.	.	PROPN
ejpam-6593	556	5	math	math	PROPN
ejpam-6593	556	6	,	,	PUNCT
ejpam-6593	556	7	18	18	NUM
ejpam-6593	556	8	(	(	PUNCT
ejpam-6593	556	9	3	3	NUM
ejpam-6593	556	10	)	)	PUNCT
ejpam-6593	556	11	(	(	PUNCT
ejpam-6593	556	12	2025	2025	NUM
ejpam-6593	556	13	)	)	PUNCT
ejpam-6593	556	14	,	,	PUNCT
ejpam-6593	556	15	6593	6593	NUM
ejpam-6593	556	16	17	17	NUM
ejpam-6593	556	17	of	of	ADP
ejpam-6593	556	18	24	24	NUM
ejpam-6593	556	19	showing	show	VERB
ejpam-6593	556	20	that	that	SCONJ
ejpam-6593	556	21	(	(	PUNCT
ejpam-6593	556	22	13	13	NUM
ejpam-6593	556	23	)	)	PUNCT
ejpam-6593	556	24	is	be	AUX
ejpam-6593	556	25	also	also	ADV
ejpam-6593	556	26	true	true	ADJ
ejpam-6593	556	27	for	for	ADP
ejpam-6593	556	28	m	m	PROPN
ejpam-6593	556	29	=	=	NOUN
ejpam-6593	556	30	a+1	a+1	PROPN
ejpam-6593	556	31	.	.	PROPN
ejpam-6593	557	1	therefore	therefore	ADV
ejpam-6593	557	2	,	,	PUNCT
ejpam-6593	557	3	(	(	PUNCT
ejpam-6593	557	4	13	13	NUM
ejpam-6593	557	5	)	)	PUNCT
ejpam-6593	557	6	is	be	AUX
ejpam-6593	557	7	true	true	ADJ
ejpam-6593	557	8	for	for	ADP
ejpam-6593	557	9	any	any	DET
ejpam-6593	557	10	m	m	NOUN
ejpam-6593	557	11	∈	∈	NOUN
ejpam-6593	557	12	n	n	CCONJ
ejpam-6593	557	13	,	,	PUNCT
ejpam-6593	557	14	where	where	SCONJ
ejpam-6593	557	15	xn	xn	PROPN
ejpam-6593	557	16	=	=	SYM
ejpam-6593	557	17	1	1	NUM
ejpam-6593	557	18	+	+	CCONJ
ejpam-6593	557	19	4n	4n	NOUN
ejpam-6593	557	20	or	or	CCONJ
ejpam-6593	557	21	xn	xn	PUNCT
ejpam-6593	557	22	=	=	SYM
ejpam-6593	557	23	3	3	NUM
ejpam-6593	558	1	+	+	CCONJ
ejpam-6593	558	2	4n	4n	NOUN
ejpam-6593	558	3	,	,	PUNCT
ejpam-6593	558	4	n	n	PROPN
ejpam-6593	558	5	∈	∈	PROPN
ejpam-6593	558	6	n0	n0	PROPN
ejpam-6593	558	7	.	.	PUNCT
ejpam-6593	559	1	the	the	DET
ejpam-6593	559	2	next	next	ADJ
ejpam-6593	559	3	remark	remark	NOUN
ejpam-6593	559	4	follows	follow	VERB
ejpam-6593	559	5	directly	directly	ADV
ejpam-6593	559	6	from	from	ADP
ejpam-6593	559	7	the	the	DET
ejpam-6593	559	8	theorem	theorem	NOUN
ejpam-6593	559	9	above	above	ADV
ejpam-6593	559	10	.	.	PUNCT
ejpam-6593	560	1	remark	remark	PROPN
ejpam-6593	560	2	2	2	NUM
ejpam-6593	560	3	.	.	PUNCT
ejpam-6593	561	1	consider	consider	VERB
ejpam-6593	561	2	the	the	DET
ejpam-6593	561	3	exponential	exponential	ADJ
ejpam-6593	561	4	diophantine	diophantine	NOUN
ejpam-6593	561	5	equation	equation	NOUN
ejpam-6593	561	6	2x	2x	NUM
ejpam-6593	561	7	+	+	CCONJ
ejpam-6593	561	8	(	(	PUNCT
ejpam-6593	561	9	2	2	NUM
ejpam-6593	561	10	+	+	NUM
ejpam-6593	561	11	5k	5k	NUM
ejpam-6593	561	12	)	)	PUNCT
ejpam-6593	562	1	=	=	SYM
ejpam-6593	562	2	z2	z2	PROPN
ejpam-6593	562	3	,	,	PUNCT
ejpam-6593	562	4	where	where	SCONJ
ejpam-6593	562	5	x	x	X
ejpam-6593	562	6	:	:	PUNCT
ejpam-6593	562	7	=	=	SYM
ejpam-6593	562	8	xn	xn	PUNCT
ejpam-6593	562	9	=	=	SYM
ejpam-6593	562	10	1	1	NUM
ejpam-6593	563	1	+	+	CCONJ
ejpam-6593	563	2	4n	4n	NOUN
ejpam-6593	563	3	or	or	CCONJ
ejpam-6593	563	4	x	x	SYM
ejpam-6593	563	5	:	:	PUNCT
ejpam-6593	563	6	=	=	SYM
ejpam-6593	563	7	xn	xn	PUNCT
ejpam-6593	563	8	=	=	SYM
ejpam-6593	563	9	3	3	NUM
ejpam-6593	563	10	+	+	CCONJ
ejpam-6593	563	11	4n	4n	NOUN
ejpam-6593	563	12	,	,	PUNCT
ejpam-6593	563	13	n	n	PROPN
ejpam-6593	563	14	∈	∈	PROPN
ejpam-6593	563	15	n0	n0	PROPN
ejpam-6593	563	16	.	.	PUNCT
ejpam-6593	564	1	then	then	ADV
ejpam-6593	564	2	,	,	PUNCT
ejpam-6593	564	3	k(m	k(m	PROPN
ejpam-6593	564	4	,	,	PUNCT
ejpam-6593	564	5	xn	xn	PROPN
ejpam-6593	564	6	)	)	PUNCT
ejpam-6593	564	7	=	=	SYM
ejpam-6593	564	8	k(m−1,xn	k(m−1,xn	PROPN
ejpam-6593	564	9	)	)	PUNCT
ejpam-6593	565	1	+	+	CCONJ
ejpam-6593	565	2	αxn	αxn	X
ejpam-6593	565	3	+	+	CCONJ
ejpam-6593	565	4	40(m−	40(m−	PROPN
ejpam-6593	565	5	1	1	NUM
ejpam-6593	565	6	)	)	PUNCT
ejpam-6593	565	7	.	.	PUNCT
ejpam-6593	566	1	tables	table	NOUN
ejpam-6593	566	2	14	14	NUM
ejpam-6593	566	3	17	17	NUM
ejpam-6593	566	4	each	each	PRON
ejpam-6593	566	5	contain	contain	VERB
ejpam-6593	566	6	the	the	DET
ejpam-6593	566	7	first	first	ADJ
ejpam-6593	566	8	five	five	NUM
ejpam-6593	566	9	solutions	solution	NOUN
ejpam-6593	566	10	of	of	ADP
ejpam-6593	566	11	equation	equation	NOUN
ejpam-6593	566	12	(	(	PUNCT
ejpam-6593	566	13	5	5	NUM
ejpam-6593	566	14	)	)	PUNCT
ejpam-6593	566	15	where	where	SCONJ
ejpam-6593	566	16	x	x	SYM
ejpam-6593	566	17	≡	≡	PROPN
ejpam-6593	566	18	1	1	NUM
ejpam-6593	566	19	or	or	CCONJ
ejpam-6593	566	20	3	3	NUM
ejpam-6593	566	21	(	(	PUNCT
ejpam-6593	566	22	mod	mod	NOUN
ejpam-6593	566	23	4	4	NUM
ejpam-6593	566	24	)	)	PUNCT
ejpam-6593	566	25	,	,	PUNCT
ejpam-6593	566	26	and	and	CCONJ
ejpam-6593	566	27	k(m	k(m	PROPN
ejpam-6593	566	28	,	,	PUNCT
ejpam-6593	566	29	xn	xn	PROPN
ejpam-6593	566	30	)	)	PUNCT
ejpam-6593	566	31	is	be	AUX
ejpam-6593	566	32	obtained	obtain	VERB
ejpam-6593	566	33	by	by	ADP
ejpam-6593	566	34	applying	apply	VERB
ejpam-6593	566	35	equation	equation	NOUN
ejpam-6593	566	36	(	(	PUNCT
ejpam-6593	566	37	6b	6b	NOUN
ejpam-6593	566	38	)	)	PUNCT
ejpam-6593	566	39	,	,	PUNCT
ejpam-6593	566	40	theorem	theorem	VERB
ejpam-6593	566	41	4	4	NUM
ejpam-6593	566	42	,	,	PUNCT
ejpam-6593	566	43	or	or	CCONJ
ejpam-6593	566	44	remark	remark	NOUN
ejpam-6593	566	45	2	2	NUM
ejpam-6593	566	46	.	.	PUNCT
ejpam-6593	567	1	m	m	VERB
ejpam-6593	568	1	k	k	NOUN
ejpam-6593	568	2	z	z	NOUN
ejpam-6593	568	3	equation	equation	NOUN
ejpam-6593	568	4	solution	solution	NOUN
ejpam-6593	568	5	(	(	PUNCT
ejpam-6593	568	6	p	p	X
ejpam-6593	568	7	,	,	PUNCT
ejpam-6593	568	8	k	k	NOUN
ejpam-6593	568	9	,	,	PUNCT
ejpam-6593	568	10	x	x	X
ejpam-6593	568	11	,	,	PUNCT
ejpam-6593	568	12	y	y	PROPN
ejpam-6593	568	13	,	,	PUNCT
ejpam-6593	568	14	z	z	NOUN
ejpam-6593	568	15	)	)	PUNCT
ejpam-6593	568	16	1	1	NUM
ejpam-6593	568	17	3	3	NUM
ejpam-6593	568	18	2	2	NUM
ejpam-6593	568	19	+	+	CCONJ
ejpam-6593	568	20	(	(	PUNCT
ejpam-6593	568	21	2	2	NUM
ejpam-6593	568	22	+	+	NUM
ejpam-6593	568	23	5(1	5(1	NUM
ejpam-6593	568	24	)	)	PUNCT
ejpam-6593	568	25	)	)	PUNCT
ejpam-6593	569	1	=	=	SYM
ejpam-6593	569	2	32	32	NUM
ejpam-6593	569	3	(	(	PUNCT
ejpam-6593	569	4	2	2	NUM
ejpam-6593	569	5	,	,	PUNCT
ejpam-6593	569	6	1	1	NUM
ejpam-6593	569	7	,	,	PUNCT
ejpam-6593	569	8	1	1	NUM
ejpam-6593	569	9	,	,	PUNCT
ejpam-6593	569	10	1	1	NUM
ejpam-6593	569	11	,	,	PUNCT
ejpam-6593	569	12	3	3	NUM
ejpam-6593	569	13	)	)	PUNCT
ejpam-6593	569	14	1	1	NUM
ejpam-6593	569	15	33	33	NUM
ejpam-6593	569	16	13	13	NUM
ejpam-6593	569	17	2	2	NUM
ejpam-6593	569	18	+	+	CCONJ
ejpam-6593	569	19	(	(	PUNCT
ejpam-6593	569	20	2	2	NUM
ejpam-6593	569	21	+	+	NUM
ejpam-6593	569	22	5(33	5(33	NUM
ejpam-6593	569	23	)	)	PUNCT
ejpam-6593	569	24	)	)	PUNCT
ejpam-6593	570	1	=	=	SYM
ejpam-6593	570	2	132	132	NUM
ejpam-6593	570	3	(	(	PUNCT
ejpam-6593	570	4	2	2	NUM
ejpam-6593	570	5	,	,	PUNCT
ejpam-6593	570	6	33	33	NUM
ejpam-6593	570	7	,	,	PUNCT
ejpam-6593	570	8	1	1	NUM
ejpam-6593	570	9	,	,	PUNCT
ejpam-6593	570	10	1	1	NUM
ejpam-6593	570	11	,	,	PUNCT
ejpam-6593	570	12	13	13	NUM
ejpam-6593	570	13	)	)	PUNCT
ejpam-6593	570	14	3	3	NUM
ejpam-6593	570	15	217	217	NUM
ejpam-6593	570	16	33	33	NUM
ejpam-6593	570	17	2	2	NUM
ejpam-6593	570	18	+	+	CCONJ
ejpam-6593	570	19	(	(	PUNCT
ejpam-6593	570	20	2	2	NUM
ejpam-6593	570	21	+	+	NUM
ejpam-6593	570	22	5(217	5(217	NUM
ejpam-6593	570	23	)	)	PUNCT
ejpam-6593	570	24	)	)	PUNCT
ejpam-6593	571	1	=	=	SYM
ejpam-6593	571	2	332	332	NUM
ejpam-6593	571	3	(	(	PUNCT
ejpam-6593	571	4	2	2	NUM
ejpam-6593	571	5	,	,	PUNCT
ejpam-6593	571	6	217	217	NUM
ejpam-6593	571	7	,	,	PUNCT
ejpam-6593	571	8	1	1	NUM
ejpam-6593	571	9	,	,	PUNCT
ejpam-6593	571	10	1	1	NUM
ejpam-6593	571	11	,	,	PUNCT
ejpam-6593	571	12	33	33	NUM
ejpam-6593	571	13	)	)	PUNCT
ejpam-6593	571	14	4	4	NUM
ejpam-6593	571	15	369	369	NUM
ejpam-6593	571	16	43	43	NUM
ejpam-6593	571	17	2	2	NUM
ejpam-6593	571	18	+	+	CCONJ
ejpam-6593	571	19	(	(	PUNCT
ejpam-6593	571	20	2	2	NUM
ejpam-6593	571	21	+	+	NUM
ejpam-6593	571	22	5(369	5(369	NUM
ejpam-6593	571	23	)	)	PUNCT
ejpam-6593	571	24	)	)	PUNCT
ejpam-6593	572	1	=	=	SYM
ejpam-6593	572	2	432	432	NUM
ejpam-6593	572	3	(	(	PUNCT
ejpam-6593	572	4	2	2	NUM
ejpam-6593	572	5	,	,	PUNCT
ejpam-6593	572	6	369	369	NUM
ejpam-6593	572	7	,	,	PUNCT
ejpam-6593	572	8	1	1	NUM
ejpam-6593	572	9	,	,	PUNCT
ejpam-6593	572	10	1	1	NUM
ejpam-6593	572	11	,	,	PUNCT
ejpam-6593	572	12	43	43	NUM
ejpam-6593	572	13	)	)	PUNCT
ejpam-6593	572	14	6	6	NUM
ejpam-6593	572	15	793	793	NUM
ejpam-6593	572	16	63	63	NUM
ejpam-6593	572	17	2	2	NUM
ejpam-6593	572	18	+	+	CCONJ
ejpam-6593	572	19	(	(	PUNCT
ejpam-6593	572	20	2	2	NUM
ejpam-6593	572	21	+	+	SYM
ejpam-6593	572	22	5(793	5(793	NUM
ejpam-6593	572	23	)	)	PUNCT
ejpam-6593	572	24	)	)	PUNCT
ejpam-6593	573	1	=	=	SYM
ejpam-6593	574	1	632	632	NUM
ejpam-6593	574	2	(	(	PUNCT
ejpam-6593	574	3	2	2	NUM
ejpam-6593	574	4	,	,	PUNCT
ejpam-6593	574	5	793	793	NUM
ejpam-6593	574	6	,	,	PUNCT
ejpam-6593	574	7	1	1	NUM
ejpam-6593	574	8	,	,	PUNCT
ejpam-6593	574	9	1	1	NUM
ejpam-6593	574	10	,	,	PUNCT
ejpam-6593	574	11	63	63	NUM
ejpam-6593	574	12	)	)	PUNCT
ejpam-6593	574	13	table	table	NOUN
ejpam-6593	574	14	14	14	NUM
ejpam-6593	574	15	:	:	PUNCT
ejpam-6593	574	16	some	some	DET
ejpam-6593	574	17	solutions	solution	NOUN
ejpam-6593	574	18	of	of	ADP
ejpam-6593	574	19	(	(	PUNCT
ejpam-6593	574	20	5	5	NUM
ejpam-6593	574	21	)	)	PUNCT
ejpam-6593	574	22	with	with	ADP
ejpam-6593	574	23	x	x	X
ejpam-6593	574	24	=	=	PUNCT
ejpam-6593	574	25	y	y	NOUN
ejpam-6593	574	26	=	=	SYM
ejpam-6593	574	27	1	1	NUM
ejpam-6593	574	28	and	and	CCONJ
ejpam-6593	574	29	z	z	PROPN
ejpam-6593	574	30	≡	≡	PROPN
ejpam-6593	574	31	3	3	NUM
ejpam-6593	574	32	(	(	PUNCT
ejpam-6593	574	33	mod	mod	PROPN
ejpam-6593	574	34	10	10	NUM
ejpam-6593	574	35	)	)	PUNCT
ejpam-6593	574	36	m	m	VERB
ejpam-6593	574	37	k	k	NOUN
ejpam-6593	574	38	z	z	NOUN
ejpam-6593	574	39	equation	equation	NOUN
ejpam-6593	574	40	solution	solution	NOUN
ejpam-6593	574	41	(	(	PUNCT
ejpam-6593	574	42	p	p	X
ejpam-6593	574	43	,	,	PUNCT
ejpam-6593	574	44	k	k	NOUN
ejpam-6593	574	45	,	,	PUNCT
ejpam-6593	574	46	x	x	X
ejpam-6593	574	47	,	,	PUNCT
ejpam-6593	574	48	y	y	PROPN
ejpam-6593	574	49	,	,	PUNCT
ejpam-6593	574	50	z	z	NOUN
ejpam-6593	574	51	)	)	PUNCT
ejpam-6593	574	52	9	9	NUM
ejpam-6593	574	53	7	7	NUM
ejpam-6593	574	54	2	2	NUM
ejpam-6593	574	55	+	+	CCONJ
ejpam-6593	574	56	(	(	PUNCT
ejpam-6593	574	57	2	2	NUM
ejpam-6593	574	58	+	+	SYM
ejpam-6593	574	59	5(9	5(9	NUM
ejpam-6593	574	60	)	)	PUNCT
ejpam-6593	574	61	)	)	PUNCT
ejpam-6593	575	1	=	=	SYM
ejpam-6593	575	2	72	72	NUM
ejpam-6593	575	3	(	(	PUNCT
ejpam-6593	575	4	2	2	NUM
ejpam-6593	575	5	,	,	PUNCT
ejpam-6593	575	6	9	9	NUM
ejpam-6593	575	7	,	,	PUNCT
ejpam-6593	575	8	1	1	NUM
ejpam-6593	575	9	,	,	PUNCT
ejpam-6593	575	10	1	1	NUM
ejpam-6593	575	11	,	,	PUNCT
ejpam-6593	575	12	7	7	NUM
ejpam-6593	575	13	)	)	SYM
ejpam-6593	575	14	2	2	NUM
ejpam-6593	575	15	145	145	NUM
ejpam-6593	575	16	27	27	NUM
ejpam-6593	575	17	2	2	NUM
ejpam-6593	575	18	+	+	CCONJ
ejpam-6593	575	19	(	(	PUNCT
ejpam-6593	575	20	2	2	NUM
ejpam-6593	575	21	+	+	SYM
ejpam-6593	575	22	5(145	5(145	NUM
ejpam-6593	575	23	)	)	PUNCT
ejpam-6593	575	24	)	)	PUNCT
ejpam-6593	576	1	=	=	SYM
ejpam-6593	576	2	272	272	NUM
ejpam-6593	576	3	(	(	PUNCT
ejpam-6593	576	4	2	2	NUM
ejpam-6593	576	5	,	,	PUNCT
ejpam-6593	576	6	145	145	NUM
ejpam-6593	576	7	,	,	PUNCT
ejpam-6593	576	8	1	1	NUM
ejpam-6593	576	9	,	,	PUNCT
ejpam-6593	576	10	1	1	NUM
ejpam-6593	576	11	,	,	PUNCT
ejpam-6593	576	12	27	27	NUM
ejpam-6593	576	13	)	)	PUNCT
ejpam-6593	576	14	3	3	NUM
ejpam-6593	576	15	273	273	NUM
ejpam-6593	576	16	37	37	NUM
ejpam-6593	576	17	2	2	NUM
ejpam-6593	576	18	+	+	CCONJ
ejpam-6593	576	19	(	(	PUNCT
ejpam-6593	576	20	2	2	NUM
ejpam-6593	576	21	+	+	NUM
ejpam-6593	576	22	5(273	5(273	NUM
ejpam-6593	576	23	)	)	PUNCT
ejpam-6593	576	24	)	)	PUNCT
ejpam-6593	577	1	=	=	SYM
ejpam-6593	577	2	372	372	NUM
ejpam-6593	577	3	(	(	PUNCT
ejpam-6593	577	4	2	2	NUM
ejpam-6593	577	5	,	,	PUNCT
ejpam-6593	577	6	273	273	NUM
ejpam-6593	577	7	,	,	PUNCT
ejpam-6593	577	8	1	1	NUM
ejpam-6593	577	9	,	,	PUNCT
ejpam-6593	577	10	1	1	NUM
ejpam-6593	577	11	,	,	PUNCT
ejpam-6593	577	12	37	37	NUM
ejpam-6593	577	13	)	)	PUNCT
ejpam-6593	577	14	4	4	NUM
ejpam-6593	577	15	441	441	NUM
ejpam-6593	577	16	47	47	NUM
ejpam-6593	577	17	2	2	NUM
ejpam-6593	577	18	+	+	CCONJ
ejpam-6593	577	19	(	(	PUNCT
ejpam-6593	577	20	2	2	NUM
ejpam-6593	577	21	+	+	NUM
ejpam-6593	577	22	5(441	5(441	NUM
ejpam-6593	577	23	)	)	PUNCT
ejpam-6593	577	24	)	)	PUNCT
ejpam-6593	578	1	=	=	SYM
ejpam-6593	578	2	472	472	NUM
ejpam-6593	578	3	(	(	PUNCT
ejpam-6593	578	4	2	2	NUM
ejpam-6593	578	5	,	,	PUNCT
ejpam-6593	578	6	441	441	NUM
ejpam-6593	578	7	,	,	PUNCT
ejpam-6593	578	8	1	1	NUM
ejpam-6593	578	9	,	,	PUNCT
ejpam-6593	578	10	1	1	NUM
ejpam-6593	578	11	,	,	PUNCT
ejpam-6593	578	12	47	47	NUM
ejpam-6593	578	13	)	)	PUNCT
ejpam-6593	578	14	7	7	NUM
ejpam-6593	578	15	1185	1185	NUM
ejpam-6593	578	16	77	77	NUM
ejpam-6593	578	17	2	2	NUM
ejpam-6593	578	18	+	+	CCONJ
ejpam-6593	578	19	(	(	PUNCT
ejpam-6593	578	20	2	2	NUM
ejpam-6593	578	21	+	+	NUM
ejpam-6593	578	22	5(1185	5(1185	NUM
ejpam-6593	578	23	)	)	PUNCT
ejpam-6593	578	24	)	)	PUNCT
ejpam-6593	579	1	=	=	SYM
ejpam-6593	579	2	772	772	NUM
ejpam-6593	579	3	(	(	PUNCT
ejpam-6593	579	4	2	2	NUM
ejpam-6593	579	5	,	,	PUNCT
ejpam-6593	579	6	1185	1185	NUM
ejpam-6593	579	7	,	,	PUNCT
ejpam-6593	579	8	1	1	NUM
ejpam-6593	579	9	,	,	PUNCT
ejpam-6593	579	10	1	1	NUM
ejpam-6593	579	11	,	,	PUNCT
ejpam-6593	579	12	77	77	NUM
ejpam-6593	579	13	)	)	PUNCT
ejpam-6593	579	14	table	table	NOUN
ejpam-6593	579	15	15	15	NUM
ejpam-6593	579	16	:	:	PUNCT
ejpam-6593	579	17	some	some	DET
ejpam-6593	579	18	solutions	solution	NOUN
ejpam-6593	579	19	of	of	ADP
ejpam-6593	579	20	(	(	PUNCT
ejpam-6593	579	21	5	5	NUM
ejpam-6593	579	22	)	)	PUNCT
ejpam-6593	579	23	with	with	ADP
ejpam-6593	579	24	x	x	X
ejpam-6593	579	25	=	=	PUNCT
ejpam-6593	579	26	y	y	NOUN
ejpam-6593	579	27	=	=	SYM
ejpam-6593	579	28	1	1	NUM
ejpam-6593	579	29	and	and	CCONJ
ejpam-6593	579	30	z	z	PROPN
ejpam-6593	579	31	≡	≡	PROPN
ejpam-6593	579	32	7	7	NUM
ejpam-6593	579	33	(	(	PUNCT
ejpam-6593	579	34	mod	mod	PROPN
ejpam-6593	579	35	10	10	NUM
ejpam-6593	579	36	)	)	PUNCT
ejpam-6593	579	37	m	m	VERB
ejpam-6593	579	38	k	k	NOUN
ejpam-6593	579	39	z	z	NOUN
ejpam-6593	579	40	equation	equation	NOUN
ejpam-6593	579	41	solution	solution	NOUN
ejpam-6593	579	42	(	(	PUNCT
ejpam-6593	579	43	p	p	X
ejpam-6593	579	44	,	,	PUNCT
ejpam-6593	579	45	k	k	NOUN
ejpam-6593	579	46	,	,	PUNCT
ejpam-6593	579	47	x	x	X
ejpam-6593	579	48	,	,	PUNCT
ejpam-6593	579	49	y	y	PROPN
ejpam-6593	579	50	,	,	PUNCT
ejpam-6593	579	51	z	z	NOUN
ejpam-6593	579	52	)	)	PUNCT
ejpam-6593	579	53	27	27	NUM
ejpam-6593	579	54	13	13	NUM
ejpam-6593	579	55	25	25	NUM
ejpam-6593	579	56	+	+	CCONJ
ejpam-6593	579	57	(	(	PUNCT
ejpam-6593	579	58	2	2	NUM
ejpam-6593	579	59	+	+	NUM
ejpam-6593	579	60	5(27	5(27	NUM
ejpam-6593	579	61	)	)	PUNCT
ejpam-6593	579	62	)	)	PUNCT
ejpam-6593	580	1	=	=	SYM
ejpam-6593	580	2	132	132	NUM
ejpam-6593	580	3	(	(	PUNCT
ejpam-6593	580	4	2	2	NUM
ejpam-6593	580	5	,	,	PUNCT
ejpam-6593	580	6	27	27	NUM
ejpam-6593	580	7	,	,	PUNCT
ejpam-6593	580	8	5	5	NUM
ejpam-6593	580	9	,	,	PUNCT
ejpam-6593	580	10	1	1	NUM
ejpam-6593	580	11	,	,	PUNCT
ejpam-6593	580	12	13	13	NUM
ejpam-6593	580	13	)	)	PUNCT
ejpam-6593	580	14	4	4	NUM
ejpam-6593	580	15	555	555	NUM
ejpam-6593	580	16	53	53	NUM
ejpam-6593	580	17	25	25	NUM
ejpam-6593	580	18	+	+	CCONJ
ejpam-6593	580	19	(	(	PUNCT
ejpam-6593	580	20	2	2	NUM
ejpam-6593	580	21	+	+	NUM
ejpam-6593	580	22	5(555	5(555	NUM
ejpam-6593	580	23	)	)	PUNCT
ejpam-6593	580	24	)	)	PUNCT
ejpam-6593	581	1	=	=	SYM
ejpam-6593	581	2	532	532	NUM
ejpam-6593	581	3	(	(	PUNCT
ejpam-6593	581	4	2	2	NUM
ejpam-6593	581	5	,	,	PUNCT
ejpam-6593	581	6	555	555	NUM
ejpam-6593	581	7	,	,	PUNCT
ejpam-6593	581	8	5	5	NUM
ejpam-6593	581	9	,	,	PUNCT
ejpam-6593	581	10	1	1	NUM
ejpam-6593	581	11	,	,	PUNCT
ejpam-6593	581	12	53	53	NUM
ejpam-6593	581	13	)	)	PUNCT
ejpam-6593	581	14	6	6	NUM
ejpam-6593	581	15	1059	1059	NUM
ejpam-6593	581	16	73	73	NUM
ejpam-6593	581	17	25	25	NUM
ejpam-6593	581	18	+	+	CCONJ
ejpam-6593	581	19	(	(	PUNCT
ejpam-6593	581	20	2	2	NUM
ejpam-6593	581	21	+	+	SYM
ejpam-6593	581	22	5(1059	5(1059	NUM
ejpam-6593	581	23	)	)	PUNCT
ejpam-6593	581	24	)	)	PUNCT
ejpam-6593	582	1	=	=	SYM
ejpam-6593	582	2	732	732	NUM
ejpam-6593	582	3	(	(	PUNCT
ejpam-6593	582	4	2	2	NUM
ejpam-6593	582	5	,	,	PUNCT
ejpam-6593	582	6	1059	1059	NUM
ejpam-6593	582	7	,	,	PUNCT
ejpam-6593	582	8	5	5	NUM
ejpam-6593	582	9	,	,	PUNCT
ejpam-6593	582	10	1	1	NUM
ejpam-6593	582	11	,	,	PUNCT
ejpam-6593	582	12	73	73	NUM
ejpam-6593	582	13	)	)	PUNCT
ejpam-6593	582	14	7	7	NUM
ejpam-6593	582	15	1371	1371	NUM
ejpam-6593	582	16	83	83	NUM
ejpam-6593	582	17	25	25	NUM
ejpam-6593	582	18	+	+	CCONJ
ejpam-6593	582	19	(	(	PUNCT
ejpam-6593	582	20	2	2	NUM
ejpam-6593	582	21	+	+	NUM
ejpam-6593	582	22	5(1371	5(1371	NUM
ejpam-6593	582	23	)	)	PUNCT
ejpam-6593	582	24	)	)	PUNCT
ejpam-6593	583	1	=	=	SYM
ejpam-6593	583	2	832	832	NUM
ejpam-6593	583	3	(	(	PUNCT
ejpam-6593	583	4	2	2	NUM
ejpam-6593	583	5	,	,	PUNCT
ejpam-6593	583	6	1371	1371	NUM
ejpam-6593	583	7	,	,	PUNCT
ejpam-6593	583	8	5	5	NUM
ejpam-6593	583	9	,	,	PUNCT
ejpam-6593	583	10	1	1	NUM
ejpam-6593	583	11	,	,	PUNCT
ejpam-6593	583	12	83	83	NUM
ejpam-6593	583	13	)	)	PUNCT
ejpam-6593	583	14	12	12	NUM
ejpam-6593	583	15	3531	3531	NUM
ejpam-6593	583	16	133	133	NUM
ejpam-6593	583	17	25	25	NUM
ejpam-6593	584	1	+	+	CCONJ
ejpam-6593	584	2	(	(	PUNCT
ejpam-6593	584	3	2	2	NUM
ejpam-6593	584	4	+	+	SYM
ejpam-6593	584	5	5(3531	5(3531	NUM
ejpam-6593	584	6	)	)	PUNCT
ejpam-6593	584	7	)	)	PUNCT
ejpam-6593	585	1	=	=	SYM
ejpam-6593	585	2	1332	1332	NUM
ejpam-6593	585	3	(	(	PUNCT
ejpam-6593	585	4	2	2	NUM
ejpam-6593	585	5	,	,	PUNCT
ejpam-6593	585	6	3531	3531	NUM
ejpam-6593	585	7	,	,	PUNCT
ejpam-6593	585	8	5	5	NUM
ejpam-6593	585	9	,	,	PUNCT
ejpam-6593	585	10	1	1	NUM
ejpam-6593	585	11	,	,	PUNCT
ejpam-6593	585	12	133	133	NUM
ejpam-6593	585	13	)	)	PUNCT
ejpam-6593	585	14	table	table	NOUN
ejpam-6593	585	15	16	16	NUM
ejpam-6593	585	16	:	:	PUNCT
ejpam-6593	585	17	some	some	DET
ejpam-6593	585	18	solutions	solution	NOUN
ejpam-6593	585	19	of	of	ADP
ejpam-6593	585	20	(	(	PUNCT
ejpam-6593	585	21	5	5	NUM
ejpam-6593	585	22	)	)	PUNCT
ejpam-6593	585	23	with	with	ADP
ejpam-6593	585	24	x	x	SYM
ejpam-6593	585	25	=	=	SYM
ejpam-6593	585	26	5	5	NUM
ejpam-6593	585	27	,	,	PUNCT
ejpam-6593	585	28	y	y	NOUN
ejpam-6593	585	29	=	=	SYM
ejpam-6593	585	30	1	1	NUM
ejpam-6593	585	31	and	and	CCONJ
ejpam-6593	585	32	z	z	PROPN
ejpam-6593	585	33	≡	≡	PROPN
ejpam-6593	585	34	3	3	NUM
ejpam-6593	585	35	(	(	PUNCT
ejpam-6593	585	36	mod	mod	PROPN
ejpam-6593	585	37	10	10	NUM
ejpam-6593	585	38	)	)	PUNCT
ejpam-6593	585	39	m	m	VERB
ejpam-6593	585	40	k	k	NOUN
ejpam-6593	585	41	z	z	NOUN
ejpam-6593	585	42	equation	equation	NOUN
ejpam-6593	585	43	solution	solution	NOUN
ejpam-6593	585	44	(	(	PUNCT
ejpam-6593	585	45	p	p	X
ejpam-6593	585	46	,	,	PUNCT
ejpam-6593	585	47	k	k	NOUN
ejpam-6593	585	48	,	,	PUNCT
ejpam-6593	585	49	x	x	X
ejpam-6593	585	50	,	,	PUNCT
ejpam-6593	585	51	y	y	PROPN
ejpam-6593	585	52	,	,	PUNCT
ejpam-6593	585	53	z	z	NOUN
ejpam-6593	585	54	)	)	PUNCT
ejpam-6593	585	55	3	3	NUM
ejpam-6593	585	56	7	7	NUM
ejpam-6593	585	57	25	25	NUM
ejpam-6593	586	1	+	+	CCONJ
ejpam-6593	586	2	(	(	PUNCT
ejpam-6593	586	3	2	2	NUM
ejpam-6593	586	4	+	+	NUM
ejpam-6593	586	5	5(3	5(3	NUM
ejpam-6593	586	6	)	)	PUNCT
ejpam-6593	586	7	)	)	PUNCT
ejpam-6593	587	1	=	=	SYM
ejpam-6593	587	2	72	72	NUM
ejpam-6593	587	3	(	(	PUNCT
ejpam-6593	587	4	2	2	NUM
ejpam-6593	587	5	,	,	PUNCT
ejpam-6593	587	6	3	3	NUM
ejpam-6593	587	7	,	,	PUNCT
ejpam-6593	587	8	5	5	NUM
ejpam-6593	587	9	,	,	PUNCT
ejpam-6593	587	10	1	1	NUM
ejpam-6593	587	11	,	,	PUNCT
ejpam-6593	587	12	7	7	NUM
ejpam-6593	587	13	)	)	SYM
ejpam-6593	587	14	1	1	NUM
ejpam-6593	587	15	51	51	NUM
ejpam-6593	587	16	17	17	NUM
ejpam-6593	587	17	25	25	NUM
ejpam-6593	587	18	+	+	CCONJ
ejpam-6593	587	19	(	(	PUNCT
ejpam-6593	587	20	2	2	NUM
ejpam-6593	587	21	+	+	NUM
ejpam-6593	587	22	5(51	5(51	NUM
ejpam-6593	587	23	)	)	PUNCT
ejpam-6593	587	24	)	)	PUNCT
ejpam-6593	588	1	=	=	SYM
ejpam-6593	588	2	172	172	NUM
ejpam-6593	588	3	(	(	PUNCT
ejpam-6593	588	4	2	2	NUM
ejpam-6593	588	5	,	,	PUNCT
ejpam-6593	588	6	51	51	NUM
ejpam-6593	588	7	,	,	PUNCT
ejpam-6593	588	8	5	5	NUM
ejpam-6593	588	9	,	,	PUNCT
ejpam-6593	588	10	1	1	NUM
ejpam-6593	588	11	,	,	PUNCT
ejpam-6593	588	12	17	17	NUM
ejpam-6593	588	13	)	)	PUNCT
ejpam-6593	588	14	5	5	NUM
ejpam-6593	588	15	643	643	NUM
ejpam-6593	588	16	57	57	NUM
ejpam-6593	588	17	25	25	NUM
ejpam-6593	588	18	+	+	CCONJ
ejpam-6593	588	19	(	(	PUNCT
ejpam-6593	588	20	2	2	NUM
ejpam-6593	588	21	+	+	NUM
ejpam-6593	588	22	5(643	5(643	NUM
ejpam-6593	588	23	)	)	PUNCT
ejpam-6593	588	24	)	)	PUNCT
ejpam-6593	589	1	=	=	SYM
ejpam-6593	589	2	572	572	NUM
ejpam-6593	589	3	(	(	PUNCT
ejpam-6593	589	4	2	2	NUM
ejpam-6593	589	5	,	,	PUNCT
ejpam-6593	589	6	643	643	NUM
ejpam-6593	589	7	,	,	PUNCT
ejpam-6593	589	8	5	5	NUM
ejpam-6593	589	9	,	,	PUNCT
ejpam-6593	589	10	1	1	NUM
ejpam-6593	589	11	,	,	PUNCT
ejpam-6593	589	12	57	57	NUM
ejpam-6593	589	13	)	)	PUNCT
ejpam-6593	589	14	6	6	NUM
ejpam-6593	589	15	891	891	NUM
ejpam-6593	589	16	67	67	NUM
ejpam-6593	589	17	25	25	NUM
ejpam-6593	589	18	+	+	CCONJ
ejpam-6593	589	19	(	(	PUNCT
ejpam-6593	589	20	2	2	NUM
ejpam-6593	589	21	+	+	NUM
ejpam-6593	589	22	5(891	5(891	NUM
ejpam-6593	589	23	)	)	PUNCT
ejpam-6593	589	24	)	)	PUNCT
ejpam-6593	590	1	=	=	PUNCT
ejpam-6593	590	2	672	672	NUM
ejpam-6593	590	3	(	(	PUNCT
ejpam-6593	590	4	2	2	NUM
ejpam-6593	590	5	,	,	PUNCT
ejpam-6593	590	6	891	891	NUM
ejpam-6593	590	7	,	,	PUNCT
ejpam-6593	590	8	5	5	NUM
ejpam-6593	590	9	,	,	PUNCT
ejpam-6593	590	10	1	1	NUM
ejpam-6593	590	11	,	,	PUNCT
ejpam-6593	590	12	67	67	NUM
ejpam-6593	590	13	)	)	PUNCT
ejpam-6593	590	14	7	7	NUM
ejpam-6593	590	15	1179	1179	NUM
ejpam-6593	590	16	77	77	NUM
ejpam-6593	590	17	25	25	NUM
ejpam-6593	590	18	+	+	CCONJ
ejpam-6593	590	19	(	(	PUNCT
ejpam-6593	590	20	2	2	NUM
ejpam-6593	590	21	+	+	NUM
ejpam-6593	590	22	5(1179	5(1179	NUM
ejpam-6593	590	23	)	)	PUNCT
ejpam-6593	590	24	)	)	PUNCT
ejpam-6593	591	1	=	=	SYM
ejpam-6593	591	2	772	772	NUM
ejpam-6593	591	3	(	(	PUNCT
ejpam-6593	591	4	2	2	NUM
ejpam-6593	591	5	,	,	PUNCT
ejpam-6593	591	6	1179	1179	NUM
ejpam-6593	591	7	,	,	PUNCT
ejpam-6593	591	8	5	5	NUM
ejpam-6593	591	9	,	,	PUNCT
ejpam-6593	591	10	1	1	NUM
ejpam-6593	591	11	,	,	PUNCT
ejpam-6593	591	12	77	77	NUM
ejpam-6593	591	13	)	)	PUNCT
ejpam-6593	591	14	table	table	NOUN
ejpam-6593	591	15	17	17	NUM
ejpam-6593	591	16	:	:	PUNCT
ejpam-6593	591	17	some	some	DET
ejpam-6593	591	18	solutions	solution	NOUN
ejpam-6593	591	19	of	of	ADP
ejpam-6593	591	20	(	(	PUNCT
ejpam-6593	591	21	5	5	NUM
ejpam-6593	591	22	)	)	PUNCT
ejpam-6593	591	23	with	with	ADP
ejpam-6593	591	24	x	x	SYM
ejpam-6593	591	25	=	=	SYM
ejpam-6593	591	26	5	5	NUM
ejpam-6593	591	27	,	,	PUNCT
ejpam-6593	591	28	y	y	NOUN
ejpam-6593	591	29	=	=	SYM
ejpam-6593	591	30	1	1	NUM
ejpam-6593	591	31	and	and	CCONJ
ejpam-6593	591	32	z	z	PROPN
ejpam-6593	591	33	≡	≡	PROPN
ejpam-6593	591	34	7	7	NUM
ejpam-6593	591	35	(	(	PUNCT
ejpam-6593	591	36	mod	mod	PROPN
ejpam-6593	591	37	10	10	NUM
ejpam-6593	591	38	)	)	PUNCT
ejpam-6593	591	39	tables	table	NOUN
ejpam-6593	591	40	18	18	NUM
ejpam-6593	591	41	19	19	NUM
ejpam-6593	591	42	present	present	ADJ
ejpam-6593	591	43	some	some	DET
ejpam-6593	591	44	solutions	solution	NOUN
ejpam-6593	591	45	of	of	ADP
ejpam-6593	591	46	(	(	PUNCT
ejpam-6593	591	47	5	5	NUM
ejpam-6593	591	48	)	)	PUNCT
ejpam-6593	591	49	,	,	PUNCT
ejpam-6593	591	50	where	where	SCONJ
ejpam-6593	591	51	z	z	NOUN
ejpam-6593	591	52	≡	≡	PROPN
ejpam-6593	591	53	5	5	NUM
ejpam-6593	591	54	(	(	PUNCT
ejpam-6593	591	55	mod	mod	PROPN
ejpam-6593	591	56	10	10	NUM
ejpam-6593	591	57	)	)	PUNCT
ejpam-6593	591	58	.	.	PUNCT
ejpam-6593	592	1	now	now	ADV
ejpam-6593	592	2	,	,	PUNCT
ejpam-6593	592	3	we	we	PRON
ejpam-6593	592	4	discuss	discuss	VERB
ejpam-6593	592	5	the	the	DET
ejpam-6593	592	6	case	case	NOUN
ejpam-6593	592	7	when	when	SCONJ
ejpam-6593	592	8	x	x	PRON
ejpam-6593	592	9	is	be	AUX
ejpam-6593	592	10	even	even	ADV
ejpam-6593	592	11	,	,	PUNCT
ejpam-6593	592	12	i.e.	i.e.	X
ejpam-6593	592	13	,	,	PUNCT
ejpam-6593	592	14	x	x	SYM
ejpam-6593	592	15	≡	≡	PROPN
ejpam-6593	592	16	0	0	PUNCT
ejpam-6593	592	17	(	(	PUNCT
ejpam-6593	592	18	mod	mod	NOUN
ejpam-6593	592	19	4	4	NUM
ejpam-6593	592	20	)	)	PUNCT
ejpam-6593	592	21	and	and	CCONJ
ejpam-6593	592	22	x	x	SYM
ejpam-6593	592	23	≡	≡	ADJ
ejpam-6593	592	24	2	2	NUM
ejpam-6593	592	25	(	(	PUNCT
ejpam-6593	592	26	mod	mod	NOUN
ejpam-6593	592	27	4	4	NUM
ejpam-6593	592	28	)	)	PUNCT
ejpam-6593	592	29	.	.	PUNCT
ejpam-6593	593	1	we	we	PRON
ejpam-6593	593	2	begin	begin	VERB
ejpam-6593	593	3	with	with	ADP
ejpam-6593	593	4	a	a	DET
ejpam-6593	593	5	remark	remark	NOUN
ejpam-6593	593	6	,	,	PUNCT
ejpam-6593	593	7	followed	follow	VERB
ejpam-6593	593	8	by	by	ADP
ejpam-6593	593	9	a	a	DET
ejpam-6593	593	10	proven	proven	ADJ
ejpam-6593	593	11	claim	claim	NOUN
ejpam-6593	593	12	.	.	PUNCT
ejpam-6593	594	1	m.	m.	NOUN
ejpam-6593	594	2	c.	c.	PROPN
ejpam-6593	594	3	avenilla	avenilla	PROPN
ejpam-6593	594	4	,	,	PUNCT
ejpam-6593	594	5	j.	j.	PROPN
ejpam-6593	594	6	b.	b.	PROPN
ejpam-6593	594	7	bacani	bacani	PROPN
ejpam-6593	594	8	/	/	SYM
ejpam-6593	594	9	eur	eur	PROPN
ejpam-6593	594	10	.	.	PUNCT
ejpam-6593	595	1	j.	j.	PROPN
ejpam-6593	595	2	pure	pure	PROPN
ejpam-6593	595	3	appl	appl	PROPN
ejpam-6593	595	4	.	.	PROPN
ejpam-6593	595	5	math	math	PROPN
ejpam-6593	595	6	,	,	PUNCT
ejpam-6593	595	7	18	18	NUM
ejpam-6593	595	8	(	(	PUNCT
ejpam-6593	595	9	3	3	NUM
ejpam-6593	595	10	)	)	PUNCT
ejpam-6593	595	11	(	(	PUNCT
ejpam-6593	595	12	2025	2025	NUM
ejpam-6593	595	13	)	)	PUNCT
ejpam-6593	595	14	,	,	PUNCT
ejpam-6593	595	15	6593	6593	NUM
ejpam-6593	595	16	18	18	NUM
ejpam-6593	595	17	of	of	ADP
ejpam-6593	595	18	24	24	NUM
ejpam-6593	595	19	m	m	PROPN
ejpam-6593	595	20	k	k	NOUN
ejpam-6593	595	21	z	z	NOUN
ejpam-6593	595	22	equation	equation	NOUN
ejpam-6593	595	23	solution	solution	NOUN
ejpam-6593	595	24	(	(	PUNCT
ejpam-6593	595	25	p	p	X
ejpam-6593	595	26	,	,	PUNCT
ejpam-6593	595	27	k	k	NOUN
ejpam-6593	595	28	,	,	PUNCT
ejpam-6593	595	29	x	x	X
ejpam-6593	595	30	,	,	PUNCT
ejpam-6593	595	31	y	y	PROPN
ejpam-6593	595	32	,	,	PUNCT
ejpam-6593	595	33	z	z	NOUN
ejpam-6593	595	34	)	)	PUNCT
ejpam-6593	595	35	3	3	NUM
ejpam-6593	595	36	5	5	NUM
ejpam-6593	595	37	23	23	NUM
ejpam-6593	595	38	+	+	CCONJ
ejpam-6593	595	39	(	(	PUNCT
ejpam-6593	595	40	2	2	NUM
ejpam-6593	595	41	+	+	NUM
ejpam-6593	595	42	5(3	5(3	NUM
ejpam-6593	595	43	)	)	PUNCT
ejpam-6593	595	44	)	)	PUNCT
ejpam-6593	596	1	=	=	SYM
ejpam-6593	597	1	52	52	NUM
ejpam-6593	597	2	(	(	PUNCT
ejpam-6593	597	3	2	2	NUM
ejpam-6593	597	4	,	,	PUNCT
ejpam-6593	597	5	3	3	NUM
ejpam-6593	597	6	,	,	PUNCT
ejpam-6593	597	7	3	3	NUM
ejpam-6593	597	8	,	,	PUNCT
ejpam-6593	597	9	1	1	NUM
ejpam-6593	597	10	,	,	PUNCT
ejpam-6593	597	11	5	5	NUM
ejpam-6593	597	12	)	)	PUNCT
ejpam-6593	597	13	2	2	NUM
ejpam-6593	597	14	123	123	NUM
ejpam-6593	597	15	25	25	NUM
ejpam-6593	597	16	23	23	NUM
ejpam-6593	597	17	+	+	CCONJ
ejpam-6593	597	18	(	(	PUNCT
ejpam-6593	597	19	2	2	NUM
ejpam-6593	597	20	+	+	NUM
ejpam-6593	597	21	5(123	5(123	NUM
ejpam-6593	597	22	)	)	PUNCT
ejpam-6593	597	23	)	)	PUNCT
ejpam-6593	598	1	=	=	PUNCT
ejpam-6593	598	2	252	252	NUM
ejpam-6593	598	3	(	(	PUNCT
ejpam-6593	598	4	2	2	NUM
ejpam-6593	598	5	,	,	PUNCT
ejpam-6593	598	6	123	123	NUM
ejpam-6593	598	7	,	,	PUNCT
ejpam-6593	598	8	3	3	NUM
ejpam-6593	598	9	,	,	PUNCT
ejpam-6593	598	10	1	1	NUM
ejpam-6593	598	11	,	,	PUNCT
ejpam-6593	598	12	25	25	NUM
ejpam-6593	598	13	)	)	PUNCT
ejpam-6593	598	14	3	3	NUM
ejpam-6593	599	1	243	243	NUM
ejpam-6593	599	2	35	35	NUM
ejpam-6593	599	3	23	23	NUM
ejpam-6593	600	1	+	+	CCONJ
ejpam-6593	600	2	(	(	PUNCT
ejpam-6593	600	3	2	2	NUM
ejpam-6593	600	4	+	+	NUM
ejpam-6593	600	5	5(243	5(243	NUM
ejpam-6593	600	6	)	)	PUNCT
ejpam-6593	600	7	)	)	PUNCT
ejpam-6593	601	1	=	=	SYM
ejpam-6593	601	2	352	352	NUM
ejpam-6593	601	3	(	(	PUNCT
ejpam-6593	601	4	2	2	NUM
ejpam-6593	601	5	,	,	PUNCT
ejpam-6593	601	6	243	243	NUM
ejpam-6593	601	7	,	,	PUNCT
ejpam-6593	601	8	3	3	NUM
ejpam-6593	601	9	,	,	PUNCT
ejpam-6593	601	10	1	1	NUM
ejpam-6593	601	11	,	,	PUNCT
ejpam-6593	601	12	35	35	NUM
ejpam-6593	601	13	)	)	PUNCT
ejpam-6593	601	14	4	4	NUM
ejpam-6593	601	15	405	405	NUM
ejpam-6593	601	16	45	45	NUM
ejpam-6593	601	17	23	23	NUM
ejpam-6593	601	18	+	+	CCONJ
ejpam-6593	601	19	(	(	PUNCT
ejpam-6593	601	20	2	2	NUM
ejpam-6593	601	21	+	+	NUM
ejpam-6593	601	22	5(405	5(405	NUM
ejpam-6593	601	23	)	)	PUNCT
ejpam-6593	601	24	)	)	PUNCT
ejpam-6593	602	1	=	=	SYM
ejpam-6593	602	2	452	452	NUM
ejpam-6593	602	3	(	(	PUNCT
ejpam-6593	602	4	2	2	NUM
ejpam-6593	602	5	,	,	PUNCT
ejpam-6593	602	6	405	405	NUM
ejpam-6593	602	7	,	,	PUNCT
ejpam-6593	602	8	3	3	NUM
ejpam-6593	602	9	,	,	PUNCT
ejpam-6593	602	10	1	1	NUM
ejpam-6593	602	11	,	,	PUNCT
ejpam-6593	602	12	45	45	NUM
ejpam-6593	602	13	)	)	PUNCT
ejpam-6593	602	14	6	6	NUM
ejpam-6593	602	15	843	843	NUM
ejpam-6593	602	16	65	65	NUM
ejpam-6593	602	17	23	23	NUM
ejpam-6593	602	18	+	+	CCONJ
ejpam-6593	602	19	(	(	PUNCT
ejpam-6593	602	20	2	2	NUM
ejpam-6593	602	21	+	+	NUM
ejpam-6593	602	22	5(843	5(843	NUM
ejpam-6593	602	23	)	)	PUNCT
ejpam-6593	602	24	)	)	PUNCT
ejpam-6593	603	1	=	=	SYM
ejpam-6593	603	2	652	652	NUM
ejpam-6593	603	3	(	(	PUNCT
ejpam-6593	603	4	2	2	NUM
ejpam-6593	603	5	,	,	PUNCT
ejpam-6593	603	6	843	843	NUM
ejpam-6593	603	7	,	,	PUNCT
ejpam-6593	603	8	3	3	NUM
ejpam-6593	603	9	,	,	PUNCT
ejpam-6593	603	10	1	1	NUM
ejpam-6593	603	11	,	,	PUNCT
ejpam-6593	603	12	65	65	NUM
ejpam-6593	603	13	)	)	PUNCT
ejpam-6593	603	14	table	table	NOUN
ejpam-6593	603	15	18	18	NUM
ejpam-6593	603	16	:	:	PUNCT
ejpam-6593	603	17	some	some	DET
ejpam-6593	603	18	solutions	solution	NOUN
ejpam-6593	603	19	of	of	ADP
ejpam-6593	603	20	(	(	PUNCT
ejpam-6593	603	21	5	5	NUM
ejpam-6593	603	22	)	)	PUNCT
ejpam-6593	603	23	with	with	ADP
ejpam-6593	603	24	x	x	X
ejpam-6593	604	1	=	=	SYM
ejpam-6593	604	2	3	3	NUM
ejpam-6593	604	3	,	,	PUNCT
ejpam-6593	604	4	y	y	PROPN
ejpam-6593	604	5	=	=	SYM
ejpam-6593	604	6	1	1	NUM
ejpam-6593	604	7	and	and	CCONJ
ejpam-6593	604	8	z	z	PROPN
ejpam-6593	604	9	≡	≡	PROPN
ejpam-6593	604	10	5	5	NUM
ejpam-6593	604	11	(	(	PUNCT
ejpam-6593	604	12	mod	mod	PROPN
ejpam-6593	604	13	10	10	NUM
ejpam-6593	604	14	)	)	PUNCT
ejpam-6593	604	15	m	m	VERB
ejpam-6593	604	16	k	k	NOUN
ejpam-6593	604	17	z	z	NOUN
ejpam-6593	604	18	equation	equation	NOUN
ejpam-6593	604	19	solution	solution	NOUN
ejpam-6593	604	20	(	(	PUNCT
ejpam-6593	604	21	p	p	X
ejpam-6593	604	22	,	,	PUNCT
ejpam-6593	604	23	k	k	NOUN
ejpam-6593	604	24	,	,	PUNCT
ejpam-6593	604	25	x	x	X
ejpam-6593	604	26	,	,	PUNCT
ejpam-6593	604	27	y	y	PROPN
ejpam-6593	604	28	,	,	PUNCT
ejpam-6593	604	29	z	z	NOUN
ejpam-6593	604	30	)	)	PUNCT
ejpam-6593	604	31	19	19	NUM
ejpam-6593	604	32	15	15	NUM
ejpam-6593	604	33	27	27	NUM
ejpam-6593	605	1	+	+	CCONJ
ejpam-6593	605	2	(	(	PUNCT
ejpam-6593	605	3	2	2	NUM
ejpam-6593	605	4	+	+	NUM
ejpam-6593	605	5	5(19	5(19	NUM
ejpam-6593	605	6	)	)	PUNCT
ejpam-6593	605	7	)	)	PUNCT
ejpam-6593	606	1	=	=	SYM
ejpam-6593	606	2	152	152	NUM
ejpam-6593	606	3	(	(	PUNCT
ejpam-6593	606	4	2	2	NUM
ejpam-6593	606	5	,	,	PUNCT
ejpam-6593	606	6	19	19	NUM
ejpam-6593	606	7	,	,	PUNCT
ejpam-6593	606	8	7	7	NUM
ejpam-6593	606	9	,	,	PUNCT
ejpam-6593	606	10	1	1	NUM
ejpam-6593	606	11	,	,	PUNCT
ejpam-6593	606	12	15	15	NUM
ejpam-6593	606	13	)	)	PUNCT
ejpam-6593	606	14	2	2	NUM
ejpam-6593	606	15	219	219	NUM
ejpam-6593	606	16	35	35	NUM
ejpam-6593	606	17	27	27	NUM
ejpam-6593	606	18	+	+	CCONJ
ejpam-6593	606	19	(	(	PUNCT
ejpam-6593	606	20	2	2	NUM
ejpam-6593	606	21	+	+	SYM
ejpam-6593	606	22	5(219	5(219	NUM
ejpam-6593	606	23	)	)	PUNCT
ejpam-6593	606	24	)	)	PUNCT
ejpam-6593	607	1	=	=	SYM
ejpam-6593	607	2	352	352	NUM
ejpam-6593	607	3	(	(	PUNCT
ejpam-6593	607	4	2	2	NUM
ejpam-6593	607	5	,	,	PUNCT
ejpam-6593	607	6	219	219	NUM
ejpam-6593	607	7	,	,	PUNCT
ejpam-6593	607	8	7	7	NUM
ejpam-6593	607	9	,	,	PUNCT
ejpam-6593	607	10	1	1	NUM
ejpam-6593	607	11	,	,	PUNCT
ejpam-6593	607	12	35	35	NUM
ejpam-6593	607	13	)	)	PUNCT
ejpam-6593	607	14	4	4	NUM
ejpam-6593	607	15	579	579	NUM
ejpam-6593	607	16	55	55	NUM
ejpam-6593	607	17	27	27	NUM
ejpam-6593	607	18	+	+	CCONJ
ejpam-6593	607	19	(	(	PUNCT
ejpam-6593	607	20	2	2	NUM
ejpam-6593	607	21	+	+	NUM
ejpam-6593	607	22	5(579	5(579	NUM
ejpam-6593	607	23	)	)	PUNCT
ejpam-6593	607	24	)	)	PUNCT
ejpam-6593	608	1	=	=	SYM
ejpam-6593	608	2	552	552	NUM
ejpam-6593	608	3	(	(	PUNCT
ejpam-6593	608	4	2	2	NUM
ejpam-6593	608	5	,	,	PUNCT
ejpam-6593	608	6	579	579	NUM
ejpam-6593	608	7	,	,	PUNCT
ejpam-6593	608	8	7	7	NUM
ejpam-6593	608	9	,	,	PUNCT
ejpam-6593	608	10	1	1	NUM
ejpam-6593	608	11	,	,	PUNCT
ejpam-6593	608	12	55	55	NUM
ejpam-6593	608	13	)	)	PUNCT
ejpam-6593	608	14	11	11	NUM
ejpam-6593	608	15	3099	3099	NUM
ejpam-6593	608	16	125	125	NUM
ejpam-6593	608	17	27	27	NUM
ejpam-6593	608	18	+	+	CCONJ
ejpam-6593	608	19	(	(	PUNCT
ejpam-6593	608	20	2	2	NUM
ejpam-6593	608	21	+	+	SYM
ejpam-6593	608	22	5(3099	5(3099	NUM
ejpam-6593	608	23	)	)	PUNCT
ejpam-6593	608	24	)	)	PUNCT
ejpam-6593	609	1	=	=	SYM
ejpam-6593	609	2	1252	1252	NUM
ejpam-6593	609	3	(	(	PUNCT
ejpam-6593	609	4	2	2	NUM
ejpam-6593	609	5	,	,	PUNCT
ejpam-6593	609	6	3099	3099	NUM
ejpam-6593	609	7	,	,	PUNCT
ejpam-6593	609	8	7	7	NUM
ejpam-6593	609	9	,	,	PUNCT
ejpam-6593	609	10	1	1	NUM
ejpam-6593	609	11	,	,	PUNCT
ejpam-6593	609	12	125	125	NUM
ejpam-6593	609	13	)	)	PUNCT
ejpam-6593	609	14	12	12	NUM
ejpam-6593	609	15	3619	3619	NUM
ejpam-6593	609	16	135	135	NUM
ejpam-6593	609	17	27	27	NUM
ejpam-6593	609	18	+	+	CCONJ
ejpam-6593	609	19	(	(	PUNCT
ejpam-6593	609	20	2	2	NUM
ejpam-6593	609	21	+	+	NUM
ejpam-6593	609	22	5(3619	5(3619	NUM
ejpam-6593	609	23	)	)	PUNCT
ejpam-6593	609	24	)	)	PUNCT
ejpam-6593	610	1	=	=	SYM
ejpam-6593	610	2	1352	1352	NUM
ejpam-6593	610	3	(	(	PUNCT
ejpam-6593	610	4	2	2	NUM
ejpam-6593	610	5	,	,	PUNCT
ejpam-6593	610	6	3619	3619	NUM
ejpam-6593	610	7	,	,	PUNCT
ejpam-6593	610	8	7	7	NUM
ejpam-6593	610	9	,	,	PUNCT
ejpam-6593	610	10	1	1	NUM
ejpam-6593	610	11	,	,	PUNCT
ejpam-6593	610	12	135	135	NUM
ejpam-6593	610	13	)	)	PUNCT
ejpam-6593	610	14	table	table	NOUN
ejpam-6593	610	15	19	19	NUM
ejpam-6593	610	16	:	:	PUNCT
ejpam-6593	610	17	some	some	DET
ejpam-6593	610	18	solutions	solution	NOUN
ejpam-6593	610	19	of	of	ADP
ejpam-6593	610	20	(	(	PUNCT
ejpam-6593	610	21	5	5	NUM
ejpam-6593	610	22	)	)	PUNCT
ejpam-6593	610	23	with	with	ADP
ejpam-6593	610	24	x	x	X
ejpam-6593	610	25	=	=	SYM
ejpam-6593	610	26	7	7	NUM
ejpam-6593	610	27	,	,	PUNCT
ejpam-6593	610	28	y	y	NOUN
ejpam-6593	610	29	=	=	SYM
ejpam-6593	610	30	1	1	NUM
ejpam-6593	610	31	and	and	CCONJ
ejpam-6593	610	32	z	z	PROPN
ejpam-6593	610	33	≡	≡	PROPN
ejpam-6593	610	34	5	5	NUM
ejpam-6593	610	35	(	(	PUNCT
ejpam-6593	610	36	mod	mod	PROPN
ejpam-6593	610	37	10	10	NUM
ejpam-6593	610	38	)	)	PUNCT
ejpam-6593	610	39	remark	remark	NOUN
ejpam-6593	610	40	3	3	NUM
ejpam-6593	610	41	.	.	PROPN
ejpam-6593	610	42	from	from	ADP
ejpam-6593	610	43	theorem	theorem	ADJ
ejpam-6593	610	44	2	2	NUM
ejpam-6593	610	45	,	,	PUNCT
ejpam-6593	610	46	the	the	DET
ejpam-6593	610	47	equation	equation	NOUN
ejpam-6593	610	48	2x	2x	NUM
ejpam-6593	611	1	+	+	ADJ
ejpam-6593	611	2	(	(	PUNCT
ejpam-6593	611	3	2	2	NUM
ejpam-6593	611	4	+	+	NUM
ejpam-6593	611	5	5k	5k	NUM
ejpam-6593	611	6	)	)	PUNCT
ejpam-6593	611	7	=	=	SYM
ejpam-6593	611	8	z2	z2	PROPN
ejpam-6593	611	9	,	,	PUNCT
ejpam-6593	611	10	where	where	SCONJ
ejpam-6593	611	11	2	2	NUM
ejpam-6593	611	12	+	+	NUM
ejpam-6593	611	13	5k	5k	NUM
ejpam-6593	611	14	is	be	AUX
ejpam-6593	611	15	prime	prime	ADJ
ejpam-6593	611	16	and	and	CCONJ
ejpam-6593	611	17	k	k	PROPN
ejpam-6593	611	18	is	be	AUX
ejpam-6593	611	19	odd	odd	ADJ
ejpam-6593	611	20	,	,	PUNCT
ejpam-6593	611	21	has	have	VERB
ejpam-6593	611	22	no	no	DET
ejpam-6593	611	23	solution	solution	NOUN
ejpam-6593	611	24	when	when	SCONJ
ejpam-6593	611	25	x	x	X
ejpam-6593	611	26	≡	≡	PROPN
ejpam-6593	611	27	0	0	PUNCT
ejpam-6593	611	28	(	(	PUNCT
ejpam-6593	611	29	mod	mod	PROPN
ejpam-6593	611	30	4	4	NUM
ejpam-6593	611	31	)	)	PUNCT
ejpam-6593	611	32	.	.	PUNCT
ejpam-6593	612	1	theorem	theorem	NOUN
ejpam-6593	612	2	5	5	NUM
ejpam-6593	612	3	.	.	PUNCT
ejpam-6593	613	1	let	let	VERB
ejpam-6593	613	2	2	2	NUM
ejpam-6593	613	3	+	+	NOUN
ejpam-6593	613	4	5k	5k	NUM
ejpam-6593	613	5	be	be	AUX
ejpam-6593	613	6	prime	prime	ADJ
ejpam-6593	613	7	,	,	PUNCT
ejpam-6593	613	8	and	and	CCONJ
ejpam-6593	613	9	x	x	X
ejpam-6593	613	10	=	=	SYM
ejpam-6593	613	11	2	2	NUM
ejpam-6593	613	12	+	+	NOUN
ejpam-6593	613	13	4n	4n	NOUN
ejpam-6593	613	14	with	with	ADP
ejpam-6593	613	15	odd	odd	ADJ
ejpam-6593	613	16	number	number	NOUN
ejpam-6593	613	17	n.	n.	NOUN
ejpam-6593	613	18	then	then	ADV
ejpam-6593	613	19	the	the	DET
ejpam-6593	613	20	exponential	exponential	ADJ
ejpam-6593	613	21	diophantine	diophantine	NOUN
ejpam-6593	613	22	equation	equation	NOUN
ejpam-6593	613	23	(	(	PUNCT
ejpam-6593	613	24	5	5	NUM
ejpam-6593	613	25	)	)	PUNCT
ejpam-6593	613	26	,	,	PUNCT
ejpam-6593	613	27	has	have	VERB
ejpam-6593	613	28	solutions	solution	NOUN
ejpam-6593	613	29	where	where	SCONJ
ejpam-6593	613	30	k	k	NOUN
ejpam-6593	613	31	=	=	PUNCT
ejpam-6593	613	32	22	22	NUM
ejpam-6593	613	33	+	+	NUM
ejpam-6593	613	34	2n	2n	NUM
ejpam-6593	613	35	−	−	ADP
ejpam-6593	613	36	1	1	NUM
ejpam-6593	613	37	5	5	NUM
ejpam-6593	613	38	and	and	CCONJ
ejpam-6593	613	39	z	z	NOUN
ejpam-6593	613	40	=	=	SYM
ejpam-6593	613	41	5k	5k	NUM
ejpam-6593	614	1	+	+	CCONJ
ejpam-6593	614	2	3	3	NUM
ejpam-6593	614	3	2	2	NUM
ejpam-6593	614	4	.	.	PUNCT
ejpam-6593	615	1	proof	proof	NOUN
ejpam-6593	615	2	.	.	PUNCT
ejpam-6593	616	1	let	let	VERB
ejpam-6593	616	2	x	x	SYM
ejpam-6593	616	3	=	=	SYM
ejpam-6593	616	4	2	2	NUM
ejpam-6593	616	5	+	+	CCONJ
ejpam-6593	616	6	4n	4n	NOUN
ejpam-6593	616	7	,	,	PUNCT
ejpam-6593	616	8	n	n	PRON
ejpam-6593	616	9	be	be	AUX
ejpam-6593	616	10	odd	odd	ADJ
ejpam-6593	616	11	,	,	PUNCT
ejpam-6593	616	12	and	and	CCONJ
ejpam-6593	616	13	q	q	AUX
ejpam-6593	616	14	=	=	SYM
ejpam-6593	616	15	2	2	NUM
ejpam-6593	616	16	+	+	NUM
ejpam-6593	616	17	5k	5k	NUM
ejpam-6593	616	18	be	be	AUX
ejpam-6593	616	19	prime	prime	ADJ
ejpam-6593	616	20	.	.	PUNCT
ejpam-6593	617	1	then	then	ADV
ejpam-6593	617	2	,	,	PUNCT
ejpam-6593	617	3	we	we	PRON
ejpam-6593	617	4	can	can	AUX
ejpam-6593	617	5	express	express	VERB
ejpam-6593	617	6	2x	2x	NUM
ejpam-6593	617	7	+	+	CCONJ
ejpam-6593	617	8	(	(	PUNCT
ejpam-6593	617	9	2	2	NUM
ejpam-6593	617	10	+	+	NUM
ejpam-6593	617	11	5k	5k	NUM
ejpam-6593	617	12	)	)	PUNCT
ejpam-6593	617	13	=	=	SYM
ejpam-6593	617	14	z2	z2	NOUN
ejpam-6593	617	15	as	as	ADP
ejpam-6593	617	16	22	22	NUM
ejpam-6593	617	17	+	+	NOUN
ejpam-6593	617	18	4n	4n	NOUN
ejpam-6593	617	19	+	+	CCONJ
ejpam-6593	617	20	q	q	NOUN
ejpam-6593	617	21	=	=	SYM
ejpam-6593	617	22	z2	z2	PROPN
ejpam-6593	617	23	.	.	PUNCT
ejpam-6593	618	1	finding	find	VERB
ejpam-6593	618	2	for	for	ADP
ejpam-6593	618	3	q	q	NOUN
ejpam-6593	618	4	we	we	PRON
ejpam-6593	618	5	have	have	VERB
ejpam-6593	618	6	,	,	PUNCT
ejpam-6593	618	7	q	q	NOUN
ejpam-6593	618	8	=	=	SYM
ejpam-6593	618	9	z2	z2	PROPN
ejpam-6593	618	10	−	−	PROPN
ejpam-6593	618	11	22	22	NUM
ejpam-6593	619	1	+	+	NOUN
ejpam-6593	619	2	4n	4n	X
ejpam-6593	619	3	=	=	SYM
ejpam-6593	619	4	(	(	PUNCT
ejpam-6593	619	5	z	z	NOUN
ejpam-6593	619	6	−	−	PROPN
ejpam-6593	619	7	21	21	NUM
ejpam-6593	619	8	+	+	NOUN
ejpam-6593	619	9	2n)(z	2n)(z	NUM
ejpam-6593	619	10	+	+	NUM
ejpam-6593	619	11	21	21	NUM
ejpam-6593	619	12	+	+	NUM
ejpam-6593	619	13	2n	2n	NUM
ejpam-6593	619	14	)	)	PUNCT
ejpam-6593	619	15	.	.	PUNCT
ejpam-6593	620	1	since	since	SCONJ
ejpam-6593	620	2	q	q	PROPN
ejpam-6593	620	3	is	be	AUX
ejpam-6593	620	4	prime	prime	ADJ
ejpam-6593	620	5	,	,	PUNCT
ejpam-6593	620	6	we	we	PRON
ejpam-6593	620	7	know	know	VERB
ejpam-6593	620	8	that	that	DET
ejpam-6593	620	9	gcd	gcd	VERB
ejpam-6593	620	10	(	(	PUNCT
ejpam-6593	620	11	z	z	NOUN
ejpam-6593	620	12	−	−	PROPN
ejpam-6593	620	13	21	21	NUM
ejpam-6593	620	14	+	+	NOUN
ejpam-6593	620	15	2n	2n	NUM
ejpam-6593	620	16	,	,	PUNCT
ejpam-6593	620	17	z	z	NOUN
ejpam-6593	620	18	+	+	NOUN
ejpam-6593	620	19	21	21	NUM
ejpam-6593	620	20	+	+	NUM
ejpam-6593	620	21	2n	2n	NUM
ejpam-6593	620	22	)	)	PUNCT
ejpam-6593	621	1	=	=	SYM
ejpam-6593	621	2	1	1	X
ejpam-6593	621	3	.	.	PUNCT
ejpam-6593	622	1	it	it	PRON
ejpam-6593	622	2	follows	follow	VERB
ejpam-6593	622	3	that	that	PRON
ejpam-6593	622	4	z	z	NOUN
ejpam-6593	622	5	−	−	NUM
ejpam-6593	622	6	21	21	NUM
ejpam-6593	622	7	+	+	NUM
ejpam-6593	622	8	2n	2n	NUM
ejpam-6593	622	9	=	=	SYM
ejpam-6593	622	10	1	1	NUM
ejpam-6593	622	11	and	and	CCONJ
ejpam-6593	622	12	z	z	NOUN
ejpam-6593	623	1	+	+	NUM
ejpam-6593	623	2	21	21	NUM
ejpam-6593	623	3	+	+	NUM
ejpam-6593	623	4	2n	2n	NUM
ejpam-6593	623	5	=	=	SYM
ejpam-6593	623	6	q.	q.	NOUN
ejpam-6593	623	7	having	have	VERB
ejpam-6593	623	8	this	this	DET
ejpam-6593	623	9	system	system	NOUN
ejpam-6593	623	10	of	of	ADP
ejpam-6593	623	11	equations	equation	NOUN
ejpam-6593	623	12	,	,	PUNCT
ejpam-6593	623	13	we	we	PRON
ejpam-6593	623	14	solve	solve	VERB
ejpam-6593	623	15	for	for	ADP
ejpam-6593	623	16	z.	z.	PROPN
ejpam-6593	623	17	thus	thus	ADV
ejpam-6593	623	18	,	,	PUNCT
ejpam-6593	623	19	we	we	PRON
ejpam-6593	623	20	get	get	VERB
ejpam-6593	623	21	2z	2z	NOUN
ejpam-6593	623	22	=	=	PUNCT
ejpam-6593	623	23	q	q	X
ejpam-6593	624	1	+	+	NUM
ejpam-6593	624	2	1	1	NUM
ejpam-6593	624	3	=	=	NOUN
ejpam-6593	624	4	⇒	⇒	NOUN
ejpam-6593	624	5	z	z	NOUN
ejpam-6593	624	6	=	=	PUNCT
ejpam-6593	624	7	q	q	NOUN
ejpam-6593	625	1	+	+	NUM
ejpam-6593	625	2	1	1	NUM
ejpam-6593	625	3	2	2	NUM
ejpam-6593	625	4	=	=	NOUN
ejpam-6593	625	5	⇒	⇒	NOUN
ejpam-6593	625	6	z	z	NOUN
ejpam-6593	626	1	=	=	SYM
ejpam-6593	626	2	5k	5k	NUM
ejpam-6593	626	3	+	+	CCONJ
ejpam-6593	626	4	3	3	NUM
ejpam-6593	626	5	2	2	NUM
ejpam-6593	626	6	.	.	PUNCT
ejpam-6593	627	1	substituting	substitute	VERB
ejpam-6593	627	2	to	to	PART
ejpam-6593	627	3	find	find	VERB
ejpam-6593	627	4	k	k	PROPN
ejpam-6593	627	5	,	,	PUNCT
ejpam-6593	627	6	we	we	PRON
ejpam-6593	627	7	obtain	obtain	VERB
ejpam-6593	627	8	q	q	NOUN
ejpam-6593	627	9	=	=	PUNCT
ejpam-6593	627	10	z	z	NOUN
ejpam-6593	628	1	+	+	NOUN
ejpam-6593	628	2	21	21	NUM
ejpam-6593	628	3	+	+	NUM
ejpam-6593	628	4	2n	2n	NUM
ejpam-6593	628	5	2	2	NUM
ejpam-6593	628	6	+	+	NUM
ejpam-6593	628	7	5k	5k	NUM
ejpam-6593	628	8	=	=	SYM
ejpam-6593	628	9	5k	5k	NUM
ejpam-6593	628	10	+	+	CCONJ
ejpam-6593	628	11	3	3	NUM
ejpam-6593	628	12	2	2	NUM
ejpam-6593	628	13	+	+	CCONJ
ejpam-6593	628	14	21	21	NUM
ejpam-6593	628	15	+	+	NUM
ejpam-6593	628	16	2n	2n	NUM
ejpam-6593	628	17	2(2	2(2	NUM
ejpam-6593	628	18	+	+	NUM
ejpam-6593	628	19	5k	5k	NUM
ejpam-6593	628	20	)	)	PUNCT
ejpam-6593	629	1	=	=	SYM
ejpam-6593	629	2	5k	5k	NUM
ejpam-6593	630	1	+	+	CCONJ
ejpam-6593	631	1	3	3	NUM
ejpam-6593	631	2	+	+	SYM
ejpam-6593	631	3	2	2	NUM
ejpam-6593	631	4	·	·	SYM
ejpam-6593	631	5	21	21	NUM
ejpam-6593	632	1	+	+	NUM
ejpam-6593	632	2	2n	2n	NUM
ejpam-6593	632	3	4	4	NUM
ejpam-6593	632	4	+	+	NOUN
ejpam-6593	632	5	10k	10k	NOUN
ejpam-6593	632	6	=	=	SYM
ejpam-6593	632	7	5k	5k	NUM
ejpam-6593	632	8	+	+	CCONJ
ejpam-6593	632	9	3	3	NUM
ejpam-6593	632	10	+	+	SYM
ejpam-6593	632	11	22	22	NUM
ejpam-6593	632	12	+	+	NUM
ejpam-6593	632	13	2n	2n	ADJ
ejpam-6593	632	14	10k	10k	NOUN
ejpam-6593	632	15	−	−	PROPN
ejpam-6593	632	16	5k	5k	NUM
ejpam-6593	632	17	=	=	SYM
ejpam-6593	632	18	22	22	NUM
ejpam-6593	632	19	+	+	NUM
ejpam-6593	632	20	2n	2n	NUM
ejpam-6593	632	21	−	−	NOUN
ejpam-6593	632	22	1	1	NUM
ejpam-6593	632	23	5k	5k	NUM
ejpam-6593	632	24	=	=	SYM
ejpam-6593	632	25	22	22	NUM
ejpam-6593	632	26	+	+	NUM
ejpam-6593	632	27	2n	2n	NUM
ejpam-6593	632	28	−	−	ADP
ejpam-6593	632	29	1	1	NUM
ejpam-6593	632	30	k	k	NOUN
ejpam-6593	632	31	=	=	PUNCT
ejpam-6593	633	1	22	22	NUM
ejpam-6593	633	2	+	+	NUM
ejpam-6593	633	3	2n	2n	NUM
ejpam-6593	633	4	−	−	NOUN
ejpam-6593	633	5	1	1	NUM
ejpam-6593	633	6	5	5	NUM
ejpam-6593	633	7	.	.	PUNCT
ejpam-6593	634	1	m.	m.	PROPN
ejpam-6593	634	2	c.	c.	PROPN
ejpam-6593	634	3	avenilla	avenilla	PROPN
ejpam-6593	634	4	,	,	PUNCT
ejpam-6593	634	5	j.	j.	PROPN
ejpam-6593	634	6	b.	b.	PROPN
ejpam-6593	634	7	bacani	bacani	PROPN
ejpam-6593	634	8	/	/	SYM
ejpam-6593	634	9	eur	eur	PROPN
ejpam-6593	634	10	.	.	PUNCT
ejpam-6593	635	1	j.	j.	PROPN
ejpam-6593	635	2	pure	pure	PROPN
ejpam-6593	635	3	appl	appl	PROPN
ejpam-6593	635	4	.	.	PROPN
ejpam-6593	635	5	math	math	PROPN
ejpam-6593	635	6	,	,	PUNCT
ejpam-6593	635	7	18	18	NUM
ejpam-6593	635	8	(	(	PUNCT
ejpam-6593	635	9	3	3	NUM
ejpam-6593	635	10	)	)	PUNCT
ejpam-6593	635	11	(	(	PUNCT
ejpam-6593	635	12	2025	2025	NUM
ejpam-6593	635	13	)	)	PUNCT
ejpam-6593	635	14	,	,	PUNCT
ejpam-6593	635	15	6593	6593	NUM
ejpam-6593	635	16	19	19	NUM
ejpam-6593	635	17	of	of	ADP
ejpam-6593	635	18	24	24	NUM
ejpam-6593	635	19	we	we	PRON
ejpam-6593	635	20	are	be	AUX
ejpam-6593	635	21	sure	sure	ADJ
ejpam-6593	635	22	that	that	SCONJ
ejpam-6593	635	23	k	k	PROPN
ejpam-6593	635	24	is	be	AUX
ejpam-6593	635	25	an	an	DET
ejpam-6593	635	26	odd	odd	ADJ
ejpam-6593	635	27	integer	integer	NOUN
ejpam-6593	635	28	because	because	SCONJ
ejpam-6593	635	29	n	n	ADV
ejpam-6593	635	30	is	be	AUX
ejpam-6593	635	31	odd	odd	ADJ
ejpam-6593	635	32	.	.	PUNCT
ejpam-6593	636	1	thus	thus	ADV
ejpam-6593	636	2	,	,	PUNCT
ejpam-6593	636	3	2x	2x	NUM
ejpam-6593	636	4	+	+	CCONJ
ejpam-6593	636	5	(	(	PUNCT
ejpam-6593	636	6	2	2	NUM
ejpam-6593	636	7	+	+	NUM
ejpam-6593	636	8	5k	5k	NUM
ejpam-6593	636	9	)	)	PUNCT
ejpam-6593	636	10	=	=	SYM
ejpam-6593	636	11	z2	z2	PROPN
ejpam-6593	636	12	has	have	VERB
ejpam-6593	636	13	a	a	DET
ejpam-6593	636	14	solution	solution	NOUN
ejpam-6593	636	15	if	if	SCONJ
ejpam-6593	636	16	y	y	PROPN
ejpam-6593	636	17	=	=	SYM
ejpam-6593	636	18	1	1	NUM
ejpam-6593	636	19	,	,	PUNCT
ejpam-6593	636	20	x	x	SYM
ejpam-6593	636	21	=	=	SYM
ejpam-6593	636	22	2	2	NUM
ejpam-6593	636	23	+	+	CCONJ
ejpam-6593	636	24	4n	4n	NOUN
ejpam-6593	636	25	,	,	PUNCT
ejpam-6593	636	26	k	k	PROPN
ejpam-6593	636	27	=	=	PUNCT
ejpam-6593	636	28	22	22	NUM
ejpam-6593	636	29	+	+	NUM
ejpam-6593	636	30	2n	2n	NUM
ejpam-6593	636	31	−	−	ADP
ejpam-6593	636	32	1	1	NUM
ejpam-6593	636	33	5	5	NUM
ejpam-6593	636	34	,	,	PUNCT
ejpam-6593	636	35	and	and	CCONJ
ejpam-6593	636	36	z	z	NOUN
ejpam-6593	636	37	=	=	SYM
ejpam-6593	636	38	5k	5k	NUM
ejpam-6593	636	39	+	+	CCONJ
ejpam-6593	636	40	3	3	NUM
ejpam-6593	636	41	2	2	NUM
ejpam-6593	636	42	,	,	PUNCT
ejpam-6593	636	43	where	where	SCONJ
ejpam-6593	636	44	n	n	PRON
ejpam-6593	636	45	is	be	AUX
ejpam-6593	636	46	an	an	DET
ejpam-6593	636	47	odd	odd	ADJ
ejpam-6593	636	48	number	number	NOUN
ejpam-6593	636	49	.	.	PUNCT
ejpam-6593	637	1	using	use	VERB
ejpam-6593	637	2	theorem	theorem	NOUN
ejpam-6593	637	3	5	5	NUM
ejpam-6593	637	4	,	,	PUNCT
ejpam-6593	637	5	one	one	PRON
ejpam-6593	637	6	can	can	AUX
ejpam-6593	637	7	verify	verify	VERB
ejpam-6593	637	8	that	that	SCONJ
ejpam-6593	637	9	(	(	PUNCT
ejpam-6593	637	10	p	p	X
ejpam-6593	637	11	,	,	PUNCT
ejpam-6593	637	12	k	k	NOUN
ejpam-6593	637	13	,	,	PUNCT
ejpam-6593	637	14	x	x	X
ejpam-6593	637	15	,	,	PUNCT
ejpam-6593	637	16	y	y	PROPN
ejpam-6593	637	17	,	,	PUNCT
ejpam-6593	637	18	z	z	NOUN
ejpam-6593	637	19	)	)	PUNCT
ejpam-6593	637	20	=	=	SYM
ejpam-6593	637	21	(	(	PUNCT
ejpam-6593	637	22	2	2	NUM
ejpam-6593	637	23	,	,	PUNCT
ejpam-6593	637	24	3	3	NUM
ejpam-6593	637	25	,	,	PUNCT
ejpam-6593	637	26	6	6	NUM
ejpam-6593	637	27	,	,	PUNCT
ejpam-6593	637	28	1	1	NUM
ejpam-6593	637	29	,	,	PUNCT
ejpam-6593	637	30	9	9	NUM
ejpam-6593	637	31	)	)	PUNCT
ejpam-6593	637	32	,	,	PUNCT
ejpam-6593	637	33	(	(	PUNCT
ejpam-6593	637	34	2	2	NUM
ejpam-6593	637	35	,	,	PUNCT
ejpam-6593	637	36	51	51	NUM
ejpam-6593	637	37	,	,	PUNCT
ejpam-6593	637	38	14	14	NUM
ejpam-6593	637	39	,	,	PUNCT
ejpam-6593	637	40	1	1	NUM
ejpam-6593	637	41	,	,	PUNCT
ejpam-6593	637	42	129	129	NUM
ejpam-6593	637	43	)	)	PUNCT
ejpam-6593	637	44	,	,	PUNCT
ejpam-6593	637	45	and	and	CCONJ
ejpam-6593	637	46	(	(	PUNCT
ejpam-6593	637	47	2	2	NUM
ejpam-6593	637	48	,	,	PUNCT
ejpam-6593	637	49	13107	13107	NUM
ejpam-6593	637	50	,	,	PUNCT
ejpam-6593	637	51	30	30	NUM
ejpam-6593	637	52	,	,	PUNCT
ejpam-6593	637	53	1	1	NUM
ejpam-6593	637	54	,	,	PUNCT
ejpam-6593	637	55	32769	32769	NUM
ejpam-6593	637	56	)	)	PUNCT
ejpam-6593	637	57	are	be	AUX
ejpam-6593	637	58	indeed	indeed	ADV
ejpam-6593	637	59	solutions	solution	NOUN
ejpam-6593	637	60	of	of	ADP
ejpam-6593	637	61	(	(	PUNCT
ejpam-6593	637	62	3	3	NUM
ejpam-6593	637	63	)	)	PUNCT
ejpam-6593	637	64	.	.	PUNCT
ejpam-6593	638	1	theorem	theorem	ADJ
ejpam-6593	638	2	6	6	NUM
ejpam-6593	638	3	.	.	PUNCT
ejpam-6593	639	1	consider	consider	VERB
ejpam-6593	639	2	the	the	DET
ejpam-6593	639	3	exponential	exponential	ADJ
ejpam-6593	639	4	diophantine	diophantine	NOUN
ejpam-6593	639	5	equation	equation	NOUN
ejpam-6593	639	6	(	(	PUNCT
ejpam-6593	639	7	3	3	NUM
ejpam-6593	639	8	)	)	PUNCT
ejpam-6593	639	9	,	,	PUNCT
ejpam-6593	639	10	where	where	SCONJ
ejpam-6593	639	11	2	2	NUM
ejpam-6593	639	12	+	+	NOUN
ejpam-6593	639	13	5k	5k	NUM
ejpam-6593	639	14	is	be	AUX
ejpam-6593	639	15	prime	prime	ADJ
ejpam-6593	639	16	.	.	PUNCT
ejpam-6593	640	1	if	if	SCONJ
ejpam-6593	640	2	y	y	PROPN
ejpam-6593	640	3	=	=	SYM
ejpam-6593	640	4	0	0	PROPN
ejpam-6593	640	5	,	,	PUNCT
ejpam-6593	640	6	the	the	DET
ejpam-6593	640	7	equation	equation	NOUN
ejpam-6593	640	8	has	have	VERB
ejpam-6593	640	9	only	only	ADV
ejpam-6593	640	10	solution	solution	NOUN
ejpam-6593	640	11	when	when	SCONJ
ejpam-6593	640	12	x	x	PROPN
ejpam-6593	640	13	=	=	SYM
ejpam-6593	640	14	3	3	X
ejpam-6593	640	15	.	.	PUNCT
ejpam-6593	640	16	consequently	consequently	ADV
ejpam-6593	640	17	,	,	PUNCT
ejpam-6593	640	18	(	(	PUNCT
ejpam-6593	640	19	p	p	X
ejpam-6593	640	20	,	,	PUNCT
ejpam-6593	640	21	k	k	NOUN
ejpam-6593	640	22	,	,	PUNCT
ejpam-6593	640	23	x	x	X
ejpam-6593	640	24	,	,	PUNCT
ejpam-6593	640	25	y	y	PROPN
ejpam-6593	640	26	,	,	PUNCT
ejpam-6593	640	27	z	z	NOUN
ejpam-6593	640	28	)	)	PUNCT
ejpam-6593	640	29	=	=	SYM
ejpam-6593	640	30	(	(	PUNCT
ejpam-6593	640	31	2	2	NUM
ejpam-6593	640	32	,	,	PUNCT
ejpam-6593	640	33	k	k	NOUN
ejpam-6593	640	34	,	,	PUNCT
ejpam-6593	640	35	3	3	NUM
ejpam-6593	640	36	,	,	PUNCT
ejpam-6593	640	37	0	0	NUM
ejpam-6593	640	38	,	,	PUNCT
ejpam-6593	640	39	3	3	NUM
ejpam-6593	640	40	)	)	PUNCT
ejpam-6593	640	41	is	be	AUX
ejpam-6593	640	42	a	a	DET
ejpam-6593	640	43	solution	solution	NOUN
ejpam-6593	640	44	for	for	ADP
ejpam-6593	640	45	some	some	DET
ejpam-6593	640	46	odd	odd	ADJ
ejpam-6593	640	47	k	k	PROPN
ejpam-6593	640	48	∈	∈	PROPN
ejpam-6593	640	49	n.	n.	NOUN
ejpam-6593	640	50	on	on	ADP
ejpam-6593	640	51	the	the	DET
ejpam-6593	640	52	other	other	ADJ
ejpam-6593	640	53	hand	hand	NOUN
ejpam-6593	640	54	,	,	PUNCT
ejpam-6593	640	55	the	the	DET
ejpam-6593	640	56	equation	equation	NOUN
ejpam-6593	640	57	has	have	VERB
ejpam-6593	640	58	no	no	DET
ejpam-6593	640	59	solution	solution	NOUN
ejpam-6593	640	60	when	when	SCONJ
ejpam-6593	640	61	x	x	PROPN
ejpam-6593	640	62	=	=	NOUN
ejpam-6593	640	63	0	0	NUM
ejpam-6593	640	64	.	.	PUNCT
ejpam-6593	641	1	the	the	DET
ejpam-6593	641	2	proof	proof	NOUN
ejpam-6593	641	3	of	of	ADP
ejpam-6593	641	4	theorem	theorem	NOUN
ejpam-6593	641	5	6	6	NUM
ejpam-6593	641	6	follows	follow	VERB
ejpam-6593	641	7	from	from	ADP
ejpam-6593	641	8	theorem	theorem	ADJ
ejpam-6593	641	9	3	3	NUM
ejpam-6593	641	10	.	.	PUNCT
ejpam-6593	642	1	the	the	DET
ejpam-6593	642	2	next	next	ADJ
ejpam-6593	642	3	conjecture	conjecture	NOUN
ejpam-6593	642	4	also	also	ADV
ejpam-6593	642	5	follows	follow	VERB
ejpam-6593	642	6	from	from	ADP
ejpam-6593	642	7	conjecture	conjecture	NOUN
ejpam-6593	642	8	1	1	NUM
ejpam-6593	642	9	.	.	PUNCT
ejpam-6593	642	10	conjecture	conjecture	NOUN
ejpam-6593	642	11	2	2	NUM
ejpam-6593	642	12	.	.	PUNCT
ejpam-6593	643	1	let	let	VERB
ejpam-6593	643	2	2	2	NUM
ejpam-6593	643	3	+	+	NUM
ejpam-6593	643	4	5k	5k	NUM
ejpam-6593	643	5	be	be	AUX
ejpam-6593	643	6	prime	prime	ADJ
ejpam-6593	643	7	,	,	PUNCT
ejpam-6593	643	8	k	k	PROPN
ejpam-6593	643	9	≤	≤	PROPN
ejpam-6593	643	10	5000	5000	NUM
ejpam-6593	643	11	,	,	PUNCT
ejpam-6593	643	12	and	and	CCONJ
ejpam-6593	643	13	x	x	SYM
ejpam-6593	643	14	≤	≤	NOUN
ejpam-6593	643	15	50	50	NUM
ejpam-6593	643	16	.	.	PUNCT
ejpam-6593	644	1	if	if	SCONJ
ejpam-6593	644	2	y	y	PROPN
ejpam-6593	644	3	=	=	SYM
ejpam-6593	644	4	2	2	NUM
ejpam-6593	644	5	,	,	PUNCT
ejpam-6593	644	6	then	then	ADV
ejpam-6593	644	7	equation	equation	NOUN
ejpam-6593	644	8	2x+(2	2x+(2	NOUN
ejpam-6593	644	9	+	+	NOUN
ejpam-6593	644	10	5k)y	5k)y	NOUN
ejpam-6593	644	11	=	=	SYM
ejpam-6593	644	12	z2	z2	PROPN
ejpam-6593	644	13	has	have	VERB
ejpam-6593	644	14	2	2	NUM
ejpam-6593	644	15	solutions	solution	NOUN
ejpam-6593	644	16	,	,	PUNCT
ejpam-6593	644	17	namely	namely	ADV
ejpam-6593	644	18	,	,	PUNCT
ejpam-6593	644	19	(	(	PUNCT
ejpam-6593	644	20	p	p	X
ejpam-6593	644	21	,	,	PUNCT
ejpam-6593	644	22	k	k	NOUN
ejpam-6593	644	23	,	,	PUNCT
ejpam-6593	644	24	x	x	X
ejpam-6593	644	25	,	,	PUNCT
ejpam-6593	644	26	y	y	PROPN
ejpam-6593	644	27	,	,	PUNCT
ejpam-6593	644	28	z	z	NOUN
ejpam-6593	644	29	)	)	PUNCT
ejpam-6593	644	30	=	=	SYM
ejpam-6593	644	31	(	(	PUNCT
ejpam-6593	644	32	2	2	NUM
ejpam-6593	644	33	,	,	PUNCT
ejpam-6593	644	34	1	1	NUM
ejpam-6593	644	35	,	,	PUNCT
ejpam-6593	644	36	5	5	NUM
ejpam-6593	644	37	,	,	PUNCT
ejpam-6593	644	38	2	2	NUM
ejpam-6593	644	39	,	,	PUNCT
ejpam-6593	644	40	9	9	NUM
ejpam-6593	644	41	)	)	PUNCT
ejpam-6593	644	42	and	and	CCONJ
ejpam-6593	644	43	(	(	PUNCT
ejpam-6593	644	44	2	2	NUM
ejpam-6593	644	45	,	,	PUNCT
ejpam-6593	644	46	25	25	NUM
ejpam-6593	644	47	,	,	PUNCT
ejpam-6593	644	48	9	9	NUM
ejpam-6593	644	49	,	,	PUNCT
ejpam-6593	644	50	2	2	NUM
ejpam-6593	644	51	,	,	PUNCT
ejpam-6593	644	52	129	129	NUM
ejpam-6593	644	53	)	)	PUNCT
ejpam-6593	644	54	.	.	PUNCT
ejpam-6593	645	1	if	if	SCONJ
ejpam-6593	645	2	y	y	PROPN
ejpam-6593	645	3	=	=	SYM
ejpam-6593	645	4	3	3	NUM
ejpam-6593	645	5	,	,	PUNCT
ejpam-6593	645	6	then	then	ADV
ejpam-6593	645	7	the	the	DET
ejpam-6593	645	8	equation	equation	NOUN
ejpam-6593	645	9	has	have	VERB
ejpam-6593	645	10	only	only	ADV
ejpam-6593	645	11	the	the	DET
ejpam-6593	645	12	solution	solution	NOUN
ejpam-6593	645	13	(	(	PUNCT
ejpam-6593	645	14	p	p	X
ejpam-6593	645	15	,	,	PUNCT
ejpam-6593	645	16	k	k	NOUN
ejpam-6593	645	17	,	,	PUNCT
ejpam-6593	645	18	x	x	X
ejpam-6593	645	19	,	,	PUNCT
ejpam-6593	645	20	y	y	PROPN
ejpam-6593	645	21	,	,	PUNCT
ejpam-6593	645	22	z	z	NOUN
ejpam-6593	645	23	)	)	PUNCT
ejpam-6593	645	24	=	=	SYM
ejpam-6593	645	25	(	(	PUNCT
ejpam-6593	645	26	2	2	NUM
ejpam-6593	645	27	,	,	PUNCT
ejpam-6593	645	28	3	3	NUM
ejpam-6593	645	29	,	,	PUNCT
ejpam-6593	645	30	7	7	NUM
ejpam-6593	645	31	,	,	PUNCT
ejpam-6593	645	32	3	3	NUM
ejpam-6593	645	33	,	,	PUNCT
ejpam-6593	645	34	71	71	NUM
ejpam-6593	645	35	)	)	PUNCT
ejpam-6593	645	36	.	.	PUNCT
ejpam-6593	646	1	2.2.2	2.2.2	X
ejpam-6593	646	2	.	.	X
ejpam-6593	646	3	sub	sub	ADJ
ejpam-6593	646	4	-	-	NOUN
ejpam-6593	646	5	case	case	ADJ
ejpam-6593	646	6	ii	ii	NOUN
ejpam-6593	646	7	:	:	PUNCT
ejpam-6593	646	8	k	k	X
ejpam-6593	646	9	is	be	AUX
ejpam-6593	646	10	even	even	ADV
ejpam-6593	646	11	.	.	PUNCT
ejpam-6593	647	1	this	this	DET
ejpam-6593	647	2	sub	sub	NOUN
ejpam-6593	647	3	-	-	NOUN
ejpam-6593	647	4	case	case	NOUN
ejpam-6593	647	5	will	will	AUX
ejpam-6593	647	6	discuss	discuss	VERB
ejpam-6593	647	7	the	the	DET
ejpam-6593	647	8	solutions	solution	NOUN
ejpam-6593	647	9	of	of	ADP
ejpam-6593	647	10	(	(	PUNCT
ejpam-6593	647	11	3	3	NUM
ejpam-6593	647	12	)	)	PUNCT
ejpam-6593	647	13	when	when	SCONJ
ejpam-6593	647	14	k	k	PROPN
ejpam-6593	647	15	is	be	AUX
ejpam-6593	647	16	even	even	ADV
ejpam-6593	647	17	,	,	PUNCT
ejpam-6593	647	18	that	that	ADV
ejpam-6593	647	19	is	is	ADV
ejpam-6593	647	20	,	,	PUNCT
ejpam-6593	647	21	k	k	PROPN
ejpam-6593	647	22	≡	≡	PROPN
ejpam-6593	647	23	0	0	PUNCT
ejpam-6593	647	24	(	(	PUNCT
ejpam-6593	647	25	mod	mod	PROPN
ejpam-6593	647	26	4	4	NUM
ejpam-6593	647	27	)	)	PUNCT
ejpam-6593	647	28	or	or	CCONJ
ejpam-6593	647	29	k	k	PROPN
ejpam-6593	647	30	≡	≡	PROPN
ejpam-6593	647	31	2	2	NUM
ejpam-6593	647	32	(	(	PUNCT
ejpam-6593	647	33	mod	mod	NOUN
ejpam-6593	647	34	4	4	NUM
ejpam-6593	647	35	)	)	PUNCT
ejpam-6593	647	36	,	,	PUNCT
ejpam-6593	647	37	and	and	CCONJ
ejpam-6593	647	38	p	p	NOUN
ejpam-6593	647	39	and	and	CCONJ
ejpam-6593	647	40	p+	p+	PROPN
ejpam-6593	647	41	5k	5k	NUM
ejpam-6593	647	42	are	be	AUX
ejpam-6593	647	43	prime	prime	ADJ
ejpam-6593	647	44	pairs	pair	NOUN
ejpam-6593	647	45	.	.	PUNCT
ejpam-6593	648	1	we	we	PRON
ejpam-6593	648	2	note	note	VERB
ejpam-6593	648	3	that	that	SCONJ
ejpam-6593	648	4	since	since	SCONJ
ejpam-6593	648	5	k	k	PROPN
ejpam-6593	648	6	is	be	AUX
ejpam-6593	648	7	even	even	ADV
ejpam-6593	648	8	,	,	PUNCT
ejpam-6593	648	9	then	then	ADV
ejpam-6593	648	10	the	the	DET
ejpam-6593	648	11	prime	prime	ADJ
ejpam-6593	648	12	gap	gap	NOUN
ejpam-6593	648	13	,	,	PUNCT
ejpam-6593	648	14	5k	5k	NUM
ejpam-6593	648	15	,	,	PUNCT
ejpam-6593	648	16	is	be	AUX
ejpam-6593	648	17	also	also	ADV
ejpam-6593	648	18	even	even	ADV
ejpam-6593	648	19	.	.	PUNCT
ejpam-6593	649	1	thus	thus	ADV
ejpam-6593	649	2	,	,	PUNCT
ejpam-6593	649	3	for	for	SCONJ
ejpam-6593	649	4	p	p	PROPN
ejpam-6593	649	5	and	and	CCONJ
ejpam-6593	649	6	p	p	NOUN
ejpam-6593	649	7	+	+	NOUN
ejpam-6593	649	8	5k	5k	NUM
ejpam-6593	649	9	to	to	PART
ejpam-6593	649	10	be	be	AUX
ejpam-6593	649	11	prime	prime	ADJ
ejpam-6593	649	12	pairs	pair	NOUN
ejpam-6593	649	13	,	,	PUNCT
ejpam-6593	649	14	both	both	PRON
ejpam-6593	649	15	of	of	ADP
ejpam-6593	649	16	them	they	PRON
ejpam-6593	649	17	must	must	AUX
ejpam-6593	649	18	be	be	AUX
ejpam-6593	649	19	odd	odd	ADJ
ejpam-6593	649	20	integers	integer	NOUN
ejpam-6593	649	21	.	.	PUNCT
ejpam-6593	650	1	we	we	PRON
ejpam-6593	650	2	begin	begin	VERB
ejpam-6593	650	3	the	the	DET
ejpam-6593	650	4	discussion	discussion	NOUN
ejpam-6593	650	5	with	with	ADP
ejpam-6593	650	6	k	k	PROPN
ejpam-6593	650	7	≡	≡	PROPN
ejpam-6593	650	8	2	2	NUM
ejpam-6593	650	9	(	(	PUNCT
ejpam-6593	650	10	mod	mod	NOUN
ejpam-6593	650	11	4	4	NUM
ejpam-6593	650	12	)	)	PUNCT
ejpam-6593	650	13	.	.	PUNCT
ejpam-6593	651	1	lemma	lemma	PROPN
ejpam-6593	651	2	6	6	NUM
ejpam-6593	651	3	.	.	PUNCT
ejpam-6593	652	1	let	let	VERB
ejpam-6593	652	2	p	p	PRON
ejpam-6593	652	3	≥	≥	NUM
ejpam-6593	652	4	3	3	NUM
ejpam-6593	652	5	and	and	CCONJ
ejpam-6593	652	6	p+	p+	PROPN
ejpam-6593	652	7	5k	5k	PRON
ejpam-6593	652	8	be	be	AUX
ejpam-6593	652	9	prime	prime	ADJ
ejpam-6593	652	10	pairs	pair	NOUN
ejpam-6593	652	11	and	and	CCONJ
ejpam-6593	652	12	k	k	PROPN
ejpam-6593	652	13	≡	≡	PROPN
ejpam-6593	652	14	2	2	NUM
ejpam-6593	652	15	(	(	PUNCT
ejpam-6593	652	16	mod	mod	NOUN
ejpam-6593	652	17	4	4	NUM
ejpam-6593	652	18	)	)	PUNCT
ejpam-6593	652	19	.	.	PUNCT
ejpam-6593	653	1	then	then	ADV
ejpam-6593	653	2	,	,	PUNCT
ejpam-6593	653	3	the	the	DET
ejpam-6593	653	4	equation	equation	NOUN
ejpam-6593	653	5	(	(	PUNCT
ejpam-6593	653	6	3	3	X
ejpam-6593	653	7	)	)	PUNCT
ejpam-6593	653	8	has	have	VERB
ejpam-6593	653	9	no	no	DET
ejpam-6593	653	10	solution	solution	NOUN
ejpam-6593	653	11	if	if	SCONJ
ejpam-6593	653	12	x	x	PROPN
ejpam-6593	653	13	and	and	CCONJ
ejpam-6593	653	14	y	y	PROPN
ejpam-6593	653	15	are	be	AUX
ejpam-6593	653	16	both	both	PRON
ejpam-6593	653	17	even	even	ADV
ejpam-6593	653	18	integers	integer	NOUN
ejpam-6593	653	19	.	.	PUNCT
ejpam-6593	654	1	proof	proof	NOUN
ejpam-6593	654	2	.	.	PUNCT
ejpam-6593	655	1	consider	consider	VERB
ejpam-6593	655	2	the	the	DET
ejpam-6593	655	3	diophantine	diophantine	NOUN
ejpam-6593	655	4	equation	equation	NOUN
ejpam-6593	655	5	px+(p+5k)y	px+(p+5k)y	NOUN
ejpam-6593	655	6	=	=	SYM
ejpam-6593	655	7	z2	z2	PROPN
ejpam-6593	655	8	,	,	PUNCT
ejpam-6593	655	9	where	where	SCONJ
ejpam-6593	655	10	p	p	NOUN
ejpam-6593	655	11	and	and	CCONJ
ejpam-6593	655	12	q	q	NOUN
ejpam-6593	655	13	=	=	NOUN
ejpam-6593	655	14	p+5k	p+5k	PROPN
ejpam-6593	655	15	are	be	AUX
ejpam-6593	655	16	odd	odd	ADJ
ejpam-6593	655	17	prime	prime	ADJ
ejpam-6593	655	18	pairs	pair	NOUN
ejpam-6593	655	19	and	and	CCONJ
ejpam-6593	655	20	k	k	PROPN
ejpam-6593	655	21	≡	≡	PROPN
ejpam-6593	655	22	2	2	NUM
ejpam-6593	655	23	(	(	PUNCT
ejpam-6593	655	24	mod	mod	NOUN
ejpam-6593	655	25	4	4	NUM
ejpam-6593	655	26	)	)	PUNCT
ejpam-6593	655	27	.	.	PUNCT
ejpam-6593	656	1	if	if	SCONJ
ejpam-6593	656	2	p	p	PRON
ejpam-6593	656	3	≡	≡	PROPN
ejpam-6593	656	4	1	1	NUM
ejpam-6593	656	5	,	,	PUNCT
ejpam-6593	656	6	3	3	NUM
ejpam-6593	656	7	(	(	PUNCT
ejpam-6593	656	8	mod	mod	NOUN
ejpam-6593	656	9	4	4	NUM
ejpam-6593	656	10	)	)	PUNCT
ejpam-6593	656	11	,	,	PUNCT
ejpam-6593	656	12	then	then	ADV
ejpam-6593	656	13	q	q	PROPN
ejpam-6593	656	14	≡	≡	PROPN
ejpam-6593	656	15	3	3	NUM
ejpam-6593	656	16	,	,	PUNCT
ejpam-6593	656	17	1	1	NUM
ejpam-6593	656	18	(	(	PUNCT
ejpam-6593	656	19	mod	mod	NOUN
ejpam-6593	656	20	4	4	NUM
ejpam-6593	656	21	)	)	PUNCT
ejpam-6593	656	22	,	,	PUNCT
ejpam-6593	656	23	respectively	respectively	ADV
ejpam-6593	656	24	.	.	PUNCT
ejpam-6593	657	1	let	let	VERB
ejpam-6593	657	2	x	x	PRON
ejpam-6593	657	3	and	and	CCONJ
ejpam-6593	657	4	y	y	PROPN
ejpam-6593	657	5	be	be	AUX
ejpam-6593	657	6	both	both	PRON
ejpam-6593	657	7	even	even	ADV
ejpam-6593	657	8	integers	integer	NOUN
ejpam-6593	657	9	.	.	PUNCT
ejpam-6593	658	1	in	in	ADP
ejpam-6593	658	2	either	either	DET
ejpam-6593	658	3	case	case	NOUN
ejpam-6593	658	4	,	,	PUNCT
ejpam-6593	658	5	we	we	PRON
ejpam-6593	658	6	have	have	VERB
ejpam-6593	658	7	px	px	NOUN
ejpam-6593	658	8	≡	≡	PROPN
ejpam-6593	658	9	1	1	NUM
ejpam-6593	658	10	(	(	PUNCT
ejpam-6593	658	11	mod	mod	NOUN
ejpam-6593	658	12	4	4	NUM
ejpam-6593	658	13	)	)	PUNCT
ejpam-6593	658	14	and	and	CCONJ
ejpam-6593	658	15	qy	qy	PROPN
ejpam-6593	658	16	≡	≡	PROPN
ejpam-6593	658	17	1	1	NUM
ejpam-6593	658	18	(	(	PUNCT
ejpam-6593	658	19	mod	mod	NOUN
ejpam-6593	658	20	4	4	NUM
ejpam-6593	658	21	)	)	PUNCT
ejpam-6593	658	22	so	so	SCONJ
ejpam-6593	658	23	that	that	SCONJ
ejpam-6593	658	24	px	px	PROPN
ejpam-6593	658	25	+	+	CCONJ
ejpam-6593	658	26	qy	qy	PROPN
ejpam-6593	658	27	≡	≡	PROPN
ejpam-6593	658	28	1	1	NUM
ejpam-6593	658	29	+	+	SYM
ejpam-6593	658	30	1	1	NUM
ejpam-6593	658	31	≡	≡	PROPN
ejpam-6593	658	32	2	2	NUM
ejpam-6593	658	33	(	(	PUNCT
ejpam-6593	658	34	mod	mod	NOUN
ejpam-6593	658	35	4	4	NUM
ejpam-6593	658	36	)	)	PUNCT
ejpam-6593	658	37	.	.	PUNCT
ejpam-6593	659	1	also	also	ADV
ejpam-6593	659	2	,	,	PUNCT
ejpam-6593	659	3	since	since	SCONJ
ejpam-6593	659	4	px	px	PROPN
ejpam-6593	659	5	and	and	CCONJ
ejpam-6593	659	6	qy	qy	PROPN
ejpam-6593	659	7	are	be	AUX
ejpam-6593	659	8	both	both	PRON
ejpam-6593	659	9	odd	odd	ADJ
ejpam-6593	659	10	,	,	PUNCT
ejpam-6593	659	11	then	then	ADV
ejpam-6593	659	12	their	their	PRON
ejpam-6593	659	13	sum	sum	NOUN
ejpam-6593	659	14	is	be	AUX
ejpam-6593	659	15	even	even	ADV
ejpam-6593	659	16	.	.	PUNCT
ejpam-6593	660	1	thus	thus	ADV
ejpam-6593	660	2	,	,	PUNCT
ejpam-6593	660	3	z2	z2	PROPN
ejpam-6593	660	4	≡	≡	PROPN
ejpam-6593	660	5	0	0	PUNCT
ejpam-6593	660	6	(	(	PUNCT
ejpam-6593	660	7	mod	mod	NOUN
ejpam-6593	660	8	4	4	NUM
ejpam-6593	660	9	)	)	PUNCT
ejpam-6593	660	10	and	and	CCONJ
ejpam-6593	660	11	we	we	PRON
ejpam-6593	660	12	’ll	’ll	AUX
ejpam-6593	660	13	have	have	VERB
ejpam-6593	660	14	a	a	DET
ejpam-6593	660	15	contradiction	contradiction	NOUN
ejpam-6593	660	16	since	since	SCONJ
ejpam-6593	660	17	px	px	PROPN
ejpam-6593	660	18	+	+	CCONJ
ejpam-6593	660	19	qy	qy	PROPN
ejpam-6593	660	20	≡	≡	PROPN
ejpam-6593	660	21	2	2	NUM
ejpam-6593	660	22	̸≡	̸≡	NOUN
ejpam-6593	660	23	0	0	NUM
ejpam-6593	660	24	≡	≡	PROPN
ejpam-6593	660	25	z2	z2	PROPN
ejpam-6593	660	26	(	(	PUNCT
ejpam-6593	660	27	mod	mod	PROPN
ejpam-6593	660	28	4	4	NUM
ejpam-6593	660	29	)	)	PUNCT
ejpam-6593	660	30	.	.	PUNCT
ejpam-6593	661	1	conclusion	conclusion	NOUN
ejpam-6593	661	2	follows	follow	VERB
ejpam-6593	661	3	.	.	PUNCT
ejpam-6593	662	1	notice	notice	VERB
ejpam-6593	662	2	that	that	SCONJ
ejpam-6593	662	3	when	when	SCONJ
ejpam-6593	662	4	x	x	PROPN
ejpam-6593	662	5	=	=	SYM
ejpam-6593	662	6	y	y	NOUN
ejpam-6593	662	7	=	=	SYM
ejpam-6593	662	8	1	1	NUM
ejpam-6593	662	9	,	,	PUNCT
ejpam-6593	662	10	we	we	PRON
ejpam-6593	662	11	have	have	VERB
ejpam-6593	662	12	the	the	DET
ejpam-6593	662	13	equation	equation	NOUN
ejpam-6593	662	14	p+	p+	X
ejpam-6593	662	15	(	(	PUNCT
ejpam-6593	662	16	p+	p+	NOUN
ejpam-6593	662	17	5k	5k	NUM
ejpam-6593	662	18	)	)	PUNCT
ejpam-6593	662	19	=	=	SYM
ejpam-6593	662	20	z2	z2	PROPN
ejpam-6593	662	21	.	.	PUNCT
ejpam-6593	663	1	(	(	PUNCT
ejpam-6593	663	2	15	15	NUM
ejpam-6593	663	3	)	)	PUNCT
ejpam-6593	663	4	we	we	PRON
ejpam-6593	663	5	use	use	VERB
ejpam-6593	663	6	the	the	DET
ejpam-6593	663	7	following	follow	VERB
ejpam-6593	663	8	variables	variable	NOUN
ejpam-6593	663	9	to	to	PART
ejpam-6593	663	10	study	study	VERB
ejpam-6593	663	11	(	(	PUNCT
ejpam-6593	663	12	15	15	NUM
ejpam-6593	663	13	)	)	PUNCT
ejpam-6593	663	14	.	.	PUNCT
ejpam-6593	664	1	m.	m.	PROPN
ejpam-6593	664	2	c.	c.	PROPN
ejpam-6593	664	3	avenilla	avenilla	PROPN
ejpam-6593	664	4	,	,	PUNCT
ejpam-6593	664	5	j.	j.	PROPN
ejpam-6593	664	6	b.	b.	PROPN
ejpam-6593	664	7	bacani	bacani	PROPN
ejpam-6593	664	8	/	/	SYM
ejpam-6593	664	9	eur	eur	PROPN
ejpam-6593	664	10	.	.	PUNCT
ejpam-6593	665	1	j.	j.	PROPN
ejpam-6593	665	2	pure	pure	PROPN
ejpam-6593	665	3	appl	appl	PROPN
ejpam-6593	665	4	.	.	PROPN
ejpam-6593	665	5	math	math	PROPN
ejpam-6593	665	6	,	,	PUNCT
ejpam-6593	665	7	18	18	NUM
ejpam-6593	665	8	(	(	PUNCT
ejpam-6593	665	9	3	3	NUM
ejpam-6593	665	10	)	)	PUNCT
ejpam-6593	665	11	(	(	PUNCT
ejpam-6593	665	12	2025	2025	NUM
ejpam-6593	665	13	)	)	PUNCT
ejpam-6593	665	14	,	,	PUNCT
ejpam-6593	665	15	6593	6593	NUM
ejpam-6593	665	16	20	20	NUM
ejpam-6593	665	17	of	of	ADP
ejpam-6593	665	18	24	24	NUM
ejpam-6593	665	19	variable	variable	NOUN
ejpam-6593	665	20	meaning	mean	VERB
ejpam-6593	665	21	kn	kn	PROPN
ejpam-6593	665	22	the	the	DET
ejpam-6593	665	23	value	value	NOUN
ejpam-6593	665	24	of	of	ADP
ejpam-6593	665	25	k	k	PROPN
ejpam-6593	665	26	at	at	ADP
ejpam-6593	665	27	a	a	DET
ejpam-6593	665	28	specific	specific	ADJ
ejpam-6593	665	29	value	value	NOUN
ejpam-6593	665	30	of	of	ADP
ejpam-6593	665	31	n	n	DET
ejpam-6593	665	32	z(0,kn	z(0,kn	PROPN
ejpam-6593	665	33	)	)	PUNCT
ejpam-6593	665	34	the	the	DET
ejpam-6593	665	35	first	first	ADJ
ejpam-6593	665	36	value	value	NOUN
ejpam-6593	665	37	of	of	ADP
ejpam-6593	665	38	z	z	NOUN
ejpam-6593	665	39	at	at	ADP
ejpam-6593	665	40	a	a	DET
ejpam-6593	665	41	specific	specific	ADJ
ejpam-6593	665	42	value	value	NOUN
ejpam-6593	665	43	of	of	ADP
ejpam-6593	665	44	kn	kn	PROPN
ejpam-6593	665	45	z(m	z(m	PROPN
ejpam-6593	665	46	,	,	PUNCT
ejpam-6593	665	47	kn	kn	PROPN
ejpam-6593	665	48	)	)	PUNCT
ejpam-6593	665	49	the	the	DET
ejpam-6593	665	50	(	(	PUNCT
ejpam-6593	665	51	m+	m+	NUM
ejpam-6593	665	52	1)st	1)st	NUM
ejpam-6593	665	53	value	value	NOUN
ejpam-6593	665	54	of	of	ADP
ejpam-6593	665	55	z	z	NOUN
ejpam-6593	665	56	at	at	ADP
ejpam-6593	665	57	a	a	DET
ejpam-6593	665	58	specific	specific	ADJ
ejpam-6593	665	59	value	value	NOUN
ejpam-6593	665	60	of	of	ADP
ejpam-6593	665	61	kn	kn	PROPN
ejpam-6593	665	62	p(0,kn	p(0,kn	PROPN
ejpam-6593	665	63	)	)	PUNCT
ejpam-6593	665	64	the	the	DET
ejpam-6593	665	65	first	first	ADJ
ejpam-6593	665	66	value	value	NOUN
ejpam-6593	665	67	of	of	ADP
ejpam-6593	665	68	p	p	NOUN
ejpam-6593	665	69	at	at	ADP
ejpam-6593	665	70	a	a	DET
ejpam-6593	665	71	specific	specific	ADJ
ejpam-6593	665	72	value	value	NOUN
ejpam-6593	665	73	of	of	ADP
ejpam-6593	665	74	kn	kn	PROPN
ejpam-6593	665	75	p(1,kn	p(1,kn	PROPN
ejpam-6593	665	76	)	)	PUNCT
ejpam-6593	665	77	the	the	DET
ejpam-6593	665	78	second	second	ADJ
ejpam-6593	665	79	value	value	NOUN
ejpam-6593	665	80	of	of	ADP
ejpam-6593	665	81	p	p	NOUN
ejpam-6593	665	82	at	at	ADP
ejpam-6593	665	83	a	a	DET
ejpam-6593	665	84	specific	specific	ADJ
ejpam-6593	665	85	value	value	NOUN
ejpam-6593	665	86	of	of	ADP
ejpam-6593	665	87	kn	kn	PROPN
ejpam-6593	665	88	ωkn	ωkn	PROPN
ejpam-6593	665	89	the	the	DET
ejpam-6593	665	90	difference	difference	NOUN
ejpam-6593	665	91	between	between	ADP
ejpam-6593	665	92	p(0,kn	p(0,kn	PROPN
ejpam-6593	665	93	)	)	PUNCT
ejpam-6593	665	94	and	and	CCONJ
ejpam-6593	665	95	p(1,kn	p(1,kn	PROPN
ejpam-6593	665	96	)	)	PUNCT
ejpam-6593	665	97	at	at	ADP
ejpam-6593	665	98	a	a	DET
ejpam-6593	665	99	specific	specific	ADJ
ejpam-6593	665	100	value	value	NOUN
ejpam-6593	665	101	of	of	ADP
ejpam-6593	665	102	kn	kn	PROPN
ejpam-6593	665	103	p(m	p(m	PROPN
ejpam-6593	665	104	,	,	PUNCT
ejpam-6593	665	105	kn	kn	PROPN
ejpam-6593	665	106	)	)	PUNCT
ejpam-6593	665	107	the	the	DET
ejpam-6593	665	108	(	(	PUNCT
ejpam-6593	665	109	m+	m+	NUM
ejpam-6593	665	110	1)st	1)st	NUM
ejpam-6593	665	111	value	value	NOUN
ejpam-6593	665	112	of	of	ADP
ejpam-6593	665	113	p	p	NOUN
ejpam-6593	665	114	at	at	ADP
ejpam-6593	665	115	a	a	DET
ejpam-6593	665	116	specific	specific	ADJ
ejpam-6593	665	117	value	value	NOUN
ejpam-6593	665	118	of	of	ADP
ejpam-6593	665	119	kn	kn	PROPN
ejpam-6593	665	120	table	table	NOUN
ejpam-6593	665	121	20	20	NUM
ejpam-6593	665	122	:	:	PUNCT
ejpam-6593	665	123	variables	variable	NOUN
ejpam-6593	665	124	considered	consider	VERB
ejpam-6593	665	125	for	for	ADP
ejpam-6593	665	126	p+	p+	PROPN
ejpam-6593	665	127	(	(	PUNCT
ejpam-6593	665	128	p+	p+	NOUN
ejpam-6593	665	129	5k	5k	NUM
ejpam-6593	665	130	)	)	PUNCT
ejpam-6593	665	131	=	=	SYM
ejpam-6593	665	132	z2	z2	PROPN
ejpam-6593	665	133	,	,	PUNCT
ejpam-6593	665	134	where	where	SCONJ
ejpam-6593	665	135	p	p	PROPN
ejpam-6593	665	136	≥	≥	PUNCT
ejpam-6593	665	137	3	3	NUM
ejpam-6593	665	138	and	and	CCONJ
ejpam-6593	665	139	p+	p+	PROPN
ejpam-6593	665	140	5k	5k	NUM
ejpam-6593	665	141	are	be	AUX
ejpam-6593	665	142	prime	prime	ADJ
ejpam-6593	665	143	pairs	pair	NOUN
ejpam-6593	665	144	we	we	PRON
ejpam-6593	665	145	derive	derive	VERB
ejpam-6593	665	146	the	the	DET
ejpam-6593	665	147	following	follow	VERB
ejpam-6593	665	148	formulas	formula	NOUN
ejpam-6593	665	149	:	:	PUNCT
ejpam-6593	665	150	k	k	X
ejpam-6593	665	151	=	=	PUNCT
ejpam-6593	665	152	kn	kn	PROPN
ejpam-6593	665	153	=	=	PUNCT
ejpam-6593	665	154	2	2	NUM
ejpam-6593	665	155	+	+	CCONJ
ejpam-6593	665	156	4n	4n	NOUN
ejpam-6593	665	157	,	,	PUNCT
ejpam-6593	665	158	(	(	PUNCT
ejpam-6593	665	159	16a	16a	NOUN
ejpam-6593	665	160	)	)	PUNCT
ejpam-6593	665	161	z(0,kn	z(0,kn	PROPN
ejpam-6593	665	162	)	)	PUNCT
ejpam-6593	665	163	=	=	PUNCT
ejpam-6593	666	1			NOUN
ejpam-6593	666	2	√	√	VERB
ejpam-6593	666	3	6	6	NUM
ejpam-6593	666	4	+	+	NUM
ejpam-6593	666	5	5k	5k	NUM
ejpam-6593	666	6	if	if	SCONJ
ejpam-6593	666	7	√	√	PROPN
ejpam-6593	666	8	6	6	NUM
ejpam-6593	666	9	+	+	NUM
ejpam-6593	666	10	5k	5k	NUM
ejpam-6593	666	11	is	be	AUX
ejpam-6593	666	12	an	an	DET
ejpam-6593	666	13	even	even	ADV
ejpam-6593	666	14	integer,⌊√	integer,⌊√	ADJ
ejpam-6593	666	15	6	6	NUM
ejpam-6593	666	16	+	+	SYM
ejpam-6593	666	17	5k	5k	NUM
ejpam-6593	666	18	⌋	⌋	NOUN
ejpam-6593	666	19	+	+	CCONJ
ejpam-6593	666	20	1	1	NUM
ejpam-6593	666	21	if	if	SCONJ
ejpam-6593	666	22	⌊√	⌊√	PROPN
ejpam-6593	666	23	6	6	NUM
ejpam-6593	666	24	+	+	NUM
ejpam-6593	666	25	5k	5k	NUM
ejpam-6593	666	26	⌋	⌋	NOUN
ejpam-6593	666	27	is	be	AUX
ejpam-6593	666	28	odd,⌊√	odd,⌊√	NOUN
ejpam-6593	666	29	6	6	NUM
ejpam-6593	666	30	+	+	SYM
ejpam-6593	666	31	5k	5k	NUM
ejpam-6593	666	32	⌋	⌋	NOUN
ejpam-6593	667	1	+	+	CCONJ
ejpam-6593	667	2	2	2	NUM
ejpam-6593	667	3	if	if	SCONJ
ejpam-6593	667	4	⌊√	⌊√	PROPN
ejpam-6593	667	5	6	6	NUM
ejpam-6593	667	6	+	+	NUM
ejpam-6593	667	7	5k	5k	NUM
ejpam-6593	667	8	⌋	⌋	NOUN
ejpam-6593	667	9	is	be	AUX
ejpam-6593	667	10	even	even	ADV
ejpam-6593	667	11	,	,	PUNCT
ejpam-6593	667	12	(	(	PUNCT
ejpam-6593	667	13	16b	16b	NOUN
ejpam-6593	667	14	)	)	PUNCT
ejpam-6593	667	15	z(m	z(m	PROPN
ejpam-6593	667	16	,	,	PUNCT
ejpam-6593	667	17	kn	kn	NOUN
ejpam-6593	667	18	)	)	PUNCT
ejpam-6593	667	19	=	=	SYM
ejpam-6593	667	20	z(0,kn	z(0,kn	PROPN
ejpam-6593	667	21	)	)	PUNCT
ejpam-6593	667	22	+	+	CCONJ
ejpam-6593	668	1	2	2	NUM
ejpam-6593	668	2	m	m	NOUN
ejpam-6593	668	3	,	,	PUNCT
ejpam-6593	668	4	(	(	PUNCT
ejpam-6593	668	5	16c	16c	NOUN
ejpam-6593	668	6	)	)	PUNCT
ejpam-6593	668	7	p(0,kn	p(0,kn	PROPN
ejpam-6593	668	8	)	)	PUNCT
ejpam-6593	668	9	=	=	SYM
ejpam-6593	668	10	z2(0,kn	z2(0,kn	PROPN
ejpam-6593	668	11	)	)	PUNCT
ejpam-6593	668	12	−	−	NUM
ejpam-6593	668	13	5kn	5kn	NOUN
ejpam-6593	668	14	2	2	NUM
ejpam-6593	668	15	,	,	PUNCT
ejpam-6593	668	16	(	(	PUNCT
ejpam-6593	668	17	16d	16d	NOUN
ejpam-6593	668	18	)	)	PUNCT
ejpam-6593	668	19	p(m	p(m	NOUN
ejpam-6593	668	20	,	,	PUNCT
ejpam-6593	668	21	kn	kn	PROPN
ejpam-6593	668	22	)	)	PUNCT
ejpam-6593	668	23	=	=	PUNCT
ejpam-6593	669	1	z2(m	z2(m	NUM
ejpam-6593	669	2	,	,	PUNCT
ejpam-6593	669	3	kn	kn	PROPN
ejpam-6593	669	4	)	)	PUNCT
ejpam-6593	669	5	−	−	PROPN
ejpam-6593	669	6	5kn	5kn	ADJ
ejpam-6593	669	7	2	2	NUM
ejpam-6593	669	8	,	,	PUNCT
ejpam-6593	669	9	(	(	PUNCT
ejpam-6593	669	10	16e	16e	NUM
ejpam-6593	669	11	)	)	PUNCT
ejpam-6593	669	12	ωkn	ωkn	NOUN
ejpam-6593	669	13	=	=	SYM
ejpam-6593	669	14	p(1,kn	p(1,kn	PROPN
ejpam-6593	669	15	)	)	PUNCT
ejpam-6593	669	16	−	−	PROPN
ejpam-6593	669	17	p(0,kn	p(0,kn	PROPN
ejpam-6593	669	18	)	)	PUNCT
ejpam-6593	669	19	,	,	PUNCT
ejpam-6593	669	20	(	(	PUNCT
ejpam-6593	669	21	16f	16f	NOUN
ejpam-6593	669	22	)	)	PUNCT
ejpam-6593	669	23	where	where	SCONJ
ejpam-6593	669	24	n	n	X
ejpam-6593	669	25	∈	∈	PROPN
ejpam-6593	669	26	n0	n0	NOUN
ejpam-6593	669	27	and	and	CCONJ
ejpam-6593	669	28	for	for	ADP
ejpam-6593	669	29	some	some	DET
ejpam-6593	669	30	m	m	NOUN
ejpam-6593	669	31	∈	∈	ADJ
ejpam-6593	669	32	n.	n.	NOUN
ejpam-6593	669	33	we	we	PRON
ejpam-6593	669	34	use	use	VERB
ejpam-6593	669	35	the	the	DET
ejpam-6593	669	36	floor	floor	NOUN
ejpam-6593	669	37	function	function	NOUN
ejpam-6593	669	38	of	of	ADP
ejpam-6593	669	39	√	√	NOUN
ejpam-6593	669	40	6	6	NUM
ejpam-6593	669	41	+	+	NUM
ejpam-6593	669	42	5k	5k	NUM
ejpam-6593	669	43	for	for	ADP
ejpam-6593	669	44	z(0,kn	z(0,kn	PROPN
ejpam-6593	669	45	)	)	PUNCT
ejpam-6593	669	46	since	since	SCONJ
ejpam-6593	669	47	we	we	PRON
ejpam-6593	669	48	know	know	VERB
ejpam-6593	669	49	that	that	SCONJ
ejpam-6593	669	50	the	the	DET
ejpam-6593	669	51	smallest	small	ADJ
ejpam-6593	669	52	possible	possible	ADJ
ejpam-6593	669	53	value	value	NOUN
ejpam-6593	669	54	of	of	ADP
ejpam-6593	669	55	p	p	NOUN
ejpam-6593	669	56	is	be	AUX
ejpam-6593	669	57	3	3	NUM
ejpam-6593	669	58	.	.	PUNCT
ejpam-6593	669	59	also	also	ADV
ejpam-6593	669	60	,	,	PUNCT
ejpam-6593	669	61	from	from	ADP
ejpam-6593	669	62	equation	equation	NOUN
ejpam-6593	669	63	(	(	PUNCT
ejpam-6593	669	64	15	15	NUM
ejpam-6593	669	65	)	)	PUNCT
ejpam-6593	669	66	,	,	PUNCT
ejpam-6593	669	67	we	we	PRON
ejpam-6593	669	68	have	have	VERB
ejpam-6593	669	69	3	3	NUM
ejpam-6593	669	70	+	+	SYM
ejpam-6593	669	71	3	3	NUM
ejpam-6593	669	72	+	+	NUM
ejpam-6593	669	73	5k	5k	NUM
ejpam-6593	669	74	=	=	SYM
ejpam-6593	669	75	z2	z2	PROPN
ejpam-6593	669	76	will	will	AUX
ejpam-6593	669	77	mean	mean	VERB
ejpam-6593	669	78	that	that	SCONJ
ejpam-6593	669	79	z	z	NOUN
ejpam-6593	669	80	=	=	PUNCT
ejpam-6593	669	81	√	√	ADV
ejpam-6593	669	82	6	6	NUM
ejpam-6593	669	83	+	+	SYM
ejpam-6593	669	84	5k	5k	NUM
ejpam-6593	669	85	.	.	PUNCT
ejpam-6593	670	1	since	since	SCONJ
ejpam-6593	670	2	k	k	PROPN
ejpam-6593	670	3	is	be	AUX
ejpam-6593	670	4	even	even	ADV
ejpam-6593	670	5	,	,	PUNCT
ejpam-6593	670	6	√	√	PROPN
ejpam-6593	670	7	6	6	NUM
ejpam-6593	670	8	+	+	NUM
ejpam-6593	670	9	5k	5k	NUM
ejpam-6593	670	10	is	be	AUX
ejpam-6593	670	11	even	even	ADV
ejpam-6593	670	12	if	if	SCONJ
ejpam-6593	670	13	it	it	PRON
ejpam-6593	670	14	is	be	AUX
ejpam-6593	670	15	an	an	DET
ejpam-6593	670	16	integer	integer	NOUN
ejpam-6593	670	17	.	.	PUNCT
ejpam-6593	671	1	otherwise	otherwise	ADV
ejpam-6593	671	2	,	,	PUNCT
ejpam-6593	671	3	we	we	PRON
ejpam-6593	671	4	have	have	VERB
ejpam-6593	671	5	another	another	DET
ejpam-6593	671	6	two	two	NUM
ejpam-6593	671	7	conditions	condition	NOUN
ejpam-6593	671	8	as	as	SCONJ
ejpam-6593	671	9	seen	see	VERB
ejpam-6593	671	10	below	below	ADV
ejpam-6593	671	11	.	.	PUNCT
ejpam-6593	672	1	the	the	DET
ejpam-6593	672	2	five	five	NUM
ejpam-6593	672	3	-	-	PUNCT
ejpam-6593	672	4	tuple	tuple	NOUN
ejpam-6593	672	5	(	(	PUNCT
ejpam-6593	672	6	p	p	X
ejpam-6593	672	7	,	,	PUNCT
ejpam-6593	672	8	k	k	NOUN
ejpam-6593	672	9	,	,	PUNCT
ejpam-6593	672	10	x	x	X
ejpam-6593	672	11	,	,	PUNCT
ejpam-6593	672	12	y	y	PROPN
ejpam-6593	672	13	,	,	PUNCT
ejpam-6593	672	14	z	z	NOUN
ejpam-6593	672	15	)	)	PUNCT
ejpam-6593	672	16	=	=	SYM
ejpam-6593	672	17	(	(	PUNCT
ejpam-6593	672	18	p(m	p(m	NOUN
ejpam-6593	672	19	,	,	PUNCT
ejpam-6593	672	20	kn	kn	PROPN
ejpam-6593	672	21	)	)	PUNCT
ejpam-6593	672	22	,	,	PUNCT
ejpam-6593	672	23	kn	kn	PROPN
ejpam-6593	672	24	,	,	PUNCT
ejpam-6593	672	25	1	1	NUM
ejpam-6593	672	26	,	,	PUNCT
ejpam-6593	672	27	1	1	NUM
ejpam-6593	672	28	,	,	PUNCT
ejpam-6593	672	29	z(m	z(m	PROPN
ejpam-6593	672	30	,	,	PUNCT
ejpam-6593	672	31	kn	kn	PROPN
ejpam-6593	672	32	)	)	PUNCT
ejpam-6593	672	33	)	)	PUNCT
ejpam-6593	672	34	will	will	AUX
ejpam-6593	672	35	become	become	VERB
ejpam-6593	672	36	a	a	DET
ejpam-6593	672	37	solution	solution	NOUN
ejpam-6593	672	38	of	of	ADP
ejpam-6593	672	39	equation	equation	NOUN
ejpam-6593	672	40	(	(	PUNCT
ejpam-6593	672	41	3	3	NUM
ejpam-6593	672	42	)	)	PUNCT
ejpam-6593	672	43	.	.	PUNCT
ejpam-6593	673	1	below	below	ADV
ejpam-6593	673	2	is	be	AUX
ejpam-6593	673	3	another	another	DET
ejpam-6593	673	4	result	result	NOUN
ejpam-6593	673	5	.	.	PUNCT
ejpam-6593	674	1	the	the	DET
ejpam-6593	674	2	proof	proof	NOUN
ejpam-6593	674	3	is	be	AUX
ejpam-6593	674	4	similar	similar	ADJ
ejpam-6593	674	5	to	to	ADP
ejpam-6593	674	6	the	the	DET
ejpam-6593	674	7	theorems	theorem	NOUN
ejpam-6593	674	8	above	above	ADP
ejpam-6593	674	9	that	that	PRON
ejpam-6593	674	10	use	use	VERB
ejpam-6593	674	11	mathematical	mathematical	ADJ
ejpam-6593	674	12	induction	induction	NOUN
ejpam-6593	674	13	,	,	PUNCT
ejpam-6593	674	14	hence	hence	ADV
ejpam-6593	674	15	we	we	PRON
ejpam-6593	674	16	omit	omit	VERB
ejpam-6593	674	17	it	it	PRON
ejpam-6593	674	18	.	.	PUNCT
ejpam-6593	675	1	theorem	theorem	ADJ
ejpam-6593	675	2	7	7	NUM
ejpam-6593	675	3	.	.	PUNCT
ejpam-6593	675	4	suppose	suppose	VERB
ejpam-6593	675	5	that	that	SCONJ
ejpam-6593	675	6	the	the	DET
ejpam-6593	675	7	exponential	exponential	ADJ
ejpam-6593	675	8	diophantine	diophantine	NOUN
ejpam-6593	675	9	equation	equation	NOUN
ejpam-6593	675	10	(	(	PUNCT
ejpam-6593	675	11	15	15	NUM
ejpam-6593	675	12	)	)	PUNCT
ejpam-6593	675	13	,	,	PUNCT
ejpam-6593	675	14	where	where	SCONJ
ejpam-6593	675	15	k	k	NOUN
ejpam-6593	675	16	:	:	PUNCT
ejpam-6593	675	17	=	=	PUNCT
ejpam-6593	675	18	kn	kn	NOUN
ejpam-6593	675	19	=	=	PUNCT
ejpam-6593	675	20	2	2	NUM
ejpam-6593	675	21	+	+	CCONJ
ejpam-6593	675	22	4n	4n	NOUN
ejpam-6593	675	23	,	,	PUNCT
ejpam-6593	675	24	n	n	PROPN
ejpam-6593	675	25	∈	∈	PROPN
ejpam-6593	675	26	n0	n0	NOUN
ejpam-6593	675	27	,	,	PUNCT
ejpam-6593	675	28	has	have	VERB
ejpam-6593	675	29	a	a	DET
ejpam-6593	675	30	solution	solution	NOUN
ejpam-6593	675	31	.	.	PUNCT
ejpam-6593	676	1	then	then	ADV
ejpam-6593	676	2	,	,	PUNCT
ejpam-6593	676	3	p(m	p(m	NOUN
ejpam-6593	676	4	,	,	PUNCT
ejpam-6593	676	5	kn	kn	PROPN
ejpam-6593	676	6	)	)	PUNCT
ejpam-6593	676	7	=	=	SYM
ejpam-6593	676	8	p(0,kn	p(0,kn	PROPN
ejpam-6593	676	9	)	)	PUNCT
ejpam-6593	677	1	+	+	CCONJ
ejpam-6593	677	2	m−1∑	m−1∑	PROPN
ejpam-6593	677	3	i=0	i=0	PROPN
ejpam-6593	677	4	(	(	PUNCT
ejpam-6593	677	5	ωkn	ωkn	NOUN
ejpam-6593	677	6	+	+	CCONJ
ejpam-6593	677	7	4i	4i	NUM
ejpam-6593	677	8	)	)	PUNCT
ejpam-6593	677	9	.	.	PUNCT
ejpam-6593	678	1	this	this	DET
ejpam-6593	678	2	remark	remark	NOUN
ejpam-6593	678	3	follows	follow	VERB
ejpam-6593	678	4	directly	directly	ADV
ejpam-6593	678	5	from	from	ADP
ejpam-6593	678	6	the	the	DET
ejpam-6593	678	7	theorem	theorem	ADJ
ejpam-6593	678	8	7	7	NUM
ejpam-6593	678	9	.	.	PUNCT
ejpam-6593	678	10	corollary	corollary	ADJ
ejpam-6593	678	11	1	1	NUM
ejpam-6593	678	12	.	.	PUNCT
ejpam-6593	679	1	consider	consider	VERB
ejpam-6593	679	2	the	the	DET
ejpam-6593	679	3	diophantine	diophantine	NOUN
ejpam-6593	679	4	equation	equation	NOUN
ejpam-6593	679	5	(	(	PUNCT
ejpam-6593	679	6	15	15	NUM
ejpam-6593	679	7	)	)	PUNCT
ejpam-6593	679	8	,	,	PUNCT
ejpam-6593	679	9	where	where	SCONJ
ejpam-6593	679	10	k	k	PROPN
ejpam-6593	679	11	=	=	PUNCT
ejpam-6593	679	12	kn	kn	PROPN
ejpam-6593	679	13	=	=	PUNCT
ejpam-6593	679	14	2	2	NUM
ejpam-6593	679	15	+	+	CCONJ
ejpam-6593	679	16	4n	4n	NOUN
ejpam-6593	679	17	,	,	PUNCT
ejpam-6593	679	18	n	n	PROPN
ejpam-6593	679	19	∈	∈	PROPN
ejpam-6593	679	20	n0	n0	PROPN
ejpam-6593	679	21	.	.	PUNCT
ejpam-6593	680	1	then	then	ADV
ejpam-6593	680	2	,	,	PUNCT
ejpam-6593	680	3	p(m	p(m	NOUN
ejpam-6593	680	4	,	,	PUNCT
ejpam-6593	680	5	kn	kn	PROPN
ejpam-6593	680	6	)	)	PUNCT
ejpam-6593	680	7	=	=	PUNCT
ejpam-6593	680	8	p(m−1,kn	p(m−1,kn	PROPN
ejpam-6593	680	9	)	)	PUNCT
ejpam-6593	681	1	+	+	CCONJ
ejpam-6593	681	2	ωkn	ωkn	PRON
ejpam-6593	681	3	+	+	CCONJ
ejpam-6593	681	4	4(m−	4(m−	NUM
ejpam-6593	681	5	1	1	NUM
ejpam-6593	681	6	)	)	PUNCT
ejpam-6593	681	7	.	.	PUNCT
ejpam-6593	682	1	m.	m.	PROPN
ejpam-6593	682	2	c.	c.	PROPN
ejpam-6593	682	3	avenilla	avenilla	PROPN
ejpam-6593	682	4	,	,	PUNCT
ejpam-6593	682	5	j.	j.	PROPN
ejpam-6593	682	6	b.	b.	PROPN
ejpam-6593	682	7	bacani	bacani	PROPN
ejpam-6593	682	8	/	/	SYM
ejpam-6593	682	9	eur	eur	PROPN
ejpam-6593	682	10	.	.	PUNCT
ejpam-6593	683	1	j.	j.	PROPN
ejpam-6593	683	2	pure	pure	PROPN
ejpam-6593	683	3	appl	appl	PROPN
ejpam-6593	683	4	.	.	PROPN
ejpam-6593	683	5	math	math	PROPN
ejpam-6593	683	6	,	,	PUNCT
ejpam-6593	683	7	18	18	NUM
ejpam-6593	683	8	(	(	PUNCT
ejpam-6593	683	9	3	3	NUM
ejpam-6593	683	10	)	)	PUNCT
ejpam-6593	683	11	(	(	PUNCT
ejpam-6593	683	12	2025	2025	NUM
ejpam-6593	683	13	)	)	PUNCT
ejpam-6593	683	14	,	,	PUNCT
ejpam-6593	683	15	6593	6593	NUM
ejpam-6593	683	16	21	21	NUM
ejpam-6593	683	17	of	of	ADP
ejpam-6593	683	18	24	24	NUM
ejpam-6593	683	19	given	give	VERB
ejpam-6593	683	20	below	below	ADV
ejpam-6593	683	21	are	be	AUX
ejpam-6593	683	22	tables	table	NOUN
ejpam-6593	683	23	containing	contain	VERB
ejpam-6593	683	24	the	the	DET
ejpam-6593	683	25	first	first	ADJ
ejpam-6593	683	26	five	five	NUM
ejpam-6593	683	27	solutions	solution	NOUN
ejpam-6593	683	28	of	of	ADP
ejpam-6593	683	29	equation	equation	NOUN
ejpam-6593	683	30	(	(	PUNCT
ejpam-6593	683	31	15	15	NUM
ejpam-6593	683	32	)	)	PUNCT
ejpam-6593	683	33	,	,	PUNCT
ejpam-6593	683	34	where	where	SCONJ
ejpam-6593	683	35	k	k	NOUN
ejpam-6593	683	36	:	:	PUNCT
ejpam-6593	683	37	=	=	PUNCT
ejpam-6593	683	38	kn	kn	NOUN
ejpam-6593	683	39	=	=	PUNCT
ejpam-6593	683	40	2	2	NUM
ejpam-6593	683	41	+	+	CCONJ
ejpam-6593	683	42	4n	4n	NOUN
ejpam-6593	683	43	,	,	PUNCT
ejpam-6593	683	44	and	and	CCONJ
ejpam-6593	683	45	p(m	p(m	NOUN
ejpam-6593	683	46	,	,	PUNCT
ejpam-6593	683	47	kn	kn	PROPN
ejpam-6593	683	48	)	)	PUNCT
ejpam-6593	683	49	is	be	AUX
ejpam-6593	683	50	obtained	obtain	VERB
ejpam-6593	683	51	by	by	ADP
ejpam-6593	683	52	applying	apply	VERB
ejpam-6593	683	53	(	(	PUNCT
ejpam-6593	683	54	16e	16e	NUM
ejpam-6593	683	55	)	)	PUNCT
ejpam-6593	683	56	,	,	PUNCT
ejpam-6593	683	57	or	or	CCONJ
ejpam-6593	683	58	theorem	theorem	VERB
ejpam-6593	683	59	7	7	NUM
ejpam-6593	683	60	,	,	PUNCT
ejpam-6593	683	61	or	or	CCONJ
ejpam-6593	683	62	remark	remark	NOUN
ejpam-6593	683	63	1	1	NUM
ejpam-6593	683	64	.	.	PUNCT
ejpam-6593	684	1	tables	table	NOUN
ejpam-6593	684	2	21	21	NUM
ejpam-6593	684	3	and	and	CCONJ
ejpam-6593	684	4	22	22	NUM
ejpam-6593	684	5	present	present	VERB
ejpam-6593	684	6	some	some	DET
ejpam-6593	684	7	solutions	solution	NOUN
ejpam-6593	684	8	of	of	ADP
ejpam-6593	684	9	(	(	PUNCT
ejpam-6593	684	10	15	15	NUM
ejpam-6593	684	11	)	)	PUNCT
ejpam-6593	684	12	when	when	SCONJ
ejpam-6593	684	13	n	n	X
ejpam-6593	684	14	=	=	SYM
ejpam-6593	684	15	0	0	NUM
ejpam-6593	684	16	and	and	CCONJ
ejpam-6593	684	17	n	n	CCONJ
ejpam-6593	684	18	=	=	SYM
ejpam-6593	684	19	1	1	NUM
ejpam-6593	684	20	in	in	ADP
ejpam-6593	684	21	k	k	PROPN
ejpam-6593	684	22	=	=	PUNCT
ejpam-6593	684	23	kn	kn	PROPN
ejpam-6593	684	24	=	=	PUNCT
ejpam-6593	684	25	2	2	NUM
ejpam-6593	684	26	+	+	CCONJ
ejpam-6593	684	27	4n	4n	NOUN
ejpam-6593	684	28	,	,	PUNCT
ejpam-6593	684	29	respectively	respectively	ADV
ejpam-6593	684	30	.	.	PUNCT
ejpam-6593	685	1	if	if	SCONJ
ejpam-6593	685	2	n	n	NOUN
ejpam-6593	685	3	=	=	SYM
ejpam-6593	685	4	0	0	NUM
ejpam-6593	685	5	,	,	PUNCT
ejpam-6593	685	6	we	we	PRON
ejpam-6593	685	7	have	have	VERB
ejpam-6593	685	8	k	k	NOUN
ejpam-6593	685	9	=	=	SYM
ejpam-6593	685	10	2	2	NUM
ejpam-6593	685	11	,	,	PUNCT
ejpam-6593	685	12	z(0,2	z(0,2	NOUN
ejpam-6593	685	13	)	)	PUNCT
ejpam-6593	685	14	=	=	SYM
ejpam-6593	685	15	4	4	NUM
ejpam-6593	685	16	,	,	PUNCT
ejpam-6593	685	17	z(1,2	z(1,2	NOUN
ejpam-6593	685	18	)	)	PUNCT
ejpam-6593	685	19	=	=	SYM
ejpam-6593	685	20	6	6	NUM
ejpam-6593	685	21	,	,	PUNCT
ejpam-6593	685	22	p(0,2	p(0,2	NOUN
ejpam-6593	685	23	)	)	PUNCT
ejpam-6593	685	24	=	=	SYM
ejpam-6593	685	25	3	3	NUM
ejpam-6593	685	26	,	,	PUNCT
ejpam-6593	685	27	p(1,1	p(1,1	NOUN
ejpam-6593	685	28	)	)	PUNCT
ejpam-6593	685	29	=	=	SYM
ejpam-6593	685	30	13	13	NUM
ejpam-6593	685	31	,	,	PUNCT
ejpam-6593	685	32	and	and	CCONJ
ejpam-6593	685	33	ω2	ω2	ADJ
ejpam-6593	685	34	=	=	SYM
ejpam-6593	685	35	10	10	NUM
ejpam-6593	685	36	.	.	PUNCT
ejpam-6593	686	1	for	for	ADP
ejpam-6593	686	2	n	n	NOUN
ejpam-6593	686	3	=	=	SYM
ejpam-6593	686	4	1	1	NUM
ejpam-6593	686	5	,	,	PUNCT
ejpam-6593	686	6	we	we	PRON
ejpam-6593	686	7	have	have	VERB
ejpam-6593	686	8	k	k	NOUN
ejpam-6593	686	9	=	=	SYM
ejpam-6593	686	10	6	6	NUM
ejpam-6593	686	11	,	,	PUNCT
ejpam-6593	686	12	z(0,6	z(0,6	NUM
ejpam-6593	686	13	)	)	PUNCT
ejpam-6593	686	14	=	=	SYM
ejpam-6593	686	15	6	6	NUM
ejpam-6593	686	16	,	,	PUNCT
ejpam-6593	686	17	z(1,6	z(1,6	PROPN
ejpam-6593	686	18	)	)	PUNCT
ejpam-6593	686	19	=	=	SYM
ejpam-6593	686	20	8	8	NUM
ejpam-6593	686	21	,	,	PUNCT
ejpam-6593	686	22	p(0,6	p(0,6	NOUN
ejpam-6593	686	23	)	)	PUNCT
ejpam-6593	686	24	=	=	SYM
ejpam-6593	687	1	3	3	NUM
ejpam-6593	687	2	,	,	PUNCT
ejpam-6593	687	3	p(1,6	p(1,6	NOUN
ejpam-6593	687	4	)	)	PUNCT
ejpam-6593	687	5	=	=	SYM
ejpam-6593	687	6	17	17	NUM
ejpam-6593	687	7	,	,	PUNCT
ejpam-6593	687	8	and	and	CCONJ
ejpam-6593	687	9	ω6	ω6	PROPN
ejpam-6593	687	10	=	=	SYM
ejpam-6593	687	11	14	14	NUM
ejpam-6593	687	12	.	.	PUNCT
ejpam-6593	688	1	m	m	VERB
ejpam-6593	689	1	p	p	NOUN
ejpam-6593	689	2	z	z	NOUN
ejpam-6593	689	3	equation	equation	NOUN
ejpam-6593	689	4	solution	solution	NOUN
ejpam-6593	689	5	(	(	PUNCT
ejpam-6593	689	6	p	p	X
ejpam-6593	689	7	,	,	PUNCT
ejpam-6593	689	8	k	k	NOUN
ejpam-6593	689	9	,	,	PUNCT
ejpam-6593	689	10	x	x	X
ejpam-6593	689	11	,	,	PUNCT
ejpam-6593	689	12	y	y	PROPN
ejpam-6593	689	13	,	,	PUNCT
ejpam-6593	689	14	z	z	NOUN
ejpam-6593	689	15	)	)	PUNCT
ejpam-6593	689	16	3	3	NUM
ejpam-6593	689	17	4	4	NUM
ejpam-6593	689	18	3	3	NUM
ejpam-6593	689	19	+	+	NUM
ejpam-6593	689	20	13	13	NUM
ejpam-6593	689	21	=	=	SYM
ejpam-6593	689	22	42	42	NUM
ejpam-6593	689	23	(	(	PUNCT
ejpam-6593	689	24	3	3	NUM
ejpam-6593	689	25	,	,	PUNCT
ejpam-6593	689	26	2	2	NUM
ejpam-6593	689	27	,	,	PUNCT
ejpam-6593	689	28	1	1	NUM
ejpam-6593	689	29	,	,	PUNCT
ejpam-6593	689	30	1	1	NUM
ejpam-6593	689	31	,	,	PUNCT
ejpam-6593	689	32	4	4	NUM
ejpam-6593	689	33	)	)	PUNCT
ejpam-6593	689	34	1	1	NUM
ejpam-6593	689	35	13	13	NUM
ejpam-6593	689	36	6	6	NUM
ejpam-6593	689	37	13	13	NUM
ejpam-6593	689	38	+	+	CCONJ
ejpam-6593	689	39	23	23	NUM
ejpam-6593	689	40	=	=	SYM
ejpam-6593	689	41	62	62	NUM
ejpam-6593	689	42	(	(	PUNCT
ejpam-6593	689	43	13	13	NUM
ejpam-6593	689	44	,	,	PUNCT
ejpam-6593	689	45	2	2	NUM
ejpam-6593	689	46	,	,	PUNCT
ejpam-6593	689	47	1	1	NUM
ejpam-6593	689	48	,	,	PUNCT
ejpam-6593	689	49	1	1	NUM
ejpam-6593	689	50	,	,	PUNCT
ejpam-6593	689	51	6	6	NUM
ejpam-6593	689	52	)	)	PUNCT
ejpam-6593	689	53	7	7	NUM
ejpam-6593	689	54	157	157	NUM
ejpam-6593	689	55	18	18	NUM
ejpam-6593	689	56	157	157	NUM
ejpam-6593	689	57	+	+	CCONJ
ejpam-6593	689	58	167	167	NUM
ejpam-6593	689	59	=	=	SYM
ejpam-6593	689	60	182	182	NUM
ejpam-6593	689	61	(	(	PUNCT
ejpam-6593	689	62	157	157	NUM
ejpam-6593	689	63	,	,	PUNCT
ejpam-6593	689	64	2	2	NUM
ejpam-6593	689	65	,	,	PUNCT
ejpam-6593	689	66	1	1	NUM
ejpam-6593	689	67	,	,	PUNCT
ejpam-6593	689	68	1	1	NUM
ejpam-6593	689	69	,	,	PUNCT
ejpam-6593	689	70	18	18	NUM
ejpam-6593	689	71	)	)	PUNCT
ejpam-6593	689	72	10	10	NUM
ejpam-6593	689	73	283	283	NUM
ejpam-6593	689	74	24	24	NUM
ejpam-6593	689	75	283	283	NUM
ejpam-6593	689	76	+	+	CCONJ
ejpam-6593	689	77	293	293	NUM
ejpam-6593	689	78	=	=	SYM
ejpam-6593	689	79	242	242	NUM
ejpam-6593	689	80	(	(	PUNCT
ejpam-6593	689	81	283	283	NUM
ejpam-6593	689	82	,	,	PUNCT
ejpam-6593	689	83	2	2	NUM
ejpam-6593	689	84	,	,	PUNCT
ejpam-6593	689	85	1	1	NUM
ejpam-6593	689	86	,	,	PUNCT
ejpam-6593	689	87	1	1	NUM
ejpam-6593	689	88	,	,	PUNCT
ejpam-6593	689	89	24	24	NUM
ejpam-6593	689	90	)	)	PUNCT
ejpam-6593	689	91	16	16	NUM
ejpam-6593	689	92	643	643	NUM
ejpam-6593	689	93	36	36	NUM
ejpam-6593	689	94	643	643	NUM
ejpam-6593	689	95	+	+	CCONJ
ejpam-6593	689	96	653	653	NUM
ejpam-6593	689	97	=	=	SYM
ejpam-6593	689	98	362	362	NUM
ejpam-6593	689	99	(	(	PUNCT
ejpam-6593	689	100	643	643	NUM
ejpam-6593	689	101	,	,	PUNCT
ejpam-6593	689	102	2	2	NUM
ejpam-6593	689	103	,	,	PUNCT
ejpam-6593	689	104	1	1	NUM
ejpam-6593	689	105	,	,	PUNCT
ejpam-6593	689	106	1	1	NUM
ejpam-6593	689	107	,	,	PUNCT
ejpam-6593	689	108	36	36	NUM
ejpam-6593	689	109	)	)	PUNCT
ejpam-6593	689	110	table	table	NOUN
ejpam-6593	689	111	21	21	NUM
ejpam-6593	689	112	:	:	PUNCT
ejpam-6593	689	113	some	some	DET
ejpam-6593	689	114	solutions	solution	NOUN
ejpam-6593	689	115	of	of	ADP
ejpam-6593	689	116	(	(	PUNCT
ejpam-6593	689	117	15	15	NUM
ejpam-6593	689	118	)	)	PUNCT
ejpam-6593	689	119	with	with	ADP
ejpam-6593	689	120	k	k	PROPN
ejpam-6593	689	121	=	=	SYM
ejpam-6593	689	122	2	2	NUM
ejpam-6593	689	123	,	,	PUNCT
ejpam-6593	689	124	x	x	SYM
ejpam-6593	689	125	=	=	SYM
ejpam-6593	689	126	1	1	NUM
ejpam-6593	689	127	,	,	PUNCT
ejpam-6593	689	128	y	y	NOUN
ejpam-6593	689	129	=	=	SYM
ejpam-6593	689	130	1	1	NUM
ejpam-6593	689	131	and	and	CCONJ
ejpam-6593	689	132	z	z	NOUN
ejpam-6593	689	133	is	be	AUX
ejpam-6593	689	134	even	even	ADV
ejpam-6593	689	135	m	m	PROPN
ejpam-6593	689	136	p	p	ADJ
ejpam-6593	689	137	z	z	NOUN
ejpam-6593	689	138	equation	equation	NOUN
ejpam-6593	689	139	solution	solution	NOUN
ejpam-6593	689	140	(	(	PUNCT
ejpam-6593	689	141	p	p	X
ejpam-6593	689	142	,	,	PUNCT
ejpam-6593	689	143	k	k	NOUN
ejpam-6593	689	144	,	,	PUNCT
ejpam-6593	689	145	x	x	X
ejpam-6593	689	146	,	,	PUNCT
ejpam-6593	689	147	y	y	PROPN
ejpam-6593	689	148	,	,	PUNCT
ejpam-6593	689	149	z	z	NOUN
ejpam-6593	689	150	)	)	PUNCT
ejpam-6593	689	151	1	1	NUM
ejpam-6593	689	152	17	17	NUM
ejpam-6593	689	153	8	8	NUM
ejpam-6593	689	154	17	17	NUM
ejpam-6593	689	155	+	+	CCONJ
ejpam-6593	689	156	(	(	PUNCT
ejpam-6593	689	157	17	17	NUM
ejpam-6593	689	158	+	+	SYM
ejpam-6593	689	159	5(6	5(6	NUM
ejpam-6593	689	160	)	)	PUNCT
ejpam-6593	689	161	)	)	PUNCT
ejpam-6593	690	1	=	=	SYM
ejpam-6593	690	2	82	82	NUM
ejpam-6593	690	3	(	(	PUNCT
ejpam-6593	690	4	17	17	NUM
ejpam-6593	690	5	,	,	PUNCT
ejpam-6593	690	6	6	6	NUM
ejpam-6593	690	7	,	,	PUNCT
ejpam-6593	690	8	1	1	NUM
ejpam-6593	690	9	,	,	PUNCT
ejpam-6593	690	10	1	1	NUM
ejpam-6593	690	11	,	,	PUNCT
ejpam-6593	690	12	8)	8)	NUM
ejpam-6593	690	13	4	4	NUM
ejpam-6593	690	14	83	83	NUM
ejpam-6593	690	15	14	14	NUM
ejpam-6593	690	16	83	83	NUM
ejpam-6593	690	17	+	+	CCONJ
ejpam-6593	690	18	(	(	PUNCT
ejpam-6593	690	19	83	83	NUM
ejpam-6593	690	20	+	+	NUM
ejpam-6593	690	21	5(6	5(6	NUM
ejpam-6593	690	22	)	)	PUNCT
ejpam-6593	690	23	)	)	PUNCT
ejpam-6593	691	1	=	=	SYM
ejpam-6593	691	2	142	142	NUM
ejpam-6593	691	3	(	(	PUNCT
ejpam-6593	691	4	83	83	NUM
ejpam-6593	691	5	,	,	PUNCT
ejpam-6593	691	6	6	6	NUM
ejpam-6593	691	7	,	,	PUNCT
ejpam-6593	691	8	1	1	NUM
ejpam-6593	691	9	,	,	PUNCT
ejpam-6593	691	10	1	1	NUM
ejpam-6593	691	11	,	,	PUNCT
ejpam-6593	691	12	14	14	NUM
ejpam-6593	691	13	)	)	PUNCT
ejpam-6593	691	14	8	8	NUM
ejpam-6593	691	15	227	227	NUM
ejpam-6593	691	16	22	22	NUM
ejpam-6593	691	17	227	227	NUM
ejpam-6593	691	18	+	+	CCONJ
ejpam-6593	691	19	(	(	PUNCT
ejpam-6593	691	20	227	227	NUM
ejpam-6593	691	21	+	+	NUM
ejpam-6593	691	22	5(6	5(6	NUM
ejpam-6593	691	23	)	)	PUNCT
ejpam-6593	691	24	)	)	PUNCT
ejpam-6593	692	1	=	=	SYM
ejpam-6593	692	2	222	222	NUM
ejpam-6593	692	3	(	(	PUNCT
ejpam-6593	692	4	227	227	NUM
ejpam-6593	692	5	,	,	PUNCT
ejpam-6593	692	6	6	6	NUM
ejpam-6593	692	7	,	,	PUNCT
ejpam-6593	692	8	1	1	NUM
ejpam-6593	692	9	,	,	PUNCT
ejpam-6593	692	10	1	1	NUM
ejpam-6593	692	11	,	,	PUNCT
ejpam-6593	692	12	22	22	NUM
ejpam-6593	692	13	)	)	PUNCT
ejpam-6593	692	14	14	14	NUM
ejpam-6593	692	15	563	563	NUM
ejpam-6593	692	16	34	34	NUM
ejpam-6593	692	17	563	563	NUM
ejpam-6593	692	18	+	+	CCONJ
ejpam-6593	692	19	(	(	PUNCT
ejpam-6593	692	20	563	563	NUM
ejpam-6593	692	21	+	+	NUM
ejpam-6593	692	22	5(6	5(6	NUM
ejpam-6593	692	23	)	)	PUNCT
ejpam-6593	692	24	)	)	PUNCT
ejpam-6593	693	1	=	=	SYM
ejpam-6593	693	2	342	342	NUM
ejpam-6593	693	3	(	(	PUNCT
ejpam-6593	693	4	563	563	NUM
ejpam-6593	693	5	,	,	PUNCT
ejpam-6593	693	6	6	6	NUM
ejpam-6593	693	7	,	,	PUNCT
ejpam-6593	693	8	1	1	NUM
ejpam-6593	693	9	,	,	PUNCT
ejpam-6593	693	10	1	1	NUM
ejpam-6593	693	11	,	,	PUNCT
ejpam-6593	693	12	34	34	NUM
ejpam-6593	693	13	)	)	PUNCT
ejpam-6593	693	14	19	19	NUM
ejpam-6593	693	15	953	953	NUM
ejpam-6593	693	16	44	44	NUM
ejpam-6593	693	17	953	953	NUM
ejpam-6593	693	18	+	+	CCONJ
ejpam-6593	693	19	(	(	PUNCT
ejpam-6593	693	20	953	953	NUM
ejpam-6593	693	21	+	+	NUM
ejpam-6593	693	22	5(6	5(6	NUM
ejpam-6593	693	23	)	)	PUNCT
ejpam-6593	693	24	)	)	PUNCT
ejpam-6593	694	1	=	=	SYM
ejpam-6593	694	2	442	442	NUM
ejpam-6593	694	3	(	(	PUNCT
ejpam-6593	694	4	953	953	NUM
ejpam-6593	694	5	,	,	PUNCT
ejpam-6593	694	6	6	6	NUM
ejpam-6593	694	7	,	,	PUNCT
ejpam-6593	694	8	1	1	NUM
ejpam-6593	694	9	,	,	PUNCT
ejpam-6593	694	10	1	1	NUM
ejpam-6593	694	11	,	,	PUNCT
ejpam-6593	694	12	44	44	NUM
ejpam-6593	694	13	)	)	PUNCT
ejpam-6593	694	14	table	table	NOUN
ejpam-6593	694	15	22	22	NUM
ejpam-6593	694	16	:	:	PUNCT
ejpam-6593	694	17	some	some	DET
ejpam-6593	694	18	solutions	solution	NOUN
ejpam-6593	694	19	of	of	ADP
ejpam-6593	694	20	(	(	PUNCT
ejpam-6593	694	21	15	15	NUM
ejpam-6593	694	22	)	)	PUNCT
ejpam-6593	694	23	with	with	ADP
ejpam-6593	694	24	k	k	PROPN
ejpam-6593	694	25	=	=	SYM
ejpam-6593	694	26	6	6	NUM
ejpam-6593	694	27	,	,	PUNCT
ejpam-6593	694	28	x	x	SYM
ejpam-6593	694	29	=	=	SYM
ejpam-6593	694	30	1	1	NUM
ejpam-6593	694	31	,	,	PUNCT
ejpam-6593	694	32	y	y	NOUN
ejpam-6593	694	33	=	=	SYM
ejpam-6593	694	34	1	1	NUM
ejpam-6593	694	35	and	and	CCONJ
ejpam-6593	694	36	z	z	NOUN
ejpam-6593	694	37	is	be	AUX
ejpam-6593	694	38	even	even	ADV
ejpam-6593	694	39	for	for	ADP
ejpam-6593	694	40	the	the	DET
ejpam-6593	694	41	next	next	ADJ
ejpam-6593	694	42	theorem	theorem	NOUN
ejpam-6593	694	43	,	,	PUNCT
ejpam-6593	694	44	we	we	PRON
ejpam-6593	694	45	discuss	discuss	VERB
ejpam-6593	694	46	the	the	DET
ejpam-6593	694	47	case	case	NOUN
ejpam-6593	694	48	when	when	SCONJ
ejpam-6593	694	49	k	k	PROPN
ejpam-6593	694	50	is	be	AUX
ejpam-6593	694	51	even	even	ADV
ejpam-6593	694	52	and	and	CCONJ
ejpam-6593	694	53	exactly	exactly	ADV
ejpam-6593	694	54	either	either	CCONJ
ejpam-6593	694	55	x	x	SYM
ejpam-6593	694	56	or	or	CCONJ
ejpam-6593	694	57	y	y	PROPN
ejpam-6593	694	58	is	be	AUX
ejpam-6593	694	59	zero	zero	NUM
ejpam-6593	694	60	.	.	PUNCT
ejpam-6593	695	1	the	the	DET
ejpam-6593	695	2	case	case	NOUN
ejpam-6593	695	3	when	when	SCONJ
ejpam-6593	695	4	both	both	DET
ejpam-6593	695	5	x	x	X
ejpam-6593	695	6	and	and	CCONJ
ejpam-6593	695	7	y	y	PROPN
ejpam-6593	695	8	are	be	AUX
ejpam-6593	695	9	zero	zero	NUM
ejpam-6593	695	10	are	be	AUX
ejpam-6593	695	11	impossible	impossible	ADJ
ejpam-6593	695	12	since	since	SCONJ
ejpam-6593	695	13	2	2	NUM
ejpam-6593	695	14	is	be	AUX
ejpam-6593	695	15	not	not	PART
ejpam-6593	695	16	a	a	DET
ejpam-6593	695	17	perfect	perfect	ADJ
ejpam-6593	695	18	square	square	NOUN
ejpam-6593	695	19	.	.	PUNCT
ejpam-6593	696	1	theorem	theorem	ADJ
ejpam-6593	696	2	8	8	NUM
ejpam-6593	696	3	.	.	PUNCT
ejpam-6593	697	1	consider	consider	VERB
ejpam-6593	697	2	the	the	DET
ejpam-6593	697	3	diophantine	diophantine	NOUN
ejpam-6593	697	4	equation	equation	NOUN
ejpam-6593	697	5	(	(	PUNCT
ejpam-6593	697	6	3	3	NUM
ejpam-6593	697	7	)	)	PUNCT
ejpam-6593	698	1	where	where	SCONJ
ejpam-6593	698	2	p	p	PRON
ejpam-6593	698	3	≥	≥	PUNCT
ejpam-6593	698	4	3	3	NUM
ejpam-6593	698	5	and	and	CCONJ
ejpam-6593	698	6	p	p	PRON
ejpam-6593	698	7	+	+	NOUN
ejpam-6593	698	8	5k	5k	NUM
ejpam-6593	698	9	are	be	AUX
ejpam-6593	698	10	prime	prime	ADJ
ejpam-6593	698	11	pairs	pair	NOUN
ejpam-6593	698	12	,	,	PUNCT
ejpam-6593	698	13	and	and	CCONJ
ejpam-6593	698	14	k	k	PROPN
ejpam-6593	698	15	is	be	AUX
ejpam-6593	698	16	a	a	DET
ejpam-6593	698	17	positive	positive	ADJ
ejpam-6593	698	18	even	even	ADJ
ejpam-6593	698	19	number	number	NOUN
ejpam-6593	698	20	.	.	PUNCT
ejpam-6593	699	1	let	let	VERB
ejpam-6593	699	2	x	x	SYM
ejpam-6593	699	3	=	=	SYM
ejpam-6593	699	4	0	0	NUM
ejpam-6593	699	5	or	or	CCONJ
ejpam-6593	699	6	y	y	PROPN
ejpam-6593	699	7	=	=	SYM
ejpam-6593	699	8	0	0	PROPN
ejpam-6593	699	9	.	.	PUNCT
ejpam-6593	700	1	then	then	ADV
ejpam-6593	700	2	,	,	PUNCT
ejpam-6593	700	3	(	(	PUNCT
ejpam-6593	700	4	p	p	X
ejpam-6593	700	5	,	,	PUNCT
ejpam-6593	700	6	k	k	NOUN
ejpam-6593	700	7	,	,	PUNCT
ejpam-6593	700	8	x	x	X
ejpam-6593	700	9	,	,	PUNCT
ejpam-6593	700	10	y	y	PROPN
ejpam-6593	700	11	,	,	PUNCT
ejpam-6593	700	12	z	z	NOUN
ejpam-6593	700	13	)	)	PUNCT
ejpam-6593	700	14	=	=	SYM
ejpam-6593	700	15	(	(	PUNCT
ejpam-6593	700	16	3	3	NUM
ejpam-6593	700	17	,	,	PUNCT
ejpam-6593	700	18	k	k	NOUN
ejpam-6593	700	19	,	,	PUNCT
ejpam-6593	700	20	1	1	NUM
ejpam-6593	700	21	,	,	PUNCT
ejpam-6593	700	22	0	0	NUM
ejpam-6593	700	23	,	,	PUNCT
ejpam-6593	700	24	2	2	NUM
ejpam-6593	700	25	)	)	PUNCT
ejpam-6593	700	26	for	for	ADP
ejpam-6593	700	27	some	some	DET
ejpam-6593	700	28	even	even	ADV
ejpam-6593	700	29	k	k	PROPN
ejpam-6593	700	30	∈	∈	PROPN
ejpam-6593	700	31	n	n	PRON
ejpam-6593	700	32	is	be	AUX
ejpam-6593	700	33	the	the	DET
ejpam-6593	700	34	only	only	ADJ
ejpam-6593	700	35	solution	solution	NOUN
ejpam-6593	700	36	of	of	ADP
ejpam-6593	700	37	the	the	DET
ejpam-6593	700	38	equation	equation	NOUN
ejpam-6593	700	39	.	.	PUNCT
ejpam-6593	701	1	proof	proof	NOUN
ejpam-6593	701	2	.	.	PUNCT
ejpam-6593	702	1	consider	consider	VERB
ejpam-6593	702	2	the	the	DET
ejpam-6593	702	3	equation	equation	NOUN
ejpam-6593	702	4	(	(	PUNCT
ejpam-6593	702	5	3	3	NUM
ejpam-6593	702	6	)	)	PUNCT
ejpam-6593	702	7	.	.	PUNCT
ejpam-6593	703	1	let	let	VERB
ejpam-6593	703	2	p	p	PRON
ejpam-6593	703	3	≥	≥	NOUN
ejpam-6593	703	4	3	3	NUM
ejpam-6593	703	5	and	and	CCONJ
ejpam-6593	703	6	q	q	NOUN
ejpam-6593	703	7	=	=	X
ejpam-6593	703	8	p+	p+	ADJ
ejpam-6593	703	9	5k	5k	NOUN
ejpam-6593	703	10	be	be	AUX
ejpam-6593	703	11	prime	prime	ADJ
ejpam-6593	703	12	pairs	pair	NOUN
ejpam-6593	703	13	,	,	PUNCT
ejpam-6593	703	14	k	k	PROPN
ejpam-6593	703	15	is	be	AUX
ejpam-6593	703	16	even	even	ADV
ejpam-6593	703	17	,	,	PUNCT
ejpam-6593	703	18	and	and	CCONJ
ejpam-6593	703	19	x	x	X
ejpam-6593	703	20	=	=	SYM
ejpam-6593	703	21	0	0	NUM
ejpam-6593	703	22	or	or	CCONJ
ejpam-6593	703	23	y	y	PROPN
ejpam-6593	703	24	=	=	SYM
ejpam-6593	703	25	0	0	PROPN
ejpam-6593	703	26	.	.	PUNCT
ejpam-6593	704	1	case	case	NOUN
ejpam-6593	704	2	1	1	X
ejpam-6593	704	3	.	.	PUNCT
ejpam-6593	705	1	let	let	VERB
ejpam-6593	705	2	x	x	SYM
ejpam-6593	705	3	=	=	SYM
ejpam-6593	705	4	0	0	X
ejpam-6593	705	5	.	.	PUNCT
ejpam-6593	706	1	then	then	ADV
ejpam-6593	706	2	,	,	PUNCT
ejpam-6593	706	3	we	we	PRON
ejpam-6593	706	4	have	have	VERB
ejpam-6593	706	5	1	1	NUM
ejpam-6593	706	6	+	+	NUM
ejpam-6593	706	7	(	(	PUNCT
ejpam-6593	706	8	p+	p+	PROPN
ejpam-6593	706	9	5k)y	5k)y	NOUN
ejpam-6593	706	10	=	=	SYM
ejpam-6593	706	11	z2	z2	PROPN
ejpam-6593	706	12	.	.	PUNCT
ejpam-6593	707	1	if	if	SCONJ
ejpam-6593	707	2	y	y	PROPN
ejpam-6593	707	3	>	>	X
ejpam-6593	707	4	1	1	NUM
ejpam-6593	707	5	,	,	PUNCT
ejpam-6593	707	6	then	then	ADV
ejpam-6593	707	7	by	by	ADP
ejpam-6593	707	8	mihailescu	mihailescu	PROPN
ejpam-6593	707	9	’s	’s	PART
ejpam-6593	707	10	theorem	theorem	NOUN
ejpam-6593	707	11	,	,	PUNCT
ejpam-6593	707	12	this	this	DET
ejpam-6593	707	13	equation	equation	NOUN
ejpam-6593	707	14	will	will	AUX
ejpam-6593	707	15	only	only	ADV
ejpam-6593	707	16	have	have	VERB
ejpam-6593	707	17	a	a	DET
ejpam-6593	707	18	solution	solution	NOUN
ejpam-6593	707	19	when	when	SCONJ
ejpam-6593	707	20	z	z	NOUN
ejpam-6593	707	21	=	=	SYM
ejpam-6593	707	22	3	3	NUM
ejpam-6593	707	23	and	and	CCONJ
ejpam-6593	707	24	p	p	NOUN
ejpam-6593	707	25	+	+	NOUN
ejpam-6593	707	26	5k	5k	NUM
ejpam-6593	707	27	=	=	SYM
ejpam-6593	707	28	2	2	NUM
ejpam-6593	707	29	,	,	PUNCT
ejpam-6593	707	30	which	which	PRON
ejpam-6593	707	31	is	be	AUX
ejpam-6593	707	32	absurd	absurd	ADJ
ejpam-6593	707	33	since	since	SCONJ
ejpam-6593	707	34	p	p	X
ejpam-6593	707	35	≥	≥	NUM
ejpam-6593	707	36	3	3	NUM
ejpam-6593	707	37	.	.	PUNCT
ejpam-6593	708	1	if	if	SCONJ
ejpam-6593	708	2	y	y	PROPN
ejpam-6593	708	3	=	=	SYM
ejpam-6593	708	4	1	1	NUM
ejpam-6593	708	5	,	,	PUNCT
ejpam-6593	708	6	then	then	ADV
ejpam-6593	708	7	the	the	DET
ejpam-6593	708	8	equation	equation	NOUN
ejpam-6593	708	9	reduces	reduce	VERB
ejpam-6593	708	10	to	to	ADP
ejpam-6593	708	11	1	1	NUM
ejpam-6593	708	12	+	+	CCONJ
ejpam-6593	708	13	p	p	NOUN
ejpam-6593	708	14	+	+	NUM
ejpam-6593	708	15	5k	5k	NUM
ejpam-6593	708	16	=	=	SYM
ejpam-6593	708	17	z2	z2	PROPN
ejpam-6593	708	18	.	.	PUNCT
ejpam-6593	709	1	we	we	PRON
ejpam-6593	709	2	first	first	ADV
ejpam-6593	709	3	claim	claim	VERB
ejpam-6593	709	4	that	that	SCONJ
ejpam-6593	709	5	the	the	DET
ejpam-6593	709	6	only	only	ADJ
ejpam-6593	709	7	solution	solution	NOUN
ejpam-6593	709	8	to	to	ADP
ejpam-6593	709	9	the	the	DET
ejpam-6593	709	10	equation	equation	NOUN
ejpam-6593	709	11	1	1	NUM
ejpam-6593	709	12	+	+	CCONJ
ejpam-6593	709	13	q	q	NOUN
ejpam-6593	709	14	=	=	SYM
ejpam-6593	709	15	z2	z2	PROPN
ejpam-6593	709	16	,	,	PUNCT
ejpam-6593	709	17	where	where	SCONJ
ejpam-6593	709	18	q	q	NOUN
ejpam-6593	709	19	is	be	AUX
ejpam-6593	709	20	a	a	DET
ejpam-6593	709	21	prime	prime	ADJ
ejpam-6593	709	22	number	number	NOUN
ejpam-6593	709	23	,	,	PUNCT
ejpam-6593	709	24	is	be	AUX
ejpam-6593	709	25	(	(	PUNCT
ejpam-6593	709	26	q	q	ADJ
ejpam-6593	709	27	,	,	PUNCT
ejpam-6593	709	28	z	z	NOUN
ejpam-6593	709	29	)	)	PUNCT
ejpam-6593	709	30	=	=	SYM
ejpam-6593	709	31	(	(	PUNCT
ejpam-6593	709	32	3	3	NUM
ejpam-6593	709	33	,	,	PUNCT
ejpam-6593	709	34	2	2	NUM
ejpam-6593	709	35	)	)	PUNCT
ejpam-6593	709	36	.	.	PUNCT
ejpam-6593	710	1	indeed	indeed	ADV
ejpam-6593	710	2	,	,	PUNCT
ejpam-6593	710	3	rewriting	rewrite	VERB
ejpam-6593	710	4	the	the	DET
ejpam-6593	710	5	equation	equation	NOUN
ejpam-6593	710	6	gives	give	VERB
ejpam-6593	710	7	q	q	PROPN
ejpam-6593	710	8	=	=	PUNCT
ejpam-6593	710	9	z2−1	z2−1	NOUN
ejpam-6593	710	10	=	=	SYM
ejpam-6593	710	11	(	(	PUNCT
ejpam-6593	710	12	z−1)(z+1	z−1)(z+1	NOUN
ejpam-6593	710	13	)	)	PUNCT
ejpam-6593	710	14	.	.	PUNCT
ejpam-6593	711	1	since	since	SCONJ
ejpam-6593	711	2	z−1	z−1	PROPN
ejpam-6593	711	3	and	and	CCONJ
ejpam-6593	711	4	z+1	z+1	NUM
ejpam-6593	711	5	are	be	AUX
ejpam-6593	711	6	consecutive	consecutive	ADJ
ejpam-6593	711	7	even	even	ADV
ejpam-6593	711	8	integers	integer	NOUN
ejpam-6593	711	9	,	,	PUNCT
ejpam-6593	711	10	their	their	PRON
ejpam-6593	711	11	product	product	NOUN
ejpam-6593	711	12	is	be	AUX
ejpam-6593	711	13	greater	great	ADJ
ejpam-6593	711	14	than	than	ADP
ejpam-6593	711	15	1	1	NUM
ejpam-6593	711	16	for	for	ADP
ejpam-6593	711	17	all	all	DET
ejpam-6593	711	18	z	z	NOUN
ejpam-6593	711	19	>	>	X
ejpam-6593	711	20	2	2	NUM
ejpam-6593	711	21	,	,	PUNCT
ejpam-6593	711	22	making	make	VERB
ejpam-6593	711	23	q	q	NOUN
ejpam-6593	711	24	composite	composite	NOUN
ejpam-6593	711	25	in	in	ADP
ejpam-6593	711	26	those	those	DET
ejpam-6593	711	27	cases	case	NOUN
ejpam-6593	711	28	.	.	PUNCT
ejpam-6593	712	1	hence	hence	ADV
ejpam-6593	712	2	,	,	PUNCT
ejpam-6593	712	3	the	the	DET
ejpam-6593	712	4	only	only	ADJ
ejpam-6593	712	5	valid	valid	ADJ
ejpam-6593	712	6	solution	solution	NOUN
ejpam-6593	712	7	occurs	occur	VERB
ejpam-6593	712	8	when	when	SCONJ
ejpam-6593	712	9	z	z	NOUN
ejpam-6593	712	10	=	=	SYM
ejpam-6593	712	11	2	2	NUM
ejpam-6593	712	12	,	,	PUNCT
ejpam-6593	712	13	which	which	PRON
ejpam-6593	712	14	gives	give	VERB
ejpam-6593	712	15	q	q	PROPN
ejpam-6593	713	1	=	=	SYM
ejpam-6593	714	1	3	3	X
ejpam-6593	714	2	.	.	PUNCT
ejpam-6593	714	3	returning	return	VERB
ejpam-6593	714	4	to	to	ADP
ejpam-6593	714	5	the	the	DET
ejpam-6593	714	6	original	original	ADJ
ejpam-6593	714	7	equation	equation	NOUN
ejpam-6593	714	8	,	,	PUNCT
ejpam-6593	714	9	this	this	PRON
ejpam-6593	714	10	implies	imply	VERB
ejpam-6593	714	11	that	that	SCONJ
ejpam-6593	715	1	p	p	PROPN
ejpam-6593	715	2	+	+	NUM
ejpam-6593	715	3	5k	5k	NUM
ejpam-6593	715	4	=	=	SYM
ejpam-6593	715	5	3	3	X
ejpam-6593	715	6	.	.	PUNCT
ejpam-6593	716	1	however	however	ADV
ejpam-6593	716	2	,	,	PUNCT
ejpam-6593	716	3	since	since	SCONJ
ejpam-6593	716	4	k	k	PROPN
ejpam-6593	716	5	is	be	AUX
ejpam-6593	716	6	assumed	assume	VERB
ejpam-6593	716	7	to	to	PART
ejpam-6593	716	8	be	be	AUX
ejpam-6593	716	9	a	a	DET
ejpam-6593	716	10	positive	positive	ADJ
ejpam-6593	716	11	integer	integer	NOUN
ejpam-6593	716	12	,	,	PUNCT
ejpam-6593	716	13	the	the	DET
ejpam-6593	716	14	left	left	ADJ
ejpam-6593	716	15	-	-	PUNCT
ejpam-6593	716	16	hand	hand	NOUN
ejpam-6593	716	17	side	side	NOUN
ejpam-6593	716	18	p	p	NOUN
ejpam-6593	717	1	+	+	NUM
ejpam-6593	717	2	5k	5k	NUM
ejpam-6593	717	3	>	>	X
ejpam-6593	717	4	3	3	NUM
ejpam-6593	717	5	,	,	PUNCT
ejpam-6593	717	6	and	and	CCONJ
ejpam-6593	717	7	thus	thus	ADV
ejpam-6593	717	8	no	no	DET
ejpam-6593	717	9	prime	prime	ADJ
ejpam-6593	717	10	value	value	NOUN
ejpam-6593	717	11	of	of	ADP
ejpam-6593	717	12	p	p	NOUN
ejpam-6593	717	13	satisfies	satisfie	NOUN
ejpam-6593	717	14	the	the	DET
ejpam-6593	717	15	equation	equation	NOUN
ejpam-6593	717	16	.	.	PUNCT
ejpam-6593	718	1	therefore	therefore	ADV
ejpam-6593	718	2	,	,	PUNCT
ejpam-6593	718	3	there	there	PRON
ejpam-6593	718	4	is	be	VERB
ejpam-6593	718	5	no	no	DET
ejpam-6593	718	6	solution	solution	NOUN
ejpam-6593	718	7	with	with	ADP
ejpam-6593	718	8	p	p	PROPN
ejpam-6593	718	9	prime	prime	NOUN
ejpam-6593	718	10	and	and	CCONJ
ejpam-6593	719	1	y	y	NOUN
ejpam-6593	719	2	=	=	SYM
ejpam-6593	719	3	1	1	X
ejpam-6593	719	4	.	.	PUNCT
ejpam-6593	719	5	case	case	NOUN
ejpam-6593	719	6	2	2	X
ejpam-6593	719	7	.	.	PUNCT
ejpam-6593	720	1	let	let	VERB
ejpam-6593	720	2	y	y	PROPN
ejpam-6593	720	3	=	=	SYM
ejpam-6593	720	4	0	0	PROPN
ejpam-6593	720	5	.	.	PUNCT
ejpam-6593	721	1	then	then	ADV
ejpam-6593	721	2	,	,	PUNCT
ejpam-6593	721	3	(	(	PUNCT
ejpam-6593	721	4	p	p	NOUN
ejpam-6593	721	5	+	+	NOUN
ejpam-6593	721	6	5k)y	5k)y	NUM
ejpam-6593	721	7	=	=	SYM
ejpam-6593	721	8	1	1	NUM
ejpam-6593	721	9	for	for	ADP
ejpam-6593	721	10	all	all	DET
ejpam-6593	721	11	even	even	ADV
ejpam-6593	721	12	k.	k.	PROPN
ejpam-6593	721	13	from	from	ADP
ejpam-6593	721	14	that	that	PRON
ejpam-6593	721	15	,	,	PUNCT
ejpam-6593	721	16	we	we	PRON
ejpam-6593	721	17	have	have	VERB
ejpam-6593	721	18	px	px	NOUN
ejpam-6593	721	19	=	=	PROPN
ejpam-6593	721	20	z2	z2	PROPN
ejpam-6593	721	21	−	−	PROPN
ejpam-6593	721	22	1	1	NUM
ejpam-6593	721	23	=	=	SYM
ejpam-6593	721	24	(	(	PUNCT
ejpam-6593	721	25	z	z	NOUN
ejpam-6593	721	26	+	+	NOUN
ejpam-6593	721	27	1)(z	1)(z	NUM
ejpam-6593	721	28	−	−	NOUN
ejpam-6593	721	29	1	1	NUM
ejpam-6593	721	30	)	)	PUNCT
ejpam-6593	721	31	.	.	PUNCT
ejpam-6593	722	1	it	it	PRON
ejpam-6593	722	2	follows	follow	VERB
ejpam-6593	722	3	that	that	DET
ejpam-6593	722	4	gcd	gcd	NOUN
ejpam-6593	722	5	(	(	PUNCT
ejpam-6593	722	6	z	z	NOUN
ejpam-6593	722	7	+	+	NOUN
ejpam-6593	722	8	1	1	NUM
ejpam-6593	722	9	,	,	PUNCT
ejpam-6593	722	10	z	z	NOUN
ejpam-6593	722	11	−	−	NOUN
ejpam-6593	722	12	1	1	NUM
ejpam-6593	722	13	)	)	PUNCT
ejpam-6593	722	14	=	=	SYM
ejpam-6593	722	15	1	1	NUM
ejpam-6593	722	16	,	,	PUNCT
ejpam-6593	722	17	which	which	PRON
ejpam-6593	722	18	further	far	ADV
ejpam-6593	722	19	implies	imply	VERB
ejpam-6593	722	20	m.	m.	PROPN
ejpam-6593	722	21	c.	c.	PROPN
ejpam-6593	722	22	avenilla	avenilla	PROPN
ejpam-6593	722	23	,	,	PUNCT
ejpam-6593	722	24	j.	j.	PROPN
ejpam-6593	722	25	b.	b.	PROPN
ejpam-6593	722	26	bacani	bacani	PROPN
ejpam-6593	722	27	/	/	SYM
ejpam-6593	722	28	eur	eur	PROPN
ejpam-6593	722	29	.	.	PUNCT
ejpam-6593	723	1	j.	j.	PROPN
ejpam-6593	723	2	pure	pure	PROPN
ejpam-6593	723	3	appl	appl	PROPN
ejpam-6593	723	4	.	.	PROPN
ejpam-6593	723	5	math	math	PROPN
ejpam-6593	723	6	,	,	PUNCT
ejpam-6593	723	7	18	18	NUM
ejpam-6593	723	8	(	(	PUNCT
ejpam-6593	723	9	3	3	NUM
ejpam-6593	723	10	)	)	PUNCT
ejpam-6593	723	11	(	(	PUNCT
ejpam-6593	723	12	2025	2025	NUM
ejpam-6593	723	13	)	)	PUNCT
ejpam-6593	723	14	,	,	PUNCT
ejpam-6593	723	15	6593	6593	NUM
ejpam-6593	723	16	22	22	NUM
ejpam-6593	723	17	of	of	ADP
ejpam-6593	723	18	24	24	NUM
ejpam-6593	723	19	that	that	SCONJ
ejpam-6593	723	20	z−1	z−1	NUM
ejpam-6593	723	21	=	=	SYM
ejpam-6593	723	22	1	1	NUM
ejpam-6593	723	23	and	and	CCONJ
ejpam-6593	723	24	z+1	z+1	NUM
ejpam-6593	723	25	=	=	SYM
ejpam-6593	724	1	px	px	AUX
ejpam-6593	724	2	.	.	PROPN
ejpam-6593	724	3	from	from	ADP
ejpam-6593	724	4	z−1	z−1	PROPN
ejpam-6593	724	5	=	=	SYM
ejpam-6593	724	6	1	1	NUM
ejpam-6593	724	7	,	,	PUNCT
ejpam-6593	724	8	we	we	PRON
ejpam-6593	724	9	obtain	obtain	VERB
ejpam-6593	724	10	z	z	NOUN
ejpam-6593	724	11	=	=	SYM
ejpam-6593	724	12	2	2	NUM
ejpam-6593	724	13	.	.	PUNCT
ejpam-6593	725	1	therefore	therefore	ADV
ejpam-6593	725	2	,	,	PUNCT
ejpam-6593	725	3	z+1	z+1	PROPN
ejpam-6593	725	4	=	=	SYM
ejpam-6593	725	5	3	3	NUM
ejpam-6593	725	6	=	=	SYM
ejpam-6593	725	7	px	px	PROPN
ejpam-6593	725	8	,	,	PUNCT
ejpam-6593	725	9	which	which	PRON
ejpam-6593	725	10	implies	imply	VERB
ejpam-6593	725	11	that	that	SCONJ
ejpam-6593	725	12	p	p	X
ejpam-6593	725	13	=	=	NOUN
ejpam-6593	725	14	3	3	NUM
ejpam-6593	725	15	and	and	CCONJ
ejpam-6593	725	16	x	x	SYM
ejpam-6593	726	1	=	=	SYM
ejpam-6593	726	2	1	1	X
ejpam-6593	726	3	.	.	PUNCT
ejpam-6593	727	1	therefore	therefore	ADV
ejpam-6593	727	2	,	,	PUNCT
ejpam-6593	727	3	(	(	PUNCT
ejpam-6593	727	4	p	p	X
ejpam-6593	727	5	,	,	PUNCT
ejpam-6593	727	6	k	k	NOUN
ejpam-6593	727	7	,	,	PUNCT
ejpam-6593	727	8	x	x	X
ejpam-6593	727	9	,	,	PUNCT
ejpam-6593	727	10	y	y	PROPN
ejpam-6593	727	11	,	,	PUNCT
ejpam-6593	727	12	z	z	NOUN
ejpam-6593	727	13	)	)	PUNCT
ejpam-6593	727	14	=	=	SYM
ejpam-6593	727	15	(	(	PUNCT
ejpam-6593	727	16	3	3	NUM
ejpam-6593	727	17	,	,	PUNCT
ejpam-6593	727	18	k	k	NOUN
ejpam-6593	727	19	,	,	PUNCT
ejpam-6593	727	20	1	1	NUM
ejpam-6593	727	21	,	,	PUNCT
ejpam-6593	727	22	0	0	NUM
ejpam-6593	727	23	,	,	PUNCT
ejpam-6593	727	24	2	2	NUM
ejpam-6593	727	25	)	)	PUNCT
ejpam-6593	727	26	is	be	AUX
ejpam-6593	727	27	the	the	DET
ejpam-6593	727	28	only	only	ADJ
ejpam-6593	727	29	solution	solution	NOUN
ejpam-6593	727	30	of	of	ADP
ejpam-6593	727	31	px	px	PROPN
ejpam-6593	727	32	+	+	CCONJ
ejpam-6593	727	33	(	(	PUNCT
ejpam-6593	727	34	p	p	X
ejpam-6593	727	35	+	+	NUM
ejpam-6593	727	36	5k)y	5k)y	NOUN
ejpam-6593	727	37	=	=	SYM
ejpam-6593	727	38	z2	z2	PROPN
ejpam-6593	727	39	for	for	ADP
ejpam-6593	727	40	even	even	ADV
ejpam-6593	727	41	k	k	NOUN
ejpam-6593	727	42	,	,	PUNCT
ejpam-6593	727	43	where	where	SCONJ
ejpam-6593	727	44	p	p	PROPN
ejpam-6593	727	45	≥	≥	PUNCT
ejpam-6593	727	46	3	3	NUM
ejpam-6593	727	47	and	and	CCONJ
ejpam-6593	727	48	p+	p+	PROPN
ejpam-6593	727	49	5k	5k	NUM
ejpam-6593	727	50	are	be	AUX
ejpam-6593	727	51	prime	prime	ADJ
ejpam-6593	727	52	pairs	pair	NOUN
ejpam-6593	727	53	,	,	PUNCT
ejpam-6593	727	54	and	and	CCONJ
ejpam-6593	727	55	x	x	X
ejpam-6593	727	56	=	=	SYM
ejpam-6593	727	57	0	0	NUM
ejpam-6593	727	58	or	or	CCONJ
ejpam-6593	727	59	y	y	PROPN
ejpam-6593	727	60	=	=	SYM
ejpam-6593	727	61	0	0	PROPN
ejpam-6593	727	62	.	.	PUNCT
ejpam-6593	728	1	the	the	DET
ejpam-6593	728	2	following	following	ADJ
ejpam-6593	728	3	result	result	NOUN
ejpam-6593	728	4	is	be	AUX
ejpam-6593	728	5	obtained	obtain	VERB
ejpam-6593	728	6	when	when	SCONJ
ejpam-6593	728	7	k	k	PROPN
ejpam-6593	728	8	≡	≡	PROPN
ejpam-6593	728	9	0	0	PUNCT
ejpam-6593	728	10	(	(	PUNCT
ejpam-6593	728	11	mod	mod	PROPN
ejpam-6593	728	12	4	4	NUM
ejpam-6593	728	13	)	)	PUNCT
ejpam-6593	728	14	.	.	PUNCT
ejpam-6593	729	1	theorem	theorem	VERB
ejpam-6593	729	2	9	9	NUM
ejpam-6593	729	3	.	.	PUNCT
ejpam-6593	730	1	the	the	DET
ejpam-6593	730	2	diophantine	diophantine	NOUN
ejpam-6593	730	3	equation	equation	NOUN
ejpam-6593	730	4	(	(	PUNCT
ejpam-6593	730	5	3	3	NUM
ejpam-6593	730	6	)	)	PUNCT
ejpam-6593	730	7	,	,	PUNCT
ejpam-6593	730	8	where	where	SCONJ
ejpam-6593	730	9	p	p	PROPN
ejpam-6593	730	10	≥	≥	PUNCT
ejpam-6593	730	11	3	3	NUM
ejpam-6593	730	12	and	and	CCONJ
ejpam-6593	730	13	p+5k	p+5k	PROPN
ejpam-6593	730	14	are	be	AUX
ejpam-6593	730	15	prime	prime	ADJ
ejpam-6593	730	16	pairs	pair	NOUN
ejpam-6593	730	17	such	such	ADJ
ejpam-6593	730	18	that	that	SCONJ
ejpam-6593	730	19	k	k	PROPN
ejpam-6593	730	20	≡	≡	PROPN
ejpam-6593	730	21	0	0	PUNCT
ejpam-6593	731	1	(	(	PUNCT
ejpam-6593	731	2	mod	mod	NOUN
ejpam-6593	731	3	4	4	NUM
ejpam-6593	731	4	)	)	PUNCT
ejpam-6593	731	5	and	and	CCONJ
ejpam-6593	731	6	x	x	SYM
ejpam-6593	731	7	and	and	CCONJ
ejpam-6593	731	8	y	y	PROPN
ejpam-6593	731	9	have	have	VERB
ejpam-6593	731	10	the	the	DET
ejpam-6593	731	11	same	same	ADJ
ejpam-6593	731	12	parity	parity	NOUN
ejpam-6593	731	13	,	,	PUNCT
ejpam-6593	731	14	has	have	VERB
ejpam-6593	731	15	no	no	DET
ejpam-6593	731	16	solution	solution	NOUN
ejpam-6593	731	17	.	.	PUNCT
ejpam-6593	732	1	proof	proof	NOUN
ejpam-6593	732	2	.	.	PUNCT
ejpam-6593	733	1	suppose	suppose	VERB
ejpam-6593	733	2	x	x	X
ejpam-6593	733	3	≥	≥	NUM
ejpam-6593	733	4	1	1	NUM
ejpam-6593	733	5	and	and	CCONJ
ejpam-6593	733	6	y	y	PROPN
ejpam-6593	733	7	≥	≥	NUM
ejpam-6593	733	8	1	1	NUM
ejpam-6593	733	9	are	be	AUX
ejpam-6593	733	10	of	of	ADP
ejpam-6593	733	11	the	the	DET
ejpam-6593	733	12	same	same	ADJ
ejpam-6593	733	13	parity	parity	NOUN
ejpam-6593	733	14	.	.	PUNCT
ejpam-6593	734	1	let	let	VERB
ejpam-6593	734	2	x	x	PRON
ejpam-6593	734	3	and	and	CCONJ
ejpam-6593	734	4	y	y	PROPN
ejpam-6593	734	5	be	be	AUX
ejpam-6593	734	6	odd	odd	ADJ
ejpam-6593	734	7	integers	integer	NOUN
ejpam-6593	734	8	,	,	PUNCT
ejpam-6593	734	9	then	then	ADV
ejpam-6593	734	10	px	px	PROPN
ejpam-6593	734	11	≡	≡	PROPN
ejpam-6593	734	12	(	(	PUNCT
ejpam-6593	734	13	p	p	X
ejpam-6593	734	14	+	+	PROPN
ejpam-6593	734	15	5k)y	5k)y	NUM
ejpam-6593	734	16	≡	≡	PROPN
ejpam-6593	734	17	1	1	NUM
ejpam-6593	734	18	(	(	PUNCT
ejpam-6593	734	19	mod	mod	NOUN
ejpam-6593	734	20	4	4	NUM
ejpam-6593	734	21	)	)	PUNCT
ejpam-6593	734	22	or	or	CCONJ
ejpam-6593	734	23	px	px	PROPN
ejpam-6593	734	24	≡	≡	PROPN
ejpam-6593	734	25	(	(	PUNCT
ejpam-6593	734	26	p	p	X
ejpam-6593	734	27	+	+	PROPN
ejpam-6593	734	28	5k)y	5k)y	NUM
ejpam-6593	734	29	≡	≡	PROPN
ejpam-6593	734	30	3	3	NUM
ejpam-6593	734	31	(	(	PUNCT
ejpam-6593	734	32	mod	mod	NOUN
ejpam-6593	734	33	4	4	NUM
ejpam-6593	734	34	)	)	PUNCT
ejpam-6593	734	35	.	.	PUNCT
ejpam-6593	735	1	if	if	SCONJ
ejpam-6593	735	2	x	x	PRON
ejpam-6593	735	3	and	and	CCONJ
ejpam-6593	735	4	y	y	PROPN
ejpam-6593	735	5	are	be	AUX
ejpam-6593	735	6	even	even	ADV
ejpam-6593	735	7	integers	integer	NOUN
ejpam-6593	735	8	,	,	PUNCT
ejpam-6593	735	9	then	then	ADV
ejpam-6593	735	10	px	px	PROPN
ejpam-6593	735	11	≡	≡	PROPN
ejpam-6593	735	12	1	1	NUM
ejpam-6593	735	13	(	(	PUNCT
ejpam-6593	735	14	mod	mod	NOUN
ejpam-6593	735	15	4	4	NUM
ejpam-6593	735	16	)	)	PUNCT
ejpam-6593	735	17	and	and	CCONJ
ejpam-6593	735	18	(	(	PUNCT
ejpam-6593	735	19	p+5k)y	p+5k)y	PROPN
ejpam-6593	735	20	≡	≡	PROPN
ejpam-6593	735	21	1	1	NUM
ejpam-6593	735	22	(	(	PUNCT
ejpam-6593	735	23	mod	mod	NOUN
ejpam-6593	735	24	4	4	NUM
ejpam-6593	735	25	)	)	PUNCT
ejpam-6593	735	26	.	.	PUNCT
ejpam-6593	736	1	in	in	ADP
ejpam-6593	736	2	any	any	DET
ejpam-6593	736	3	case	case	NOUN
ejpam-6593	736	4	,	,	PUNCT
ejpam-6593	736	5	px	px	PROPN
ejpam-6593	736	6	+	+	PROPN
ejpam-6593	736	7	(	(	PUNCT
ejpam-6593	736	8	p+5k)y	p+5k)y	PROPN
ejpam-6593	736	9	≡	≡	PROPN
ejpam-6593	736	10	2	2	NUM
ejpam-6593	736	11	(	(	PUNCT
ejpam-6593	736	12	mod	mod	NOUN
ejpam-6593	736	13	4	4	NUM
ejpam-6593	736	14	)	)	PUNCT
ejpam-6593	736	15	.	.	PUNCT
ejpam-6593	737	1	on	on	ADP
ejpam-6593	737	2	the	the	DET
ejpam-6593	737	3	other	other	ADJ
ejpam-6593	737	4	hand	hand	NOUN
ejpam-6593	737	5	,	,	PUNCT
ejpam-6593	737	6	since	since	SCONJ
ejpam-6593	737	7	px	px	PROPN
ejpam-6593	737	8	and	and	CCONJ
ejpam-6593	737	9	(	(	PUNCT
ejpam-6593	737	10	p	p	X
ejpam-6593	737	11	+	+	PROPN
ejpam-6593	737	12	5k)y	5k)y	NUM
ejpam-6593	737	13	are	be	AUX
ejpam-6593	737	14	both	both	PRON
ejpam-6593	737	15	odd	odd	ADJ
ejpam-6593	737	16	,	,	PUNCT
ejpam-6593	737	17	their	their	PRON
ejpam-6593	737	18	sum	sum	NOUN
ejpam-6593	737	19	is	be	AUX
ejpam-6593	737	20	even	even	ADV
ejpam-6593	737	21	.	.	PUNCT
ejpam-6593	738	1	hence	hence	ADV
ejpam-6593	738	2	,	,	PUNCT
ejpam-6593	738	3	z2	z2	PROPN
ejpam-6593	738	4	≡	≡	PROPN
ejpam-6593	738	5	0	0	PUNCT
ejpam-6593	738	6	(	(	PUNCT
ejpam-6593	738	7	mod	mod	NOUN
ejpam-6593	738	8	4	4	NUM
ejpam-6593	738	9	)	)	PUNCT
ejpam-6593	738	10	and	and	CCONJ
ejpam-6593	738	11	thus	thus	ADV
ejpam-6593	738	12	,	,	PUNCT
ejpam-6593	738	13	px	px	X
ejpam-6593	738	14	+	+	CCONJ
ejpam-6593	738	15	(	(	PUNCT
ejpam-6593	738	16	p+	p+	VERB
ejpam-6593	738	17	5k)y	5k)y	NOUN
ejpam-6593	738	18	̸≡	̸≡	NOUN
ejpam-6593	738	19	z2	z2	PROPN
ejpam-6593	738	20	.	.	PUNCT
ejpam-6593	739	1	3	3	NUM
ejpam-6593	739	2	.	.	X
ejpam-6593	739	3	conclusions	conclusion	NOUN
ejpam-6593	739	4	in	in	ADP
ejpam-6593	739	5	this	this	DET
ejpam-6593	739	6	paper	paper	NOUN
ejpam-6593	739	7	,	,	PUNCT
ejpam-6593	739	8	the	the	DET
ejpam-6593	739	9	authors	author	NOUN
ejpam-6593	739	10	tried	try	VERB
ejpam-6593	739	11	to	to	PART
ejpam-6593	739	12	provide	provide	VERB
ejpam-6593	739	13	solutions	solution	NOUN
ejpam-6593	739	14	of	of	ADP
ejpam-6593	739	15	an	an	DET
ejpam-6593	739	16	exponential	exponential	ADJ
ejpam-6593	739	17	diophantine	diophantine	NOUN
ejpam-6593	739	18	equation	equation	NOUN
ejpam-6593	739	19	of	of	ADP
ejpam-6593	739	20	the	the	DET
ejpam-6593	739	21	form	form	NOUN
ejpam-6593	739	22	px	px	X
ejpam-6593	740	1	+	+	CCONJ
ejpam-6593	740	2	(	(	PUNCT
ejpam-6593	740	3	p+	p+	PROPN
ejpam-6593	740	4	5k)y	5k)y	NOUN
ejpam-6593	740	5	=	=	SYM
ejpam-6593	740	6	z2	z2	PROPN
ejpam-6593	740	7	,	,	PUNCT
ejpam-6593	740	8	where	where	SCONJ
ejpam-6593	740	9	k	k	PROPN
ejpam-6593	740	10	∈	∈	PROPN
ejpam-6593	740	11	n.	n.	NOUN
ejpam-6593	740	12	the	the	DET
ejpam-6593	740	13	authors	author	NOUN
ejpam-6593	740	14	considered	consider	VERB
ejpam-6593	740	15	the	the	DET
ejpam-6593	740	16	cases	case	NOUN
ejpam-6593	740	17	(	(	PUNCT
ejpam-6593	740	18	i	i	NOUN
ejpam-6593	740	19	)	)	PUNCT
ejpam-6593	740	20	when	when	SCONJ
ejpam-6593	740	21	p	p	NOUN
ejpam-6593	740	22	=	=	NOUN
ejpam-6593	740	23	2	2	NUM
ejpam-6593	740	24	;	;	PUNCT
ejpam-6593	740	25	or	or	CCONJ
ejpam-6593	740	26	(	(	PUNCT
ejpam-6593	740	27	ii	ii	NOUN
ejpam-6593	740	28	)	)	PUNCT
ejpam-6593	740	29	when	when	SCONJ
ejpam-6593	740	30	p	p	NOUN
ejpam-6593	740	31	and	and	CCONJ
ejpam-6593	740	32	p+5k	p+5k	PROPN
ejpam-6593	740	33	are	be	AUX
ejpam-6593	740	34	prime	prime	ADJ
ejpam-6593	740	35	pairs	pair	NOUN
ejpam-6593	740	36	are	be	AUX
ejpam-6593	740	37	given	give	VERB
ejpam-6593	740	38	.	.	PUNCT
ejpam-6593	741	1	in	in	ADP
ejpam-6593	741	2	addition	addition	NOUN
ejpam-6593	741	3	,	,	PUNCT
ejpam-6593	741	4	the	the	DET
ejpam-6593	741	5	study	study	NOUN
ejpam-6593	741	6	is	be	AUX
ejpam-6593	741	7	limited	limit	VERB
ejpam-6593	741	8	only	only	ADV
ejpam-6593	741	9	to	to	ADP
ejpam-6593	741	10	integer	integer	NOUN
ejpam-6593	741	11	solutions	solution	NOUN
ejpam-6593	741	12	(	(	PUNCT
ejpam-6593	741	13	x	x	X
ejpam-6593	741	14	,	,	PUNCT
ejpam-6593	741	15	y	y	PROPN
ejpam-6593	741	16	,	,	PUNCT
ejpam-6593	741	17	z	z	NOUN
ejpam-6593	741	18	)	)	PUNCT
ejpam-6593	741	19	,	,	PUNCT
ejpam-6593	741	20	where	where	SCONJ
ejpam-6593	741	21	x	x	PRON
ejpam-6593	741	22	and	and	CCONJ
ejpam-6593	741	23	y	y	PROPN
ejpam-6593	741	24	are	be	AUX
ejpam-6593	741	25	not	not	PART
ejpam-6593	741	26	simultaneously	simultaneously	ADV
ejpam-6593	741	27	greater	great	ADJ
ejpam-6593	741	28	than	than	ADP
ejpam-6593	741	29	1	1	NUM
ejpam-6593	741	30	.	.	PUNCT
ejpam-6593	742	1	for	for	ADP
ejpam-6593	742	2	the	the	DET
ejpam-6593	742	3	first	first	ADJ
ejpam-6593	742	4	case	case	NOUN
ejpam-6593	742	5	,	,	PUNCT
ejpam-6593	742	6	it	it	PRON
ejpam-6593	742	7	is	be	AUX
ejpam-6593	742	8	concluded	conclude	VERB
ejpam-6593	742	9	that	that	SCONJ
ejpam-6593	742	10	if	if	SCONJ
ejpam-6593	742	11	y	y	PROPN
ejpam-6593	742	12	=	=	SYM
ejpam-6593	742	13	1	1	NUM
ejpam-6593	742	14	,	,	PUNCT
ejpam-6593	742	15	then	then	ADV
ejpam-6593	742	16	the	the	DET
ejpam-6593	742	17	diophantine	diophantine	NOUN
ejpam-6593	742	18	equation	equation	NOUN
ejpam-6593	742	19	has	have	VERB
ejpam-6593	742	20	infinitely	infinitely	ADV
ejpam-6593	742	21	many	many	ADJ
ejpam-6593	742	22	solutions	solution	NOUN
ejpam-6593	742	23	that	that	PRON
ejpam-6593	742	24	can	can	AUX
ejpam-6593	742	25	be	be	AUX
ejpam-6593	742	26	further	far	ADV
ejpam-6593	742	27	divided	divide	VERB
ejpam-6593	742	28	based	base	VERB
ejpam-6593	742	29	on	on	ADP
ejpam-6593	742	30	the	the	DET
ejpam-6593	742	31	value	value	NOUN
ejpam-6593	742	32	of	of	ADP
ejpam-6593	742	33	x	x	PUNCT
ejpam-6593	742	34	taking	take	VERB
ejpam-6593	742	35	modulo	modulo	NOUN
ejpam-6593	742	36	4	4	NUM
ejpam-6593	742	37	.	.	PUNCT
ejpam-6593	743	1	if	if	SCONJ
ejpam-6593	743	2	x	x	SYM
ejpam-6593	743	3	≡	≡	PROPN
ejpam-6593	743	4	1	1	NUM
ejpam-6593	743	5	(	(	PUNCT
ejpam-6593	743	6	mod	mod	NOUN
ejpam-6593	743	7	4	4	NUM
ejpam-6593	743	8	)	)	PUNCT
ejpam-6593	743	9	,	,	PUNCT
ejpam-6593	743	10	z	z	PROPN
ejpam-6593	743	11	can	can	AUX
ejpam-6593	743	12	be	be	AUX
ejpam-6593	743	13	either	either	CCONJ
ejpam-6593	743	14	z	z	PROPN
ejpam-6593	743	15	≡	≡	PROPN
ejpam-6593	743	16	2	2	NUM
ejpam-6593	743	17	,	,	PUNCT
ejpam-6593	743	18	3	3	NUM
ejpam-6593	743	19	(	(	PUNCT
ejpam-6593	743	20	mod	mod	NOUN
ejpam-6593	743	21	5	5	NUM
ejpam-6593	743	22	)	)	PUNCT
ejpam-6593	743	23	.	.	PUNCT
ejpam-6593	744	1	if	if	SCONJ
ejpam-6593	744	2	x	x	SYM
ejpam-6593	744	3	≡	≡	PROPN
ejpam-6593	744	4	2	2	NUM
ejpam-6593	744	5	(	(	PUNCT
ejpam-6593	744	6	mod	mod	NOUN
ejpam-6593	744	7	4	4	NUM
ejpam-6593	744	8	)	)	PUNCT
ejpam-6593	744	9	,	,	PUNCT
ejpam-6593	744	10	then	then	ADV
ejpam-6593	744	11	z	z	PROPN
ejpam-6593	744	12	≡	≡	PROPN
ejpam-6593	744	13	1	1	NUM
ejpam-6593	744	14	,	,	PUNCT
ejpam-6593	744	15	4	4	NUM
ejpam-6593	744	16	(	(	PUNCT
ejpam-6593	744	17	mod	mod	NOUN
ejpam-6593	744	18	5	5	NUM
ejpam-6593	744	19	)	)	PUNCT
ejpam-6593	744	20	.	.	PUNCT
ejpam-6593	745	1	if	if	SCONJ
ejpam-6593	745	2	x	x	SYM
ejpam-6593	745	3	≡	≡	PROPN
ejpam-6593	745	4	3	3	NUM
ejpam-6593	745	5	(	(	PUNCT
ejpam-6593	745	6	mod	mod	NOUN
ejpam-6593	745	7	4	4	NUM
ejpam-6593	745	8	)	)	PUNCT
ejpam-6593	745	9	,	,	PUNCT
ejpam-6593	745	10	then	then	ADV
ejpam-6593	745	11	z	z	PROPN
ejpam-6593	745	12	≡	≡	PROPN
ejpam-6593	745	13	0	0	PUNCT
ejpam-6593	745	14	(	(	PUNCT
ejpam-6593	745	15	mod	mod	PROPN
ejpam-6593	745	16	5	5	NUM
ejpam-6593	745	17	)	)	PUNCT
ejpam-6593	745	18	.	.	PUNCT
ejpam-6593	746	1	in	in	ADP
ejpam-6593	746	2	the	the	DET
ejpam-6593	746	3	case	case	NOUN
ejpam-6593	746	4	where	where	SCONJ
ejpam-6593	746	5	z	z	NOUN
ejpam-6593	746	6	have	have	VERB
ejpam-6593	746	7	two	two	NUM
ejpam-6593	746	8	possible	possible	ADJ
ejpam-6593	746	9	equivalence	equivalence	NOUN
ejpam-6593	746	10	modulo	modulo	NOUN
ejpam-6593	746	11	4	4	NUM
ejpam-6593	746	12	,	,	PUNCT
ejpam-6593	746	13	the	the	DET
ejpam-6593	746	14	union	union	NOUN
ejpam-6593	746	15	of	of	ADP
ejpam-6593	746	16	all	all	DET
ejpam-6593	746	17	these	these	DET
ejpam-6593	746	18	solutions	solution	NOUN
ejpam-6593	746	19	form	form	VERB
ejpam-6593	746	20	all	all	DET
ejpam-6593	746	21	the	the	DET
ejpam-6593	746	22	solutions	solution	NOUN
ejpam-6593	746	23	at	at	ADP
ejpam-6593	746	24	a	a	DET
ejpam-6593	746	25	specific	specific	ADJ
ejpam-6593	746	26	value	value	NOUN
ejpam-6593	746	27	of	of	ADP
ejpam-6593	746	28	x.	x.	NOUN
ejpam-6593	746	29	moreover	moreover	ADV
ejpam-6593	746	30	,	,	PUNCT
ejpam-6593	746	31	when	when	SCONJ
ejpam-6593	746	32	y	y	PROPN
ejpam-6593	746	33	=	=	SYM
ejpam-6593	746	34	0	0	PROPN
ejpam-6593	746	35	,	,	PUNCT
ejpam-6593	746	36	(	(	PUNCT
ejpam-6593	746	37	p	p	X
ejpam-6593	746	38	,	,	PUNCT
ejpam-6593	746	39	k	k	NOUN
ejpam-6593	746	40	,	,	PUNCT
ejpam-6593	746	41	x	x	X
ejpam-6593	746	42	,	,	PUNCT
ejpam-6593	746	43	y	y	PROPN
ejpam-6593	746	44	,	,	PUNCT
ejpam-6593	746	45	z	z	NOUN
ejpam-6593	746	46	)	)	PUNCT
ejpam-6593	746	47	=	=	SYM
ejpam-6593	746	48	(	(	PUNCT
ejpam-6593	746	49	2	2	NUM
ejpam-6593	746	50	,	,	PUNCT
ejpam-6593	746	51	k	k	NOUN
ejpam-6593	746	52	,	,	PUNCT
ejpam-6593	746	53	3	3	NUM
ejpam-6593	746	54	,	,	PUNCT
ejpam-6593	746	55	0	0	NUM
ejpam-6593	746	56	,	,	PUNCT
ejpam-6593	746	57	3	3	NUM
ejpam-6593	746	58	)	)	PUNCT
ejpam-6593	746	59	is	be	AUX
ejpam-6593	746	60	the	the	DET
ejpam-6593	746	61	only	only	ADJ
ejpam-6593	746	62	solution	solution	NOUN
ejpam-6593	746	63	of	of	ADP
ejpam-6593	746	64	the	the	DET
ejpam-6593	746	65	equation	equation	NOUN
ejpam-6593	746	66	for	for	ADP
ejpam-6593	746	67	all	all	DET
ejpam-6593	746	68	k	k	PROPN
ejpam-6593	746	69	∈	∈	PROPN
ejpam-6593	746	70	n.	n.	NOUN
ejpam-6593	746	71	when	when	SCONJ
ejpam-6593	746	72	y	y	PROPN
ejpam-6593	746	73	=	=	SYM
ejpam-6593	746	74	2	2	NUM
ejpam-6593	746	75	,	,	PUNCT
ejpam-6593	746	76	3	3	NUM
ejpam-6593	746	77	such	such	ADJ
ejpam-6593	746	78	that	that	SCONJ
ejpam-6593	746	79	k	k	PROPN
ejpam-6593	746	80	≤	≤	ADV
ejpam-6593	746	81	5000	5000	NUM
ejpam-6593	746	82	and	and	CCONJ
ejpam-6593	746	83	x	x	SYM
ejpam-6593	746	84	≤	≤	NOUN
ejpam-6593	746	85	50	50	NUM
ejpam-6593	746	86	,	,	PUNCT
ejpam-6593	746	87	there	there	PRON
ejpam-6593	746	88	are	be	VERB
ejpam-6593	746	89	finitely	finitely	ADV
ejpam-6593	746	90	many	many	ADJ
ejpam-6593	746	91	solutions	solution	NOUN
ejpam-6593	746	92	mentioned	mention	VERB
ejpam-6593	746	93	.	.	PUNCT
ejpam-6593	747	1	in	in	ADP
ejpam-6593	747	2	particular	particular	ADJ
ejpam-6593	747	3	,	,	PUNCT
ejpam-6593	747	4	21	21	NUM
ejpam-6593	747	5	solutions	solution	NOUN
ejpam-6593	747	6	were	be	AUX
ejpam-6593	747	7	mentioned	mention	VERB
ejpam-6593	747	8	when	when	SCONJ
ejpam-6593	747	9	y	y	PROPN
ejpam-6593	747	10	=	=	SYM
ejpam-6593	747	11	2	2	NUM
ejpam-6593	747	12	and	and	CCONJ
ejpam-6593	747	13	9	9	NUM
ejpam-6593	747	14	solutions	solution	NOUN
ejpam-6593	747	15	were	be	AUX
ejpam-6593	747	16	mentioned	mention	VERB
ejpam-6593	747	17	when	when	SCONJ
ejpam-6593	747	18	y	y	PROPN
ejpam-6593	747	19	=	=	SYM
ejpam-6593	747	20	3	3	X
ejpam-6593	747	21	.	.	PUNCT
ejpam-6593	748	1	the	the	DET
ejpam-6593	748	2	equation	equation	NOUN
ejpam-6593	748	3	has	have	VERB
ejpam-6593	748	4	no	no	DET
ejpam-6593	748	5	solution	solution	NOUN
ejpam-6593	748	6	when	when	SCONJ
ejpam-6593	748	7	y	y	PROPN
ejpam-6593	748	8	=	=	SYM
ejpam-6593	748	9	1	1	NUM
ejpam-6593	748	10	and	and	CCONJ
ejpam-6593	748	11	x	x	PRON
ejpam-6593	748	12	is	be	AUX
ejpam-6593	748	13	a	a	DET
ejpam-6593	748	14	multiple	multiple	NOUN
ejpam-6593	748	15	of	of	ADP
ejpam-6593	748	16	4	4	NUM
ejpam-6593	748	17	,	,	PUNCT
ejpam-6593	748	18	i.e.	i.e.	X
ejpam-6593	748	19	,	,	PUNCT
ejpam-6593	748	20	x	x	SYM
ejpam-6593	748	21	≡	≡	PROPN
ejpam-6593	748	22	0	0	PUNCT
ejpam-6593	748	23	(	(	PUNCT
ejpam-6593	748	24	mod	mod	PROPN
ejpam-6593	748	25	4	4	NUM
ejpam-6593	748	26	)	)	PUNCT
ejpam-6593	748	27	,	,	PUNCT
ejpam-6593	748	28	and	and	CCONJ
ejpam-6593	748	29	if	if	SCONJ
ejpam-6593	748	30	x	x	SYM
ejpam-6593	748	31	=	=	NOUN
ejpam-6593	748	32	0	0	NUM
ejpam-6593	748	33	.	.	PUNCT
ejpam-6593	749	1	the	the	DET
ejpam-6593	749	2	discussion	discussion	NOUN
ejpam-6593	749	3	for	for	ADP
ejpam-6593	749	4	the	the	DET
ejpam-6593	749	5	second	second	ADJ
ejpam-6593	749	6	case	case	NOUN
ejpam-6593	749	7	was	be	AUX
ejpam-6593	749	8	divided	divide	VERB
ejpam-6593	749	9	into	into	ADP
ejpam-6593	749	10	two	two	NUM
ejpam-6593	749	11	,	,	PUNCT
ejpam-6593	749	12	based	base	VERB
ejpam-6593	749	13	on	on	ADP
ejpam-6593	749	14	the	the	DET
ejpam-6593	749	15	parity	parity	NOUN
ejpam-6593	749	16	of	of	ADP
ejpam-6593	749	17	k.	k.	PROPN
ejpam-6593	749	18	if	if	SCONJ
ejpam-6593	749	19	k	k	PROPN
ejpam-6593	749	20	is	be	AUX
ejpam-6593	749	21	odd	odd	ADJ
ejpam-6593	749	22	,	,	PUNCT
ejpam-6593	749	23	some	some	DET
ejpam-6593	749	24	solutions	solution	NOUN
ejpam-6593	749	25	are	be	AUX
ejpam-6593	749	26	already	already	ADV
ejpam-6593	749	27	mentioned	mention	VERB
ejpam-6593	749	28	in	in	ADP
ejpam-6593	749	29	the	the	DET
ejpam-6593	749	30	first	first	ADJ
ejpam-6593	749	31	case	case	NOUN
ejpam-6593	749	32	since	since	SCONJ
ejpam-6593	749	33	p	p	NOUN
ejpam-6593	749	34	=	=	NOUN
ejpam-6593	749	35	2	2	X
ejpam-6593	749	36	.	.	PUNCT
ejpam-6593	750	1	in	in	ADP
ejpam-6593	750	2	this	this	DET
ejpam-6593	750	3	case	case	NOUN
ejpam-6593	750	4	,	,	PUNCT
ejpam-6593	750	5	modulo	modulo	PROPN
ejpam-6593	750	6	10	10	NUM
ejpam-6593	750	7	was	be	AUX
ejpam-6593	750	8	used	use	VERB
ejpam-6593	750	9	for	for	ADP
ejpam-6593	750	10	the	the	DET
ejpam-6593	750	11	value	value	NOUN
ejpam-6593	750	12	of	of	ADP
ejpam-6593	750	13	z	z	NOUN
ejpam-6593	750	14	since	since	SCONJ
ejpam-6593	750	15	we	we	PRON
ejpam-6593	750	16	are	be	AUX
ejpam-6593	750	17	dealing	deal	VERB
ejpam-6593	750	18	with	with	ADP
ejpam-6593	750	19	prime	prime	ADJ
ejpam-6593	750	20	numbers	number	NOUN
ejpam-6593	750	21	and	and	CCONJ
ejpam-6593	750	22	z	z	NOUN
ejpam-6593	750	23	should	should	AUX
ejpam-6593	750	24	be	be	AUX
ejpam-6593	750	25	odd	odd	ADJ
ejpam-6593	750	26	for	for	ADP
ejpam-6593	750	27	p	p	PROPN
ejpam-6593	751	1	+	+	ADJ
ejpam-6593	751	2	5k	5k	NUM
ejpam-6593	751	3	to	to	PART
ejpam-6593	751	4	be	be	AUX
ejpam-6593	751	5	an	an	DET
ejpam-6593	751	6	odd	odd	ADJ
ejpam-6593	751	7	integer	integer	NOUN
ejpam-6593	751	8	and	and	CCONJ
ejpam-6593	751	9	prime	prime	ADJ
ejpam-6593	751	10	number	number	NOUN
ejpam-6593	751	11	.	.	PUNCT
ejpam-6593	752	1	similar	similar	ADJ
ejpam-6593	752	2	to	to	ADP
ejpam-6593	752	3	that	that	PRON
ejpam-6593	752	4	of	of	ADP
ejpam-6593	752	5	the	the	DET
ejpam-6593	752	6	first	first	ADJ
ejpam-6593	752	7	case	case	NOUN
ejpam-6593	752	8	,	,	PUNCT
ejpam-6593	752	9	when	when	SCONJ
ejpam-6593	752	10	y	y	PROPN
ejpam-6593	752	11	=	=	SYM
ejpam-6593	752	12	1	1	NUM
ejpam-6593	752	13	,	,	PUNCT
ejpam-6593	752	14	the	the	DET
ejpam-6593	752	15	diophantine	diophantine	NOUN
ejpam-6593	752	16	equation	equation	NOUN
ejpam-6593	752	17	also	also	ADV
ejpam-6593	752	18	have	have	VERB
ejpam-6593	752	19	infinitely	infinitely	ADV
ejpam-6593	752	20	many	many	ADJ
ejpam-6593	752	21	solutions	solution	NOUN
ejpam-6593	752	22	for	for	ADP
ejpam-6593	752	23	some	some	DET
ejpam-6593	752	24	value	value	NOUN
ejpam-6593	752	25	of	of	ADP
ejpam-6593	752	26	x	x	PUNCT
ejpam-6593	752	27	with	with	ADP
ejpam-6593	752	28	the	the	DET
ejpam-6593	752	29	note	note	NOUN
ejpam-6593	752	30	that	that	SCONJ
ejpam-6593	752	31	there	there	PRON
ejpam-6593	752	32	are	be	VERB
ejpam-6593	752	33	infinitely	infinitely	ADV
ejpam-6593	752	34	many	many	ADJ
ejpam-6593	752	35	prime	prime	ADJ
ejpam-6593	752	36	numbers	number	NOUN
ejpam-6593	752	37	of	of	ADP
ejpam-6593	752	38	the	the	DET
ejpam-6593	752	39	form	form	NOUN
ejpam-6593	752	40	p	p	NOUN
ejpam-6593	752	41	+	+	NOUN
ejpam-6593	752	42	5k	5k	NUM
ejpam-6593	752	43	.	.	PUNCT
ejpam-6593	753	1	if	if	SCONJ
ejpam-6593	753	2	x	x	SYM
ejpam-6593	753	3	≡	≡	PROPN
ejpam-6593	753	4	1	1	NUM
ejpam-6593	753	5	(	(	PUNCT
ejpam-6593	753	6	mod	mod	NOUN
ejpam-6593	753	7	4	4	NUM
ejpam-6593	753	8	)	)	PUNCT
ejpam-6593	753	9	,	,	PUNCT
ejpam-6593	753	10	then	then	ADV
ejpam-6593	753	11	the	the	DET
ejpam-6593	753	12	equation	equation	NOUN
ejpam-6593	753	13	has	have	VERB
ejpam-6593	753	14	a	a	DET
ejpam-6593	753	15	solution	solution	NOUN
ejpam-6593	753	16	for	for	ADP
ejpam-6593	753	17	some	some	DET
ejpam-6593	753	18	z	z	NOUN
ejpam-6593	753	19	≡	≡	PROPN
ejpam-6593	753	20	3	3	NUM
ejpam-6593	753	21	,	,	PUNCT
ejpam-6593	753	22	7	7	NUM
ejpam-6593	753	23	(	(	PUNCT
ejpam-6593	753	24	mod	mod	NOUN
ejpam-6593	753	25	10	10	NUM
ejpam-6593	753	26	)	)	PUNCT
ejpam-6593	753	27	and	and	CCONJ
ejpam-6593	753	28	if	if	SCONJ
ejpam-6593	753	29	x	x	SYM
ejpam-6593	753	30	≡	≡	PROPN
ejpam-6593	753	31	3	3	NUM
ejpam-6593	753	32	(	(	PUNCT
ejpam-6593	753	33	mod	mod	NOUN
ejpam-6593	753	34	4	4	NUM
ejpam-6593	753	35	)	)	PUNCT
ejpam-6593	753	36	,	,	PUNCT
ejpam-6593	753	37	then	then	ADV
ejpam-6593	753	38	the	the	DET
ejpam-6593	753	39	equation	equation	NOUN
ejpam-6593	753	40	has	have	VERB
ejpam-6593	753	41	a	a	DET
ejpam-6593	753	42	solution	solution	NOUN
ejpam-6593	753	43	for	for	ADP
ejpam-6593	753	44	some	some	DET
ejpam-6593	753	45	z	z	NOUN
ejpam-6593	753	46	≡	≡	PROPN
ejpam-6593	753	47	5	5	NUM
ejpam-6593	753	48	(	(	PUNCT
ejpam-6593	753	49	mod	mod	PROPN
ejpam-6593	753	50	10	10	NUM
ejpam-6593	753	51	)	)	PUNCT
ejpam-6593	753	52	.	.	PUNCT
ejpam-6593	754	1	m.	m.	PROPN
ejpam-6593	754	2	c.	c.	PROPN
ejpam-6593	754	3	avenilla	avenilla	PROPN
ejpam-6593	754	4	,	,	PUNCT
ejpam-6593	754	5	j.	j.	PROPN
ejpam-6593	754	6	b.	b.	PROPN
ejpam-6593	754	7	bacani	bacani	PROPN
ejpam-6593	754	8	/	/	SYM
ejpam-6593	754	9	eur	eur	PROPN
ejpam-6593	754	10	.	.	PUNCT
ejpam-6593	755	1	j.	j.	PROPN
ejpam-6593	755	2	pure	pure	PROPN
ejpam-6593	755	3	appl	appl	PROPN
ejpam-6593	755	4	.	.	PROPN
ejpam-6593	755	5	math	math	PROPN
ejpam-6593	755	6	,	,	PUNCT
ejpam-6593	755	7	18	18	NUM
ejpam-6593	755	8	(	(	PUNCT
ejpam-6593	755	9	3	3	NUM
ejpam-6593	755	10	)	)	PUNCT
ejpam-6593	755	11	(	(	PUNCT
ejpam-6593	755	12	2025	2025	NUM
ejpam-6593	755	13	)	)	PUNCT
ejpam-6593	755	14	,	,	PUNCT
ejpam-6593	755	15	6593	6593	NUM
ejpam-6593	755	16	23	23	NUM
ejpam-6593	755	17	of	of	ADP
ejpam-6593	755	18	24	24	NUM
ejpam-6593	755	19	there	there	PRON
ejpam-6593	755	20	are	be	VERB
ejpam-6593	755	21	finitely	finitely	ADV
ejpam-6593	755	22	many	many	ADJ
ejpam-6593	755	23	solutions	solution	NOUN
ejpam-6593	755	24	when	when	SCONJ
ejpam-6593	755	25	y	y	PROPN
ejpam-6593	755	26	=	=	SYM
ejpam-6593	755	27	1	1	NUM
ejpam-6593	755	28	and	and	CCONJ
ejpam-6593	755	29	x	x	SYM
ejpam-6593	755	30	=	=	SYM
ejpam-6593	755	31	2	2	NUM
ejpam-6593	755	32	+	+	CCONJ
ejpam-6593	755	33	4n	4n	NOUN
ejpam-6593	755	34	,	,	PUNCT
ejpam-6593	755	35	n	n	PROPN
ejpam-6593	755	36	∈	∈	PROPN
ejpam-6593	755	37	n0	n0	PROPN
ejpam-6593	755	38	,	,	PUNCT
ejpam-6593	755	39	where	where	SCONJ
ejpam-6593	755	40	the	the	DET
ejpam-6593	755	41	value	value	NOUN
ejpam-6593	755	42	of	of	ADP
ejpam-6593	755	43	k	k	PROPN
ejpam-6593	755	44	and	and	CCONJ
ejpam-6593	755	45	z	z	PROPN
ejpam-6593	755	46	are	be	AUX
ejpam-6593	755	47	given	give	VERB
ejpam-6593	755	48	by	by	ADP
ejpam-6593	755	49	k	k	PROPN
ejpam-6593	755	50	=	=	PUNCT
ejpam-6593	755	51	(	(	PUNCT
ejpam-6593	755	52	22	22	NUM
ejpam-6593	755	53	+	+	NOUN
ejpam-6593	755	54	2n	2n	NUM
ejpam-6593	755	55	−	−	ADP
ejpam-6593	755	56	1)/5	1)/5	NUM
ejpam-6593	755	57	and	and	CCONJ
ejpam-6593	755	58	z	z	NOUN
ejpam-6593	755	59	=	=	SYM
ejpam-6593	755	60	(	(	PUNCT
ejpam-6593	755	61	5k	5k	NUM
ejpam-6593	755	62	+	+	CCONJ
ejpam-6593	755	63	3)/2	3)/2	NUM
ejpam-6593	755	64	.	.	PUNCT
ejpam-6593	756	1	three	three	NUM
ejpam-6593	756	2	of	of	ADP
ejpam-6593	756	3	them	they	PRON
ejpam-6593	756	4	were	be	AUX
ejpam-6593	756	5	mentioned	mention	VERB
ejpam-6593	756	6	and	and	CCONJ
ejpam-6593	756	7	they	they	PRON
ejpam-6593	756	8	are	be	AUX
ejpam-6593	756	9	the	the	DET
ejpam-6593	756	10	following	follow	VERB
ejpam-6593	756	11	:	:	PUNCT
ejpam-6593	756	12	(	(	PUNCT
ejpam-6593	756	13	p	p	X
ejpam-6593	756	14	,	,	PUNCT
ejpam-6593	756	15	k	k	NOUN
ejpam-6593	756	16	,	,	PUNCT
ejpam-6593	756	17	x	x	X
ejpam-6593	756	18	,	,	PUNCT
ejpam-6593	756	19	y	y	PROPN
ejpam-6593	756	20	,	,	PUNCT
ejpam-6593	756	21	z	z	NOUN
ejpam-6593	756	22	)	)	PUNCT
ejpam-6593	756	23	=	=	SYM
ejpam-6593	756	24	(	(	PUNCT
ejpam-6593	756	25	2	2	NUM
ejpam-6593	756	26	,	,	PUNCT
ejpam-6593	756	27	3	3	NUM
ejpam-6593	756	28	,	,	PUNCT
ejpam-6593	756	29	6	6	NUM
ejpam-6593	756	30	,	,	PUNCT
ejpam-6593	756	31	1	1	NUM
ejpam-6593	756	32	,	,	PUNCT
ejpam-6593	756	33	9	9	NUM
ejpam-6593	756	34	)	)	PUNCT
ejpam-6593	756	35	,	,	PUNCT
ejpam-6593	756	36	(	(	PUNCT
ejpam-6593	756	37	2	2	NUM
ejpam-6593	756	38	,	,	PUNCT
ejpam-6593	756	39	51	51	NUM
ejpam-6593	756	40	,	,	PUNCT
ejpam-6593	756	41	14	14	NUM
ejpam-6593	756	42	,	,	PUNCT
ejpam-6593	756	43	1	1	NUM
ejpam-6593	756	44	,	,	PUNCT
ejpam-6593	756	45	129	129	NUM
ejpam-6593	756	46	)	)	PUNCT
ejpam-6593	756	47	,	,	PUNCT
ejpam-6593	756	48	and	and	CCONJ
ejpam-6593	756	49	(	(	PUNCT
ejpam-6593	756	50	2	2	NUM
ejpam-6593	756	51	,	,	PUNCT
ejpam-6593	756	52	13107	13107	NUM
ejpam-6593	756	53	,	,	PUNCT
ejpam-6593	756	54	30	30	NUM
ejpam-6593	756	55	,	,	PUNCT
ejpam-6593	756	56	1	1	NUM
ejpam-6593	756	57	,	,	PUNCT
ejpam-6593	756	58	129	129	NUM
ejpam-6593	756	59	)	)	PUNCT
ejpam-6593	756	60	.	.	PUNCT
ejpam-6593	757	1	when	when	SCONJ
ejpam-6593	757	2	y	y	PROPN
ejpam-6593	757	3	=	=	SYM
ejpam-6593	757	4	2	2	NUM
ejpam-6593	757	5	and	and	CCONJ
ejpam-6593	757	6	y	y	NOUN
ejpam-6593	757	7	=	=	NOUN
ejpam-6593	757	8	3	3	NUM
ejpam-6593	757	9	with	with	ADP
ejpam-6593	757	10	the	the	DET
ejpam-6593	757	11	same	same	ADJ
ejpam-6593	757	12	values	value	NOUN
ejpam-6593	757	13	of	of	ADP
ejpam-6593	757	14	k	k	PROPN
ejpam-6593	757	15	and	and	CCONJ
ejpam-6593	757	16	x	x	X
ejpam-6593	757	17	in	in	ADP
ejpam-6593	757	18	the	the	DET
ejpam-6593	757	19	first	first	ADJ
ejpam-6593	757	20	case	case	NOUN
ejpam-6593	757	21	,	,	PUNCT
ejpam-6593	757	22	there	there	PRON
ejpam-6593	757	23	are	be	VERB
ejpam-6593	757	24	three	three	NUM
ejpam-6593	757	25	solutions	solution	NOUN
ejpam-6593	757	26	that	that	PRON
ejpam-6593	757	27	were	be	AUX
ejpam-6593	757	28	mentioned	mention	VERB
ejpam-6593	757	29	.	.	PUNCT
ejpam-6593	758	1	in	in	ADP
ejpam-6593	758	2	other	other	ADJ
ejpam-6593	758	3	words	word	NOUN
ejpam-6593	758	4	,	,	PUNCT
ejpam-6593	758	5	there	there	PRON
ejpam-6593	758	6	are	be	VERB
ejpam-6593	758	7	three	three	NUM
ejpam-6593	758	8	(	(	PUNCT
ejpam-6593	758	9	2	2	NUM
ejpam-6593	758	10	+	+	NUM
ejpam-6593	758	11	5k	5k	NUM
ejpam-6593	758	12	)	)	PUNCT
ejpam-6593	758	13	out	out	ADP
ejpam-6593	758	14	of	of	ADP
ejpam-6593	758	15	the	the	DET
ejpam-6593	758	16	30	30	NUM
ejpam-6593	758	17	solutions	solution	NOUN
ejpam-6593	758	18	mentioned	mention	VERB
ejpam-6593	758	19	in	in	ADP
ejpam-6593	758	20	the	the	DET
ejpam-6593	758	21	first	first	ADJ
ejpam-6593	758	22	case	case	NOUN
ejpam-6593	758	23	that	that	PRON
ejpam-6593	758	24	were	be	AUX
ejpam-6593	758	25	prime	prime	ADJ
ejpam-6593	758	26	,	,	PUNCT
ejpam-6593	758	27	namely	namely	ADV
ejpam-6593	758	28	,	,	PUNCT
ejpam-6593	758	29	(	(	PUNCT
ejpam-6593	758	30	p	p	X
ejpam-6593	758	31	,	,	PUNCT
ejpam-6593	758	32	k	k	NOUN
ejpam-6593	758	33	,	,	PUNCT
ejpam-6593	758	34	x	x	X
ejpam-6593	758	35	,	,	PUNCT
ejpam-6593	758	36	y	y	PROPN
ejpam-6593	758	37	,	,	PUNCT
ejpam-6593	758	38	z	z	NOUN
ejpam-6593	758	39	)	)	PUNCT
ejpam-6593	758	40	=	=	SYM
ejpam-6593	758	41	(	(	PUNCT
ejpam-6593	758	42	2	2	NUM
ejpam-6593	758	43	,	,	PUNCT
ejpam-6593	758	44	1	1	NUM
ejpam-6593	758	45	,	,	PUNCT
ejpam-6593	758	46	5	5	NUM
ejpam-6593	758	47	,	,	PUNCT
ejpam-6593	758	48	2	2	NUM
ejpam-6593	758	49	,	,	PUNCT
ejpam-6593	758	50	9	9	NUM
ejpam-6593	758	51	)	)	PUNCT
ejpam-6593	758	52	,	,	PUNCT
ejpam-6593	758	53	(	(	PUNCT
ejpam-6593	758	54	2	2	NUM
ejpam-6593	758	55	,	,	PUNCT
ejpam-6593	758	56	25	25	NUM
ejpam-6593	758	57	,	,	PUNCT
ejpam-6593	758	58	9	9	NUM
ejpam-6593	758	59	,	,	PUNCT
ejpam-6593	758	60	2	2	NUM
ejpam-6593	758	61	,	,	PUNCT
ejpam-6593	758	62	129	129	NUM
ejpam-6593	758	63	)	)	PUNCT
ejpam-6593	758	64	,	,	PUNCT
ejpam-6593	758	65	and	and	CCONJ
ejpam-6593	758	66	(	(	PUNCT
ejpam-6593	758	67	2	2	NUM
ejpam-6593	758	68	,	,	PUNCT
ejpam-6593	758	69	3	3	NUM
ejpam-6593	758	70	,	,	PUNCT
ejpam-6593	758	71	7	7	NUM
ejpam-6593	758	72	,	,	PUNCT
ejpam-6593	758	73	3	3	NUM
ejpam-6593	758	74	,	,	PUNCT
ejpam-6593	758	75	71	71	NUM
ejpam-6593	758	76	)	)	PUNCT
ejpam-6593	758	77	.	.	PUNCT
ejpam-6593	759	1	similar	similar	ADJ
ejpam-6593	759	2	to	to	ADP
ejpam-6593	759	3	the	the	DET
ejpam-6593	759	4	first	first	ADJ
ejpam-6593	759	5	case	case	NOUN
ejpam-6593	759	6	,	,	PUNCT
ejpam-6593	759	7	the	the	DET
ejpam-6593	759	8	equation	equation	NOUN
ejpam-6593	759	9	has	have	VERB
ejpam-6593	759	10	no	no	DET
ejpam-6593	759	11	solution	solution	NOUN
ejpam-6593	759	12	when	when	SCONJ
ejpam-6593	759	13	y	y	PROPN
ejpam-6593	759	14	=	=	SYM
ejpam-6593	759	15	1	1	NUM
ejpam-6593	759	16	and	and	CCONJ
ejpam-6593	759	17	x	x	PUNCT
ejpam-6593	759	18	≡	≡	PROPN
ejpam-6593	759	19	0	0	NUM
ejpam-6593	759	20	(	(	PUNCT
ejpam-6593	759	21	mod	mod	PROPN
ejpam-6593	759	22	4	4	NUM
ejpam-6593	759	23	)	)	PUNCT
ejpam-6593	759	24	,	,	PUNCT
ejpam-6593	759	25	and	and	CCONJ
ejpam-6593	759	26	when	when	SCONJ
ejpam-6593	759	27	x	x	X
ejpam-6593	759	28	=	=	NOUN
ejpam-6593	759	29	0	0	NUM
ejpam-6593	759	30	.	.	PUNCT
ejpam-6593	760	1	for	for	ADP
ejpam-6593	760	2	even	even	ADV
ejpam-6593	760	3	integers	integer	NOUN
ejpam-6593	760	4	k	k	NOUN
ejpam-6593	760	5	,	,	PUNCT
ejpam-6593	760	6	the	the	DET
ejpam-6593	760	7	discussion	discussion	NOUN
ejpam-6593	760	8	was	be	AUX
ejpam-6593	760	9	also	also	ADV
ejpam-6593	760	10	divided	divide	VERB
ejpam-6593	760	11	into	into	ADP
ejpam-6593	760	12	two	two	NUM
ejpam-6593	760	13	:	:	PUNCT
ejpam-6593	760	14	when	when	SCONJ
ejpam-6593	760	15	k	k	PROPN
ejpam-6593	760	16	≡	≡	PROPN
ejpam-6593	760	17	2	2	NUM
ejpam-6593	760	18	(	(	PUNCT
ejpam-6593	760	19	mod	mod	NOUN
ejpam-6593	760	20	4	4	NUM
ejpam-6593	760	21	)	)	PUNCT
ejpam-6593	760	22	;	;	PUNCT
ejpam-6593	760	23	and	and	CCONJ
ejpam-6593	760	24	when	when	SCONJ
ejpam-6593	760	25	k	k	PROPN
ejpam-6593	760	26	≡	≡	PROPN
ejpam-6593	760	27	0	0	PUNCT
ejpam-6593	760	28	(	(	PUNCT
ejpam-6593	760	29	mod	mod	PROPN
ejpam-6593	760	30	4	4	NUM
ejpam-6593	760	31	)	)	PUNCT
ejpam-6593	760	32	.	.	PUNCT
ejpam-6593	761	1	it	it	PRON
ejpam-6593	761	2	has	have	VERB
ejpam-6593	761	3	infinitely	infinitely	ADV
ejpam-6593	761	4	many	many	ADJ
ejpam-6593	761	5	solutions	solution	NOUN
ejpam-6593	762	1	when	when	SCONJ
ejpam-6593	762	2	k	k	PROPN
ejpam-6593	762	3	≡	≡	PROPN
ejpam-6593	762	4	2	2	NUM
ejpam-6593	762	5	(	(	PUNCT
ejpam-6593	762	6	mod	mod	NOUN
ejpam-6593	762	7	4	4	NUM
ejpam-6593	762	8	)	)	PUNCT
ejpam-6593	762	9	and	and	CCONJ
ejpam-6593	762	10	x	x	X
ejpam-6593	762	11	=	=	SYM
ejpam-6593	762	12	y	y	NOUN
ejpam-6593	762	13	=	=	SYM
ejpam-6593	762	14	1	1	X
ejpam-6593	762	15	.	.	PUNCT
ejpam-6593	762	16	moreover	moreover	ADV
ejpam-6593	762	17	,	,	PUNCT
ejpam-6593	762	18	(	(	PUNCT
ejpam-6593	762	19	p	p	X
ejpam-6593	762	20	,	,	PUNCT
ejpam-6593	762	21	k	k	NOUN
ejpam-6593	762	22	,	,	PUNCT
ejpam-6593	762	23	x	x	X
ejpam-6593	762	24	,	,	PUNCT
ejpam-6593	762	25	y	y	PROPN
ejpam-6593	762	26	,	,	PUNCT
ejpam-6593	762	27	z	z	NOUN
ejpam-6593	762	28	)	)	PUNCT
ejpam-6593	762	29	=	=	SYM
ejpam-6593	762	30	(	(	PUNCT
ejpam-6593	762	31	3	3	NUM
ejpam-6593	762	32	,	,	PUNCT
ejpam-6593	762	33	k	k	NOUN
ejpam-6593	762	34	,	,	PUNCT
ejpam-6593	762	35	1	1	NUM
ejpam-6593	762	36	,	,	PUNCT
ejpam-6593	762	37	0	0	NUM
ejpam-6593	762	38	,	,	PUNCT
ejpam-6593	762	39	2	2	NUM
ejpam-6593	762	40	)	)	PUNCT
ejpam-6593	762	41	is	be	AUX
ejpam-6593	762	42	a	a	DET
ejpam-6593	762	43	solution	solution	NOUN
ejpam-6593	762	44	for	for	ADP
ejpam-6593	762	45	some	some	DET
ejpam-6593	762	46	even	even	ADV
ejpam-6593	762	47	integers	integer	NOUN
ejpam-6593	762	48	k	k	NOUN
ejpam-6593	762	49	,	,	PUNCT
ejpam-6593	762	50	that	that	ADV
ejpam-6593	762	51	is	is	ADV
ejpam-6593	762	52	,	,	PUNCT
ejpam-6593	762	53	only	only	ADV
ejpam-6593	762	54	when	when	SCONJ
ejpam-6593	762	55	3	3	NUM
ejpam-6593	762	56	+	+	NUM
ejpam-6593	762	57	5k	5k	NUM
ejpam-6593	762	58	is	be	AUX
ejpam-6593	762	59	a	a	DET
ejpam-6593	762	60	prime	prime	NOUN
ejpam-6593	762	61	.	.	PUNCT
ejpam-6593	763	1	it	it	PRON
ejpam-6593	763	2	has	have	VERB
ejpam-6593	763	3	no	no	DET
ejpam-6593	763	4	solution	solution	NOUN
ejpam-6593	763	5	for	for	ADP
ejpam-6593	763	6	the	the	DET
ejpam-6593	763	7	most	most	ADJ
ejpam-6593	763	8	part	part	NOUN
ejpam-6593	763	9	.	.	PUNCT
ejpam-6593	764	1	for	for	ADP
ejpam-6593	764	2	the	the	DET
ejpam-6593	764	3	last	last	ADJ
ejpam-6593	764	4	case	case	NOUN
ejpam-6593	764	5	of	of	ADP
ejpam-6593	764	6	this	this	DET
ejpam-6593	764	7	study	study	NOUN
ejpam-6593	764	8	,	,	PUNCT
ejpam-6593	764	9	it	it	PRON
ejpam-6593	764	10	is	be	AUX
ejpam-6593	764	11	concluded	conclude	VERB
ejpam-6593	764	12	that	that	SCONJ
ejpam-6593	764	13	the	the	DET
ejpam-6593	764	14	equation	equation	NOUN
ejpam-6593	764	15	has	have	VERB
ejpam-6593	764	16	infinitely	infinitely	ADV
ejpam-6593	764	17	many	many	ADJ
ejpam-6593	764	18	solution	solution	NOUN
ejpam-6593	764	19	when	when	SCONJ
ejpam-6593	764	20	x	x	X
ejpam-6593	764	21	=	=	SYM
ejpam-6593	764	22	y	y	NOUN
ejpam-6593	764	23	=	=	SYM
ejpam-6593	764	24	1	1	NUM
ejpam-6593	764	25	,	,	PUNCT
ejpam-6593	764	26	and	and	CCONJ
ejpam-6593	764	27	that	that	SCONJ
ejpam-6593	764	28	z	z	PROPN
ejpam-6593	764	29	and	and	CCONJ
ejpam-6593	764	30	k	k	PROPN
ejpam-6593	764	31	have	have	VERB
ejpam-6593	764	32	the	the	DET
ejpam-6593	764	33	same	same	ADJ
ejpam-6593	764	34	parity	parity	NOUN
ejpam-6593	764	35	.	.	PUNCT
ejpam-6593	765	1	for	for	ADP
ejpam-6593	765	2	future	future	ADJ
ejpam-6593	765	3	study	study	NOUN
ejpam-6593	765	4	,	,	PUNCT
ejpam-6593	765	5	the	the	DET
ejpam-6593	765	6	authors	author	NOUN
ejpam-6593	765	7	recommend	recommend	VERB
ejpam-6593	765	8	the	the	DET
ejpam-6593	765	9	examination	examination	NOUN
ejpam-6593	765	10	of	of	ADP
ejpam-6593	765	11	the	the	DET
ejpam-6593	765	12	same	same	ADJ
ejpam-6593	765	13	cases	case	NOUN
ejpam-6593	765	14	,	,	PUNCT
ejpam-6593	765	15	but	but	CCONJ
ejpam-6593	765	16	to	to	PART
ejpam-6593	765	17	explore	explore	VERB
ejpam-6593	765	18	solutions	solution	NOUN
ejpam-6593	765	19	where	where	SCONJ
ejpam-6593	765	20	min	min	NOUN
ejpam-6593	765	21	(	(	PUNCT
ejpam-6593	765	22	x	x	PROPN
ejpam-6593	765	23	,	,	PUNCT
ejpam-6593	765	24	y	y	PROPN
ejpam-6593	765	25	)	)	PUNCT
ejpam-6593	765	26	>	>	X
ejpam-6593	766	1	1	1	X
ejpam-6593	766	2	.	.	PUNCT
ejpam-6593	766	3	acknowledgements	acknowledgement	NOUN
ejpam-6593	766	4	the	the	DET
ejpam-6593	766	5	authors	author	NOUN
ejpam-6593	766	6	thank	thank	VERB
ejpam-6593	766	7	the	the	DET
ejpam-6593	766	8	university	university	NOUN
ejpam-6593	766	9	of	of	ADP
ejpam-6593	766	10	the	the	DET
ejpam-6593	766	11	philippines	philippine	NOUN
ejpam-6593	766	12	baguio	baguio	PROPN
ejpam-6593	766	13	for	for	ADP
ejpam-6593	766	14	supporting	support	VERB
ejpam-6593	766	15	the	the	DET
ejpam-6593	766	16	dissemination	dissemination	NOUN
ejpam-6593	766	17	and	and	CCONJ
ejpam-6593	766	18	publication	publication	NOUN
ejpam-6593	766	19	of	of	ADP
ejpam-6593	766	20	the	the	DET
ejpam-6593	766	21	research	research	NOUN
ejpam-6593	766	22	results	result	NOUN
ejpam-6593	766	23	.	.	PUNCT
ejpam-6593	767	1	the	the	DET
ejpam-6593	767	2	authors	author	NOUN
ejpam-6593	767	3	also	also	ADV
ejpam-6593	767	4	thank	thank	VERB
ejpam-6593	767	5	the	the	DET
ejpam-6593	767	6	referees	referee	NOUN
ejpam-6593	767	7	and	and	CCONJ
ejpam-6593	767	8	editors	editor	NOUN
ejpam-6593	767	9	for	for	ADP
ejpam-6593	767	10	their	their	PRON
ejpam-6593	767	11	valuable	valuable	ADJ
ejpam-6593	767	12	comments	comment	NOUN
ejpam-6593	767	13	and	and	CCONJ
ejpam-6593	767	14	suggestions	suggestion	NOUN
ejpam-6593	767	15	.	.	PUNCT
ejpam-6593	768	1	references	reference	NOUN
ejpam-6593	768	2	[	[	X
ejpam-6593	768	3	1	1	X
ejpam-6593	768	4	]	]	PUNCT
ejpam-6593	768	5	a	a	DET
ejpam-6593	768	6	singta	singta	NOUN
ejpam-6593	768	7	,	,	PUNCT
ejpam-6593	768	8	a	a	DET
ejpam-6593	768	9	suvarnamani	suvarnamani	NOUN
ejpam-6593	768	10	,	,	PUNCT
ejpam-6593	768	11	and	and	CCONJ
ejpam-6593	768	12	s	s	AUX
ejpam-6593	768	13	chotchaisthit	chotchaisthit	VERB
ejpam-6593	768	14	.	.	PUNCT
ejpam-6593	769	1	on	on	ADP
ejpam-6593	769	2	two	two	NUM
ejpam-6593	769	3	diophantine	diophantine	NOUN
ejpam-6593	769	4	equations	equation	NOUN
ejpam-6593	769	5	4x	4x	NOUN
ejpam-6593	769	6	+	+	CCONJ
ejpam-6593	769	7	7y	7y	NOUN
ejpam-6593	769	8	=	=	SYM
ejpam-6593	769	9	z2	z2	PROPN
ejpam-6593	769	10	and	and	CCONJ
ejpam-6593	769	11	4x	4x	NUM
ejpam-6593	769	12	+	+	ADJ
ejpam-6593	769	13	11y	11y	NOUN
ejpam-6593	769	14	=	=	SYM
ejpam-6593	769	15	z2	z2	PROPN
ejpam-6593	769	16	.	.	PUNCT
ejpam-6593	770	1	science	science	NOUN
ejpam-6593	770	2	and	and	CCONJ
ejpam-6593	770	3	technology	technology	NOUN
ejpam-6593	770	4	rmutt	rmutt	PROPN
ejpam-6593	770	5	journal	journal	NOUN
ejpam-6593	770	6	,	,	PUNCT
ejpam-6593	770	7	1:25–28	1:25–28	NUM
ejpam-6593	770	8	,	,	PUNCT
ejpam-6593	770	9	2011	2011	NUM
ejpam-6593	770	10	.	.	PUNCT
ejpam-6593	771	1	[	[	X
ejpam-6593	771	2	2	2	NUM
ejpam-6593	771	3	]	]	SYM
ejpam-6593	771	4	b	b	X
ejpam-6593	771	5	sroysang	sroysang	PROPN
ejpam-6593	771	6	.	.	PUNCT
ejpam-6593	772	1	on	on	ADP
ejpam-6593	772	2	the	the	DET
ejpam-6593	772	3	diophantine	diophantine	NOUN
ejpam-6593	772	4	equation	equation	NOUN
ejpam-6593	772	5	3x	3x	NUM
ejpam-6593	772	6	+	+	CCONJ
ejpam-6593	772	7	5y	5y	NOUN
ejpam-6593	772	8	=	=	SYM
ejpam-6593	772	9	z2	z2	PROPN
ejpam-6593	772	10	.	.	PUNCT
ejpam-6593	773	1	international	international	ADJ
ejpam-6593	773	2	journal	journal	NOUN
ejpam-6593	773	3	of	of	ADP
ejpam-6593	773	4	pure	pure	ADJ
ejpam-6593	773	5	and	and	CCONJ
ejpam-6593	773	6	applied	applied	ADJ
ejpam-6593	773	7	mathematics	mathematic	NOUN
ejpam-6593	773	8	,	,	PUNCT
ejpam-6593	773	9	81:605–608	81:605–608	NUM
ejpam-6593	773	10	,	,	PUNCT
ejpam-6593	773	11	2012	2012	NUM
ejpam-6593	773	12	.	.	PUNCT
ejpam-6593	774	1	[	[	X
ejpam-6593	774	2	3	3	NUM
ejpam-6593	774	3	]	]	SYM
ejpam-6593	774	4	b	b	X
ejpam-6593	774	5	sroysang	sroysang	PROPN
ejpam-6593	774	6	.	.	PUNCT
ejpam-6593	775	1	more	more	ADJ
ejpam-6593	775	2	on	on	ADP
ejpam-6593	775	3	the	the	DET
ejpam-6593	775	4	diophantine	diophantine	NOUN
ejpam-6593	775	5	equation	equation	NOUN
ejpam-6593	775	6	8x	8x	VERB
ejpam-6593	775	7	+19y	+19y	X
ejpam-6593	775	8	=	=	SYM
ejpam-6593	775	9	z2	z2	PROPN
ejpam-6593	775	10	.	.	PUNCT
ejpam-6593	776	1	international	international	ADJ
ejpam-6593	776	2	journal	journal	NOUN
ejpam-6593	776	3	of	of	ADP
ejpam-6593	776	4	pure	pure	ADJ
ejpam-6593	776	5	and	and	CCONJ
ejpam-6593	776	6	applied	applied	ADJ
ejpam-6593	776	7	mathematics	mathematic	NOUN
ejpam-6593	776	8	,	,	PUNCT
ejpam-6593	776	9	81:601–604	81:601–604	PROPN
ejpam-6593	776	10	,	,	PUNCT
ejpam-6593	776	11	2012	2012	NUM
ejpam-6593	776	12	.	.	PUNCT
ejpam-6593	777	1	[	[	X
ejpam-6593	777	2	4	4	X
ejpam-6593	777	3	]	]	X
ejpam-6593	777	4	j	j	PROPN
ejpam-6593	777	5	f	f	PROPN
ejpam-6593	777	6	t	t	PROPN
ejpam-6593	777	7	rabago	rabago	PROPN
ejpam-6593	777	8	.	.	PUNCT
ejpam-6593	778	1	on	on	ADP
ejpam-6593	778	2	an	an	DET
ejpam-6593	778	3	open	open	ADJ
ejpam-6593	778	4	problem	problem	NOUN
ejpam-6593	778	5	by	by	ADP
ejpam-6593	778	6	b.	b.	PROPN
ejpam-6593	778	7	sroysang	sroysang	PROPN
ejpam-6593	778	8	.	.	PROPN
ejpam-6593	778	9	konuralp	konuralp	PROPN
ejpam-6593	778	10	journal	journal	PROPN
ejpam-6593	778	11	of	of	ADP
ejpam-6593	778	12	mathematics	mathematic	NOUN
ejpam-6593	778	13	,	,	PUNCT
ejpam-6593	778	14	1:30–32	1:30–32	NUM
ejpam-6593	778	15	,	,	PUNCT
ejpam-6593	778	16	2013	2013	NUM
ejpam-6593	778	17	.	.	PUNCT
ejpam-6593	779	1	[	[	X
ejpam-6593	779	2	5	5	NUM
ejpam-6593	779	3	]	]	SYM
ejpam-6593	779	4	b	b	X
ejpam-6593	779	5	sroysang	sroysang	PROPN
ejpam-6593	779	6	.	.	PUNCT
ejpam-6593	780	1	on	on	ADP
ejpam-6593	780	2	the	the	DET
ejpam-6593	780	3	diophantine	diophantine	NOUN
ejpam-6593	780	4	equation	equation	NOUN
ejpam-6593	780	5	5x	5x	NOUN
ejpam-6593	780	6	+	+	CCONJ
ejpam-6593	780	7	7y	7y	NOUN
ejpam-6593	780	8	=	=	SYM
ejpam-6593	780	9	z2	z2	PROPN
ejpam-6593	780	10	.	.	PUNCT
ejpam-6593	780	11	international	international	ADJ
ejpam-6593	780	12	journal	journal	NOUN
ejpam-6593	780	13	of	of	ADP
ejpam-6593	780	14	pure	pure	ADJ
ejpam-6593	780	15	and	and	CCONJ
ejpam-6593	780	16	applied	applied	ADJ
ejpam-6593	780	17	mathematics	mathematic	NOUN
ejpam-6593	780	18	,	,	PUNCT
ejpam-6593	780	19	89:115–118	89:115–118	PROPN
ejpam-6593	780	20	,	,	PUNCT
ejpam-6593	780	21	2013	2013	NUM
ejpam-6593	780	22	.	.	PUNCT
ejpam-6593	781	1	[	[	X
ejpam-6593	781	2	6	6	NUM
ejpam-6593	781	3	]	]	PUNCT
ejpam-6593	781	4	s	s	AUX
ejpam-6593	781	5	chotchaisthit	chotchaisthit	VERB
ejpam-6593	781	6	.	.	PUNCT
ejpam-6593	782	1	on	on	ADP
ejpam-6593	782	2	the	the	DET
ejpam-6593	782	3	diophantine	diophantine	NOUN
ejpam-6593	782	4	equation	equation	NOUN
ejpam-6593	782	5	px+(p+1)y	px+(p+1)y	NOUN
ejpam-6593	782	6	=	=	SYM
ejpam-6593	782	7	z2	z2	PROPN
ejpam-6593	782	8	where	where	SCONJ
ejpam-6593	782	9	p	p	NOUN
ejpam-6593	782	10	is	be	AUX
ejpam-6593	782	11	a	a	DET
ejpam-6593	782	12	mersenne	mersenne	NOUN
ejpam-6593	782	13	prime	prime	NOUN
ejpam-6593	782	14	.	.	PUNCT
ejpam-6593	783	1	international	international	ADJ
ejpam-6593	783	2	journal	journal	NOUN
ejpam-6593	783	3	of	of	ADP
ejpam-6593	783	4	pure	pure	ADJ
ejpam-6593	783	5	and	and	CCONJ
ejpam-6593	783	6	applied	applied	ADJ
ejpam-6593	783	7	mathematics	mathematic	NOUN
ejpam-6593	783	8	,	,	PUNCT
ejpam-6593	783	9	88:169–172	88:169–172	PROPN
ejpam-6593	783	10	,	,	PUNCT
ejpam-6593	783	11	2013	2013	NUM
ejpam-6593	783	12	.	.	PUNCT
ejpam-6593	784	1	[	[	X
ejpam-6593	784	2	7	7	X
ejpam-6593	784	3	]	]	X
ejpam-6593	784	4	w	w	PROPN
ejpam-6593	784	5	s	s	PROPN
ejpam-6593	784	6	gayo	gayo	NOUN
ejpam-6593	784	7	,	,	PUNCT
ejpam-6593	784	8	jr	jr	PROPN
ejpam-6593	784	9	and	and	CCONJ
ejpam-6593	784	10	j	j	PROPN
ejpam-6593	784	11	b	b	PROPN
ejpam-6593	784	12	bacani	bacani	PROPN
ejpam-6593	784	13	.	.	PUNCT
ejpam-6593	785	1	on	on	ADP
ejpam-6593	785	2	the	the	DET
ejpam-6593	785	3	diophantine	diophantine	NOUN
ejpam-6593	785	4	equation	equation	NOUN
ejpam-6593	785	5	mx	mx	PROPN
ejpam-6593	785	6	p	p	PROPN
ejpam-6593	785	7	+	+	X
ejpam-6593	785	8	(	(	PUNCT
ejpam-6593	785	9	mq	mq	PROPN
ejpam-6593	785	10	+	+	CCONJ
ejpam-6593	785	11	1)y	1)y	NUM
ejpam-6593	785	12	=	=	SYM
ejpam-6593	785	13	z2	z2	PROPN
ejpam-6593	785	14	.	.	PUNCT
ejpam-6593	785	15	european	european	PROPN
ejpam-6593	785	16	journal	journal	PROPN
ejpam-6593	785	17	of	of	ADP
ejpam-6593	785	18	pure	pure	ADJ
ejpam-6593	785	19	and	and	CCONJ
ejpam-6593	785	20	applied	applied	ADJ
ejpam-6593	785	21	mathematics	mathematic	NOUN
ejpam-6593	785	22	,	,	PUNCT
ejpam-6593	785	23	14:396–403	14:396–403	PROPN
ejpam-6593	785	24	,	,	PUNCT
ejpam-6593	785	25	2021	2021	NUM
ejpam-6593	785	26	.	.	PUNCT
ejpam-6593	786	1	[	[	X
ejpam-6593	786	2	8	8	NUM
ejpam-6593	786	3	]	]	X
ejpam-6593	786	4	w	w	PROPN
ejpam-6593	786	5	s	s	PROPN
ejpam-6593	786	6	gayo	gayo	NOUN
ejpam-6593	786	7	,	,	PUNCT
ejpam-6593	786	8	jr	jr	PROPN
ejpam-6593	786	9	and	and	CCONJ
ejpam-6593	786	10	j	j	PROPN
ejpam-6593	786	11	b	b	PROPN
ejpam-6593	786	12	bacani	bacani	PROPN
ejpam-6593	786	13	.	.	PUNCT
ejpam-6593	787	1	on	on	ADP
ejpam-6593	787	2	the	the	DET
ejpam-6593	787	3	solutions	solution	NOUN
ejpam-6593	787	4	of	of	ADP
ejpam-6593	787	5	the	the	DET
ejpam-6593	787	6	diophantine	diophantine	NOUN
ejpam-6593	787	7	equation	equation	NOUN
ejpam-6593	787	8	mx	mx	PROPN
ejpam-6593	788	1	+	+	CCONJ
ejpam-6593	788	2	(	(	PUNCT
ejpam-6593	788	3	m−1)y	m−1)y	NOUN
ejpam-6593	788	4	=	=	SYM
ejpam-6593	788	5	z2	z2	PROPN
ejpam-6593	788	6	.	.	PUNCT
ejpam-6593	789	1	italian	italian	ADJ
ejpam-6593	789	2	journal	journal	NOUN
ejpam-6593	789	3	of	of	ADP
ejpam-6593	789	4	pure	pure	ADJ
ejpam-6593	789	5	and	and	CCONJ
ejpam-6593	789	6	applied	applied	ADJ
ejpam-6593	789	7	mathematics	mathematic	NOUN
ejpam-6593	789	8	,	,	PUNCT
ejpam-6593	789	9	47:1113–1117	47:1113–1117	NUM
ejpam-6593	789	10	,	,	PUNCT
ejpam-6593	789	11	2022	2022	NUM
ejpam-6593	789	12	.	.	PUNCT
ejpam-6593	790	1	[	[	X
ejpam-6593	790	2	9	9	NUM
ejpam-6593	790	3	]	]	X
ejpam-6593	790	4	w	w	PROPN
ejpam-6593	790	5	s	s	PROPN
ejpam-6593	790	6	gayo	gayo	NOUN
ejpam-6593	790	7	,	,	PUNCT
ejpam-6593	790	8	jr	jr	PROPN
ejpam-6593	790	9	and	and	CCONJ
ejpam-6593	790	10	j	j	PROPN
ejpam-6593	790	11	b	b	PROPN
ejpam-6593	790	12	bacani	bacani	PROPN
ejpam-6593	790	13	.	.	PUNCT
ejpam-6593	791	1	on	on	ADP
ejpam-6593	791	2	the	the	DET
ejpam-6593	791	3	solutions	solution	NOUN
ejpam-6593	791	4	of	of	ADP
ejpam-6593	791	5	some	some	DET
ejpam-6593	791	6	mersenne	mersenne	NOUN
ejpam-6593	791	7	prime	prime	ADV
ejpam-6593	791	8	-	-	PUNCT
ejpam-6593	791	9	involved	involve	VERB
ejpam-6593	791	10	m.	m.	NOUN
ejpam-6593	791	11	c.	c.	PROPN
ejpam-6593	791	12	avenilla	avenilla	PROPN
ejpam-6593	791	13	,	,	PUNCT
ejpam-6593	791	14	j.	j.	PROPN
ejpam-6593	791	15	b.	b.	PROPN
ejpam-6593	791	16	bacani	bacani	PROPN
ejpam-6593	791	17	/	/	SYM
ejpam-6593	791	18	eur	eur	PROPN
ejpam-6593	791	19	.	.	PUNCT
ejpam-6593	792	1	j.	j.	PROPN
ejpam-6593	792	2	pure	pure	PROPN
ejpam-6593	792	3	appl	appl	PROPN
ejpam-6593	792	4	.	.	PROPN
ejpam-6593	792	5	math	math	PROPN
ejpam-6593	792	6	,	,	PUNCT
ejpam-6593	792	7	18	18	NUM
ejpam-6593	792	8	(	(	PUNCT
ejpam-6593	792	9	3	3	NUM
ejpam-6593	792	10	)	)	PUNCT
ejpam-6593	792	11	(	(	PUNCT
ejpam-6593	792	12	2025	2025	NUM
ejpam-6593	792	13	)	)	PUNCT
ejpam-6593	792	14	,	,	PUNCT
ejpam-6593	792	15	6593	6593	NUM
ejpam-6593	792	16	24	24	NUM
ejpam-6593	792	17	of	of	ADP
ejpam-6593	792	18	24	24	NUM
ejpam-6593	792	19	diophantine	diophantine	NOUN
ejpam-6593	792	20	equations	equation	NOUN
ejpam-6593	792	21	.	.	PUNCT
ejpam-6593	793	1	international	international	ADJ
ejpam-6593	793	2	journal	journal	PROPN
ejpam-6593	793	3	of	of	ADP
ejpam-6593	793	4	mathematics	mathematic	NOUN
ejpam-6593	793	5	and	and	CCONJ
ejpam-6593	793	6	computer	computer	NOUN
ejpam-6593	793	7	science	science	NOUN
ejpam-6593	793	8	,	,	PUNCT
ejpam-6593	793	9	18:487–495	18:487–495	NUM
ejpam-6593	793	10	,	,	PUNCT
ejpam-6593	793	11	2023	2023	NUM
ejpam-6593	793	12	.	.	PUNCT
ejpam-6593	794	1	[	[	X
ejpam-6593	794	2	10	10	NUM
ejpam-6593	794	3	]	]	X
ejpam-6593	794	4	r	r	NOUN
ejpam-6593	794	5	j	j	PROPN
ejpam-6593	794	6	s	s	X
ejpam-6593	794	7	mina	mina	PROPN
ejpam-6593	794	8	and	and	CCONJ
ejpam-6593	794	9	j	j	PROPN
ejpam-6593	794	10	b	b	PROPN
ejpam-6593	794	11	bacani	bacani	PROPN
ejpam-6593	794	12	.	.	PUNCT
ejpam-6593	795	1	on	on	ADP
ejpam-6593	795	2	nonsolvability	nonsolvability	NOUN
ejpam-6593	795	3	of	of	ADP
ejpam-6593	795	4	exponential	exponential	ADJ
ejpam-6593	795	5	diophantine	diophantine	NOUN
ejpam-6593	795	6	equations	equation	NOUN
ejpam-6593	795	7	via	via	ADP
ejpam-6593	795	8	transformation	transformation	NOUN
ejpam-6593	795	9	to	to	ADP
ejpam-6593	795	10	elliptic	elliptic	ADJ
ejpam-6593	795	11	curves	curve	NOUN
ejpam-6593	795	12	.	.	PUNCT
ejpam-6593	796	1	italian	italian	ADJ
ejpam-6593	796	2	journal	journal	NOUN
ejpam-6593	796	3	of	of	ADP
ejpam-6593	796	4	pure	pure	ADJ
ejpam-6593	796	5	and	and	CCONJ
ejpam-6593	796	6	applied	applied	ADJ
ejpam-6593	796	7	mathematics	mathematic	NOUN
ejpam-6593	796	8	,	,	PUNCT
ejpam-6593	796	9	49:196–205	49:196–205	PROPN
ejpam-6593	796	10	,	,	PUNCT
ejpam-6593	796	11	2023	2023	NUM
ejpam-6593	796	12	.	.	PUNCT
ejpam-6593	797	1	[	[	X
ejpam-6593	797	2	11	11	NUM
ejpam-6593	797	3	]	]	X
ejpam-6593	797	4	r	r	NOUN
ejpam-6593	797	5	j	j	PROPN
ejpam-6593	797	6	s	s	X
ejpam-6593	797	7	mina	mina	PROPN
ejpam-6593	797	8	and	and	CCONJ
ejpam-6593	797	9	j	j	PROPN
ejpam-6593	797	10	b	b	PROPN
ejpam-6593	797	11	bacani	bacani	PROPN
ejpam-6593	797	12	.	.	PUNCT
ejpam-6593	798	1	on	on	ADP
ejpam-6593	798	2	the	the	DET
ejpam-6593	798	3	diophantine	diophantine	NOUN
ejpam-6593	798	4	equation	equation	NOUN
ejpam-6593	798	5	px	px	X
ejpam-6593	798	6	+	+	CCONJ
ejpam-6593	798	7	(	(	PUNCT
ejpam-6593	798	8	p+	p+	X
ejpam-6593	798	9	5)y	5)y	X
ejpam-6593	798	10	=	=	SYM
ejpam-6593	798	11	z2	z2	PROPN
ejpam-6593	798	12	,	,	PUNCT
ejpam-6593	798	13	where	where	SCONJ
ejpam-6593	798	14	p	p	NOUN
ejpam-6593	798	15	is	be	AUX
ejpam-6593	798	16	odd	odd	ADJ
ejpam-6593	798	17	prime	prime	NOUN
ejpam-6593	798	18	.	.	PUNCT
ejpam-6593	799	1	thai	thai	PROPN
ejpam-6593	799	2	journal	journal	PROPN
ejpam-6593	799	3	of	of	ADP
ejpam-6593	799	4	mathematics	mathematic	NOUN
ejpam-6593	799	5	,	,	PUNCT
ejpam-6593	799	6	2:67–75	2:67–75	NUM
ejpam-6593	799	7	,	,	PUNCT
ejpam-6593	799	8	2023	2023	NUM
ejpam-6593	799	9	.	.	PUNCT
ejpam-6593	800	1	[	[	X
ejpam-6593	800	2	12	12	NUM
ejpam-6593	800	3	]	]	PUNCT
ejpam-6593	800	4	p	p	PROPN
ejpam-6593	800	5	mihǎilescu	mihǎilescu	PROPN
ejpam-6593	800	6	.	.	PUNCT
ejpam-6593	801	1	primary	primary	ADJ
ejpam-6593	801	2	cyclotomic	cyclotomic	ADJ
ejpam-6593	801	3	units	unit	NOUN
ejpam-6593	801	4	and	and	CCONJ
ejpam-6593	801	5	a	a	DET
ejpam-6593	801	6	proof	proof	NOUN
ejpam-6593	801	7	of	of	ADP
ejpam-6593	801	8	catalan	catalan	NOUN
ejpam-6593	801	9	’s	’s	PART
ejpam-6593	801	10	conjecture	conjecture	NOUN
ejpam-6593	801	11	.	.	PUNCT
ejpam-6593	802	1	journal	journal	PROPN
ejpam-6593	802	2	für	für	AUX
ejpam-6593	802	3	die	die	VERB
ejpam-6593	802	4	reine	reine	PROPN
ejpam-6593	802	5	und	und	PROPN
ejpam-6593	802	6	angewandte	angewandte	PROPN
ejpam-6593	802	7	mathematik	mathematik	PROPN
ejpam-6593	802	8	,	,	PUNCT
ejpam-6593	802	9	572:167–195	572:167–195	NUM
ejpam-6593	802	10	,	,	PUNCT
ejpam-6593	802	11	2004	2004	NUM
ejpam-6593	802	12	.	.	PUNCT
ejpam-6593	803	1	[	[	X
ejpam-6593	803	2	13	13	NUM
ejpam-6593	803	3	]	]	SYM
ejpam-6593	803	4	s	s	PART
ejpam-6593	803	5	gupta	gupta	PROPN
ejpam-6593	803	6	,	,	PUNCT
ejpam-6593	803	7	s	s	PART
ejpam-6593	803	8	kumar	kumar	PROPN
ejpam-6593	803	9	,	,	PUNCT
ejpam-6593	803	10	and	and	CCONJ
ejpam-6593	803	11	h	h	PROPN
ejpam-6593	803	12	kishan	kishan	PROPN
ejpam-6593	803	13	.	.	PUNCT
ejpam-6593	804	1	on	on	ADP
ejpam-6593	804	2	the	the	DET
ejpam-6593	804	3	non	non	ADJ
ejpam-6593	804	4	-	-	ADJ
ejpam-6593	804	5	linear	linear	ADJ
ejpam-6593	804	6	diophantine	diophantine	NOUN
ejpam-6593	804	7	equation	equation	NOUN
ejpam-6593	804	8	61x	61x	PUNCT
ejpam-6593	805	1	+	+	CCONJ
ejpam-6593	805	2	67y	67y	NOUN
ejpam-6593	805	3	=	=	SYM
ejpam-6593	805	4	z2	z2	PROPN
ejpam-6593	805	5	and	and	CCONJ
ejpam-6593	805	6	67x	67x	NUM
ejpam-6593	805	7	+	+	NUM
ejpam-6593	805	8	73y	73y	NOUN
ejpam-6593	805	9	=	=	SYM
ejpam-6593	805	10	z2	z2	PROPN
ejpam-6593	805	11	.	.	PUNCT
ejpam-6593	806	1	annals	annal	NOUN
ejpam-6593	806	2	of	of	ADP
ejpam-6593	806	3	pure	pure	ADJ
ejpam-6593	806	4	and	and	CCONJ
ejpam-6593	806	5	applied	applied	ADJ
ejpam-6593	806	6	mathematics	mathematic	NOUN
ejpam-6593	806	7	,	,	PUNCT
ejpam-6593	806	8	18:91–94	18:91–94	NUM
ejpam-6593	806	9	,	,	PUNCT
ejpam-6593	806	10	2018	2018	NUM
ejpam-6593	806	11	.	.	PUNCT
ejpam-6593	807	1	[	[	X
ejpam-6593	807	2	14	14	NUM
ejpam-6593	807	3	]	]	X
ejpam-6593	807	4	j	j	PROPN
ejpam-6593	807	5	b	b	PROPN
ejpam-6593	807	6	bacani	bacani	PROPN
ejpam-6593	807	7	and	and	CCONJ
ejpam-6593	807	8	j	j	PROPN
ejpam-6593	807	9	f	f	PROPN
ejpam-6593	807	10	t	t	PROPN
ejpam-6593	807	11	rabago	rabago	PROPN
ejpam-6593	807	12	.	.	PUNCT
ejpam-6593	808	1	the	the	DET
ejpam-6593	808	2	complete	complete	ADJ
ejpam-6593	808	3	set	set	NOUN
ejpam-6593	808	4	of	of	ADP
ejpam-6593	808	5	solutions	solution	NOUN
ejpam-6593	808	6	of	of	ADP
ejpam-6593	808	7	the	the	DET
ejpam-6593	808	8	diophantine	diophantine	NOUN
ejpam-6593	808	9	equation	equation	NOUN
ejpam-6593	808	10	px	px	X
ejpam-6593	808	11	+	+	CCONJ
ejpam-6593	808	12	qy	qy	NOUN
ejpam-6593	808	13	=	=	PROPN
ejpam-6593	808	14	z2	z2	PROPN
ejpam-6593	808	15	for	for	ADP
ejpam-6593	808	16	twin	twin	ADJ
ejpam-6593	808	17	primes	prime	NOUN
ejpam-6593	808	18	p	p	NOUN
ejpam-6593	808	19	and	and	CCONJ
ejpam-6593	808	20	q.	q.	PROPN
ejpam-6593	808	21	international	international	PROPN
ejpam-6593	808	22	journal	journal	PROPN
ejpam-6593	808	23	of	of	ADP
ejpam-6593	808	24	pure	pure	ADJ
ejpam-6593	808	25	and	and	CCONJ
ejpam-6593	808	26	applied	applied	ADJ
ejpam-6593	808	27	mathematics	mathematic	NOUN
ejpam-6593	808	28	,	,	PUNCT
ejpam-6593	808	29	104:517–521	104:517–521	NUM
ejpam-6593	808	30	,	,	PUNCT
ejpam-6593	808	31	2016	2016	NUM
ejpam-6593	808	32	.	.	PUNCT
ejpam-6593	809	1	[	[	X
ejpam-6593	809	2	15	15	NUM
ejpam-6593	809	3	]	]	PUNCT
ejpam-6593	809	4	n	n	CCONJ
ejpam-6593	809	5	burshtein	burshtein	ADV
ejpam-6593	809	6	.	.	PUNCT
ejpam-6593	810	1	all	all	DET
ejpam-6593	810	2	the	the	DET
ejpam-6593	810	3	solutions	solution	NOUN
ejpam-6593	810	4	of	of	ADP
ejpam-6593	810	5	the	the	DET
ejpam-6593	810	6	diophantine	diophantine	NOUN
ejpam-6593	810	7	equation	equation	NOUN
ejpam-6593	810	8	px	px	X
ejpam-6593	810	9	+	+	CCONJ
ejpam-6593	810	10	(	(	PUNCT
ejpam-6593	810	11	p+	p+	NOUN
ejpam-6593	810	12	4)y	4)y	PROPN
ejpam-6593	810	13	=	=	SYM
ejpam-6593	810	14	z2	z2	PROPN
ejpam-6593	810	15	when	when	SCONJ
ejpam-6593	810	16	p	p	X
ejpam-6593	810	17	,	,	PUNCT
ejpam-6593	810	18	(	(	PUNCT
ejpam-6593	810	19	p	p	NOUN
ejpam-6593	810	20	+	+	NOUN
ejpam-6593	810	21	4	4	NUM
ejpam-6593	810	22	)	)	PUNCT
ejpam-6593	810	23	are	be	AUX
ejpam-6593	810	24	primes	prime	NOUN
ejpam-6593	810	25	and	and	CCONJ
ejpam-6593	810	26	x	x	PUNCT
ejpam-6593	811	1	+	+	CCONJ
ejpam-6593	811	2	y	y	NOUN
ejpam-6593	811	3	=	=	SYM
ejpam-6593	811	4	2	2	NUM
ejpam-6593	811	5	,	,	PUNCT
ejpam-6593	811	6	3	3	NUM
ejpam-6593	811	7	,	,	PUNCT
ejpam-6593	811	8	4	4	NUM
ejpam-6593	811	9	.	.	PUNCT
ejpam-6593	811	10	annals	annal	NOUN
ejpam-6593	811	11	of	of	ADP
ejpam-6593	811	12	pure	pure	ADJ
ejpam-6593	811	13	and	and	CCONJ
ejpam-6593	811	14	applied	applied	ADJ
ejpam-6593	811	15	mathematics	mathematic	NOUN
ejpam-6593	811	16	,	,	PUNCT
ejpam-6593	811	17	16:241–244	16:241–244	NUM
ejpam-6593	811	18	,	,	PUNCT
ejpam-6593	811	19	2018	2018	NUM
ejpam-6593	811	20	.	.	PUNCT
ejpam-6593	812	1	[	[	X
ejpam-6593	812	2	16	16	NUM
ejpam-6593	812	3	]	]	PUNCT
ejpam-6593	812	4	n	n	CCONJ
ejpam-6593	812	5	burshtein	burshtein	ADV
ejpam-6593	812	6	.	.	PUNCT
ejpam-6593	813	1	solutions	solution	NOUN
ejpam-6593	813	2	of	of	ADP
ejpam-6593	813	3	the	the	DET
ejpam-6593	813	4	diophantine	diophantine	NOUN
ejpam-6593	813	5	equation	equation	NOUN
ejpam-6593	813	6	px+(p+6)y	px+(p+6)y	NOUN
ejpam-6593	813	7	=	=	SYM
ejpam-6593	813	8	z2	z2	NOUN
ejpam-6593	813	9	when	when	SCONJ
ejpam-6593	813	10	p	p	X
ejpam-6593	813	11	,	,	PUNCT
ejpam-6593	813	12	(	(	PUNCT
ejpam-6593	813	13	p+6	p+6	NUM
ejpam-6593	813	14	)	)	PUNCT
ejpam-6593	813	15	are	be	AUX
ejpam-6593	813	16	primes	prime	NOUN
ejpam-6593	813	17	and	and	CCONJ
ejpam-6593	813	18	x+	x+	ADJ
ejpam-6593	813	19	y	y	NOUN
ejpam-6593	813	20	=	=	SYM
ejpam-6593	813	21	2	2	NUM
ejpam-6593	813	22	,	,	PUNCT
ejpam-6593	813	23	3	3	NUM
ejpam-6593	813	24	,	,	PUNCT
ejpam-6593	813	25	4	4	NUM
ejpam-6593	813	26	.	.	PUNCT
ejpam-6593	813	27	annals	annal	NOUN
ejpam-6593	813	28	of	of	ADP
ejpam-6593	813	29	pure	pure	ADJ
ejpam-6593	813	30	and	and	CCONJ
ejpam-6593	813	31	applied	applied	ADJ
ejpam-6593	813	32	mathematics	mathematic	NOUN
ejpam-6593	813	33	,	,	PUNCT
ejpam-6593	813	34	17:101–106	17:101–106	NUM
ejpam-6593	813	35	,	,	PUNCT
ejpam-6593	813	36	2018	2018	NUM
ejpam-6593	813	37	.	.	PUNCT
ejpam-6593	814	1	[	[	X
ejpam-6593	814	2	17	17	NUM
ejpam-6593	814	3	]	]	X
ejpam-6593	814	4	f	f	PROPN
ejpam-6593	814	5	neres	nere	NOUN
ejpam-6593	814	6	.	.	PUNCT
ejpam-6593	815	1	on	on	ADP
ejpam-6593	815	2	the	the	DET
ejpam-6593	815	3	solvability	solvability	NOUN
ejpam-6593	815	4	of	of	ADP
ejpam-6593	815	5	the	the	DET
ejpam-6593	815	6	diophantine	diophantine	NOUN
ejpam-6593	815	7	equation	equation	NOUN
ejpam-6593	815	8	px	px	X
ejpam-6593	815	9	+	+	CCONJ
ejpam-6593	815	10	(	(	PUNCT
ejpam-6593	815	11	p	p	X
ejpam-6593	815	12	+	+	NUM
ejpam-6593	815	13	8)y	8)y	NOUN
ejpam-6593	815	14	=	=	SYM
ejpam-6593	815	15	z2	z2	NOUN
ejpam-6593	815	16	when	when	SCONJ
ejpam-6593	815	17	p	p	PROPN
ejpam-6593	815	18	>	>	X
ejpam-6593	815	19	3	3	NUM
ejpam-6593	815	20	and	and	CCONJ
ejpam-6593	815	21	p+8	p+8	PROPN
ejpam-6593	815	22	are	be	AUX
ejpam-6593	815	23	primes	prime	NOUN
ejpam-6593	815	24	.	.	PUNCT
ejpam-6593	815	25	annals	annal	NOUN
ejpam-6593	815	26	of	of	ADP
ejpam-6593	815	27	pure	pure	ADJ
ejpam-6593	815	28	and	and	CCONJ
ejpam-6593	815	29	applied	applied	ADJ
ejpam-6593	815	30	mathematics	mathematic	NOUN
ejpam-6593	815	31	,	,	PUNCT
ejpam-6593	815	32	18:9–13	18:9–13	NUM
ejpam-6593	815	33	,	,	PUNCT
ejpam-6593	815	34	2018	2018	NUM
ejpam-6593	815	35	.	.	PUNCT
ejpam-6593	816	1	[	[	X
ejpam-6593	816	2	18	18	NUM
ejpam-6593	816	3	]	]	X
ejpam-6593	816	4	s	s	VERB
ejpam-6593	816	5	tadee	tadee	NOUN
ejpam-6593	816	6	.	.	PUNCT
ejpam-6593	817	1	on	on	ADP
ejpam-6593	817	2	the	the	DET
ejpam-6593	817	3	diophantine	diophantine	NOUN
ejpam-6593	817	4	equation	equation	NOUN
ejpam-6593	817	5	px	px	X
ejpam-6593	817	6	+	+	CCONJ
ejpam-6593	817	7	(	(	PUNCT
ejpam-6593	817	8	p	p	X
ejpam-6593	817	9	+	+	NOUN
ejpam-6593	817	10	14)y	14)y	NUM
ejpam-6593	817	11	=	=	SYM
ejpam-6593	817	12	z2	z2	PROPN
ejpam-6593	817	13	where	where	SCONJ
ejpam-6593	817	14	p	p	NOUN
ejpam-6593	817	15	and	and	CCONJ
ejpam-6593	817	16	p	p	NOUN
ejpam-6593	817	17	+	+	NOUN
ejpam-6593	817	18	14	14	NUM
ejpam-6593	817	19	are	be	AUX
ejpam-6593	817	20	primes	prime	NOUN
ejpam-6593	817	21	.	.	PUNCT
ejpam-6593	817	22	annals	annal	NOUN
ejpam-6593	817	23	of	of	ADP
ejpam-6593	817	24	pure	pure	ADJ
ejpam-6593	817	25	and	and	CCONJ
ejpam-6593	817	26	applied	applied	ADJ
ejpam-6593	817	27	mathematics	mathematic	NOUN
ejpam-6593	817	28	,	,	PUNCT
ejpam-6593	817	29	26:125–130	26:125–130	NUM
ejpam-6593	817	30	,	,	PUNCT
ejpam-6593	817	31	2022	2022	NUM
ejpam-6593	817	32	.	.	PUNCT
ejpam-6593	818	1	[	[	X
ejpam-6593	818	2	19	19	NUM
ejpam-6593	818	3	]	]	X
ejpam-6593	818	4	r	r	NOUN
ejpam-6593	818	5	j	j	PROPN
ejpam-6593	818	6	s	s	X
ejpam-6593	818	7	mina	mina	PROPN
ejpam-6593	818	8	and	and	CCONJ
ejpam-6593	818	9	j	j	PROPN
ejpam-6593	818	10	b	b	PROPN
ejpam-6593	818	11	bacani	bacani	PROPN
ejpam-6593	818	12	.	.	PUNCT
ejpam-6593	819	1	on	on	ADP
ejpam-6593	819	2	the	the	DET
ejpam-6593	819	3	solutions	solution	NOUN
ejpam-6593	819	4	of	of	ADP
ejpam-6593	819	5	the	the	DET
ejpam-6593	819	6	diophantine	diophantine	NOUN
ejpam-6593	819	7	equation	equation	NOUN
ejpam-6593	819	8	px	px	X
ejpam-6593	819	9	+	+	CCONJ
ejpam-6593	819	10	(	(	PUNCT
ejpam-6593	819	11	p	p	X
ejpam-6593	819	12	+	+	NOUN
ejpam-6593	819	13	4k)y	4k)y	NOUN
ejpam-6593	819	14	=	=	SYM
ejpam-6593	819	15	z2	z2	PROPN
ejpam-6593	819	16	for	for	ADP
ejpam-6593	819	17	prime	prime	ADJ
ejpam-6593	819	18	pairs	pair	NOUN
ejpam-6593	819	19	p	p	NOUN
ejpam-6593	819	20	and	and	CCONJ
ejpam-6593	819	21	p	p	NOUN
ejpam-6593	819	22	+	+	X
ejpam-6593	819	23	4k	4k	NOUN
ejpam-6593	819	24	.	.	PUNCT
ejpam-6593	820	1	european	european	ADJ
ejpam-6593	820	2	journal	journal	PROPN
ejpam-6593	820	3	of	of	ADP
ejpam-6593	820	4	pure	pure	ADJ
ejpam-6593	820	5	and	and	CCONJ
ejpam-6593	820	6	applied	applied	ADJ
ejpam-6593	820	7	mathematics	mathematic	NOUN
ejpam-6593	820	8	,	,	PUNCT
ejpam-6593	820	9	14:471–479	14:471–479	NUM
ejpam-6593	820	10	,	,	PUNCT
ejpam-6593	820	11	2021	2021	NUM
ejpam-6593	820	12	.	.	PUNCT
ejpam-6593	821	1	[	[	X
ejpam-6593	821	2	20	20	NUM
ejpam-6593	821	3	]	]	PUNCT
ejpam-6593	821	4	w	w	NOUN
ejpam-6593	821	5	orosram	orosram	NOUN
ejpam-6593	821	6	et	et	PROPN
ejpam-6593	821	7	al	al	PROPN
ejpam-6593	821	8	.	.	PROPN
ejpam-6593	822	1	on	on	ADP
ejpam-6593	822	2	the	the	DET
ejpam-6593	822	3	diophantine	diophantine	NOUN
ejpam-6593	822	4	equation	equation	NOUN
ejpam-6593	822	5	(	(	PUNCT
ejpam-6593	822	6	p+4n)x+py	p+4n)x+py	NOUN
ejpam-6593	822	7	=	=	SYM
ejpam-6593	822	8	z2	z2	PROPN
ejpam-6593	822	9	.	.	PUNCT
ejpam-6593	822	10	european	european	PROPN
ejpam-6593	822	11	journal	journal	PROPN
ejpam-6593	822	12	of	of	ADP
ejpam-6593	822	13	pure	pure	ADJ
ejpam-6593	822	14	and	and	CCONJ
ejpam-6593	822	15	applied	applied	ADJ
ejpam-6593	822	16	mathematics	mathematic	NOUN
ejpam-6593	822	17	,	,	PUNCT
ejpam-6593	822	18	15:1593–1596	15:1593–1596	NUM
ejpam-6593	822	19	,	,	PUNCT
ejpam-6593	822	20	2022	2022	NUM
ejpam-6593	822	21	.	.	PUNCT
ejpam-6593	823	1	[	[	X
ejpam-6593	823	2	21	21	NUM
ejpam-6593	823	3	]	]	X
ejpam-6593	823	4	r	r	NOUN
ejpam-6593	823	5	dokchan	dokchan	NOUN
ejpam-6593	823	6	and	and	CCONJ
ejpam-6593	823	7	n	n	ADV
ejpam-6593	823	8	panngam	panngam	NOUN
ejpam-6593	823	9	.	.	PUNCT
ejpam-6593	824	1	on	on	ADP
ejpam-6593	824	2	the	the	DET
ejpam-6593	824	3	diophantine	diophantine	NOUN
ejpam-6593	824	4	equation	equation	NOUN
ejpam-6593	824	5	ax	ax	NOUN
ejpam-6593	824	6	+	+	CCONJ
ejpam-6593	824	7	(	(	PUNCT
ejpam-6593	824	8	a	a	DET
ejpam-6593	824	9	+	+	NUM
ejpam-6593	824	10	5b)y	5b)y	NUM
ejpam-6593	824	11	=	=	SYM
ejpam-6593	824	12	z2	z2	PROPN
ejpam-6593	824	13	.	.	PUNCT
ejpam-6593	825	1	international	international	ADJ
ejpam-6593	825	2	journal	journal	PROPN
ejpam-6593	825	3	of	of	ADP
ejpam-6593	825	4	mathematics	mathematic	NOUN
ejpam-6593	825	5	and	and	CCONJ
ejpam-6593	825	6	computer	computer	NOUN
ejpam-6593	825	7	science	science	NOUN
ejpam-6593	825	8	,	,	PUNCT
ejpam-6593	825	9	20:63–66	20:63–66	PROPN
ejpam-6593	825	10	,	,	PUNCT
ejpam-6593	825	11	2025	2025	NUM
ejpam-6593	825	12	.	.	PUNCT