id	sid	tid	token	lemma	pos
ejpam-2333	1	1	compile	compile	VERB
ejpam-2333	1	2	/	/	SYM
ejpam-2333	1	3	output.dvi	output.dvi	NOUN
ejpam-2333	1	4	on	on	ADP
ejpam-2333	1	5	the	the	DET
ejpam-2333	1	6	exponential	exponential	ADJ
ejpam-2333	1	7	diophantine	diophantine	NOUN
ejpam-2333	1	8	equation	equation	NOUN
ejpam-2333	1	9	(	(	PUNCT
ejpam-2333	1	10	mpq	mpq	X
ejpam-2333	1	11	)	)	PUNCT
ejpam-2333	1	12	x	x	PUNCT
ejpam-2333	2	1	+	+	PUNCT
ejpam-2333	2	2	(	(	PUNCT
ejpam-2333	2	3	mpq	mpq	X
ejpam-2333	2	4	+	+	CCONJ
ejpam-2333	2	5	1)y	1)y	NUM
ejpam-2333	2	6	=	=	SYM
ejpam-2333	2	7	z2	z2	ADJ
ejpam-2333	2	8	azizul	azizul	ADJ
ejpam-2333	2	9	hoque	hoque	NOUN
ejpam-2333	2	10	department	department	PROPN
ejpam-2333	2	11	of	of	ADP
ejpam-2333	2	12	mathematics	mathematics	PROPN
ejpam-2333	2	13	,	,	PUNCT
ejpam-2333	2	14	gauhati	gauhati	PROPN
ejpam-2333	2	15	university	university	PROPN
ejpam-2333	2	16	,	,	PUNCT
ejpam-2333	2	17	guwahati	guwahati	PROPN
ejpam-2333	2	18	,	,	PUNCT
ejpam-2333	2	19	india-781014	india-781014	NOUN
ejpam-2333	2	20	abstract	abstract	NOUN
ejpam-2333	2	21	.	.	PUNCT
ejpam-2333	3	1	in	in	ADP
ejpam-2333	3	2	this	this	DET
ejpam-2333	3	3	paper	paper	NOUN
ejpam-2333	3	4	,	,	PUNCT
ejpam-2333	3	5	we	we	PRON
ejpam-2333	3	6	consider	consider	VERB
ejpam-2333	3	7	the	the	DET
ejpam-2333	3	8	number	number	NOUN
ejpam-2333	3	9	mpq	mpq	NOUN
ejpam-2333	4	1	=	=	SYM
ejpam-2333	4	2	pq−1	pq−1	PROPN
ejpam-2333	4	3	,	,	PUNCT
ejpam-2333	4	4	where	where	SCONJ
ejpam-2333	4	5	p	p	NOUN
ejpam-2333	4	6	>	>	X
ejpam-2333	4	7	0	0	PUNCT
ejpam-2333	4	8	and	and	CCONJ
ejpam-2333	4	9	q	q	ADJ
ejpam-2333	4	10	>	>	X
ejpam-2333	4	11	1	1	NUM
ejpam-2333	4	12	are	be	AUX
ejpam-2333	4	13	integers	integer	NOUN
ejpam-2333	4	14	,	,	PUNCT
ejpam-2333	4	15	and	and	CCONJ
ejpam-2333	4	16	the	the	DET
ejpam-2333	4	17	exponential	exponential	ADJ
ejpam-2333	4	18	diophantine	diophantine	NOUN
ejpam-2333	4	19	equation	equation	NOUN
ejpam-2333	4	20	(	(	PUNCT
ejpam-2333	4	21	mpq	mpq	X
ejpam-2333	4	22	)	)	PUNCT
ejpam-2333	4	23	x	x	PUNCT
ejpam-2333	5	1	+	+	ADJ
ejpam-2333	5	2	(	(	PUNCT
ejpam-2333	5	3	mpq+1)y	mpq+1)y	NOUN
ejpam-2333	5	4	=	=	SYM
ejpam-2333	5	5	z2	z2	PROPN
ejpam-2333	5	6	,	,	PUNCT
ejpam-2333	5	7	where	where	SCONJ
ejpam-2333	5	8	x	x	X
ejpam-2333	5	9	,	,	PUNCT
ejpam-2333	5	10	y	y	PROPN
ejpam-2333	5	11	and	and	CCONJ
ejpam-2333	5	12	z	z	NOUN
ejpam-2333	5	13	are	be	AUX
ejpam-2333	5	14	positive	positive	ADJ
ejpam-2333	5	15	integers	integer	NOUN
ejpam-2333	5	16	.	.	PUNCT
ejpam-2333	6	1	we	we	PRON
ejpam-2333	6	2	find	find	VERB
ejpam-2333	6	3	the	the	DET
ejpam-2333	6	4	solutions	solution	NOUN
ejpam-2333	6	5	to	to	ADP
ejpam-2333	6	6	the	the	DET
ejpam-2333	6	7	title	title	NOUN
ejpam-2333	6	8	equation	equation	NOUN
ejpam-2333	6	9	expect	expect	VERB
ejpam-2333	6	10	the	the	DET
ejpam-2333	6	11	case	case	NOUN
ejpam-2333	6	12	only	only	ADV
ejpam-2333	6	13	when	when	SCONJ
ejpam-2333	6	14	both	both	DET
ejpam-2333	6	15	p	p	NOUN
ejpam-2333	6	16	and	and	CCONJ
ejpam-2333	6	17	y	y	PROPN
ejpam-2333	6	18	are	be	AUX
ejpam-2333	6	19	odd	odd	ADJ
ejpam-2333	6	20	integers	integer	NOUN
ejpam-2333	6	21	.	.	PUNCT
ejpam-2333	7	1	2010	2010	NUM
ejpam-2333	7	2	mathematics	mathematic	NOUN
ejpam-2333	7	3	subject	subject	NOUN
ejpam-2333	7	4	classifications	classification	NOUN
ejpam-2333	7	5	:	:	PUNCT
ejpam-2333	7	6	11d61	11d61	NUM
ejpam-2333	7	7	;	;	PUNCT
ejpam-2333	7	8	11d41	11d41	NUM
ejpam-2333	7	9	key	key	ADJ
ejpam-2333	7	10	words	word	NOUN
ejpam-2333	7	11	and	and	CCONJ
ejpam-2333	7	12	phrases	phrase	NOUN
ejpam-2333	7	13	:	:	PUNCT
ejpam-2333	7	14	exponential	exponential	ADJ
ejpam-2333	7	15	diophantine	diophantine	NOUN
ejpam-2333	7	16	equation	equation	NOUN
ejpam-2333	7	17	1	1	NUM
ejpam-2333	7	18	.	.	PUNCT
ejpam-2333	8	1	introduction	introduction	NOUN
ejpam-2333	8	2	sroysang	sroysang	PROPN
ejpam-2333	9	1	[	[	X
ejpam-2333	9	2	2	2	NUM
ejpam-2333	9	3	]	]	PUNCT
ejpam-2333	9	4	established	establish	VERB
ejpam-2333	9	5	that	that	SCONJ
ejpam-2333	9	6	the	the	DET
ejpam-2333	9	7	exponential	exponential	ADJ
ejpam-2333	9	8	diophantine	diophantine	NOUN
ejpam-2333	9	9	equation	equation	NOUN
ejpam-2333	9	10	31x+32y	31x+32y	NUM
ejpam-2333	9	11	=	=	SYM
ejpam-2333	9	12	z2	z2	PROPN
ejpam-2333	9	13	has	have	VERB
ejpam-2333	9	14	no	no	DET
ejpam-2333	9	15	non	non	ADJ
ejpam-2333	9	16	-	-	ADJ
ejpam-2333	9	17	negative	negative	ADJ
ejpam-2333	9	18	solution	solution	NOUN
ejpam-2333	9	19	.	.	PUNCT
ejpam-2333	10	1	recently	recently	ADV
ejpam-2333	10	2	,	,	PUNCT
ejpam-2333	10	3	sroysang	sroysang	X
ejpam-2333	11	1	[	[	X
ejpam-2333	11	2	3	3	NUM
ejpam-2333	11	3	]	]	PUNCT
ejpam-2333	11	4	also	also	ADV
ejpam-2333	11	5	showed	show	VERB
ejpam-2333	11	6	that	that	SCONJ
ejpam-2333	11	7	the	the	DET
ejpam-2333	11	8	exponential	exponential	ADJ
ejpam-2333	11	9	diophantine	diophantine	NOUN
ejpam-2333	11	10	equation	equation	NOUN
ejpam-2333	11	11	7x+8y	7x+8y	NUM
ejpam-2333	11	12	=	=	SYM
ejpam-2333	11	13	z2	z2	PROPN
ejpam-2333	11	14	has	have	VERB
ejpam-2333	11	15	only	only	ADV
ejpam-2333	11	16	one	one	NUM
ejpam-2333	11	17	solution	solution	NOUN
ejpam-2333	11	18	,	,	PUNCT
ejpam-2333	11	19	that	that	ADV
ejpam-2333	11	20	is	is	ADV
ejpam-2333	11	21	(	(	PUNCT
ejpam-2333	11	22	x	x	INTJ
ejpam-2333	11	23	,	,	PUNCT
ejpam-2333	11	24	y	y	PROPN
ejpam-2333	11	25	,	,	PUNCT
ejpam-2333	11	26	z	z	NOUN
ejpam-2333	11	27	)	)	PUNCT
ejpam-2333	11	28	=	=	SYM
ejpam-2333	11	29	(	(	PUNCT
ejpam-2333	11	30	0,1,3	0,1,3	PROPN
ejpam-2333	11	31	)	)	PUNCT
ejpam-2333	11	32	.	.	PUNCT
ejpam-2333	12	1	sroysang	sroysang	PROPN
ejpam-2333	13	1	[	[	X
ejpam-2333	13	2	3	3	NUM
ejpam-2333	13	3	]	]	PUNCT
ejpam-2333	13	4	introduced	introduce	VERB
ejpam-2333	13	5	an	an	DET
ejpam-2333	13	6	open	open	ADJ
ejpam-2333	13	7	problem	problem	NOUN
ejpam-2333	13	8	regarding	regard	VERB
ejpam-2333	13	9	the	the	DET
ejpam-2333	13	10	set	set	NOUN
ejpam-2333	13	11	of	of	ADP
ejpam-2333	13	12	all	all	DET
ejpam-2333	13	13	solutions	solution	NOUN
ejpam-2333	13	14	(	(	PUNCT
ejpam-2333	13	15	x	x	X
ejpam-2333	13	16	,	,	PUNCT
ejpam-2333	13	17	y	y	PROPN
ejpam-2333	13	18	,	,	PUNCT
ejpam-2333	13	19	z	z	NOUN
ejpam-2333	13	20	)	)	PUNCT
ejpam-2333	13	21	for	for	ADP
ejpam-2333	13	22	the	the	DET
ejpam-2333	13	23	exponential	exponential	ADJ
ejpam-2333	13	24	diophantine	diophantine	NOUN
ejpam-2333	13	25	equation	equation	NOUN
ejpam-2333	13	26	px	px	X
ejpam-2333	13	27	+	+	CCONJ
ejpam-2333	13	28	(	(	PUNCT
ejpam-2333	13	29	p+	p+	NOUN
ejpam-2333	13	30	1)y	1)y	NUM
ejpam-2333	13	31	=	=	SYM
ejpam-2333	13	32	z2	z2	PROPN
ejpam-2333	13	33	,	,	PUNCT
ejpam-2333	13	34	where	where	SCONJ
ejpam-2333	13	35	x	x	X
ejpam-2333	13	36	,	,	PUNCT
ejpam-2333	13	37	y	y	PROPN
ejpam-2333	13	38	and	and	CCONJ
ejpam-2333	13	39	z	z	PROPN
ejpam-2333	13	40	are	be	AUX
ejpam-2333	13	41	non	non	ADJ
ejpam-2333	13	42	-	-	ADJ
ejpam-2333	13	43	negative	negative	ADJ
ejpam-2333	13	44	integers	integer	NOUN
ejpam-2333	13	45	.	.	PUNCT
ejpam-2333	14	1	in	in	ADP
ejpam-2333	14	2	this	this	DET
ejpam-2333	14	3	paper	paper	NOUN
ejpam-2333	14	4	,	,	PUNCT
ejpam-2333	14	5	we	we	PRON
ejpam-2333	14	6	consider	consider	VERB
ejpam-2333	14	7	the	the	DET
ejpam-2333	14	8	number	number	NOUN
ejpam-2333	14	9	mpq	mpq	NOUN
ejpam-2333	15	1	=	=	SYM
ejpam-2333	15	2	pq	pq	NOUN
ejpam-2333	15	3	−	−	NOUN
ejpam-2333	15	4	1	1	NUM
ejpam-2333	15	5	,	,	PUNCT
ejpam-2333	15	6	where	where	SCONJ
ejpam-2333	15	7	p	p	NOUN
ejpam-2333	15	8	>	>	X
ejpam-2333	15	9	0	0	PUNCT
ejpam-2333	16	1	and	and	CCONJ
ejpam-2333	16	2	q	q	ADJ
ejpam-2333	16	3	>	>	X
ejpam-2333	16	4	1	1	NUM
ejpam-2333	16	5	are	be	AUX
ejpam-2333	16	6	integers	integer	NOUN
ejpam-2333	16	7	,	,	PUNCT
ejpam-2333	16	8	and	and	CCONJ
ejpam-2333	16	9	the	the	DET
ejpam-2333	16	10	exponential	exponential	ADJ
ejpam-2333	16	11	diophantine	diophantine	NOUN
ejpam-2333	16	12	equation	equation	NOUN
ejpam-2333	16	13	(	(	PUNCT
ejpam-2333	16	14	mpq	mpq	X
ejpam-2333	16	15	)	)	PUNCT
ejpam-2333	16	16	x	x	PUNCT
ejpam-2333	17	1	+	+	PUNCT
ejpam-2333	17	2	(	(	PUNCT
ejpam-2333	17	3	mpq	mpq	X
ejpam-2333	17	4	+	+	NUM
ejpam-2333	17	5	1)y	1)y	NUM
ejpam-2333	17	6	=	=	SYM
ejpam-2333	17	7	z2	z2	PROPN
ejpam-2333	17	8	,	,	PUNCT
ejpam-2333	17	9	where	where	SCONJ
ejpam-2333	17	10	x	x	X
ejpam-2333	17	11	,	,	PUNCT
ejpam-2333	17	12	y	y	PROPN
ejpam-2333	17	13	and	and	CCONJ
ejpam-2333	17	14	z	z	NOUN
ejpam-2333	17	15	are	be	AUX
ejpam-2333	17	16	positive	positive	ADJ
ejpam-2333	17	17	integers	integer	NOUN
ejpam-2333	17	18	.	.	PUNCT
ejpam-2333	18	1	we	we	PRON
ejpam-2333	18	2	show	show	VERB
ejpam-2333	18	3	that	that	SCONJ
ejpam-2333	18	4	(	(	PUNCT
ejpam-2333	18	5	mpq	mpq	X
ejpam-2333	18	6	,	,	PUNCT
ejpam-2333	18	7	x	x	SYM
ejpam-2333	18	8	,	,	PUNCT
ejpam-2333	18	9	y	y	PROPN
ejpam-2333	18	10	,	,	PUNCT
ejpam-2333	18	11	z	z	NOUN
ejpam-2333	18	12	)	)	PUNCT
ejpam-2333	18	13	=	=	SYM
ejpam-2333	18	14	(	(	PUNCT
ejpam-2333	18	15	7,0,1,3	7,0,1,3	NUM
ejpam-2333	18	16	)	)	PUNCT
ejpam-2333	18	17	and	and	CCONJ
ejpam-2333	18	18	(	(	PUNCT
ejpam-2333	18	19	mpq	mpq	X
ejpam-2333	18	20	,	,	PUNCT
ejpam-2333	18	21	x	x	SYM
ejpam-2333	18	22	,	,	PUNCT
ejpam-2333	18	23	y	y	PROPN
ejpam-2333	18	24	,	,	PUNCT
ejpam-2333	18	25	z	z	NOUN
ejpam-2333	18	26	)	)	PUNCT
ejpam-2333	18	27	=	=	SYM
ejpam-2333	18	28	(	(	PUNCT
ejpam-2333	18	29	3,2,2,5	3,2,2,5	NUM
ejpam-2333	18	30	)	)	PUNCT
ejpam-2333	18	31	are	be	AUX
ejpam-2333	18	32	the	the	DET
ejpam-2333	18	33	only	only	ADJ
ejpam-2333	18	34	solutions	solution	NOUN
ejpam-2333	18	35	to	to	ADP
ejpam-2333	18	36	the	the	DET
ejpam-2333	18	37	above	above	ADJ
ejpam-2333	18	38	equation	equation	NOUN
ejpam-2333	18	39	except	except	SCONJ
ejpam-2333	18	40	the	the	DET
ejpam-2333	18	41	case	case	NOUN
ejpam-2333	18	42	when	when	SCONJ
ejpam-2333	18	43	both	both	DET
ejpam-2333	18	44	p	p	NOUN
ejpam-2333	18	45	and	and	CCONJ
ejpam-2333	18	46	y	y	PROPN
ejpam-2333	18	47	are	be	AUX
ejpam-2333	18	48	odd	odd	ADJ
ejpam-2333	18	49	integers	integer	NOUN
ejpam-2333	18	50	.	.	PUNCT
ejpam-2333	19	1	2	2	X
ejpam-2333	19	2	.	.	X
ejpam-2333	19	3	main	main	ADJ
ejpam-2333	19	4	results	result	NOUN
ejpam-2333	19	5	in	in	ADP
ejpam-2333	19	6	this	this	DET
ejpam-2333	19	7	article	article	NOUN
ejpam-2333	19	8	,	,	PUNCT
ejpam-2333	19	9	we	we	PRON
ejpam-2333	19	10	use	use	VERB
ejpam-2333	19	11	catalan	catalan	NOUN
ejpam-2333	19	12	’s	’s	PART
ejpam-2333	19	13	conjecture	conjecture	NOUN
ejpam-2333	20	1	[	[	X
ejpam-2333	20	2	1	1	NUM
ejpam-2333	20	3	]	]	PUNCT
ejpam-2333	20	4	,	,	PUNCT
ejpam-2333	20	5	which	which	PRON
ejpam-2333	20	6	states	state	VERB
ejpam-2333	20	7	that	that	SCONJ
ejpam-2333	20	8	the	the	DET
ejpam-2333	20	9	only	only	ADJ
ejpam-2333	20	10	solution	solution	NOUN
ejpam-2333	20	11	in	in	ADP
ejpam-2333	20	12	integers	integer	NOUN
ejpam-2333	20	13	a	a	DET
ejpam-2333	20	14	>	>	X
ejpam-2333	20	15	1	1	NUM
ejpam-2333	20	16	,	,	PUNCT
ejpam-2333	20	17	b	b	PROPN
ejpam-2333	20	18	>	>	X
ejpam-2333	20	19	1	1	NUM
ejpam-2333	20	20	,	,	PUNCT
ejpam-2333	20	21	x	x	PROPN
ejpam-2333	20	22	>	>	X
ejpam-2333	20	23	1	1	NUM
ejpam-2333	20	24	,	,	PUNCT
ejpam-2333	20	25	y	y	PROPN
ejpam-2333	20	26	>	>	X
ejpam-2333	20	27	1	1	NUM
ejpam-2333	20	28	to	to	ADP
ejpam-2333	20	29	the	the	DET
ejpam-2333	20	30	equation	equation	NOUN
ejpam-2333	20	31	ax	ax	NOUN
ejpam-2333	20	32	−	−	PROPN
ejpam-2333	20	33	b	b	PROPN
ejpam-2333	20	34	y	y	PROPN
ejpam-2333	20	35	=	=	SYM
ejpam-2333	20	36	1	1	NUM
ejpam-2333	20	37	is	be	AUX
ejpam-2333	20	38	(	(	PUNCT
ejpam-2333	20	39	a	a	PRON
ejpam-2333	20	40	,	,	PUNCT
ejpam-2333	20	41	b	b	NOUN
ejpam-2333	20	42	,	,	PUNCT
ejpam-2333	20	43	x	x	INTJ
ejpam-2333	20	44	,	,	PUNCT
ejpam-2333	20	45	y	y	PROPN
ejpam-2333	20	46	)	)	PUNCT
ejpam-2333	20	47	=	=	PUNCT
ejpam-2333	20	48	(	(	PUNCT
ejpam-2333	20	49	3,2,2,3	3,2,2,3	NUM
ejpam-2333	20	50	)	)	PUNCT
ejpam-2333	20	51	.	.	PUNCT
ejpam-2333	21	1	we	we	PRON
ejpam-2333	21	2	shall	shall	AUX
ejpam-2333	21	3	now	now	ADV
ejpam-2333	21	4	solve	solve	VERB
ejpam-2333	21	5	the	the	DET
ejpam-2333	21	6	exponential	exponential	ADJ
ejpam-2333	21	7	diophantine	diophantine	NOUN
ejpam-2333	21	8	equation	equation	NOUN
ejpam-2333	21	9	(	(	PUNCT
ejpam-2333	21	10	mpq	mpq	X
ejpam-2333	21	11	)	)	PUNCT
ejpam-2333	21	12	x+(mpq+1)y	x+(mpq+1)y	PROPN
ejpam-2333	21	13	=	=	SYM
ejpam-2333	21	14	z2	z2	PROPN
ejpam-2333	21	15	,	,	PUNCT
ejpam-2333	21	16	where	where	SCONJ
ejpam-2333	21	17	x	x	X
ejpam-2333	21	18	,	,	PUNCT
ejpam-2333	21	19	y	y	PROPN
ejpam-2333	21	20	,	,	PUNCT
ejpam-2333	21	21	z	z	PROPN
ejpam-2333	21	22	,	,	PUNCT
ejpam-2333	21	23	p	p	X
ejpam-2333	21	24	,	,	PUNCT
ejpam-2333	21	25	q	q	X
ejpam-2333	21	26	are	be	AUX
ejpam-2333	21	27	non	non	ADJ
ejpam-2333	21	28	-	-	ADJ
ejpam-2333	21	29	negative	negative	ADJ
ejpam-2333	21	30	integers	integer	NOUN
ejpam-2333	21	31	and	and	CCONJ
ejpam-2333	21	32	mpq	mpq	NOUN
ejpam-2333	21	33	=	=	SYM
ejpam-2333	21	34	pq	pq	NOUN
ejpam-2333	21	35	−	−	NOUN
ejpam-2333	21	36	1	1	NUM
ejpam-2333	21	37	with	with	ADP
ejpam-2333	21	38	q	q	ADJ
ejpam-2333	21	39	>	>	X
ejpam-2333	21	40	1	1	X
ejpam-2333	21	41	.	.	PUNCT
ejpam-2333	22	1	we	we	PRON
ejpam-2333	22	2	exclude	exclude	VERB
ejpam-2333	22	3	the	the	DET
ejpam-2333	22	4	case	case	NOUN
ejpam-2333	22	5	when	when	SCONJ
ejpam-2333	22	6	both	both	DET
ejpam-2333	22	7	p	p	NOUN
ejpam-2333	22	8	and	and	CCONJ
ejpam-2333	22	9	y	y	PROPN
ejpam-2333	22	10	are	be	AUX
ejpam-2333	22	11	odd	odd	ADJ
ejpam-2333	22	12	positive	positive	ADJ
ejpam-2333	22	13	integers	integer	NOUN
ejpam-2333	22	14	.	.	PUNCT
ejpam-2333	23	1	email	email	NOUN
ejpam-2333	23	2	address	address	NOUN
ejpam-2333	23	3	:	:	PUNCT
ejpam-2333	23	4	ahoque.ms@gmail.com	ahoque.ms@gmail.com	PROPN
ejpam-2333	23	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2333	24	1	240	240	NUM
ejpam-2333	24	2	c	c	X
ejpam-2333	24	3	©	©	PROPN
ejpam-2333	24	4	2016	2016	NUM
ejpam-2333	24	5	ejpam	ejpam	VERB
ejpam-2333	24	6	all	all	DET
ejpam-2333	24	7	rights	right	NOUN
ejpam-2333	24	8	reserved	reserve	VERB
ejpam-2333	24	9	.	.	PUNCT
ejpam-2333	25	1	european	european	ADJ
ejpam-2333	25	2	journal	journal	PROPN
ejpam-2333	25	3	of	of	ADP
ejpam-2333	25	4	pure	pure	ADJ
ejpam-2333	25	5	and	and	CCONJ
ejpam-2333	25	6	applied	apply	VERB
ejpam-2333	25	7	mathematics	mathematic	NOUN
ejpam-2333	25	8	vol	vol	NOUN
ejpam-2333	25	9	.	.	PROPN
ejpam-2333	26	1	9	9	NUM
ejpam-2333	26	2	,	,	PUNCT
ejpam-2333	26	3	no	no	INTJ
ejpam-2333	26	4	.	.	NOUN
ejpam-2333	26	5	2	2	NUM
ejpam-2333	26	6	,	,	PUNCT
ejpam-2333	26	7	2016	2016	NUM
ejpam-2333	26	8	,	,	PUNCT
ejpam-2333	26	9	240	240	NUM
ejpam-2333	26	10	-	-	SYM
ejpam-2333	26	11	243	243	NUM
ejpam-2333	26	12	issn	issn	PROPN
ejpam-2333	26	13	1307	1307	NUM
ejpam-2333	26	14	-	-	SYM
ejpam-2333	26	15	5543	5543	NUM
ejpam-2333	26	16	–	–	PUNCT
ejpam-2333	26	17	www.ejpam.com	www.ejpam.com	X
ejpam-2333	26	18	a.	a.	NOUN
ejpam-2333	26	19	hoque	hoque	PROPN
ejpam-2333	26	20	/	/	SYM
ejpam-2333	26	21	eur	eur	NOUN
ejpam-2333	26	22	.	.	PUNCT
ejpam-2333	27	1	j.	j.	PROPN
ejpam-2333	27	2	pure	pure	PROPN
ejpam-2333	27	3	appl	appl	PROPN
ejpam-2333	27	4	.	.	PROPN
ejpam-2333	27	5	math	math	PROPN
ejpam-2333	27	6	,	,	PUNCT
ejpam-2333	27	7	9	9	NUM
ejpam-2333	27	8	(	(	PUNCT
ejpam-2333	27	9	2016	2016	NUM
ejpam-2333	27	10	)	)	PUNCT
ejpam-2333	27	11	,	,	PUNCT
ejpam-2333	27	12	240	240	NUM
ejpam-2333	27	13	-	-	SYM
ejpam-2333	27	14	243	243	NUM
ejpam-2333	27	15	241	241	NUM
ejpam-2333	27	16	theorem	theorem	VERB
ejpam-2333	27	17	1	1	NUM
ejpam-2333	27	18	.	.	PUNCT
ejpam-2333	28	1	the	the	DET
ejpam-2333	28	2	exponential	exponential	ADJ
ejpam-2333	28	3	diophantine	diophantine	NOUN
ejpam-2333	28	4	equation	equation	NOUN
ejpam-2333	28	5	(	(	PUNCT
ejpam-2333	28	6	mpq	mpq	X
ejpam-2333	28	7	)	)	PUNCT
ejpam-2333	28	8	x	x	PUNCT
ejpam-2333	29	1	+	+	PUNCT
ejpam-2333	29	2	(	(	PUNCT
ejpam-2333	29	3	mpq	mpq	X
ejpam-2333	29	4	+	+	CCONJ
ejpam-2333	29	5	1)y	1)y	NUM
ejpam-2333	29	6	=	=	SYM
ejpam-2333	29	7	z2	z2	PROPN
ejpam-2333	29	8	(	(	PUNCT
ejpam-2333	29	9	1	1	NUM
ejpam-2333	29	10	)	)	PUNCT
ejpam-2333	29	11	except	except	SCONJ
ejpam-2333	29	12	the	the	DET
ejpam-2333	29	13	case	case	NOUN
ejpam-2333	29	14	when	when	SCONJ
ejpam-2333	29	15	both	both	DET
ejpam-2333	29	16	p	p	NOUN
ejpam-2333	29	17	and	and	CCONJ
ejpam-2333	29	18	y	y	PROPN
ejpam-2333	29	19	are	be	AUX
ejpam-2333	29	20	odd	odd	ADJ
ejpam-2333	29	21	positive	positive	ADJ
ejpam-2333	29	22	integers	integer	NOUN
ejpam-2333	29	23	,	,	PUNCT
ejpam-2333	29	24	has	have	VERB
ejpam-2333	29	25	only	only	ADV
ejpam-2333	29	26	two	two	NUM
ejpam-2333	29	27	solutions	solution	NOUN
ejpam-2333	29	28	in	in	ADP
ejpam-2333	29	29	non	non	ADJ
ejpam-2333	29	30	-	-	ADJ
ejpam-2333	29	31	negative	negative	ADJ
ejpam-2333	29	32	integer	integer	NOUN
ejpam-2333	29	33	,	,	PUNCT
ejpam-2333	29	34	(	(	PUNCT
ejpam-2333	29	35	mpq	mpq	X
ejpam-2333	29	36	,	,	PUNCT
ejpam-2333	29	37	x	x	SYM
ejpam-2333	29	38	,	,	PUNCT
ejpam-2333	29	39	y	y	PROPN
ejpam-2333	29	40	,	,	PUNCT
ejpam-2333	29	41	z	z	NOUN
ejpam-2333	29	42	)	)	PUNCT
ejpam-2333	29	43	=	=	SYM
ejpam-2333	29	44	(	(	PUNCT
ejpam-2333	29	45	7,0,2,3	7,0,2,3	NUM
ejpam-2333	29	46	)	)	PUNCT
ejpam-2333	29	47	and	and	CCONJ
ejpam-2333	29	48	(	(	PUNCT
ejpam-2333	29	49	mpq	mpq	X
ejpam-2333	29	50	,	,	PUNCT
ejpam-2333	29	51	x	x	SYM
ejpam-2333	29	52	,	,	PUNCT
ejpam-2333	29	53	y	y	PROPN
ejpam-2333	29	54	,	,	PUNCT
ejpam-2333	29	55	z	z	NOUN
ejpam-2333	29	56	)	)	PUNCT
ejpam-2333	29	57	=	=	SYM
ejpam-2333	29	58	(	(	PUNCT
ejpam-2333	29	59	3,2,2,5	3,2,2,5	NUM
ejpam-2333	29	60	)	)	PUNCT
ejpam-2333	29	61	.	.	PUNCT
ejpam-2333	30	1	proof	proof	NOUN
ejpam-2333	30	2	.	.	PUNCT
ejpam-2333	31	1	we	we	PRON
ejpam-2333	31	2	divide	divide	VERB
ejpam-2333	31	3	the	the	DET
ejpam-2333	31	4	problem	problem	NOUN
ejpam-2333	31	5	into	into	ADP
ejpam-2333	31	6	two	two	NUM
ejpam-2333	31	7	cases	case	NOUN
ejpam-2333	31	8	.	.	PUNCT
ejpam-2333	32	1	case	case	NOUN
ejpam-2333	32	2	1	1	NUM
ejpam-2333	32	3	:	:	PUNCT
ejpam-2333	32	4	let	let	VERB
ejpam-2333	32	5	p	p	PRON
ejpam-2333	32	6	be	be	AUX
ejpam-2333	32	7	an	an	DET
ejpam-2333	32	8	even	even	ADV
ejpam-2333	32	9	positive	positive	ADJ
ejpam-2333	32	10	integer	integer	NOUN
ejpam-2333	32	11	.	.	PUNCT
ejpam-2333	33	1	then	then	ADV
ejpam-2333	33	2	mpq	mpq	PROPN
ejpam-2333	33	3	≡	≡	PROPN
ejpam-2333	33	4	3(mod	3(mod	NUM
ejpam-2333	33	5	4	4	NUM
ejpam-2333	33	6	)	)	PUNCT
ejpam-2333	33	7	.	.	PUNCT
ejpam-2333	34	1	from	from	ADP
ejpam-2333	34	2	eq.(1	eq.(1	ADJ
ejpam-2333	34	3	)	)	PUNCT
ejpam-2333	34	4	we	we	PRON
ejpam-2333	34	5	observe	observe	VERB
ejpam-2333	34	6	that	that	SCONJ
ejpam-2333	34	7	z	z	NOUN
ejpam-2333	34	8	must	must	AUX
ejpam-2333	34	9	be	be	AUX
ejpam-2333	34	10	odd	odd	ADJ
ejpam-2333	34	11	,	,	PUNCT
ejpam-2333	34	12	and	and	CCONJ
ejpam-2333	34	13	thus	thus	ADV
ejpam-2333	34	14	z2	z2	PROPN
ejpam-2333	34	15	≡	≡	PROPN
ejpam-2333	34	16	1(mod	1(mod	NUM
ejpam-2333	34	17	4	4	NUM
ejpam-2333	34	18	)	)	PUNCT
ejpam-2333	34	19	and	and	CCONJ
ejpam-2333	34	20	mpq	mpq	X
ejpam-2333	35	1	+	+	CCONJ
ejpam-2333	35	2	1	1	NUM
ejpam-2333	35	3	≡	≡	ADJ
ejpam-2333	35	4	0(mod	0(mod	NOUN
ejpam-2333	35	5	4	4	NUM
ejpam-2333	35	6	)	)	PUNCT
ejpam-2333	35	7	.	.	PUNCT
ejpam-2333	36	1	sub	sub	ADJ
ejpam-2333	36	2	-	-	NOUN
ejpam-2333	36	3	case	case	NOUN
ejpam-2333	36	4	1.1	1.1	NUM
ejpam-2333	36	5	:	:	PUNCT
ejpam-2333	36	6	let	let	VERB
ejpam-2333	36	7	x	x	SYM
ejpam-2333	36	8	=	=	SYM
ejpam-2333	36	9	0	0	NUM
ejpam-2333	36	10	,	,	PUNCT
ejpam-2333	36	11	then	then	ADV
ejpam-2333	36	12	eq	eq	ADJ
ejpam-2333	36	13	.	.	PUNCT
ejpam-2333	37	1	(	(	PUNCT
ejpam-2333	37	2	1	1	X
ejpam-2333	37	3	)	)	PUNCT
ejpam-2333	37	4	becomes	become	VERB
ejpam-2333	37	5	1	1	NUM
ejpam-2333	37	6	+	+	CCONJ
ejpam-2333	37	7	(	(	PUNCT
ejpam-2333	37	8	mpq	mpq	X
ejpam-2333	37	9	+	+	NUM
ejpam-2333	37	10	1)y	1)y	NUM
ejpam-2333	37	11	=	=	SYM
ejpam-2333	37	12	z2	z2	PROPN
ejpam-2333	37	13	.	.	PUNCT
ejpam-2333	38	1	this	this	PRON
ejpam-2333	38	2	gives	give	VERB
ejpam-2333	38	3	pq	pq	INTJ
ejpam-2333	38	4	y	y	NOUN
ejpam-2333	38	5	=	=	SYM
ejpam-2333	38	6	z2−1	z2−1	PROPN
ejpam-2333	38	7	and	and	CCONJ
ejpam-2333	38	8	thus	thus	ADV
ejpam-2333	38	9	pq	pq	VERB
ejpam-2333	38	10	y	y	PROPN
ejpam-2333	38	11	=	=	SYM
ejpam-2333	38	12	(	(	PUNCT
ejpam-2333	38	13	z+1)(z−1	z+1)(z−1	PROPN
ejpam-2333	38	14	)	)	PUNCT
ejpam-2333	38	15	.	.	PUNCT
ejpam-2333	39	1	hence	hence	ADV
ejpam-2333	39	2	there	there	PRON
ejpam-2333	39	3	exists	exist	VERB
ejpam-2333	39	4	non	non	ADJ
ejpam-2333	39	5	-	-	ADJ
ejpam-2333	39	6	negative	negative	ADJ
ejpam-2333	39	7	integers	integer	NOUN
ejpam-2333	39	8	m	m	VERB
ejpam-2333	39	9	and	and	CCONJ
ejpam-2333	39	10	n	n	CCONJ
ejpam-2333	39	11	such	such	ADJ
ejpam-2333	39	12	that	that	DET
ejpam-2333	39	13	pm	pm	NOUN
ejpam-2333	39	14	=	=	SYM
ejpam-2333	39	15	z	z	NOUN
ejpam-2333	40	1	+	+	NOUN
ejpam-2333	40	2	1	1	NUM
ejpam-2333	40	3	and	and	CCONJ
ejpam-2333	40	4	pn	pn	X
ejpam-2333	41	1	=	=	SYM
ejpam-2333	41	2	z	z	PROPN
ejpam-2333	41	3	−	−	PROPN
ejpam-2333	41	4	1	1	NUM
ejpam-2333	41	5	,	,	PUNCT
ejpam-2333	41	6	where	where	SCONJ
ejpam-2333	41	7	m	m	VERB
ejpam-2333	41	8	>	>	X
ejpam-2333	41	9	n	n	PROPN
ejpam-2333	41	10	and	and	CCONJ
ejpam-2333	41	11	m+	m+	NUM
ejpam-2333	41	12	n=	n=	ADJ
ejpam-2333	41	13	q	q	ADJ
ejpam-2333	41	14	y	y	PROPN
ejpam-2333	41	15	(	(	PUNCT
ejpam-2333	41	16	2	2	NUM
ejpam-2333	41	17	)	)	PUNCT
ejpam-2333	41	18	now	now	ADV
ejpam-2333	41	19	we	we	PRON
ejpam-2333	41	20	have	have	VERB
ejpam-2333	41	21	,	,	PUNCT
ejpam-2333	41	22	pn(pm−n	pn(pm−n	PROPN
ejpam-2333	41	23	−	−	PROPN
ejpam-2333	41	24	1	1	NUM
ejpam-2333	41	25	)	)	PUNCT
ejpam-2333	41	26	=	=	PRON
ejpam-2333	42	1	pm	pm	NOUN
ejpam-2333	42	2	−	−	PROPN
ejpam-2333	42	3	pn	pn	NOUN
ejpam-2333	42	4	=	=	SYM
ejpam-2333	42	5	(	(	PUNCT
ejpam-2333	42	6	z	z	PROPN
ejpam-2333	42	7	+	+	PROPN
ejpam-2333	42	8	1)−	1)−	NUM
ejpam-2333	42	9	(	(	PUNCT
ejpam-2333	42	10	z	z	NOUN
ejpam-2333	42	11	−	−	PROPN
ejpam-2333	42	12	1	1	NUM
ejpam-2333	42	13	)	)	PUNCT
ejpam-2333	42	14	=	=	SYM
ejpam-2333	43	1	2	2	X
ejpam-2333	43	2	.	.	PUNCT
ejpam-2333	44	1	this	this	PRON
ejpam-2333	44	2	implies	imply	VERB
ejpam-2333	44	3	p	p	X
ejpam-2333	44	4	=	=	SYM
ejpam-2333	44	5	2	2	NUM
ejpam-2333	44	6	,	,	PUNCT
ejpam-2333	44	7	n=	n=	ADJ
ejpam-2333	44	8	1	1	NUM
ejpam-2333	44	9	and	and	CCONJ
ejpam-2333	44	10	m=	m=	X
ejpam-2333	44	11	2	2	NUM
ejpam-2333	44	12	.	.	PUNCT
ejpam-2333	44	13	thus	thus	ADV
ejpam-2333	44	14	eq	eq	ADJ
ejpam-2333	44	15	.	.	PUNCT
ejpam-2333	45	1	(	(	PUNCT
ejpam-2333	45	2	2	2	X
ejpam-2333	45	3	)	)	PUNCT
ejpam-2333	45	4	gives	give	VERB
ejpam-2333	45	5	q	q	PROPN
ejpam-2333	45	6	y	y	NOUN
ejpam-2333	45	7	=	=	SYM
ejpam-2333	45	8	3	3	NUM
ejpam-2333	45	9	and	and	CCONJ
ejpam-2333	45	10	hence	hence	ADV
ejpam-2333	45	11	either	either	CCONJ
ejpam-2333	45	12	q	q	PUNCT
ejpam-2333	45	13	=	=	SYM
ejpam-2333	45	14	1	1	NUM
ejpam-2333	45	15	,	,	PUNCT
ejpam-2333	45	16	y	y	PROPN
ejpam-2333	45	17	=	=	SYM
ejpam-2333	45	18	3	3	NUM
ejpam-2333	45	19	or	or	CCONJ
ejpam-2333	45	20	q	q	NOUN
ejpam-2333	46	1	=	=	SYM
ejpam-2333	46	2	3	3	NUM
ejpam-2333	46	3	,	,	PUNCT
ejpam-2333	46	4	y	y	PROPN
ejpam-2333	46	5	=	=	SYM
ejpam-2333	46	6	1	1	X
ejpam-2333	46	7	.	.	PUNCT
ejpam-2333	47	1	since	since	SCONJ
ejpam-2333	47	2	q	q	PROPN
ejpam-2333	47	3	>	>	X
ejpam-2333	47	4	1	1	NUM
ejpam-2333	47	5	,	,	PUNCT
ejpam-2333	47	6	so	so	SCONJ
ejpam-2333	47	7	that	that	SCONJ
ejpam-2333	47	8	q	q	NOUN
ejpam-2333	47	9	=	=	SYM
ejpam-2333	47	10	3	3	NUM
ejpam-2333	47	11	,	,	PUNCT
ejpam-2333	47	12	y	y	PROPN
ejpam-2333	47	13	=	=	SYM
ejpam-2333	47	14	1	1	X
ejpam-2333	47	15	.	.	PUNCT
ejpam-2333	48	1	now	now	ADV
ejpam-2333	48	2	z	z	NOUN
ejpam-2333	48	3	=	=	SYM
ejpam-2333	48	4	pn	pn	PROPN
ejpam-2333	49	1	+	+	CCONJ
ejpam-2333	49	2	1	1	NUM
ejpam-2333	49	3	=	=	SYM
ejpam-2333	49	4	3	3	NUM
ejpam-2333	49	5	and	and	CCONJ
ejpam-2333	49	6	mpq	mpq	X
ejpam-2333	50	1	=	=	SYM
ejpam-2333	50	2	7	7	X
ejpam-2333	50	3	.	.	PUNCT
ejpam-2333	50	4	hence	hence	ADV
ejpam-2333	50	5	(	(	PUNCT
ejpam-2333	50	6	mpq	mpq	X
ejpam-2333	50	7	,	,	PUNCT
ejpam-2333	50	8	x	x	SYM
ejpam-2333	50	9	,	,	PUNCT
ejpam-2333	50	10	y	y	PROPN
ejpam-2333	50	11	,	,	PUNCT
ejpam-2333	50	12	z	z	NOUN
ejpam-2333	50	13	)	)	PUNCT
ejpam-2333	50	14	=	=	SYM
ejpam-2333	50	15	(	(	PUNCT
ejpam-2333	50	16	7,0,1,3	7,0,1,3	NUM
ejpam-2333	50	17	)	)	PUNCT
ejpam-2333	50	18	is	be	AUX
ejpam-2333	50	19	the	the	DET
ejpam-2333	50	20	only	only	ADJ
ejpam-2333	50	21	solution	solution	NOUN
ejpam-2333	50	22	to	to	ADP
ejpam-2333	50	23	the	the	DET
ejpam-2333	50	24	eq	eq	NOUN
ejpam-2333	50	25	.	.	PUNCT
ejpam-2333	51	1	(	(	PUNCT
ejpam-2333	51	2	1	1	X
ejpam-2333	51	3	)	)	PUNCT
ejpam-2333	51	4	in	in	ADP
ejpam-2333	51	5	this	this	DET
ejpam-2333	51	6	sub	sub	NOUN
ejpam-2333	51	7	-	-	NOUN
ejpam-2333	51	8	case	case	NOUN
ejpam-2333	51	9	.	.	PUNCT
ejpam-2333	52	1	sub	sub	ADJ
ejpam-2333	52	2	-	-	NOUN
ejpam-2333	52	3	case	case	NOUN
ejpam-2333	52	4	1.2	1.2	NUM
ejpam-2333	52	5	:	:	PUNCT
ejpam-2333	52	6	let	let	VERB
ejpam-2333	52	7	x	x	X
ejpam-2333	52	8	≥	≥	NUM
ejpam-2333	52	9	1	1	NUM
ejpam-2333	52	10	.	.	PUNCT
ejpam-2333	53	1	since	since	SCONJ
ejpam-2333	53	2	(	(	PUNCT
ejpam-2333	53	3	mpq	mpq	X
ejpam-2333	53	4	+	+	SYM
ejpam-2333	53	5	1)y	1)y	NUM
ejpam-2333	53	6	≡	≡	PROPN
ejpam-2333	53	7	0(mod	0(mod	NOUN
ejpam-2333	53	8	4	4	X
ejpam-2333	53	9	)	)	PUNCT
ejpam-2333	53	10	and	and	CCONJ
ejpam-2333	53	11	z2	z2	PROPN
ejpam-2333	53	12	≡	≡	PROPN
ejpam-2333	53	13	1(mod	1(mod	NUM
ejpam-2333	53	14	4	4	NUM
ejpam-2333	53	15	)	)	PUNCT
ejpam-2333	53	16	,	,	PUNCT
ejpam-2333	53	17	the	the	DET
ejpam-2333	53	18	eq	eq	NOUN
ejpam-2333	53	19	.	.	PUNCT
ejpam-2333	53	20	(	(	PUNCT
ejpam-2333	53	21	1	1	X
ejpam-2333	53	22	)	)	PUNCT
ejpam-2333	53	23	gives	give	VERB
ejpam-2333	53	24	(	(	PUNCT
ejpam-2333	53	25	mpq	mpq	PROPN
ejpam-2333	53	26	)	)	PUNCT
ejpam-2333	53	27	x	x	SYM
ejpam-2333	53	28	≡	≡	PROPN
ejpam-2333	53	29	1(mod	1(mod	NUM
ejpam-2333	53	30	4	4	NUM
ejpam-2333	53	31	)	)	PUNCT
ejpam-2333	53	32	.	.	PUNCT
ejpam-2333	54	1	again	again	ADV
ejpam-2333	54	2	since	since	SCONJ
ejpam-2333	54	3	mpq	mpq	PROPN
ejpam-2333	54	4	≡	≡	PROPN
ejpam-2333	54	5	3(mod	3(mod	NUM
ejpam-2333	54	6	4	4	NUM
ejpam-2333	54	7	)	)	PUNCT
ejpam-2333	54	8	,	,	PUNCT
ejpam-2333	54	9	x	x	PRON
ejpam-2333	54	10	must	must	AUX
ejpam-2333	54	11	be	be	AUX
ejpam-2333	54	12	even	even	ADV
ejpam-2333	54	13	.	.	PUNCT
ejpam-2333	55	1	let	let	VERB
ejpam-2333	55	2	x	x	PUNCT
ejpam-2333	55	3	=	=	PUNCT
ejpam-2333	55	4	2k	2k	NUM
ejpam-2333	55	5	for	for	ADP
ejpam-2333	55	6	some	some	DET
ejpam-2333	55	7	integer	integer	NOUN
ejpam-2333	55	8	k	k	PROPN
ejpam-2333	55	9	≥	≥	NUM
ejpam-2333	55	10	1	1	NUM
ejpam-2333	55	11	.	.	PUNCT
ejpam-2333	56	1	then	then	ADV
ejpam-2333	56	2	eq	eq	ADP
ejpam-2333	56	3	.	.	PUNCT
ejpam-2333	57	1	(	(	PUNCT
ejpam-2333	57	2	1	1	X
ejpam-2333	57	3	)	)	PUNCT
ejpam-2333	57	4	implies	imply	VERB
ejpam-2333	57	5	(	(	PUNCT
ejpam-2333	57	6	mpq	mpq	X
ejpam-2333	57	7	)	)	PUNCT
ejpam-2333	57	8	2k	2k	NOUN
ejpam-2333	58	1	+	+	CCONJ
ejpam-2333	58	2	pq	pq	INTJ
ejpam-2333	58	3	y	y	PROPN
ejpam-2333	58	4	=	=	PROPN
ejpam-2333	58	5	z2	z2	PROPN
ejpam-2333	58	6	.	.	PUNCT
ejpam-2333	59	1	this	this	PRON
ejpam-2333	59	2	gives	give	VERB
ejpam-2333	59	3	pq	pq	INTJ
ejpam-2333	59	4	y	y	NOUN
ejpam-2333	59	5	=	=	PROPN
ejpam-2333	59	6	z2	z2	PROPN
ejpam-2333	60	1	−	−	PROPN
ejpam-2333	60	2	(	(	PUNCT
ejpam-2333	60	3	mpq	mpq	X
ejpam-2333	60	4	k)2	k)2	PROPN
ejpam-2333	60	5	and	and	CCONJ
ejpam-2333	60	6	thus	thus	ADV
ejpam-2333	60	7	pq	pq	VERB
ejpam-2333	60	8	y	y	NOUN
ejpam-2333	61	1	=	=	PUNCT
ejpam-2333	62	1	(	(	PUNCT
ejpam-2333	62	2	z	z	X
ejpam-2333	62	3	+	+	CCONJ
ejpam-2333	62	4	mpq	mpq	X
ejpam-2333	62	5	k)(z	k)(z	NOUN
ejpam-2333	62	6	−	−	PROPN
ejpam-2333	62	7	mpq	mpq	X
ejpam-2333	63	1	k	k	NOUN
ejpam-2333	63	2	)	)	PUNCT
ejpam-2333	63	3	.	.	PUNCT
ejpam-2333	64	1	hence	hence	ADV
ejpam-2333	64	2	there	there	PRON
ejpam-2333	64	3	exists	exist	VERB
ejpam-2333	64	4	nonnegative	nonnegative	ADJ
ejpam-2333	64	5	integers	integer	NOUN
ejpam-2333	64	6	i	i	PRON
ejpam-2333	64	7	and	and	CCONJ
ejpam-2333	64	8	j	j	PROPN
ejpam-2333	64	9	such	such	ADJ
ejpam-2333	64	10	that	that	DET
ejpam-2333	64	11	pi	pi	NOUN
ejpam-2333	64	12	=	=	PUNCT
ejpam-2333	64	13	z	z	PUNCT
ejpam-2333	65	1	+	+	PROPN
ejpam-2333	65	2	mpq	mpq	PROPN
ejpam-2333	65	3	k	k	PROPN
ejpam-2333	65	4	and	and	CCONJ
ejpam-2333	65	5	p	p	NOUN
ejpam-2333	65	6	j	j	PROPN
ejpam-2333	66	1	=	=	PUNCT
ejpam-2333	66	2	z	z	NOUN
ejpam-2333	67	1	−mpq	−mpq	NOUN
ejpam-2333	68	1	k	k	NOUN
ejpam-2333	68	2	,	,	PUNCT
ejpam-2333	68	3	where	where	SCONJ
ejpam-2333	68	4	i	i	PRON
ejpam-2333	68	5	>	>	X
ejpam-2333	68	6	j	j	PROPN
ejpam-2333	68	7	and	and	CCONJ
ejpam-2333	68	8	i	i	PRON
ejpam-2333	68	9	+	+	CCONJ
ejpam-2333	68	10	j	j	X
ejpam-2333	69	1	=	=	X
ejpam-2333	69	2	q	q	PROPN
ejpam-2333	69	3	y.	y.	NOUN
ejpam-2333	69	4	(	(	PUNCT
ejpam-2333	69	5	3	3	NUM
ejpam-2333	69	6	)	)	PUNCT
ejpam-2333	69	7	now	now	ADV
ejpam-2333	69	8	we	we	PRON
ejpam-2333	69	9	have	have	VERB
ejpam-2333	69	10	p	p	NOUN
ejpam-2333	69	11	j(pi−	j(pi−	VERB
ejpam-2333	69	12	j	j	NOUN
ejpam-2333	70	1	−	−	NOUN
ejpam-2333	70	2	1	1	NUM
ejpam-2333	70	3	)	)	PUNCT
ejpam-2333	70	4	=	=	VERB
ejpam-2333	71	1	pi	pi	NOUN
ejpam-2333	72	1	−	−	PROPN
ejpam-2333	73	1	p	p	PROPN
ejpam-2333	73	2	j	j	PROPN
ejpam-2333	73	3	=	=	SYM
ejpam-2333	73	4	2(mpq	2(mpq	NUM
ejpam-2333	73	5	)	)	PUNCT
ejpam-2333	74	1	k.	k.	NOUN
ejpam-2333	74	2	since	since	SCONJ
ejpam-2333	74	3	p	p	NOUN
ejpam-2333	74	4	is	be	AUX
ejpam-2333	74	5	even	even	ADV
ejpam-2333	74	6	,	,	PUNCT
ejpam-2333	74	7	let	let	VERB
ejpam-2333	74	8	p	p	NOUN
ejpam-2333	74	9	=	=	SYM
ejpam-2333	74	10	2	2	NUM
ejpam-2333	74	11	t	t	NOUN
ejpam-2333	74	12	for	for	ADP
ejpam-2333	74	13	some	some	DET
ejpam-2333	74	14	positive	positive	ADJ
ejpam-2333	74	15	integer	integer	NOUN
ejpam-2333	74	16	t.	t.	NOUN
ejpam-2333	75	1	then	then	ADV
ejpam-2333	75	2	we	we	PRON
ejpam-2333	75	3	have	have	VERB
ejpam-2333	75	4	2	2	NUM
ejpam-2333	75	5	j−1	j−1	PROPN
ejpam-2333	75	6	t	t	PROPN
ejpam-2333	75	7	j(pi−	j(pi−	VERB
ejpam-2333	75	8	j	j	PROPN
ejpam-2333	76	1	−	−	NOUN
ejpam-2333	76	2	1	1	NUM
ejpam-2333	76	3	)	)	PUNCT
ejpam-2333	76	4	=	=	SYM
ejpam-2333	76	5	(	(	PUNCT
ejpam-2333	76	6	mpq	mpq	PROPN
ejpam-2333	76	7	)	)	PUNCT
ejpam-2333	76	8	k.	k.	PROPN
ejpam-2333	76	9	(	(	PUNCT
ejpam-2333	76	10	4	4	X
ejpam-2333	76	11	)	)	PUNCT
ejpam-2333	76	12	if	if	SCONJ
ejpam-2333	76	13	t	t	PROPN
ejpam-2333	76	14	>	>	X
ejpam-2333	76	15	1	1	NUM
ejpam-2333	77	1	then	then	ADV
ejpam-2333	77	2	t	t	PROPN
ejpam-2333	77	3	|	|	ADV
ejpam-2333	77	4	(	(	PUNCT
ejpam-2333	77	5	mpq	mpq	PROPN
ejpam-2333	77	6	)	)	PUNCT
ejpam-2333	77	7	k	k	NOUN
ejpam-2333	77	8	and	and	CCONJ
ejpam-2333	77	9	hence	hence	ADV
ejpam-2333	77	10	p	p	X
ejpam-2333	77	11	|	|	NOUN
ejpam-2333	77	12	2(mpq	2(mpq	NUM
ejpam-2333	77	13	)	)	PUNCT
ejpam-2333	78	1	k.	k.	PROPN
ejpam-2333	79	1	since	since	SCONJ
ejpam-2333	79	2	gcd(p	gcd(p	PROPN
ejpam-2333	79	3	,	,	PUNCT
ejpam-2333	79	4	mpq	mpq	X
ejpam-2333	79	5	)	)	PUNCT
ejpam-2333	79	6	=	=	SYM
ejpam-2333	79	7	1	1	NUM
ejpam-2333	79	8	,	,	PUNCT
ejpam-2333	79	9	we	we	PRON
ejpam-2333	79	10	have	have	VERB
ejpam-2333	79	11	p	p	NOUN
ejpam-2333	79	12	|	|	ADV
ejpam-2333	79	13	2	2	NUM
ejpam-2333	79	14	,	,	PUNCT
ejpam-2333	79	15	a	a	DET
ejpam-2333	79	16	contradiction	contradiction	NOUN
ejpam-2333	79	17	.	.	PUNCT
ejpam-2333	80	1	hence	hence	ADV
ejpam-2333	80	2	t	t	NOUN
ejpam-2333	80	3	=	=	PUNCT
ejpam-2333	80	4	1	1	NUM
ejpam-2333	80	5	and	and	CCONJ
ejpam-2333	80	6	p	p	X
ejpam-2333	80	7	=	=	ADJ
ejpam-2333	80	8	2	2	X
ejpam-2333	80	9	.	.	PUNCT
ejpam-2333	80	10	a.	a.	NOUN
ejpam-2333	80	11	hoque	hoque	PROPN
ejpam-2333	80	12	/	/	SYM
ejpam-2333	80	13	eur	eur	NOUN
ejpam-2333	80	14	.	.	PUNCT
ejpam-2333	81	1	j.	j.	PROPN
ejpam-2333	81	2	pure	pure	PROPN
ejpam-2333	81	3	appl	appl	PROPN
ejpam-2333	81	4	.	.	PROPN
ejpam-2333	81	5	math	math	PROPN
ejpam-2333	81	6	,	,	PUNCT
ejpam-2333	81	7	9	9	NUM
ejpam-2333	81	8	(	(	PUNCT
ejpam-2333	81	9	2016	2016	NUM
ejpam-2333	81	10	)	)	PUNCT
ejpam-2333	81	11	,	,	PUNCT
ejpam-2333	81	12	240	240	NUM
ejpam-2333	81	13	-	-	SYM
ejpam-2333	81	14	243	243	NUM
ejpam-2333	81	15	242	242	NUM
ejpam-2333	81	16	now	now	ADV
ejpam-2333	81	17	eq	eq	ADP
ejpam-2333	81	18	.	.	PUNCT
ejpam-2333	82	1	(	(	PUNCT
ejpam-2333	82	2	4	4	X
ejpam-2333	82	3	)	)	PUNCT
ejpam-2333	82	4	gives	give	VERB
ejpam-2333	82	5	,	,	PUNCT
ejpam-2333	82	6	j	j	PROPN
ejpam-2333	82	7	=	=	SYM
ejpam-2333	82	8	1	1	NUM
ejpam-2333	82	9	and	and	CCONJ
ejpam-2333	82	10	it	it	PRON
ejpam-2333	82	11	becomes	become	VERB
ejpam-2333	82	12	,	,	PUNCT
ejpam-2333	82	13	pi−1	pi−1	NOUN
ejpam-2333	82	14	−	−	NUM
ejpam-2333	82	15	1=	1=	X
ejpam-2333	82	16	(	(	PUNCT
ejpam-2333	82	17	mpq	mpq	X
ejpam-2333	82	18	)	)	PUNCT
ejpam-2333	82	19	k	k	NOUN
ejpam-2333	82	20	(	(	PUNCT
ejpam-2333	82	21	5	5	NUM
ejpam-2333	82	22	)	)	PUNCT
ejpam-2333	82	23	by	by	ADP
ejpam-2333	82	24	using	use	VERB
ejpam-2333	82	25	catalan	catalan	NOUN
ejpam-2333	82	26	’s	’s	PART
ejpam-2333	82	27	conjecture	conjecture	NOUN
ejpam-2333	82	28	,	,	PUNCT
ejpam-2333	82	29	the	the	DET
ejpam-2333	82	30	equation	equation	NOUN
ejpam-2333	82	31	pi−1	pi−1	NOUN
ejpam-2333	82	32	−	−	PROPN
ejpam-2333	82	33	(	(	PUNCT
ejpam-2333	82	34	mpq	mpq	X
ejpam-2333	82	35	)	)	PUNCT
ejpam-2333	82	36	k	k	NOUN
ejpam-2333	83	1	=	=	SYM
ejpam-2333	83	2	1	1	NUM
ejpam-2333	83	3	has	have	VERB
ejpam-2333	83	4	only	only	ADV
ejpam-2333	83	5	one	one	NUM
ejpam-2333	83	6	solution	solution	NOUN
ejpam-2333	83	7	(	(	PUNCT
ejpam-2333	83	8	p	p	X
ejpam-2333	83	9	,	,	PUNCT
ejpam-2333	83	10	mpq	mpq	X
ejpam-2333	83	11	,	,	PUNCT
ejpam-2333	83	12	i	i	PRON
ejpam-2333	83	13	−	−	PROPN
ejpam-2333	83	14	1	1	NUM
ejpam-2333	83	15	,	,	PUNCT
ejpam-2333	83	16	k	k	NOUN
ejpam-2333	83	17	)	)	PUNCT
ejpam-2333	83	18	=	=	SYM
ejpam-2333	83	19	(	(	PUNCT
ejpam-2333	83	20	3,2,2,3	3,2,2,3	NUM
ejpam-2333	83	21	)	)	PUNCT
ejpam-2333	83	22	only	only	ADV
ejpam-2333	83	23	when	when	SCONJ
ejpam-2333	83	24	i	i	PRON
ejpam-2333	83	25	>	>	X
ejpam-2333	83	26	2	2	NUM
ejpam-2333	83	27	and	and	CCONJ
ejpam-2333	83	28	k	k	X
ejpam-2333	83	29	>	>	X
ejpam-2333	83	30	1	1	NUM
ejpam-2333	83	31	.	.	PUNCT
ejpam-2333	84	1	but	but	CCONJ
ejpam-2333	84	2	since	since	SCONJ
ejpam-2333	84	3	p	p	NOUN
ejpam-2333	84	4	=	=	PROPN
ejpam-2333	84	5	2	2	NUM
ejpam-2333	84	6	,	,	PUNCT
ejpam-2333	84	7	eq	eq	NOUN
ejpam-2333	84	8	.	.	PUNCT
ejpam-2333	84	9	(	(	PUNCT
ejpam-2333	84	10	5	5	NUM
ejpam-2333	84	11	)	)	PUNCT
ejpam-2333	84	12	has	have	VERB
ejpam-2333	84	13	no	no	DET
ejpam-2333	84	14	solution	solution	NOUN
ejpam-2333	84	15	only	only	ADV
ejpam-2333	84	16	when	when	SCONJ
ejpam-2333	84	17	i	i	PRON
ejpam-2333	84	18	>	>	X
ejpam-2333	84	19	2	2	NUM
ejpam-2333	84	20	and	and	CCONJ
ejpam-2333	84	21	k	k	X
ejpam-2333	84	22	>	>	X
ejpam-2333	85	1	1	1	X
ejpam-2333	85	2	.	.	PUNCT
ejpam-2333	86	1	it	it	PRON
ejpam-2333	86	2	is	be	AUX
ejpam-2333	86	3	now	now	ADV
ejpam-2333	86	4	remaining	remain	VERB
ejpam-2333	86	5	to	to	PART
ejpam-2333	86	6	examine	examine	VERB
ejpam-2333	86	7	only	only	ADV
ejpam-2333	86	8	when	when	SCONJ
ejpam-2333	86	9	either	either	CCONJ
ejpam-2333	86	10	i	i	PRON
ejpam-2333	86	11	≥	≥	VERB
ejpam-2333	86	12	2	2	NUM
ejpam-2333	86	13	or	or	CCONJ
ejpam-2333	86	14	k	k	PROPN
ejpam-2333	86	15	≥	≥	NUM
ejpam-2333	86	16	1	1	NUM
ejpam-2333	86	17	.	.	PUNCT
ejpam-2333	87	1	but	but	CCONJ
ejpam-2333	87	2	we	we	PRON
ejpam-2333	87	3	have	have	VERB
ejpam-2333	87	4	i	i	PRON
ejpam-2333	87	5	>	>	X
ejpam-2333	87	6	1	1	NUM
ejpam-2333	87	7	,	,	PUNCT
ejpam-2333	87	8	q	q	ADJ
ejpam-2333	87	9	>	>	X
ejpam-2333	87	10	1	1	NUM
ejpam-2333	87	11	,	,	PUNCT
ejpam-2333	87	12	k	k	X
ejpam-2333	87	13	≥	≥	NUM
ejpam-2333	87	14	1	1	NUM
ejpam-2333	87	15	and	and	CCONJ
ejpam-2333	87	16	eq	eq	NOUN
ejpam-2333	87	17	.	.	PUNCT
ejpam-2333	88	1	(	(	PUNCT
ejpam-2333	88	2	3	3	X
ejpam-2333	88	3	)	)	PUNCT
ejpam-2333	88	4	gives	give	VERB
ejpam-2333	88	5	i	i	PRON
ejpam-2333	88	6	+	+	PUNCT
ejpam-2333	88	7	1=	1=	NUM
ejpam-2333	88	8	q	q	NOUN
ejpam-2333	88	9	y	y	NOUN
ejpam-2333	88	10	.	.	PUNCT
ejpam-2333	89	1	thus	thus	ADV
ejpam-2333	89	2	we	we	PRON
ejpam-2333	89	3	get	get	VERB
ejpam-2333	89	4	i	i	PRON
ejpam-2333	89	5	=	=	NOUN
ejpam-2333	89	6	2	2	NUM
ejpam-2333	89	7	,	,	PUNCT
ejpam-2333	89	8	q	q	NOUN
ejpam-2333	89	9	=	=	SYM
ejpam-2333	89	10	3	3	NUM
ejpam-2333	89	11	,	,	PUNCT
ejpam-2333	89	12	y	y	PROPN
ejpam-2333	89	13	=	=	SYM
ejpam-2333	89	14	1	1	NUM
ejpam-2333	89	15	or	or	CCONJ
ejpam-2333	89	16	k	k	NOUN
ejpam-2333	89	17	=	=	SYM
ejpam-2333	89	18	1	1	X
ejpam-2333	89	19	.	.	PUNCT
ejpam-2333	90	1	now	now	ADV
ejpam-2333	90	2	if	if	SCONJ
ejpam-2333	90	3	i	i	PRON
ejpam-2333	90	4	=	=	NOUN
ejpam-2333	90	5	2	2	NUM
ejpam-2333	90	6	,	,	PUNCT
ejpam-2333	90	7	q	q	NOUN
ejpam-2333	90	8	=	=	SYM
ejpam-2333	90	9	3	3	NUM
ejpam-2333	90	10	and	and	CCONJ
ejpam-2333	90	11	y	y	NOUN
ejpam-2333	90	12	=	=	SYM
ejpam-2333	90	13	1	1	NUM
ejpam-2333	90	14	,	,	PUNCT
ejpam-2333	90	15	then	then	ADV
ejpam-2333	90	16	eq.(5	eq.(5	NOUN
ejpam-2333	90	17	)	)	PUNCT
ejpam-2333	90	18	gives	give	VERB
ejpam-2333	90	19	,	,	PUNCT
ejpam-2333	90	20	p−	p−	NOUN
ejpam-2333	90	21	1=	1=	X
ejpam-2333	90	22	(	(	PUNCT
ejpam-2333	90	23	mpq	mpq	X
ejpam-2333	90	24	)	)	PUNCT
ejpam-2333	90	25	k⇒	k⇒	PROPN
ejpam-2333	90	26	1=	1=	X
ejpam-2333	90	27	(	(	PUNCT
ejpam-2333	90	28	mpq	mpq	X
ejpam-2333	90	29	)	)	PUNCT
ejpam-2333	90	30	k⇒	k⇒	PROPN
ejpam-2333	91	1	k	k	X
ejpam-2333	92	1	=	=	PUNCT
ejpam-2333	92	2	0	0	PUNCT
ejpam-2333	93	1	this	this	PRON
ejpam-2333	93	2	contradicts	contradict	VERB
ejpam-2333	93	3	to	to	ADP
ejpam-2333	93	4	k	k	PROPN
ejpam-2333	93	5	≥	≥	NUM
ejpam-2333	93	6	1	1	NUM
ejpam-2333	93	7	.	.	PUNCT
ejpam-2333	93	8	hence	hence	ADV
ejpam-2333	93	9	eq	eq	ADP
ejpam-2333	93	10	.	.	PUNCT
ejpam-2333	94	1	(	(	PUNCT
ejpam-2333	94	2	1	1	X
ejpam-2333	94	3	)	)	PUNCT
ejpam-2333	94	4	has	have	VERB
ejpam-2333	94	5	no	no	DET
ejpam-2333	94	6	solution	solution	NOUN
ejpam-2333	94	7	in	in	ADP
ejpam-2333	94	8	this	this	DET
ejpam-2333	94	9	case	case	NOUN
ejpam-2333	94	10	.	.	PUNCT
ejpam-2333	95	1	again	again	ADV
ejpam-2333	95	2	,	,	PUNCT
ejpam-2333	95	3	if	if	SCONJ
ejpam-2333	95	4	k	k	PROPN
ejpam-2333	95	5	=	=	SYM
ejpam-2333	95	6	1	1	NUM
ejpam-2333	95	7	,	,	PUNCT
ejpam-2333	95	8	then	then	ADV
ejpam-2333	95	9	eq	eq	ADJ
ejpam-2333	95	10	.	.	PUNCT
ejpam-2333	96	1	(	(	PUNCT
ejpam-2333	96	2	5	5	X
ejpam-2333	96	3	)	)	PUNCT
ejpam-2333	96	4	gives	give	VERB
ejpam-2333	96	5	pi−1	pi−1	PROPN
ejpam-2333	96	6	−	−	PROPN
ejpam-2333	96	7	1	1	NUM
ejpam-2333	96	8	=	=	PROPN
ejpam-2333	96	9	mpq	mpq	ADJ
ejpam-2333	96	10	⇒	⇒	NOUN
ejpam-2333	96	11	pi−1	pi−1	PROPN
ejpam-2333	96	12	−	−	NUM
ejpam-2333	96	13	1=	1=	NUM
ejpam-2333	96	14	pq	pq	NOUN
ejpam-2333	96	15	−	−	NOUN
ejpam-2333	96	16	1	1	NUM
ejpam-2333	96	17	⇒	⇒	NOUN
ejpam-2333	97	1	i	i	PRON
ejpam-2333	97	2	−	−	VERB
ejpam-2333	97	3	1=	1=	X
ejpam-2333	97	4	q	q	PROPN
ejpam-2333	97	5	⇒	⇒	X
ejpam-2333	97	6	q	q	PROPN
ejpam-2333	98	1	y	y	PROPN
ejpam-2333	98	2	−	−	PROPN
ejpam-2333	98	3	2=	2=	NUM
ejpam-2333	98	4	q	q	PUNCT
ejpam-2333	98	5	⇒	⇒	NOUN
ejpam-2333	98	6	q(y	q(y	PROPN
ejpam-2333	98	7	−	−	PROPN
ejpam-2333	98	8	1	1	NUM
ejpam-2333	98	9	)	)	PUNCT
ejpam-2333	98	10	=	=	SYM
ejpam-2333	98	11	2	2	NUM
ejpam-2333	98	12	⇒	⇒	NOUN
ejpam-2333	98	13	q	q	NOUN
ejpam-2333	99	1	=	=	SYM
ejpam-2333	99	2	2	2	NUM
ejpam-2333	99	3	,	,	PUNCT
ejpam-2333	99	4	y	y	NOUN
ejpam-2333	99	5	=	=	SYM
ejpam-2333	99	6	2	2	X
ejpam-2333	99	7	.	.	PUNCT
ejpam-2333	100	1	thus	thus	ADV
ejpam-2333	100	2	we	we	PRON
ejpam-2333	100	3	have	have	VERB
ejpam-2333	100	4	mpq	mpq	NOUN
ejpam-2333	100	5	=	=	SYM
ejpam-2333	100	6	3	3	NUM
ejpam-2333	100	7	,	,	PUNCT
ejpam-2333	100	8	x	x	PUNCT
ejpam-2333	101	1	=	=	PUNCT
ejpam-2333	101	2	2k	2k	NUM
ejpam-2333	101	3	=	=	SYM
ejpam-2333	101	4	2	2	NUM
ejpam-2333	101	5	,	,	PUNCT
ejpam-2333	101	6	y	y	NOUN
ejpam-2333	101	7	=	=	SYM
ejpam-2333	101	8	2	2	NUM
ejpam-2333	101	9	and	and	CCONJ
ejpam-2333	101	10	z	z	NOUN
ejpam-2333	101	11	=	=	PUNCT
ejpam-2333	102	1	p	p	PRON
ejpam-2333	102	2	j	j	PROPN
ejpam-2333	102	3	+	+	CCONJ
ejpam-2333	102	4	(	(	PUNCT
ejpam-2333	102	5	mpq	mpq	X
ejpam-2333	102	6	)	)	PUNCT
ejpam-2333	102	7	k	k	NOUN
ejpam-2333	103	1	=	=	PUNCT
ejpam-2333	103	2	5	5	X
ejpam-2333	103	3	.	.	PUNCT
ejpam-2333	103	4	therefore	therefore	ADV
ejpam-2333	103	5	(	(	PUNCT
ejpam-2333	103	6	mpq	mpq	X
ejpam-2333	103	7	,	,	PUNCT
ejpam-2333	103	8	x	x	SYM
ejpam-2333	103	9	,	,	PUNCT
ejpam-2333	103	10	y	y	PROPN
ejpam-2333	103	11	,	,	PUNCT
ejpam-2333	103	12	z	z	NOUN
ejpam-2333	103	13	)	)	PUNCT
ejpam-2333	103	14	=	=	SYM
ejpam-2333	103	15	(	(	PUNCT
ejpam-2333	103	16	3,2,2,5	3,2,2,5	NUM
ejpam-2333	103	17	)	)	PUNCT
ejpam-2333	103	18	is	be	AUX
ejpam-2333	103	19	the	the	DET
ejpam-2333	103	20	only	only	ADJ
ejpam-2333	103	21	solution	solution	NOUN
ejpam-2333	103	22	to	to	ADP
ejpam-2333	103	23	eq	eq	PROPN
ejpam-2333	103	24	.	.	PUNCT
ejpam-2333	104	1	(	(	PUNCT
ejpam-2333	104	2	1	1	X
ejpam-2333	104	3	)	)	PUNCT
ejpam-2333	104	4	in	in	ADP
ejpam-2333	104	5	this	this	DET
ejpam-2333	104	6	sub	sub	NOUN
ejpam-2333	104	7	-	-	NOUN
ejpam-2333	104	8	case	case	NOUN
ejpam-2333	104	9	.	.	PUNCT
ejpam-2333	105	1	case	case	NOUN
ejpam-2333	105	2	2	2	NUM
ejpam-2333	105	3	:	:	PUNCT
ejpam-2333	105	4	let	let	VERB
ejpam-2333	105	5	p	p	PRON
ejpam-2333	105	6	be	be	AUX
ejpam-2333	105	7	an	an	DET
ejpam-2333	105	8	odd	odd	ADJ
ejpam-2333	105	9	positive	positive	ADJ
ejpam-2333	105	10	integer	integer	NOUN
ejpam-2333	105	11	.	.	PUNCT
ejpam-2333	106	1	then	then	ADV
ejpam-2333	106	2	mpq	mpq	PROPN
ejpam-2333	106	3	≡	≡	PROPN
ejpam-2333	106	4	0(mod	0(mod	NOUN
ejpam-2333	106	5	4	4	NUM
ejpam-2333	106	6	)	)	PUNCT
ejpam-2333	106	7	.	.	PUNCT
ejpam-2333	107	1	from	from	ADP
ejpam-2333	107	2	eq	eq	ADP
ejpam-2333	107	3	.	.	PUNCT
ejpam-2333	108	1	(	(	PUNCT
ejpam-2333	108	2	1	1	X
ejpam-2333	108	3	)	)	PUNCT
ejpam-2333	108	4	we	we	PRON
ejpam-2333	108	5	observe	observe	VERB
ejpam-2333	108	6	that	that	SCONJ
ejpam-2333	108	7	z	z	NOUN
ejpam-2333	108	8	must	must	AUX
ejpam-2333	108	9	be	be	AUX
ejpam-2333	108	10	odd	odd	ADJ
ejpam-2333	108	11	,	,	PUNCT
ejpam-2333	108	12	and	and	CCONJ
ejpam-2333	108	13	thus	thus	ADV
ejpam-2333	108	14	z2	z2	PROPN
ejpam-2333	108	15	≡	≡	PROPN
ejpam-2333	108	16	1(mod	1(mod	NUM
ejpam-2333	108	17	4	4	NUM
ejpam-2333	108	18	)	)	PUNCT
ejpam-2333	108	19	.	.	PUNCT
ejpam-2333	109	1	sub	sub	ADJ
ejpam-2333	109	2	-	-	NOUN
ejpam-2333	109	3	case	case	NOUN
ejpam-2333	109	4	2.1	2.1	NUM
ejpam-2333	109	5	:	:	PUNCT
ejpam-2333	109	6	let	let	VERB
ejpam-2333	109	7	y	y	PROPN
ejpam-2333	109	8	=	=	NOUN
ejpam-2333	109	9	0	0	PROPN
ejpam-2333	109	10	.	.	PUNCT
ejpam-2333	110	1	then	then	ADV
ejpam-2333	110	2	eq	eq	X
ejpam-2333	110	3	.	.	PUNCT
ejpam-2333	111	1	(	(	PUNCT
ejpam-2333	111	2	1	1	X
ejpam-2333	111	3	)	)	PUNCT
ejpam-2333	111	4	becomes	become	VERB
ejpam-2333	111	5	(	(	PUNCT
ejpam-2333	111	6	mpq	mpq	X
ejpam-2333	111	7	)	)	PUNCT
ejpam-2333	111	8	x	x	PUNCT
ejpam-2333	112	1	+	+	PUNCT
ejpam-2333	112	2	1=	1=	NUM
ejpam-2333	112	3	z2	z2	NOUN
ejpam-2333	112	4	.	.	PUNCT
ejpam-2333	113	1	this	this	PRON
ejpam-2333	113	2	implies	imply	VERB
ejpam-2333	113	3	(	(	PUNCT
ejpam-2333	113	4	mpq	mpq	X
ejpam-2333	113	5	)	)	PUNCT
ejpam-2333	113	6	x	x	X
ejpam-2333	114	1	=	=	SYM
ejpam-2333	114	2	(	(	PUNCT
ejpam-2333	114	3	z+1)(z−1	z+1)(z−1	NUM
ejpam-2333	114	4	)	)	PUNCT
ejpam-2333	114	5	and	and	CCONJ
ejpam-2333	114	6	thus	thus	ADV
ejpam-2333	114	7	there	there	PRON
ejpam-2333	114	8	exists	exist	VERB
ejpam-2333	114	9	non	non	ADJ
ejpam-2333	114	10	-	-	ADJ
ejpam-2333	114	11	negative	negative	ADJ
ejpam-2333	114	12	integers	integer	NOUN
ejpam-2333	114	13	a	a	PRON
ejpam-2333	114	14	,	,	PUNCT
ejpam-2333	114	15	b	b	X
ejpam-2333	114	16	such	such	ADJ
ejpam-2333	114	17	that	that	PRON
ejpam-2333	114	18	(	(	PUNCT
ejpam-2333	114	19	mpq	mpq	X
ejpam-2333	114	20	)	)	PUNCT
ejpam-2333	114	21	a	a	PRON
ejpam-2333	114	22	=	=	SYM
ejpam-2333	114	23	z+1	z+1	PROPN
ejpam-2333	114	24	and	and	CCONJ
ejpam-2333	114	25	(	(	PUNCT
ejpam-2333	114	26	mpq	mpq	PROPN
ejpam-2333	114	27	)	)	PUNCT
ejpam-2333	114	28	b	b	NOUN
ejpam-2333	115	1	=	=	SYM
ejpam-2333	115	2	z	z	NOUN
ejpam-2333	116	1	−	−	NOUN
ejpam-2333	116	2	1	1	NUM
ejpam-2333	116	3	,	,	PUNCT
ejpam-2333	116	4	where	where	SCONJ
ejpam-2333	116	5	a	a	DET
ejpam-2333	116	6	>	>	X
ejpam-2333	116	7	b	b	PROPN
ejpam-2333	116	8	and	and	CCONJ
ejpam-2333	116	9	x	x	SYM
ejpam-2333	116	10	=	=	SYM
ejpam-2333	116	11	a+	a+	PUNCT
ejpam-2333	116	12	b.	b.	PROPN
ejpam-2333	116	13	now	now	ADV
ejpam-2333	116	14	(	(	PUNCT
ejpam-2333	116	15	mpq	mpq	X
ejpam-2333	116	16	)	)	PUNCT
ejpam-2333	116	17	b(m	b(m	NOUN
ejpam-2333	116	18	a−b	a−b	NOUN
ejpam-2333	116	19	pq	pq	INTJ
ejpam-2333	116	20	−	−	NOUN
ejpam-2333	116	21	1	1	NUM
ejpam-2333	116	22	)	)	PUNCT
ejpam-2333	116	23	=	=	SYM
ejpam-2333	116	24	(	(	PUNCT
ejpam-2333	116	25	mpq	mpq	X
ejpam-2333	116	26	)	)	PUNCT
ejpam-2333	116	27	a	a	DET
ejpam-2333	116	28	−	−	PROPN
ejpam-2333	116	29	(	(	PUNCT
ejpam-2333	116	30	mpq	mpq	PROPN
ejpam-2333	116	31	)	)	PUNCT
ejpam-2333	116	32	b	b	NOUN
ejpam-2333	117	1	=	=	SYM
ejpam-2333	117	2	2	2	X
ejpam-2333	117	3	.	.	PUNCT
ejpam-2333	118	1	this	this	PRON
ejpam-2333	118	2	gives	give	VERB
ejpam-2333	118	3	2≡	2≡	NUM
ejpam-2333	118	4	0(mod	0(mod	NOUN
ejpam-2333	118	5	4	4	NUM
ejpam-2333	118	6	)	)	PUNCT
ejpam-2333	118	7	,	,	PUNCT
ejpam-2333	118	8	an	an	DET
ejpam-2333	118	9	absurdity	absurdity	NOUN
ejpam-2333	118	10	.	.	PUNCT
ejpam-2333	119	1	thus	thus	ADV
ejpam-2333	119	2	there	there	PRON
ejpam-2333	119	3	is	be	VERB
ejpam-2333	119	4	no	no	DET
ejpam-2333	119	5	solution	solution	NOUN
ejpam-2333	119	6	to	to	ADP
ejpam-2333	119	7	eq	eq	PROPN
ejpam-2333	119	8	.	.	PUNCT
ejpam-2333	120	1	(	(	PUNCT
ejpam-2333	120	2	1	1	X
ejpam-2333	120	3	)	)	PUNCT
ejpam-2333	120	4	in	in	ADP
ejpam-2333	120	5	this	this	DET
ejpam-2333	120	6	sub	sub	NOUN
ejpam-2333	120	7	-	-	NOUN
ejpam-2333	120	8	case	case	NOUN
ejpam-2333	120	9	.	.	PUNCT
ejpam-2333	121	1	sub	sub	ADJ
ejpam-2333	121	2	-	-	NOUN
ejpam-2333	121	3	case	case	NOUN
ejpam-2333	121	4	2.2	2.2	NUM
ejpam-2333	121	5	:	:	PUNCT
ejpam-2333	121	6	let	let	VERB
ejpam-2333	121	7	y	y	PRON
ejpam-2333	121	8	≥	≥	VERB
ejpam-2333	121	9	1	1	NUM
ejpam-2333	121	10	even	even	ADV
ejpam-2333	121	11	integer	integer	VERB
ejpam-2333	121	12	and	and	CCONJ
ejpam-2333	121	13	let	let	VERB
ejpam-2333	121	14	y	y	PROPN
ejpam-2333	121	15	=	=	PUNCT
ejpam-2333	121	16	2k	2k	NUM
ejpam-2333	121	17	.	.	PUNCT
ejpam-2333	122	1	then	then	ADV
ejpam-2333	122	2	eq	eq	X
ejpam-2333	122	3	.	.	PUNCT
ejpam-2333	123	1	(	(	PUNCT
ejpam-2333	123	2	1	1	X
ejpam-2333	123	3	)	)	PUNCT
ejpam-2333	123	4	becomes	become	VERB
ejpam-2333	123	5	(	(	PUNCT
ejpam-2333	123	6	mpq	mpq	X
ejpam-2333	123	7	)	)	PUNCT
ejpam-2333	123	8	x	x	PUNCT
ejpam-2333	124	1	+	+	PUNCT
ejpam-2333	124	2	(	(	PUNCT
ejpam-2333	124	3	mpq	mpq	X
ejpam-2333	124	4	+	+	CCONJ
ejpam-2333	124	5	1)2k	1)2k	PROPN
ejpam-2333	124	6	=	=	SYM
ejpam-2333	124	7	z2	z2	PROPN
ejpam-2333	124	8	.	.	PUNCT
ejpam-2333	125	1	this	this	DET
ejpam-2333	125	2	equation	equation	NOUN
ejpam-2333	125	3	implies	imply	VERB
ejpam-2333	125	4	(	(	PUNCT
ejpam-2333	125	5	mpq	mpq	X
ejpam-2333	125	6	)	)	PUNCT
ejpam-2333	125	7	x	x	PUNCT
ejpam-2333	126	1	=	=	PUNCT
ejpam-2333	126	2	z2	z2	PROPN
ejpam-2333	126	3	−	−	PROPN
ejpam-2333	126	4	(	(	PUNCT
ejpam-2333	126	5	pkq)2	pkq)2	PROPN
ejpam-2333	126	6	=	=	SYM
ejpam-2333	126	7	(	(	PUNCT
ejpam-2333	126	8	z	z	NOUN
ejpam-2333	126	9	+	+	NUM
ejpam-2333	126	10	pkq)(z	pkq)(z	NOUN
ejpam-2333	126	11	−	−	NOUN
ejpam-2333	126	12	pkq	pkq	NOUN
ejpam-2333	126	13	)	)	PUNCT
ejpam-2333	126	14	.	.	PUNCT
ejpam-2333	127	1	thus	thus	ADV
ejpam-2333	127	2	there	there	PRON
ejpam-2333	127	3	are	be	VERB
ejpam-2333	127	4	non	non	ADJ
ejpam-2333	127	5	-	-	ADJ
ejpam-2333	127	6	negative	negative	ADJ
ejpam-2333	127	7	integers	integer	NOUN
ejpam-2333	127	8	c	c	VERB
ejpam-2333	127	9	,	,	PUNCT
ejpam-2333	127	10	d	d	X
ejpam-2333	127	11	such	such	ADJ
ejpam-2333	127	12	that	that	SCONJ
ejpam-2333	127	13	(	(	PUNCT
ejpam-2333	127	14	mpq	mpq	X
ejpam-2333	127	15	)	)	PUNCT
ejpam-2333	127	16	c	c	NOUN
ejpam-2333	127	17	=	=	PUNCT
ejpam-2333	127	18	z	z	PROPN
ejpam-2333	127	19	+	+	CCONJ
ejpam-2333	127	20	pkq	pkq	ADJ
ejpam-2333	127	21	and	and	CCONJ
ejpam-2333	127	22	(	(	PUNCT
ejpam-2333	127	23	mpq	mpq	X
ejpam-2333	127	24	)	)	PUNCT
ejpam-2333	127	25	d	d	NOUN
ejpam-2333	127	26	=	=	PUNCT
ejpam-2333	127	27	z	z	PROPN
ejpam-2333	127	28	−	−	NOUN
ejpam-2333	127	29	pkq	pkq	ADJ
ejpam-2333	127	30	,	,	PUNCT
ejpam-2333	127	31	where	where	SCONJ
ejpam-2333	127	32	c	c	X
ejpam-2333	127	33	>	>	X
ejpam-2333	127	34	d	d	PROPN
ejpam-2333	127	35	and	and	CCONJ
ejpam-2333	127	36	c	c	PROPN
ejpam-2333	127	37	+	+	CCONJ
ejpam-2333	127	38	d	d	NOUN
ejpam-2333	127	39	=	=	SYM
ejpam-2333	127	40	x	x	X
ejpam-2333	127	41	.	.	PUNCT
ejpam-2333	128	1	now	now	ADV
ejpam-2333	128	2	,	,	PUNCT
ejpam-2333	128	3	(	(	PUNCT
ejpam-2333	128	4	mpq	mpq	X
ejpam-2333	128	5	)	)	PUNCT
ejpam-2333	128	6	d(m	d(m	NOUN
ejpam-2333	128	7	c−d	c−d	NOUN
ejpam-2333	128	8	pq	pq	INTJ
ejpam-2333	128	9	−	−	NOUN
ejpam-2333	128	10	1	1	NUM
ejpam-2333	128	11	)	)	PUNCT
ejpam-2333	128	12	=	=	SYM
ejpam-2333	128	13	(	(	PUNCT
ejpam-2333	128	14	mpq	mpq	X
ejpam-2333	128	15	)	)	PUNCT
ejpam-2333	128	16	c	c	NOUN
ejpam-2333	129	1	−	−	PROPN
ejpam-2333	129	2	(	(	PUNCT
ejpam-2333	129	3	mpq	mpq	X
ejpam-2333	129	4	)	)	PUNCT
ejpam-2333	129	5	d	d	NOUN
ejpam-2333	129	6	=	=	SYM
ejpam-2333	130	1	2pkq	2pkq	NUM
ejpam-2333	130	2	=	=	PUNCT
ejpam-2333	130	3	2(mpq	2(mpq	NOUN
ejpam-2333	130	4	+	+	CCONJ
ejpam-2333	130	5	1)k	1)k	NUM
ejpam-2333	130	6	.	.	PUNCT
ejpam-2333	131	1	this	this	PRON
ejpam-2333	131	2	implies	imply	VERB
ejpam-2333	131	3	0≡	0≡	NUM
ejpam-2333	132	1	2(mod	2(mod	NUM
ejpam-2333	132	2	4	4	NUM
ejpam-2333	132	3	)	)	PUNCT
ejpam-2333	132	4	.	.	PUNCT
ejpam-2333	133	1	this	this	PRON
ejpam-2333	133	2	is	be	AUX
ejpam-2333	133	3	an	an	DET
ejpam-2333	133	4	absurdity	absurdity	NOUN
ejpam-2333	133	5	.	.	PUNCT
ejpam-2333	134	1	hence	hence	ADV
ejpam-2333	134	2	eq	eq	ADP
ejpam-2333	134	3	.	.	PUNCT
ejpam-2333	135	1	(	(	PUNCT
ejpam-2333	135	2	1	1	X
ejpam-2333	135	3	)	)	PUNCT
ejpam-2333	135	4	has	have	VERB
ejpam-2333	135	5	no	no	DET
ejpam-2333	135	6	solution	solution	NOUN
ejpam-2333	135	7	in	in	ADP
ejpam-2333	135	8	this	this	DET
ejpam-2333	135	9	case	case	NOUN
ejpam-2333	135	10	.	.	PUNCT
ejpam-2333	136	1	references	reference	NOUN
ejpam-2333	136	2	243	243	NUM
ejpam-2333	136	3	acknowledgements	acknowledgement	NOUN
ejpam-2333	136	4	the	the	DET
ejpam-2333	136	5	author	author	NOUN
ejpam-2333	136	6	acknowledges	acknowledge	VERB
ejpam-2333	136	7	ugc	ugc	PROPN
ejpam-2333	136	8	for	for	ADP
ejpam-2333	136	9	jrf	jrf	PROPN
ejpam-2333	136	10	fellowship	fellowship	NOUN
ejpam-2333	136	11	(	(	PUNCT
ejpam-2333	136	12	no.gu/	no.gu/	NUM
ejpam-2333	136	13	ugc	ugc	PROPN
ejpam-2333	136	14	/	/	SYM
ejpam-2333	136	15	vi(3)/jrf/2012	vi(3)/jrf/2012	NOUN
ejpam-2333	136	16	/2985	/2985	PUNCT
ejpam-2333	136	17	)	)	PUNCT
ejpam-2333	136	18	.	.	PUNCT
ejpam-2333	137	1	references	reference	NOUN
ejpam-2333	137	2	[	[	X
ejpam-2333	137	3	1	1	NUM
ejpam-2333	137	4	]	]	PUNCT
ejpam-2333	137	5	p.	p.	NOUN
ejpam-2333	137	6	mihailescu	mihailescu	PROPN
ejpam-2333	137	7	.	.	PUNCT
ejpam-2333	138	1	primary	primary	ADJ
ejpam-2333	138	2	cyclotomic	cyclotomic	ADJ
ejpam-2333	138	3	units	unit	NOUN
ejpam-2333	138	4	and	and	CCONJ
ejpam-2333	138	5	a	a	DET
ejpam-2333	138	6	proof	proof	NOUN
ejpam-2333	138	7	of	of	ADP
ejpam-2333	138	8	catalan	catalan	NOUN
ejpam-2333	138	9	’s	’s	PART
ejpam-2333	138	10	conjecture	conjecture	NOUN
ejpam-2333	138	11	,	,	PUNCT
ejpam-2333	138	12	journal	journal	NOUN
ejpam-2333	138	13	für	für	PROPN
ejpam-2333	138	14	die	die	VERB
ejpam-2333	138	15	reine	reine	PROPN
ejpam-2333	138	16	und	und	PROPN
ejpam-2333	138	17	angewandte	angewandte	PROPN
ejpam-2333	138	18	mathematik	mathematik	PROPN
ejpam-2333	138	19	,	,	PUNCT
ejpam-2333	138	20	27	27	NUM
ejpam-2333	138	21	,	,	PUNCT
ejpam-2333	138	22	167	167	NUM
ejpam-2333	138	23	-	-	SYM
ejpam-2333	138	24	195	195	NUM
ejpam-2333	138	25	.	.	NOUN
ejpam-2333	138	26	2004	2004	NUM
ejpam-2333	138	27	.	.	PUNCT
ejpam-2333	139	1	[	[	X
ejpam-2333	139	2	2	2	NUM
ejpam-2333	139	3	]	]	X
ejpam-2333	139	4	b.	b.	PROPN
ejpam-2333	139	5	sroysang	sroysang	PROPN
ejpam-2333	139	6	.	.	PUNCT
ejpam-2333	140	1	on	on	ADP
ejpam-2333	140	2	the	the	DET
ejpam-2333	140	3	diophantine	diophantine	NOUN
ejpam-2333	140	4	equation	equation	NOUN
ejpam-2333	140	5	31x	31x	NOUN
ejpam-2333	140	6	+	+	SYM
ejpam-2333	140	7	32y	32y	NOUN
ejpam-2333	140	8	=	=	SYM
ejpam-2333	140	9	z2	z2	PROPN
ejpam-2333	140	10	,	,	PUNCT
ejpam-2333	140	11	international	international	ADJ
ejpam-2333	140	12	journal	journal	NOUN
ejpam-2333	140	13	of	of	ADP
ejpam-2333	140	14	pure	pure	ADJ
ejpam-2333	140	15	and	and	CCONJ
ejpam-2333	140	16	applied	applied	ADJ
ejpam-2333	140	17	mathematics	mathematic	NOUN
ejpam-2333	140	18	,	,	PUNCT
ejpam-2333	140	19	81	81	NUM
ejpam-2333	140	20	,	,	PUNCT
ejpam-2333	140	21	609	609	NUM
ejpam-2333	140	22	-	-	SYM
ejpam-2333	140	23	612	612	NUM
ejpam-2333	140	24	.	.	PUNCT
ejpam-2333	140	25	2012	2012	NUM
ejpam-2333	140	26	.	.	PUNCT
ejpam-2333	141	1	[	[	X
ejpam-2333	141	2	3	3	X
ejpam-2333	141	3	]	]	X
ejpam-2333	141	4	b.	b.	PROPN
ejpam-2333	141	5	sroysang	sroysang	PROPN
ejpam-2333	141	6	.	.	PUNCT
ejpam-2333	142	1	on	on	ADP
ejpam-2333	142	2	the	the	DET
ejpam-2333	142	3	diophantine	diophantine	NOUN
ejpam-2333	142	4	equation	equation	NOUN
ejpam-2333	142	5	7x	7x	NOUN
ejpam-2333	142	6	+8y	+8y	NUM
ejpam-2333	142	7	=	=	SYM
ejpam-2333	142	8	z2	z2	PROPN
ejpam-2333	142	9	,	,	PUNCT
ejpam-2333	142	10	international	international	ADJ
ejpam-2333	142	11	journal	journal	NOUN
ejpam-2333	142	12	of	of	ADP
ejpam-2333	142	13	pure	pure	ADJ
ejpam-2333	142	14	and	and	CCONJ
ejpam-2333	142	15	applied	applied	ADJ
ejpam-2333	142	16	mathematics	mathematic	NOUN
ejpam-2333	142	17	,	,	PUNCT
ejpam-2333	142	18	84	84	NUM
ejpam-2333	142	19	,	,	PUNCT
ejpam-2333	142	20	111	111	NUM
ejpam-2333	142	21	-	-	SYM
ejpam-2333	142	22	114	114	NUM
ejpam-2333	142	23	.	.	PUNCT
ejpam-2333	142	24	2013	2013	NUM
ejpam-2333	142	25	.	.	PUNCT