id	sid	tid	token	lemma	pos
ejpam-3947	1	1	european	european	PROPN
ejpam-3947	1	2	journal	journal	PROPN
ejpam-3947	1	3	of	of	ADP
ejpam-3947	1	4	pure	pure	ADJ
ejpam-3947	1	5	and	and	CCONJ
ejpam-3947	1	6	applied	apply	VERB
ejpam-3947	1	7	mathematics	mathematic	NOUN
ejpam-3947	1	8	vol	vol	NOUN
ejpam-3947	1	9	.	.	PUNCT
ejpam-3947	2	1	14	14	NUM
ejpam-3947	2	2	,	,	PUNCT
ejpam-3947	2	3	no	no	INTJ
ejpam-3947	2	4	.	.	NOUN
ejpam-3947	2	5	2	2	NUM
ejpam-3947	2	6	,	,	PUNCT
ejpam-3947	2	7	2021	2021	NUM
ejpam-3947	2	8	,	,	PUNCT
ejpam-3947	2	9	471	471	NUM
ejpam-3947	2	10	-	-	SYM
ejpam-3947	2	11	479	479	NUM
ejpam-3947	2	12	issn	issn	PROPN
ejpam-3947	2	13	1307	1307	NUM
ejpam-3947	2	14	-	-	SYM
ejpam-3947	2	15	5543	5543	NUM
ejpam-3947	2	16	–	–	PUNCT
ejpam-3947	3	1	ejpam.com	ejpam.com	X
ejpam-3947	3	2	published	publish	VERB
ejpam-3947	3	3	by	by	ADP
ejpam-3947	3	4	new	new	PROPN
ejpam-3947	3	5	york	york	PROPN
ejpam-3947	3	6	business	business	PROPN
ejpam-3947	3	7	global	global	PROPN
ejpam-3947	3	8	on	on	ADP
ejpam-3947	3	9	the	the	DET
ejpam-3947	3	10	solutions	solution	NOUN
ejpam-3947	3	11	of	of	ADP
ejpam-3947	3	12	the	the	DET
ejpam-3947	3	13	diophantine	diophantine	NOUN
ejpam-3947	3	14	equation	equation	NOUN
ejpam-3947	3	15	px	px	X
ejpam-3947	3	16	+	+	CCONJ
ejpam-3947	3	17	(	(	PUNCT
ejpam-3947	3	18	p+	p+	PROPN
ejpam-3947	3	19	4k)y	4k)y	X
ejpam-3947	3	20	=	=	SYM
ejpam-3947	3	21	z2	z2	PROPN
ejpam-3947	3	22	for	for	ADP
ejpam-3947	3	23	prime	prime	ADJ
ejpam-3947	3	24	pairs	pair	NOUN
ejpam-3947	3	25	p	p	NOUN
ejpam-3947	3	26	and	and	CCONJ
ejpam-3947	3	27	p+	p+	PROPN
ejpam-3947	3	28	4k	4k	PROPN
ejpam-3947	3	29	renz	renz	PROPN
ejpam-3947	3	30	jimwel	jimwel	PROPN
ejpam-3947	3	31	s.	s.	PROPN
ejpam-3947	3	32	mina1	mina1	PROPN
ejpam-3947	3	33	,	,	PUNCT
ejpam-3947	3	34	jerico	jerico	PROPN
ejpam-3947	3	35	b.	b.	PROPN
ejpam-3947	3	36	bacani1,∗	bacani1,∗	PROPN
ejpam-3947	3	37	department	department	PROPN
ejpam-3947	3	38	of	of	ADP
ejpam-3947	3	39	mathematics	mathematics	PROPN
ejpam-3947	3	40	and	and	CCONJ
ejpam-3947	3	41	computer	computer	NOUN
ejpam-3947	3	42	science	science	NOUN
ejpam-3947	3	43	,	,	PUNCT
ejpam-3947	3	44	college	college	NOUN
ejpam-3947	3	45	of	of	ADP
ejpam-3947	3	46	science	science	NOUN
ejpam-3947	3	47	,	,	PUNCT
ejpam-3947	3	48	university	university	NOUN
ejpam-3947	3	49	of	of	ADP
ejpam-3947	3	50	the	the	DET
ejpam-3947	3	51	philippines	philippines	PROPN
ejpam-3947	3	52	baguio	baguio	PROPN
ejpam-3947	3	53	,	,	PUNCT
ejpam-3947	3	54	baguio	baguio	PROPN
ejpam-3947	3	55	city	city	PROPN
ejpam-3947	3	56	2600	2600	NUM
ejpam-3947	3	57	,	,	PUNCT
ejpam-3947	3	58	benguet	benguet	PROPN
ejpam-3947	3	59	,	,	PUNCT
ejpam-3947	3	60	philippines	philippine	NOUN
ejpam-3947	3	61	abstract	abstract	ADJ
ejpam-3947	3	62	.	.	PUNCT
ejpam-3947	4	1	in	in	ADP
ejpam-3947	4	2	this	this	DET
ejpam-3947	4	3	paper	paper	NOUN
ejpam-3947	4	4	,	,	PUNCT
ejpam-3947	4	5	we	we	PRON
ejpam-3947	4	6	solve	solve	VERB
ejpam-3947	4	7	the	the	DET
ejpam-3947	4	8	diophantine	diophantine	NOUN
ejpam-3947	4	9	equation	equation	NOUN
ejpam-3947	4	10	px	px	X
ejpam-3947	4	11	+	+	CCONJ
ejpam-3947	4	12	(	(	PUNCT
ejpam-3947	4	13	p+	p+	PROPN
ejpam-3947	4	14	4k)y	4k)y	X
ejpam-3947	4	15	=	=	SYM
ejpam-3947	4	16	z2	z2	PROPN
ejpam-3947	4	17	in	in	ADP
ejpam-3947	4	18	n0	n0	NUM
ejpam-3947	4	19	for	for	ADP
ejpam-3947	4	20	prime	prime	ADJ
ejpam-3947	4	21	pairs	pair	NOUN
ejpam-3947	4	22	(	(	PUNCT
ejpam-3947	4	23	p	p	X
ejpam-3947	4	24	,	,	PUNCT
ejpam-3947	4	25	p+4k	p+4k	PROPN
ejpam-3947	4	26	)	)	PUNCT
ejpam-3947	4	27	.	.	PUNCT
ejpam-3947	5	1	first	first	ADV
ejpam-3947	5	2	,	,	PUNCT
ejpam-3947	5	3	we	we	PRON
ejpam-3947	5	4	consider	consider	VERB
ejpam-3947	5	5	cousin	cousin	NOUN
ejpam-3947	5	6	primes	prime	NOUN
ejpam-3947	5	7	p	p	NOUN
ejpam-3947	5	8	and	and	CCONJ
ejpam-3947	5	9	p+4	p+4	PROPN
ejpam-3947	5	10	.	.	PUNCT
ejpam-3947	6	1	then	then	ADV
ejpam-3947	6	2	we	we	PRON
ejpam-3947	6	3	extend	extend	VERB
ejpam-3947	6	4	the	the	DET
ejpam-3947	6	5	study	study	NOUN
ejpam-3947	6	6	to	to	ADP
ejpam-3947	6	7	solving	solve	VERB
ejpam-3947	6	8	px	px	NOUN
ejpam-3947	6	9	+	+	CCONJ
ejpam-3947	6	10	(	(	PUNCT
ejpam-3947	6	11	p	p	X
ejpam-3947	6	12	+	+	NOUN
ejpam-3947	6	13	4)y	4)y	X
ejpam-3947	6	14	=	=	SYM
ejpam-3947	6	15	z2n	z2n	NOUN
ejpam-3947	6	16	,	,	PUNCT
ejpam-3947	6	17	where	where	SCONJ
ejpam-3947	6	18	n	n	DET
ejpam-3947	6	19	∈	∈	PROPN
ejpam-3947	6	20	n\{1	n\{1	PROPN
ejpam-3947	6	21	}	}	PUNCT
ejpam-3947	6	22	.	.	PUNCT
ejpam-3947	7	1	furthermore	furthermore	ADV
ejpam-3947	7	2	,	,	PUNCT
ejpam-3947	7	3	we	we	PRON
ejpam-3947	7	4	solve	solve	VERB
ejpam-3947	7	5	the	the	DET
ejpam-3947	7	6	equation	equation	NOUN
ejpam-3947	7	7	px	px	X
ejpam-3947	8	1	+	+	CCONJ
ejpam-3947	8	2	(	(	PUNCT
ejpam-3947	8	3	p	p	X
ejpam-3947	8	4	+	+	NOUN
ejpam-3947	8	5	4k)y	4k)y	NOUN
ejpam-3947	8	6	=	=	SYM
ejpam-3947	8	7	z2	z2	PROPN
ejpam-3947	8	8	for	for	ADP
ejpam-3947	8	9	k	k	PROPN
ejpam-3947	8	10	≥	≥	PROPN
ejpam-3947	8	11	2	2	NUM
ejpam-3947	8	12	.	.	PUNCT
ejpam-3947	9	1	as	as	ADP
ejpam-3947	9	2	a	a	DET
ejpam-3947	9	3	result	result	NOUN
ejpam-3947	9	4	,	,	PUNCT
ejpam-3947	9	5	we	we	PRON
ejpam-3947	9	6	show	show	VERB
ejpam-3947	9	7	that	that	SCONJ
ejpam-3947	9	8	this	this	DET
ejpam-3947	9	9	equation	equation	NOUN
ejpam-3947	9	10	has	have	VERB
ejpam-3947	9	11	a	a	DET
ejpam-3947	9	12	unique	unique	ADJ
ejpam-3947	9	13	solution	solution	NOUN
ejpam-3947	9	14	(	(	PUNCT
ejpam-3947	9	15	p	p	NOUN
ejpam-3947	9	16	,	,	PUNCT
ejpam-3947	9	17	p	p	X
ejpam-3947	9	18	+	+	X
ejpam-3947	9	19	4k	4k	NOUN
ejpam-3947	9	20	,	,	PUNCT
ejpam-3947	9	21	x	x	X
ejpam-3947	9	22	,	,	PUNCT
ejpam-3947	9	23	y	y	PROPN
ejpam-3947	9	24	,	,	PUNCT
ejpam-3947	9	25	z	z	NOUN
ejpam-3947	9	26	)	)	PUNCT
ejpam-3947	9	27	=	=	SYM
ejpam-3947	9	28	(	(	PUNCT
ejpam-3947	9	29	3	3	NUM
ejpam-3947	9	30	,	,	PUNCT
ejpam-3947	9	31	11	11	NUM
ejpam-3947	9	32	,	,	PUNCT
ejpam-3947	9	33	5	5	NUM
ejpam-3947	9	34	,	,	PUNCT
ejpam-3947	9	35	2	2	NUM
ejpam-3947	9	36	,	,	PUNCT
ejpam-3947	9	37	122	122	NUM
ejpam-3947	9	38	)	)	PUNCT
ejpam-3947	9	39	whenever	whenever	SCONJ
ejpam-3947	9	40	x	x	PUNCT
ejpam-3947	9	41	>	>	X
ejpam-3947	9	42	1	1	NUM
ejpam-3947	9	43	and	and	CCONJ
ejpam-3947	9	44	y	y	PROPN
ejpam-3947	9	45	>	>	X
ejpam-3947	9	46	1	1	X
ejpam-3947	9	47	.	.	PUNCT
ejpam-3947	10	1	finally	finally	ADV
ejpam-3947	10	2	,	,	PUNCT
ejpam-3947	10	3	we	we	PRON
ejpam-3947	10	4	show	show	VERB
ejpam-3947	10	5	the	the	DET
ejpam-3947	10	6	finiteness	finiteness	NOUN
ejpam-3947	10	7	of	of	ADP
ejpam-3947	10	8	number	number	NOUN
ejpam-3947	10	9	of	of	ADP
ejpam-3947	10	10	solutions	solution	NOUN
ejpam-3947	10	11	in	in	ADP
ejpam-3947	10	12	n.	n.	NOUN
ejpam-3947	10	13	2020	2020	NUM
ejpam-3947	10	14	mathematics	mathematic	NOUN
ejpam-3947	10	15	subject	subject	NOUN
ejpam-3947	10	16	classifications	classification	NOUN
ejpam-3947	10	17	:	:	PUNCT
ejpam-3947	10	18	11a07	11a07	NUM
ejpam-3947	10	19	,	,	PUNCT
ejpam-3947	10	20	11a41	11a41	NUM
ejpam-3947	10	21	,	,	PUNCT
ejpam-3947	10	22	11d61	11d61	NUM
ejpam-3947	10	23	,	,	PUNCT
ejpam-3947	10	24	11d72	11d72	NUM
ejpam-3947	10	25	key	key	ADJ
ejpam-3947	10	26	words	word	NOUN
ejpam-3947	10	27	and	and	CCONJ
ejpam-3947	10	28	phrases	phrase	NOUN
ejpam-3947	10	29	:	:	PUNCT
ejpam-3947	10	30	diophantine	diophantine	VERB
ejpam-3947	10	31	equation	equation	NOUN
ejpam-3947	10	32	,	,	PUNCT
ejpam-3947	10	33	exponential	exponential	ADJ
ejpam-3947	10	34	diophantine	diophantine	NOUN
ejpam-3947	10	35	equation	equation	NOUN
ejpam-3947	10	36	,	,	PUNCT
ejpam-3947	10	37	nonlinear	nonlinear	ADJ
ejpam-3947	10	38	diophantine	diophantine	NOUN
ejpam-3947	10	39	equation	equation	NOUN
ejpam-3947	10	40	,	,	PUNCT
ejpam-3947	10	41	cousin	cousin	NOUN
ejpam-3947	10	42	primes	prime	NOUN
ejpam-3947	10	43	,	,	PUNCT
ejpam-3947	10	44	legendre	legendre	NOUN
ejpam-3947	10	45	symbol	symbol	NOUN
ejpam-3947	10	46	1	1	NUM
ejpam-3947	10	47	.	.	PUNCT
ejpam-3947	11	1	introduction	introduction	NOUN
ejpam-3947	11	2	diophantine	diophantine	NOUN
ejpam-3947	11	3	equations	equation	NOUN
ejpam-3947	11	4	of	of	ADP
ejpam-3947	11	5	type	type	NOUN
ejpam-3947	11	6	px	px	PROPN
ejpam-3947	11	7	+	+	CCONJ
ejpam-3947	11	8	qy	qy	NOUN
ejpam-3947	11	9	=	=	PROPN
ejpam-3947	11	10	z2	z2	PROPN
ejpam-3947	11	11	(	(	PUNCT
ejpam-3947	11	12	1	1	NUM
ejpam-3947	11	13	)	)	PUNCT
ejpam-3947	11	14	have	have	AUX
ejpam-3947	11	15	been	be	AUX
ejpam-3947	11	16	widely	widely	ADV
ejpam-3947	11	17	studied	study	VERB
ejpam-3947	11	18	for	for	ADP
ejpam-3947	11	19	various	various	ADJ
ejpam-3947	11	20	fixed	fix	VERB
ejpam-3947	11	21	values	value	NOUN
ejpam-3947	11	22	of	of	ADP
ejpam-3947	11	23	p	p	NOUN
ejpam-3947	11	24	and	and	CCONJ
ejpam-3947	11	25	q.	q.	NOUN
ejpam-3947	11	26	some	some	PRON
ejpam-3947	11	27	of	of	ADP
ejpam-3947	11	28	these	these	PRON
ejpam-3947	11	29	can	can	AUX
ejpam-3947	11	30	be	be	AUX
ejpam-3947	11	31	seen	see	VERB
ejpam-3947	11	32	in	in	ADP
ejpam-3947	11	33	[	[	X
ejpam-3947	11	34	1	1	NUM
ejpam-3947	11	35	,	,	PUNCT
ejpam-3947	11	36	2	2	NUM
ejpam-3947	11	37	,	,	PUNCT
ejpam-3947	11	38	11	11	NUM
ejpam-3947	11	39	,	,	PUNCT
ejpam-3947	11	40	14–17	14–17	NUM
ejpam-3947	11	41	,	,	PUNCT
ejpam-3947	11	42	19	19	NUM
ejpam-3947	11	43	]	]	PUNCT
ejpam-3947	11	44	and	and	CCONJ
ejpam-3947	12	1	[	[	X
ejpam-3947	12	2	20	20	NUM
ejpam-3947	12	3	]	]	PUNCT
ejpam-3947	12	4	.	.	PUNCT
ejpam-3947	13	1	in	in	ADP
ejpam-3947	13	2	2015	2015	NUM
ejpam-3947	13	3	,	,	PUNCT
ejpam-3947	13	4	bacani	bacani	NOUN
ejpam-3947	13	5	and	and	CCONJ
ejpam-3947	13	6	rabago	rabago	VERB
ejpam-3947	13	7	[	[	X
ejpam-3947	13	8	3	3	X
ejpam-3947	13	9	]	]	PUNCT
ejpam-3947	13	10	provided	provide	VERB
ejpam-3947	13	11	the	the	DET
ejpam-3947	13	12	solutions	solution	NOUN
ejpam-3947	13	13	of	of	ADP
ejpam-3947	13	14	the	the	DET
ejpam-3947	13	15	diophantine	diophantine	NOUN
ejpam-3947	13	16	equation	equation	NOUN
ejpam-3947	13	17	px	px	X
ejpam-3947	13	18	+	+	CCONJ
ejpam-3947	13	19	qy	qy	NOUN
ejpam-3947	13	20	=	=	SYM
ejpam-3947	13	21	z2	z2	PROPN
ejpam-3947	13	22	,	,	PUNCT
ejpam-3947	13	23	where	where	SCONJ
ejpam-3947	13	24	p	p	NOUN
ejpam-3947	13	25	and	and	CCONJ
ejpam-3947	13	26	q	q	NOUN
ejpam-3947	13	27	are	be	AUX
ejpam-3947	13	28	twin	twin	ADJ
ejpam-3947	13	29	primes	prime	NOUN
ejpam-3947	13	30	;	;	PUNCT
ejpam-3947	13	31	that	that	PRON
ejpam-3947	13	32	is	be	AUX
ejpam-3947	13	33	,	,	PUNCT
ejpam-3947	13	34	p	p	NOUN
ejpam-3947	13	35	and	and	CCONJ
ejpam-3947	13	36	q	q	NOUN
ejpam-3947	13	37	differ	differ	VERB
ejpam-3947	13	38	by	by	ADP
ejpam-3947	13	39	2	2	NUM
ejpam-3947	13	40	.	.	PUNCT
ejpam-3947	14	1	it	it	PRON
ejpam-3947	14	2	was	be	AUX
ejpam-3947	14	3	shown	show	VERB
ejpam-3947	14	4	that	that	SCONJ
ejpam-3947	14	5	this	this	DET
ejpam-3947	14	6	equation	equation	NOUN
ejpam-3947	14	7	has	have	VERB
ejpam-3947	14	8	infinitely	infinitely	ADV
ejpam-3947	14	9	many	many	ADJ
ejpam-3947	14	10	solutions	solution	NOUN
ejpam-3947	14	11	in	in	ADP
ejpam-3947	14	12	the	the	DET
ejpam-3947	14	13	set	set	NOUN
ejpam-3947	14	14	n0	n0	NOUN
ejpam-3947	14	15	of	of	ADP
ejpam-3947	14	16	nonnegative	nonnegative	ADJ
ejpam-3947	14	17	integers	integer	NOUN
ejpam-3947	14	18	,	,	PUNCT
ejpam-3947	14	19	assuming	assume	VERB
ejpam-3947	14	20	that	that	SCONJ
ejpam-3947	14	21	the	the	DET
ejpam-3947	14	22	twin	twin	ADJ
ejpam-3947	14	23	prime	prime	ADJ
ejpam-3947	14	24	conjecture	conjecture	NOUN
ejpam-3947	14	25	,	,	PUNCT
ejpam-3947	14	26	also	also	ADV
ejpam-3947	14	27	known	know	VERB
ejpam-3947	14	28	as	as	ADP
ejpam-3947	14	29	polignac	polignac	NOUN
ejpam-3947	14	30	’s	’s	PART
ejpam-3947	14	31	conjecture	conjecture	NOUN
ejpam-3947	14	32	,	,	PUNCT
ejpam-3947	14	33	holds	hold	VERB
ejpam-3947	14	34	.	.	PUNCT
ejpam-3947	15	1	in	in	ADP
ejpam-3947	15	2	2018	2018	NUM
ejpam-3947	15	3	,	,	PUNCT
ejpam-3947	15	4	burshtein	burshtein	ADV
ejpam-3947	15	5	[	[	X
ejpam-3947	15	6	4	4	X
ejpam-3947	15	7	]	]	PUNCT
ejpam-3947	15	8	made	make	VERB
ejpam-3947	15	9	a	a	DET
ejpam-3947	15	10	study	study	NOUN
ejpam-3947	15	11	on	on	ADP
ejpam-3947	15	12	the	the	DET
ejpam-3947	15	13	diophantine	diophantine	NOUN
ejpam-3947	15	14	equation	equation	NOUN
ejpam-3947	15	15	px	px	X
ejpam-3947	16	1	+	+	CCONJ
ejpam-3947	16	2	(	(	PUNCT
ejpam-3947	16	3	p	p	X
ejpam-3947	16	4	+	+	NUM
ejpam-3947	16	5	4)y	4)y	PROPN
ejpam-3947	16	6	=	=	SYM
ejpam-3947	16	7	z2	z2	PROPN
ejpam-3947	16	8	,	,	PUNCT
ejpam-3947	16	9	where	where	SCONJ
ejpam-3947	16	10	p	p	NOUN
ejpam-3947	16	11	and	and	CCONJ
ejpam-3947	16	12	p	p	NOUN
ejpam-3947	16	13	+	+	CCONJ
ejpam-3947	16	14	4	4	NUM
ejpam-3947	16	15	are	be	AUX
ejpam-3947	16	16	primes	prime	NOUN
ejpam-3947	16	17	,	,	PUNCT
ejpam-3947	16	18	and	and	CCONJ
ejpam-3947	16	19	x	x	X
ejpam-3947	17	1	+	+	CCONJ
ejpam-3947	17	2	y	y	NOUN
ejpam-3947	17	3	=	=	SYM
ejpam-3947	17	4	2	2	NUM
ejpam-3947	17	5	,	,	PUNCT
ejpam-3947	17	6	3	3	NUM
ejpam-3947	17	7	,	,	PUNCT
ejpam-3947	17	8	4	4	NUM
ejpam-3947	17	9	.	.	PUNCT
ejpam-3947	17	10	also	also	ADV
ejpam-3947	17	11	in	in	ADP
ejpam-3947	17	12	2018	2018	NUM
ejpam-3947	17	13	,	,	PUNCT
ejpam-3947	17	14	neres	nere	NOUN
ejpam-3947	17	15	[	[	X
ejpam-3947	17	16	13	13	NUM
ejpam-3947	17	17	]	]	PUNCT
ejpam-3947	17	18	investigated	investigate	VERB
ejpam-3947	17	19	the	the	DET
ejpam-3947	17	20	solvability	solvability	NOUN
ejpam-3947	17	21	of	of	ADP
ejpam-3947	17	22	the	the	DET
ejpam-3947	17	23	diophantine	diophantine	NOUN
ejpam-3947	17	24	equation	equation	NOUN
ejpam-3947	17	25	px	px	X
ejpam-3947	17	26	+	+	CCONJ
ejpam-3947	17	27	(	(	PUNCT
ejpam-3947	17	28	p+	p+	PROPN
ejpam-3947	17	29	8)	8)	NUM
ejpam-3947	17	30	=	=	SYM
ejpam-3947	17	31	z2	z2	PROPN
ejpam-3947	17	32	for	for	ADP
ejpam-3947	17	33	prime	prime	ADJ
ejpam-3947	17	34	pairs	pair	NOUN
ejpam-3947	17	35	p	p	NOUN
ejpam-3947	17	36	>	>	X
ejpam-3947	17	37	3	3	NUM
ejpam-3947	17	38	and	and	CCONJ
ejpam-3947	17	39	p+	p+	PROPN
ejpam-3947	17	40	8	8	NUM
ejpam-3947	17	41	.	.	PUNCT
ejpam-3947	18	1	most	most	ADV
ejpam-3947	18	2	recently	recently	ADV
ejpam-3947	18	3	,	,	PUNCT
ejpam-3947	18	4	dockan	dockan	ADJ
ejpam-3947	18	5	and	and	CCONJ
ejpam-3947	18	6	pakapongpun	pakapongpun	VERB
ejpam-3947	19	1	[	[	X
ejpam-3947	19	2	6	6	NUM
ejpam-3947	19	3	]	]	PUNCT
ejpam-3947	19	4	published	publish	VERB
ejpam-3947	19	5	a	a	DET
ejpam-3947	19	6	paper	paper	NOUN
ejpam-3947	19	7	on	on	ADP
ejpam-3947	19	8	the	the	DET
ejpam-3947	19	9	diophantine	diophantine	NOUN
ejpam-3947	19	10	equation	equation	NOUN
ejpam-3947	19	11	px	px	X
ejpam-3947	19	12	+	+	CCONJ
ejpam-3947	19	13	(	(	PUNCT
ejpam-3947	19	14	p+	p+	NOUN
ejpam-3947	19	15	20)y	20)y	PROPN
ejpam-3947	19	16	=	=	SYM
ejpam-3947	19	17	z2	z2	PROPN
ejpam-3947	19	18	for	for	ADP
ejpam-3947	19	19	prime	prime	ADJ
ejpam-3947	19	20	pairs	pair	NOUN
ejpam-3947	19	21	p	p	NOUN
ejpam-3947	19	22	and	and	CCONJ
ejpam-3947	19	23	p+	p+	PROPN
ejpam-3947	19	24	20	20	NUM
ejpam-3947	19	25	.	.	PUNCT
ejpam-3947	20	1	∗corresponding	∗corresponde	VERB
ejpam-3947	20	2	author	author	NOUN
ejpam-3947	20	3	.	.	PUNCT
ejpam-3947	21	1	doi	doi	NOUN
ejpam-3947	21	2	:	:	PUNCT
ejpam-3947	21	3	https://doi.org/10.29020/nybg.ejpam.v14i2.3947	https://doi.org/10.29020/nybg.ejpam.v14i2.3947	ADJ
ejpam-3947	21	4	email	email	NOUN
ejpam-3947	21	5	addresses	address	VERB
ejpam-3947	21	6	:	:	PUNCT
ejpam-3947	21	7	rsmina1@up.edu.ph	rsmina1@up.edu.ph	PROPN
ejpam-3947	21	8	(	(	PUNCT
ejpam-3947	21	9	r.	r.	PROPN
ejpam-3947	21	10	j.	j.	PROPN
ejpam-3947	21	11	s.	s.	PROPN
ejpam-3947	21	12	mina	mina	PROPN
ejpam-3947	21	13	)	)	PUNCT
ejpam-3947	21	14	,	,	PUNCT
ejpam-3947	22	1	jbbacani@up.edu.ph	jbbacani@up.edu.ph	PROPN
ejpam-3947	22	2	(	(	PUNCT
ejpam-3947	22	3	j.	j.	PROPN
ejpam-3947	22	4	b.	b.	PROPN
ejpam-3947	22	5	bacani	bacani	PROPN
ejpam-3947	22	6	)	)	PUNCT
ejpam-3947	22	7	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3947	23	1	471	471	NUM
ejpam-3947	23	2	c	c	AUX
ejpam-3947	23	3	©	©	PROPN
ejpam-3947	23	4	2021	2021	NUM
ejpam-3947	23	5	ejpam	ejpam	VERB
ejpam-3947	23	6	all	all	DET
ejpam-3947	23	7	rights	right	NOUN
ejpam-3947	23	8	reserved	reserve	VERB
ejpam-3947	23	9	.	.	PUNCT
ejpam-3947	24	1	r.	r.	PROPN
ejpam-3947	24	2	j.	j.	PROPN
ejpam-3947	24	3	s.	s.	PROPN
ejpam-3947	24	4	mina	mina	PROPN
ejpam-3947	24	5	,	,	PUNCT
ejpam-3947	24	6	j.	j.	PROPN
ejpam-3947	24	7	b.	b.	PROPN
ejpam-3947	24	8	bacani	bacani	PROPN
ejpam-3947	24	9	/	/	SYM
ejpam-3947	24	10	eur	eur	PROPN
ejpam-3947	24	11	.	.	PUNCT
ejpam-3947	25	1	j.	j.	PROPN
ejpam-3947	25	2	pure	pure	PROPN
ejpam-3947	25	3	appl	appl	PROPN
ejpam-3947	25	4	.	.	PROPN
ejpam-3947	25	5	math	math	PROPN
ejpam-3947	25	6	,	,	PUNCT
ejpam-3947	25	7	14	14	NUM
ejpam-3947	25	8	(	(	PUNCT
ejpam-3947	25	9	2	2	NUM
ejpam-3947	25	10	)	)	PUNCT
ejpam-3947	25	11	(	(	PUNCT
ejpam-3947	25	12	2021	2021	NUM
ejpam-3947	25	13	)	)	PUNCT
ejpam-3947	25	14	,	,	PUNCT
ejpam-3947	25	15	471	471	NUM
ejpam-3947	25	16	-	-	SYM
ejpam-3947	25	17	479	479	NUM
ejpam-3947	25	18	472	472	NUM
ejpam-3947	25	19	motivated	motivate	VERB
ejpam-3947	25	20	by	by	ADP
ejpam-3947	25	21	the	the	DET
ejpam-3947	25	22	papers	paper	NOUN
ejpam-3947	25	23	mentioned	mention	VERB
ejpam-3947	25	24	above	above	ADV
ejpam-3947	25	25	,	,	PUNCT
ejpam-3947	25	26	this	this	DET
ejpam-3947	25	27	work	work	NOUN
ejpam-3947	25	28	will	will	AUX
ejpam-3947	25	29	deal	deal	VERB
ejpam-3947	25	30	with	with	ADP
ejpam-3947	25	31	the	the	DET
ejpam-3947	25	32	diophantine	diophantine	NOUN
ejpam-3947	25	33	equations	equation	NOUN
ejpam-3947	25	34	of	of	ADP
ejpam-3947	25	35	the	the	DET
ejpam-3947	25	36	form	form	NOUN
ejpam-3947	25	37	px	px	X
ejpam-3947	25	38	+	+	CCONJ
ejpam-3947	25	39	(	(	PUNCT
ejpam-3947	25	40	p	p	X
ejpam-3947	25	41	+	+	PROPN
ejpam-3947	25	42	4k)y	4k)y	NOUN
ejpam-3947	25	43	=	=	SYM
ejpam-3947	25	44	z2	z2	PROPN
ejpam-3947	25	45	,	,	PUNCT
ejpam-3947	25	46	k	k	PROPN
ejpam-3947	25	47	∈	∈	PROPN
ejpam-3947	25	48	n	n	CCONJ
ejpam-3947	25	49	,	,	PUNCT
ejpam-3947	25	50	in	in	ADP
ejpam-3947	25	51	the	the	DET
ejpam-3947	25	52	set	set	NOUN
ejpam-3947	25	53	of	of	ADP
ejpam-3947	25	54	nonnegative	nonnegative	ADJ
ejpam-3947	25	55	integers	integer	NOUN
ejpam-3947	25	56	.	.	PUNCT
ejpam-3947	26	1	we	we	PRON
ejpam-3947	26	2	first	first	ADV
ejpam-3947	26	3	deal	deal	VERB
ejpam-3947	26	4	with	with	ADP
ejpam-3947	26	5	the	the	DET
ejpam-3947	26	6	case	case	NOUN
ejpam-3947	26	7	where	where	SCONJ
ejpam-3947	26	8	k	k	PROPN
ejpam-3947	26	9	=	=	NOUN
ejpam-3947	26	10	1	1	X
ejpam-3947	26	11	.	.	X
ejpam-3947	27	1	that	that	PRON
ejpam-3947	27	2	is	is	ADV
ejpam-3947	27	3	,	,	PUNCT
ejpam-3947	27	4	we	we	PRON
ejpam-3947	27	5	consider	consider	VERB
ejpam-3947	27	6	the	the	DET
ejpam-3947	27	7	equation	equation	NOUN
ejpam-3947	27	8	px	px	X
ejpam-3947	27	9	+	+	CCONJ
ejpam-3947	27	10	(	(	PUNCT
ejpam-3947	27	11	p+	p+	NOUN
ejpam-3947	27	12	4)y	4)y	PROPN
ejpam-3947	27	13	=	=	SYM
ejpam-3947	27	14	z2	z2	PROPN
ejpam-3947	27	15	,	,	PUNCT
ejpam-3947	27	16	(	(	PUNCT
ejpam-3947	27	17	2	2	X
ejpam-3947	27	18	)	)	PUNCT
ejpam-3947	27	19	where	where	SCONJ
ejpam-3947	27	20	p	p	NOUN
ejpam-3947	27	21	and	and	CCONJ
ejpam-3947	27	22	p	p	NOUN
ejpam-3947	27	23	+	+	CCONJ
ejpam-3947	27	24	4	4	NUM
ejpam-3947	27	25	are	be	AUX
ejpam-3947	27	26	primes	prime	NOUN
ejpam-3947	27	27	.	.	PUNCT
ejpam-3947	28	1	these	these	DET
ejpam-3947	28	2	primes	prime	NOUN
ejpam-3947	28	3	which	which	PRON
ejpam-3947	28	4	differ	differ	VERB
ejpam-3947	28	5	by	by	ADP
ejpam-3947	28	6	4	4	NUM
ejpam-3947	28	7	are	be	AUX
ejpam-3947	28	8	called	call	VERB
ejpam-3947	28	9	cousin	cousin	NOUN
ejpam-3947	28	10	primes	prime	NOUN
ejpam-3947	28	11	.	.	PUNCT
ejpam-3947	29	1	we	we	PRON
ejpam-3947	29	2	then	then	ADV
ejpam-3947	29	3	extend	extend	VERB
ejpam-3947	29	4	the	the	DET
ejpam-3947	29	5	work	work	NOUN
ejpam-3947	29	6	to	to	ADP
ejpam-3947	29	7	solving	solve	VERB
ejpam-3947	29	8	the	the	DET
ejpam-3947	29	9	diophantine	diophantine	NOUN
ejpam-3947	29	10	equation	equation	NOUN
ejpam-3947	29	11	px	px	X
ejpam-3947	29	12	+	+	CCONJ
ejpam-3947	29	13	(	(	PUNCT
ejpam-3947	29	14	p+	p+	NOUN
ejpam-3947	29	15	4)y	4)y	X
ejpam-3947	29	16	=	=	SYM
ejpam-3947	29	17	z2n	z2n	PROPN
ejpam-3947	29	18	for	for	ADP
ejpam-3947	29	19	all	all	DET
ejpam-3947	29	20	n	n	CCONJ
ejpam-3947	29	21	>	>	X
ejpam-3947	29	22	1	1	X
ejpam-3947	29	23	.	.	PUNCT
ejpam-3947	30	1	lastly	lastly	ADV
ejpam-3947	30	2	,	,	PUNCT
ejpam-3947	30	3	we	we	PRON
ejpam-3947	30	4	study	study	VERB
ejpam-3947	30	5	the	the	DET
ejpam-3947	30	6	solutions	solution	NOUN
ejpam-3947	30	7	of	of	ADP
ejpam-3947	30	8	diophantine	diophantine	NOUN
ejpam-3947	30	9	equations	equation	NOUN
ejpam-3947	30	10	of	of	ADP
ejpam-3947	30	11	the	the	DET
ejpam-3947	30	12	form	form	NOUN
ejpam-3947	30	13	px	px	X
ejpam-3947	30	14	+	+	CCONJ
ejpam-3947	30	15	(	(	PUNCT
ejpam-3947	30	16	p+	p+	VERB
ejpam-3947	30	17	4k)y	4k)y	X
ejpam-3947	30	18	=	=	SYM
ejpam-3947	30	19	z2	z2	PROPN
ejpam-3947	30	20	,	,	PUNCT
ejpam-3947	30	21	k	k	PROPN
ejpam-3947	30	22	≥	≥	NUM
ejpam-3947	30	23	2	2	NUM
ejpam-3947	30	24	(	(	PUNCT
ejpam-3947	30	25	3	3	NUM
ejpam-3947	30	26	)	)	PUNCT
ejpam-3947	30	27	where	where	SCONJ
ejpam-3947	30	28	p	p	NOUN
ejpam-3947	30	29	and	and	CCONJ
ejpam-3947	30	30	p+	p+	PROPN
ejpam-3947	30	31	4k	4k	PRON
ejpam-3947	30	32	are	be	AUX
ejpam-3947	30	33	both	both	DET
ejpam-3947	30	34	primes	prime	NOUN
ejpam-3947	30	35	.	.	PUNCT
ejpam-3947	31	1	2	2	X
ejpam-3947	31	2	.	.	X
ejpam-3947	31	3	preliminaries	preliminary	NOUN
ejpam-3947	31	4	diophantine	diophantine	VERB
ejpam-3947	31	5	equations	equation	NOUN
ejpam-3947	31	6	usually	usually	ADV
ejpam-3947	31	7	refer	refer	VERB
ejpam-3947	31	8	to	to	ADP
ejpam-3947	31	9	any	any	DET
ejpam-3947	31	10	equations	equation	NOUN
ejpam-3947	31	11	in	in	ADP
ejpam-3947	31	12	one	one	NUM
ejpam-3947	31	13	or	or	CCONJ
ejpam-3947	31	14	more	more	ADJ
ejpam-3947	31	15	unknowns	unknown	NOUN
ejpam-3947	31	16	that	that	PRON
ejpam-3947	31	17	are	be	AUX
ejpam-3947	31	18	to	to	PART
ejpam-3947	31	19	be	be	AUX
ejpam-3947	31	20	solved	solve	VERB
ejpam-3947	31	21	in	in	ADP
ejpam-3947	31	22	the	the	DET
ejpam-3947	31	23	set	set	NOUN
ejpam-3947	31	24	z	z	NOUN
ejpam-3947	31	25	of	of	ADP
ejpam-3947	31	26	integers	integer	NOUN
ejpam-3947	31	27	[	[	X
ejpam-3947	31	28	5	5	NUM
ejpam-3947	31	29	]	]	PUNCT
ejpam-3947	31	30	.	.	PUNCT
ejpam-3947	32	1	the	the	DET
ejpam-3947	32	2	simplest	simple	ADJ
ejpam-3947	32	3	equation	equation	NOUN
ejpam-3947	32	4	known	know	VERB
ejpam-3947	32	5	is	be	AUX
ejpam-3947	32	6	the	the	DET
ejpam-3947	32	7	linear	linear	ADJ
ejpam-3947	32	8	diophantine	diophantine	NOUN
ejpam-3947	32	9	equation	equation	NOUN
ejpam-3947	32	10	in	in	ADP
ejpam-3947	32	11	two	two	NUM
ejpam-3947	32	12	unknowns	unknown	NOUN
ejpam-3947	32	13	,	,	PUNCT
ejpam-3947	32	14	written	write	VERB
ejpam-3947	32	15	as	as	ADP
ejpam-3947	32	16	ax	ax	NOUN
ejpam-3947	32	17	+	+	X
ejpam-3947	32	18	by	by	ADP
ejpam-3947	32	19	=	=	SYM
ejpam-3947	32	20	c	c	NOUN
ejpam-3947	32	21	,	,	PUNCT
ejpam-3947	32	22	where	where	SCONJ
ejpam-3947	32	23	a	a	DET
ejpam-3947	32	24	,	,	PUNCT
ejpam-3947	32	25	b	b	NOUN
ejpam-3947	32	26	and	and	CCONJ
ejpam-3947	32	27	c	c	PROPN
ejpam-3947	32	28	are	be	AUX
ejpam-3947	32	29	integers	integer	NOUN
ejpam-3947	32	30	.	.	PUNCT
ejpam-3947	33	1	indian	indian	ADJ
ejpam-3947	33	2	mathematician	mathematician	ADJ
ejpam-3947	33	3	brahmagupta	brahmagupta	NOUN
ejpam-3947	33	4	is	be	AUX
ejpam-3947	33	5	believed	believe	VERB
ejpam-3947	33	6	to	to	PART
ejpam-3947	33	7	be	be	AUX
ejpam-3947	33	8	the	the	DET
ejpam-3947	33	9	first	first	ADJ
ejpam-3947	33	10	person	person	NOUN
ejpam-3947	33	11	to	to	PART
ejpam-3947	33	12	describe	describe	VERB
ejpam-3947	33	13	the	the	DET
ejpam-3947	33	14	general	general	ADJ
ejpam-3947	33	15	solution	solution	NOUN
ejpam-3947	33	16	of	of	ADP
ejpam-3947	33	17	such	such	ADJ
ejpam-3947	33	18	equations	equation	NOUN
ejpam-3947	33	19	.	.	PUNCT
ejpam-3947	34	1	now	now	ADV
ejpam-3947	34	2	,	,	PUNCT
ejpam-3947	34	3	the	the	DET
ejpam-3947	34	4	general	general	ADJ
ejpam-3947	34	5	solution	solution	NOUN
ejpam-3947	34	6	is	be	AUX
ejpam-3947	34	7	already	already	ADV
ejpam-3947	34	8	well	well	ADV
ejpam-3947	34	9	-	-	PUNCT
ejpam-3947	34	10	established	establish	VERB
ejpam-3947	34	11	(	(	PUNCT
ejpam-3947	34	12	cf	cf	NOUN
ejpam-3947	34	13	.	.	PUNCT
ejpam-3947	35	1	[	[	X
ejpam-3947	35	2	18	18	NUM
ejpam-3947	35	3	]	]	PUNCT
ejpam-3947	35	4	,	,	PUNCT
ejpam-3947	35	5	p.134	p.134	PROPN
ejpam-3947	35	6	)	)	PUNCT
ejpam-3947	35	7	.	.	PUNCT
ejpam-3947	36	1	euclidean	euclidean	ADJ
ejpam-3947	36	2	algorithm	algorithm	PROPN
ejpam-3947	36	3	is	be	AUX
ejpam-3947	36	4	one	one	NUM
ejpam-3947	36	5	of	of	ADP
ejpam-3947	36	6	the	the	DET
ejpam-3947	36	7	ways	way	NOUN
ejpam-3947	36	8	to	to	PART
ejpam-3947	36	9	solve	solve	VERB
ejpam-3947	36	10	linear	linear	ADJ
ejpam-3947	36	11	diophantine	diophantine	NOUN
ejpam-3947	36	12	equations	equation	NOUN
ejpam-3947	36	13	.	.	PUNCT
ejpam-3947	37	1	if	if	SCONJ
ejpam-3947	37	2	there	there	PRON
ejpam-3947	37	3	are	be	VERB
ejpam-3947	37	4	linear	linear	ADJ
ejpam-3947	37	5	diophantine	diophantine	NOUN
ejpam-3947	37	6	equations	equation	NOUN
ejpam-3947	37	7	,	,	PUNCT
ejpam-3947	37	8	there	there	PRON
ejpam-3947	37	9	are	be	VERB
ejpam-3947	37	10	also	also	ADV
ejpam-3947	37	11	nonlinear	nonlinear	ADJ
ejpam-3947	37	12	diophantine	diophantine	NOUN
ejpam-3947	37	13	equations	equation	NOUN
ejpam-3947	37	14	.	.	PUNCT
ejpam-3947	38	1	quadratic	quadratic	ADJ
ejpam-3947	38	2	equations	equation	NOUN
ejpam-3947	38	3	in	in	ADP
ejpam-3947	38	4	two	two	NUM
ejpam-3947	38	5	unknowns	unknown	NOUN
ejpam-3947	38	6	x	x	PUNCT
ejpam-3947	38	7	and	and	CCONJ
ejpam-3947	38	8	y	y	PROPN
ejpam-3947	38	9	(	(	PUNCT
ejpam-3947	38	10	ex2	ex2	PROPN
ejpam-3947	38	11	+	+	CCONJ
ejpam-3947	38	12	fxy	fxy	NOUN
ejpam-3947	38	13	+	+	CCONJ
ejpam-3947	38	14	gy2	gy2	NOUN
ejpam-3947	38	15	+	+	CCONJ
ejpam-3947	38	16	hx	hx	PROPN
ejpam-3947	38	17	+	+	CCONJ
ejpam-3947	38	18	jy	jy	PROPN
ejpam-3947	38	19	=	=	SYM
ejpam-3947	38	20	k	k	PROPN
ejpam-3947	38	21	)	)	PUNCT
ejpam-3947	38	22	for	for	ADP
ejpam-3947	38	23	fixed	fix	VERB
ejpam-3947	38	24	integers	integer	NOUN
ejpam-3947	38	25	e	e	NOUN
ejpam-3947	38	26	,	,	PUNCT
ejpam-3947	38	27	f	f	PROPN
ejpam-3947	38	28	,	,	PUNCT
ejpam-3947	38	29	g	g	PROPN
ejpam-3947	38	30	,	,	PUNCT
ejpam-3947	38	31	h	h	NOUN
ejpam-3947	38	32	,	,	PUNCT
ejpam-3947	38	33	j	j	PROPN
ejpam-3947	38	34	and	and	CCONJ
ejpam-3947	38	35	k	k	NOUN
ejpam-3947	38	36	)	)	PUNCT
ejpam-3947	38	37	are	be	AUX
ejpam-3947	38	38	considered	consider	VERB
ejpam-3947	38	39	nonlinear	nonlinear	ADJ
ejpam-3947	38	40	.	.	PUNCT
ejpam-3947	39	1	the	the	DET
ejpam-3947	39	2	famous	famous	ADJ
ejpam-3947	39	3	quadratic	quadratic	ADJ
ejpam-3947	39	4	diophantine	diophantine	NOUN
ejpam-3947	39	5	equation	equation	NOUN
ejpam-3947	39	6	is	be	AUX
ejpam-3947	39	7	the	the	DET
ejpam-3947	39	8	pythagoras	pythagoras	PROPN
ejpam-3947	39	9	equation	equation	NOUN
ejpam-3947	39	10	:	:	PUNCT
ejpam-3947	40	1	x2	x2	PROPN
ejpam-3947	40	2	+	+	CCONJ
ejpam-3947	40	3	y2	y2	NOUN
ejpam-3947	40	4	=	=	SYM
ejpam-3947	40	5	z2	z2	PROPN
ejpam-3947	40	6	.	.	PUNCT
ejpam-3947	41	1	(	(	PUNCT
ejpam-3947	41	2	4	4	X
ejpam-3947	41	3	)	)	PUNCT
ejpam-3947	41	4	the	the	DET
ejpam-3947	41	5	triples	triple	NOUN
ejpam-3947	41	6	(	(	PUNCT
ejpam-3947	41	7	3	3	NUM
ejpam-3947	41	8	,	,	PUNCT
ejpam-3947	41	9	4	4	NUM
ejpam-3947	41	10	,	,	PUNCT
ejpam-3947	41	11	5	5	NUM
ejpam-3947	41	12	)	)	PUNCT
ejpam-3947	41	13	,	,	PUNCT
ejpam-3947	41	14	(	(	PUNCT
ejpam-3947	41	15	5	5	NUM
ejpam-3947	41	16	,	,	PUNCT
ejpam-3947	41	17	12	12	NUM
ejpam-3947	41	18	,	,	PUNCT
ejpam-3947	41	19	13	13	NUM
ejpam-3947	41	20	)	)	PUNCT
ejpam-3947	41	21	,	,	PUNCT
ejpam-3947	41	22	and	and	CCONJ
ejpam-3947	41	23	(	(	PUNCT
ejpam-3947	41	24	7	7	NUM
ejpam-3947	41	25	,	,	PUNCT
ejpam-3947	41	26	24	24	NUM
ejpam-3947	41	27	,	,	PUNCT
ejpam-3947	41	28	25	25	NUM
ejpam-3947	41	29	)	)	PUNCT
ejpam-3947	41	30	are	be	AUX
ejpam-3947	41	31	just	just	ADV
ejpam-3947	41	32	a	a	DET
ejpam-3947	41	33	few	few	ADJ
ejpam-3947	41	34	of	of	ADP
ejpam-3947	41	35	the	the	DET
ejpam-3947	41	36	infinitely	infinitely	ADV
ejpam-3947	41	37	many	many	ADJ
ejpam-3947	41	38	solutions	solution	NOUN
ejpam-3947	41	39	of	of	ADP
ejpam-3947	41	40	(	(	PUNCT
ejpam-3947	41	41	4	4	NUM
ejpam-3947	41	42	)	)	PUNCT
ejpam-3947	41	43	.	.	PUNCT
ejpam-3947	42	1	another	another	DET
ejpam-3947	42	2	famous	famous	ADJ
ejpam-3947	42	3	nonlinear	nonlinear	ADJ
ejpam-3947	42	4	diophantine	diophantine	NOUN
ejpam-3947	42	5	equation	equation	NOUN
ejpam-3947	42	6	is	be	AUX
ejpam-3947	42	7	given	give	VERB
ejpam-3947	42	8	in	in	ADP
ejpam-3947	42	9	the	the	DET
ejpam-3947	42	10	fermat	fermat	PROPN
ejpam-3947	42	11	’s	’s	PART
ejpam-3947	42	12	last	last	ADJ
ejpam-3947	42	13	theorem	theorem	NOUN
ejpam-3947	42	14	,	,	PUNCT
ejpam-3947	42	15	which	which	PRON
ejpam-3947	42	16	states	state	VERB
ejpam-3947	42	17	that	that	SCONJ
ejpam-3947	42	18	the	the	DET
ejpam-3947	42	19	equation	equation	NOUN
ejpam-3947	42	20	xn	xn	PUNCT
ejpam-3947	43	1	+	+	CCONJ
ejpam-3947	43	2	yn	yn	X
ejpam-3947	43	3	=	=	PUNCT
ejpam-3947	43	4	zn	zn	PROPN
ejpam-3947	43	5	has	have	VERB
ejpam-3947	43	6	no	no	DET
ejpam-3947	43	7	solutions	solution	NOUN
ejpam-3947	43	8	in	in	ADP
ejpam-3947	43	9	z	z	PROPN
ejpam-3947	43	10	for	for	ADP
ejpam-3947	43	11	n	n	X
ejpam-3947	43	12	>	>	X
ejpam-3947	43	13	2	2	X
ejpam-3947	43	14	.	.	PUNCT
ejpam-3947	44	1	in	in	ADP
ejpam-3947	44	2	our	our	PRON
ejpam-3947	44	3	time	time	NOUN
ejpam-3947	44	4	,	,	PUNCT
ejpam-3947	44	5	many	many	ADJ
ejpam-3947	44	6	mathematicians	mathematician	NOUN
ejpam-3947	44	7	study	study	VERB
ejpam-3947	44	8	various	various	ADJ
ejpam-3947	44	9	nonlinear	nonlinear	ADJ
ejpam-3947	44	10	diophantine	diophantine	NOUN
ejpam-3947	44	11	equations	equation	NOUN
ejpam-3947	44	12	.	.	PUNCT
ejpam-3947	45	1	keskin	keskin	VERB
ejpam-3947	46	1	[	[	X
ejpam-3947	46	2	7	7	NUM
ejpam-3947	46	3	]	]	PUNCT
ejpam-3947	46	4	investigated	investigate	VERB
ejpam-3947	46	5	positive	positive	ADJ
ejpam-3947	46	6	integer	integer	NOUN
ejpam-3947	46	7	solutions	solution	NOUN
ejpam-3947	46	8	of	of	ADP
ejpam-3947	46	9	x2	x2	PROPN
ejpam-3947	46	10	−	−	PROPN
ejpam-3947	46	11	kxy	kxy	NOUN
ejpam-3947	46	12	∓	∓	NOUN
ejpam-3947	47	1	y2	y2	NOUN
ejpam-3947	47	2	∓	∓	NOUN
ejpam-3947	47	3	x	x	PUNCT
ejpam-3947	48	1	=	=	SYM
ejpam-3947	48	2	0	0	NUM
ejpam-3947	48	3	and	and	CCONJ
ejpam-3947	48	4	x2	x2	PROPN
ejpam-3947	48	5	−	−	PROPN
ejpam-3947	48	6	kxy	kxy	NOUN
ejpam-3947	48	7	−	−	PROPN
ejpam-3947	48	8	y2	y2	INTJ
ejpam-3947	48	9	∓	∓	NOUN
ejpam-3947	49	1	y	y	PROPN
ejpam-3947	50	1	=	=	SYM
ejpam-3947	51	1	0	0	PROPN
ejpam-3947	52	1	,	,	PUNCT
ejpam-3947	52	2	abu	abu	PROPN
ejpam-3947	52	3	muriefah	muriefah	PROPN
ejpam-3947	52	4	and	and	CCONJ
ejpam-3947	52	5	al	al	PROPN
ejpam-3947	52	6	-	-	PUNCT
ejpam-3947	52	7	rashed	rashed	PROPN
ejpam-3947	52	8	[	[	X
ejpam-3947	52	9	12	12	NUM
ejpam-3947	52	10	]	]	PUNCT
ejpam-3947	52	11	studied	study	VERB
ejpam-3947	52	12	the	the	DET
ejpam-3947	52	13	diophantine	diophantine	NOUN
ejpam-3947	52	14	equation	equation	NOUN
ejpam-3947	52	15	x2	x2	NOUN
ejpam-3947	52	16	−	−	PROPN
ejpam-3947	52	17	4	4	NUM
ejpam-3947	52	18	pm	pm	NOUN
ejpam-3947	52	19	=	=	SYM
ejpam-3947	52	20	±yn	±yn	NOUN
ejpam-3947	52	21	,	,	PUNCT
ejpam-3947	52	22	and	and	CCONJ
ejpam-3947	52	23	luca	luca	PROPN
ejpam-3947	52	24	and	and	CCONJ
ejpam-3947	52	25	soydan	soydan	PROPN
ejpam-3947	52	26	[	[	X
ejpam-3947	52	27	10	10	NUM
ejpam-3947	52	28	]	]	PUNCT
ejpam-3947	52	29	considered	consider	VERB
ejpam-3947	52	30	diophantine	diophantine	NOUN
ejpam-3947	52	31	equation	equation	NOUN
ejpam-3947	52	32	2	2	NUM
ejpam-3947	52	33	m	m	NOUN
ejpam-3947	52	34	+	+	X
ejpam-3947	52	35	nx2	nx2	PROPN
ejpam-3947	52	36	=	=	SYM
ejpam-3947	52	37	yn	yn	PROPN
ejpam-3947	52	38	.	.	PUNCT
ejpam-3947	52	39	acu	acu	PROPN
ejpam-3947	52	40	,	,	PUNCT
ejpam-3947	52	41	burshtein	burshtein	PROPN
ejpam-3947	52	42	,	,	PUNCT
ejpam-3947	52	43	dockan	dockan	ADJ
ejpam-3947	52	44	,	,	PUNCT
ejpam-3947	52	45	neres	nere	NOUN
ejpam-3947	52	46	,	,	PUNCT
ejpam-3947	52	47	rabago	rabago	PROPN
ejpam-3947	52	48	,	,	PUNCT
ejpam-3947	52	49	sroysang	sroysang	PROPN
ejpam-3947	52	50	,	,	PUNCT
ejpam-3947	52	51	and	and	CCONJ
ejpam-3947	52	52	suvarnamani	suvarnamani	PROPN
ejpam-3947	52	53	are	be	AUX
ejpam-3947	52	54	among	among	ADP
ejpam-3947	52	55	the	the	DET
ejpam-3947	52	56	mathematicians	mathematician	NOUN
ejpam-3947	52	57	who	who	PRON
ejpam-3947	52	58	studied	study	VERB
ejpam-3947	52	59	diophantine	diophantine	NOUN
ejpam-3947	52	60	equations	equation	NOUN
ejpam-3947	52	61	of	of	ADP
ejpam-3947	52	62	the	the	DET
ejpam-3947	52	63	form	form	NOUN
ejpam-3947	52	64	ax	ax	NOUN
ejpam-3947	52	65	+	+	CCONJ
ejpam-3947	52	66	by	by	ADP
ejpam-3947	52	67	=	=	PROPN
ejpam-3947	52	68	z2	z2	PROPN
ejpam-3947	52	69	(	(	PUNCT
ejpam-3947	52	70	cf	cf	NOUN
ejpam-3947	52	71	.	.	PUNCT
ejpam-3947	53	1	[	[	X
ejpam-3947	53	2	1	1	NUM
ejpam-3947	53	3	,	,	PUNCT
ejpam-3947	53	4	2	2	NUM
ejpam-3947	53	5	,	,	PUNCT
ejpam-3947	53	6	4	4	NUM
ejpam-3947	53	7	,	,	PUNCT
ejpam-3947	53	8	6	6	NUM
ejpam-3947	53	9	,	,	PUNCT
ejpam-3947	53	10	13–17	13–17	NUM
ejpam-3947	53	11	,	,	PUNCT
ejpam-3947	53	12	19	19	NUM
ejpam-3947	53	13	,	,	PUNCT
ejpam-3947	53	14	20	20	NUM
ejpam-3947	53	15	]	]	PUNCT
ejpam-3947	53	16	)	)	PUNCT
ejpam-3947	53	17	.	.	PUNCT
ejpam-3947	54	1	3	3	X
ejpam-3947	54	2	.	.	X
ejpam-3947	54	3	main	main	ADJ
ejpam-3947	54	4	results	result	NOUN
ejpam-3947	54	5	3.1	3.1	NUM
ejpam-3947	54	6	.	.	PUNCT
ejpam-3947	55	1	on	on	ADP
ejpam-3947	55	2	the	the	DET
ejpam-3947	55	3	diophantine	diophantine	NOUN
ejpam-3947	55	4	equation	equation	NOUN
ejpam-3947	55	5	px	px	X
ejpam-3947	55	6	+	+	CCONJ
ejpam-3947	55	7	(	(	PUNCT
ejpam-3947	55	8	p+	p+	NOUN
ejpam-3947	55	9	4)y	4)y	PROPN
ejpam-3947	55	10	=	=	SYM
ejpam-3947	55	11	z2	z2	PROPN
ejpam-3947	55	12	we	we	PRON
ejpam-3947	55	13	begin	begin	VERB
ejpam-3947	55	14	the	the	DET
ejpam-3947	55	15	discussion	discussion	NOUN
ejpam-3947	55	16	by	by	ADP
ejpam-3947	55	17	considering	consider	VERB
ejpam-3947	55	18	the	the	DET
ejpam-3947	55	19	following	follow	VERB
ejpam-3947	55	20	two	two	NUM
ejpam-3947	55	21	lemmas	lemma	NOUN
ejpam-3947	55	22	.	.	PUNCT
ejpam-3947	56	1	r.	r.	PROPN
ejpam-3947	56	2	j.	j.	PROPN
ejpam-3947	56	3	s.	s.	PROPN
ejpam-3947	56	4	mina	mina	PROPN
ejpam-3947	56	5	,	,	PUNCT
ejpam-3947	56	6	j.	j.	PROPN
ejpam-3947	56	7	b.	b.	PROPN
ejpam-3947	56	8	bacani	bacani	PROPN
ejpam-3947	56	9	/	/	SYM
ejpam-3947	56	10	eur	eur	PROPN
ejpam-3947	56	11	.	.	PUNCT
ejpam-3947	57	1	j.	j.	PROPN
ejpam-3947	57	2	pure	pure	PROPN
ejpam-3947	57	3	appl	appl	PROPN
ejpam-3947	57	4	.	.	PROPN
ejpam-3947	57	5	math	math	PROPN
ejpam-3947	57	6	,	,	PUNCT
ejpam-3947	57	7	14	14	NUM
ejpam-3947	57	8	(	(	PUNCT
ejpam-3947	57	9	2	2	NUM
ejpam-3947	57	10	)	)	PUNCT
ejpam-3947	57	11	(	(	PUNCT
ejpam-3947	57	12	2021	2021	NUM
ejpam-3947	57	13	)	)	PUNCT
ejpam-3947	57	14	,	,	PUNCT
ejpam-3947	57	15	471	471	NUM
ejpam-3947	57	16	-	-	SYM
ejpam-3947	57	17	479	479	NUM
ejpam-3947	57	18	473	473	NUM
ejpam-3947	57	19	lemma	lemma	PROPN
ejpam-3947	57	20	1	1	NUM
ejpam-3947	57	21	.	.	PUNCT
ejpam-3947	58	1	the	the	DET
ejpam-3947	58	2	diophantine	diophantine	NOUN
ejpam-3947	58	3	equation	equation	NOUN
ejpam-3947	58	4	(	(	PUNCT
ejpam-3947	58	5	2	2	NUM
ejpam-3947	58	6	)	)	PUNCT
ejpam-3947	58	7	,	,	PUNCT
ejpam-3947	58	8	where	where	SCONJ
ejpam-3947	58	9	p	p	NOUN
ejpam-3947	58	10	and	and	CCONJ
ejpam-3947	58	11	p	p	NOUN
ejpam-3947	58	12	+	+	CCONJ
ejpam-3947	58	13	4	4	NUM
ejpam-3947	58	14	are	be	AUX
ejpam-3947	58	15	cousin	cousin	NOUN
ejpam-3947	58	16	primes	prime	NOUN
ejpam-3947	58	17	,	,	PUNCT
ejpam-3947	58	18	has	have	VERB
ejpam-3947	58	19	no	no	DET
ejpam-3947	58	20	solutions	solution	NOUN
ejpam-3947	58	21	in	in	ADP
ejpam-3947	58	22	n0	n0	NOUN
ejpam-3947	58	23	if	if	SCONJ
ejpam-3947	58	24	x	x	PRON
ejpam-3947	58	25	and	and	CCONJ
ejpam-3947	58	26	y	y	PROPN
ejpam-3947	58	27	are	be	AUX
ejpam-3947	58	28	of	of	ADP
ejpam-3947	58	29	the	the	DET
ejpam-3947	58	30	same	same	ADJ
ejpam-3947	58	31	parity	parity	NOUN
ejpam-3947	58	32	.	.	PUNCT
ejpam-3947	59	1	proof	proof	NOUN
ejpam-3947	59	2	.	.	PUNCT
ejpam-3947	60	1	suppose	suppose	VERB
ejpam-3947	61	1	that	that	SCONJ
ejpam-3947	61	2	x	x	PROPN
ejpam-3947	61	3	and	and	CCONJ
ejpam-3947	61	4	y	y	PROPN
ejpam-3947	61	5	are	be	AUX
ejpam-3947	61	6	both	both	PRON
ejpam-3947	61	7	even	even	ADV
ejpam-3947	61	8	.	.	PUNCT
ejpam-3947	61	9	taking	take	VERB
ejpam-3947	61	10	equation	equation	NOUN
ejpam-3947	61	11	(	(	PUNCT
ejpam-3947	61	12	2	2	X
ejpam-3947	61	13	)	)	PUNCT
ejpam-3947	61	14	modulo	modulo	NOUN
ejpam-3947	61	15	4	4	NUM
ejpam-3947	61	16	,	,	PUNCT
ejpam-3947	61	17	by	by	ADP
ejpam-3947	61	18	first	first	ADV
ejpam-3947	61	19	replacing	replace	VERB
ejpam-3947	61	20	p	p	X
ejpam-3947	61	21	+	+	ADP
ejpam-3947	61	22	4	4	NUM
ejpam-3947	61	23	by	by	ADP
ejpam-3947	61	24	q	q	PROPN
ejpam-3947	61	25	,	,	PUNCT
ejpam-3947	61	26	we	we	PRON
ejpam-3947	61	27	get	get	VERB
ejpam-3947	61	28	px	px	X
ejpam-3947	61	29	+	+	CCONJ
ejpam-3947	61	30	qy	qy	PROPN
ejpam-3947	61	31	≡	≡	PROPN
ejpam-3947	61	32	2	2	NUM
ejpam-3947	61	33	(	(	PUNCT
ejpam-3947	61	34	mod	mod	NOUN
ejpam-3947	61	35	4	4	X
ejpam-3947	61	36	)	)	PUNCT
ejpam-3947	61	37	whenever	whenever	SCONJ
ejpam-3947	61	38	p	p	PRON
ejpam-3947	61	39	≡	≡	PROPN
ejpam-3947	61	40	1	1	NUM
ejpam-3947	61	41	(	(	PUNCT
ejpam-3947	61	42	mod	mod	NOUN
ejpam-3947	61	43	4	4	NUM
ejpam-3947	61	44	)	)	PUNCT
ejpam-3947	61	45	or	or	CCONJ
ejpam-3947	61	46	p	p	PRON
ejpam-3947	61	47	≡	≡	PROPN
ejpam-3947	61	48	−1	−1	NOUN
ejpam-3947	61	49	(	(	PUNCT
ejpam-3947	61	50	mod	mod	PROPN
ejpam-3947	61	51	4	4	NUM
ejpam-3947	61	52	)	)	PUNCT
ejpam-3947	61	53	.	.	PUNCT
ejpam-3947	62	1	on	on	ADP
ejpam-3947	62	2	the	the	DET
ejpam-3947	62	3	other	other	ADJ
ejpam-3947	62	4	hand	hand	NOUN
ejpam-3947	62	5	,	,	PUNCT
ejpam-3947	62	6	since	since	SCONJ
ejpam-3947	62	7	px	px	PROPN
ejpam-3947	62	8	+	+	PROPN
ejpam-3947	62	9	qy	qy	NOUN
ejpam-3947	62	10	is	be	AUX
ejpam-3947	62	11	even	even	ADV
ejpam-3947	62	12	for	for	ADP
ejpam-3947	62	13	any	any	DET
ejpam-3947	62	14	cousin	cousin	NOUN
ejpam-3947	62	15	primes	prime	NOUN
ejpam-3947	62	16	p	p	NOUN
ejpam-3947	62	17	and	and	CCONJ
ejpam-3947	62	18	q	q	NOUN
ejpam-3947	62	19	,	,	PUNCT
ejpam-3947	62	20	then	then	ADV
ejpam-3947	62	21	z2	z2	PROPN
ejpam-3947	62	22	is	be	AUX
ejpam-3947	62	23	even	even	ADV
ejpam-3947	62	24	and	and	CCONJ
ejpam-3947	62	25	z2	z2	PROPN
ejpam-3947	62	26	≡	≡	PROPN
ejpam-3947	62	27	0	0	PUNCT
ejpam-3947	63	1	(	(	PUNCT
ejpam-3947	63	2	mod	mod	PROPN
ejpam-3947	63	3	4	4	NUM
ejpam-3947	63	4	)	)	PUNCT
ejpam-3947	63	5	.	.	PUNCT
ejpam-3947	64	1	now	now	ADV
ejpam-3947	64	2	,	,	PUNCT
ejpam-3947	64	3	suppose	suppose	VERB
ejpam-3947	64	4	that	that	SCONJ
ejpam-3947	64	5	x	x	PROPN
ejpam-3947	64	6	and	and	CCONJ
ejpam-3947	64	7	y	y	PROPN
ejpam-3947	64	8	are	be	AUX
ejpam-3947	64	9	both	both	PRON
ejpam-3947	64	10	odd	odd	ADJ
ejpam-3947	64	11	.	.	PUNCT
ejpam-3947	65	1	if	if	SCONJ
ejpam-3947	65	2	p	p	PRON
ejpam-3947	65	3	≡	≡	PROPN
ejpam-3947	65	4	1	1	NUM
ejpam-3947	65	5	(	(	PUNCT
ejpam-3947	65	6	mod	mod	NOUN
ejpam-3947	65	7	4	4	NUM
ejpam-3947	65	8	)	)	PUNCT
ejpam-3947	65	9	,	,	PUNCT
ejpam-3947	65	10	then	then	ADV
ejpam-3947	65	11	px	px	PROPN
ejpam-3947	65	12	+	+	PROPN
ejpam-3947	65	13	qy	qy	PROPN
ejpam-3947	65	14	≡	≡	PROPN
ejpam-3947	65	15	1	1	NUM
ejpam-3947	65	16	+	+	SYM
ejpam-3947	65	17	1	1	NUM
ejpam-3947	65	18	≡	≡	PROPN
ejpam-3947	65	19	2	2	NUM
ejpam-3947	65	20	(	(	PUNCT
ejpam-3947	65	21	mod	mod	NOUN
ejpam-3947	65	22	4	4	NUM
ejpam-3947	65	23	)	)	PUNCT
ejpam-3947	65	24	.	.	PUNCT
ejpam-3947	66	1	if	if	SCONJ
ejpam-3947	66	2	p	p	PRON
ejpam-3947	66	3	≡	≡	PROPN
ejpam-3947	66	4	−1	−1	NOUN
ejpam-3947	66	5	(	(	PUNCT
ejpam-3947	66	6	mod	mod	PROPN
ejpam-3947	66	7	4	4	NUM
ejpam-3947	66	8	)	)	PUNCT
ejpam-3947	66	9	,	,	PUNCT
ejpam-3947	66	10	then	then	ADV
ejpam-3947	66	11	px	px	PROPN
ejpam-3947	66	12	+	+	PROPN
ejpam-3947	66	13	qy	qy	PROPN
ejpam-3947	66	14	≡	≡	PROPN
ejpam-3947	66	15	(	(	PUNCT
ejpam-3947	66	16	−1	−1	NOUN
ejpam-3947	66	17	)	)	PUNCT
ejpam-3947	66	18	+	+	CCONJ
ejpam-3947	66	19	(	(	PUNCT
ejpam-3947	66	20	−1	−1	NOUN
ejpam-3947	66	21	)	)	PUNCT
ejpam-3947	66	22	≡	≡	PROPN
ejpam-3947	66	23	2	2	NUM
ejpam-3947	66	24	(	(	PUNCT
ejpam-3947	66	25	mod	mod	NOUN
ejpam-3947	66	26	4	4	NUM
ejpam-3947	66	27	)	)	PUNCT
ejpam-3947	66	28	.	.	PUNCT
ejpam-3947	67	1	therefore	therefore	ADV
ejpam-3947	67	2	,	,	PUNCT
ejpam-3947	67	3	in	in	ADP
ejpam-3947	67	4	any	any	DET
ejpam-3947	67	5	case	case	NOUN
ejpam-3947	67	6	,	,	PUNCT
ejpam-3947	67	7	px	px	PROPN
ejpam-3947	67	8	+	+	CCONJ
ejpam-3947	67	9	qy	qy	PROPN
ejpam-3947	67	10	6≡	6≡	NUM
ejpam-3947	67	11	z2	z2	PROPN
ejpam-3947	67	12	(	(	PUNCT
ejpam-3947	67	13	mod	mod	PROPN
ejpam-3947	67	14	4	4	NUM
ejpam-3947	67	15	)	)	PUNCT
ejpam-3947	67	16	.	.	PUNCT
ejpam-3947	68	1	we	we	PRON
ejpam-3947	68	2	now	now	ADV
ejpam-3947	68	3	consider	consider	VERB
ejpam-3947	68	4	the	the	DET
ejpam-3947	68	5	case	case	NOUN
ejpam-3947	68	6	where	where	SCONJ
ejpam-3947	68	7	x	x	PRON
ejpam-3947	68	8	and	and	CCONJ
ejpam-3947	68	9	y	y	PROPN
ejpam-3947	68	10	are	be	AUX
ejpam-3947	68	11	of	of	ADP
ejpam-3947	68	12	different	different	ADJ
ejpam-3947	68	13	parity	parity	NOUN
ejpam-3947	68	14	.	.	PUNCT
ejpam-3947	69	1	lemma	lemma	PROPN
ejpam-3947	69	2	2	2	NUM
ejpam-3947	69	3	.	.	PUNCT
ejpam-3947	70	1	the	the	DET
ejpam-3947	70	2	diophantine	diophantine	NOUN
ejpam-3947	70	3	equation	equation	NOUN
ejpam-3947	70	4	(	(	PUNCT
ejpam-3947	70	5	2	2	NUM
ejpam-3947	70	6	)	)	PUNCT
ejpam-3947	70	7	,	,	PUNCT
ejpam-3947	70	8	where	where	SCONJ
ejpam-3947	70	9	p	p	NOUN
ejpam-3947	70	10	and	and	CCONJ
ejpam-3947	70	11	q	q	NOUN
ejpam-3947	70	12	are	be	AUX
ejpam-3947	70	13	cousin	cousin	NOUN
ejpam-3947	70	14	primes	prime	NOUN
ejpam-3947	70	15	,	,	PUNCT
ejpam-3947	70	16	and	and	CCONJ
ejpam-3947	70	17	x	x	X
ejpam-3947	70	18	and	and	CCONJ
ejpam-3947	70	19	y	y	PROPN
ejpam-3947	70	20	are	be	AUX
ejpam-3947	70	21	of	of	ADP
ejpam-3947	70	22	different	different	ADJ
ejpam-3947	70	23	parity	parity	NOUN
ejpam-3947	70	24	,	,	PUNCT
ejpam-3947	70	25	has	have	VERB
ejpam-3947	70	26	exactly	exactly	ADV
ejpam-3947	70	27	two	two	NUM
ejpam-3947	70	28	solutions	solution	NOUN
ejpam-3947	70	29	in	in	ADP
ejpam-3947	70	30	n0	n0	PROPN
ejpam-3947	70	31	,	,	PUNCT
ejpam-3947	70	32	namely	namely	ADV
ejpam-3947	70	33	,	,	PUNCT
ejpam-3947	70	34	(	(	PUNCT
ejpam-3947	70	35	p	p	X
ejpam-3947	70	36	,	,	PUNCT
ejpam-3947	70	37	q	q	ADJ
ejpam-3947	70	38	,	,	PUNCT
ejpam-3947	70	39	x	x	NOUN
ejpam-3947	70	40	,	,	PUNCT
ejpam-3947	70	41	y	y	PROPN
ejpam-3947	70	42	,	,	PUNCT
ejpam-3947	70	43	z	z	NOUN
ejpam-3947	70	44	)	)	PUNCT
ejpam-3947	70	45	=	=	SYM
ejpam-3947	70	46	(	(	PUNCT
ejpam-3947	70	47	3	3	NUM
ejpam-3947	70	48	,	,	PUNCT
ejpam-3947	70	49	7	7	NUM
ejpam-3947	70	50	,	,	PUNCT
ejpam-3947	70	51	1	1	NUM
ejpam-3947	70	52	,	,	PUNCT
ejpam-3947	70	53	0	0	NUM
ejpam-3947	70	54	,	,	PUNCT
ejpam-3947	70	55	2	2	NUM
ejpam-3947	70	56	)	)	PUNCT
ejpam-3947	70	57	and	and	CCONJ
ejpam-3947	70	58	(	(	PUNCT
ejpam-3947	70	59	3	3	NUM
ejpam-3947	70	60	,	,	PUNCT
ejpam-3947	70	61	7	7	NUM
ejpam-3947	70	62	,	,	PUNCT
ejpam-3947	70	63	2	2	NUM
ejpam-3947	70	64	,	,	PUNCT
ejpam-3947	70	65	1	1	NUM
ejpam-3947	70	66	,	,	PUNCT
ejpam-3947	70	67	4	4	NUM
ejpam-3947	70	68	)	)	PUNCT
ejpam-3947	70	69	.	.	PUNCT
ejpam-3947	71	1	proof	proof	NOUN
ejpam-3947	71	2	.	.	PUNCT
ejpam-3947	72	1	case	case	NOUN
ejpam-3947	72	2	1	1	NUM
ejpam-3947	72	3	:	:	PUNCT
ejpam-3947	72	4	x	x	X
ejpam-3947	72	5	is	be	AUX
ejpam-3947	72	6	odd	odd	ADJ
ejpam-3947	72	7	and	and	CCONJ
ejpam-3947	72	8	y	y	PROPN
ejpam-3947	72	9	is	be	AUX
ejpam-3947	72	10	even	even	ADV
ejpam-3947	72	11	,	,	PUNCT
ejpam-3947	72	12	i.e.	i.e.	X
ejpam-3947	72	13	y	y	X
ejpam-3947	72	14	=	=	PUNCT
ejpam-3947	72	15	2l	2l	PROPN
ejpam-3947	72	16	for	for	ADP
ejpam-3947	72	17	some	some	DET
ejpam-3947	72	18	l	l	NOUN
ejpam-3947	72	19	∈	∈	PROPN
ejpam-3947	72	20	n0	n0	PROPN
ejpam-3947	72	21	.	.	PUNCT
ejpam-3947	73	1	write	write	VERB
ejpam-3947	73	2	px	px	PROPN
ejpam-3947	73	3	as	as	ADP
ejpam-3947	73	4	px	px	PROPN
ejpam-3947	73	5	=	=	PROPN
ejpam-3947	73	6	z2	z2	PROPN
ejpam-3947	73	7	−	−	PROPN
ejpam-3947	73	8	q2l	q2l	PROPN
ejpam-3947	73	9	=	=	SYM
ejpam-3947	73	10	(	(	PUNCT
ejpam-3947	73	11	z	z	NOUN
ejpam-3947	73	12	+	+	NUM
ejpam-3947	73	13	ql)(z	ql)(z	NOUN
ejpam-3947	73	14	−	−	NUM
ejpam-3947	73	15	ql	ql	NOUN
ejpam-3947	73	16	)	)	PUNCT
ejpam-3947	73	17	.	.	PUNCT
ejpam-3947	74	1	since	since	SCONJ
ejpam-3947	74	2	p	p	NOUN
ejpam-3947	74	3	is	be	AUX
ejpam-3947	74	4	prime	prime	ADJ
ejpam-3947	74	5	,	,	PUNCT
ejpam-3947	74	6	there	there	PRON
ejpam-3947	74	7	exist	exist	VERB
ejpam-3947	74	8	integers	integer	NOUN
ejpam-3947	74	9	α	α	NOUN
ejpam-3947	74	10	and	and	CCONJ
ejpam-3947	74	11	β	β	X
ejpam-3947	74	12	with	with	ADP
ejpam-3947	74	13	α	α	PROPN
ejpam-3947	74	14	<	<	X
ejpam-3947	74	15	β	β	X
ejpam-3947	74	16	s.t	s.t	PROPN
ejpam-3947	74	17	.	.	PROPN
ejpam-3947	75	1	α+	α+	X
ejpam-3947	75	2	β	β	X
ejpam-3947	75	3	=	=	PUNCT
ejpam-3947	75	4	x	x	X
ejpam-3947	75	5	and	and	CCONJ
ejpam-3947	75	6	pα(pβ−α	pα(pβ−α	NOUN
ejpam-3947	75	7	−	−	NOUN
ejpam-3947	75	8	1	1	NUM
ejpam-3947	75	9	)	)	PUNCT
ejpam-3947	75	10	=	=	PUNCT
ejpam-3947	76	1	(	(	PUNCT
ejpam-3947	76	2	z	z	NOUN
ejpam-3947	76	3	+	+	X
ejpam-3947	76	4	ql)−	ql)−	NOUN
ejpam-3947	76	5	(	(	PUNCT
ejpam-3947	76	6	z	z	NOUN
ejpam-3947	76	7	−	−	PROPN
ejpam-3947	76	8	ql	ql	PROPN
ejpam-3947	76	9	)	)	PUNCT
ejpam-3947	76	10	=	=	SYM
ejpam-3947	76	11	2ql	2ql	NOUN
ejpam-3947	76	12	.	.	PUNCT
ejpam-3947	77	1	since	since	SCONJ
ejpam-3947	77	2	p	p	PRON
ejpam-3947	77	3	6=	6=	NUM
ejpam-3947	77	4	2	2	NUM
ejpam-3947	77	5	,	,	PUNCT
ejpam-3947	77	6	q	q	INTJ
ejpam-3947	77	7	,	,	PUNCT
ejpam-3947	77	8	we	we	PRON
ejpam-3947	77	9	have	have	VERB
ejpam-3947	77	10	α	α	NOUN
ejpam-3947	77	11	=	=	SYM
ejpam-3947	77	12	0	0	NUM
ejpam-3947	77	13	and	and	CCONJ
ejpam-3947	77	14	will	will	AUX
ejpam-3947	77	15	imply	imply	VERB
ejpam-3947	77	16	that	that	SCONJ
ejpam-3947	77	17	px	px	PROPN
ejpam-3947	77	18	−	−	NUM
ejpam-3947	77	19	1	1	NUM
ejpam-3947	77	20	=	=	NOUN
ejpam-3947	77	21	2ql	2ql	NOUN
ejpam-3947	77	22	.	.	PUNCT
ejpam-3947	78	1	by	by	ADP
ejpam-3947	78	2	factoring	factor	VERB
ejpam-3947	78	3	,	,	PUNCT
ejpam-3947	78	4	we	we	PRON
ejpam-3947	78	5	get	get	VERB
ejpam-3947	78	6	(	(	PUNCT
ejpam-3947	78	7	p−	p−	NOUN
ejpam-3947	78	8	1)(px−1	1)(px−1	NUM
ejpam-3947	78	9	+	+	CCONJ
ejpam-3947	78	10	px−2	px−2	NOUN
ejpam-3947	78	11	+	+	X
ejpam-3947	78	12	·	·	PUNCT
ejpam-3947	78	13	·	·	PUNCT
ejpam-3947	78	14	·	·	PUNCT
ejpam-3947	79	1	+	+	CCONJ
ejpam-3947	79	2	1	1	X
ejpam-3947	79	3	)	)	PUNCT
ejpam-3947	79	4	=	=	PUNCT
ejpam-3947	79	5	2ql	2ql	NOUN
ejpam-3947	79	6	.	.	PUNCT
ejpam-3947	80	1	(	(	PUNCT
ejpam-3947	80	2	5	5	X
ejpam-3947	80	3	)	)	PUNCT
ejpam-3947	80	4	note	note	NOUN
ejpam-3947	80	5	that	that	SCONJ
ejpam-3947	80	6	q	q	NOUN
ejpam-3947	80	7	is	be	AUX
ejpam-3947	80	8	prime	prime	ADJ
ejpam-3947	80	9	.	.	PUNCT
ejpam-3947	81	1	so	so	ADV
ejpam-3947	81	2	,	,	PUNCT
ejpam-3947	81	3	p	p	NOUN
ejpam-3947	81	4	−	−	PROPN
ejpam-3947	81	5	1	1	NUM
ejpam-3947	81	6	=	=	SYM
ejpam-3947	81	7	2qj	2qj	NOUN
ejpam-3947	81	8	for	for	ADP
ejpam-3947	81	9	some	some	DET
ejpam-3947	81	10	j	j	PROPN
ejpam-3947	81	11	≤	≤	PROPN
ejpam-3947	81	12	l.	l.	PROPN
ejpam-3947	81	13	if	if	SCONJ
ejpam-3947	81	14	j	j	PROPN
ejpam-3947	81	15	≥	≥	NUM
ejpam-3947	81	16	1	1	NUM
ejpam-3947	81	17	,	,	PUNCT
ejpam-3947	81	18	then	then	ADV
ejpam-3947	81	19	p	p	NOUN
ejpam-3947	81	20	−	−	PROPN
ejpam-3947	81	21	1	1	NUM
ejpam-3947	81	22	<	<	X
ejpam-3947	81	23	2(p	2(p	NUM
ejpam-3947	81	24	+	+	NUM
ejpam-3947	81	25	4)j	4)j	NOUN
ejpam-3947	81	26	.	.	PUNCT
ejpam-3947	82	1	hence	hence	ADV
ejpam-3947	82	2	this	this	PRON
ejpam-3947	82	3	can	can	AUX
ejpam-3947	82	4	only	only	ADV
ejpam-3947	82	5	have	have	VERB
ejpam-3947	82	6	a	a	DET
ejpam-3947	82	7	solution	solution	NOUN
ejpam-3947	82	8	if	if	SCONJ
ejpam-3947	82	9	j	j	PROPN
ejpam-3947	82	10	=	=	NOUN
ejpam-3947	82	11	0	0	PROPN
ejpam-3947	82	12	.	.	PUNCT
ejpam-3947	83	1	if	if	SCONJ
ejpam-3947	83	2	j	j	PROPN
ejpam-3947	83	3	=	=	SYM
ejpam-3947	83	4	0	0	PROPN
ejpam-3947	83	5	,	,	PUNCT
ejpam-3947	83	6	then	then	ADV
ejpam-3947	83	7	p	p	NOUN
ejpam-3947	83	8	=	=	PROPN
ejpam-3947	83	9	3	3	NUM
ejpam-3947	83	10	and	and	CCONJ
ejpam-3947	83	11	we	we	PRON
ejpam-3947	83	12	have	have	VERB
ejpam-3947	83	13	from	from	ADP
ejpam-3947	83	14	(	(	PUNCT
ejpam-3947	83	15	5	5	NUM
ejpam-3947	83	16	)	)	PUNCT
ejpam-3947	84	1	that	that	PRON
ejpam-3947	84	2	3x−1	3x−1	NUM
ejpam-3947	84	3	+	+	CCONJ
ejpam-3947	84	4	3x−2	3x−2	NUM
ejpam-3947	84	5	+	+	X
ejpam-3947	84	6	·	·	PUNCT
ejpam-3947	84	7	·	·	PUNCT
ejpam-3947	84	8	·	·	PUNCT
ejpam-3947	85	1	+	+	NUM
ejpam-3947	85	2	1	1	NUM
ejpam-3947	85	3	=	=	SYM
ejpam-3947	85	4	7l	7l	NUM
ejpam-3947	85	5	.	.	PUNCT
ejpam-3947	86	1	(	(	PUNCT
ejpam-3947	86	2	6	6	X
ejpam-3947	86	3	)	)	PUNCT
ejpam-3947	86	4	substituting	substitute	VERB
ejpam-3947	86	5	x	x	PUNCT
ejpam-3947	86	6	=	=	SYM
ejpam-3947	86	7	1	1	NUM
ejpam-3947	86	8	to	to	PART
ejpam-3947	86	9	(	(	PUNCT
ejpam-3947	86	10	6	6	NUM
ejpam-3947	86	11	)	)	PUNCT
ejpam-3947	86	12	,	,	PUNCT
ejpam-3947	86	13	we	we	PRON
ejpam-3947	86	14	get	get	VERB
ejpam-3947	86	15	l	l	NOUN
ejpam-3947	86	16	=	=	SYM
ejpam-3947	86	17	0	0	NUM
ejpam-3947	86	18	,	,	PUNCT
ejpam-3947	86	19	and	and	CCONJ
ejpam-3947	86	20	(	(	PUNCT
ejpam-3947	86	21	p	p	X
ejpam-3947	86	22	,	,	PUNCT
ejpam-3947	86	23	q	q	ADJ
ejpam-3947	86	24	,	,	PUNCT
ejpam-3947	86	25	x	x	NOUN
ejpam-3947	86	26	,	,	PUNCT
ejpam-3947	86	27	y	y	PROPN
ejpam-3947	86	28	,	,	PUNCT
ejpam-3947	86	29	z	z	NOUN
ejpam-3947	86	30	)	)	PUNCT
ejpam-3947	86	31	=	=	SYM
ejpam-3947	86	32	(	(	PUNCT
ejpam-3947	86	33	3	3	NUM
ejpam-3947	86	34	,	,	PUNCT
ejpam-3947	86	35	7	7	NUM
ejpam-3947	86	36	,	,	PUNCT
ejpam-3947	86	37	1	1	NUM
ejpam-3947	86	38	,	,	PUNCT
ejpam-3947	86	39	0	0	NUM
ejpam-3947	86	40	,	,	PUNCT
ejpam-3947	86	41	2	2	NUM
ejpam-3947	86	42	)	)	PUNCT
ejpam-3947	86	43	is	be	AUX
ejpam-3947	86	44	a	a	DET
ejpam-3947	86	45	solution	solution	NOUN
ejpam-3947	86	46	to	to	ADP
ejpam-3947	86	47	(	(	PUNCT
ejpam-3947	86	48	2	2	NUM
ejpam-3947	86	49	)	)	PUNCT
ejpam-3947	86	50	.	.	PUNCT
ejpam-3947	87	1	if	if	SCONJ
ejpam-3947	87	2	x	x	PROPN
ejpam-3947	87	3	>	>	X
ejpam-3947	87	4	1	1	NUM
ejpam-3947	87	5	then	then	ADV
ejpam-3947	87	6	l	l	NOUN
ejpam-3947	87	7	>	>	X
ejpam-3947	88	1	1	1	X
ejpam-3947	88	2	.	.	X
ejpam-3947	88	3	take	take	VERB
ejpam-3947	88	4	modulo	modulo	NOUN
ejpam-3947	88	5	7	7	NUM
ejpam-3947	88	6	to	to	PART
ejpam-3947	88	7	(	(	PUNCT
ejpam-3947	88	8	6	6	NUM
ejpam-3947	88	9	)	)	PUNCT
ejpam-3947	88	10	to	to	PART
ejpam-3947	88	11	obtain	obtain	VERB
ejpam-3947	88	12	3x−1	3x−1	NUM
ejpam-3947	88	13	+	+	CCONJ
ejpam-3947	88	14	3x−2	3x−2	NUM
ejpam-3947	88	15	+	+	X
ejpam-3947	88	16	·	·	PUNCT
ejpam-3947	88	17	·	·	PUNCT
ejpam-3947	88	18	·	·	PUNCT
ejpam-3947	89	1	+	+	CCONJ
ejpam-3947	89	2	1	1	NUM
ejpam-3947	89	3	≡	≡	PROPN
ejpam-3947	89	4	0	0	NUM
ejpam-3947	89	5	(	(	PUNCT
ejpam-3947	89	6	mod	mod	PROPN
ejpam-3947	89	7	7	7	NUM
ejpam-3947	89	8	)	)	PUNCT
ejpam-3947	89	9	.	.	PUNCT
ejpam-3947	90	1	multiply	multiply	VERB
ejpam-3947	90	2	this	this	DET
ejpam-3947	90	3	congruence	congruence	NOUN
ejpam-3947	90	4	by	by	ADP
ejpam-3947	90	5	3	3	NUM
ejpam-3947	90	6	−	−	PROPN
ejpam-3947	90	7	1	1	NUM
ejpam-3947	90	8	to	to	PART
ejpam-3947	90	9	get	get	VERB
ejpam-3947	90	10	3x	3x	NUM
ejpam-3947	90	11	−	−	PROPN
ejpam-3947	90	12	1	1	NUM
ejpam-3947	90	13	≡	≡	PROPN
ejpam-3947	90	14	0	0	PUNCT
ejpam-3947	91	1	(	(	PUNCT
ejpam-3947	91	2	mod	mod	PROPN
ejpam-3947	91	3	7	7	NUM
ejpam-3947	91	4	)	)	PUNCT
ejpam-3947	91	5	,	,	PUNCT
ejpam-3947	91	6	or	or	CCONJ
ejpam-3947	91	7	equivalently	equivalently	ADV
ejpam-3947	91	8	3x	3x	PRON
ejpam-3947	91	9	≡	≡	PROPN
ejpam-3947	91	10	1	1	NUM
ejpam-3947	91	11	(	(	PUNCT
ejpam-3947	91	12	mod	mod	PROPN
ejpam-3947	91	13	7	7	NUM
ejpam-3947	91	14	)	)	PUNCT
ejpam-3947	91	15	.	.	PUNCT
ejpam-3947	92	1	this	this	PRON
ejpam-3947	92	2	can	can	AUX
ejpam-3947	92	3	only	only	ADV
ejpam-3947	92	4	happen	happen	VERB
ejpam-3947	92	5	if	if	SCONJ
ejpam-3947	92	6	x	x	SYM
ejpam-3947	92	7	≡	≡	PROPN
ejpam-3947	92	8	0	0	PUNCT
ejpam-3947	92	9	(	(	PUNCT
ejpam-3947	92	10	mod	mod	PROPN
ejpam-3947	92	11	6	6	NUM
ejpam-3947	92	12	)	)	PUNCT
ejpam-3947	92	13	,	,	PUNCT
ejpam-3947	92	14	which	which	PRON
ejpam-3947	92	15	will	will	AUX
ejpam-3947	92	16	yield	yield	VERB
ejpam-3947	92	17	no	no	DET
ejpam-3947	92	18	solutions	solution	NOUN
ejpam-3947	92	19	since	since	SCONJ
ejpam-3947	92	20	we	we	PRON
ejpam-3947	92	21	assumed	assume	VERB
ejpam-3947	92	22	x	x	PUNCT
ejpam-3947	92	23	to	to	PART
ejpam-3947	92	24	be	be	AUX
ejpam-3947	92	25	odd	odd	ADJ
ejpam-3947	92	26	.	.	PUNCT
ejpam-3947	93	1	case	case	NOUN
ejpam-3947	93	2	2	2	NUM
ejpam-3947	93	3	:	:	PUNCT
ejpam-3947	93	4	x	x	X
ejpam-3947	93	5	is	be	AUX
ejpam-3947	93	6	even	even	ADV
ejpam-3947	93	7	and	and	CCONJ
ejpam-3947	93	8	y	y	PROPN
ejpam-3947	93	9	is	be	AUX
ejpam-3947	93	10	odd	odd	ADJ
ejpam-3947	93	11	,	,	PUNCT
ejpam-3947	93	12	i.e.	i.e.	X
ejpam-3947	93	13	x	x	SYM
ejpam-3947	93	14	=	=	SYM
ejpam-3947	93	15	2	2	NUM
ejpam-3947	93	16	m	m	NOUN
ejpam-3947	93	17	for	for	ADP
ejpam-3947	93	18	some	some	DET
ejpam-3947	93	19	m	m	NOUN
ejpam-3947	93	20	∈	∈	PROPN
ejpam-3947	93	21	n0	n0	PROPN
ejpam-3947	93	22	.	.	PUNCT
ejpam-3947	94	1	using	use	VERB
ejpam-3947	94	2	the	the	DET
ejpam-3947	94	3	same	same	ADJ
ejpam-3947	94	4	argument	argument	NOUN
ejpam-3947	94	5	as	as	ADP
ejpam-3947	94	6	in	in	ADP
ejpam-3947	94	7	case	case	NOUN
ejpam-3947	94	8	1	1	NUM
ejpam-3947	94	9	,	,	PUNCT
ejpam-3947	94	10	we	we	PRON
ejpam-3947	94	11	arrive	arrive	VERB
ejpam-3947	94	12	at	at	ADP
ejpam-3947	94	13	an	an	DET
ejpam-3947	94	14	analogous	analogous	ADJ
ejpam-3947	94	15	equation	equation	NOUN
ejpam-3947	94	16	qy	qy	NOUN
ejpam-3947	94	17	−	−	PROPN
ejpam-3947	94	18	1	1	NUM
ejpam-3947	94	19	=	=	SYM
ejpam-3947	94	20	2	2	NUM
ejpam-3947	94	21	pm	pm	NOUN
ejpam-3947	94	22	.	.	PUNCT
ejpam-3947	95	1	by	by	ADP
ejpam-3947	95	2	factoring	factor	VERB
ejpam-3947	95	3	,	,	PUNCT
ejpam-3947	95	4	we	we	PRON
ejpam-3947	95	5	get	get	VERB
ejpam-3947	95	6	(	(	PUNCT
ejpam-3947	95	7	q	q	NOUN
ejpam-3947	95	8	−	−	PROPN
ejpam-3947	95	9	1)(qy−1	1)(qy−1	NUM
ejpam-3947	96	1	+	+	CCONJ
ejpam-3947	96	2	qy−2	qy−2	NOUN
ejpam-3947	96	3	+	+	X
ejpam-3947	96	4	·	·	PUNCT
ejpam-3947	96	5	·	·	PUNCT
ejpam-3947	96	6	·	·	PUNCT
ejpam-3947	97	1	+	+	CCONJ
ejpam-3947	97	2	1	1	X
ejpam-3947	97	3	)	)	PUNCT
ejpam-3947	97	4	=	=	SYM
ejpam-3947	97	5	2	2	NUM
ejpam-3947	97	6	pm	pm	NOUN
ejpam-3947	97	7	(	(	PUNCT
ejpam-3947	97	8	7	7	NUM
ejpam-3947	97	9	)	)	PUNCT
ejpam-3947	97	10	which	which	PRON
ejpam-3947	97	11	implies	imply	VERB
ejpam-3947	97	12	that	that	SCONJ
ejpam-3947	97	13	q−	q−	PROPN
ejpam-3947	97	14	1	1	NUM
ejpam-3947	97	15	=	=	SYM
ejpam-3947	97	16	2pj	2pj	NOUN
ejpam-3947	97	17	for	for	ADP
ejpam-3947	97	18	some	some	DET
ejpam-3947	97	19	j	j	PROPN
ejpam-3947	97	20	≤	≤	NUM
ejpam-3947	97	21	m.	m.	NOUN
ejpam-3947	97	22	if	if	SCONJ
ejpam-3947	97	23	j	j	PROPN
ejpam-3947	97	24	=	=	SYM
ejpam-3947	97	25	0	0	PROPN
ejpam-3947	97	26	,	,	PUNCT
ejpam-3947	97	27	then	then	ADV
ejpam-3947	97	28	q	q	NOUN
ejpam-3947	97	29	=	=	SYM
ejpam-3947	97	30	3	3	NUM
ejpam-3947	97	31	which	which	PRON
ejpam-3947	97	32	is	be	AUX
ejpam-3947	97	33	not	not	PART
ejpam-3947	97	34	possible	possible	ADJ
ejpam-3947	97	35	.	.	PUNCT
ejpam-3947	98	1	if	if	SCONJ
ejpam-3947	98	2	j	j	PROPN
ejpam-3947	98	3	>	>	X
ejpam-3947	98	4	1	1	NUM
ejpam-3947	98	5	,	,	PUNCT
ejpam-3947	98	6	then	then	ADV
ejpam-3947	98	7	q	q	NOUN
ejpam-3947	98	8	−	−	PROPN
ejpam-3947	99	1	1	1	NUM
ejpam-3947	99	2	=	=	SYM
ejpam-3947	99	3	p	p	NOUN
ejpam-3947	100	1	+	+	CCONJ
ejpam-3947	100	2	3	3	NUM
ejpam-3947	100	3	<	<	X
ejpam-3947	100	4	2pj	2pj	NOUN
ejpam-3947	100	5	for	for	ADP
ejpam-3947	100	6	any	any	DET
ejpam-3947	100	7	odd	odd	ADJ
ejpam-3947	100	8	prime	prime	ADJ
ejpam-3947	100	9	p.	p.	NOUN
ejpam-3947	100	10	hence	hence	ADV
ejpam-3947	100	11	,	,	PUNCT
ejpam-3947	100	12	this	this	PRON
ejpam-3947	100	13	can	can	AUX
ejpam-3947	100	14	only	only	ADV
ejpam-3947	100	15	have	have	VERB
ejpam-3947	100	16	a	a	DET
ejpam-3947	100	17	solution	solution	NOUN
ejpam-3947	100	18	if	if	SCONJ
ejpam-3947	100	19	j	j	PROPN
ejpam-3947	100	20	=	=	NOUN
ejpam-3947	100	21	1	1	X
ejpam-3947	100	22	.	.	X
ejpam-3947	101	1	using	use	VERB
ejpam-3947	101	2	(	(	PUNCT
ejpam-3947	101	3	7	7	NUM
ejpam-3947	101	4	)	)	PUNCT
ejpam-3947	101	5	,	,	PUNCT
ejpam-3947	101	6	we	we	PRON
ejpam-3947	101	7	have	have	VERB
ejpam-3947	101	8	7y−1	7y−1	NUM
ejpam-3947	101	9	+	+	NOUN
ejpam-3947	101	10	7y−2	7y−2	NUM
ejpam-3947	101	11	+	+	NUM
ejpam-3947	101	12	·	·	PUNCT
ejpam-3947	101	13	·	·	PUNCT
ejpam-3947	101	14	·	·	PUNCT
ejpam-3947	102	1	+	+	NUM
ejpam-3947	102	2	1	1	NUM
ejpam-3947	102	3	=	=	SYM
ejpam-3947	102	4	3m−j	3m−j	NUM
ejpam-3947	102	5	=	=	SYM
ejpam-3947	102	6	3m−1	3m−1	NUM
ejpam-3947	102	7	.	.	PUNCT
ejpam-3947	103	1	(	(	PUNCT
ejpam-3947	103	2	8)	8)	NUM
ejpam-3947	103	3	substituting	substitute	VERB
ejpam-3947	103	4	y	y	NOUN
ejpam-3947	103	5	=	=	SYM
ejpam-3947	103	6	1	1	NUM
ejpam-3947	103	7	to	to	ADP
ejpam-3947	103	8	(	(	PUNCT
ejpam-3947	103	9	8)	8)	NUM
ejpam-3947	103	10	,	,	PUNCT
ejpam-3947	103	11	we	we	PRON
ejpam-3947	103	12	getm	getm	NOUN
ejpam-3947	103	13	=	=	SYM
ejpam-3947	103	14	1	1	NUM
ejpam-3947	103	15	,	,	PUNCT
ejpam-3947	103	16	and	and	CCONJ
ejpam-3947	103	17	(	(	PUNCT
ejpam-3947	103	18	p	p	X
ejpam-3947	103	19	,	,	PUNCT
ejpam-3947	103	20	q	q	ADJ
ejpam-3947	103	21	,	,	PUNCT
ejpam-3947	103	22	x	x	NOUN
ejpam-3947	103	23	,	,	PUNCT
ejpam-3947	103	24	y	y	PROPN
ejpam-3947	103	25	,	,	PUNCT
ejpam-3947	103	26	z	z	NOUN
ejpam-3947	103	27	)	)	PUNCT
ejpam-3947	103	28	=	=	SYM
ejpam-3947	103	29	(	(	PUNCT
ejpam-3947	103	30	3	3	NUM
ejpam-3947	103	31	,	,	PUNCT
ejpam-3947	103	32	7	7	NUM
ejpam-3947	103	33	,	,	PUNCT
ejpam-3947	103	34	2	2	NUM
ejpam-3947	103	35	,	,	PUNCT
ejpam-3947	103	36	1	1	NUM
ejpam-3947	103	37	,	,	PUNCT
ejpam-3947	103	38	4	4	NUM
ejpam-3947	103	39	)	)	PUNCT
ejpam-3947	103	40	becomes	become	VERB
ejpam-3947	103	41	a	a	DET
ejpam-3947	103	42	solution	solution	NOUN
ejpam-3947	103	43	to	to	ADP
ejpam-3947	103	44	(	(	PUNCT
ejpam-3947	103	45	2	2	NUM
ejpam-3947	103	46	)	)	PUNCT
ejpam-3947	103	47	.	.	PUNCT
ejpam-3947	104	1	if	if	SCONJ
ejpam-3947	104	2	j	j	PROPN
ejpam-3947	104	3	>	>	X
ejpam-3947	104	4	1	1	NUM
ejpam-3947	104	5	then	then	ADV
ejpam-3947	104	6	m	m	VERB
ejpam-3947	104	7	>	>	X
ejpam-3947	104	8	1	1	X
ejpam-3947	104	9	.	.	PUNCT
ejpam-3947	105	1	taking	take	VERB
ejpam-3947	105	2	modulo	modulo	NOUN
ejpam-3947	105	3	3	3	NUM
ejpam-3947	105	4	to	to	ADP
ejpam-3947	105	5	equation	equation	NOUN
ejpam-3947	105	6	(	(	PUNCT
ejpam-3947	105	7	8)	8)	NUM
ejpam-3947	105	8	,	,	PUNCT
ejpam-3947	105	9	we	we	PRON
ejpam-3947	105	10	get	get	VERB
ejpam-3947	105	11	y	y	NOUN
ejpam-3947	105	12	−	−	NOUN
ejpam-3947	105	13	1	1	NUM
ejpam-3947	105	14	+	+	SYM
ejpam-3947	105	15	1	1	NUM
ejpam-3947	105	16	≡	≡	PROPN
ejpam-3947	105	17	0	0	PUNCT
ejpam-3947	106	1	(	(	PUNCT
ejpam-3947	106	2	mod	mod	PROPN
ejpam-3947	106	3	3	3	NUM
ejpam-3947	106	4	)	)	PUNCT
ejpam-3947	106	5	.	.	PUNCT
ejpam-3947	107	1	thus	thus	ADV
ejpam-3947	107	2	,	,	PUNCT
ejpam-3947	107	3	y	y	PROPN
ejpam-3947	107	4	≡	≡	PROPN
ejpam-3947	107	5	0	0	PUNCT
ejpam-3947	107	6	(	(	PUNCT
ejpam-3947	107	7	mod	mod	NOUN
ejpam-3947	107	8	3	3	NUM
ejpam-3947	107	9	)	)	PUNCT
ejpam-3947	107	10	.	.	PUNCT
ejpam-3947	108	1	by	by	ADP
ejpam-3947	108	2	letting	let	VERB
ejpam-3947	108	3	y	y	PROPN
ejpam-3947	108	4	=	=	SYM
ejpam-3947	108	5	3y1	3y1	NUM
ejpam-3947	108	6	and	and	CCONJ
ejpam-3947	108	7	substituting	substitute	VERB
ejpam-3947	108	8	this	this	PRON
ejpam-3947	108	9	to	to	ADP
ejpam-3947	108	10	(	(	PUNCT
ejpam-3947	108	11	8)	8)	NUM
ejpam-3947	108	12	,	,	PUNCT
ejpam-3947	108	13	we	we	PRON
ejpam-3947	108	14	r.	r.	PROPN
ejpam-3947	108	15	j.	j.	PROPN
ejpam-3947	108	16	s.	s.	PROPN
ejpam-3947	108	17	mina	mina	PROPN
ejpam-3947	108	18	,	,	PUNCT
ejpam-3947	108	19	j.	j.	PROPN
ejpam-3947	108	20	b.	b.	PROPN
ejpam-3947	108	21	bacani	bacani	PROPN
ejpam-3947	108	22	/	/	SYM
ejpam-3947	108	23	eur	eur	PROPN
ejpam-3947	108	24	.	.	PUNCT
ejpam-3947	109	1	j.	j.	PROPN
ejpam-3947	109	2	pure	pure	PROPN
ejpam-3947	109	3	appl	appl	PROPN
ejpam-3947	109	4	.	.	PROPN
ejpam-3947	109	5	math	math	PROPN
ejpam-3947	109	6	,	,	PUNCT
ejpam-3947	109	7	14	14	NUM
ejpam-3947	109	8	(	(	PUNCT
ejpam-3947	109	9	2	2	NUM
ejpam-3947	109	10	)	)	PUNCT
ejpam-3947	109	11	(	(	PUNCT
ejpam-3947	109	12	2021	2021	NUM
ejpam-3947	109	13	)	)	PUNCT
ejpam-3947	109	14	,	,	PUNCT
ejpam-3947	109	15	471	471	NUM
ejpam-3947	109	16	-	-	SYM
ejpam-3947	109	17	479	479	NUM
ejpam-3947	109	18	474	474	NUM
ejpam-3947	109	19	arrive	arrive	NOUN
ejpam-3947	109	20	at	at	ADP
ejpam-3947	109	21	73y1−1	73y1−1	NUM
ejpam-3947	109	22	+	+	CCONJ
ejpam-3947	110	1	73y1−2	73y1−2	NUM
ejpam-3947	110	2	+	+	CCONJ
ejpam-3947	110	3	·	·	PUNCT
ejpam-3947	110	4	·	·	PUNCT
ejpam-3947	110	5	·	·	PUNCT
ejpam-3947	111	1	+	+	PUNCT
ejpam-3947	111	2	1	1	X
ejpam-3947	111	3	=	=	SYM
ejpam-3947	111	4	3m−1	3m−1	NUM
ejpam-3947	111	5	.	.	PUNCT
ejpam-3947	112	1	multiply	multiply	VERB
ejpam-3947	112	2	this	this	DET
ejpam-3947	112	3	equation	equation	NOUN
ejpam-3947	112	4	by	by	ADP
ejpam-3947	112	5	7	7	NUM
ejpam-3947	112	6	−	−	NOUN
ejpam-3947	112	7	1	1	NUM
ejpam-3947	112	8	to	to	PART
ejpam-3947	112	9	get	get	VERB
ejpam-3947	112	10	73y1	73y1	NUM
ejpam-3947	112	11	−	−	NOUN
ejpam-3947	112	12	1	1	NUM
ejpam-3947	112	13	=	=	SYM
ejpam-3947	112	14	6	6	NUM
ejpam-3947	112	15	·	·	SYM
ejpam-3947	112	16	3m−1	3m−1	NUM
ejpam-3947	112	17	=	=	SYM
ejpam-3947	112	18	2	2	NUM
ejpam-3947	112	19	·	·	SYM
ejpam-3947	112	20	3	3	NUM
ejpam-3947	112	21	m.	m.	NOUN
ejpam-3947	112	22	we	we	PRON
ejpam-3947	112	23	then	then	ADV
ejpam-3947	112	24	have	have	VERB
ejpam-3947	112	25	(	(	PUNCT
ejpam-3947	112	26	73	73	NUM
ejpam-3947	112	27	−	−	NUM
ejpam-3947	112	28	1	1	NUM
ejpam-3947	112	29	)	)	PUNCT
ejpam-3947	112	30	·	·	PUNCT
ejpam-3947	112	31	y1−1∑	y1−1∑	PROPN
ejpam-3947	113	1	i=0	i=0	PROPN
ejpam-3947	113	2	(	(	PUNCT
ejpam-3947	113	3	73)i	73)i	NUM
ejpam-3947	113	4	=	=	SYM
ejpam-3947	113	5	2	2	NUM
ejpam-3947	113	6	·	·	SYM
ejpam-3947	113	7	3	3	NUM
ejpam-3947	113	8	m	m	NOUN
ejpam-3947	113	9	,	,	PUNCT
ejpam-3947	113	10	which	which	PRON
ejpam-3947	113	11	implies	imply	VERB
ejpam-3947	113	12	that	that	SCONJ
ejpam-3947	113	13	2	2	NUM
ejpam-3947	113	14	·	·	SYM
ejpam-3947	113	15	32	32	NUM
ejpam-3947	113	16	·	·	SYM
ejpam-3947	113	17	19	19	NUM
ejpam-3947	113	18	·	·	PUNCT
ejpam-3947	113	19	y1−1∑	y1−1∑	X
ejpam-3947	113	20	i=0	i=0	PROPN
ejpam-3947	113	21	(	(	PUNCT
ejpam-3947	113	22	73)i	73)i	NUM
ejpam-3947	113	23	=	=	SYM
ejpam-3947	113	24	2	2	NUM
ejpam-3947	113	25	·	·	SYM
ejpam-3947	113	26	3	3	NUM
ejpam-3947	113	27	m	m	NOUN
ejpam-3947	113	28	,	,	PUNCT
ejpam-3947	113	29	which	which	PRON
ejpam-3947	113	30	is	be	AUX
ejpam-3947	113	31	not	not	PART
ejpam-3947	113	32	possible	possible	ADJ
ejpam-3947	113	33	since	since	SCONJ
ejpam-3947	113	34	19	19	NUM
ejpam-3947	113	35	does	do	AUX
ejpam-3947	113	36	not	not	PART
ejpam-3947	113	37	divide	divide	VERB
ejpam-3947	113	38	2	2	NUM
ejpam-3947	113	39	·	·	SYM
ejpam-3947	113	40	3	3	NUM
ejpam-3947	113	41	m.	m.	NOUN
ejpam-3947	113	42	we	we	PRON
ejpam-3947	113	43	have	have	AUX
ejpam-3947	113	44	proven	prove	VERB
ejpam-3947	113	45	lemma	lemma	PROPN
ejpam-3947	113	46	2	2	NUM
ejpam-3947	113	47	.	.	PUNCT
ejpam-3947	113	48	by	by	ADP
ejpam-3947	113	49	using	use	VERB
ejpam-3947	113	50	the	the	DET
ejpam-3947	113	51	above	above	ADJ
ejpam-3947	113	52	two	two	NUM
ejpam-3947	113	53	lemmas	lemma	NOUN
ejpam-3947	113	54	,	,	PUNCT
ejpam-3947	113	55	we	we	PRON
ejpam-3947	113	56	now	now	ADV
ejpam-3947	113	57	have	have	VERB
ejpam-3947	113	58	our	our	PRON
ejpam-3947	113	59	main	main	ADJ
ejpam-3947	113	60	theorem	theorem	NOUN
ejpam-3947	113	61	.	.	PUNCT
ejpam-3947	113	62	theorem	theorem	NOUN
ejpam-3947	113	63	1	1	NUM
ejpam-3947	113	64	.	.	PUNCT
ejpam-3947	114	1	the	the	DET
ejpam-3947	114	2	diophantine	diophantine	NOUN
ejpam-3947	114	3	equation	equation	NOUN
ejpam-3947	114	4	(	(	PUNCT
ejpam-3947	114	5	2	2	NUM
ejpam-3947	114	6	)	)	PUNCT
ejpam-3947	114	7	,	,	PUNCT
ejpam-3947	114	8	where	where	SCONJ
ejpam-3947	114	9	p	p	NOUN
ejpam-3947	114	10	and	and	CCONJ
ejpam-3947	114	11	q	q	NOUN
ejpam-3947	114	12	are	be	AUX
ejpam-3947	114	13	cousin	cousin	NOUN
ejpam-3947	114	14	primes	prime	NOUN
ejpam-3947	114	15	,	,	PUNCT
ejpam-3947	114	16	has	have	VERB
ejpam-3947	114	17	exactly	exactly	ADV
ejpam-3947	114	18	two	two	NUM
ejpam-3947	114	19	solutions	solution	NOUN
ejpam-3947	114	20	(	(	PUNCT
ejpam-3947	114	21	p	p	X
ejpam-3947	114	22	,	,	PUNCT
ejpam-3947	114	23	q	q	ADJ
ejpam-3947	114	24	,	,	PUNCT
ejpam-3947	114	25	x	x	NOUN
ejpam-3947	114	26	,	,	PUNCT
ejpam-3947	114	27	y	y	PROPN
ejpam-3947	114	28	,	,	PUNCT
ejpam-3947	114	29	z	z	NOUN
ejpam-3947	114	30	)	)	PUNCT
ejpam-3947	114	31	in	in	ADP
ejpam-3947	114	32	n0	n0	PROPN
ejpam-3947	114	33	,	,	PUNCT
ejpam-3947	114	34	namely	namely	ADV
ejpam-3947	114	35	,	,	PUNCT
ejpam-3947	114	36	(	(	PUNCT
ejpam-3947	114	37	3	3	NUM
ejpam-3947	114	38	,	,	PUNCT
ejpam-3947	114	39	7	7	NUM
ejpam-3947	114	40	,	,	PUNCT
ejpam-3947	114	41	1	1	NUM
ejpam-3947	114	42	,	,	PUNCT
ejpam-3947	114	43	0	0	NUM
ejpam-3947	114	44	,	,	PUNCT
ejpam-3947	114	45	2	2	NUM
ejpam-3947	114	46	)	)	PUNCT
ejpam-3947	114	47	and	and	CCONJ
ejpam-3947	114	48	(	(	PUNCT
ejpam-3947	114	49	3	3	NUM
ejpam-3947	114	50	,	,	PUNCT
ejpam-3947	114	51	7	7	NUM
ejpam-3947	114	52	,	,	PUNCT
ejpam-3947	114	53	2	2	NUM
ejpam-3947	114	54	,	,	PUNCT
ejpam-3947	114	55	1	1	NUM
ejpam-3947	114	56	,	,	PUNCT
ejpam-3947	114	57	4	4	NUM
ejpam-3947	114	58	)	)	PUNCT
ejpam-3947	114	59	.	.	PUNCT
ejpam-3947	115	1	corollary	corollary	ADJ
ejpam-3947	115	2	to	to	ADP
ejpam-3947	115	3	the	the	DET
ejpam-3947	115	4	theorem	theorem	NOUN
ejpam-3947	115	5	is	be	AUX
ejpam-3947	115	6	the	the	DET
ejpam-3947	115	7	following	follow	VERB
ejpam-3947	115	8	result	result	NOUN
ejpam-3947	115	9	.	.	PUNCT
ejpam-3947	116	1	corollary	corollary	ADJ
ejpam-3947	116	2	1	1	NUM
ejpam-3947	116	3	.	.	PUNCT
ejpam-3947	117	1	the	the	DET
ejpam-3947	117	2	diophantine	diophantine	NOUN
ejpam-3947	117	3	equation	equation	NOUN
ejpam-3947	117	4	px	px	X
ejpam-3947	117	5	+	+	CCONJ
ejpam-3947	117	6	qy	qy	NOUN
ejpam-3947	117	7	=	=	SYM
ejpam-3947	117	8	z2n	z2n	NOUN
ejpam-3947	117	9	,	,	PUNCT
ejpam-3947	117	10	where	where	SCONJ
ejpam-3947	117	11	p	p	NOUN
ejpam-3947	117	12	and	and	CCONJ
ejpam-3947	117	13	q	q	NOUN
ejpam-3947	117	14	are	be	AUX
ejpam-3947	117	15	cousin	cousin	NOUN
ejpam-3947	117	16	primes	prime	NOUN
ejpam-3947	117	17	,	,	PUNCT
ejpam-3947	117	18	and	and	CCONJ
ejpam-3947	117	19	z	z	NOUN
ejpam-3947	117	20	is	be	AUX
ejpam-3947	117	21	not	not	PART
ejpam-3947	117	22	a	a	DET
ejpam-3947	117	23	perfect	perfect	ADJ
ejpam-3947	117	24	square	square	NOUN
ejpam-3947	117	25	,	,	PUNCT
ejpam-3947	117	26	has	have	VERB
ejpam-3947	117	27	exactly	exactly	ADV
ejpam-3947	117	28	two	two	NUM
ejpam-3947	117	29	solutions	solution	NOUN
ejpam-3947	117	30	(	(	PUNCT
ejpam-3947	117	31	p	p	X
ejpam-3947	117	32	,	,	PUNCT
ejpam-3947	117	33	q	q	ADJ
ejpam-3947	117	34	,	,	PUNCT
ejpam-3947	117	35	x	x	NOUN
ejpam-3947	117	36	,	,	PUNCT
ejpam-3947	117	37	y	y	PROPN
ejpam-3947	117	38	,	,	PUNCT
ejpam-3947	117	39	z	z	PROPN
ejpam-3947	117	40	,	,	PUNCT
ejpam-3947	117	41	n	n	CCONJ
ejpam-3947	117	42	)	)	PUNCT
ejpam-3947	117	43	in	in	ADP
ejpam-3947	117	44	n0	n0	NUM
ejpam-3947	117	45	,	,	PUNCT
ejpam-3947	117	46	namely	namely	ADV
ejpam-3947	117	47	,	,	PUNCT
ejpam-3947	117	48	(	(	PUNCT
ejpam-3947	117	49	3	3	NUM
ejpam-3947	117	50	,	,	PUNCT
ejpam-3947	117	51	7	7	NUM
ejpam-3947	117	52	,	,	PUNCT
ejpam-3947	117	53	1	1	NUM
ejpam-3947	117	54	,	,	PUNCT
ejpam-3947	117	55	0	0	NUM
ejpam-3947	117	56	,	,	PUNCT
ejpam-3947	117	57	2	2	NUM
ejpam-3947	117	58	,	,	PUNCT
ejpam-3947	117	59	1	1	NUM
ejpam-3947	117	60	)	)	PUNCT
ejpam-3947	117	61	,	,	PUNCT
ejpam-3947	117	62	and	and	CCONJ
ejpam-3947	117	63	(	(	PUNCT
ejpam-3947	117	64	3	3	NUM
ejpam-3947	117	65	,	,	PUNCT
ejpam-3947	117	66	7	7	NUM
ejpam-3947	117	67	,	,	PUNCT
ejpam-3947	117	68	2	2	NUM
ejpam-3947	117	69	,	,	PUNCT
ejpam-3947	117	70	1	1	NUM
ejpam-3947	117	71	,	,	PUNCT
ejpam-3947	117	72	2	2	NUM
ejpam-3947	117	73	,	,	PUNCT
ejpam-3947	117	74	2	2	NUM
ejpam-3947	117	75	)	)	PUNCT
ejpam-3947	117	76	.	.	PUNCT
ejpam-3947	118	1	proof	proof	NOUN
ejpam-3947	118	2	.	.	PUNCT
ejpam-3947	119	1	here	here	ADV
ejpam-3947	119	2	,	,	PUNCT
ejpam-3947	119	3	we	we	PRON
ejpam-3947	119	4	are	be	AUX
ejpam-3947	119	5	considering	consider	VERB
ejpam-3947	119	6	the	the	DET
ejpam-3947	119	7	diophantine	diophantine	NOUN
ejpam-3947	119	8	equation	equation	NOUN
ejpam-3947	119	9	px+qy	px+qy	ADJ
ejpam-3947	119	10	=	=	SYM
ejpam-3947	119	11	(	(	PUNCT
ejpam-3947	119	12	zn)2	zn)2	PROPN
ejpam-3947	119	13	.	.	PUNCT
ejpam-3947	120	1	by	by	ADP
ejpam-3947	120	2	theorem	theorem	NOUN
ejpam-3947	120	3	1	1	NUM
ejpam-3947	120	4	,	,	PUNCT
ejpam-3947	120	5	this	this	PRON
ejpam-3947	120	6	has	have	VERB
ejpam-3947	120	7	only	only	ADV
ejpam-3947	120	8	two	two	NUM
ejpam-3947	120	9	solutions	solution	NOUN
ejpam-3947	120	10	in	in	ADP
ejpam-3947	120	11	n0	n0	NUM
ejpam-3947	121	1	and	and	CCONJ
ejpam-3947	121	2	we	we	PRON
ejpam-3947	121	3	get	get	VERB
ejpam-3947	121	4	those	those	DET
ejpam-3947	121	5	solutions	solution	NOUN
ejpam-3947	121	6	when	when	SCONJ
ejpam-3947	121	7	zn	zn	PROPN
ejpam-3947	121	8	=	=	SYM
ejpam-3947	121	9	2	2	NUM
ejpam-3947	121	10	or	or	CCONJ
ejpam-3947	121	11	zn	zn	NUM
ejpam-3947	121	12	=	=	SYM
ejpam-3947	121	13	4	4	X
ejpam-3947	121	14	.	.	PUNCT
ejpam-3947	122	1	the	the	DET
ejpam-3947	122	2	first	first	ADJ
ejpam-3947	122	3	equality	equality	NOUN
ejpam-3947	122	4	gives	give	VERB
ejpam-3947	122	5	us	we	PRON
ejpam-3947	122	6	that	that	PRON
ejpam-3947	122	7	z	z	NOUN
ejpam-3947	122	8	=	=	SYM
ejpam-3947	122	9	2	2	NUM
ejpam-3947	122	10	and	and	CCONJ
ejpam-3947	122	11	n	n	NOUN
ejpam-3947	122	12	=	=	SYM
ejpam-3947	122	13	1	1	NUM
ejpam-3947	122	14	,	,	PUNCT
ejpam-3947	122	15	hence	hence	ADV
ejpam-3947	122	16	the	the	DET
ejpam-3947	122	17	solution	solution	NOUN
ejpam-3947	122	18	(	(	PUNCT
ejpam-3947	122	19	p	p	X
ejpam-3947	122	20	,	,	PUNCT
ejpam-3947	122	21	q	q	ADJ
ejpam-3947	122	22	,	,	PUNCT
ejpam-3947	122	23	x	x	NOUN
ejpam-3947	122	24	,	,	PUNCT
ejpam-3947	122	25	y	y	PROPN
ejpam-3947	122	26	,	,	PUNCT
ejpam-3947	122	27	z	z	PROPN
ejpam-3947	122	28	,	,	PUNCT
ejpam-3947	122	29	n	n	CCONJ
ejpam-3947	122	30	)	)	PUNCT
ejpam-3947	122	31	=	=	SYM
ejpam-3947	122	32	(	(	PUNCT
ejpam-3947	122	33	3	3	NUM
ejpam-3947	122	34	,	,	PUNCT
ejpam-3947	122	35	7	7	NUM
ejpam-3947	122	36	,	,	PUNCT
ejpam-3947	122	37	1	1	NUM
ejpam-3947	122	38	,	,	PUNCT
ejpam-3947	122	39	0	0	NUM
ejpam-3947	122	40	,	,	PUNCT
ejpam-3947	122	41	2	2	NUM
ejpam-3947	122	42	,	,	PUNCT
ejpam-3947	122	43	1	1	NUM
ejpam-3947	122	44	)	)	PUNCT
ejpam-3947	122	45	.	.	PUNCT
ejpam-3947	123	1	the	the	DET
ejpam-3947	123	2	second	second	ADJ
ejpam-3947	123	3	one	one	NOUN
ejpam-3947	123	4	has	have	VERB
ejpam-3947	123	5	a	a	DET
ejpam-3947	123	6	solution	solution	NOUN
ejpam-3947	123	7	(	(	PUNCT
ejpam-3947	123	8	z	z	NOUN
ejpam-3947	123	9	,	,	PUNCT
ejpam-3947	123	10	n	n	CCONJ
ejpam-3947	123	11	)	)	PUNCT
ejpam-3947	123	12	=	=	SYM
ejpam-3947	123	13	(	(	PUNCT
ejpam-3947	123	14	4	4	NUM
ejpam-3947	123	15	,	,	PUNCT
ejpam-3947	123	16	1	1	NUM
ejpam-3947	123	17	)	)	PUNCT
ejpam-3947	123	18	or	or	CCONJ
ejpam-3947	123	19	(	(	PUNCT
ejpam-3947	123	20	2	2	NUM
ejpam-3947	123	21	,	,	PUNCT
ejpam-3947	123	22	2	2	NUM
ejpam-3947	123	23	)	)	PUNCT
ejpam-3947	123	24	.	.	PUNCT
ejpam-3947	124	1	since	since	SCONJ
ejpam-3947	124	2	z	z	PROPN
ejpam-3947	124	3	is	be	AUX
ejpam-3947	124	4	assumed	assume	VERB
ejpam-3947	124	5	to	to	PART
ejpam-3947	124	6	be	be	AUX
ejpam-3947	124	7	not	not	PART
ejpam-3947	124	8	a	a	DET
ejpam-3947	124	9	perfect	perfect	ADJ
ejpam-3947	124	10	square	square	NOUN
ejpam-3947	124	11	,	,	PUNCT
ejpam-3947	124	12	then	then	ADV
ejpam-3947	124	13	we	we	PRON
ejpam-3947	124	14	get	get	VERB
ejpam-3947	124	15	(	(	PUNCT
ejpam-3947	124	16	z	z	NOUN
ejpam-3947	124	17	,	,	PUNCT
ejpam-3947	124	18	n	n	CCONJ
ejpam-3947	124	19	)	)	PUNCT
ejpam-3947	124	20	=	=	SYM
ejpam-3947	124	21	(	(	PUNCT
ejpam-3947	124	22	2	2	NUM
ejpam-3947	124	23	,	,	PUNCT
ejpam-3947	124	24	2	2	NUM
ejpam-3947	124	25	)	)	PUNCT
ejpam-3947	124	26	.	.	PUNCT
ejpam-3947	125	1	this	this	PRON
ejpam-3947	125	2	gives	give	VERB
ejpam-3947	125	3	the	the	DET
ejpam-3947	125	4	solution	solution	NOUN
ejpam-3947	125	5	(	(	PUNCT
ejpam-3947	125	6	3	3	NUM
ejpam-3947	125	7	,	,	PUNCT
ejpam-3947	125	8	7	7	NUM
ejpam-3947	125	9	,	,	PUNCT
ejpam-3947	125	10	2	2	NUM
ejpam-3947	125	11	,	,	PUNCT
ejpam-3947	125	12	1	1	NUM
ejpam-3947	125	13	,	,	PUNCT
ejpam-3947	125	14	2	2	NUM
ejpam-3947	125	15	,	,	PUNCT
ejpam-3947	125	16	2	2	NUM
ejpam-3947	125	17	)	)	PUNCT
ejpam-3947	125	18	.	.	PUNCT
ejpam-3947	126	1	remark	remark	PROPN
ejpam-3947	126	2	1	1	NUM
ejpam-3947	126	3	.	.	PUNCT
ejpam-3947	127	1	in	in	ADP
ejpam-3947	127	2	the	the	DET
ejpam-3947	127	3	corollary	corollary	NOUN
ejpam-3947	127	4	,	,	PUNCT
ejpam-3947	127	5	if	if	SCONJ
ejpam-3947	127	6	z	z	NOUN
ejpam-3947	127	7	happens	happen	VERB
ejpam-3947	127	8	to	to	PART
ejpam-3947	127	9	be	be	AUX
ejpam-3947	127	10	a	a	DET
ejpam-3947	127	11	perfect	perfect	ADJ
ejpam-3947	127	12	square	square	NOUN
ejpam-3947	127	13	,	,	PUNCT
ejpam-3947	127	14	then	then	ADV
ejpam-3947	127	15	just	just	ADV
ejpam-3947	127	16	put	put	VERB
ejpam-3947	127	17	its	its	PRON
ejpam-3947	127	18	power	power	NOUN
ejpam-3947	127	19	to	to	PART
ejpam-3947	127	20	n.	n.	VERB
ejpam-3947	127	21	3.2	3.2	NUM
ejpam-3947	127	22	.	.	PUNCT
ejpam-3947	128	1	the	the	DET
ejpam-3947	128	2	diophantine	diophantine	NOUN
ejpam-3947	128	3	equation	equation	NOUN
ejpam-3947	128	4	px	px	X
ejpam-3947	128	5	+	+	CCONJ
ejpam-3947	128	6	(	(	PUNCT
ejpam-3947	128	7	p+	p+	PROPN
ejpam-3947	128	8	4k)y	4k)y	X
ejpam-3947	128	9	=	=	SYM
ejpam-3947	128	10	z2	z2	PROPN
ejpam-3947	128	11	we	we	PRON
ejpam-3947	128	12	now	now	ADV
ejpam-3947	128	13	extend	extend	VERB
ejpam-3947	128	14	the	the	DET
ejpam-3947	128	15	work	work	NOUN
ejpam-3947	128	16	to	to	ADP
ejpam-3947	128	17	solving	solve	VERB
ejpam-3947	128	18	the	the	DET
ejpam-3947	128	19	diophantine	diophantine	NOUN
ejpam-3947	128	20	equation	equation	NOUN
ejpam-3947	128	21	(	(	PUNCT
ejpam-3947	128	22	3	3	NUM
ejpam-3947	128	23	)	)	PUNCT
ejpam-3947	128	24	,	,	PUNCT
ejpam-3947	128	25	where	where	SCONJ
ejpam-3947	128	26	p	p	PROPN
ejpam-3947	128	27	and	and	CCONJ
ejpam-3947	128	28	p+	p+	PROPN
ejpam-3947	128	29	4k	4k	PRON
ejpam-3947	128	30	are	be	AUX
ejpam-3947	128	31	both	both	PRON
ejpam-3947	128	32	primes	prime	NOUN
ejpam-3947	128	33	such	such	ADJ
ejpam-3947	128	34	that	that	SCONJ
ejpam-3947	128	35	k	k	PROPN
ejpam-3947	128	36	≥	≥	NUM
ejpam-3947	128	37	2	2	X
ejpam-3947	128	38	.	.	PUNCT
ejpam-3947	129	1	we	we	PRON
ejpam-3947	129	2	first	first	ADV
ejpam-3947	129	3	consider	consider	VERB
ejpam-3947	129	4	the	the	DET
ejpam-3947	129	5	generalization	generalization	NOUN
ejpam-3947	129	6	of	of	ADP
ejpam-3947	129	7	lemma	lemma	PROPN
ejpam-3947	129	8	1	1	NUM
ejpam-3947	129	9	.	.	PUNCT
ejpam-3947	129	10	theorem	theorem	NOUN
ejpam-3947	129	11	2	2	NUM
ejpam-3947	129	12	.	.	PUNCT
ejpam-3947	129	13	the	the	DET
ejpam-3947	129	14	diophantine	diophantine	NOUN
ejpam-3947	129	15	equation	equation	NOUN
ejpam-3947	129	16	(	(	PUNCT
ejpam-3947	129	17	3	3	NUM
ejpam-3947	129	18	)	)	PUNCT
ejpam-3947	129	19	,	,	PUNCT
ejpam-3947	129	20	where	where	SCONJ
ejpam-3947	129	21	p	p	PROPN
ejpam-3947	129	22	and	and	CCONJ
ejpam-3947	129	23	p+	p+	PROPN
ejpam-3947	129	24	4k	4k	PRON
ejpam-3947	129	25	are	be	AUX
ejpam-3947	129	26	both	both	DET
ejpam-3947	129	27	primes	prime	NOUN
ejpam-3947	129	28	,	,	PUNCT
ejpam-3947	129	29	has	have	VERB
ejpam-3947	129	30	no	no	DET
ejpam-3947	129	31	solution	solution	NOUN
ejpam-3947	129	32	in	in	ADP
ejpam-3947	129	33	n0	n0	NOUN
ejpam-3947	129	34	if	if	SCONJ
ejpam-3947	129	35	x	x	PRON
ejpam-3947	129	36	and	and	CCONJ
ejpam-3947	129	37	y	y	PROPN
ejpam-3947	129	38	are	be	AUX
ejpam-3947	129	39	of	of	ADP
ejpam-3947	129	40	the	the	DET
ejpam-3947	129	41	same	same	ADJ
ejpam-3947	129	42	parity	parity	NOUN
ejpam-3947	129	43	.	.	PUNCT
ejpam-3947	130	1	proof	proof	NOUN
ejpam-3947	130	2	.	.	PUNCT
ejpam-3947	131	1	suppose	suppose	VERB
ejpam-3947	131	2	that	that	SCONJ
ejpam-3947	131	3	x	x	PROPN
ejpam-3947	131	4	and	and	CCONJ
ejpam-3947	131	5	y	y	PROPN
ejpam-3947	131	6	are	be	AUX
ejpam-3947	131	7	both	both	PRON
ejpam-3947	131	8	odd	odd	ADJ
ejpam-3947	131	9	.	.	PUNCT
ejpam-3947	132	1	if	if	SCONJ
ejpam-3947	132	2	p	p	DET
ejpam-3947	132	3	≡	≡	PROPN
ejpam-3947	132	4	1	1	NUM
ejpam-3947	132	5	(	(	PUNCT
ejpam-3947	132	6	mod	mod	NOUN
ejpam-3947	132	7	4	4	NUM
ejpam-3947	132	8	)	)	PUNCT
ejpam-3947	132	9	then	then	ADV
ejpam-3947	132	10	p	p	X
ejpam-3947	132	11	+	+	CCONJ
ejpam-3947	132	12	4k	4k	NUM
ejpam-3947	132	13	≡	≡	PROPN
ejpam-3947	132	14	1	1	NUM
ejpam-3947	132	15	(	(	PUNCT
ejpam-3947	132	16	mod	mod	NOUN
ejpam-3947	132	17	4	4	NUM
ejpam-3947	132	18	)	)	PUNCT
ejpam-3947	132	19	.	.	PUNCT
ejpam-3947	133	1	it	it	PRON
ejpam-3947	133	2	follows	follow	VERB
ejpam-3947	133	3	that	that	SCONJ
ejpam-3947	133	4	px	px	VERB
ejpam-3947	133	5	+	+	CCONJ
ejpam-3947	133	6	(	(	PUNCT
ejpam-3947	133	7	p	p	X
ejpam-3947	133	8	+	+	PROPN
ejpam-3947	133	9	4k)y	4k)y	NUM
ejpam-3947	133	10	≡	≡	ADJ
ejpam-3947	133	11	2	2	NUM
ejpam-3947	133	12	(	(	PUNCT
ejpam-3947	133	13	mod	mod	NOUN
ejpam-3947	133	14	4	4	NUM
ejpam-3947	133	15	)	)	PUNCT
ejpam-3947	133	16	.	.	PUNCT
ejpam-3947	134	1	also	also	ADV
ejpam-3947	134	2	,	,	PUNCT
ejpam-3947	134	3	if	if	SCONJ
ejpam-3947	134	4	p	p	DET
ejpam-3947	134	5	≡	≡	PROPN
ejpam-3947	134	6	−1	−1	NOUN
ejpam-3947	134	7	(	(	PUNCT
ejpam-3947	134	8	mod	mod	PROPN
ejpam-3947	134	9	4	4	NUM
ejpam-3947	134	10	)	)	PUNCT
ejpam-3947	134	11	then	then	ADV
ejpam-3947	134	12	p+	p+	VERB
ejpam-3947	134	13	4k	4k	X
ejpam-3947	134	14	≡	≡	PROPN
ejpam-3947	134	15	−1	−1	NOUN
ejpam-3947	134	16	(	(	PUNCT
ejpam-3947	134	17	mod	mod	PROPN
ejpam-3947	134	18	4	4	NUM
ejpam-3947	134	19	)	)	PUNCT
ejpam-3947	134	20	and	and	CCONJ
ejpam-3947	134	21	px	px	X
ejpam-3947	134	22	+	+	CCONJ
ejpam-3947	134	23	(	(	PUNCT
ejpam-3947	134	24	p+	p+	VERB
ejpam-3947	134	25	4k)y	4k)y	PROPN
ejpam-3947	134	26	≡	≡	PROPN
ejpam-3947	134	27	−1	−1	NOUN
ejpam-3947	135	1	+	+	CCONJ
ejpam-3947	135	2	(	(	PUNCT
ejpam-3947	135	3	−1	−1	NOUN
ejpam-3947	135	4	)	)	PUNCT
ejpam-3947	135	5	≡	≡	PROPN
ejpam-3947	135	6	2	2	NUM
ejpam-3947	135	7	(	(	PUNCT
ejpam-3947	135	8	mod	mod	NOUN
ejpam-3947	135	9	4	4	NUM
ejpam-3947	135	10	)	)	PUNCT
ejpam-3947	135	11	.	.	PUNCT
ejpam-3947	136	1	on	on	ADP
ejpam-3947	136	2	the	the	DET
ejpam-3947	136	3	other	other	ADJ
ejpam-3947	136	4	hand	hand	NOUN
ejpam-3947	136	5	,	,	PUNCT
ejpam-3947	136	6	since	since	SCONJ
ejpam-3947	136	7	px	px	PROPN
ejpam-3947	136	8	+	+	CCONJ
ejpam-3947	136	9	(	(	PUNCT
ejpam-3947	136	10	p	p	X
ejpam-3947	136	11	+	+	NOUN
ejpam-3947	136	12	4k)y	4k)y	NUM
ejpam-3947	136	13	is	be	AUX
ejpam-3947	136	14	even	even	ADV
ejpam-3947	136	15	,	,	PUNCT
ejpam-3947	136	16	it	it	PRON
ejpam-3947	136	17	follows	follow	VERB
ejpam-3947	136	18	that	that	SCONJ
ejpam-3947	136	19	z2	z2	PROPN
ejpam-3947	136	20	is	be	AUX
ejpam-3947	136	21	even	even	ADV
ejpam-3947	136	22	.	.	PUNCT
ejpam-3947	137	1	hence	hence	ADV
ejpam-3947	137	2	,	,	PUNCT
ejpam-3947	137	3	z2	z2	PROPN
ejpam-3947	137	4	≡	≡	PROPN
ejpam-3947	137	5	0	0	PUNCT
ejpam-3947	137	6	(	(	PUNCT
ejpam-3947	137	7	mod	mod	PROPN
ejpam-3947	137	8	4	4	NUM
ejpam-3947	137	9	)	)	PUNCT
ejpam-3947	137	10	.	.	PUNCT
ejpam-3947	138	1	thus	thus	ADV
ejpam-3947	138	2	,	,	PUNCT
ejpam-3947	138	3	px	px	X
ejpam-3947	138	4	+	+	CCONJ
ejpam-3947	138	5	(	(	PUNCT
ejpam-3947	138	6	p+	p+	VERB
ejpam-3947	138	7	4k)y	4k)y	NUM
ejpam-3947	138	8	6≡	6≡	NUM
ejpam-3947	138	9	z2	z2	PROPN
ejpam-3947	138	10	(	(	PUNCT
ejpam-3947	138	11	mod	mod	PROPN
ejpam-3947	138	12	4	4	NUM
ejpam-3947	138	13	)	)	PUNCT
ejpam-3947	138	14	.	.	PUNCT
ejpam-3947	139	1	r.	r.	PROPN
ejpam-3947	139	2	j.	j.	PROPN
ejpam-3947	139	3	s.	s.	PROPN
ejpam-3947	139	4	mina	mina	PROPN
ejpam-3947	139	5	,	,	PUNCT
ejpam-3947	139	6	j.	j.	PROPN
ejpam-3947	139	7	b.	b.	PROPN
ejpam-3947	139	8	bacani	bacani	PROPN
ejpam-3947	139	9	/	/	SYM
ejpam-3947	139	10	eur	eur	PROPN
ejpam-3947	139	11	.	.	PUNCT
ejpam-3947	140	1	j.	j.	PROPN
ejpam-3947	140	2	pure	pure	PROPN
ejpam-3947	140	3	appl	appl	PROPN
ejpam-3947	140	4	.	.	PROPN
ejpam-3947	140	5	math	math	PROPN
ejpam-3947	140	6	,	,	PUNCT
ejpam-3947	140	7	14	14	NUM
ejpam-3947	140	8	(	(	PUNCT
ejpam-3947	140	9	2	2	NUM
ejpam-3947	140	10	)	)	PUNCT
ejpam-3947	140	11	(	(	PUNCT
ejpam-3947	140	12	2021	2021	NUM
ejpam-3947	140	13	)	)	PUNCT
ejpam-3947	140	14	,	,	PUNCT
ejpam-3947	140	15	471	471	NUM
ejpam-3947	140	16	-	-	SYM
ejpam-3947	140	17	479	479	NUM
ejpam-3947	140	18	475	475	NUM
ejpam-3947	140	19	now	now	ADV
ejpam-3947	140	20	,	,	PUNCT
ejpam-3947	140	21	suppose	suppose	VERB
ejpam-3947	140	22	that	that	SCONJ
ejpam-3947	140	23	x	x	PROPN
ejpam-3947	140	24	and	and	CCONJ
ejpam-3947	140	25	y	y	PROPN
ejpam-3947	140	26	are	be	AUX
ejpam-3947	140	27	both	both	PRON
ejpam-3947	140	28	even	even	ADV
ejpam-3947	140	29	.	.	PUNCT
ejpam-3947	141	1	then	then	ADV
ejpam-3947	141	2	,	,	PUNCT
ejpam-3947	141	3	px	px	PROPN
ejpam-3947	141	4	+	+	CCONJ
ejpam-3947	141	5	(	(	PUNCT
ejpam-3947	141	6	p+	p+	VERB
ejpam-3947	141	7	4k)y	4k)y	PROPN
ejpam-3947	141	8	≡	≡	PROPN
ejpam-3947	141	9	1	1	NUM
ejpam-3947	142	1	+	+	SYM
ejpam-3947	142	2	1	1	NUM
ejpam-3947	142	3	≡	≡	PROPN
ejpam-3947	142	4	2	2	NUM
ejpam-3947	142	5	(	(	PUNCT
ejpam-3947	142	6	mod	mod	NOUN
ejpam-3947	142	7	4	4	NUM
ejpam-3947	142	8	)	)	PUNCT
ejpam-3947	142	9	.	.	PUNCT
ejpam-3947	143	1	hence	hence	ADV
ejpam-3947	143	2	,	,	PUNCT
ejpam-3947	143	3	px	px	X
ejpam-3947	143	4	+	+	CCONJ
ejpam-3947	143	5	(	(	PUNCT
ejpam-3947	143	6	p+	p+	VERB
ejpam-3947	143	7	4k)y	4k)y	NUM
ejpam-3947	143	8	6≡	6≡	NUM
ejpam-3947	143	9	z2	z2	PROPN
ejpam-3947	143	10	(	(	PUNCT
ejpam-3947	143	11	mod	mod	PROPN
ejpam-3947	143	12	4	4	NUM
ejpam-3947	143	13	)	)	PUNCT
ejpam-3947	143	14	.	.	PUNCT
ejpam-3947	144	1	therefore	therefore	ADV
ejpam-3947	144	2	,	,	PUNCT
ejpam-3947	144	3	the	the	DET
ejpam-3947	144	4	diophantine	diophantine	NOUN
ejpam-3947	144	5	equation	equation	NOUN
ejpam-3947	144	6	(	(	PUNCT
ejpam-3947	144	7	3	3	X
ejpam-3947	144	8	)	)	PUNCT
ejpam-3947	144	9	has	have	VERB
ejpam-3947	144	10	no	no	DET
ejpam-3947	144	11	solutions	solution	NOUN
ejpam-3947	144	12	in	in	ADP
ejpam-3947	144	13	n0	n0	NUM
ejpam-3947	144	14	for	for	ADP
ejpam-3947	144	15	both	both	DET
ejpam-3947	144	16	cases	case	NOUN
ejpam-3947	144	17	.	.	PUNCT
ejpam-3947	145	1	because	because	SCONJ
ejpam-3947	145	2	of	of	ADP
ejpam-3947	145	3	the	the	DET
ejpam-3947	145	4	previous	previous	ADJ
ejpam-3947	145	5	theorem	theorem	NOUN
ejpam-3947	145	6	,	,	PUNCT
ejpam-3947	145	7	from	from	ADP
ejpam-3947	145	8	now	now	ADV
ejpam-3947	145	9	on	on	ADV
ejpam-3947	145	10	,	,	PUNCT
ejpam-3947	145	11	we	we	PRON
ejpam-3947	145	12	will	will	AUX
ejpam-3947	145	13	only	only	ADV
ejpam-3947	145	14	be	be	AUX
ejpam-3947	145	15	considering	consider	VERB
ejpam-3947	145	16	the	the	DET
ejpam-3947	145	17	case	case	NOUN
ejpam-3947	145	18	where	where	SCONJ
ejpam-3947	145	19	x	x	X
ejpam-3947	145	20	≥	≥	NUM
ejpam-3947	145	21	1	1	NUM
ejpam-3947	145	22	and	and	CCONJ
ejpam-3947	145	23	y	y	PROPN
ejpam-3947	145	24	≥	≥	NUM
ejpam-3947	145	25	1	1	NUM
ejpam-3947	145	26	because	because	SCONJ
ejpam-3947	145	27	the	the	DET
ejpam-3947	145	28	case	case	NOUN
ejpam-3947	145	29	x	x	X
ejpam-3947	145	30	=	=	SYM
ejpam-3947	145	31	0	0	NUM
ejpam-3947	145	32	or	or	CCONJ
ejpam-3947	145	33	y	y	PROPN
ejpam-3947	145	34	=	=	SYM
ejpam-3947	145	35	0	0	NUM
ejpam-3947	145	36	can	can	AUX
ejpam-3947	145	37	easily	easily	ADV
ejpam-3947	145	38	be	be	AUX
ejpam-3947	145	39	handled	handle	VERB
ejpam-3947	145	40	.	.	PUNCT
ejpam-3947	146	1	we	we	PRON
ejpam-3947	146	2	divide	divide	VERB
ejpam-3947	146	3	the	the	DET
ejpam-3947	146	4	proof	proof	NOUN
ejpam-3947	146	5	into	into	ADP
ejpam-3947	146	6	three	three	NUM
ejpam-3947	146	7	cases	case	NOUN
ejpam-3947	146	8	:	:	PUNCT
ejpam-3947	146	9	(	(	PUNCT
ejpam-3947	146	10	1	1	X
ejpam-3947	146	11	)	)	PUNCT
ejpam-3947	146	12	x	x	SYM
ejpam-3947	147	1	=	=	SYM
ejpam-3947	147	2	1	1	NUM
ejpam-3947	147	3	or	or	CCONJ
ejpam-3947	147	4	y	y	NOUN
ejpam-3947	147	5	=	=	SYM
ejpam-3947	147	6	1	1	NUM
ejpam-3947	147	7	,	,	PUNCT
ejpam-3947	147	8	(	(	PUNCT
ejpam-3947	147	9	2	2	NUM
ejpam-3947	147	10	)	)	PUNCT
ejpam-3947	147	11	x	x	X
ejpam-3947	147	12	>	>	X
ejpam-3947	147	13	1	1	NUM
ejpam-3947	147	14	even	even	ADV
ejpam-3947	147	15	and	and	CCONJ
ejpam-3947	147	16	y	y	X
ejpam-3947	147	17	>	>	X
ejpam-3947	147	18	1	1	NUM
ejpam-3947	147	19	odd	odd	ADJ
ejpam-3947	147	20	;	;	PUNCT
ejpam-3947	147	21	and	and	CCONJ
ejpam-3947	147	22	(	(	PUNCT
ejpam-3947	147	23	3	3	X
ejpam-3947	147	24	)	)	PUNCT
ejpam-3947	147	25	x	x	SYM
ejpam-3947	147	26	>	>	X
ejpam-3947	147	27	1	1	NUM
ejpam-3947	147	28	odd	odd	ADJ
ejpam-3947	147	29	and	and	CCONJ
ejpam-3947	147	30	y	y	X
ejpam-3947	147	31	>	>	X
ejpam-3947	147	32	1	1	NUM
ejpam-3947	147	33	even	even	ADV
ejpam-3947	147	34	.	.	PUNCT
ejpam-3947	148	1	we	we	PRON
ejpam-3947	148	2	have	have	VERB
ejpam-3947	148	3	the	the	DET
ejpam-3947	148	4	first	first	ADJ
ejpam-3947	148	5	case	case	NOUN
ejpam-3947	148	6	.	.	PUNCT
ejpam-3947	149	1	theorem	theorem	NOUN
ejpam-3947	149	2	3	3	X
ejpam-3947	149	3	.	.	PUNCT
ejpam-3947	149	4	consider	consider	VERB
ejpam-3947	149	5	the	the	DET
ejpam-3947	149	6	diophantine	diophantine	NOUN
ejpam-3947	149	7	equation	equation	NOUN
ejpam-3947	149	8	(	(	PUNCT
ejpam-3947	149	9	3	3	NUM
ejpam-3947	149	10	)	)	PUNCT
ejpam-3947	149	11	,	,	PUNCT
ejpam-3947	149	12	where	where	SCONJ
ejpam-3947	149	13	p	p	PROPN
ejpam-3947	149	14	and	and	CCONJ
ejpam-3947	149	15	p+	p+	PROPN
ejpam-3947	149	16	4k	4k	PRON
ejpam-3947	149	17	are	be	AUX
ejpam-3947	149	18	primes	prime	NOUN
ejpam-3947	149	19	and	and	CCONJ
ejpam-3947	149	20	x	x	SYM
ejpam-3947	149	21	=	=	SYM
ejpam-3947	149	22	1	1	NUM
ejpam-3947	149	23	or	or	CCONJ
ejpam-3947	149	24	y	y	NOUN
ejpam-3947	149	25	=	=	SYM
ejpam-3947	149	26	1	1	X
ejpam-3947	149	27	.	.	PUNCT
ejpam-3947	150	1	then	then	ADV
ejpam-3947	150	2	(	(	PUNCT
ejpam-3947	150	3	3	3	X
ejpam-3947	150	4	)	)	PUNCT
ejpam-3947	150	5	has	have	VERB
ejpam-3947	150	6	a	a	DET
ejpam-3947	150	7	solution	solution	NOUN
ejpam-3947	150	8	if	if	SCONJ
ejpam-3947	150	9	and	and	CCONJ
ejpam-3947	150	10	only	only	ADV
ejpam-3947	150	11	if	if	SCONJ
ejpam-3947	150	12	p	p	PRON
ejpam-3947	150	13	≡	≡	PROPN
ejpam-3947	150	14	3	3	NUM
ejpam-3947	150	15	(	(	PUNCT
ejpam-3947	150	16	mod	mod	NOUN
ejpam-3947	150	17	4	4	NUM
ejpam-3947	150	18	)	)	PUNCT
ejpam-3947	150	19	,	,	PUNCT
ejpam-3947	150	20	x	x	PUNCT
ejpam-3947	151	1	=	=	PUNCT
ejpam-3947	151	2	2	2	NUM
ejpam-3947	151	3	m	m	NOUN
ejpam-3947	151	4	for	for	ADP
ejpam-3947	151	5	some	some	DET
ejpam-3947	151	6	positive	positive	ADJ
ejpam-3947	151	7	integer	integer	NOUN
ejpam-3947	151	8	m	m	NOUN
ejpam-3947	151	9	,	,	PUNCT
ejpam-3947	151	10	y	y	PROPN
ejpam-3947	151	11	=	=	SYM
ejpam-3947	151	12	1	1	NUM
ejpam-3947	151	13	and	and	CCONJ
ejpam-3947	151	14	k	k	NOUN
ejpam-3947	152	1	=	=	PUNCT
ejpam-3947	152	2	(	(	PUNCT
ejpam-3947	152	3	2	2	NUM
ejpam-3947	152	4	pm	pm	NOUN
ejpam-3947	152	5	−	−	PROPN
ejpam-3947	152	6	p+	p+	NOUN
ejpam-3947	152	7	1)/4	1)/4	NUM
ejpam-3947	152	8	.	.	PUNCT
ejpam-3947	153	1	proof	proof	NOUN
ejpam-3947	153	2	.	.	PUNCT
ejpam-3947	154	1	firstly	firstly	ADV
ejpam-3947	154	2	,	,	PUNCT
ejpam-3947	154	3	take	take	VERB
ejpam-3947	154	4	x	x	SYM
ejpam-3947	154	5	=	=	SYM
ejpam-3947	154	6	1	1	NUM
ejpam-3947	154	7	and	and	CCONJ
ejpam-3947	154	8	y	y	PRON
ejpam-3947	154	9	even	even	ADV
ejpam-3947	154	10	,	,	PUNCT
ejpam-3947	154	11	then	then	ADV
ejpam-3947	154	12	take	take	VERB
ejpam-3947	154	13	y	y	NOUN
ejpam-3947	154	14	=	=	SYM
ejpam-3947	154	15	1	1	NUM
ejpam-3947	154	16	and	and	CCONJ
ejpam-3947	154	17	x	x	SYM
ejpam-3947	154	18	even	even	ADV
ejpam-3947	154	19	.	.	PUNCT
ejpam-3947	155	1	so	so	ADV
ejpam-3947	155	2	we	we	PRON
ejpam-3947	155	3	get	get	VERB
ejpam-3947	155	4	p+	p+	NOUN
ejpam-3947	155	5	(	(	PUNCT
ejpam-3947	155	6	p+	p+	PROPN
ejpam-3947	155	7	4k)y	4k)y	X
ejpam-3947	155	8	=	=	SYM
ejpam-3947	155	9	z2	z2	PROPN
ejpam-3947	155	10	with	with	ADP
ejpam-3947	155	11	y	y	PROPN
ejpam-3947	156	1	even	even	ADV
ejpam-3947	156	2	and	and	CCONJ
ejpam-3947	156	3	px	px	X
ejpam-3947	156	4	+	+	CCONJ
ejpam-3947	156	5	(	(	PUNCT
ejpam-3947	156	6	p+	p+	NOUN
ejpam-3947	156	7	4k	4k	NOUN
ejpam-3947	156	8	)	)	PUNCT
ejpam-3947	156	9	=	=	SYM
ejpam-3947	156	10	z2	z2	PROPN
ejpam-3947	156	11	with	with	ADP
ejpam-3947	156	12	x	x	SYM
ejpam-3947	156	13	even	even	ADV
ejpam-3947	156	14	,	,	PUNCT
ejpam-3947	156	15	respectively	respectively	ADV
ejpam-3947	156	16	.	.	PUNCT
ejpam-3947	157	1	assume	assume	VERB
ejpam-3947	157	2	that	that	SCONJ
ejpam-3947	157	3	p	p	PRON
ejpam-3947	158	1	+	+	X
ejpam-3947	158	2	(	(	PUNCT
ejpam-3947	158	3	p	p	X
ejpam-3947	158	4	+	+	PROPN
ejpam-3947	158	5	4k)y	4k)y	NOUN
ejpam-3947	158	6	=	=	SYM
ejpam-3947	158	7	z2	z2	PROPN
ejpam-3947	158	8	,	,	PUNCT
ejpam-3947	158	9	where	where	SCONJ
ejpam-3947	158	10	y	y	PROPN
ejpam-3947	158	11	is	be	AUX
ejpam-3947	158	12	even	even	ADV
ejpam-3947	158	13	.	.	PUNCT
ejpam-3947	159	1	then	then	ADV
ejpam-3947	159	2	z	z	NOUN
ejpam-3947	159	3	is	be	AUX
ejpam-3947	159	4	even	even	ADV
ejpam-3947	159	5	and	and	CCONJ
ejpam-3947	159	6	therefore	therefore	ADV
ejpam-3947	159	7	p	p	X
ejpam-3947	160	1	+	+	X
ejpam-3947	160	2	(	(	PUNCT
ejpam-3947	160	3	p	p	X
ejpam-3947	160	4	+	+	PROPN
ejpam-3947	160	5	4k)y	4k)y	NUM
ejpam-3947	160	6	≡	≡	PROPN
ejpam-3947	160	7	0	0	PUNCT
ejpam-3947	160	8	(	(	PUNCT
ejpam-3947	160	9	mod	mod	PROPN
ejpam-3947	160	10	4	4	NUM
ejpam-3947	160	11	)	)	PUNCT
ejpam-3947	160	12	.	.	PUNCT
ejpam-3947	161	1	since	since	SCONJ
ejpam-3947	161	2	y	y	PROPN
ejpam-3947	161	3	is	be	AUX
ejpam-3947	161	4	even	even	ADV
ejpam-3947	161	5	we	we	PRON
ejpam-3947	161	6	get	get	VERB
ejpam-3947	161	7	p	p	PRON
ejpam-3947	161	8	≡	≡	PROPN
ejpam-3947	161	9	3	3	NUM
ejpam-3947	161	10	(	(	PUNCT
ejpam-3947	161	11	mod	mod	NOUN
ejpam-3947	161	12	4	4	NUM
ejpam-3947	161	13	)	)	PUNCT
ejpam-3947	161	14	.	.	PUNCT
ejpam-3947	162	1	let	let	VERB
ejpam-3947	162	2	y	y	NOUN
ejpam-3947	162	3	=	=	SYM
ejpam-3947	162	4	2	2	NUM
ejpam-3947	162	5	m.	m.	NOUN
ejpam-3947	162	6	then	then	ADV
ejpam-3947	162	7	z	z	NOUN
ejpam-3947	162	8	−	−	PROPN
ejpam-3947	163	1	(	(	PUNCT
ejpam-3947	163	2	p	p	X
ejpam-3947	163	3	+	+	NOUN
ejpam-3947	163	4	4k)m	4k)m	NUM
ejpam-3947	163	5	=	=	SYM
ejpam-3947	163	6	1	1	NUM
ejpam-3947	163	7	and	and	CCONJ
ejpam-3947	163	8	z	z	NOUN
ejpam-3947	164	1	+	+	CCONJ
ejpam-3947	164	2	(	(	PUNCT
ejpam-3947	164	3	p	p	X
ejpam-3947	164	4	+	+	NOUN
ejpam-3947	164	5	4k)m	4k)m	NUM
ejpam-3947	164	6	=	=	PUNCT
ejpam-3947	165	1	p.	p.	NOUN
ejpam-3947	165	2	it	it	PRON
ejpam-3947	165	3	follows	follow	VERB
ejpam-3947	165	4	that	that	SCONJ
ejpam-3947	165	5	2(p	2(p	NUM
ejpam-3947	166	1	+	+	CCONJ
ejpam-3947	166	2	4k)m	4k)m	NUM
ejpam-3947	166	3	+	+	CCONJ
ejpam-3947	166	4	1	1	NUM
ejpam-3947	166	5	=	=	SYM
ejpam-3947	166	6	p	p	NOUN
ejpam-3947	166	7	,	,	PUNCT
ejpam-3947	166	8	which	which	PRON
ejpam-3947	166	9	is	be	AUX
ejpam-3947	166	10	impossible	impossible	ADJ
ejpam-3947	166	11	because	because	SCONJ
ejpam-3947	166	12	2(p+	2(p+	NUM
ejpam-3947	166	13	4k)m	4k)m	NUM
ejpam-3947	166	14	+	+	CCONJ
ejpam-3947	166	15	1	1	NUM
ejpam-3947	166	16	>	>	PUNCT
ejpam-3947	166	17	p.	p.	NOUN
ejpam-3947	166	18	now	now	ADV
ejpam-3947	166	19	,	,	PUNCT
ejpam-3947	166	20	consider	consider	VERB
ejpam-3947	166	21	the	the	DET
ejpam-3947	166	22	equation	equation	NOUN
ejpam-3947	166	23	px	px	X
ejpam-3947	166	24	+	+	CCONJ
ejpam-3947	166	25	(	(	PUNCT
ejpam-3947	166	26	p	p	X
ejpam-3947	166	27	+	+	NOUN
ejpam-3947	166	28	4k	4k	NUM
ejpam-3947	166	29	)	)	PUNCT
ejpam-3947	167	1	=	=	SYM
ejpam-3947	167	2	z2	z2	PROPN
ejpam-3947	167	3	,	,	PUNCT
ejpam-3947	167	4	where	where	SCONJ
ejpam-3947	167	5	x	x	PRON
ejpam-3947	167	6	is	be	AUX
ejpam-3947	167	7	even	even	ADV
ejpam-3947	167	8	.	.	PUNCT
ejpam-3947	168	1	then	then	ADV
ejpam-3947	168	2	,	,	PUNCT
ejpam-3947	168	3	p	p	X
ejpam-3947	168	4	+	+	NOUN
ejpam-3947	168	5	1	1	NUM
ejpam-3947	168	6	≡	≡	PROPN
ejpam-3947	168	7	0	0	NUM
ejpam-3947	168	8	(	(	PUNCT
ejpam-3947	168	9	mod	mod	PROPN
ejpam-3947	168	10	4	4	NUM
ejpam-3947	168	11	)	)	PUNCT
ejpam-3947	168	12	since	since	SCONJ
ejpam-3947	168	13	z	z	NOUN
ejpam-3947	168	14	is	be	AUX
ejpam-3947	168	15	even	even	ADV
ejpam-3947	168	16	.	.	PUNCT
ejpam-3947	169	1	therefore	therefore	ADV
ejpam-3947	169	2	,	,	PUNCT
ejpam-3947	169	3	p	p	PROPN
ejpam-3947	169	4	≡	≡	PROPN
ejpam-3947	169	5	−1	−1	NOUN
ejpam-3947	169	6	(	(	PUNCT
ejpam-3947	169	7	mod	mod	PROPN
ejpam-3947	169	8	4	4	NUM
ejpam-3947	169	9	)	)	PUNCT
ejpam-3947	169	10	.	.	PUNCT
ejpam-3947	170	1	let	let	VERB
ejpam-3947	170	2	x	x	SYM
ejpam-3947	170	3	=	=	SYM
ejpam-3947	170	4	2	2	NUM
ejpam-3947	170	5	m.	m.	NOUN
ejpam-3947	170	6	then	then	ADV
ejpam-3947	170	7	z	z	NOUN
ejpam-3947	170	8	−	−	PROPN
ejpam-3947	170	9	pm	pm	NOUN
ejpam-3947	170	10	=	=	SYM
ejpam-3947	170	11	1	1	NUM
ejpam-3947	170	12	and	and	CCONJ
ejpam-3947	170	13	z	z	NOUN
ejpam-3947	170	14	+	+	CCONJ
ejpam-3947	170	15	pm	pm	NOUN
ejpam-3947	170	16	=	=	SYM
ejpam-3947	170	17	p	p	NOUN
ejpam-3947	170	18	+	+	X
ejpam-3947	170	19	4k	4k	NOUN
ejpam-3947	170	20	.	.	PUNCT
ejpam-3947	171	1	therefore	therefore	ADV
ejpam-3947	171	2	,	,	PUNCT
ejpam-3947	171	3	2	2	NUM
ejpam-3947	171	4	pm	pm	NOUN
ejpam-3947	171	5	+	+	CCONJ
ejpam-3947	171	6	1	1	NUM
ejpam-3947	171	7	=	=	SYM
ejpam-3947	171	8	p	p	NOUN
ejpam-3947	171	9	+	+	NUM
ejpam-3947	171	10	4k	4k	NUM
ejpam-3947	171	11	and	and	CCONJ
ejpam-3947	171	12	so	so	ADV
ejpam-3947	171	13	k	k	NOUN
ejpam-3947	172	1	=	=	SYM
ejpam-3947	172	2	2	2	NUM
ejpam-3947	172	3	pm	pm	NOUN
ejpam-3947	172	4	−	−	PROPN
ejpam-3947	172	5	p+	p+	NOUN
ejpam-3947	172	6	1	1	NUM
ejpam-3947	172	7	4	4	NUM
ejpam-3947	172	8	.	.	PUNCT
ejpam-3947	173	1	since	since	SCONJ
ejpam-3947	173	2	p	p	PRON
ejpam-3947	173	3	≡	≡	PROPN
ejpam-3947	173	4	−1	−1	NOUN
ejpam-3947	173	5	(	(	PUNCT
ejpam-3947	173	6	mod	mod	PROPN
ejpam-3947	173	7	4	4	NUM
ejpam-3947	173	8	)	)	PUNCT
ejpam-3947	173	9	,	,	PUNCT
ejpam-3947	173	10	it	it	PRON
ejpam-3947	173	11	follows	follow	VERB
ejpam-3947	173	12	that	that	SCONJ
ejpam-3947	173	13	k	k	PROPN
ejpam-3947	173	14	is	be	AUX
ejpam-3947	173	15	an	an	DET
ejpam-3947	173	16	integer	integer	NOUN
ejpam-3947	173	17	for	for	ADP
ejpam-3947	173	18	any	any	DET
ejpam-3947	173	19	positive	positive	ADJ
ejpam-3947	173	20	integer	integer	NOUN
ejpam-3947	173	21	m.	m.	NOUN
ejpam-3947	173	22	therefore	therefore	ADV
ejpam-3947	173	23	taking	take	VERB
ejpam-3947	173	24	x	x	PUNCT
ejpam-3947	173	25	=	=	SYM
ejpam-3947	173	26	2	2	NUM
ejpam-3947	173	27	m	m	NOUN
ejpam-3947	173	28	,	,	PUNCT
ejpam-3947	173	29	p	p	PROPN
ejpam-3947	173	30	≡	≡	PROPN
ejpam-3947	173	31	−1	−1	NOUN
ejpam-3947	173	32	(	(	PUNCT
ejpam-3947	173	33	mod	mod	PROPN
ejpam-3947	173	34	4	4	NUM
ejpam-3947	173	35	)	)	PUNCT
ejpam-3947	173	36	,	,	PUNCT
ejpam-3947	173	37	and	and	CCONJ
ejpam-3947	173	38	k	k	X
ejpam-3947	173	39	=	=	SYM
ejpam-3947	173	40	2	2	NUM
ejpam-3947	173	41	pm	pm	NOUN
ejpam-3947	173	42	−	−	PROPN
ejpam-3947	173	43	p+	p+	NOUN
ejpam-3947	173	44	1	1	NUM
ejpam-3947	173	45	4	4	NUM
ejpam-3947	173	46	,	,	PUNCT
ejpam-3947	173	47	it	it	PRON
ejpam-3947	173	48	can	can	AUX
ejpam-3947	173	49	be	be	AUX
ejpam-3947	173	50	seen	see	VERB
ejpam-3947	173	51	that	that	SCONJ
ejpam-3947	173	52	px	px	VERB
ejpam-3947	173	53	+	+	CCONJ
ejpam-3947	173	54	(	(	PUNCT
ejpam-3947	173	55	p	p	X
ejpam-3947	173	56	+	+	NOUN
ejpam-3947	173	57	4k	4k	NOUN
ejpam-3947	173	58	)	)	PUNCT
ejpam-3947	173	59	=	=	SYM
ejpam-3947	173	60	(	(	PUNCT
ejpam-3947	173	61	pm	pm	NOUN
ejpam-3947	174	1	+	+	X
ejpam-3947	174	2	1)2	1)2	NUM
ejpam-3947	174	3	.	.	PUNCT
ejpam-3947	175	1	therefore	therefore	ADV
ejpam-3947	175	2	,	,	PUNCT
ejpam-3947	175	3	px	px	X
ejpam-3947	175	4	+	+	CCONJ
ejpam-3947	175	5	(	(	PUNCT
ejpam-3947	175	6	p	p	X
ejpam-3947	175	7	+	+	NOUN
ejpam-3947	175	8	4k	4k	NUM
ejpam-3947	175	9	)	)	PUNCT
ejpam-3947	176	1	=	=	SYM
ejpam-3947	176	2	z2	z2	PROPN
ejpam-3947	176	3	has	have	VERB
ejpam-3947	176	4	a	a	DET
ejpam-3947	176	5	solution	solution	NOUN
ejpam-3947	176	6	if	if	SCONJ
ejpam-3947	176	7	and	and	CCONJ
ejpam-3947	176	8	only	only	ADV
ejpam-3947	176	9	if	if	SCONJ
ejpam-3947	176	10	p	p	PRON
ejpam-3947	176	11	≡	≡	PROPN
ejpam-3947	176	12	3	3	NUM
ejpam-3947	176	13	(	(	PUNCT
ejpam-3947	176	14	mod	mod	NOUN
ejpam-3947	176	15	4	4	NUM
ejpam-3947	176	16	)	)	PUNCT
ejpam-3947	176	17	,	,	PUNCT
ejpam-3947	176	18	x	x	PUNCT
ejpam-3947	176	19	=	=	PUNCT
ejpam-3947	176	20	2	2	NUM
ejpam-3947	176	21	m	m	NOUN
ejpam-3947	176	22	,	,	PUNCT
ejpam-3947	176	23	and	and	CCONJ
ejpam-3947	176	24	k	k	X
ejpam-3947	176	25	=	=	SYM
ejpam-3947	176	26	2	2	NUM
ejpam-3947	176	27	pm	pm	NOUN
ejpam-3947	176	28	−	−	PROPN
ejpam-3947	176	29	p+	p+	NOUN
ejpam-3947	176	30	1	1	NUM
ejpam-3947	176	31	4	4	NUM
ejpam-3947	176	32	.	.	PUNCT
ejpam-3947	177	1	from	from	ADP
ejpam-3947	177	2	this	this	DET
ejpam-3947	177	3	theorem	theorem	NOUN
ejpam-3947	177	4	,	,	PUNCT
ejpam-3947	177	5	some	some	DET
ejpam-3947	177	6	solutions	solution	NOUN
ejpam-3947	177	7	to	to	ADP
ejpam-3947	177	8	(	(	PUNCT
ejpam-3947	177	9	3	3	X
ejpam-3947	177	10	)	)	PUNCT
ejpam-3947	177	11	are	be	AUX
ejpam-3947	177	12	given	give	VERB
ejpam-3947	177	13	by	by	ADP
ejpam-3947	177	14	(	(	PUNCT
ejpam-3947	177	15	p	p	X
ejpam-3947	177	16	,	,	PUNCT
ejpam-3947	177	17	p+4k	p+4k	PROPN
ejpam-3947	177	18	,	,	PUNCT
ejpam-3947	177	19	x	x	NOUN
ejpam-3947	177	20	,	,	PUNCT
ejpam-3947	177	21	y	y	PROPN
ejpam-3947	177	22	,	,	PUNCT
ejpam-3947	177	23	z	z	NOUN
ejpam-3947	177	24	)	)	PUNCT
ejpam-3947	177	25	=	=	PUNCT
ejpam-3947	177	26	(	(	PUNCT
ejpam-3947	177	27	11	11	NUM
ejpam-3947	177	28	,	,	PUNCT
ejpam-3947	177	29	23	23	NUM
ejpam-3947	177	30	,	,	PUNCT
ejpam-3947	177	31	2	2	NUM
ejpam-3947	177	32	,	,	PUNCT
ejpam-3947	177	33	1	1	NUM
ejpam-3947	177	34	,	,	PUNCT
ejpam-3947	177	35	12	12	NUM
ejpam-3947	177	36	)	)	PUNCT
ejpam-3947	177	37	,	,	PUNCT
ejpam-3947	177	38	(	(	PUNCT
ejpam-3947	177	39	3	3	NUM
ejpam-3947	177	40	,	,	PUNCT
ejpam-3947	177	41	19	19	NUM
ejpam-3947	177	42	,	,	PUNCT
ejpam-3947	177	43	4	4	NUM
ejpam-3947	177	44	,	,	PUNCT
ejpam-3947	177	45	1	1	NUM
ejpam-3947	177	46	,	,	PUNCT
ejpam-3947	177	47	10	10	NUM
ejpam-3947	177	48	)	)	PUNCT
ejpam-3947	177	49	and	and	CCONJ
ejpam-3947	177	50	(	(	PUNCT
ejpam-3947	177	51	3	3	NUM
ejpam-3947	177	52	,	,	PUNCT
ejpam-3947	177	53	163	163	NUM
ejpam-3947	177	54	,	,	PUNCT
ejpam-3947	177	55	8	8	NUM
ejpam-3947	177	56	,	,	PUNCT
ejpam-3947	177	57	1	1	NUM
ejpam-3947	177	58	,	,	PUNCT
ejpam-3947	177	59	82	82	NUM
ejpam-3947	177	60	)	)	PUNCT
ejpam-3947	177	61	.	.	PUNCT
ejpam-3947	178	1	we	we	PRON
ejpam-3947	178	2	also	also	ADV
ejpam-3947	178	3	have	have	VERB
ejpam-3947	178	4	the	the	DET
ejpam-3947	178	5	following	follow	VERB
ejpam-3947	178	6	result	result	NOUN
ejpam-3947	178	7	.	.	PUNCT
ejpam-3947	179	1	theorem	theorem	ADJ
ejpam-3947	179	2	4	4	NUM
ejpam-3947	179	3	.	.	PUNCT
ejpam-3947	179	4	consider	consider	VERB
ejpam-3947	179	5	the	the	DET
ejpam-3947	179	6	diophantine	diophantine	NOUN
ejpam-3947	179	7	equation	equation	NOUN
ejpam-3947	179	8	(	(	PUNCT
ejpam-3947	179	9	3	3	NUM
ejpam-3947	179	10	)	)	PUNCT
ejpam-3947	179	11	,	,	PUNCT
ejpam-3947	179	12	where	where	SCONJ
ejpam-3947	179	13	p	p	PROPN
ejpam-3947	179	14	and	and	CCONJ
ejpam-3947	179	15	p+	p+	PROPN
ejpam-3947	179	16	4k	4k	PRON
ejpam-3947	179	17	are	be	AUX
ejpam-3947	179	18	primes	prime	NOUN
ejpam-3947	179	19	.	.	PUNCT
ejpam-3947	180	1	let	let	VERB
ejpam-3947	180	2	x	x	PRON
ejpam-3947	180	3	>	>	X
ejpam-3947	180	4	1	1	NUM
ejpam-3947	180	5	and	and	CCONJ
ejpam-3947	180	6	y	y	PROPN
ejpam-3947	180	7	>	>	X
ejpam-3947	180	8	1	1	NUM
ejpam-3947	180	9	be	be	AUX
ejpam-3947	180	10	odd	odd	ADJ
ejpam-3947	180	11	and	and	CCONJ
ejpam-3947	180	12	even	even	ADV
ejpam-3947	180	13	integers	integer	NOUN
ejpam-3947	180	14	,	,	PUNCT
ejpam-3947	180	15	respectively	respectively	ADV
ejpam-3947	180	16	.	.	PUNCT
ejpam-3947	181	1	then	then	ADV
ejpam-3947	181	2	,	,	PUNCT
ejpam-3947	181	3	(	(	PUNCT
ejpam-3947	181	4	3	3	X
ejpam-3947	181	5	)	)	PUNCT
ejpam-3947	181	6	has	have	VERB
ejpam-3947	181	7	only	only	ADV
ejpam-3947	181	8	the	the	DET
ejpam-3947	181	9	solution	solution	NOUN
ejpam-3947	181	10	(	(	PUNCT
ejpam-3947	181	11	p	p	X
ejpam-3947	181	12	,	,	PUNCT
ejpam-3947	181	13	p+	p+	NOUN
ejpam-3947	181	14	4k	4k	NOUN
ejpam-3947	181	15	,	,	PUNCT
ejpam-3947	181	16	x	x	X
ejpam-3947	181	17	,	,	PUNCT
ejpam-3947	181	18	y	y	PROPN
ejpam-3947	181	19	,	,	PUNCT
ejpam-3947	181	20	z	z	NOUN
ejpam-3947	181	21	)	)	PUNCT
ejpam-3947	181	22	=	=	SYM
ejpam-3947	181	23	(	(	PUNCT
ejpam-3947	181	24	3	3	NUM
ejpam-3947	181	25	,	,	PUNCT
ejpam-3947	181	26	11	11	NUM
ejpam-3947	181	27	,	,	PUNCT
ejpam-3947	181	28	5	5	NUM
ejpam-3947	181	29	,	,	PUNCT
ejpam-3947	181	30	4	4	NUM
ejpam-3947	181	31	,	,	PUNCT
ejpam-3947	181	32	122	122	NUM
ejpam-3947	181	33	)	)	PUNCT
ejpam-3947	181	34	.	.	PUNCT
ejpam-3947	182	1	proof	proof	NOUN
ejpam-3947	182	2	.	.	PUNCT
ejpam-3947	183	1	let	let	VERB
ejpam-3947	183	2	y	y	NOUN
ejpam-3947	183	3	=	=	PUNCT
ejpam-3947	183	4	2l	2l	NOUN
ejpam-3947	183	5	with	with	ADP
ejpam-3947	183	6	l	l	PROPN
ejpam-3947	183	7	≥	≥	NUM
ejpam-3947	183	8	1	1	NUM
ejpam-3947	183	9	and	and	CCONJ
ejpam-3947	183	10	q	q	NOUN
ejpam-3947	184	1	=	=	PROPN
ejpam-3947	184	2	p+	p+	PRON
ejpam-3947	184	3	4k	4k	NOUN
ejpam-3947	184	4	.	.	PUNCT
ejpam-3947	185	1	then	then	ADV
ejpam-3947	185	2	we	we	PRON
ejpam-3947	185	3	get	get	VERB
ejpam-3947	185	4	px	px	NOUN
ejpam-3947	185	5	=	=	PROPN
ejpam-3947	185	6	z2	z2	PROPN
ejpam-3947	185	7	−	−	PROPN
ejpam-3947	186	1	q2l	q2l	PROPN
ejpam-3947	187	1	=	=	SYM
ejpam-3947	188	1	(	(	PUNCT
ejpam-3947	188	2	z	z	NOUN
ejpam-3947	188	3	−	−	NOUN
ejpam-3947	188	4	ql)(z	ql)(z	NOUN
ejpam-3947	188	5	+	+	CCONJ
ejpam-3947	188	6	ql	ql	NOUN
ejpam-3947	188	7	)	)	PUNCT
ejpam-3947	188	8	.	.	PUNCT
ejpam-3947	189	1	it	it	PRON
ejpam-3947	189	2	can	can	AUX
ejpam-3947	189	3	be	be	AUX
ejpam-3947	189	4	shown	show	VERB
ejpam-3947	189	5	that	that	SCONJ
ejpam-3947	189	6	gcd(z	gcd(z	PROPN
ejpam-3947	189	7	−	−	PROPN
ejpam-3947	189	8	ql	ql	PROPN
ejpam-3947	189	9	,	,	PUNCT
ejpam-3947	189	10	z	z	PROPN
ejpam-3947	189	11	+	+	X
ejpam-3947	189	12	ql	ql	X
ejpam-3947	189	13	)	)	PUNCT
ejpam-3947	190	1	=	=	SYM
ejpam-3947	190	2	1	1	X
ejpam-3947	190	3	.	.	PUNCT
ejpam-3947	191	1	so	so	ADV
ejpam-3947	191	2	it	it	PRON
ejpam-3947	191	3	follows	follow	VERB
ejpam-3947	191	4	that	that	PRON
ejpam-3947	191	5	z	z	NOUN
ejpam-3947	192	1	−	−	NOUN
ejpam-3947	193	1	ql	ql	NOUN
ejpam-3947	194	1	=	=	SYM
ejpam-3947	194	2	1	1	NUM
ejpam-3947	194	3	and	and	CCONJ
ejpam-3947	194	4	z	z	NOUN
ejpam-3947	195	1	+	+	CCONJ
ejpam-3947	195	2	ql	ql	X
ejpam-3947	195	3	=	=	SYM
ejpam-3947	195	4	px	px	PROPN
ejpam-3947	195	5	.	.	PROPN
ejpam-3947	196	1	from	from	ADP
ejpam-3947	196	2	here	here	ADV
ejpam-3947	196	3	,	,	PUNCT
ejpam-3947	196	4	we	we	PRON
ejpam-3947	196	5	get	get	VERB
ejpam-3947	196	6	2ql	2ql	ADJ
ejpam-3947	196	7	=	=	PUNCT
ejpam-3947	196	8	px	px	NOUN
ejpam-3947	196	9	−	−	NOUN
ejpam-3947	196	10	1	1	NUM
ejpam-3947	196	11	.	.	PUNCT
ejpam-3947	197	1	thus	thus	ADV
ejpam-3947	197	2	,	,	PUNCT
ejpam-3947	197	3	2ql	2ql	NOUN
ejpam-3947	197	4	=	=	SYM
ejpam-3947	197	5	(	(	PUNCT
ejpam-3947	197	6	p	p	NOUN
ejpam-3947	197	7	−	−	PROPN
ejpam-3947	197	8	1)(1	1)(1	NUM
ejpam-3947	197	9	+	+	CCONJ
ejpam-3947	197	10	p	p	NOUN
ejpam-3947	197	11	+	+	NUM
ejpam-3947	197	12	p2	p2	PROPN
ejpam-3947	197	13	+	+	CCONJ
ejpam-3947	197	14	...	...	PUNCT
ejpam-3947	198	1	+	+	CCONJ
ejpam-3947	198	2	px−1	px−1	NOUN
ejpam-3947	198	3	)	)	PUNCT
ejpam-3947	198	4	.	.	PUNCT
ejpam-3947	199	1	assume	assume	VERB
ejpam-3947	199	2	that	that	SCONJ
ejpam-3947	200	1	p	p	X
ejpam-3947	200	2	>	>	X
ejpam-3947	200	3	3	3	X
ejpam-3947	200	4	.	.	PUNCT
ejpam-3947	201	1	then	then	ADV
ejpam-3947	201	2	p	p	NOUN
ejpam-3947	201	3	−	−	PROPN
ejpam-3947	201	4	1	1	NUM
ejpam-3947	201	5	=	=	SYM
ejpam-3947	201	6	2qj	2qj	NOUN
ejpam-3947	201	7	=	=	SYM
ejpam-3947	201	8	2(p	2(p	NUM
ejpam-3947	201	9	+	+	NUM
ejpam-3947	201	10	4k)j	4k)j	NUM
ejpam-3947	201	11	for	for	ADP
ejpam-3947	201	12	some	some	DET
ejpam-3947	201	13	j	j	PROPN
ejpam-3947	201	14	≥	≥	NUM
ejpam-3947	201	15	1	1	NUM
ejpam-3947	201	16	.	.	PUNCT
ejpam-3947	202	1	this	this	PRON
ejpam-3947	202	2	is	be	AUX
ejpam-3947	202	3	impossible	impossible	ADJ
ejpam-3947	202	4	since	since	SCONJ
ejpam-3947	202	5	p	p	NOUN
ejpam-3947	202	6	−	−	PROPN
ejpam-3947	202	7	1	1	NUM
ejpam-3947	202	8	<	<	X
ejpam-3947	202	9	2(p	2(p	NUM
ejpam-3947	203	1	+	+	CCONJ
ejpam-3947	203	2	4k)j	4k)j	NUM
ejpam-3947	203	3	for	for	ADP
ejpam-3947	203	4	j	j	PROPN
ejpam-3947	203	5	≥	≥	PROPN
ejpam-3947	203	6	1	1	NUM
ejpam-3947	203	7	.	.	PUNCT
ejpam-3947	204	1	therefore	therefore	ADV
ejpam-3947	204	2	,	,	PUNCT
ejpam-3947	204	3	p	p	X
ejpam-3947	204	4	=	=	NOUN
ejpam-3947	204	5	3	3	X
ejpam-3947	204	6	.	.	PUNCT
ejpam-3947	205	1	so	so	ADV
ejpam-3947	205	2	we	we	PRON
ejpam-3947	205	3	get	get	VERB
ejpam-3947	205	4	3x	3x	NUM
ejpam-3947	205	5	−	−	NOUN
ejpam-3947	205	6	1	1	NUM
ejpam-3947	205	7	=	=	SYM
ejpam-3947	205	8	2(3	2(3	NUM
ejpam-3947	205	9	+	+	X
ejpam-3947	205	10	4k)l	4k)l	NUM
ejpam-3947	205	11	.	.	PUNCT
ejpam-3947	206	1	having	have	VERB
ejpam-3947	206	2	r.	r.	PROPN
ejpam-3947	206	3	j.	j.	PROPN
ejpam-3947	206	4	s.	s.	PROPN
ejpam-3947	206	5	mina	mina	PROPN
ejpam-3947	206	6	,	,	PUNCT
ejpam-3947	206	7	j.	j.	PROPN
ejpam-3947	206	8	b.	b.	PROPN
ejpam-3947	206	9	bacani	bacani	PROPN
ejpam-3947	206	10	/	/	SYM
ejpam-3947	206	11	eur	eur	PROPN
ejpam-3947	206	12	.	.	PUNCT
ejpam-3947	207	1	j.	j.	PROPN
ejpam-3947	207	2	pure	pure	PROPN
ejpam-3947	207	3	appl	appl	PROPN
ejpam-3947	207	4	.	.	PROPN
ejpam-3947	207	5	math	math	PROPN
ejpam-3947	207	6	,	,	PUNCT
ejpam-3947	207	7	14	14	NUM
ejpam-3947	207	8	(	(	PUNCT
ejpam-3947	207	9	2	2	NUM
ejpam-3947	207	10	)	)	PUNCT
ejpam-3947	207	11	(	(	PUNCT
ejpam-3947	207	12	2021	2021	NUM
ejpam-3947	207	13	)	)	PUNCT
ejpam-3947	207	14	,	,	PUNCT
ejpam-3947	207	15	471	471	NUM
ejpam-3947	207	16	-	-	SYM
ejpam-3947	207	17	479	479	NUM
ejpam-3947	207	18	476	476	NUM
ejpam-3947	208	1	3x	3x	NUM
ejpam-3947	208	2	−	−	NOUN
ejpam-3947	208	3	1	1	NUM
ejpam-3947	208	4	=	=	SYM
ejpam-3947	208	5	2(3	2(3	NUM
ejpam-3947	208	6	+	+	SYM
ejpam-3947	208	7	4k)l	4k)l	NUM
ejpam-3947	208	8	,	,	PUNCT
ejpam-3947	208	9	it	it	PRON
ejpam-3947	208	10	is	be	AUX
ejpam-3947	208	11	seen	see	VERB
ejpam-3947	208	12	that	that	SCONJ
ejpam-3947	208	13	3	3	NUM
ejpam-3947	208	14	k	k	NOUN
ejpam-3947	208	15	and	and	CCONJ
ejpam-3947	208	16	the	the	DET
ejpam-3947	208	17	legendre	legendre	PROPN
ejpam-3947	208	18	symbol	symbol	NOUN
ejpam-3947	208	19	(	(	PUNCT
ejpam-3947	208	20	3	3	NUM
ejpam-3947	208	21	3	3	NUM
ejpam-3947	208	22	+	+	NUM
ejpam-3947	208	23	4k	4k	NOUN
ejpam-3947	208	24	)	)	PUNCT
ejpam-3947	208	25	x	x	X
ejpam-3947	208	26	is	be	AUX
ejpam-3947	208	27	equal	equal	ADJ
ejpam-3947	208	28	to	to	ADP
ejpam-3947	208	29	1	1	NUM
ejpam-3947	208	30	.	.	PUNCT
ejpam-3947	209	1	thus	thus	ADV
ejpam-3947	209	2	,	,	PUNCT
ejpam-3947	209	3	(	(	PUNCT
ejpam-3947	209	4	3	3	NUM
ejpam-3947	209	5	3	3	NUM
ejpam-3947	209	6	+	+	NUM
ejpam-3947	209	7	4k	4k	NOUN
ejpam-3947	209	8	)	)	PUNCT
ejpam-3947	209	9	=	=	PUNCT
ejpam-3947	209	10	1	1	NUM
ejpam-3947	209	11	since	since	SCONJ
ejpam-3947	209	12	x	x	PRON
ejpam-3947	209	13	is	be	AUX
ejpam-3947	209	14	odd	odd	ADJ
ejpam-3947	209	15	.	.	PUNCT
ejpam-3947	210	1	this	this	PRON
ejpam-3947	210	2	implies	imply	VERB
ejpam-3947	210	3	that	that	SCONJ
ejpam-3947	210	4	(	(	PUNCT
ejpam-3947	210	5	k	k	NOUN
ejpam-3947	210	6	3	3	X
ejpam-3947	210	7	)	)	PUNCT
ejpam-3947	210	8	=	=	PUNCT
ejpam-3947	210	9	(	(	PUNCT
ejpam-3947	210	10	3	3	NUM
ejpam-3947	210	11	+	+	X
ejpam-3947	210	12	4k	4k	X
ejpam-3947	210	13	3	3	NUM
ejpam-3947	210	14	)	)	PUNCT
ejpam-3947	210	15	=	=	SYM
ejpam-3947	210	16	(	(	PUNCT
ejpam-3947	210	17	−1	−1	NOUN
ejpam-3947	210	18	)	)	PUNCT
ejpam-3947	210	19	3−1	3−1	NUM
ejpam-3947	210	20	2	2	NUM
ejpam-3947	210	21	·	·	SYM
ejpam-3947	210	22	3	3	NUM
ejpam-3947	210	23	+	+	NOUN
ejpam-3947	210	24	4k−1	4k−1	NUM
ejpam-3947	210	25	2	2	NUM
ejpam-3947	210	26	(	(	PUNCT
ejpam-3947	210	27	3	3	NUM
ejpam-3947	210	28	3	3	NUM
ejpam-3947	210	29	+	+	NUM
ejpam-3947	210	30	4k	4k	NOUN
ejpam-3947	210	31	)	)	PUNCT
ejpam-3947	210	32	=	=	PUNCT
ejpam-3947	210	33	−1	−1	NOUN
ejpam-3947	210	34	.	.	PUNCT
ejpam-3947	211	1	therefore	therefore	ADV
ejpam-3947	211	2	k	k	PROPN
ejpam-3947	211	3	≡	≡	PROPN
ejpam-3947	211	4	2	2	NUM
ejpam-3947	211	5	(	(	PUNCT
ejpam-3947	211	6	mod	mod	NOUN
ejpam-3947	211	7	3	3	NUM
ejpam-3947	211	8	)	)	PUNCT
ejpam-3947	211	9	.	.	PUNCT
ejpam-3947	212	1	let	let	VERB
ejpam-3947	212	2	k	k	NOUN
ejpam-3947	213	1	=	=	NOUN
ejpam-3947	214	1	3a+	3a+	NUM
ejpam-3947	214	2	2	2	NUM
ejpam-3947	214	3	with	with	ADP
ejpam-3947	214	4	a	a	DET
ejpam-3947	214	5	≥	≥	NOUN
ejpam-3947	214	6	0	0	NUM
ejpam-3947	214	7	.	.	PUNCT
ejpam-3947	215	1	then	then	ADV
ejpam-3947	215	2	,	,	PUNCT
ejpam-3947	215	3	3x	3x	PROPN
ejpam-3947	215	4	−	−	PROPN
ejpam-3947	215	5	1	1	NUM
ejpam-3947	215	6	=	=	SYM
ejpam-3947	215	7	2(3	2(3	NUM
ejpam-3947	215	8	+	+	CCONJ
ejpam-3947	215	9	4k)l	4k)l	NUM
ejpam-3947	215	10	=	=	SYM
ejpam-3947	215	11	2(11	2(11	NUM
ejpam-3947	215	12	+	+	SYM
ejpam-3947	215	13	12a)l	12a)l	NUM
ejpam-3947	215	14	.	.	PUNCT
ejpam-3947	216	1	this	this	PRON
ejpam-3947	216	2	shows	show	VERB
ejpam-3947	216	3	that	that	SCONJ
ejpam-3947	216	4	−1	−1	NOUN
ejpam-3947	216	5	≡	≡	PROPN
ejpam-3947	216	6	2(−1)l	2(−1)l	PROPN
ejpam-3947	216	7	(	(	PUNCT
ejpam-3947	216	8	mod	mod	PROPN
ejpam-3947	216	9	3	3	NUM
ejpam-3947	216	10	)	)	PUNCT
ejpam-3947	216	11	,	,	PUNCT
ejpam-3947	216	12	hence	hence	ADV
ejpam-3947	216	13	l	l	NOUN
ejpam-3947	216	14	is	be	AUX
ejpam-3947	216	15	even	even	ADV
ejpam-3947	216	16	.	.	PUNCT
ejpam-3947	217	1	suppose	suppose	VERB
ejpam-3947	217	2	l	l	NOUN
ejpam-3947	217	3	=	=	SYM
ejpam-3947	217	4	2r	2r	NUM
ejpam-3947	217	5	for	for	ADP
ejpam-3947	217	6	some	some	DET
ejpam-3947	217	7	positive	positive	ADJ
ejpam-3947	217	8	integer	integer	NOUN
ejpam-3947	217	9	r.	r.	PROPN
ejpam-3947	218	1	so	so	ADV
ejpam-3947	218	2	we	we	PRON
ejpam-3947	218	3	get	get	VERB
ejpam-3947	218	4	3x	3x	NUM
ejpam-3947	218	5	−	−	NOUN
ejpam-3947	218	6	1	1	NUM
ejpam-3947	218	7	=	=	SYM
ejpam-3947	218	8	2[(11	2[(11	NUM
ejpam-3947	219	1	+	+	CCONJ
ejpam-3947	219	2	12a)r]2	12a)r]2	X
ejpam-3947	219	3	.	.	PUNCT
ejpam-3947	219	4	by	by	ADP
ejpam-3947	219	5	theorem	theorem	NOUN
ejpam-3947	219	6	2.3	2.3	NUM
ejpam-3947	219	7	given	give	VERB
ejpam-3947	219	8	in	in	ADP
ejpam-3947	219	9	[	[	NOUN
ejpam-3947	219	10	8	8	NUM
ejpam-3947	219	11	]	]	PUNCT
ejpam-3947	219	12	,	,	PUNCT
ejpam-3947	219	13	the	the	DET
ejpam-3947	219	14	equation	equation	NOUN
ejpam-3947	219	15	2x2	2x2	NUM
ejpam-3947	219	16	+	+	CCONJ
ejpam-3947	219	17	1	1	NUM
ejpam-3947	219	18	=	=	NOUN
ejpam-3947	219	19	3n	3n	NOUN
ejpam-3947	219	20	has	have	VERB
ejpam-3947	219	21	only	only	ADV
ejpam-3947	219	22	three	three	NUM
ejpam-3947	219	23	positive	positive	ADJ
ejpam-3947	219	24	solutions	solution	NOUN
ejpam-3947	219	25	(	(	PUNCT
ejpam-3947	219	26	x	x	NOUN
ejpam-3947	219	27	,	,	PUNCT
ejpam-3947	219	28	n	n	CCONJ
ejpam-3947	219	29	)	)	PUNCT
ejpam-3947	219	30	=	=	SYM
ejpam-3947	219	31	(	(	PUNCT
ejpam-3947	219	32	1	1	NUM
ejpam-3947	219	33	,	,	PUNCT
ejpam-3947	219	34	1	1	NUM
ejpam-3947	219	35	)	)	PUNCT
ejpam-3947	219	36	,	,	PUNCT
ejpam-3947	219	37	(	(	PUNCT
ejpam-3947	219	38	2	2	NUM
ejpam-3947	219	39	,	,	PUNCT
ejpam-3947	219	40	2	2	NUM
ejpam-3947	219	41	)	)	PUNCT
ejpam-3947	219	42	,	,	PUNCT
ejpam-3947	219	43	(	(	PUNCT
ejpam-3947	219	44	11	11	NUM
ejpam-3947	219	45	,	,	PUNCT
ejpam-3947	219	46	5	5	NUM
ejpam-3947	219	47	)	)	PUNCT
ejpam-3947	219	48	.	.	PUNCT
ejpam-3947	220	1	therefore	therefore	ADV
ejpam-3947	220	2	,	,	PUNCT
ejpam-3947	220	3	we	we	PRON
ejpam-3947	220	4	get	get	VERB
ejpam-3947	220	5	x	x	X
ejpam-3947	220	6	=	=	SYM
ejpam-3947	220	7	5	5	NUM
ejpam-3947	220	8	and	and	CCONJ
ejpam-3947	220	9	(	(	PUNCT
ejpam-3947	220	10	11	11	NUM
ejpam-3947	220	11	+	+	NOUN
ejpam-3947	220	12	12a)r	12a)r	NUM
ejpam-3947	220	13	=	=	SYM
ejpam-3947	220	14	11	11	NUM
ejpam-3947	220	15	;	;	PUNCT
ejpam-3947	220	16	that	that	PRON
ejpam-3947	220	17	is	be	AUX
ejpam-3947	220	18	,	,	PUNCT
ejpam-3947	220	19	11	11	NUM
ejpam-3947	220	20	+	+	NUM
ejpam-3947	220	21	12a	12a	NOUN
ejpam-3947	220	22	=	=	SYM
ejpam-3947	220	23	11	11	NUM
ejpam-3947	220	24	and	and	CCONJ
ejpam-3947	220	25	r	r	NOUN
ejpam-3947	220	26	=	=	SYM
ejpam-3947	220	27	1	1	NUM
ejpam-3947	220	28	.	.	PUNCT
ejpam-3947	221	1	thus	thus	ADV
ejpam-3947	221	2	,	,	PUNCT
ejpam-3947	221	3	y	y	PROPN
ejpam-3947	221	4	=	=	PUNCT
ejpam-3947	221	5	2l	2l	NUM
ejpam-3947	221	6	=	=	NOUN
ejpam-3947	221	7	4r	4r	NOUN
ejpam-3947	221	8	=	=	SYM
ejpam-3947	221	9	4	4	X
ejpam-3947	221	10	.	.	PUNCT
ejpam-3947	222	1	this	this	PRON
ejpam-3947	222	2	shows	show	VERB
ejpam-3947	222	3	that	that	SCONJ
ejpam-3947	222	4	the	the	DET
ejpam-3947	222	5	equation	equation	NOUN
ejpam-3947	222	6	px	px	X
ejpam-3947	222	7	+	+	CCONJ
ejpam-3947	222	8	(	(	PUNCT
ejpam-3947	222	9	p+	p+	VERB
ejpam-3947	222	10	4k)y	4k)y	X
ejpam-3947	222	11	=	=	SYM
ejpam-3947	222	12	z2	z2	PROPN
ejpam-3947	222	13	,	,	PUNCT
ejpam-3947	222	14	x	x	X
ejpam-3947	222	15	>	>	X
ejpam-3947	222	16	1	1	NUM
ejpam-3947	222	17	,	,	PUNCT
ejpam-3947	222	18	y	y	PROPN
ejpam-3947	222	19	>	>	X
ejpam-3947	222	20	1	1	NUM
ejpam-3947	222	21	with	with	ADP
ejpam-3947	222	22	x	x	SYM
ejpam-3947	222	23	odd	odd	ADJ
ejpam-3947	222	24	and	and	CCONJ
ejpam-3947	222	25	y	y	PROPN
ejpam-3947	222	26	even	even	ADV
ejpam-3947	222	27	has	have	VERB
ejpam-3947	222	28	only	only	ADV
ejpam-3947	222	29	the	the	DET
ejpam-3947	222	30	solution	solution	NOUN
ejpam-3947	222	31	(	(	PUNCT
ejpam-3947	222	32	p	p	X
ejpam-3947	222	33	,	,	PUNCT
ejpam-3947	222	34	p+	p+	NOUN
ejpam-3947	222	35	4k	4k	NOUN
ejpam-3947	222	36	,	,	PUNCT
ejpam-3947	222	37	x	x	X
ejpam-3947	222	38	,	,	PUNCT
ejpam-3947	222	39	y	y	PROPN
ejpam-3947	222	40	,	,	PUNCT
ejpam-3947	222	41	z	z	NOUN
ejpam-3947	222	42	)	)	PUNCT
ejpam-3947	222	43	=	=	SYM
ejpam-3947	222	44	(	(	PUNCT
ejpam-3947	222	45	3	3	NUM
ejpam-3947	222	46	,	,	PUNCT
ejpam-3947	222	47	11	11	NUM
ejpam-3947	222	48	,	,	PUNCT
ejpam-3947	222	49	5	5	NUM
ejpam-3947	222	50	,	,	PUNCT
ejpam-3947	222	51	4	4	NUM
ejpam-3947	222	52	,	,	PUNCT
ejpam-3947	222	53	122	122	NUM
ejpam-3947	222	54	)	)	PUNCT
ejpam-3947	222	55	.	.	PUNCT
ejpam-3947	223	1	here	here	ADV
ejpam-3947	223	2	is	be	AUX
ejpam-3947	223	3	an	an	DET
ejpam-3947	223	4	analog	analog	NOUN
ejpam-3947	223	5	of	of	ADP
ejpam-3947	223	6	theorem	theorem	NOUN
ejpam-3947	223	7	4	4	NUM
ejpam-3947	223	8	for	for	ADP
ejpam-3947	223	9	the	the	DET
ejpam-3947	223	10	case	case	NOUN
ejpam-3947	223	11	where	where	SCONJ
ejpam-3947	223	12	x	x	PRON
ejpam-3947	223	13	is	be	AUX
ejpam-3947	223	14	even	even	ADV
ejpam-3947	223	15	and	and	CCONJ
ejpam-3947	223	16	y	y	PROPN
ejpam-3947	223	17	is	be	AUX
ejpam-3947	223	18	odd	odd	ADJ
ejpam-3947	223	19	.	.	PUNCT
ejpam-3947	224	1	theorem	theorem	NOUN
ejpam-3947	224	2	5	5	NUM
ejpam-3947	224	3	.	.	PUNCT
ejpam-3947	225	1	consider	consider	VERB
ejpam-3947	225	2	the	the	DET
ejpam-3947	225	3	diophantine	diophantine	NOUN
ejpam-3947	225	4	equation(3	equation(3	X
ejpam-3947	225	5	)	)	PUNCT
ejpam-3947	225	6	where	where	SCONJ
ejpam-3947	225	7	p	p	NOUN
ejpam-3947	225	8	and	and	CCONJ
ejpam-3947	225	9	p	p	NOUN
ejpam-3947	225	10	+	+	NOUN
ejpam-3947	225	11	4k	4k	PRON
ejpam-3947	225	12	are	be	AUX
ejpam-3947	225	13	primes	prime	NOUN
ejpam-3947	225	14	.	.	PUNCT
ejpam-3947	226	1	let	let	VERB
ejpam-3947	226	2	x	x	PRON
ejpam-3947	226	3	>	>	X
ejpam-3947	226	4	1	1	NUM
ejpam-3947	226	5	and	and	CCONJ
ejpam-3947	226	6	y	y	PROPN
ejpam-3947	226	7	>	>	X
ejpam-3947	226	8	1	1	NUM
ejpam-3947	226	9	be	be	AUX
ejpam-3947	226	10	positive	positive	ADJ
ejpam-3947	226	11	even	even	ADV
ejpam-3947	226	12	and	and	CCONJ
ejpam-3947	226	13	odd	odd	ADJ
ejpam-3947	226	14	integers	integer	NOUN
ejpam-3947	226	15	,	,	PUNCT
ejpam-3947	226	16	respectively	respectively	ADV
ejpam-3947	226	17	.	.	PUNCT
ejpam-3947	227	1	then	then	ADV
ejpam-3947	227	2	,	,	PUNCT
ejpam-3947	227	3	(	(	PUNCT
ejpam-3947	227	4	3	3	X
ejpam-3947	227	5	)	)	PUNCT
ejpam-3947	227	6	has	have	VERB
ejpam-3947	227	7	no	no	DET
ejpam-3947	227	8	solutions	solution	NOUN
ejpam-3947	227	9	in	in	ADP
ejpam-3947	227	10	n.	n.	NOUN
ejpam-3947	227	11	proof	proof	NOUN
ejpam-3947	227	12	.	.	PUNCT
ejpam-3947	228	1	let	let	VERB
ejpam-3947	228	2	q	q	NOUN
ejpam-3947	228	3	=	=	SYM
ejpam-3947	228	4	p+4k	p+4k	PROPN
ejpam-3947	228	5	.	.	PUNCT
ejpam-3947	229	1	then	then	ADV
ejpam-3947	229	2	qy−1	qy−1	NOUN
ejpam-3947	229	3	=	=	NOUN
ejpam-3947	229	4	2	2	NUM
ejpam-3947	229	5	pm	pm	NOUN
ejpam-3947	229	6	.	.	PUNCT
ejpam-3947	230	1	hence	hence	ADV
ejpam-3947	230	2	,	,	PUNCT
ejpam-3947	230	3	q−1	q−1	PROPN
ejpam-3947	230	4	=	=	PUNCT
ejpam-3947	230	5	2pα	2pα	PROPN
ejpam-3947	230	6	and	and	CCONJ
ejpam-3947	230	7	1+q+q2+	1+q+q2+	NUM
ejpam-3947	230	8	...	...	PUNCT
ejpam-3947	231	1	+qy−1	+qy−1	NOUN
ejpam-3947	231	2	=	=	X
ejpam-3947	232	1	pβ	pβ	ADP
ejpam-3947	232	2	for	for	ADP
ejpam-3947	232	3	some	some	DET
ejpam-3947	232	4	positive	positive	ADJ
ejpam-3947	232	5	integers	integer	NOUN
ejpam-3947	232	6	α	α	NOUN
ejpam-3947	232	7	and	and	CCONJ
ejpam-3947	232	8	β	β	X
ejpam-3947	232	9	.	.	PUNCT
ejpam-3947	233	1	since	since	SCONJ
ejpam-3947	233	2	q	q	PROPN
ejpam-3947	233	3	−	−	PROPN
ejpam-3947	233	4	1	1	NUM
ejpam-3947	233	5	=	=	SYM
ejpam-3947	233	6	2pα	2pα	NOUN
ejpam-3947	233	7	,	,	PUNCT
ejpam-3947	233	8	it	it	PRON
ejpam-3947	233	9	follows	follow	VERB
ejpam-3947	233	10	that	that	SCONJ
ejpam-3947	233	11	q	q	PROPN
ejpam-3947	233	12	≡	≡	PROPN
ejpam-3947	233	13	3	3	NUM
ejpam-3947	233	14	(	(	PUNCT
ejpam-3947	233	15	mod	mod	NOUN
ejpam-3947	233	16	4	4	NUM
ejpam-3947	233	17	)	)	PUNCT
ejpam-3947	233	18	.	.	PUNCT
ejpam-3947	234	1	consequently	consequently	ADV
ejpam-3947	234	2	,	,	PUNCT
ejpam-3947	234	3	p	p	PROPN
ejpam-3947	234	4	≡	≡	PROPN
ejpam-3947	234	5	3	3	NUM
ejpam-3947	234	6	(	(	PUNCT
ejpam-3947	234	7	mod	mod	NOUN
ejpam-3947	234	8	4	4	NUM
ejpam-3947	234	9	)	)	PUNCT
ejpam-3947	234	10	since	since	SCONJ
ejpam-3947	234	11	p	p	NOUN
ejpam-3947	234	12	=	=	X
ejpam-3947	234	13	q	q	NOUN
ejpam-3947	234	14	−	−	PROPN
ejpam-3947	234	15	4k	4k	NOUN
ejpam-3947	234	16	.	.	PUNCT
ejpam-3947	235	1	using	use	VERB
ejpam-3947	235	2	the	the	DET
ejpam-3947	235	3	fact	fact	NOUN
ejpam-3947	235	4	that	that	SCONJ
ejpam-3947	235	5	q	q	PUNCT
ejpam-3947	235	6	−	−	PROPN
ejpam-3947	235	7	1	1	NUM
ejpam-3947	235	8	=	=	SYM
ejpam-3947	235	9	2pα	2pα	NOUN
ejpam-3947	235	10	,	,	PUNCT
ejpam-3947	235	11	it	it	PRON
ejpam-3947	235	12	is	be	AUX
ejpam-3947	235	13	seen	see	VERB
ejpam-3947	235	14	that	that	SCONJ
ejpam-3947	235	15	the	the	DET
ejpam-3947	235	16	legendre	legendre	PROPN
ejpam-3947	235	17	symbol	symbol	NOUN
ejpam-3947	235	18	(	(	PUNCT
ejpam-3947	235	19	q	q	PROPN
ejpam-3947	235	20	p	p	NOUN
ejpam-3947	235	21	)	)	PUNCT
ejpam-3947	235	22	is	be	AUX
ejpam-3947	235	23	equal	equal	ADJ
ejpam-3947	235	24	to	to	ADP
ejpam-3947	235	25	1	1	NUM
ejpam-3947	235	26	.	.	PUNCT
ejpam-3947	236	1	since	since	SCONJ
ejpam-3947	236	2	p	p	PRON
ejpam-3947	236	3	≡	≡	PROPN
ejpam-3947	236	4	3	3	NUM
ejpam-3947	236	5	(	(	PUNCT
ejpam-3947	236	6	mod	mod	NOUN
ejpam-3947	236	7	4	4	NUM
ejpam-3947	236	8	)	)	PUNCT
ejpam-3947	236	9	and	and	CCONJ
ejpam-3947	236	10	q	q	PROPN
ejpam-3947	236	11	≡	≡	PROPN
ejpam-3947	236	12	3	3	NUM
ejpam-3947	236	13	(	(	PUNCT
ejpam-3947	236	14	mod	mod	NOUN
ejpam-3947	236	15	4	4	NUM
ejpam-3947	236	16	)	)	PUNCT
ejpam-3947	236	17	,	,	PUNCT
ejpam-3947	236	18	then	then	ADV
ejpam-3947	236	19	by	by	ADP
ejpam-3947	236	20	using	use	VERB
ejpam-3947	236	21	the	the	DET
ejpam-3947	236	22	quadratic	quadratic	ADJ
ejpam-3947	236	23	reciprocity	reciprocity	NOUN
ejpam-3947	236	24	law	law	NOUN
ejpam-3947	236	25	,	,	PUNCT
ejpam-3947	236	26	we	we	PRON
ejpam-3947	236	27	get	get	VERB
ejpam-3947	236	28	(	(	PUNCT
ejpam-3947	236	29	q	q	NOUN
ejpam-3947	236	30	p	p	NOUN
ejpam-3947	236	31	)	)	PUNCT
ejpam-3947	236	32	=	=	SYM
ejpam-3947	236	33	−1	−1	NOUN
ejpam-3947	236	34	.	.	PUNCT
ejpam-3947	237	1	on	on	ADP
ejpam-3947	237	2	the	the	DET
ejpam-3947	237	3	other	other	ADJ
ejpam-3947	237	4	hand	hand	NOUN
ejpam-3947	237	5	,	,	PUNCT
ejpam-3947	237	6	the	the	DET
ejpam-3947	237	7	equality	equality	NOUN
ejpam-3947	237	8	1	1	NUM
ejpam-3947	237	9	+	+	CCONJ
ejpam-3947	237	10	q	q	NOUN
ejpam-3947	237	11	+	+	NUM
ejpam-3947	237	12	q2	q2	NOUN
ejpam-3947	237	13	+	+	CCONJ
ejpam-3947	237	14	...	...	PUNCT
ejpam-3947	238	1	+	+	CCONJ
ejpam-3947	238	2	qy−1	qy−1	ADJ
ejpam-3947	238	3	=	=	PRON
ejpam-3947	238	4	pβ	pβ	ADV
ejpam-3947	238	5	implies	imply	VERB
ejpam-3947	238	6	pβ	pβ	ADP
ejpam-3947	238	7	≡	≡	PROPN
ejpam-3947	238	8	1	1	NUM
ejpam-3947	238	9	(	(	PUNCT
ejpam-3947	238	10	mod	mod	PROPN
ejpam-3947	238	11	q	q	PROPN
ejpam-3947	238	12	)	)	PUNCT
ejpam-3947	238	13	,	,	PUNCT
ejpam-3947	238	14	so	so	ADV
ejpam-3947	238	15	we	we	PRON
ejpam-3947	238	16	have	have	VERB
ejpam-3947	238	17	(	(	PUNCT
ejpam-3947	238	18	−1)β	−1)β	PROPN
ejpam-3947	238	19	=	=	PUNCT
ejpam-3947	238	20	(	(	PUNCT
ejpam-3947	238	21	p	p	X
ejpam-3947	238	22	q	q	NOUN
ejpam-3947	238	23	)	)	PUNCT
ejpam-3947	238	24	β	β	NOUN
ejpam-3947	238	25	=	=	SYM
ejpam-3947	238	26	1	1	NUM
ejpam-3947	238	27	,	,	PUNCT
ejpam-3947	238	28	which	which	PRON
ejpam-3947	238	29	shows	show	VERB
ejpam-3947	238	30	that	that	SCONJ
ejpam-3947	238	31	β	β	NOUN
ejpam-3947	238	32	is	be	AUX
ejpam-3947	238	33	even	even	ADV
ejpam-3947	238	34	.	.	PUNCT
ejpam-3947	239	1	let	let	VERB
ejpam-3947	239	2	β	β	X
ejpam-3947	239	3	=	=	SYM
ejpam-3947	239	4	2r	2r	NUM
ejpam-3947	239	5	.	.	PUNCT
ejpam-3947	240	1	then	then	ADV
ejpam-3947	240	2	,	,	PUNCT
ejpam-3947	240	3	we	we	PRON
ejpam-3947	240	4	get	get	VERB
ejpam-3947	240	5	1	1	NUM
ejpam-3947	240	6	+	+	CCONJ
ejpam-3947	240	7	q	q	NOUN
ejpam-3947	240	8	+	+	NUM
ejpam-3947	240	9	q2	q2	NOUN
ejpam-3947	240	10	+	+	CCONJ
ejpam-3947	240	11	...	...	PUNCT
ejpam-3947	241	1	+	+	X
ejpam-3947	241	2	qy−1	qy−1	ADJ
ejpam-3947	241	3	=	=	SYM
ejpam-3947	241	4	(	(	PUNCT
ejpam-3947	241	5	pr)2	pr)2	NOUN
ejpam-3947	241	6	.	.	PUNCT
ejpam-3947	242	1	that	that	PRON
ejpam-3947	242	2	is	be	AUX
ejpam-3947	242	3	,	,	PUNCT
ejpam-3947	242	4	1−	1−	NUM
ejpam-3947	242	5	qy	qy	NOUN
ejpam-3947	242	6	1−	1−	NUM
ejpam-3947	242	7	q	q	NOUN
ejpam-3947	243	1	=	=	PUNCT
ejpam-3947	243	2	(	(	PUNCT
ejpam-3947	243	3	pr)2	pr)2	NOUN
ejpam-3947	243	4	.	.	PUNCT
ejpam-3947	244	1	by	by	ADP
ejpam-3947	244	2	the	the	DET
ejpam-3947	244	3	result	result	NOUN
ejpam-3947	244	4	given	give	VERB
ejpam-3947	244	5	in	in	ADP
ejpam-3947	244	6	[	[	PUNCT
ejpam-3947	244	7	9	9	NUM
ejpam-3947	244	8	]	]	PUNCT
ejpam-3947	244	9	,	,	PUNCT
ejpam-3947	244	10	the	the	DET
ejpam-3947	244	11	equation	equation	NOUN
ejpam-3947	244	12	xn	xn	PUNCT
ejpam-3947	245	1	−	−	PROPN
ejpam-3947	245	2	1	1	NUM
ejpam-3947	245	3	x−	x−	PROPN
ejpam-3947	245	4	1	1	NUM
ejpam-3947	245	5	=	=	SYM
ejpam-3947	245	6	y2	y2	PROPN
ejpam-3947	245	7	,	,	PUNCT
ejpam-3947	245	8	x	x	X
ejpam-3947	245	9	>	>	X
ejpam-3947	245	10	1	1	NUM
ejpam-3947	245	11	,	,	PUNCT
ejpam-3947	245	12	y	y	PROPN
ejpam-3947	245	13	>	>	X
ejpam-3947	245	14	1	1	NUM
ejpam-3947	245	15	,	,	PUNCT
ejpam-3947	245	16	n	n	CCONJ
ejpam-3947	245	17	>	>	X
ejpam-3947	245	18	2	2	NUM
ejpam-3947	245	19	r.	r.	PROPN
ejpam-3947	245	20	j.	j.	PROPN
ejpam-3947	245	21	s.	s.	PROPN
ejpam-3947	245	22	mina	mina	PROPN
ejpam-3947	245	23	,	,	PUNCT
ejpam-3947	245	24	j.	j.	PROPN
ejpam-3947	245	25	b.	b.	PROPN
ejpam-3947	245	26	bacani	bacani	PROPN
ejpam-3947	245	27	/	/	SYM
ejpam-3947	245	28	eur	eur	PROPN
ejpam-3947	245	29	.	.	PUNCT
ejpam-3947	246	1	j.	j.	PROPN
ejpam-3947	246	2	pure	pure	PROPN
ejpam-3947	246	3	appl	appl	PROPN
ejpam-3947	246	4	.	.	PROPN
ejpam-3947	246	5	math	math	PROPN
ejpam-3947	246	6	,	,	PUNCT
ejpam-3947	246	7	14	14	NUM
ejpam-3947	246	8	(	(	PUNCT
ejpam-3947	246	9	2	2	NUM
ejpam-3947	246	10	)	)	PUNCT
ejpam-3947	246	11	(	(	PUNCT
ejpam-3947	246	12	2021	2021	NUM
ejpam-3947	246	13	)	)	PUNCT
ejpam-3947	246	14	,	,	PUNCT
ejpam-3947	246	15	471	471	NUM
ejpam-3947	246	16	-	-	SYM
ejpam-3947	246	17	479	479	NUM
ejpam-3947	246	18	477	477	NUM
ejpam-3947	246	19	has	have	VERB
ejpam-3947	246	20	only	only	ADJ
ejpam-3947	246	21	solutions	solution	NOUN
ejpam-3947	246	22	(	(	PUNCT
ejpam-3947	246	23	x	x	NOUN
ejpam-3947	246	24	,	,	PUNCT
ejpam-3947	246	25	n	n	CCONJ
ejpam-3947	246	26	)	)	PUNCT
ejpam-3947	246	27	=	=	SYM
ejpam-3947	246	28	(	(	PUNCT
ejpam-3947	246	29	7	7	NUM
ejpam-3947	246	30	,	,	PUNCT
ejpam-3947	246	31	4	4	NUM
ejpam-3947	246	32	)	)	PUNCT
ejpam-3947	246	33	,	,	PUNCT
ejpam-3947	246	34	(	(	PUNCT
ejpam-3947	246	35	3	3	NUM
ejpam-3947	246	36	,	,	PUNCT
ejpam-3947	246	37	5	5	NUM
ejpam-3947	246	38	)	)	PUNCT
ejpam-3947	246	39	.	.	PUNCT
ejpam-3947	247	1	since	since	SCONJ
ejpam-3947	247	2	q	q	PROPN
ejpam-3947	247	3	=	=	SYM
ejpam-3947	247	4	p+	p+	X
ejpam-3947	247	5	4k	4k	X
ejpam-3947	247	6	>	>	X
ejpam-3947	247	7	7	7	NUM
ejpam-3947	247	8	,	,	PUNCT
ejpam-3947	247	9	and	and	CCONJ
ejpam-3947	247	10	y	y	PROPN
ejpam-3947	247	11	is	be	AUX
ejpam-3947	247	12	odd	odd	ADJ
ejpam-3947	247	13	with	with	ADP
ejpam-3947	247	14	y	y	PROPN
ejpam-3947	247	15	>	>	X
ejpam-3947	247	16	2	2	NUM
ejpam-3947	247	17	,	,	PUNCT
ejpam-3947	247	18	we	we	PRON
ejpam-3947	247	19	see	see	VERB
ejpam-3947	247	20	that	that	SCONJ
ejpam-3947	247	21	1−	1−	NUM
ejpam-3947	247	22	qy	qy	NOUN
ejpam-3947	247	23	1−	1−	NUM
ejpam-3947	247	24	q	q	NOUN
ejpam-3947	248	1	=	=	PUNCT
ejpam-3947	248	2	(	(	PUNCT
ejpam-3947	248	3	pr)2	pr)2	NOUN
ejpam-3947	248	4	has	have	VERB
ejpam-3947	248	5	no	no	DET
ejpam-3947	248	6	solutions	solution	NOUN
ejpam-3947	248	7	.	.	PUNCT
ejpam-3947	249	1	therefore	therefore	ADV
ejpam-3947	249	2	,	,	PUNCT
ejpam-3947	249	3	equation	equation	NOUN
ejpam-3947	249	4	(	(	PUNCT
ejpam-3947	249	5	3	3	X
ejpam-3947	249	6	)	)	PUNCT
ejpam-3947	249	7	has	have	VERB
ejpam-3947	249	8	no	no	DET
ejpam-3947	249	9	solutions	solution	NOUN
ejpam-3947	249	10	if	if	SCONJ
ejpam-3947	249	11	x	x	PROPN
ejpam-3947	249	12	>	>	X
ejpam-3947	249	13	1	1	NUM
ejpam-3947	249	14	,	,	PUNCT
ejpam-3947	249	15	y	y	PROPN
ejpam-3947	249	16	>	>	X
ejpam-3947	249	17	1	1	NUM
ejpam-3947	249	18	,	,	PUNCT
ejpam-3947	249	19	y	y	PROPN
ejpam-3947	249	20	is	be	AUX
ejpam-3947	249	21	odd	odd	ADJ
ejpam-3947	249	22	,	,	PUNCT
ejpam-3947	249	23	and	and	CCONJ
ejpam-3947	249	24	x	x	X
ejpam-3947	249	25	is	be	AUX
ejpam-3947	249	26	even	even	ADV
ejpam-3947	249	27	.	.	PUNCT
ejpam-3947	250	1	from	from	ADP
ejpam-3947	250	2	lemma	lemma	PROPN
ejpam-3947	250	3	2	2	NUM
ejpam-3947	250	4	and	and	CCONJ
ejpam-3947	250	5	theorems	theorem	NOUN
ejpam-3947	250	6	4	4	NUM
ejpam-3947	250	7	and	and	CCONJ
ejpam-3947	250	8	5	5	NUM
ejpam-3947	250	9	,	,	PUNCT
ejpam-3947	250	10	we	we	PRON
ejpam-3947	250	11	get	get	VERB
ejpam-3947	250	12	the	the	DET
ejpam-3947	250	13	following	follow	VERB
ejpam-3947	250	14	corollary	corollary	NOUN
ejpam-3947	250	15	.	.	PUNCT
ejpam-3947	251	1	corollary	corollary	ADJ
ejpam-3947	251	2	2	2	NUM
ejpam-3947	251	3	.	.	PUNCT
ejpam-3947	252	1	let	let	VERB
ejpam-3947	252	2	p	p	NOUN
ejpam-3947	252	3	and	and	CCONJ
ejpam-3947	252	4	p	p	NOUN
ejpam-3947	252	5	+	+	CCONJ
ejpam-3947	252	6	4k	4k	PRON
ejpam-3947	252	7	be	be	VERB
ejpam-3947	252	8	prime	prime	ADJ
ejpam-3947	252	9	numbers	number	NOUN
ejpam-3947	252	10	.	.	PUNCT
ejpam-3947	253	1	then	then	ADV
ejpam-3947	253	2	,	,	PUNCT
ejpam-3947	253	3	the	the	DET
ejpam-3947	253	4	equation	equation	NOUN
ejpam-3947	253	5	px	px	X
ejpam-3947	253	6	+	+	CCONJ
ejpam-3947	253	7	(	(	PUNCT
ejpam-3947	253	8	p	p	X
ejpam-3947	253	9	+	+	PROPN
ejpam-3947	253	10	4k)y	4k)y	NOUN
ejpam-3947	253	11	=	=	SYM
ejpam-3947	253	12	z2	z2	PROPN
ejpam-3947	253	13	,	,	PUNCT
ejpam-3947	253	14	x	x	X
ejpam-3947	253	15	>	>	X
ejpam-3947	253	16	1	1	NUM
ejpam-3947	253	17	,	,	PUNCT
ejpam-3947	253	18	y	y	PROPN
ejpam-3947	253	19	>	>	X
ejpam-3947	253	20	1	1	NUM
ejpam-3947	253	21	has	have	VERB
ejpam-3947	253	22	only	only	ADV
ejpam-3947	253	23	the	the	DET
ejpam-3947	253	24	solution	solution	NOUN
ejpam-3947	253	25	(	(	PUNCT
ejpam-3947	253	26	p	p	X
ejpam-3947	253	27	,	,	PUNCT
ejpam-3947	253	28	p+	p+	NOUN
ejpam-3947	253	29	4k	4k	NOUN
ejpam-3947	253	30	,	,	PUNCT
ejpam-3947	253	31	x	x	X
ejpam-3947	253	32	,	,	PUNCT
ejpam-3947	253	33	y	y	PROPN
ejpam-3947	253	34	,	,	PUNCT
ejpam-3947	253	35	z	z	NOUN
ejpam-3947	253	36	)	)	PUNCT
ejpam-3947	253	37	=	=	SYM
ejpam-3947	253	38	(	(	PUNCT
ejpam-3947	253	39	3	3	NUM
ejpam-3947	253	40	,	,	PUNCT
ejpam-3947	253	41	11	11	NUM
ejpam-3947	253	42	,	,	PUNCT
ejpam-3947	253	43	5	5	NUM
ejpam-3947	253	44	,	,	PUNCT
ejpam-3947	253	45	4	4	NUM
ejpam-3947	253	46	,	,	PUNCT
ejpam-3947	253	47	122	122	NUM
ejpam-3947	253	48	)	)	PUNCT
ejpam-3947	253	49	.	.	PUNCT
ejpam-3947	254	1	3.3	3.3	NUM
ejpam-3947	254	2	.	.	PUNCT
ejpam-3947	254	3	finiteness	finiteness	NOUN
ejpam-3947	254	4	of	of	ADP
ejpam-3947	254	5	number	number	NOUN
ejpam-3947	254	6	of	of	ADP
ejpam-3947	254	7	solutions	solution	NOUN
ejpam-3947	254	8	in	in	ADP
ejpam-3947	254	9	this	this	DET
ejpam-3947	254	10	section	section	NOUN
ejpam-3947	254	11	,	,	PUNCT
ejpam-3947	254	12	we	we	PRON
ejpam-3947	254	13	prove	prove	VERB
ejpam-3947	254	14	that	that	SCONJ
ejpam-3947	254	15	(	(	PUNCT
ejpam-3947	254	16	3	3	X
ejpam-3947	254	17	)	)	PUNCT
ejpam-3947	254	18	has	have	VERB
ejpam-3947	254	19	a	a	DET
ejpam-3947	254	20	finite	finite	ADJ
ejpam-3947	254	21	number	number	NOUN
ejpam-3947	254	22	of	of	ADP
ejpam-3947	254	23	solutions	solution	NOUN
ejpam-3947	254	24	for	for	ADP
ejpam-3947	254	25	any	any	DET
ejpam-3947	254	26	given	give	VERB
ejpam-3947	254	27	value	value	NOUN
ejpam-3947	254	28	of	of	ADP
ejpam-3947	254	29	p	p	PROPN
ejpam-3947	254	30	and	and	CCONJ
ejpam-3947	254	31	k.	k.	PROPN
ejpam-3947	254	32	theorem	theorem	NOUN
ejpam-3947	254	33	6	6	NUM
ejpam-3947	254	34	.	.	PUNCT
ejpam-3947	255	1	let	let	VERB
ejpam-3947	255	2	k	k	PRON
ejpam-3947	255	3	be	be	AUX
ejpam-3947	255	4	a	a	DET
ejpam-3947	255	5	fixed	fix	VERB
ejpam-3947	255	6	positive	positive	ADJ
ejpam-3947	255	7	integer	integer	NOUN
ejpam-3947	255	8	such	such	ADJ
ejpam-3947	255	9	that	that	SCONJ
ejpam-3947	255	10	p	p	PROPN
ejpam-3947	255	11	and	and	CCONJ
ejpam-3947	255	12	p	p	NOUN
ejpam-3947	255	13	+	+	CCONJ
ejpam-3947	255	14	4k	4k	PRON
ejpam-3947	255	15	are	be	AUX
ejpam-3947	255	16	primes	prime	NOUN
ejpam-3947	255	17	.	.	PUNCT
ejpam-3947	256	1	then	then	ADV
ejpam-3947	256	2	,	,	PUNCT
ejpam-3947	256	3	the	the	DET
ejpam-3947	256	4	diophantine	diophantine	NOUN
ejpam-3947	256	5	equation	equation	NOUN
ejpam-3947	256	6	(	(	PUNCT
ejpam-3947	256	7	3	3	X
ejpam-3947	256	8	)	)	PUNCT
ejpam-3947	256	9	has	have	VERB
ejpam-3947	256	10	at	at	ADP
ejpam-3947	256	11	most	most	ADV
ejpam-3947	256	12	two	two	NUM
ejpam-3947	256	13	solutions	solution	NOUN
ejpam-3947	256	14	(	(	PUNCT
ejpam-3947	256	15	x	x	X
ejpam-3947	256	16	,	,	PUNCT
ejpam-3947	256	17	y	y	PROPN
ejpam-3947	256	18	,	,	PUNCT
ejpam-3947	256	19	z	z	NOUN
ejpam-3947	256	20	)	)	PUNCT
ejpam-3947	256	21	in	in	ADP
ejpam-3947	256	22	n.	n.	NOUN
ejpam-3947	256	23	proof	proof	NOUN
ejpam-3947	256	24	.	.	PUNCT
ejpam-3947	257	1	fix	fix	VERB
ejpam-3947	257	2	a	a	DET
ejpam-3947	257	3	value	value	NOUN
ejpam-3947	257	4	for	for	ADP
ejpam-3947	257	5	p	p	PROPN
ejpam-3947	257	6	and	and	CCONJ
ejpam-3947	257	7	k.	k.	NOUN
ejpam-3947	258	1	we	we	PRON
ejpam-3947	258	2	have	have	VERB
ejpam-3947	258	3	the	the	DET
ejpam-3947	258	4	following	follow	VERB
ejpam-3947	258	5	cases	case	NOUN
ejpam-3947	258	6	.	.	PUNCT
ejpam-3947	259	1	if	if	SCONJ
ejpam-3947	259	2	x	x	SYM
ejpam-3947	259	3	=	=	SYM
ejpam-3947	259	4	1	1	NUM
ejpam-3947	259	5	,	,	PUNCT
ejpam-3947	259	6	then	then	ADV
ejpam-3947	259	7	by	by	ADP
ejpam-3947	259	8	theorem	theorem	NOUN
ejpam-3947	259	9	3	3	NUM
ejpam-3947	259	10	,	,	PUNCT
ejpam-3947	259	11	there	there	PRON
ejpam-3947	259	12	are	be	VERB
ejpam-3947	259	13	no	no	DET
ejpam-3947	259	14	solutions	solution	NOUN
ejpam-3947	259	15	.	.	PUNCT
ejpam-3947	260	1	if	if	SCONJ
ejpam-3947	260	2	y	y	PROPN
ejpam-3947	260	3	=	=	SYM
ejpam-3947	260	4	1	1	NUM
ejpam-3947	260	5	,	,	PUNCT
ejpam-3947	260	6	then	then	ADV
ejpam-3947	260	7	there	there	PRON
ejpam-3947	260	8	is	be	VERB
ejpam-3947	260	9	only	only	ADV
ejpam-3947	260	10	one	one	NUM
ejpam-3947	260	11	solution	solution	NOUN
ejpam-3947	260	12	for	for	ADP
ejpam-3947	260	13	a	a	DET
ejpam-3947	260	14	fixed	fix	VERB
ejpam-3947	260	15	value	value	NOUN
ejpam-3947	260	16	of	of	ADP
ejpam-3947	260	17	p	p	PROPN
ejpam-3947	260	18	and	and	CCONJ
ejpam-3947	260	19	k.	k.	PROPN
ejpam-3947	260	20	finally	finally	ADV
ejpam-3947	260	21	,	,	PUNCT
ejpam-3947	260	22	if	if	SCONJ
ejpam-3947	260	23	x	x	PROPN
ejpam-3947	260	24	>	>	X
ejpam-3947	260	25	1	1	NUM
ejpam-3947	260	26	and	and	CCONJ
ejpam-3947	260	27	y	y	PROPN
ejpam-3947	260	28	>	>	X
ejpam-3947	260	29	1	1	NUM
ejpam-3947	260	30	,	,	PUNCT
ejpam-3947	260	31	then	then	ADV
ejpam-3947	260	32	by	by	ADP
ejpam-3947	260	33	corollary	corollary	ADJ
ejpam-3947	260	34	2	2	NUM
ejpam-3947	260	35	,	,	PUNCT
ejpam-3947	260	36	there	there	PRON
ejpam-3947	260	37	is	be	VERB
ejpam-3947	260	38	only	only	ADV
ejpam-3947	260	39	one	one	NUM
ejpam-3947	260	40	solution	solution	NOUN
ejpam-3947	260	41	.	.	PUNCT
ejpam-3947	261	1	hence	hence	ADV
ejpam-3947	261	2	,	,	PUNCT
ejpam-3947	261	3	in	in	ADP
ejpam-3947	261	4	any	any	DET
ejpam-3947	261	5	case	case	NOUN
ejpam-3947	261	6	,	,	PUNCT
ejpam-3947	261	7	there	there	PRON
ejpam-3947	261	8	are	be	VERB
ejpam-3947	261	9	at	at	ADP
ejpam-3947	261	10	most	most	ADV
ejpam-3947	261	11	two	two	NUM
ejpam-3947	261	12	solutions	solution	NOUN
ejpam-3947	261	13	.	.	PUNCT
ejpam-3947	262	1	remark	remark	NOUN
ejpam-3947	262	2	2	2	NUM
ejpam-3947	262	3	.	.	PUNCT
ejpam-3947	263	1	by	by	ADP
ejpam-3947	263	2	applying	apply	VERB
ejpam-3947	263	3	the	the	DET
ejpam-3947	263	4	results	result	NOUN
ejpam-3947	263	5	in	in	ADP
ejpam-3947	263	6	theorem	theorem	ADJ
ejpam-3947	263	7	6	6	NUM
ejpam-3947	263	8	and	and	CCONJ
ejpam-3947	263	9	corollary	corollary	ADJ
ejpam-3947	263	10	1	1	NUM
ejpam-3947	263	11	,	,	PUNCT
ejpam-3947	263	12	it	it	PRON
ejpam-3947	263	13	follows	follow	VERB
ejpam-3947	263	14	that	that	SCONJ
ejpam-3947	263	15	for	for	ADP
ejpam-3947	263	16	each	each	DET
ejpam-3947	263	17	k	k	PROPN
ejpam-3947	263	18	∈	∈	PROPN
ejpam-3947	263	19	n	n	CCONJ
ejpam-3947	263	20	,	,	PUNCT
ejpam-3947	263	21	the	the	DET
ejpam-3947	263	22	diophantine	diophantine	NOUN
ejpam-3947	263	23	equation	equation	NOUN
ejpam-3947	263	24	px+(p+4k)y	px+(p+4k)y	NOUN
ejpam-3947	263	25	=	=	PUNCT
ejpam-3947	263	26	z2n	z2n	PROPN
ejpam-3947	263	27	has	have	VERB
ejpam-3947	263	28	only	only	ADV
ejpam-3947	263	29	a	a	DET
ejpam-3947	263	30	finite	finite	ADJ
ejpam-3947	263	31	number	number	NOUN
ejpam-3947	263	32	of	of	ADP
ejpam-3947	263	33	solutions	solution	NOUN
ejpam-3947	263	34	(	(	PUNCT
ejpam-3947	263	35	x	x	X
ejpam-3947	263	36	,	,	PUNCT
ejpam-3947	263	37	y	y	PROPN
ejpam-3947	263	38	,	,	PUNCT
ejpam-3947	263	39	z	z	PROPN
ejpam-3947	263	40	,	,	PUNCT
ejpam-3947	263	41	n	n	CCONJ
ejpam-3947	263	42	)	)	PUNCT
ejpam-3947	263	43	.	.	PUNCT
ejpam-3947	264	1	4	4	X
ejpam-3947	264	2	.	.	X
ejpam-3947	264	3	conclusion	conclusion	NOUN
ejpam-3947	264	4	in	in	ADP
ejpam-3947	264	5	this	this	DET
ejpam-3947	264	6	paper	paper	NOUN
ejpam-3947	264	7	,	,	PUNCT
ejpam-3947	264	8	we	we	PRON
ejpam-3947	264	9	have	have	AUX
ejpam-3947	264	10	shown	show	VERB
ejpam-3947	264	11	that	that	SCONJ
ejpam-3947	264	12	there	there	PRON
ejpam-3947	264	13	are	be	VERB
ejpam-3947	264	14	only	only	ADV
ejpam-3947	264	15	two	two	NUM
ejpam-3947	264	16	solutions	solution	NOUN
ejpam-3947	264	17	to	to	ADP
ejpam-3947	264	18	the	the	DET
ejpam-3947	264	19	diophantine	diophantine	NOUN
ejpam-3947	264	20	equation	equation	NOUN
ejpam-3947	264	21	(	(	PUNCT
ejpam-3947	264	22	2	2	NUM
ejpam-3947	264	23	)	)	PUNCT
ejpam-3947	264	24	in	in	ADP
ejpam-3947	264	25	n0	n0	NOUN
ejpam-3947	264	26	when	when	SCONJ
ejpam-3947	264	27	p	p	NOUN
ejpam-3947	264	28	and	and	CCONJ
ejpam-3947	264	29	p	p	NOUN
ejpam-3947	264	30	+	+	CCONJ
ejpam-3947	264	31	4	4	NUM
ejpam-3947	264	32	are	be	AUX
ejpam-3947	264	33	primes	prime	NOUN
ejpam-3947	264	34	.	.	PUNCT
ejpam-3947	265	1	there	there	PRON
ejpam-3947	265	2	are	be	VERB
ejpam-3947	265	3	also	also	ADV
ejpam-3947	265	4	two	two	NUM
ejpam-3947	265	5	solutions	solution	NOUN
ejpam-3947	265	6	for	for	ADP
ejpam-3947	265	7	the	the	DET
ejpam-3947	265	8	equation	equation	NOUN
ejpam-3947	265	9	px	px	X
ejpam-3947	265	10	+	+	CCONJ
ejpam-3947	265	11	(	(	PUNCT
ejpam-3947	265	12	p	p	X
ejpam-3947	265	13	+	+	NOUN
ejpam-3947	265	14	4)y	4)y	X
ejpam-3947	265	15	=	=	SYM
ejpam-3947	265	16	z2n	z2n	NOUN
ejpam-3947	265	17	,	,	PUNCT
ejpam-3947	265	18	whenever	whenever	SCONJ
ejpam-3947	265	19	z	z	NOUN
ejpam-3947	265	20	is	be	AUX
ejpam-3947	265	21	not	not	PART
ejpam-3947	265	22	a	a	DET
ejpam-3947	265	23	perfect	perfect	ADJ
ejpam-3947	265	24	square	square	NOUN
ejpam-3947	265	25	.	.	PUNCT
ejpam-3947	266	1	lastly	lastly	ADV
ejpam-3947	266	2	,	,	PUNCT
ejpam-3947	266	3	we	we	PRON
ejpam-3947	266	4	studied	study	VERB
ejpam-3947	266	5	the	the	DET
ejpam-3947	266	6	more	more	ADV
ejpam-3947	266	7	general	general	ADJ
ejpam-3947	266	8	form	form	NOUN
ejpam-3947	266	9	px	px	X
ejpam-3947	266	10	+	+	CCONJ
ejpam-3947	266	11	(	(	PUNCT
ejpam-3947	266	12	p+	p+	PROPN
ejpam-3947	266	13	4k)y	4k)y	X
ejpam-3947	266	14	=	=	SYM
ejpam-3947	266	15	z2	z2	PROPN
ejpam-3947	266	16	and	and	CCONJ
ejpam-3947	266	17	have	have	AUX
ejpam-3947	266	18	shown	show	VERB
ejpam-3947	266	19	that	that	SCONJ
ejpam-3947	266	20	there	there	PRON
ejpam-3947	266	21	’s	’	VERB
ejpam-3947	266	22	a	a	DET
ejpam-3947	266	23	unique	unique	ADJ
ejpam-3947	266	24	solution	solution	NOUN
ejpam-3947	266	25	if	if	SCONJ
ejpam-3947	266	26	x	x	PROPN
ejpam-3947	266	27	and	and	CCONJ
ejpam-3947	266	28	y	y	PROPN
ejpam-3947	266	29	are	be	AUX
ejpam-3947	266	30	both	both	ADV
ejpam-3947	266	31	greater	great	ADJ
ejpam-3947	266	32	than	than	ADP
ejpam-3947	266	33	1	1	NUM
ejpam-3947	266	34	.	.	PUNCT
ejpam-3947	267	1	in	in	ADP
ejpam-3947	267	2	general	general	ADJ
ejpam-3947	267	3	,	,	PUNCT
ejpam-3947	267	4	there	there	PRON
ejpam-3947	267	5	’s	’	VERB
ejpam-3947	267	6	a	a	DET
ejpam-3947	267	7	finite	finite	ADJ
ejpam-3947	267	8	number	number	NOUN
ejpam-3947	267	9	of	of	ADP
ejpam-3947	267	10	solutions	solution	NOUN
ejpam-3947	267	11	in	in	ADP
ejpam-3947	267	12	the	the	DET
ejpam-3947	267	13	set	set	ADJ
ejpam-3947	267	14	n.	n.	NOUN
ejpam-3947	267	15	acknowledgment	acknowledgment	NOUN
ejpam-3947	267	16	the	the	DET
ejpam-3947	267	17	authors	author	NOUN
ejpam-3947	267	18	would	would	AUX
ejpam-3947	267	19	like	like	VERB
ejpam-3947	267	20	to	to	PART
ejpam-3947	267	21	thank	thank	VERB
ejpam-3947	267	22	the	the	DET
ejpam-3947	267	23	university	university	NOUN
ejpam-3947	267	24	of	of	ADP
ejpam-3947	267	25	the	the	DET
ejpam-3947	267	26	philippines	philippine	NOUN
ejpam-3947	267	27	baguio	baguio	VERB
ejpam-3947	267	28	for	for	ADP
ejpam-3947	267	29	the	the	DET
ejpam-3947	267	30	support	support	NOUN
ejpam-3947	267	31	given	give	VERB
ejpam-3947	267	32	in	in	ADP
ejpam-3947	267	33	the	the	DET
ejpam-3947	267	34	conduct	conduct	NOUN
ejpam-3947	267	35	of	of	ADP
ejpam-3947	267	36	this	this	DET
ejpam-3947	267	37	study	study	NOUN
ejpam-3947	267	38	and	and	CCONJ
ejpam-3947	267	39	its	its	PRON
ejpam-3947	267	40	publication	publication	NOUN
ejpam-3947	267	41	.	.	PUNCT
ejpam-3947	268	1	the	the	DET
ejpam-3947	268	2	authors	author	NOUN
ejpam-3947	268	3	are	be	AUX
ejpam-3947	268	4	also	also	ADV
ejpam-3947	268	5	grateful	grateful	ADJ
ejpam-3947	268	6	to	to	ADP
ejpam-3947	268	7	the	the	DET
ejpam-3947	268	8	referees	referee	NOUN
ejpam-3947	268	9	for	for	ADP
ejpam-3947	268	10	their	their	PRON
ejpam-3947	268	11	valuable	valuable	ADJ
ejpam-3947	268	12	comments	comment	NOUN
ejpam-3947	268	13	and	and	CCONJ
ejpam-3947	268	14	suggestions	suggestion	NOUN
ejpam-3947	268	15	–	–	PUNCT
ejpam-3947	268	16	for	for	ADP
ejpam-3947	268	17	extending	extend	VERB
ejpam-3947	268	18	their	their	PRON
ejpam-3947	268	19	help	help	NOUN
ejpam-3947	268	20	and	and	CCONJ
ejpam-3947	268	21	expertise	expertise	NOUN
ejpam-3947	268	22	in	in	ADP
ejpam-3947	268	23	improving	improve	VERB
ejpam-3947	268	24	the	the	DET
ejpam-3947	268	25	manuscript	manuscript	NOUN
ejpam-3947	268	26	that	that	PRON
ejpam-3947	268	27	was	be	AUX
ejpam-3947	268	28	originally	originally	ADV
ejpam-3947	268	29	submitted	submit	VERB
ejpam-3947	268	30	.	.	PUNCT
ejpam-3947	269	1	references	reference	NOUN
ejpam-3947	269	2	478	478	NUM
ejpam-3947	269	3	references	reference	NOUN
ejpam-3947	269	4	[	[	X
ejpam-3947	269	5	1	1	NUM
ejpam-3947	269	6	]	]	PUNCT
ejpam-3947	269	7	a	a	DET
ejpam-3947	269	8	singta	singta	NOUN
ejpam-3947	269	9	a	a	DET
ejpam-3947	269	10	suvarnamani	suvarnamani	NOUN
ejpam-3947	269	11	and	and	CCONJ
ejpam-3947	269	12	s	s	AUX
ejpam-3947	269	13	chotchaisthit	chotchaisthit	VERB
ejpam-3947	269	14	.	.	PUNCT
ejpam-3947	270	1	on	on	ADP
ejpam-3947	270	2	two	two	NUM
ejpam-3947	270	3	diophantine	diophantine	NOUN
ejpam-3947	270	4	equations	equation	NOUN
ejpam-3947	270	5	4x	4x	NOUN
ejpam-3947	270	6	+	+	CCONJ
ejpam-3947	270	7	7y	7y	NOUN
ejpam-3947	270	8	=	=	SYM
ejpam-3947	270	9	z2	z2	PROPN
ejpam-3947	270	10	and	and	CCONJ
ejpam-3947	270	11	4x	4x	NUM
ejpam-3947	270	12	+	+	ADJ
ejpam-3947	270	13	11y	11y	NOUN
ejpam-3947	270	14	=	=	SYM
ejpam-3947	270	15	z2	z2	PROPN
ejpam-3947	270	16	.	.	PUNCT
ejpam-3947	271	1	sci	sci	PROPN
ejpam-3947	271	2	.	.	PROPN
ejpam-3947	271	3	technol	technol	PROPN
ejpam-3947	271	4	.	.	PUNCT
ejpam-3947	271	5	rmutt	rmutt	PROPN
ejpam-3947	271	6	j.	j.	PROPN
ejpam-3947	271	7	,	,	PUNCT
ejpam-3947	271	8	1:25–28	1:25–28	NUM
ejpam-3947	271	9	,	,	PUNCT
ejpam-3947	271	10	2011	2011	NUM
ejpam-3947	271	11	.	.	PUNCT
ejpam-3947	272	1	[	[	X
ejpam-3947	272	2	2	2	NUM
ejpam-3947	272	3	]	]	X
ejpam-3947	272	4	d	d	X
ejpam-3947	272	5	acu	acu	PROPN
ejpam-3947	272	6	.	.	PUNCT
ejpam-3947	273	1	on	on	ADP
ejpam-3947	273	2	a	a	DET
ejpam-3947	273	3	diophantine	diophantine	NOUN
ejpam-3947	273	4	equation	equation	NOUN
ejpam-3947	273	5	2x	2x	NUM
ejpam-3947	273	6	+	+	CCONJ
ejpam-3947	273	7	5y	5y	NOUN
ejpam-3947	273	8	=	=	SYM
ejpam-3947	273	9	z2	z2	PROPN
ejpam-3947	273	10	.	.	PUNCT
ejpam-3947	274	1	gen	gen	PROPN
ejpam-3947	274	2	.	.	PROPN
ejpam-3947	274	3	math	math	PROPN
ejpam-3947	274	4	.	.	PUNCT
ejpam-3947	274	5	,	,	PUNCT
ejpam-3947	274	6	15:145–148	15:145–148	PROPN
ejpam-3947	274	7	,	,	PUNCT
ejpam-3947	274	8	2007	2007	NUM
ejpam-3947	274	9	.	.	PUNCT
ejpam-3947	275	1	[	[	X
ejpam-3947	275	2	3	3	X
ejpam-3947	275	3	]	]	X
ejpam-3947	275	4	j	j	PROPN
ejpam-3947	275	5	b	b	PROPN
ejpam-3947	275	6	bacani	bacani	PROPN
ejpam-3947	275	7	and	and	CCONJ
ejpam-3947	275	8	j	j	PROPN
ejpam-3947	275	9	f	f	PROPN
ejpam-3947	275	10	t	t	PROPN
ejpam-3947	275	11	rabago	rabago	PROPN
ejpam-3947	275	12	.	.	PUNCT
ejpam-3947	276	1	the	the	DET
ejpam-3947	276	2	complete	complete	ADJ
ejpam-3947	276	3	set	set	NOUN
ejpam-3947	276	4	of	of	ADP
ejpam-3947	276	5	solutions	solution	NOUN
ejpam-3947	276	6	of	of	ADP
ejpam-3947	276	7	the	the	DET
ejpam-3947	276	8	diophantine	diophantine	NOUN
ejpam-3947	276	9	equation	equation	NOUN
ejpam-3947	276	10	px+qy	px+qy	ADJ
ejpam-3947	276	11	=	=	SYM
ejpam-3947	276	12	z2	z2	PROPN
ejpam-3947	276	13	for	for	ADP
ejpam-3947	276	14	twin	twin	ADJ
ejpam-3947	276	15	primes	prime	NOUN
ejpam-3947	276	16	p	p	NOUN
ejpam-3947	276	17	and	and	CCONJ
ejpam-3947	276	18	q.	q.	PROPN
ejpam-3947	276	19	int	int	PROPN
ejpam-3947	276	20	.	.	PUNCT
ejpam-3947	277	1	j.	j.	PROPN
ejpam-3947	277	2	pure	pure	PROPN
ejpam-3947	277	3	appl	appl	PROPN
ejpam-3947	277	4	.	.	PUNCT
ejpam-3947	277	5	math	math	PROPN
ejpam-3947	277	6	.	.	PUNCT
ejpam-3947	277	7	,	,	PUNCT
ejpam-3947	277	8	104:517–521	104:517–521	NUM
ejpam-3947	277	9	,	,	PUNCT
ejpam-3947	277	10	2015	2015	NUM
ejpam-3947	277	11	.	.	PUNCT
ejpam-3947	278	1	[	[	X
ejpam-3947	278	2	4	4	X
ejpam-3947	278	3	]	]	PUNCT
ejpam-3947	278	4	n	n	CCONJ
ejpam-3947	278	5	burshtein	burshtein	ADV
ejpam-3947	278	6	.	.	PUNCT
ejpam-3947	279	1	all	all	DET
ejpam-3947	279	2	the	the	DET
ejpam-3947	279	3	solutions	solution	NOUN
ejpam-3947	279	4	of	of	ADP
ejpam-3947	279	5	the	the	DET
ejpam-3947	279	6	diophantine	diophantine	NOUN
ejpam-3947	279	7	equation	equation	NOUN
ejpam-3947	279	8	px	px	X
ejpam-3947	279	9	+	+	CCONJ
ejpam-3947	279	10	(	(	PUNCT
ejpam-3947	279	11	p+	p+	NOUN
ejpam-3947	279	12	4)y	4)y	PROPN
ejpam-3947	279	13	=	=	SYM
ejpam-3947	279	14	z2	z2	PROPN
ejpam-3947	279	15	when	when	SCONJ
ejpam-3947	279	16	p	p	X
ejpam-3947	279	17	,	,	PUNCT
ejpam-3947	279	18	(	(	PUNCT
ejpam-3947	279	19	p	p	NOUN
ejpam-3947	279	20	+	+	NOUN
ejpam-3947	279	21	4	4	NUM
ejpam-3947	279	22	)	)	PUNCT
ejpam-3947	279	23	are	be	AUX
ejpam-3947	279	24	primes	prime	NOUN
ejpam-3947	279	25	and	and	CCONJ
ejpam-3947	279	26	x	x	PUNCT
ejpam-3947	280	1	+	+	CCONJ
ejpam-3947	280	2	y	y	NOUN
ejpam-3947	280	3	=	=	SYM
ejpam-3947	280	4	2	2	NUM
ejpam-3947	280	5	,	,	PUNCT
ejpam-3947	280	6	3	3	NUM
ejpam-3947	280	7	,	,	PUNCT
ejpam-3947	280	8	4	4	NUM
ejpam-3947	280	9	.	.	PUNCT
ejpam-3947	280	10	annals	annal	NOUN
ejpam-3947	280	11	of	of	ADP
ejpam-3947	280	12	pure	pure	ADJ
ejpam-3947	280	13	and	and	CCONJ
ejpam-3947	280	14	applied	applied	ADJ
ejpam-3947	280	15	mathematics	mathematic	NOUN
ejpam-3947	280	16	,	,	PUNCT
ejpam-3947	280	17	1:241–244	1:241–244	NOUN
ejpam-3947	280	18	,	,	PUNCT
ejpam-3947	280	19	2018	2018	NUM
ejpam-3947	280	20	.	.	PUNCT
ejpam-3947	281	1	[	[	X
ejpam-3947	281	2	5	5	NUM
ejpam-3947	281	3	]	]	X
ejpam-3947	281	4	d	d	PROPN
ejpam-3947	281	5	m	m	PROPN
ejpam-3947	281	6	burton	burton	PROPN
ejpam-3947	281	7	.	.	PUNCT
ejpam-3947	281	8	elementary	elementary	ADJ
ejpam-3947	281	9	number	number	NOUN
ejpam-3947	281	10	theory	theory	NOUN
ejpam-3947	281	11	.	.	PUNCT
ejpam-3947	282	1	allyn	allyn	PROPN
ejpam-3947	282	2	and	and	CCONJ
ejpam-3947	282	3	bacon	bacon	PROPN
ejpam-3947	282	4	,	,	PUNCT
ejpam-3947	282	5	inc	inc	PROPN
ejpam-3947	282	6	.	.	PROPN
ejpam-3947	282	7	,	,	PUNCT
ejpam-3947	282	8	boston	boston	PROPN
ejpam-3947	282	9	,	,	PUNCT
ejpam-3947	282	10	1980	1980	NUM
ejpam-3947	282	11	.	.	PUNCT
ejpam-3947	283	1	[	[	X
ejpam-3947	283	2	6	6	NUM
ejpam-3947	283	3	]	]	X
ejpam-3947	283	4	r	r	NOUN
ejpam-3947	283	5	dockan	dockan	PROPN
ejpam-3947	283	6	and	and	CCONJ
ejpam-3947	283	7	a	a	DET
ejpam-3947	283	8	pakapongpun	pakapongpun	NOUN
ejpam-3947	283	9	.	.	PUNCT
ejpam-3947	284	1	on	on	ADP
ejpam-3947	284	2	the	the	DET
ejpam-3947	284	3	diophantine	diophantine	NOUN
ejpam-3947	284	4	equation	equation	NOUN
ejpam-3947	284	5	px	px	X
ejpam-3947	284	6	+	+	CCONJ
ejpam-3947	284	7	(	(	PUNCT
ejpam-3947	284	8	p	p	X
ejpam-3947	284	9	+	+	NOUN
ejpam-3947	284	10	20)y	20)y	NUM
ejpam-3947	284	11	=	=	SYM
ejpam-3947	284	12	z2	z2	PROPN
ejpam-3947	284	13	,	,	PUNCT
ejpam-3947	284	14	where	where	SCONJ
ejpam-3947	284	15	p	p	PROPN
ejpam-3947	284	16	and	and	CCONJ
ejpam-3947	284	17	p+	p+	PROPN
ejpam-3947	284	18	20	20	NUM
ejpam-3947	284	19	are	be	AUX
ejpam-3947	284	20	primes	prime	NOUN
ejpam-3947	284	21	.	.	PUNCT
ejpam-3947	285	1	international	international	ADJ
ejpam-3947	285	2	journal	journal	PROPN
ejpam-3947	285	3	of	of	ADP
ejpam-3947	285	4	mathematics	mathematic	NOUN
ejpam-3947	285	5	and	and	CCONJ
ejpam-3947	285	6	computer	computer	NOUN
ejpam-3947	285	7	science	science	NOUN
ejpam-3947	285	8	,	,	PUNCT
ejpam-3947	285	9	16:179–183	16:179–183	NUM
ejpam-3947	285	10	,	,	PUNCT
ejpam-3947	285	11	2021	2021	NUM
ejpam-3947	285	12	.	.	PUNCT
ejpam-3947	286	1	[	[	X
ejpam-3947	286	2	7	7	NUM
ejpam-3947	286	3	]	]	X
ejpam-3947	286	4	r	r	NOUN
ejpam-3947	286	5	keskin	keskin	NOUN
ejpam-3947	286	6	.	.	PUNCT
ejpam-3947	287	1	solutions	solution	NOUN
ejpam-3947	287	2	of	of	ADP
ejpam-3947	287	3	some	some	DET
ejpam-3947	287	4	quadratic	quadratic	ADJ
ejpam-3947	287	5	diophantine	diophantine	NOUN
ejpam-3947	287	6	equations	equation	NOUN
ejpam-3947	287	7	.	.	PUNCT
ejpam-3947	288	1	computers	computer	NOUN
ejpam-3947	288	2	&	&	CCONJ
ejpam-3947	288	3	and	and	CCONJ
ejpam-3947	288	4	mathematics	mathematic	NOUN
ejpam-3947	288	5	with	with	ADP
ejpam-3947	288	6	applications	application	NOUN
ejpam-3947	288	7	,	,	PUNCT
ejpam-3947	288	8	18:97–103	18:97–103	NUM
ejpam-3947	288	9	,	,	PUNCT
ejpam-3947	288	10	2012	2012	NUM
ejpam-3947	288	11	.	.	PUNCT
ejpam-3947	289	1	[	[	X
ejpam-3947	289	2	8	8	NUM
ejpam-3947	289	3	]	]	X
ejpam-3947	289	4	m	m	VERB
ejpam-3947	289	5	g	g	NOUN
ejpam-3947	289	6	leu	leu	PROPN
ejpam-3947	289	7	and	and	CCONJ
ejpam-3947	289	8	g	g	PROPN
ejpam-3947	289	9	w	w	PROPN
ejpam-3947	289	10	li	li	PROPN
ejpam-3947	289	11	.	.	PUNCT
ejpam-3947	290	1	the	the	DET
ejpam-3947	290	2	diophantine	diophantine	NOUN
ejpam-3947	290	3	equation	equation	NOUN
ejpam-3947	290	4	2x2	2x2	NUM
ejpam-3947	290	5	+	+	CCONJ
ejpam-3947	290	6	1	1	NUM
ejpam-3947	290	7	=	=	SYM
ejpam-3947	290	8	3n	3n	NUM
ejpam-3947	290	9	.	.	PUNCT
ejpam-3947	291	1	proc	proc	NOUN
ejpam-3947	291	2	.	.	PUNCT
ejpam-3947	292	1	amer	amer	PROPN
ejpam-3947	292	2	.	.	PUNCT
ejpam-3947	292	3	math	math	PROPN
ejpam-3947	292	4	.	.	PUNCT
ejpam-3947	293	1	soc	soc	PROPN
ejpam-3947	293	2	.	.	PUNCT
ejpam-3947	293	3	,	,	PUNCT
ejpam-3947	293	4	131:3643–3645	131:3643–3645	NUM
ejpam-3947	293	5	,	,	PUNCT
ejpam-3947	293	6	2003	2003	NUM
ejpam-3947	293	7	.	.	PUNCT
ejpam-3947	294	1	[	[	X
ejpam-3947	294	2	9	9	NUM
ejpam-3947	294	3	]	]	PUNCT
ejpam-3947	294	4	w	w	NOUN
ejpam-3947	294	5	ljunggren	ljunggren	PROPN
ejpam-3947	294	6	.	.	PUNCT
ejpam-3947	295	1	some	some	DET
ejpam-3947	295	2	theorems	theorem	NOUN
ejpam-3947	295	3	on	on	ADP
ejpam-3947	295	4	indeterminate	indeterminate	ADJ
ejpam-3947	295	5	equations	equation	NOUN
ejpam-3947	295	6	of	of	ADP
ejpam-3947	295	7	the	the	DET
ejpam-3947	295	8	form	form	NOUN
ejpam-3947	296	1	xn−1	xn−1	PROPN
ejpam-3947	296	2	x−1	x−1	PROPN
ejpam-3947	296	3	=	=	PROPN
ejpam-3947	296	4	yq	yq	PROPN
ejpam-3947	296	5	.	.	PUNCT
ejpam-3947	297	1	(	(	PUNCT
ejpam-3947	297	2	norwegian	norwegian	PROPN
ejpam-3947	297	3	)	)	PUNCT
ejpam-3947	297	4	norsk	norsk	PROPN
ejpam-3947	297	5	mat	mat	PROPN
ejpam-3947	297	6	.	.	PUNCT
ejpam-3947	297	7	tidsskr	tidsskr	PROPN
ejpam-3947	297	8	.	.	PROPN
ejpam-3947	297	9	,	,	PUNCT
ejpam-3947	297	10	25:17–20	25:17–20	NUM
ejpam-3947	297	11	,	,	PUNCT
ejpam-3947	297	12	1943	1943	NUM
ejpam-3947	297	13	.	.	PUNCT
ejpam-3947	298	1	[	[	X
ejpam-3947	298	2	10	10	NUM
ejpam-3947	298	3	]	]	X
ejpam-3947	298	4	f	f	PROPN
ejpam-3947	298	5	luca	luca	PROPN
ejpam-3947	298	6	and	and	CCONJ
ejpam-3947	298	7	g	g	PROPN
ejpam-3947	298	8	soydan	soydan	NOUN
ejpam-3947	298	9	.	.	PUNCT
ejpam-3947	299	1	on	on	ADP
ejpam-3947	299	2	the	the	DET
ejpam-3947	299	3	diophantine	diophantine	NOUN
ejpam-3947	299	4	equation	equation	NOUN
ejpam-3947	299	5	2	2	NUM
ejpam-3947	299	6	m	m	NOUN
ejpam-3947	299	7	+	+	X
ejpam-3947	299	8	nx2	nx2	PROPN
ejpam-3947	299	9	=	=	SYM
ejpam-3947	299	10	yn	yn	PROPN
ejpam-3947	299	11	.	.	PROPN
ejpam-3947	299	12	journal	journal	PROPN
ejpam-3947	299	13	of	of	ADP
ejpam-3947	299	14	number	number	NOUN
ejpam-3947	299	15	theory	theory	NOUN
ejpam-3947	299	16	,	,	PUNCT
ejpam-3947	299	17	132:2604–2609	132:2604–2609	NUM
ejpam-3947	299	18	,	,	PUNCT
ejpam-3947	299	19	2012	2012	NUM
ejpam-3947	299	20	.	.	PUNCT
ejpam-3947	300	1	[	[	X
ejpam-3947	300	2	11	11	NUM
ejpam-3947	300	3	]	]	X
ejpam-3947	300	4	r	r	NOUN
ejpam-3947	300	5	j	j	PROPN
ejpam-3947	300	6	s	s	X
ejpam-3947	300	7	mina	mina	PROPN
ejpam-3947	300	8	and	and	CCONJ
ejpam-3947	300	9	j	j	PROPN
ejpam-3947	300	10	b	b	PROPN
ejpam-3947	300	11	bacani	bacani	PROPN
ejpam-3947	300	12	.	.	PUNCT
ejpam-3947	301	1	non	non	ADJ
ejpam-3947	301	2	-	-	NOUN
ejpam-3947	301	3	existence	existence	NOUN
ejpam-3947	301	4	of	of	ADP
ejpam-3947	301	5	solutions	solution	NOUN
ejpam-3947	301	6	of	of	ADP
ejpam-3947	301	7	diophantine	diophantine	NOUN
ejpam-3947	301	8	equations	equation	NOUN
ejpam-3947	301	9	of	of	ADP
ejpam-3947	301	10	the	the	DET
ejpam-3947	301	11	form	form	NOUN
ejpam-3947	301	12	px	px	X
ejpam-3947	301	13	+	+	CCONJ
ejpam-3947	301	14	qy	qy	NOUN
ejpam-3947	301	15	=	=	SYM
ejpam-3947	301	16	z2n	z2n	PROPN
ejpam-3947	301	17	.	.	PUNCT
ejpam-3947	302	1	mathematics	mathematic	NOUN
ejpam-3947	302	2	and	and	CCONJ
ejpam-3947	302	3	statistics	statistic	NOUN
ejpam-3947	302	4	,	,	PUNCT
ejpam-3947	302	5	7:78–81	7:78–81	NUM
ejpam-3947	302	6	,	,	PUNCT
ejpam-3947	302	7	2019	2019	NUM
ejpam-3947	302	8	.	.	PUNCT
ejpam-3947	303	1	[	[	X
ejpam-3947	303	2	12	12	NUM
ejpam-3947	303	3	]	]	X
ejpam-3947	303	4	f	f	PROPN
ejpam-3947	303	5	s	s	PROPN
ejpam-3947	303	6	abu	abu	PROPN
ejpam-3947	303	7	muriefah	muriefah	PROPN
ejpam-3947	303	8	and	and	CCONJ
ejpam-3947	303	9	a	a	DET
ejpam-3947	303	10	al	al	PROPN
ejpam-3947	303	11	-	-	PUNCT
ejpam-3947	303	12	rashed	rashe	VERB
ejpam-3947	303	13	.	.	PUNCT
ejpam-3947	304	1	on	on	ADP
ejpam-3947	304	2	the	the	DET
ejpam-3947	304	3	diophantine	diophantine	NOUN
ejpam-3947	304	4	equation	equation	NOUN
ejpam-3947	304	5	x2−4pm	x2−4pm	NOUN
ejpam-3947	304	6	=	=	SYM
ejpam-3947	304	7	±yn	±yn	PROPN
ejpam-3947	304	8	.	.	PUNCT
ejpam-3947	305	1	arab	arab	PROPN
ejpam-3947	305	2	journal	journal	PROPN
ejpam-3947	305	3	of	of	ADP
ejpam-3947	305	4	mathematical	mathematical	ADJ
ejpam-3947	305	5	sciences	science	NOUN
ejpam-3947	305	6	,	,	PUNCT
ejpam-3947	305	7	18:97–103	18:97–103	NUM
ejpam-3947	305	8	,	,	PUNCT
ejpam-3947	305	9	2012	2012	NUM
ejpam-3947	305	10	.	.	PUNCT
ejpam-3947	306	1	[	[	X
ejpam-3947	306	2	13	13	NUM
ejpam-3947	306	3	]	]	X
ejpam-3947	306	4	f	f	PROPN
ejpam-3947	306	5	neres	nere	NOUN
ejpam-3947	306	6	.	.	PUNCT
ejpam-3947	307	1	on	on	ADP
ejpam-3947	307	2	the	the	DET
ejpam-3947	307	3	solvability	solvability	NOUN
ejpam-3947	307	4	of	of	ADP
ejpam-3947	307	5	the	the	DET
ejpam-3947	307	6	diophantine	diophantine	NOUN
ejpam-3947	307	7	equation	equation	NOUN
ejpam-3947	307	8	px	px	X
ejpam-3947	307	9	+	+	CCONJ
ejpam-3947	307	10	(	(	PUNCT
ejpam-3947	307	11	p	p	X
ejpam-3947	307	12	+	+	NUM
ejpam-3947	307	13	8)y	8)y	NOUN
ejpam-3947	307	14	=	=	SYM
ejpam-3947	307	15	z2	z2	NOUN
ejpam-3947	307	16	when	when	SCONJ
ejpam-3947	307	17	p	p	PROPN
ejpam-3947	307	18	>	>	X
ejpam-3947	307	19	3	3	NUM
ejpam-3947	307	20	and	and	CCONJ
ejpam-3947	307	21	p	p	PRON
ejpam-3947	307	22	+	+	NOUN
ejpam-3947	307	23	8	8	NUM
ejpam-3947	307	24	are	be	AUX
ejpam-3947	307	25	primes	prime	NOUN
ejpam-3947	307	26	.	.	PUNCT
ejpam-3947	308	1	annals	annal	NOUN
ejpam-3947	308	2	of	of	ADP
ejpam-3947	308	3	pure	pure	ADJ
ejpam-3947	308	4	and	and	CCONJ
ejpam-3947	308	5	applied	applied	ADJ
ejpam-3947	308	6	mathematics	mathematic	NOUN
ejpam-3947	308	7	,	,	PUNCT
ejpam-3947	308	8	18:179–183	18:179–183	NUM
ejpam-3947	308	9	,	,	PUNCT
ejpam-3947	308	10	2018	2018	NUM
ejpam-3947	308	11	.	.	PUNCT
ejpam-3947	309	1	[	[	X
ejpam-3947	309	2	14	14	NUM
ejpam-3947	309	3	]	]	X
ejpam-3947	309	4	j	j	PROPN
ejpam-3947	309	5	f	f	PROPN
ejpam-3947	309	6	t	t	PROPN
ejpam-3947	309	7	rabago	rabago	PROPN
ejpam-3947	309	8	.	.	PUNCT
ejpam-3947	310	1	a	a	DET
ejpam-3947	310	2	note	note	NOUN
ejpam-3947	310	3	on	on	ADP
ejpam-3947	310	4	two	two	NUM
ejpam-3947	310	5	diophantine	diophantine	NOUN
ejpam-3947	310	6	equations	equation	NOUN
ejpam-3947	310	7	17x+19y	17x+19y	NUM
ejpam-3947	310	8	=	=	SYM
ejpam-3947	310	9	z2	z2	PROPN
ejpam-3947	310	10	and	and	CCONJ
ejpam-3947	310	11	71x+73y	71x+73y	NUM
ejpam-3947	310	12	=	=	SYM
ejpam-3947	310	13	z2	z2	PROPN
ejpam-3947	310	14	.	.	PUNCT
ejpam-3947	310	15	math	math	PROPN
ejpam-3947	310	16	.	.	PUNCT
ejpam-3947	311	1	j.	j.	PROPN
ejpam-3947	311	2	interdisciplinary	interdisciplinary	PROPN
ejpam-3947	311	3	sci	sci	PROPN
ejpam-3947	311	4	.	.	PROPN
ejpam-3947	311	5	,	,	PUNCT
ejpam-3947	311	6	2:19–24	2:19–24	NUM
ejpam-3947	311	7	,	,	PUNCT
ejpam-3947	311	8	2013	2013	NUM
ejpam-3947	311	9	.	.	PUNCT
ejpam-3947	312	1	[	[	X
ejpam-3947	312	2	15	15	NUM
ejpam-3947	312	3	]	]	X
ejpam-3947	312	4	j	j	PROPN
ejpam-3947	312	5	f	f	PROPN
ejpam-3947	312	6	t	t	PROPN
ejpam-3947	312	7	rabago	rabago	PROPN
ejpam-3947	312	8	.	.	PUNCT
ejpam-3947	313	1	more	more	ADJ
ejpam-3947	313	2	on	on	ADP
ejpam-3947	313	3	diophantine	diophantine	NOUN
ejpam-3947	313	4	equations	equation	NOUN
ejpam-3947	313	5	of	of	ADP
ejpam-3947	313	6	type	type	NOUN
ejpam-3947	313	7	px	px	PROPN
ejpam-3947	313	8	+	+	CCONJ
ejpam-3947	313	9	qy	qy	NOUN
ejpam-3947	313	10	=	=	PROPN
ejpam-3947	313	11	z2	z2	PROPN
ejpam-3947	313	12	.	.	PUNCT
ejpam-3947	313	13	int	int	PROPN
ejpam-3947	313	14	.	.	PUNCT
ejpam-3947	314	1	j.	j.	PROPN
ejpam-3947	314	2	math	math	PROPN
ejpam-3947	314	3	.	.	PUNCT
ejpam-3947	315	1	sci	sci	PROPN
ejpam-3947	315	2	.	.	PROPN
ejpam-3947	315	3	comp	comp	PROPN
ejpam-3947	315	4	.	.	PUNCT
ejpam-3947	315	5	,	,	PUNCT
ejpam-3947	315	6	3:15–16	3:15–16	NUM
ejpam-3947	315	7	,	,	PUNCT
ejpam-3947	315	8	2013	2013	NUM
ejpam-3947	315	9	.	.	PUNCT
ejpam-3947	316	1	references	reference	NOUN
ejpam-3947	316	2	479	479	NUM
ejpam-3947	317	1	[	[	X
ejpam-3947	317	2	16	16	NUM
ejpam-3947	317	3	]	]	X
ejpam-3947	317	4	j	j	PROPN
ejpam-3947	317	5	f	f	PROPN
ejpam-3947	317	6	t	t	PROPN
ejpam-3947	317	7	rabago	rabago	PROPN
ejpam-3947	317	8	.	.	PUNCT
ejpam-3947	318	1	on	on	ADP
ejpam-3947	318	2	an	an	DET
ejpam-3947	318	3	open	open	ADJ
ejpam-3947	318	4	problem	problem	NOUN
ejpam-3947	318	5	by	by	ADP
ejpam-3947	318	6	b.	b.	PROPN
ejpam-3947	318	7	sroysang	sroysang	PROPN
ejpam-3947	318	8	.	.	PROPN
ejpam-3947	318	9	konuralp	konuralp	PROPN
ejpam-3947	318	10	j.	j.	PROPN
ejpam-3947	318	11	math	math	PROPN
ejpam-3947	318	12	.	.	PUNCT
ejpam-3947	318	13	,	,	PUNCT
ejpam-3947	318	14	1:30–32	1:30–32	NUM
ejpam-3947	318	15	,	,	PUNCT
ejpam-3947	318	16	2013	2013	NUM
ejpam-3947	318	17	.	.	PUNCT
ejpam-3947	319	1	[	[	X
ejpam-3947	319	2	17	17	NUM
ejpam-3947	319	3	]	]	X
ejpam-3947	319	4	j	j	PROPN
ejpam-3947	319	5	f	f	PROPN
ejpam-3947	319	6	t	t	PROPN
ejpam-3947	319	7	rabago	rabago	PROPN
ejpam-3947	319	8	.	.	PUNCT
ejpam-3947	320	1	on	on	ADP
ejpam-3947	320	2	two	two	NUM
ejpam-3947	320	3	diophantine	diophantine	NOUN
ejpam-3947	320	4	equations	equation	NOUN
ejpam-3947	320	5	3x	3x	NUM
ejpam-3947	320	6	+	+	CCONJ
ejpam-3947	320	7	19y	19y	NOUN
ejpam-3947	320	8	=	=	SYM
ejpam-3947	320	9	z2	z2	PROPN
ejpam-3947	320	10	and	and	CCONJ
ejpam-3947	320	11	3x	3x	NUM
ejpam-3947	320	12	+	+	NUM
ejpam-3947	320	13	91y	91y	NOUN
ejpam-3947	320	14	=	=	SYM
ejpam-3947	320	15	z2	z2	PROPN
ejpam-3947	320	16	.	.	PUNCT
ejpam-3947	320	17	int	int	PROPN
ejpam-3947	320	18	.	.	PUNCT
ejpam-3947	321	1	j.	j.	PROPN
ejpam-3947	321	2	math	math	PROPN
ejpam-3947	321	3	.	.	PUNCT
ejpam-3947	322	1	sci	sci	PROPN
ejpam-3947	322	2	.	.	PROPN
ejpam-3947	322	3	comp	comp	PROPN
ejpam-3947	322	4	.	.	PUNCT
ejpam-3947	322	5	,	,	PUNCT
ejpam-3947	322	6	3:28–29	3:28–29	PROPN
ejpam-3947	322	7	,	,	PUNCT
ejpam-3947	322	8	2013	2013	NUM
ejpam-3947	322	9	.	.	PUNCT
ejpam-3947	323	1	[	[	X
ejpam-3947	323	2	18	18	NUM
ejpam-3947	323	3	]	]	X
ejpam-3947	323	4	k	k	PROPN
ejpam-3947	323	5	h	h	PROPN
ejpam-3947	323	6	rosen	rosen	PROPN
ejpam-3947	323	7	.	.	PUNCT
ejpam-3947	324	1	elementary	elementary	ADJ
ejpam-3947	324	2	number	number	NOUN
ejpam-3947	324	3	theory	theory	NOUN
ejpam-3947	324	4	and	and	CCONJ
ejpam-3947	324	5	its	its	PRON
ejpam-3947	324	6	applications	application	NOUN
ejpam-3947	324	7	.	.	PUNCT
ejpam-3947	325	1	pearson	pearson	PROPN
ejpam-3947	325	2	-	-	PUNCT
ejpam-3947	325	3	addison	addison	PROPN
ejpam-3947	325	4	wesley	wesley	PROPN
ejpam-3947	325	5	,	,	PUNCT
ejpam-3947	325	6	new	new	PROPN
ejpam-3947	325	7	york	york	PROPN
ejpam-3947	325	8	,	,	PUNCT
ejpam-3947	325	9	2005	2005	NUM
ejpam-3947	325	10	.	.	PUNCT
ejpam-3947	326	1	[	[	X
ejpam-3947	326	2	19	19	NUM
ejpam-3947	326	3	]	]	SYM
ejpam-3947	326	4	b	b	X
ejpam-3947	326	5	sroysang	sroysang	PROPN
ejpam-3947	326	6	.	.	PUNCT
ejpam-3947	327	1	more	more	ADJ
ejpam-3947	327	2	on	on	ADP
ejpam-3947	327	3	the	the	DET
ejpam-3947	327	4	diophantine	diophantine	NOUN
ejpam-3947	327	5	equation	equation	NOUN
ejpam-3947	327	6	8x	8x	NOUN
ejpam-3947	327	7	+	+	CCONJ
ejpam-3947	327	8	19y	19y	NOUN
ejpam-3947	327	9	=	=	SYM
ejpam-3947	327	10	z2	z2	PROPN
ejpam-3947	327	11	.	.	PUNCT
ejpam-3947	328	1	int	int	PROPN
ejpam-3947	328	2	.	.	PUNCT
ejpam-3947	329	1	j.	j.	PROPN
ejpam-3947	329	2	pure	pure	PROPN
ejpam-3947	329	3	appl	appl	PROPN
ejpam-3947	329	4	.	.	PUNCT
ejpam-3947	329	5	math	math	PROPN
ejpam-3947	329	6	.	.	PUNCT
ejpam-3947	329	7	,	,	PUNCT
ejpam-3947	330	1	81:601–604	81:601–604	PROPN
ejpam-3947	330	2	,	,	PUNCT
ejpam-3947	330	3	2012	2012	NUM
ejpam-3947	330	4	.	.	PUNCT
ejpam-3947	331	1	[	[	X
ejpam-3947	331	2	20	20	NUM
ejpam-3947	331	3	]	]	SYM
ejpam-3947	331	4	b	b	X
ejpam-3947	331	5	sroysang	sroysang	PROPN
ejpam-3947	331	6	.	.	PUNCT
ejpam-3947	332	1	on	on	ADP
ejpam-3947	332	2	the	the	DET
ejpam-3947	332	3	diophantine	diophantine	NOUN
ejpam-3947	332	4	equation	equation	NOUN
ejpam-3947	332	5	3x	3x	NUM
ejpam-3947	332	6	+	+	CCONJ
ejpam-3947	332	7	5y	5y	NOUN
ejpam-3947	332	8	=	=	SYM
ejpam-3947	332	9	z2	z2	PROPN
ejpam-3947	332	10	.	.	PUNCT
ejpam-3947	333	1	int	int	PROPN
ejpam-3947	333	2	.	.	PUNCT
ejpam-3947	334	1	j.	j.	PROPN
ejpam-3947	334	2	pure	pure	PROPN
ejpam-3947	334	3	appl	appl	PROPN
ejpam-3947	334	4	.	.	PUNCT
ejpam-3947	334	5	math	math	PROPN
ejpam-3947	334	6	.	.	PUNCT
ejpam-3947	334	7	,	,	PUNCT
ejpam-3947	334	8	81:605–608	81:605–608	NUM
ejpam-3947	334	9	,	,	PUNCT
ejpam-3947	334	10	2012	2012	NUM
ejpam-3947	334	11	.	.	PUNCT