id	sid	tid	token	lemma	pos
ejpam-4940	1	1	european	european	PROPN
ejpam-4940	1	2	journal	journal	PROPN
ejpam-4940	1	3	of	of	ADP
ejpam-4940	1	4	pure	pure	ADJ
ejpam-4940	1	5	and	and	CCONJ
ejpam-4940	1	6	applied	apply	VERB
ejpam-4940	1	7	mathematics	mathematic	NOUN
ejpam-4940	1	8	vol	vol	NOUN
ejpam-4940	1	9	.	.	PUNCT
ejpam-4940	2	1	16	16	NUM
ejpam-4940	2	2	,	,	PUNCT
ejpam-4940	2	3	no	no	INTJ
ejpam-4940	2	4	.	.	NOUN
ejpam-4940	2	5	4	4	NUM
ejpam-4940	2	6	,	,	PUNCT
ejpam-4940	2	7	2023	2023	NUM
ejpam-4940	2	8	,	,	PUNCT
ejpam-4940	2	9	2693	2693	NUM
ejpam-4940	2	10	-	-	SYM
ejpam-4940	2	11	2702	2702	NUM
ejpam-4940	2	12	issn	issn	PROPN
ejpam-4940	2	13	1307	1307	NUM
ejpam-4940	2	14	-	-	SYM
ejpam-4940	2	15	5543	5543	NUM
ejpam-4940	2	16	–	–	PUNCT
ejpam-4940	3	1	ejpam.com	ejpam.com	X
ejpam-4940	3	2	published	publish	VERB
ejpam-4940	3	3	by	by	ADP
ejpam-4940	3	4	new	new	PROPN
ejpam-4940	3	5	york	york	PROPN
ejpam-4940	3	6	business	business	PROPN
ejpam-4940	3	7	global	global	ADJ
ejpam-4940	3	8	solutions	solution	NOUN
ejpam-4940	3	9	of	of	ADP
ejpam-4940	3	10	some	some	DET
ejpam-4940	3	11	quadratic	quadratic	ADJ
ejpam-4940	3	12	diophantine	diophantine	NOUN
ejpam-4940	3	13	equations	equation	NOUN
ejpam-4940	3	14	alanod	alanod	PROPN
ejpam-4940	3	15	m.	m.	PROPN
ejpam-4940	3	16	sibih	sibih	PROPN
ejpam-4940	3	17	department	department	PROPN
ejpam-4940	3	18	of	of	ADP
ejpam-4940	3	19	mathematics	mathematic	NOUN
ejpam-4940	3	20	,	,	PUNCT
ejpam-4940	3	21	jamoum	jamoum	PROPN
ejpam-4940	3	22	university	university	PROPN
ejpam-4940	3	23	college	college	NOUN
ejpam-4940	3	24	,	,	PUNCT
ejpam-4940	3	25	umm	umm	INTJ
ejpam-4940	3	26	al	al	PROPN
ejpam-4940	3	27	-	-	PUNCT
ejpam-4940	3	28	qura	qura	PROPN
ejpam-4940	3	29	university	university	NOUN
ejpam-4940	3	30	,	,	PUNCT
ejpam-4940	3	31	holly	holly	PROPN
ejpam-4940	3	32	makkah	makkah	PROPN
ejpam-4940	3	33	21955	21955	NUM
ejpam-4940	3	34	,	,	PUNCT
ejpam-4940	3	35	saudi	saudi	PROPN
ejpam-4940	3	36	arabia	arabia	PROPN
ejpam-4940	3	37	abstract	abstract	NOUN
ejpam-4940	3	38	.	.	PUNCT
ejpam-4940	4	1	let	let	VERB
ejpam-4940	4	2	p	p	NOUN
ejpam-4940	4	3	(	(	PUNCT
ejpam-4940	4	4	t)±i	t)±i	NOUN
ejpam-4940	4	5	=	=	X
ejpam-4940	4	6	t2k±itm	t2k±itm	PROPN
ejpam-4940	4	7	be	be	AUX
ejpam-4940	4	8	a	a	DET
ejpam-4940	4	9	non	non	ADJ
ejpam-4940	4	10	square	square	ADJ
ejpam-4940	4	11	polynomial	polynomial	NOUN
ejpam-4940	4	12	and	and	CCONJ
ejpam-4940	4	13	q(t)±i	q(t)±i	PUNCT
ejpam-4940	5	1	=	=	NOUN
ejpam-4940	5	2	4k2t4k−2+i2m2t2m−2±	4k2t4k−2+i2m2t2m−2±	NUM
ejpam-4940	5	3	4imkt2k+m−2	4imkt2k+m−2	NUM
ejpam-4940	5	4	−	−	NOUN
ejpam-4940	5	5	4t2k	4t2k	NOUN
ejpam-4940	6	1	∓	∓	NOUN
ejpam-4940	6	2	4itm	4itm	NOUN
ejpam-4940	6	3	−	−	NOUN
ejpam-4940	6	4	1	1	NUM
ejpam-4940	6	5	be	be	AUX
ejpam-4940	6	6	a	a	DET
ejpam-4940	6	7	polynomial	polynomial	ADJ
ejpam-4940	6	8	,	,	PUNCT
ejpam-4940	6	9	such	such	ADJ
ejpam-4940	6	10	that	that	SCONJ
ejpam-4940	6	11	k	k	PROPN
ejpam-4940	6	12	≥	≥	NUM
ejpam-4940	6	13	2	2	NUM
ejpam-4940	6	14	m	m	VERB
ejpam-4940	6	15	and	and	CCONJ
ejpam-4940	6	16	i	i	PRON
ejpam-4940	6	17	∈	∈	PROPN
ejpam-4940	6	18	{	{	PUNCT
ejpam-4940	6	19	1	1	NUM
ejpam-4940	6	20	,	,	PUNCT
ejpam-4940	6	21	2	2	NUM
ejpam-4940	6	22	}	}	PUNCT
ejpam-4940	6	23	.	.	PUNCT
ejpam-4940	7	1	in	in	ADP
ejpam-4940	7	2	this	this	DET
ejpam-4940	7	3	paper	paper	NOUN
ejpam-4940	7	4	,	,	PUNCT
ejpam-4940	7	5	we	we	PRON
ejpam-4940	7	6	consider	consider	VERB
ejpam-4940	7	7	the	the	DET
ejpam-4940	7	8	number	number	NOUN
ejpam-4940	7	9	of	of	ADP
ejpam-4940	7	10	integer	integer	NOUN
ejpam-4940	7	11	solutions	solution	NOUN
ejpam-4940	7	12	of	of	ADP
ejpam-4940	7	13	diophantine	diophantine	NOUN
ejpam-4940	7	14	equation	equation	NOUN
ejpam-4940	7	15	e	e	NOUN
ejpam-4940	7	16	:	:	PUNCT
ejpam-4940	8	1	x2	x2	PROPN
ejpam-4940	8	2	−	−	PROPN
ejpam-4940	9	1	p	p	X
ejpam-4940	9	2	(	(	PUNCT
ejpam-4940	9	3	t)±i	t)±i	NOUN
ejpam-4940	9	4	y	y	PROPN
ejpam-4940	9	5	2	2	NUM
ejpam-4940	9	6	−	−	NOUN
ejpam-4940	9	7	2p	2p	NUM
ejpam-4940	9	8	′(t)±i	′(t)±i	NOUN
ejpam-4940	9	9	x+	x+	PROPN
ejpam-4940	9	10	4p	4p	NOUN
ejpam-4940	9	11	(	(	PUNCT
ejpam-4940	9	12	t)±i	t)±i	X
ejpam-4940	9	13	y	y	PROPN
ejpam-4940	9	14	+	+	NOUN
ejpam-4940	9	15	q(t)±i	q(t)±i	NOUN
ejpam-4940	9	16	=	=	NOUN
ejpam-4940	9	17	0	0	X
ejpam-4940	9	18	.	.	PUNCT
ejpam-4940	10	1	we	we	PRON
ejpam-4940	10	2	extend	extend	VERB
ejpam-4940	10	3	a	a	DET
ejpam-4940	10	4	previous	previous	ADJ
ejpam-4940	10	5	results	result	NOUN
ejpam-4940	10	6	given	give	VERB
ejpam-4940	10	7	by	by	ADP
ejpam-4940	10	8	a.	a.	NOUN
ejpam-4940	10	9	tekcan	tekcan	PROPN
ejpam-4940	10	10	and	and	CCONJ
ejpam-4940	10	11	a.	a.	PROPN
ejpam-4940	10	12	chandoul	chandoul	PROPN
ejpam-4940	10	13	et	et	PROPN
ejpam-4940	10	14	al	al	PROPN
ejpam-4940	10	15	.	.	PUNCT
ejpam-4940	11	1	we	we	PRON
ejpam-4940	11	2	also	also	ADV
ejpam-4940	11	3	derive	derive	VERB
ejpam-4940	11	4	some	some	DET
ejpam-4940	11	5	recurrence	recurrence	NOUN
ejpam-4940	11	6	relations	relation	NOUN
ejpam-4940	11	7	on	on	ADP
ejpam-4940	11	8	the	the	DET
ejpam-4940	11	9	integer	integer	NOUN
ejpam-4940	11	10	solutions	solution	NOUN
ejpam-4940	11	11	of	of	ADP
ejpam-4940	11	12	a	a	DET
ejpam-4940	11	13	pell	pell	NOUN
ejpam-4940	11	14	equation	equation	NOUN
ejpam-4940	11	15	.	.	PUNCT
ejpam-4940	12	1	2020	2020	NUM
ejpam-4940	12	2	mathematics	mathematic	NOUN
ejpam-4940	12	3	subject	subject	NOUN
ejpam-4940	12	4	classifications	classification	NOUN
ejpam-4940	12	5	:	:	PUNCT
ejpam-4940	12	6	11d45	11d45	NUM
ejpam-4940	12	7	,	,	PUNCT
ejpam-4940	12	8	11y65	11y65	NUM
ejpam-4940	12	9	key	key	ADJ
ejpam-4940	12	10	words	word	NOUN
ejpam-4940	12	11	and	and	CCONJ
ejpam-4940	12	12	phrases	phrase	NOUN
ejpam-4940	12	13	:	:	PUNCT
ejpam-4940	12	14	diophantine	diophantine	VERB
ejpam-4940	12	15	equation	equation	NOUN
ejpam-4940	12	16	,	,	PUNCT
ejpam-4940	12	17	pell	pell	PROPN
ejpam-4940	12	18	’s	’s	PART
ejpam-4940	12	19	equation	equation	NOUN
ejpam-4940	12	20	,	,	PUNCT
ejpam-4940	12	21	continued	continued	ADJ
ejpam-4940	12	22	fraction	fraction	NOUN
ejpam-4940	12	23	,	,	PUNCT
ejpam-4940	12	24	quadratic	quadratic	ADJ
ejpam-4940	12	25	residue	residue	NOUN
ejpam-4940	12	26	1	1	NUM
ejpam-4940	12	27	.	.	PUNCT
ejpam-4940	13	1	introduction	introduction	NOUN
ejpam-4940	13	2	let	let	VERB
ejpam-4940	13	3	f(x1	f(x1	ADJ
ejpam-4940	13	4	,	,	PUNCT
ejpam-4940	13	5	x2	x2	PROPN
ejpam-4940	13	6	,	,	PUNCT
ejpam-4940	13	7	.	.	PUNCT
ejpam-4940	13	8	.	.	PUNCT
ejpam-4940	14	1	.	.	PUNCT
ejpam-4940	15	1	,	,	PUNCT
ejpam-4940	15	2	xn	xn	X
ejpam-4940	15	3	)	)	PUNCT
ejpam-4940	15	4	be	be	VERB
ejpam-4940	15	5	a	a	DET
ejpam-4940	15	6	polynomial	polynomial	NOUN
ejpam-4940	15	7	with	with	ADP
ejpam-4940	15	8	integer	integer	NOUN
ejpam-4940	15	9	coefficients	coefficient	NOUN
ejpam-4940	15	10	in	in	ADP
ejpam-4940	15	11	one	one	NUM
ejpam-4940	15	12	or	or	CCONJ
ejpam-4940	15	13	more	more	ADJ
ejpam-4940	15	14	variables	variable	NOUN
ejpam-4940	15	15	.	.	PUNCT
ejpam-4940	16	1	a	a	DET
ejpam-4940	16	2	diophantine	diophantine	NOUN
ejpam-4940	16	3	equation	equation	NOUN
ejpam-4940	16	4	is	be	AUX
ejpam-4940	16	5	an	an	DET
ejpam-4940	16	6	algebraic	algebraic	ADJ
ejpam-4940	16	7	equation	equation	NOUN
ejpam-4940	16	8	f(x1	f(x1	NOUN
ejpam-4940	16	9	,	,	PUNCT
ejpam-4940	16	10	x2	x2	PROPN
ejpam-4940	16	11	,	,	PUNCT
ejpam-4940	16	12	.	.	PUNCT
ejpam-4940	16	13	.	.	PUNCT
ejpam-4940	17	1	.	.	PUNCT
ejpam-4940	18	1	,	,	PUNCT
ejpam-4940	18	2	xn	xn	X
ejpam-4940	18	3	)	)	PUNCT
ejpam-4940	19	1	=	=	SYM
ejpam-4940	19	2	0	0	NUM
ejpam-4940	19	3	for	for	ADP
ejpam-4940	19	4	which	which	PRON
ejpam-4940	19	5	integer	integer	NOUN
ejpam-4940	19	6	solutions	solution	NOUN
ejpam-4940	19	7	are	be	AUX
ejpam-4940	19	8	sought	seek	VERB
ejpam-4940	19	9	.	.	PUNCT
ejpam-4940	20	1	the	the	DET
ejpam-4940	20	2	problem	problem	NOUN
ejpam-4940	20	3	to	to	PART
ejpam-4940	20	4	be	be	AUX
ejpam-4940	20	5	solved	solve	VERB
ejpam-4940	20	6	is	be	AUX
ejpam-4940	20	7	to	to	PART
ejpam-4940	20	8	determine	determine	VERB
ejpam-4940	20	9	whether	whether	SCONJ
ejpam-4940	20	10	or	or	CCONJ
ejpam-4940	20	11	not	not	PART
ejpam-4940	20	12	a	a	DET
ejpam-4940	20	13	given	give	VERB
ejpam-4940	20	14	diophantine	diophantine	NOUN
ejpam-4940	20	15	equation	equation	NOUN
ejpam-4940	20	16	has	have	VERB
ejpam-4940	20	17	solutions	solution	NOUN
ejpam-4940	20	18	in	in	ADP
ejpam-4940	20	19	the	the	DET
ejpam-4940	20	20	domain	domain	NOUN
ejpam-4940	20	21	of	of	ADP
ejpam-4940	20	22	integer	integer	NOUN
ejpam-4940	20	23	numbers	number	NOUN
ejpam-4940	20	24	.	.	PUNCT
ejpam-4940	21	1	in	in	ADP
ejpam-4940	21	2	the	the	DET
ejpam-4940	21	3	case	case	NOUN
ejpam-4940	21	4	where	where	SCONJ
ejpam-4940	21	5	the	the	DET
ejpam-4940	21	6	diophantine	diophantine	NOUN
ejpam-4940	21	7	equation	equation	NOUN
ejpam-4940	21	8	is	be	AUX
ejpam-4940	21	9	solvable	solvable	ADJ
ejpam-4940	21	10	,	,	PUNCT
ejpam-4940	21	11	there	there	PRON
ejpam-4940	21	12	are	be	VERB
ejpam-4940	21	13	some	some	DET
ejpam-4940	21	14	natural	natural	ADJ
ejpam-4940	21	15	questions	question	NOUN
ejpam-4940	21	16	:	:	PUNCT
ejpam-4940	21	17	∗	∗	NOUN
ejpam-4940	21	18	)	)	PUNCT
ejpam-4940	21	19	is	be	AUX
ejpam-4940	21	20	the	the	DET
ejpam-4940	21	21	number	number	NOUN
ejpam-4940	21	22	of	of	ADP
ejpam-4940	21	23	solutions	solution	NOUN
ejpam-4940	21	24	finite	finite	NOUN
ejpam-4940	21	25	or	or	CCONJ
ejpam-4940	21	26	infinite	infinite	ADJ
ejpam-4940	21	27	?	?	PUNCT
ejpam-4940	22	1	∗∗	∗∗	X
ejpam-4940	22	2	)	)	PUNCT
ejpam-4940	23	1	is	be	AUX
ejpam-4940	23	2	it	it	PRON
ejpam-4940	23	3	possible	possible	ADJ
ejpam-4940	23	4	to	to	PART
ejpam-4940	23	5	determine	determine	VERB
ejpam-4940	23	6	all	all	DET
ejpam-4940	23	7	solutions	solution	NOUN
ejpam-4940	23	8	?	?	PUNCT
ejpam-4940	24	1	in	in	ADP
ejpam-4940	24	2	1900	1900	NUM
ejpam-4940	24	3	,	,	PUNCT
ejpam-4940	24	4	hilbert	hilbert	PROPN
ejpam-4940	24	5	[	[	X
ejpam-4940	24	6	4	4	X
ejpam-4940	24	7	]	]	PUNCT
ejpam-4940	24	8	asked	ask	VERB
ejpam-4940	24	9	for	for	ADP
ejpam-4940	24	10	general	general	ADJ
ejpam-4940	24	11	algorithm	algorithm	NOUN
ejpam-4940	24	12	to	to	PART
ejpam-4940	24	13	determine	determine	VERB
ejpam-4940	24	14	,	,	PUNCT
ejpam-4940	24	15	in	in	ADP
ejpam-4940	24	16	a	a	DET
ejpam-4940	24	17	finite	finite	ADJ
ejpam-4940	24	18	number	number	NOUN
ejpam-4940	24	19	of	of	ADP
ejpam-4940	24	20	steps	step	NOUN
ejpam-4940	24	21	,	,	PUNCT
ejpam-4940	24	22	the	the	DET
ejpam-4940	24	23	solvability	solvability	NOUN
ejpam-4940	24	24	of	of	ADP
ejpam-4940	24	25	any	any	DET
ejpam-4940	24	26	given	give	VERB
ejpam-4940	24	27	diophantine	diophantine	NOUN
ejpam-4940	24	28	equation	equation	NOUN
ejpam-4940	24	29	.	.	PUNCT
ejpam-4940	25	1	in	in	ADP
ejpam-4940	25	2	other	other	ADJ
ejpam-4940	25	3	words	word	NOUN
ejpam-4940	25	4	,	,	PUNCT
ejpam-4940	25	5	he	he	PRON
ejpam-4940	25	6	asked	ask	VERB
ejpam-4940	25	7	if	if	SCONJ
ejpam-4940	25	8	there	there	PRON
ejpam-4940	25	9	are	be	VERB
ejpam-4940	25	10	any	any	DET
ejpam-4940	25	11	universal	universal	ADJ
ejpam-4940	25	12	method	method	NOUN
ejpam-4940	25	13	of	of	ADP
ejpam-4940	25	14	solving	solve	VERB
ejpam-4940	25	15	all	all	DET
ejpam-4940	25	16	diophantine	diophantine	NOUN
ejpam-4940	25	17	equations	equation	NOUN
ejpam-4940	25	18	.	.	PUNCT
ejpam-4940	26	1	unfortunately	unfortunately	ADV
ejpam-4940	26	2	,	,	PUNCT
ejpam-4940	26	3	it	it	PRON
ejpam-4940	26	4	was	be	AUX
ejpam-4940	26	5	proven	prove	VERB
ejpam-4940	26	6	by	by	ADP
ejpam-4940	26	7	matyasevich	matyasevich	PROPN
ejpam-4940	26	8	,	,	PUNCT
ejpam-4940	26	9	in	in	ADP
ejpam-4940	26	10	1970	1970	NUM
ejpam-4940	26	11	,	,	PUNCT
ejpam-4940	26	12	that	that	SCONJ
ejpam-4940	26	13	this	this	DET
ejpam-4940	26	14	problem	problem	NOUN
ejpam-4940	26	15	is	be	AUX
ejpam-4940	26	16	unsolvable	unsolvable	ADJ
ejpam-4940	26	17	[	[	X
ejpam-4940	26	18	3	3	NUM
ejpam-4940	26	19	]	]	PUNCT
ejpam-4940	26	20	.	.	PUNCT
ejpam-4940	27	1	doi	doi	NOUN
ejpam-4940	27	2	:	:	PUNCT
ejpam-4940	27	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4940	https://doi.org/10.29020/nybg.ejpam.v16i4.4940	NOUN
ejpam-4940	27	4	email	email	NOUN
ejpam-4940	27	5	address	address	NOUN
ejpam-4940	27	6	:	:	PUNCT
ejpam-4940	27	7	amsibih@uqu.edu.sa	amsibih@uqu.edu.sa	PROPN
ejpam-4940	27	8	(	(	PUNCT
ejpam-4940	27	9	alanod	alanod	PROPN
ejpam-4940	27	10	m.	m.	PROPN
ejpam-4940	27	11	sibih	sibih	PROPN
ejpam-4940	27	12	)	)	PUNCT
ejpam-4940	27	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4940	27	14	2693	2693	NUM
ejpam-4940	28	1	©	©	PROPN
ejpam-4940	28	2	2023	2023	NUM
ejpam-4940	28	3	ejpam	ejpam	NOUN
ejpam-4940	28	4	all	all	DET
ejpam-4940	28	5	rights	right	NOUN
ejpam-4940	28	6	reserved	reserve	VERB
ejpam-4940	28	7	.	.	PUNCT
ejpam-4940	29	1	a.	a.	NOUN
ejpam-4940	29	2	m.	m.	PROPN
ejpam-4940	29	3	sibih	sibih	PROPN
ejpam-4940	29	4	/	/	SYM
ejpam-4940	29	5	eur	eur	PROPN
ejpam-4940	29	6	.	.	PUNCT
ejpam-4940	30	1	j.	j.	PROPN
ejpam-4940	30	2	pure	pure	PROPN
ejpam-4940	30	3	appl	appl	PROPN
ejpam-4940	30	4	.	.	PROPN
ejpam-4940	30	5	math	math	PROPN
ejpam-4940	30	6	,	,	PUNCT
ejpam-4940	30	7	16	16	NUM
ejpam-4940	30	8	(	(	PUNCT
ejpam-4940	30	9	4	4	NUM
ejpam-4940	30	10	)	)	PUNCT
ejpam-4940	30	11	(	(	PUNCT
ejpam-4940	30	12	2023	2023	NUM
ejpam-4940	30	13	)	)	PUNCT
ejpam-4940	30	14	,	,	PUNCT
ejpam-4940	30	15	2693	2693	NUM
ejpam-4940	30	16	-	-	SYM
ejpam-4940	30	17	2702	2702	NUM
ejpam-4940	30	18	2694	2694	NUM
ejpam-4940	30	19	the	the	DET
ejpam-4940	30	20	absence	absence	NOUN
ejpam-4940	30	21	of	of	ADP
ejpam-4940	30	22	a	a	DET
ejpam-4940	30	23	general	general	ADJ
ejpam-4940	30	24	algorithm	algorithm	NOUN
ejpam-4940	30	25	was	be	AUX
ejpam-4940	30	26	not	not	PART
ejpam-4940	30	27	by	by	ADP
ejpam-4940	30	28	itself	itself	PRON
ejpam-4940	30	29	obstacle	obstacle	VERB
ejpam-4940	30	30	to	to	PART
ejpam-4940	30	31	involve	involve	VERB
ejpam-4940	30	32	more	more	ADJ
ejpam-4940	30	33	than	than	ADP
ejpam-4940	30	34	technique	technique	NOUN
ejpam-4940	30	35	in	in	ADP
ejpam-4940	30	36	solving	solve	VERB
ejpam-4940	30	37	diophantine	diophantine	NOUN
ejpam-4940	30	38	equations	equation	NOUN
ejpam-4940	30	39	.	.	PUNCT
ejpam-4940	31	1	in	in	ADP
ejpam-4940	31	2	fact	fact	NOUN
ejpam-4940	31	3	,	,	PUNCT
ejpam-4940	31	4	diophantine	diophantine	VERB
ejpam-4940	31	5	equations	equation	NOUN
ejpam-4940	31	6	can	can	AUX
ejpam-4940	31	7	be	be	AUX
ejpam-4940	31	8	very	very	ADV
ejpam-4940	31	9	creative	creative	ADJ
ejpam-4940	31	10	and	and	CCONJ
ejpam-4940	31	11	mathematiciens	mathematicien	NOUN
ejpam-4940	31	12	usually	usually	ADV
ejpam-4940	31	13	have	have	VERB
ejpam-4940	31	14	to	to	PART
ejpam-4940	31	15	exhibit	exhibit	VERB
ejpam-4940	31	16	creativity	creativity	NOUN
ejpam-4940	31	17	to	to	PART
ejpam-4940	31	18	solve	solve	VERB
ejpam-4940	31	19	these	these	DET
ejpam-4940	31	20	questions	question	NOUN
ejpam-4940	31	21	.	.	PUNCT
ejpam-4940	32	1	one	one	NUM
ejpam-4940	32	2	of	of	ADP
ejpam-4940	32	3	the	the	DET
ejpam-4940	32	4	best	well	ADV
ejpam-4940	32	5	-	-	PUNCT
ejpam-4940	32	6	known	know	VERB
ejpam-4940	32	7	techniques	technique	NOUN
ejpam-4940	32	8	is	be	AUX
ejpam-4940	32	9	that	that	SCONJ
ejpam-4940	32	10	one	one	NUM
ejpam-4940	32	11	based	base	VERB
ejpam-4940	32	12	on	on	ADP
ejpam-4940	32	13	reduction	reduction	NOUN
ejpam-4940	32	14	of	of	ADP
ejpam-4940	32	15	the	the	DET
ejpam-4940	32	16	diophantine	diophantine	NOUN
ejpam-4940	32	17	equation	equation	NOUN
ejpam-4940	32	18	of	of	ADP
ejpam-4940	32	19	arbitrary	arbitrary	ADJ
ejpam-4940	32	20	size	size	NOUN
ejpam-4940	32	21	with	with	ADP
ejpam-4940	32	22	many	many	ADJ
ejpam-4940	32	23	arbitrary	arbitrary	ADJ
ejpam-4940	32	24	unknowns	unknown	NOUN
ejpam-4940	32	25	to	to	ADP
ejpam-4940	32	26	another	another	DET
ejpam-4940	32	27	equation	equation	NOUN
ejpam-4940	32	28	having	have	VERB
ejpam-4940	32	29	a	a	DET
ejpam-4940	32	30	fixed	fix	VERB
ejpam-4940	32	31	degree	degree	NOUN
ejpam-4940	32	32	and	and	CCONJ
ejpam-4940	32	33	fixed	fix	VERB
ejpam-4940	32	34	number	number	NOUN
ejpam-4940	32	35	of	of	ADP
ejpam-4940	32	36	unknowns	unknown	NOUN
ejpam-4940	32	37	.	.	PUNCT
ejpam-4940	33	1	another	another	DET
ejpam-4940	33	2	one	one	NUM
ejpam-4940	33	3	of	of	ADP
ejpam-4940	33	4	the	the	DET
ejpam-4940	33	5	most	most	ADV
ejpam-4940	33	6	common	common	ADJ
ejpam-4940	33	7	techniques	technique	NOUN
ejpam-4940	33	8	used	use	VERB
ejpam-4940	33	9	to	to	PART
ejpam-4940	33	10	examine	examine	VERB
ejpam-4940	33	11	diophantine	diophantine	NOUN
ejpam-4940	33	12	equations	equation	NOUN
ejpam-4940	33	13	problem	problem	NOUN
ejpam-4940	33	14	is	be	AUX
ejpam-4940	33	15	that	that	SCONJ
ejpam-4940	33	16	based	base	VERB
ejpam-4940	33	17	on	on	ADP
ejpam-4940	33	18	considering	consider	VERB
ejpam-4940	33	19	residues	residue	NOUN
ejpam-4940	33	20	by	by	ADP
ejpam-4940	33	21	checking	check	VERB
ejpam-4940	33	22	certain	certain	ADJ
ejpam-4940	33	23	common	common	ADJ
ejpam-4940	33	24	modulos	modulo	NOUN
ejpam-4940	33	25	on	on	ADP
ejpam-4940	33	26	each	each	DET
ejpam-4940	33	27	term	term	NOUN
ejpam-4940	33	28	of	of	ADP
ejpam-4940	33	29	the	the	DET
ejpam-4940	33	30	equation	equation	NOUN
ejpam-4940	33	31	,	,	PUNCT
ejpam-4940	33	32	one	one	PRON
ejpam-4940	33	33	can	can	AUX
ejpam-4940	33	34	either	either	ADV
ejpam-4940	33	35	arrive	arrive	VERB
ejpam-4940	33	36	at	at	ADP
ejpam-4940	33	37	a	a	DET
ejpam-4940	33	38	contradiction	contradiction	NOUN
ejpam-4940	33	39	to	to	PART
ejpam-4940	33	40	prove	prove	VERB
ejpam-4940	33	41	that	that	SCONJ
ejpam-4940	33	42	there	there	PRON
ejpam-4940	33	43	’s	’	VERB
ejpam-4940	33	44	no	no	DET
ejpam-4940	33	45	solution	solution	NOUN
ejpam-4940	33	46	,	,	PUNCT
ejpam-4940	33	47	or	or	CCONJ
ejpam-4940	33	48	to	to	PART
ejpam-4940	33	49	find	find	VERB
ejpam-4940	33	50	the	the	DET
ejpam-4940	33	51	unique	unique	ADJ
ejpam-4940	33	52	solutions	solution	NOUN
ejpam-4940	33	53	that	that	PRON
ejpam-4940	33	54	satisfy	satisfy	VERB
ejpam-4940	33	55	the	the	DET
ejpam-4940	33	56	equation	equation	NOUN
ejpam-4940	33	57	.	.	PUNCT
ejpam-4940	34	1	this	this	DET
ejpam-4940	34	2	technique	technique	NOUN
ejpam-4940	34	3	assumes	assume	VERB
ejpam-4940	34	4	basic	basic	ADJ
ejpam-4940	34	5	knowledge	knowledge	NOUN
ejpam-4940	34	6	of	of	ADP
ejpam-4940	34	7	modular	modular	ADJ
ejpam-4940	34	8	arithmetic	arithmetic	ADJ
ejpam-4940	34	9	as	as	ADV
ejpam-4940	34	10	well	well	ADV
ejpam-4940	34	11	as	as	ADP
ejpam-4940	34	12	important	important	ADJ
ejpam-4940	34	13	notions	notion	NOUN
ejpam-4940	34	14	and	and	CCONJ
ejpam-4940	34	15	theorem	theorem	VERB
ejpam-4940	34	16	like	like	ADP
ejpam-4940	34	17	the	the	DET
ejpam-4940	34	18	quadratic	quadratic	ADJ
ejpam-4940	34	19	residues	residue	NOUN
ejpam-4940	34	20	modulo	modulo	VERB
ejpam-4940	34	21	a	a	DET
ejpam-4940	34	22	prime	prime	ADJ
ejpam-4940	34	23	number	number	NOUN
ejpam-4940	34	24	p	p	NOUN
ejpam-4940	34	25	and	and	CCONJ
ejpam-4940	34	26	euler	euler	PROPN
ejpam-4940	34	27	theorem	theorem	PROPN
ejpam-4940	34	28	.	.	PUNCT
ejpam-4940	35	1	recently	recently	ADV
ejpam-4940	35	2	,	,	PUNCT
ejpam-4940	35	3	there	there	PRON
ejpam-4940	35	4	are	be	VERB
ejpam-4940	35	5	a	a	DET
ejpam-4940	35	6	number	number	NOUN
ejpam-4940	35	7	of	of	ADP
ejpam-4940	35	8	paper	paper	NOUN
ejpam-4940	35	9	have	have	AUX
ejpam-4940	35	10	been	be	AUX
ejpam-4940	35	11	written	write	VERB
ejpam-4940	35	12	and	and	CCONJ
ejpam-4940	35	13	published	publish	VERB
ejpam-4940	35	14	by	by	ADP
ejpam-4940	35	15	a.	a.	NOUN
ejpam-4940	35	16	tekcan	tekcan	PROPN
ejpam-4940	35	17	using	use	VERB
ejpam-4940	35	18	the	the	DET
ejpam-4940	35	19	techniques	technique	NOUN
ejpam-4940	35	20	mentioned	mention	VERB
ejpam-4940	35	21	above	above	ADV
ejpam-4940	35	22	.	.	PUNCT
ejpam-4940	36	1	this	this	DET
ejpam-4940	36	2	paper	paper	NOUN
ejpam-4940	36	3	offers	offer	VERB
ejpam-4940	36	4	an	an	DET
ejpam-4940	36	5	extension	extension	NOUN
ejpam-4940	36	6	of	of	ADP
ejpam-4940	36	7	one	one	NUM
ejpam-4940	36	8	of	of	ADP
ejpam-4940	36	9	the	the	DET
ejpam-4940	36	10	results	result	NOUN
ejpam-4940	36	11	given	give	VERB
ejpam-4940	36	12	by	by	ADP
ejpam-4940	36	13	a.	a.	NOUN
ejpam-4940	36	14	tekcan	tekcan	NOUN
ejpam-4940	37	1	[	[	X
ejpam-4940	37	2	2	2	X
ejpam-4940	37	3	]	]	PUNCT
ejpam-4940	37	4	and	and	CCONJ
ejpam-4940	37	5	a.	a.	PROPN
ejpam-4940	37	6	chandoul	chandoul	PROPN
ejpam-4940	37	7	et	et	PROPN
ejpam-4940	37	8	al	al	PROPN
ejpam-4940	37	9	.	.	PUNCT
ejpam-4940	38	1	[	[	X
ejpam-4940	38	2	1	1	NUM
ejpam-4940	38	3	]	]	PUNCT
ejpam-4940	38	4	.	.	PUNCT
ejpam-4940	39	1	in	in	ADP
ejpam-4940	39	2	[	[	X
ejpam-4940	39	3	2	2	NUM
ejpam-4940	39	4	]	]	PUNCT
ejpam-4940	39	5	,	,	PUNCT
ejpam-4940	39	6	tekcan	tekcan	PROPN
ejpam-4940	39	7	consider	consider	VERB
ejpam-4940	39	8	the	the	DET
ejpam-4940	39	9	number	number	NOUN
ejpam-4940	39	10	of	of	ADP
ejpam-4940	39	11	integer	integer	NOUN
ejpam-4940	39	12	solutions	solution	NOUN
ejpam-4940	39	13	of	of	ADP
ejpam-4940	39	14	diophantine	diophantine	NOUN
ejpam-4940	39	15	equation	equation	NOUN
ejpam-4940	39	16	e	e	NOUN
ejpam-4940	39	17	:	:	PUNCT
ejpam-4940	39	18	x2	x2	INTJ
ejpam-4940	39	19	−	−	PROPN
ejpam-4940	39	20	(	(	PUNCT
ejpam-4940	39	21	t2	t2	NOUN
ejpam-4940	39	22	−	−	PROPN
ejpam-4940	39	23	t)y2	t)y2	NOUN
ejpam-4940	39	24	−	−	PROPN
ejpam-4940	39	25	(	(	PUNCT
ejpam-4940	39	26	4	4	NUM
ejpam-4940	39	27	t	t	NOUN
ejpam-4940	39	28	−	−	NUM
ejpam-4940	39	29	2)x	2)x	NUM
ejpam-4940	39	30	+	+	CCONJ
ejpam-4940	39	31	(	(	PUNCT
ejpam-4940	39	32	4t2	4t2	NOUN
ejpam-4940	39	33	−	−	NOUN
ejpam-4940	39	34	4t)y	4t)y	NUM
ejpam-4940	39	35	=	=	NOUN
ejpam-4940	39	36	0	0	NUM
ejpam-4940	39	37	over	over	ADP
ejpam-4940	39	38	z	z	PROPN
ejpam-4940	39	39	,	,	PUNCT
ejpam-4940	39	40	where	where	SCONJ
ejpam-4940	39	41	t	t	PROPN
ejpam-4940	39	42	≥	≥	PROPN
ejpam-4940	39	43	2	2	NUM
ejpam-4940	39	44	.	.	PUNCT
ejpam-4940	40	1	then	then	ADV
ejpam-4940	40	2	,	,	PUNCT
ejpam-4940	40	3	we	we	PRON
ejpam-4940	40	4	assume	assume	VERB
ejpam-4940	40	5	that	that	SCONJ
ejpam-4940	40	6	the	the	DET
ejpam-4940	40	7	diophantine	diophantine	NOUN
ejpam-4940	40	8	equation	equation	NOUN
ejpam-4940	40	9	e	e	NOUN
ejpam-4940	40	10	can	can	AUX
ejpam-4940	40	11	be	be	AUX
ejpam-4940	40	12	extended	extend	VERB
ejpam-4940	40	13	to	to	ADP
ejpam-4940	40	14	the	the	DET
ejpam-4940	40	15	form	form	NOUN
ejpam-4940	40	16	e	e	NOUN
ejpam-4940	40	17	:	:	PUNCT
ejpam-4940	41	1	x2	x2	PROPN
ejpam-4940	41	2	−	−	PROPN
ejpam-4940	42	1	p	p	X
ejpam-4940	42	2	(	(	PUNCT
ejpam-4940	42	3	t)y2	t)y2	PROPN
ejpam-4940	42	4	−	−	PROPN
ejpam-4940	42	5	2p	2p	NUM
ejpam-4940	42	6	′(t)x+	′(t)x+	PROPN
ejpam-4940	42	7	4p	4p	NOUN
ejpam-4940	42	8	(	(	PUNCT
ejpam-4940	42	9	t)y	t)y	PUNCT
ejpam-4940	42	10	+	+	PUNCT
ejpam-4940	42	11	(	(	PUNCT
ejpam-4940	42	12	p	p	NOUN
ejpam-4940	42	13	′(t))2	′(t))2	ADP
ejpam-4940	42	14	−	−	PROPN
ejpam-4940	42	15	4p	4p	NOUN
ejpam-4940	42	16	(	(	PUNCT
ejpam-4940	42	17	t)−	t)−	PROPN
ejpam-4940	42	18	1	1	NUM
ejpam-4940	42	19	=	=	SYM
ejpam-4940	42	20	0	0	NUM
ejpam-4940	42	21	where	where	SCONJ
ejpam-4940	42	22	p	p	PROPN
ejpam-4940	42	23	(	(	PUNCT
ejpam-4940	42	24	t	t	NOUN
ejpam-4940	42	25	)	)	PUNCT
ejpam-4940	42	26	be	be	AUX
ejpam-4940	42	27	a	a	DET
ejpam-4940	42	28	non	non	ADJ
ejpam-4940	42	29	-	-	ADJ
ejpam-4940	42	30	square	square	ADJ
ejpam-4940	42	31	polynomial	polynomial	NOUN
ejpam-4940	42	32	.	.	PUNCT
ejpam-4940	43	1	few	few	ADJ
ejpam-4940	43	2	later	later	ADJ
ejpam-4940	43	3	years	year	NOUN
ejpam-4940	43	4	,	,	PUNCT
ejpam-4940	43	5	chandoul	chandoul	PROPN
ejpam-4940	43	6	et	et	PROPN
ejpam-4940	43	7	al	al	PROPN
ejpam-4940	43	8	.	.	PUNCT
ejpam-4940	44	1	[	[	X
ejpam-4940	44	2	1	1	X
ejpam-4940	44	3	]	]	PUNCT
ejpam-4940	44	4	considered	consider	VERB
ejpam-4940	44	5	the	the	DET
ejpam-4940	44	6	number	number	NOUN
ejpam-4940	44	7	of	of	ADP
ejpam-4940	44	8	integer	integer	NOUN
ejpam-4940	44	9	solutions	solution	NOUN
ejpam-4940	44	10	of	of	ADP
ejpam-4940	44	11	diophantine	diophantine	NOUN
ejpam-4940	44	12	equation	equation	NOUN
ejpam-4940	44	13	e1	e1	NOUN
ejpam-4940	44	14	:	:	PUNCT
ejpam-4940	45	1	x2	x2	PROPN
ejpam-4940	45	2	−	−	PROPN
ejpam-4940	46	1	p	p	X
ejpam-4940	46	2	(	(	PUNCT
ejpam-4940	46	3	t)y2	t)y2	PROPN
ejpam-4940	46	4	−	−	NOUN
ejpam-4940	46	5	2p	2p	NOUN
ejpam-4940	46	6	′(t)x	′(t)x	ADP
ejpam-4940	47	1	+	+	NUM
ejpam-4940	47	2	4p	4p	NOUN
ejpam-4940	47	3	(	(	PUNCT
ejpam-4940	47	4	t)y	t)y	PUNCT
ejpam-4940	47	5	+	+	PUNCT
ejpam-4940	47	6	p	p	X
ejpam-4940	47	7	′(t)2	′(t)2	X
ejpam-4940	47	8	−	−	PROPN
ejpam-4940	47	9	4p	4p	NOUN
ejpam-4940	47	10	(	(	PUNCT
ejpam-4940	47	11	t	t	NOUN
ejpam-4940	47	12	)	)	PUNCT
ejpam-4940	47	13	−	−	PROPN
ejpam-4940	47	14	1	1	NUM
ejpam-4940	47	15	=	=	SYM
ejpam-4940	47	16	0	0	NUM
ejpam-4940	47	17	.	.	PUNCT
ejpam-4940	48	1	they	they	PRON
ejpam-4940	48	2	derived	derive	VERB
ejpam-4940	48	3	some	some	DET
ejpam-4940	48	4	recurrence	recurrence	NOUN
ejpam-4940	48	5	relations	relation	NOUN
ejpam-4940	48	6	on	on	ADP
ejpam-4940	48	7	the	the	DET
ejpam-4940	48	8	integer	integer	NOUN
ejpam-4940	48	9	solutions	solution	NOUN
ejpam-4940	48	10	(	(	PUNCT
ejpam-4940	48	11	xn	xn	PROPN
ejpam-4940	48	12	,	,	PUNCT
ejpam-4940	48	13	yn	yn	PROPN
ejpam-4940	48	14	)	)	PUNCT
ejpam-4940	48	15	of	of	ADP
ejpam-4940	48	16	e1	e1	PROPN
ejpam-4940	48	17	and	and	CCONJ
ejpam-4940	48	18	giving	give	VERB
ejpam-4940	48	19	a	a	DET
ejpam-4940	48	20	nice	nice	ADJ
ejpam-4940	48	21	generaliations	generaliation	NOUN
ejpam-4940	48	22	of	of	ADP
ejpam-4940	48	23	previous	previous	ADJ
ejpam-4940	48	24	results	result	NOUN
ejpam-4940	48	25	given	give	VERB
ejpam-4940	48	26	by	by	ADP
ejpam-4940	48	27	tekcan	tekcan	NOUN
ejpam-4940	48	28	[	[	X
ejpam-4940	48	29	2	2	NUM
ejpam-4940	48	30	]	]	PUNCT
ejpam-4940	48	31	.	.	PUNCT
ejpam-4940	49	1	these	these	DET
ejpam-4940	49	2	extensions	extension	NOUN
ejpam-4940	49	3	allows	allow	VERB
ejpam-4940	49	4	us	we	PRON
ejpam-4940	49	5	to	to	PART
ejpam-4940	49	6	solve	solve	VERB
ejpam-4940	49	7	many	many	ADJ
ejpam-4940	49	8	types	type	NOUN
ejpam-4940	49	9	of	of	ADP
ejpam-4940	49	10	such	such	ADJ
ejpam-4940	49	11	equations	equation	NOUN
ejpam-4940	49	12	.	.	PUNCT
ejpam-4940	50	1	we	we	PRON
ejpam-4940	50	2	also	also	ADV
ejpam-4940	50	3	derive	derive	VERB
ejpam-4940	50	4	some	some	DET
ejpam-4940	50	5	recurrence	recurrence	NOUN
ejpam-4940	50	6	relations	relation	NOUN
ejpam-4940	50	7	on	on	ADP
ejpam-4940	50	8	the	the	DET
ejpam-4940	50	9	integer	integer	NOUN
ejpam-4940	50	10	solutions	solution	NOUN
ejpam-4940	50	11	of	of	ADP
ejpam-4940	50	12	a	a	DET
ejpam-4940	50	13	pell	pell	NOUN
ejpam-4940	50	14	equation	equation	NOUN
ejpam-4940	50	15	.	.	PUNCT
ejpam-4940	51	1	another	another	DET
ejpam-4940	51	2	advantage	advantage	NOUN
ejpam-4940	51	3	of	of	ADP
ejpam-4940	51	4	our	our	PRON
ejpam-4940	51	5	results	result	NOUN
ejpam-4940	51	6	is	be	AUX
ejpam-4940	51	7	that	that	SCONJ
ejpam-4940	51	8	the	the	DET
ejpam-4940	51	9	procedure	procedure	NOUN
ejpam-4940	51	10	can	can	AUX
ejpam-4940	51	11	be	be	AUX
ejpam-4940	51	12	implemented	implement	VERB
ejpam-4940	51	13	by	by	ADP
ejpam-4940	51	14	computer	computer	NOUN
ejpam-4940	51	15	,	,	PUNCT
ejpam-4940	51	16	which	which	PRON
ejpam-4940	51	17	allows	allow	VERB
ejpam-4940	51	18	us	we	PRON
ejpam-4940	51	19	to	to	PART
ejpam-4940	51	20	obtain	obtain	VERB
ejpam-4940	51	21	all	all	DET
ejpam-4940	51	22	the	the	DET
ejpam-4940	51	23	solutions	solution	NOUN
ejpam-4940	51	24	after	after	ADP
ejpam-4940	51	25	the	the	DET
ejpam-4940	51	26	insertion	insertion	NOUN
ejpam-4940	51	27	of	of	ADP
ejpam-4940	51	28	the	the	DET
ejpam-4940	51	29	coefficients	coefficient	NOUN
ejpam-4940	51	30	and	and	CCONJ
ejpam-4940	51	31	the	the	DET
ejpam-4940	51	32	verification	verification	NOUN
ejpam-4940	51	33	of	of	ADP
ejpam-4940	51	34	the	the	DET
ejpam-4940	51	35	conditions	condition	NOUN
ejpam-4940	51	36	of	of	ADP
ejpam-4940	51	37	the	the	DET
ejpam-4940	51	38	method	method	NOUN
ejpam-4940	51	39	.	.	PUNCT
ejpam-4940	52	1	2	2	X
ejpam-4940	52	2	.	.	X
ejpam-4940	52	3	main	main	ADJ
ejpam-4940	52	4	results	result	NOUN
ejpam-4940	52	5	let	let	VERB
ejpam-4940	52	6	p	p	PROPN
ejpam-4940	52	7	(	(	PUNCT
ejpam-4940	52	8	t	t	NOUN
ejpam-4940	52	9	)	)	PUNCT
ejpam-4940	52	10	=	=	SYM
ejpam-4940	52	11	t2k±itm	t2k±itm	NOUN
ejpam-4940	52	12	and	and	CCONJ
ejpam-4940	52	13	q(t	q(t	ADJ
ejpam-4940	52	14	)	)	PUNCT
ejpam-4940	52	15	=	=	SYM
ejpam-4940	52	16	4k2t4k−2+i2m2t2m−2±4imkt2k+m−2−4t2k∓4itm−1	4k2t4k−2+i2m2t2m−2±4imkt2k+m−2−4t2k∓4itm−1	PROPN
ejpam-4940	52	17	,	,	PUNCT
ejpam-4940	52	18	where	where	SCONJ
ejpam-4940	52	19	k	k	PROPN
ejpam-4940	52	20	≥	≥	NUM
ejpam-4940	52	21	2	2	NUM
ejpam-4940	52	22	m	m	VERB
ejpam-4940	52	23	and	and	CCONJ
ejpam-4940	52	24	i	i	PRON
ejpam-4940	52	25	∈	∈	PROPN
ejpam-4940	52	26	{	{	PUNCT
ejpam-4940	52	27	1	1	NUM
ejpam-4940	52	28	,	,	PUNCT
ejpam-4940	52	29	2	2	NUM
ejpam-4940	52	30	}	}	PUNCT
ejpam-4940	52	31	.	.	PUNCT
ejpam-4940	53	1	we	we	PRON
ejpam-4940	53	2	consider	consider	VERB
ejpam-4940	53	3	the	the	DET
ejpam-4940	53	4	equation	equation	NOUN
ejpam-4940	53	5	e	e	NOUN
ejpam-4940	53	6	:	:	PUNCT
ejpam-4940	54	1	x2	x2	PROPN
ejpam-4940	54	2	−	−	PROPN
ejpam-4940	55	1	p	p	X
ejpam-4940	55	2	(	(	PUNCT
ejpam-4940	55	3	t)y2	t)y2	PROPN
ejpam-4940	55	4	−	−	PROPN
ejpam-4940	55	5	2p	2p	NUM
ejpam-4940	55	6	′(t)x+	′(t)x+	PROPN
ejpam-4940	55	7	4p	4p	NOUN
ejpam-4940	55	8	(	(	PUNCT
ejpam-4940	55	9	t)y	t)y	X
ejpam-4940	55	10	+	+	ADJ
ejpam-4940	55	11	q(t	q(t	ADJ
ejpam-4940	55	12	)	)	PUNCT
ejpam-4940	55	13	=	=	SYM
ejpam-4940	55	14	0	0	NUM
ejpam-4940	55	15	(	(	PUNCT
ejpam-4940	55	16	1	1	NUM
ejpam-4940	55	17	)	)	PUNCT
ejpam-4940	55	18	theorem	theorem	NOUN
ejpam-4940	55	19	1	1	NUM
ejpam-4940	55	20	.	.	PUNCT
ejpam-4940	56	1	let	let	VERB
ejpam-4940	56	2	p	p	NOUN
ejpam-4940	56	3	(	(	PUNCT
ejpam-4940	56	4	t)±i	t)±i	NOUN
ejpam-4940	56	5	=	=	SYM
ejpam-4940	56	6	t2k	t2k	PROPN
ejpam-4940	56	7	±	±	NUM
ejpam-4940	56	8	itm	itm	NOUN
ejpam-4940	56	9	,	,	PUNCT
ejpam-4940	56	10	then	then	ADV
ejpam-4940	56	11	the	the	DET
ejpam-4940	56	12	continued	continue	VERB
ejpam-4940	56	13	fraction	fraction	NOUN
ejpam-4940	56	14	of	of	ADP
ejpam-4940	56	15	√	√	PROPN
ejpam-4940	56	16	p	p	NOUN
ejpam-4940	56	17	(	(	PUNCT
ejpam-4940	56	18	t)±i	t)±i	NOUN
ejpam-4940	56	19	is	be	AUX
ejpam-4940	56	20	given	give	VERB
ejpam-4940	56	21	as	as	ADP
ejpam-4940	56	22	follow	follow	NOUN
ejpam-4940	56	23	;	;	PUNCT
ejpam-4940	56	24	a.	a.	NOUN
ejpam-4940	56	25	m.	m.	NOUN
ejpam-4940	56	26	sibih	sibih	PROPN
ejpam-4940	56	27	/	/	SYM
ejpam-4940	56	28	eur	eur	PROPN
ejpam-4940	56	29	.	.	PUNCT
ejpam-4940	57	1	j.	j.	PROPN
ejpam-4940	57	2	pure	pure	PROPN
ejpam-4940	57	3	appl	appl	PROPN
ejpam-4940	57	4	.	.	PROPN
ejpam-4940	57	5	math	math	PROPN
ejpam-4940	57	6	,	,	PUNCT
ejpam-4940	57	7	16	16	NUM
ejpam-4940	57	8	(	(	PUNCT
ejpam-4940	57	9	4	4	NUM
ejpam-4940	57	10	)	)	PUNCT
ejpam-4940	57	11	(	(	PUNCT
ejpam-4940	57	12	2023	2023	NUM
ejpam-4940	57	13	)	)	PUNCT
ejpam-4940	57	14	,	,	PUNCT
ejpam-4940	57	15	2693	2693	NUM
ejpam-4940	57	16	-	-	SYM
ejpam-4940	57	17	2702	2702	NUM
ejpam-4940	57	18	2695	2695	NUM
ejpam-4940	57	19	1	1	NUM
ejpam-4940	57	20	)	)	PUNCT
ejpam-4940	57	21	√	√	NOUN
ejpam-4940	58	1	p	p	NOUN
ejpam-4940	58	2	(	(	PUNCT
ejpam-4940	58	3	t)+1	t)+1	NOUN
ejpam-4940	58	4	=	=	SYM
ejpam-4940	58	5			PROPN
ejpam-4940	58	6	[	[	PUNCT
ejpam-4940	58	7	tk	tk	PROPN
ejpam-4940	58	8	;	;	PUNCT
ejpam-4940	58	9	2	2	NUM
ejpam-4940	58	10	]	]	PUNCT
ejpam-4940	58	11	,	,	PUNCT
ejpam-4940	58	12	if	if	SCONJ
ejpam-4940	58	13	t	t	PROPN
ejpam-4940	58	14	=	=	SYM
ejpam-4940	58	15	1	1	NUM
ejpam-4940	58	16	[	[	PUNCT
ejpam-4940	58	17	tk	tk	PROPN
ejpam-4940	58	18	;	;	PUNCT
ejpam-4940	58	19	2tk−m	2tk−m	NUM
ejpam-4940	58	20	,	,	PUNCT
ejpam-4940	58	21	2tk	2tk	ADJ
ejpam-4940	58	22	]	]	PUNCT
ejpam-4940	58	23	,	,	PUNCT
ejpam-4940	58	24	if	if	SCONJ
ejpam-4940	58	25	t	t	PROPN
ejpam-4940	58	26	≥	≥	NUM
ejpam-4940	58	27	2	2	NUM
ejpam-4940	58	28	2	2	NUM
ejpam-4940	58	29	)	)	PUNCT
ejpam-4940	58	30	√	√	NOUN
ejpam-4940	59	1	p	p	NOUN
ejpam-4940	59	2	(	(	PUNCT
ejpam-4940	59	3	t)−1	t)−1	X
ejpam-4940	59	4	=	=	SYM
ejpam-4940	59	5	[	[	PUNCT
ejpam-4940	59	6	tk	tk	NOUN
ejpam-4940	59	7	;	;	PUNCT
ejpam-4940	59	8	1	1	NUM
ejpam-4940	59	9	,	,	PUNCT
ejpam-4940	59	10	2tk−m	2tk−m	NUM
ejpam-4940	59	11	−	−	PROPN
ejpam-4940	59	12	2	2	NUM
ejpam-4940	59	13	,	,	PUNCT
ejpam-4940	59	14	1	1	NUM
ejpam-4940	59	15	,	,	PUNCT
ejpam-4940	59	16	2tk	2tk	ADJ
ejpam-4940	59	17	−	−	PROPN
ejpam-4940	59	18	2	2	NUM
ejpam-4940	59	19	]	]	PUNCT
ejpam-4940	59	20	,	,	PUNCT
ejpam-4940	59	21	t	t	PROPN
ejpam-4940	59	22	≥	≥	NUM
ejpam-4940	59	23	2	2	NUM
ejpam-4940	59	24	3	3	NUM
ejpam-4940	59	25	)	)	PUNCT
ejpam-4940	59	26	√	√	NOUN
ejpam-4940	60	1	p	p	NOUN
ejpam-4940	60	2	(	(	PUNCT
ejpam-4940	60	3	t)+2	t)+2	NOUN
ejpam-4940	60	4	=	=	PRON
ejpam-4940	60	5	[	[	PUNCT
ejpam-4940	60	6	tk	tk	PROPN
ejpam-4940	60	7	;	;	PUNCT
ejpam-4940	60	8	tk−m	tk−m	NOUN
ejpam-4940	60	9	,	,	PUNCT
ejpam-4940	60	10	2tk	2tk	ADJ
ejpam-4940	60	11	]	]	PUNCT
ejpam-4940	60	12	4	4	X
ejpam-4940	60	13	)	)	PUNCT
ejpam-4940	60	14	√	√	NOUN
ejpam-4940	61	1	p	p	NOUN
ejpam-4940	61	2	(	(	PUNCT
ejpam-4940	61	3	t)+2	t)+2	NUM
ejpam-4940	61	4	=	=	SYM
ejpam-4940	61	5	[	[	PUNCT
ejpam-4940	61	6	tk	tk	PROPN
ejpam-4940	61	7	−	−	PROPN
ejpam-4940	61	8	1	1	NUM
ejpam-4940	61	9	;	;	PUNCT
ejpam-4940	61	10	1	1	NUM
ejpam-4940	61	11	,	,	PUNCT
ejpam-4940	61	12	tk−1	tk−1	ADV
ejpam-4940	61	13	−	−	PROPN
ejpam-4940	61	14	2	2	NUM
ejpam-4940	61	15	,	,	PUNCT
ejpam-4940	61	16	1	1	NUM
ejpam-4940	61	17	,	,	PUNCT
ejpam-4940	61	18	2tk−1	2tk−1	NUM
ejpam-4940	61	19	−	−	NOUN
ejpam-4940	61	20	2	2	NUM
ejpam-4940	61	21	]	]	PUNCT
ejpam-4940	61	22	,	,	PUNCT
ejpam-4940	61	23	if	if	SCONJ
ejpam-4940	61	24	t	t	PROPN
ejpam-4940	61	25	≥	≥	VERB
ejpam-4940	61	26	3	3	NUM
ejpam-4940	61	27	proof	proof	NOUN
ejpam-4940	61	28	.	.	PUNCT
ejpam-4940	62	1	we	we	PRON
ejpam-4940	62	2	have	have	VERB
ejpam-4940	62	3	;	;	PUNCT
ejpam-4940	63	1	√	√	PROPN
ejpam-4940	63	2	p	p	NOUN
ejpam-4940	63	3	(	(	PUNCT
ejpam-4940	63	4	t)+1	t)+1	NOUN
ejpam-4940	63	5	=	=	SYM
ejpam-4940	63	6	√	√	PROPN
ejpam-4940	64	1	t2k	t2k	NOUN
ejpam-4940	65	1	+	+	PUNCT
ejpam-4940	65	2	tm	tm	PROPN
ejpam-4940	65	3	=	=	PROPN
ejpam-4940	65	4	tk	tk	PROPN
ejpam-4940	65	5	+	+	CCONJ
ejpam-4940	65	6	√	√	PROPN
ejpam-4940	65	7	t2k	t2k	NOUN
ejpam-4940	65	8	+	+	PUNCT
ejpam-4940	65	9	tm	tm	PROPN
ejpam-4940	65	10	−	−	PROPN
ejpam-4940	65	11	tk	tk	PROPN
ejpam-4940	65	12	=	=	PROPN
ejpam-4940	65	13	tk	tk	PROPN
ejpam-4940	66	1	+	+	CCONJ
ejpam-4940	66	2	1√	1√	ADJ
ejpam-4940	66	3	t2k	t2k	ADJ
ejpam-4940	66	4	+	+	CCONJ
ejpam-4940	66	5	tm	tm	PROPN
ejpam-4940	66	6	+	+	NOUN
ejpam-4940	66	7	tk	tk	PROPN
ejpam-4940	66	8	tm	tm	PROPN
ejpam-4940	66	9	=	=	PROPN
ejpam-4940	66	10	tk	tk	PROPN
ejpam-4940	67	1	+	+	NOUN
ejpam-4940	67	2	1	1	NUM
ejpam-4940	67	3	2tk−m	2tk−m	NUM
ejpam-4940	67	4	+	+	CCONJ
ejpam-4940	67	5	√	√	PROPN
ejpam-4940	67	6	t2k	t2k	NOUN
ejpam-4940	67	7	+	+	PUNCT
ejpam-4940	67	8	tm	tm	PROPN
ejpam-4940	67	9	−	−	PROPN
ejpam-4940	67	10	tk	tk	PROPN
ejpam-4940	67	11	tm	tm	PROPN
ejpam-4940	67	12	=	=	PROPN
ejpam-4940	67	13	tk	tk	PROPN
ejpam-4940	68	1	+	+	NOUN
ejpam-4940	68	2	1	1	NUM
ejpam-4940	68	3	2tk−m	2tk−m	NUM
ejpam-4940	68	4	+	+	CCONJ
ejpam-4940	68	5	1√	1√	ADJ
ejpam-4940	68	6	t2k	t2k	ADJ
ejpam-4940	68	7	+	+	CCONJ
ejpam-4940	68	8	tm	tm	PROPN
ejpam-4940	68	9	+	+	NOUN
ejpam-4940	68	10	tk	tk	PROPN
ejpam-4940	68	11	=	=	PROPN
ejpam-4940	68	12	tk	tk	PROPN
ejpam-4940	69	1	+	+	NOUN
ejpam-4940	69	2	1	1	NUM
ejpam-4940	69	3	2tk−m	2tk−m	NUM
ejpam-4940	69	4	+	+	CCONJ
ejpam-4940	69	5	1	1	NUM
ejpam-4940	69	6	2tk	2tk	ADJ
ejpam-4940	69	7	+	+	CCONJ
ejpam-4940	69	8	√	√	PROPN
ejpam-4940	69	9	t2k	t2k	ADJ
ejpam-4940	69	10	+	+	PUNCT
ejpam-4940	69	11	tm	tm	PROPN
ejpam-4940	69	12	−	−	PROPN
ejpam-4940	69	13	tk	tk	PROPN
ejpam-4940	69	14	hence	hence	ADV
ejpam-4940	69	15	,	,	PUNCT
ejpam-4940	69	16	√	√	PROPN
ejpam-4940	69	17	p	p	NOUN
ejpam-4940	69	18	(	(	PUNCT
ejpam-4940	69	19	t)+1	t)+1	NOUN
ejpam-4940	70	1	=	=	SYM
ejpam-4940	70	2			PROPN
ejpam-4940	70	3	[	[	PUNCT
ejpam-4940	70	4	tk	tk	PROPN
ejpam-4940	70	5	;	;	PUNCT
ejpam-4940	70	6	2	2	NUM
ejpam-4940	70	7	]	]	PUNCT
ejpam-4940	70	8	,	,	PUNCT
ejpam-4940	70	9	if	if	SCONJ
ejpam-4940	70	10	t	t	PROPN
ejpam-4940	70	11	=	=	SYM
ejpam-4940	70	12	1	1	NUM
ejpam-4940	70	13	[	[	PUNCT
ejpam-4940	70	14	tk	tk	PROPN
ejpam-4940	70	15	;	;	PUNCT
ejpam-4940	70	16	2tk−m	2tk−m	NUM
ejpam-4940	70	17	,	,	PUNCT
ejpam-4940	70	18	2tk	2tk	ADJ
ejpam-4940	70	19	]	]	PUNCT
ejpam-4940	70	20	,	,	PUNCT
ejpam-4940	70	21	if	if	SCONJ
ejpam-4940	70	22	t	t	PROPN
ejpam-4940	70	23	≥	≥	NOUN
ejpam-4940	70	24	2	2	NUM
ejpam-4940	70	25	similarly	similarly	ADV
ejpam-4940	70	26	,	,	PUNCT
ejpam-4940	70	27	one	one	PRON
ejpam-4940	70	28	can	can	AUX
ejpam-4940	70	29	find	find	VERB
ejpam-4940	70	30	the	the	DET
ejpam-4940	70	31	requered	requere	VERB
ejpam-4940	70	32	form	form	NOUN
ejpam-4940	70	33	of	of	ADP
ejpam-4940	70	34	the	the	DET
ejpam-4940	70	35	continued	continue	VERB
ejpam-4940	70	36	fractions	fraction	NOUN
ejpam-4940	70	37	.	.	PUNCT
ejpam-4940	71	1	theorem	theorem	NOUN
ejpam-4940	71	2	2	2	NUM
ejpam-4940	71	3	.	.	PUNCT
ejpam-4940	72	1	let	let	VERB
ejpam-4940	72	2	p	p	NOUN
ejpam-4940	72	3	(	(	PUNCT
ejpam-4940	72	4	t	t	NOUN
ejpam-4940	72	5	)	)	PUNCT
ejpam-4940	73	1	=	=	PUNCT
ejpam-4940	74	1	t2k	t2k	PUNCT
ejpam-4940	74	2	±	±	NUM
ejpam-4940	74	3	itm	itm	NOUN
ejpam-4940	74	4	,	,	PUNCT
ejpam-4940	74	5	where	where	SCONJ
ejpam-4940	74	6	k	k	PROPN
ejpam-4940	74	7	≥	≥	NUM
ejpam-4940	74	8	2	2	NUM
ejpam-4940	74	9	m	m	NOUN
ejpam-4940	74	10	̸=	̸=	NOUN
ejpam-4940	74	11	0	0	NUM
ejpam-4940	75	1	and	and	CCONJ
ejpam-4940	75	2	i	i	PRON
ejpam-4940	75	3	∈	∈	PROPN
ejpam-4940	75	4	{	{	PUNCT
ejpam-4940	75	5	1	1	NUM
ejpam-4940	75	6	,	,	PUNCT
ejpam-4940	75	7	2	2	NUM
ejpam-4940	75	8	}	}	PUNCT
ejpam-4940	75	9	be	be	AUX
ejpam-4940	75	10	a	a	DET
ejpam-4940	75	11	non	non	ADJ
ejpam-4940	75	12	square	square	ADJ
ejpam-4940	75	13	polynomial	polynomial	NOUN
ejpam-4940	75	14	and	and	CCONJ
ejpam-4940	75	15	let	let	VERB
ejpam-4940	75	16	the	the	DET
ejpam-4940	75	17	diophantine	diophantine	NOUN
ejpam-4940	75	18	equation	equation	NOUN
ejpam-4940	75	19	e	e	NOUN
ejpam-4940	75	20	:	:	PUNCT
ejpam-4940	76	1	x2	x2	PROPN
ejpam-4940	76	2	−	−	PROPN
ejpam-4940	77	1	p	p	X
ejpam-4940	77	2	(	(	PUNCT
ejpam-4940	77	3	t)y2	t)y2	PROPN
ejpam-4940	77	4	−	−	PROPN
ejpam-4940	77	5	2p	2p	NUM
ejpam-4940	77	6	′(t)x+	′(t)x+	PROPN
ejpam-4940	77	7	4p	4p	NOUN
ejpam-4940	77	8	(	(	PUNCT
ejpam-4940	77	9	t)y	t)y	PUNCT
ejpam-4940	77	10	+	+	PUNCT
ejpam-4940	77	11	(	(	PUNCT
ejpam-4940	77	12	p	p	NOUN
ejpam-4940	77	13	′(t))2	′(t))2	ADP
ejpam-4940	77	14	−	−	PROPN
ejpam-4940	77	15	4p	4p	NOUN
ejpam-4940	77	16	(	(	PUNCT
ejpam-4940	77	17	t)−	t)−	PROPN
ejpam-4940	77	18	1	1	NUM
ejpam-4940	77	19	=	=	SYM
ejpam-4940	77	20	0	0	PROPN
ejpam-4940	77	21	.	.	PUNCT
ejpam-4940	78	1	then	then	ADV
ejpam-4940	78	2	(	(	PUNCT
ejpam-4940	78	3	1	1	X
ejpam-4940	78	4	)	)	PUNCT
ejpam-4940	78	5	the	the	DET
ejpam-4940	78	6	fundamental	fundamental	ADJ
ejpam-4940	78	7	(	(	PUNCT
ejpam-4940	78	8	minimal	minimal	ADJ
ejpam-4940	78	9	)	)	PUNCT
ejpam-4940	78	10	solution	solution	NOUN
ejpam-4940	78	11	of	of	ADP
ejpam-4940	78	12	e	e	PROPN
ejpam-4940	78	13	is	be	AUX
ejpam-4940	78	14	(	(	PUNCT
ejpam-4940	78	15	x1	x1	PROPN
ejpam-4940	78	16	,	,	PUNCT
ejpam-4940	78	17	y1	y1	NOUN
ejpam-4940	78	18	)	)	PUNCT
ejpam-4940	78	19	=	=	SYM
ejpam-4940	78	20	(	(	PUNCT
ejpam-4940	78	21	u1	u1	VERB
ejpam-4940	78	22	+	+	PROPN
ejpam-4940	78	23	2kt2k−1±	2kt2k−1±	NUM
ejpam-4940	78	24	imtm−1	imtm−1	NOUN
ejpam-4940	78	25	,	,	PUNCT
ejpam-4940	78	26	v1	v1	NOUN
ejpam-4940	78	27	+	+	NOUN
ejpam-4940	78	28	2	2	NUM
ejpam-4940	78	29	)	)	PUNCT
ejpam-4940	78	30	(	(	PUNCT
ejpam-4940	78	31	2	2	X
ejpam-4940	78	32	)	)	PUNCT
ejpam-4940	78	33	define	define	VERB
ejpam-4940	78	34	the	the	DET
ejpam-4940	78	35	sequence	sequence	NOUN
ejpam-4940	78	36	{	{	PUNCT
ejpam-4940	78	37	(	(	PUNCT
ejpam-4940	78	38	xn	xn	PROPN
ejpam-4940	78	39	,	,	PUNCT
ejpam-4940	78	40	yn)}n≥1	yn)}n≥1	NOUN
ejpam-4940	78	41	=	=	PRON
ejpam-4940	78	42	{	{	PUNCT
ejpam-4940	78	43	(	(	PUNCT
ejpam-4940	78	44	un	un	PROPN
ejpam-4940	78	45	+	+	PROPN
ejpam-4940	78	46	2kt2k−1	2kt2k−1	NUM
ejpam-4940	78	47	±	±	NUM
ejpam-4940	78	48	imtm−1	imtm−1	NOUN
ejpam-4940	78	49	,	,	PUNCT
ejpam-4940	78	50	vn	vn	X
ejpam-4940	78	51	+	+	NOUN
ejpam-4940	78	52	2	2	NUM
ejpam-4940	78	53	)	)	PUNCT
ejpam-4940	78	54	}	}	PUNCT
ejpam-4940	78	55	,	,	PUNCT
ejpam-4940	78	56	then	then	ADV
ejpam-4940	78	57	(	(	PUNCT
ejpam-4940	78	58	xn	xn	PROPN
ejpam-4940	78	59	,	,	PUNCT
ejpam-4940	78	60	yn	yn	PROPN
ejpam-4940	78	61	)	)	PUNCT
ejpam-4940	78	62	is	be	AUX
ejpam-4940	78	63	a	a	DET
ejpam-4940	78	64	solution	solution	NOUN
ejpam-4940	78	65	of	of	ADP
ejpam-4940	78	66	e.	e.	PROPN
ejpam-4940	79	1	so	so	SCONJ
ejpam-4940	79	2	it	it	PRON
ejpam-4940	79	3	has	have	VERB
ejpam-4940	79	4	infinitely	infinitely	ADV
ejpam-4940	79	5	many	many	ADJ
ejpam-4940	79	6	integer	integer	NOUN
ejpam-4940	79	7	solutions	solution	NOUN
ejpam-4940	79	8	(	(	PUNCT
ejpam-4940	79	9	xn	xn	PROPN
ejpam-4940	79	10	,	,	PUNCT
ejpam-4940	79	11	yn	yn	NOUN
ejpam-4940	79	12	)	)	PUNCT
ejpam-4940	79	13	∈	∈	PROPN
ejpam-4940	79	14	z×	z×	NUM
ejpam-4940	79	15	z.	z.	PROPN
ejpam-4940	79	16	a.	a.	PROPN
ejpam-4940	79	17	m.	m.	PROPN
ejpam-4940	79	18	sibih	sibih	PROPN
ejpam-4940	79	19	/	/	SYM
ejpam-4940	79	20	eur	eur	PROPN
ejpam-4940	79	21	.	.	PUNCT
ejpam-4940	80	1	j.	j.	PROPN
ejpam-4940	80	2	pure	pure	PROPN
ejpam-4940	80	3	appl	appl	PROPN
ejpam-4940	80	4	.	.	PROPN
ejpam-4940	80	5	math	math	PROPN
ejpam-4940	80	6	,	,	PUNCT
ejpam-4940	80	7	16	16	NUM
ejpam-4940	80	8	(	(	PUNCT
ejpam-4940	80	9	4	4	NUM
ejpam-4940	80	10	)	)	PUNCT
ejpam-4940	80	11	(	(	PUNCT
ejpam-4940	80	12	2023	2023	NUM
ejpam-4940	80	13	)	)	PUNCT
ejpam-4940	80	14	,	,	PUNCT
ejpam-4940	80	15	2693	2693	NUM
ejpam-4940	80	16	-	-	SYM
ejpam-4940	80	17	2702	2702	NUM
ejpam-4940	80	18	2696	2696	NUM
ejpam-4940	80	19	(	(	PUNCT
ejpam-4940	80	20	3	3	X
ejpam-4940	80	21	)	)	PUNCT
ejpam-4940	80	22	the	the	DET
ejpam-4940	80	23	solutions	solution	NOUN
ejpam-4940	80	24	(	(	PUNCT
ejpam-4940	80	25	xn	xn	PROPN
ejpam-4940	80	26	,	,	PUNCT
ejpam-4940	80	27	yn	yn	NOUN
ejpam-4940	80	28	)	)	PUNCT
ejpam-4940	80	29	satisfy	satisfy	VERB
ejpam-4940	80	30	the	the	DET
ejpam-4940	80	31	recurrence	recurrence	NOUN
ejpam-4940	80	32	relations	relations	PUNCT
ejpam-4940	80	33	xk	xk	PROPN
ejpam-4940	80	34	=	=	SYM
ejpam-4940	80	35	u1xk−1	u1xk−1	PROPN
ejpam-4940	81	1	+	+	CCONJ
ejpam-4940	81	2	(	(	PUNCT
ejpam-4940	81	3	a0u1	a0u1	PROPN
ejpam-4940	81	4	+	+	NUM
ejpam-4940	81	5	α)yn−1	α)yn−1	ADJ
ejpam-4940	81	6	−	−	PROPN
ejpam-4940	81	7	u1(2a0	u1(2a0	ADJ
ejpam-4940	81	8	+	+	NOUN
ejpam-4940	81	9	2kt2k−1	2kt2k−1	NUM
ejpam-4940	81	10	±	±	NOUN
ejpam-4940	82	1	imtm−1)−	imtm−1)−	PROPN
ejpam-4940	82	2	2α+	2α+	NUM
ejpam-4940	82	3	2kt2k−1	2kt2k−1	NUM
ejpam-4940	82	4	±	±	NOUN
ejpam-4940	82	5	imtm−1	imtm−1	NUM
ejpam-4940	82	6	yk	yk	NOUN
ejpam-4940	82	7	=	=	PUNCT
ejpam-4940	82	8	v1xk−1	v1xk−1	PROPN
ejpam-4940	82	9	+	+	CCONJ
ejpam-4940	82	10	(	(	PUNCT
ejpam-4940	82	11	a0v1	a0v1	NOUN
ejpam-4940	82	12	+	+	CCONJ
ejpam-4940	82	13	β)yn−1	β)yn−1	PROPN
ejpam-4940	82	14	−	−	PROPN
ejpam-4940	82	15	v1(2a0	v1(2a0	NOUN
ejpam-4940	82	16	+	+	CCONJ
ejpam-4940	82	17	2kt2k−1	2kt2k−1	NUM
ejpam-4940	82	18	±	±	NOUN
ejpam-4940	83	1	imtm−1)−	imtm−1)−	ADJ
ejpam-4940	83	2	2β	2β	NOUN
ejpam-4940	83	3	+	+	CCONJ
ejpam-4940	83	4	2	2	NUM
ejpam-4940	83	5	for	for	ADP
ejpam-4940	83	6	k	k	PROPN
ejpam-4940	83	7	≥	≥	NUM
ejpam-4940	83	8	2	2	NUM
ejpam-4940	83	9	.	.	PUNCT
ejpam-4940	83	10	theorem	theorem	NOUN
ejpam-4940	83	11	3	3	X
ejpam-4940	83	12	.	.	PUNCT
ejpam-4940	84	1	let	let	VERB
ejpam-4940	84	2	p	p	PROPN
ejpam-4940	84	3	(	(	PUNCT
ejpam-4940	84	4	t	t	NOUN
ejpam-4940	84	5	)	)	PUNCT
ejpam-4940	84	6	=	=	VERB
ejpam-4940	85	1	t2k	t2k	PUNCT
ejpam-4940	85	2	+	+	CCONJ
ejpam-4940	85	3	i	i	PRON
ejpam-4940	85	4	,	,	PUNCT
ejpam-4940	85	5	where	where	SCONJ
ejpam-4940	85	6	k	k	PROPN
ejpam-4940	85	7	̸=	̸=	PROPN
ejpam-4940	85	8	0	0	PUNCT
ejpam-4940	86	1	and	and	CCONJ
ejpam-4940	86	2	i	i	PRON
ejpam-4940	86	3	∈	∈	PROPN
ejpam-4940	86	4	{	{	PUNCT
ejpam-4940	86	5	−2,−1	−2,−1	PROPN
ejpam-4940	86	6	,	,	PUNCT
ejpam-4940	86	7	1	1	NUM
ejpam-4940	86	8	,	,	PUNCT
ejpam-4940	86	9	2	2	NUM
ejpam-4940	86	10	}	}	PUNCT
ejpam-4940	86	11	be	be	AUX
ejpam-4940	86	12	a	a	DET
ejpam-4940	86	13	non	non	ADJ
ejpam-4940	86	14	square	square	ADJ
ejpam-4940	86	15	polynomial	polynomial	NOUN
ejpam-4940	86	16	and	and	CCONJ
ejpam-4940	86	17	let	let	VERB
ejpam-4940	86	18	the	the	DET
ejpam-4940	86	19	diophantine	diophantine	NOUN
ejpam-4940	86	20	equation	equation	NOUN
ejpam-4940	86	21	e	e	NOUN
ejpam-4940	86	22	:	:	PUNCT
ejpam-4940	87	1	x2	x2	PROPN
ejpam-4940	87	2	−	−	PROPN
ejpam-4940	88	1	p	p	X
ejpam-4940	88	2	(	(	PUNCT
ejpam-4940	88	3	t)y2	t)y2	PROPN
ejpam-4940	88	4	−	−	PROPN
ejpam-4940	88	5	2p	2p	NUM
ejpam-4940	88	6	′(t)x+	′(t)x+	PROPN
ejpam-4940	88	7	4p	4p	NOUN
ejpam-4940	88	8	(	(	PUNCT
ejpam-4940	88	9	t)y	t)y	PUNCT
ejpam-4940	88	10	+	+	PUNCT
ejpam-4940	88	11	(	(	PUNCT
ejpam-4940	88	12	p	p	NOUN
ejpam-4940	88	13	′(t))2	′(t))2	ADP
ejpam-4940	88	14	−	−	PROPN
ejpam-4940	88	15	4p	4p	NOUN
ejpam-4940	88	16	(	(	PUNCT
ejpam-4940	88	17	t)−	t)−	PROPN
ejpam-4940	88	18	1	1	NUM
ejpam-4940	88	19	=	=	SYM
ejpam-4940	88	20	0	0	PROPN
ejpam-4940	88	21	.	.	PUNCT
ejpam-4940	89	1	then	then	ADV
ejpam-4940	89	2	(	(	PUNCT
ejpam-4940	89	3	1	1	X
ejpam-4940	89	4	)	)	PUNCT
ejpam-4940	89	5	the	the	DET
ejpam-4940	89	6	fundamental	fundamental	ADJ
ejpam-4940	89	7	(	(	PUNCT
ejpam-4940	89	8	minimal	minimal	ADJ
ejpam-4940	89	9	)	)	PUNCT
ejpam-4940	89	10	solution	solution	NOUN
ejpam-4940	89	11	of	of	ADP
ejpam-4940	89	12	e	e	PROPN
ejpam-4940	89	13	is	be	AUX
ejpam-4940	89	14	(	(	PUNCT
ejpam-4940	89	15	x1	x1	PROPN
ejpam-4940	89	16	,	,	PUNCT
ejpam-4940	89	17	y1	y1	NOUN
ejpam-4940	89	18	)	)	PUNCT
ejpam-4940	89	19	=	=	SYM
ejpam-4940	89	20	(	(	PUNCT
ejpam-4940	89	21	u1	u1	VERB
ejpam-4940	89	22	+	+	PROPN
ejpam-4940	89	23	2kt2k−1±	2kt2k−1±	NUM
ejpam-4940	89	24	imtm−1	imtm−1	NOUN
ejpam-4940	89	25	,	,	PUNCT
ejpam-4940	89	26	v1	v1	NOUN
ejpam-4940	89	27	+	+	NOUN
ejpam-4940	89	28	2	2	NUM
ejpam-4940	89	29	)	)	PUNCT
ejpam-4940	89	30	(	(	PUNCT
ejpam-4940	89	31	2	2	X
ejpam-4940	89	32	)	)	PUNCT
ejpam-4940	89	33	define	define	VERB
ejpam-4940	89	34	the	the	DET
ejpam-4940	89	35	sequence	sequence	NOUN
ejpam-4940	89	36	{	{	PUNCT
ejpam-4940	89	37	(	(	PUNCT
ejpam-4940	89	38	xn	xn	PROPN
ejpam-4940	89	39	,	,	PUNCT
ejpam-4940	89	40	yn)}n≥1	yn)}n≥1	NOUN
ejpam-4940	89	41	=	=	PRON
ejpam-4940	89	42	{	{	PUNCT
ejpam-4940	89	43	(	(	PUNCT
ejpam-4940	89	44	un	un	PROPN
ejpam-4940	89	45	+	+	PROPN
ejpam-4940	89	46	2kt2k−1	2kt2k−1	NUM
ejpam-4940	89	47	±	±	NUM
ejpam-4940	89	48	imtm−1	imtm−1	NOUN
ejpam-4940	89	49	,	,	PUNCT
ejpam-4940	89	50	vn	vn	X
ejpam-4940	89	51	+	+	NOUN
ejpam-4940	89	52	2	2	NUM
ejpam-4940	89	53	)	)	PUNCT
ejpam-4940	89	54	}	}	PUNCT
ejpam-4940	89	55	,	,	PUNCT
ejpam-4940	89	56	then	then	ADV
ejpam-4940	89	57	(	(	PUNCT
ejpam-4940	89	58	xn	xn	PROPN
ejpam-4940	89	59	,	,	PUNCT
ejpam-4940	89	60	yn	yn	PROPN
ejpam-4940	89	61	)	)	PUNCT
ejpam-4940	89	62	is	be	AUX
ejpam-4940	89	63	a	a	DET
ejpam-4940	89	64	solution	solution	NOUN
ejpam-4940	89	65	of	of	ADP
ejpam-4940	89	66	e.	e.	PROPN
ejpam-4940	90	1	so	so	SCONJ
ejpam-4940	90	2	it	it	PRON
ejpam-4940	90	3	has	have	VERB
ejpam-4940	90	4	infinitely	infinitely	ADV
ejpam-4940	90	5	many	many	ADJ
ejpam-4940	90	6	integer	integer	NOUN
ejpam-4940	90	7	solutions	solution	NOUN
ejpam-4940	90	8	(	(	PUNCT
ejpam-4940	90	9	xn	xn	PROPN
ejpam-4940	90	10	,	,	PUNCT
ejpam-4940	90	11	yn	yn	NOUN
ejpam-4940	90	12	)	)	PUNCT
ejpam-4940	90	13	∈	∈	PROPN
ejpam-4940	90	14	z×	z×	NUM
ejpam-4940	90	15	z.	z.	X
ejpam-4940	90	16	(	(	PUNCT
ejpam-4940	90	17	3	3	X
ejpam-4940	90	18	)	)	PUNCT
ejpam-4940	90	19	the	the	DET
ejpam-4940	90	20	solutions	solution	NOUN
ejpam-4940	90	21	(	(	PUNCT
ejpam-4940	90	22	xn	xn	PROPN
ejpam-4940	90	23	,	,	PUNCT
ejpam-4940	90	24	yn	yn	NOUN
ejpam-4940	90	25	)	)	PUNCT
ejpam-4940	90	26	satisfy	satisfy	VERB
ejpam-4940	90	27	the	the	DET
ejpam-4940	90	28	recurrence	recurrence	NOUN
ejpam-4940	90	29	relations	relations	PUNCT
ejpam-4940	90	30	xk	xk	PROPN
ejpam-4940	90	31	=	=	SYM
ejpam-4940	90	32	u1xk−1	u1xk−1	PROPN
ejpam-4940	91	1	+	+	CCONJ
ejpam-4940	91	2	(	(	PUNCT
ejpam-4940	91	3	a0u1	a0u1	PROPN
ejpam-4940	91	4	+	+	NUM
ejpam-4940	91	5	α)yn−1	α)yn−1	ADJ
ejpam-4940	91	6	−	−	PROPN
ejpam-4940	91	7	u1(2a0	u1(2a0	ADJ
ejpam-4940	91	8	+	+	NOUN
ejpam-4940	91	9	2kt2k−1	2kt2k−1	NUM
ejpam-4940	91	10	±	±	NOUN
ejpam-4940	92	1	imtm−1)−	imtm−1)−	PROPN
ejpam-4940	92	2	2α+	2α+	NUM
ejpam-4940	92	3	2kt2k−1	2kt2k−1	NUM
ejpam-4940	92	4	±	±	NOUN
ejpam-4940	92	5	imtm−1	imtm−1	NUM
ejpam-4940	92	6	yk	yk	NOUN
ejpam-4940	92	7	=	=	PUNCT
ejpam-4940	92	8	v1xk−1	v1xk−1	PROPN
ejpam-4940	92	9	+	+	CCONJ
ejpam-4940	92	10	(	(	PUNCT
ejpam-4940	92	11	a0v1	a0v1	NOUN
ejpam-4940	92	12	+	+	CCONJ
ejpam-4940	92	13	β)yn−1	β)yn−1	PROPN
ejpam-4940	92	14	−	−	PROPN
ejpam-4940	92	15	v1(2a0	v1(2a0	NOUN
ejpam-4940	92	16	+	+	CCONJ
ejpam-4940	92	17	2kt2k−1	2kt2k−1	NUM
ejpam-4940	92	18	±	±	NOUN
ejpam-4940	93	1	imtm−1)−	imtm−1)−	ADJ
ejpam-4940	93	2	2β	2β	NOUN
ejpam-4940	94	1	+	+	CCONJ
ejpam-4940	94	2	2	2	NUM
ejpam-4940	94	3	if	if	SCONJ
ejpam-4940	94	4	i	i	PRON
ejpam-4940	94	5	̸=	̸=	PROPN
ejpam-4940	94	6	0	0	NUM
ejpam-4940	94	7	for	for	ADP
ejpam-4940	94	8	k	k	PROPN
ejpam-4940	94	9	≥	≥	PROPN
ejpam-4940	94	10	2	2	NUM
ejpam-4940	94	11	.	.	PUNCT
ejpam-4940	94	12	here	here	ADV
ejpam-4940	94	13	,	,	PUNCT
ejpam-4940	94	14	we	we	PRON
ejpam-4940	94	15	show	show	VERB
ejpam-4940	94	16	that	that	SCONJ
ejpam-4940	94	17	:	:	PUNCT
ejpam-4940	94	18	if	if	SCONJ
ejpam-4940	94	19	p	p	NOUN
ejpam-4940	94	20	is	be	AUX
ejpam-4940	94	21	a	a	DET
ejpam-4940	94	22	non	non	ADJ
ejpam-4940	94	23	perfect	perfect	ADJ
ejpam-4940	94	24	square	square	ADJ
ejpam-4940	94	25	polynomial	polynomial	NOUN
ejpam-4940	94	26	,	,	PUNCT
ejpam-4940	94	27	then	then	ADV
ejpam-4940	94	28	(	(	PUNCT
ejpam-4940	94	29	1	1	X
ejpam-4940	94	30	)	)	PUNCT
ejpam-4940	94	31	has	have	VERB
ejpam-4940	94	32	an	an	DET
ejpam-4940	94	33	infinitude	infinitude	NOUN
ejpam-4940	94	34	of	of	ADP
ejpam-4940	94	35	integer	integer	NOUN
ejpam-4940	94	36	solutions	solution	NOUN
ejpam-4940	94	37	.	.	PUNCT
ejpam-4940	95	1	in	in	ADP
ejpam-4940	95	2	this	this	DET
ejpam-4940	95	3	case	case	NOUN
ejpam-4940	95	4	we	we	PRON
ejpam-4940	95	5	find	find	VERB
ejpam-4940	95	6	a	a	DET
ejpam-4940	95	7	closed	closed	ADJ
ejpam-4940	95	8	expression	expression	NOUN
ejpam-4940	95	9	(	(	PUNCT
ejpam-4940	95	10	xn	xn	PROPN
ejpam-4940	95	11	,	,	PUNCT
ejpam-4940	95	12	yn	yn	PROPN
ejpam-4940	95	13	)	)	PUNCT
ejpam-4940	95	14	,	,	PUNCT
ejpam-4940	95	15	the	the	DET
ejpam-4940	95	16	general	general	ADJ
ejpam-4940	95	17	positive	positive	ADJ
ejpam-4940	95	18	integer	integer	NOUN
ejpam-4940	95	19	solution	solution	NOUN
ejpam-4940	95	20	,	,	PUNCT
ejpam-4940	95	21	by	by	ADP
ejpam-4940	95	22	an	an	DET
ejpam-4940	95	23	original	original	ADJ
ejpam-4940	95	24	method	method	NOUN
ejpam-4940	95	25	.	.	PUNCT
ejpam-4940	96	1	note	note	VERB
ejpam-4940	96	2	that	that	SCONJ
ejpam-4940	96	3	the	the	DET
ejpam-4940	96	4	resolution	resolution	NOUN
ejpam-4940	96	5	of	of	ADP
ejpam-4940	96	6	e	e	PROPN
ejpam-4940	96	7	in	in	ADP
ejpam-4940	96	8	its	its	PRON
ejpam-4940	96	9	present	present	ADJ
ejpam-4940	96	10	form	form	NOUN
ejpam-4940	96	11	is	be	AUX
ejpam-4940	96	12	difficult	difficult	ADJ
ejpam-4940	96	13	,	,	PUNCT
ejpam-4940	96	14	that	that	ADV
ejpam-4940	96	15	is	is	ADV
ejpam-4940	96	16	,	,	PUNCT
ejpam-4940	96	17	we	we	PRON
ejpam-4940	96	18	can	can	AUX
ejpam-4940	96	19	not	not	PART
ejpam-4940	96	20	determine	determine	VERB
ejpam-4940	96	21	how	how	SCONJ
ejpam-4940	96	22	many	many	ADJ
ejpam-4940	96	23	solutions	solution	NOUN
ejpam-4940	96	24	e	e	NOUN
ejpam-4940	96	25	has	have	VERB
ejpam-4940	96	26	and	and	CCONJ
ejpam-4940	96	27	what	what	PRON
ejpam-4940	96	28	they	they	PRON
ejpam-4940	96	29	are	be	AUX
ejpam-4940	96	30	.	.	PUNCT
ejpam-4940	97	1	so	so	ADV
ejpam-4940	97	2	,	,	PUNCT
ejpam-4940	97	3	we	we	PRON
ejpam-4940	97	4	have	have	VERB
ejpam-4940	97	5	to	to	PART
ejpam-4940	97	6	transform	transform	VERB
ejpam-4940	97	7	e	e	NOUN
ejpam-4940	97	8	into	into	ADP
ejpam-4940	97	9	a	a	DET
ejpam-4940	97	10	pell	pell	NOUN
ejpam-4940	97	11	equation	equation	NOUN
ejpam-4940	97	12	which	which	PRON
ejpam-4940	97	13	can	can	AUX
ejpam-4940	97	14	be	be	AUX
ejpam-4940	97	15	easily	easily	ADV
ejpam-4940	97	16	solved	solve	VERB
ejpam-4940	97	17	.	.	PUNCT
ejpam-4940	98	1	to	to	PART
ejpam-4940	98	2	get	get	VERB
ejpam-4940	98	3	this	this	PRON
ejpam-4940	98	4	let	let	NOUN
ejpam-4940	98	5	t	t	NOUN
ejpam-4940	98	6	:	:	PUNCT
ejpam-4940	98	7	{	{	PUNCT
ejpam-4940	98	8	x	x	SYM
ejpam-4940	98	9	=	=	X
ejpam-4940	98	10	u+	u+	NUM
ejpam-4940	98	11	p	p	NOUN
ejpam-4940	98	12	′(t	′(t	NOUN
ejpam-4940	98	13	)	)	PUNCT
ejpam-4940	98	14	=	=	PUNCT
ejpam-4940	99	1	u+	u+	NUM
ejpam-4940	99	2	2kt2k−1	2kt2k−1	NUM
ejpam-4940	99	3	±	±	NUM
ejpam-4940	99	4	imtm−1	imtm−1	NOUN
ejpam-4940	99	5	y	y	PROPN
ejpam-4940	99	6	=	=	SYM
ejpam-4940	99	7	v	v	PROPN
ejpam-4940	99	8	+	+	CCONJ
ejpam-4940	99	9	2	2	NUM
ejpam-4940	99	10	(	(	PUNCT
ejpam-4940	99	11	2	2	NUM
ejpam-4940	99	12	)	)	PUNCT
ejpam-4940	99	13	we	we	PRON
ejpam-4940	99	14	get	get	VERB
ejpam-4940	99	15	,	,	PUNCT
ejpam-4940	99	16	t	t	PROPN
ejpam-4940	99	17	(	(	PUNCT
ejpam-4940	99	18	e	e	NOUN
ejpam-4940	99	19	)	)	PUNCT
ejpam-4940	99	20	:	:	PUNCT
ejpam-4940	100	1	=	=	SYM
ejpam-4940	100	2	ẽ	ẽ	PROPN
ejpam-4940	100	3	,	,	PUNCT
ejpam-4940	100	4	such	such	ADJ
ejpam-4940	100	5	that	that	SCONJ
ejpam-4940	100	6	ẽ	ẽ	PROPN
ejpam-4940	100	7	:	:	PUNCT
ejpam-4940	100	8	(	(	PUNCT
ejpam-4940	100	9	u+	u+	NUM
ejpam-4940	100	10	2kt2k−1	2kt2k−1	NUM
ejpam-4940	100	11	±	±	NOUN
ejpam-4940	100	12	imtm−1)2	imtm−1)2	PROPN
ejpam-4940	100	13	−	−	PROPN
ejpam-4940	100	14	(	(	PUNCT
ejpam-4940	100	15	t2k	t2k	ADJ
ejpam-4940	100	16	±	±	NUM
ejpam-4940	100	17	itm)(v	itm)(v	VERB
ejpam-4940	100	18	+	+	X
ejpam-4940	100	19	2)2	2)2	NUM
ejpam-4940	100	20	−	−	NOUN
ejpam-4940	100	21	(	(	PUNCT
ejpam-4940	100	22	4kt2k−1	4kt2k−1	PROPN
ejpam-4940	100	23	±	±	NUM
ejpam-4940	100	24	2imtm−1	2imtm−1	NUM
ejpam-4940	100	25	)	)	PUNCT
ejpam-4940	100	26	(	(	PUNCT
ejpam-4940	100	27	u+	u+	NUM
ejpam-4940	100	28	2kt2k−1	2kt2k−1	NUM
ejpam-4940	100	29	±	±	NUM
ejpam-4940	100	30	imtm−1	imtm−1	NOUN
ejpam-4940	100	31	)	)	PUNCT
ejpam-4940	101	1	+	+	CCONJ
ejpam-4940	101	2	(	(	PUNCT
ejpam-4940	101	3	4t2k	4t2k	NOUN
ejpam-4940	101	4	±	±	NOUN
ejpam-4940	101	5	4itm)(v	4itm)(v	NUM
ejpam-4940	101	6	+	+	CCONJ
ejpam-4940	101	7	2	2	NUM
ejpam-4940	101	8	)	)	PUNCT
ejpam-4940	101	9	+	+	NUM
ejpam-4940	101	10	4k2t4k−2	4k2t4k−2	NUM
ejpam-4940	101	11	+	+	CCONJ
ejpam-4940	101	12	i2m2t2m−2	i2m2t2m−2	X
ejpam-4940	101	13	±4imkt2k+m−2	±4imkt2k+m−2	PUNCT
ejpam-4940	102	1	−	−	PROPN
ejpam-4940	102	2	4t2k	4t2k	NOUN
ejpam-4940	102	3	∓	∓	NOUN
ejpam-4940	102	4	4itm	4itm	NOUN
ejpam-4940	102	5	−	−	NOUN
ejpam-4940	103	1	1	1	NUM
ejpam-4940	103	2	then	then	ADV
ejpam-4940	103	3	,	,	PUNCT
ejpam-4940	103	4	the	the	DET
ejpam-4940	103	5	equation	equation	NOUN
ejpam-4940	103	6	(	(	PUNCT
ejpam-4940	103	7	1	1	X
ejpam-4940	103	8	)	)	PUNCT
ejpam-4940	103	9	becomes	become	VERB
ejpam-4940	103	10	ẽ	ẽ	PROPN
ejpam-4940	103	11	:	:	PUNCT
ejpam-4940	103	12	u2	u2	PROPN
ejpam-4940	103	13	−	−	PROPN
ejpam-4940	103	14	(	(	PUNCT
ejpam-4940	103	15	t2k	t2k	PROPN
ejpam-4940	103	16	±	±	NOUN
ejpam-4940	103	17	itm)v2	itm)v2	NOUN
ejpam-4940	103	18	=	=	SYM
ejpam-4940	103	19	1	1	NUM
ejpam-4940	103	20	(	(	PUNCT
ejpam-4940	103	21	3	3	NUM
ejpam-4940	103	22	)	)	PUNCT
ejpam-4940	103	23	a.	a.	NOUN
ejpam-4940	103	24	m.	m.	NOUN
ejpam-4940	103	25	sibih	sibih	PROPN
ejpam-4940	103	26	/	/	SYM
ejpam-4940	103	27	eur	eur	PROPN
ejpam-4940	103	28	.	.	PUNCT
ejpam-4940	104	1	j.	j.	PROPN
ejpam-4940	104	2	pure	pure	PROPN
ejpam-4940	104	3	appl	appl	PROPN
ejpam-4940	104	4	.	.	PROPN
ejpam-4940	104	5	math	math	PROPN
ejpam-4940	104	6	,	,	PUNCT
ejpam-4940	104	7	16	16	NUM
ejpam-4940	104	8	(	(	PUNCT
ejpam-4940	104	9	4	4	NUM
ejpam-4940	104	10	)	)	PUNCT
ejpam-4940	104	11	(	(	PUNCT
ejpam-4940	104	12	2023	2023	NUM
ejpam-4940	104	13	)	)	PUNCT
ejpam-4940	104	14	,	,	PUNCT
ejpam-4940	104	15	2693	2693	NUM
ejpam-4940	104	16	-	-	SYM
ejpam-4940	104	17	2702	2702	NUM
ejpam-4940	104	18	2697	2697	NUM
ejpam-4940	104	19	which	which	PRON
ejpam-4940	104	20	is	be	AUX
ejpam-4940	104	21	a	a	DET
ejpam-4940	104	22	pell	pell	NOUN
ejpam-4940	104	23	equation	equation	NOUN
ejpam-4940	104	24	.	.	PUNCT
ejpam-4940	105	1	it	it	PRON
ejpam-4940	105	2	is	be	AUX
ejpam-4940	105	3	known	know	VERB
ejpam-4940	105	4	that	that	SCONJ
ejpam-4940	105	5	the	the	DET
ejpam-4940	105	6	above	above	ADJ
ejpam-4940	105	7	pell	pell	NOUN
ejpam-4940	105	8	equation	equation	NOUN
ejpam-4940	105	9	is	be	AUX
ejpam-4940	105	10	always	always	ADV
ejpam-4940	105	11	solvable	solvable	ADJ
ejpam-4940	105	12	.	.	PUNCT
ejpam-4940	106	1	its	its	PRON
ejpam-4940	106	2	solutions	solution	NOUN
ejpam-4940	106	3	are	be	AUX
ejpam-4940	106	4	related	relate	VERB
ejpam-4940	106	5	to	to	ADP
ejpam-4940	106	6	the	the	DET
ejpam-4940	106	7	continued	continue	VERB
ejpam-4940	106	8	fraction	fraction	NOUN
ejpam-4940	106	9	expansion	expansion	NOUN
ejpam-4940	106	10	of	of	ADP
ejpam-4940	106	11	√	√	PROPN
ejpam-4940	106	12	p	p	PROPN
ejpam-4940	106	13	(	(	PUNCT
ejpam-4940	106	14	t	t	PROPN
ejpam-4940	106	15	)	)	PUNCT
ejpam-4940	106	16	.	.	PUNCT
ejpam-4940	107	1	we	we	PRON
ejpam-4940	107	2	will	will	AUX
ejpam-4940	107	3	be	be	AUX
ejpam-4940	107	4	concerned	concern	VERB
ejpam-4940	107	5	with	with	ADP
ejpam-4940	107	6	the	the	DET
ejpam-4940	107	7	continued	continue	VERB
ejpam-4940	107	8	fraction	fraction	NOUN
ejpam-4940	107	9	expansions	expansion	NOUN
ejpam-4940	107	10	of	of	ADP
ejpam-4940	107	11	√	√	NOUN
ejpam-4940	107	12	p	p	NOUN
ejpam-4940	107	13	(	(	PUNCT
ejpam-4940	107	14	t	t	PROPN
ejpam-4940	107	15	)	)	PUNCT
ejpam-4940	107	16	,	,	PUNCT
ejpam-4940	107	17	where	where	SCONJ
ejpam-4940	107	18	p	p	PROPN
ejpam-4940	107	19	(	(	PUNCT
ejpam-4940	107	20	t	t	PROPN
ejpam-4940	107	21	)	)	PUNCT
ejpam-4940	107	22	is	be	AUX
ejpam-4940	107	23	a	a	DET
ejpam-4940	107	24	non	non	ADJ
ejpam-4940	107	25	-	-	ADJ
ejpam-4940	107	26	square	square	ADJ
ejpam-4940	107	27	.	.	PUNCT
ejpam-4940	108	1	in	in	ADP
ejpam-4940	108	2	fact	fact	NOUN
ejpam-4940	108	3	,	,	PUNCT
ejpam-4940	108	4	this	this	DET
ejpam-4940	108	5	continued	continue	VERB
ejpam-4940	108	6	fractions	fraction	NOUN
ejpam-4940	108	7	have	have	VERB
ejpam-4940	108	8	a	a	DET
ejpam-4940	108	9	very	very	ADV
ejpam-4940	108	10	interesting	interesting	ADJ
ejpam-4940	108	11	form	form	NOUN
ejpam-4940	108	12	,	,	PUNCT
ejpam-4940	108	13	which	which	PRON
ejpam-4940	108	14	is	be	AUX
ejpam-4940	108	15	summarized	summarize	VERB
ejpam-4940	108	16	in	in	ADP
ejpam-4940	108	17	the	the	DET
ejpam-4940	108	18	next	next	ADJ
ejpam-4940	108	19	theorem	theorem	PROPN
ejpam-4940	108	20	.	.	PUNCT
ejpam-4940	108	21	theorem	theorem	NOUN
ejpam-4940	108	22	4	4	NUM
ejpam-4940	108	23	.	.	PUNCT
ejpam-4940	109	1	let	let	VERB
ejpam-4940	109	2	p	p	PROPN
ejpam-4940	109	3	(	(	PUNCT
ejpam-4940	109	4	t	t	NOUN
ejpam-4940	109	5	)	)	PUNCT
ejpam-4940	109	6	be	be	AUX
ejpam-4940	109	7	a	a	DET
ejpam-4940	109	8	prime	prime	NOUN
ejpam-4940	109	9	.	.	PUNCT
ejpam-4940	110	1	then	then	ADV
ejpam-4940	110	2	√	√	VERB
ejpam-4940	110	3	p	p	PROPN
ejpam-4940	110	4	(	(	PUNCT
ejpam-4940	110	5	t	t	NOUN
ejpam-4940	110	6	)	)	PUNCT
ejpam-4940	110	7	=	=	PUNCT
ejpam-4940	111	1	[	[	X
ejpam-4940	111	2	a0	a0	NOUN
ejpam-4940	111	3	;	;	PUNCT
ejpam-4940	111	4	a1	a1	NOUN
ejpam-4940	111	5	,	,	PUNCT
ejpam-4940	111	6	a2	a2	PROPN
ejpam-4940	111	7	,	,	PUNCT
ejpam-4940	111	8	·	·	PUNCT
ejpam-4940	111	9	·	·	PUNCT
ejpam-4940	111	10	·	·	PUNCT
ejpam-4940	111	11	,	,	PUNCT
ejpam-4940	111	12	al	al	PROPN
ejpam-4940	111	13	,	,	PUNCT
ejpam-4940	111	14	2a0	2a0	NUM
ejpam-4940	111	15	]	]	PUNCT
ejpam-4940	111	16	,	,	PUNCT
ejpam-4940	111	17	where	where	SCONJ
ejpam-4940	111	18	the	the	DET
ejpam-4940	111	19	repeating	repeat	VERB
ejpam-4940	111	20	portion	portion	NOUN
ejpam-4940	111	21	,	,	PUNCT
ejpam-4940	111	22	excluding	exclude	VERB
ejpam-4940	111	23	the	the	DET
ejpam-4940	111	24	last	last	ADJ
ejpam-4940	111	25	term	term	NOUN
ejpam-4940	111	26	,	,	PUNCT
ejpam-4940	111	27	is	be	AUX
ejpam-4940	111	28	symmetric	symmetric	ADJ
ejpam-4940	111	29	upon	upon	SCONJ
ejpam-4940	111	30	reversal	reversal	NOUN
ejpam-4940	111	31	,	,	PUNCT
ejpam-4940	111	32	and	and	CCONJ
ejpam-4940	111	33	the	the	DET
ejpam-4940	111	34	central	central	ADJ
ejpam-4940	111	35	term	term	NOUN
ejpam-4940	111	36	may	may	AUX
ejpam-4940	111	37	appear	appear	VERB
ejpam-4940	111	38	either	either	CCONJ
ejpam-4940	111	39	once	once	ADV
ejpam-4940	111	40	or	or	CCONJ
ejpam-4940	111	41	twice	twice	ADV
ejpam-4940	111	42	.	.	PUNCT
ejpam-4940	112	1	theorem	theorem	NOUN
ejpam-4940	112	2	5	5	NUM
ejpam-4940	112	3	.	.	PUNCT
ejpam-4940	113	1	let	let	VERB
ejpam-4940	113	2	√	√	VERB
ejpam-4940	114	1	p	p	NOUN
ejpam-4940	114	2	(	(	PUNCT
ejpam-4940	114	3	t	t	NOUN
ejpam-4940	114	4	)	)	PUNCT
ejpam-4940	114	5	=	=	PUNCT
ejpam-4940	114	6	[	[	PUNCT
ejpam-4940	114	7	a0	a0	NOUN
ejpam-4940	114	8	;	;	PUNCT
ejpam-4940	114	9	a1	a1	PROPN
ejpam-4940	114	10	,	,	PUNCT
ejpam-4940	114	11	a2	a2	PROPN
ejpam-4940	114	12	,	,	PUNCT
ejpam-4940	114	13	·	·	PUNCT
ejpam-4940	114	14	·	·	PUNCT
ejpam-4940	114	15	·	·	PUNCT
ejpam-4940	114	16	,	,	PUNCT
ejpam-4940	114	17	al	al	PROPN
ejpam-4940	114	18	,	,	PUNCT
ejpam-4940	114	19	2a0	2a0	NUM
ejpam-4940	114	20	]	]	PUNCT
ejpam-4940	114	21	denote	denote	VERB
ejpam-4940	114	22	the	the	DET
ejpam-4940	114	23	continued	continue	VERB
ejpam-4940	114	24	fraction	fraction	NOUN
ejpam-4940	114	25	expansion	expansion	NOUN
ejpam-4940	114	26	of	of	ADP
ejpam-4940	114	27	period	period	NOUN
ejpam-4940	114	28	lenght	lenght	ADJ
ejpam-4940	114	29	l	l	NOUN
ejpam-4940	114	30	,	,	PUNCT
ejpam-4940	114	31	where	where	SCONJ
ejpam-4940	114	32	p	p	PROPN
ejpam-4940	114	33	(	(	PUNCT
ejpam-4940	114	34	t	t	NOUN
ejpam-4940	114	35	)	)	PUNCT
ejpam-4940	114	36	be	be	AUX
ejpam-4940	114	37	a	a	DET
ejpam-4940	114	38	non	non	ADJ
ejpam-4940	114	39	-	-	ADJ
ejpam-4940	114	40	square	square	ADJ
ejpam-4940	114	41	polynomial	polynomial	NOUN
ejpam-4940	114	42	.	.	PUNCT
ejpam-4940	115	1	let	let	VERB
ejpam-4940	115	2	pn	pn	PROPN
ejpam-4940	115	3	qn	qn	PROPN
ejpam-4940	115	4	be	be	AUX
ejpam-4940	115	5	the	the	DET
ejpam-4940	115	6	nth	nth	ADJ
ejpam-4940	115	7	convergent	convergent	NOUN
ejpam-4940	115	8	of	of	ADP
ejpam-4940	115	9	√	√	PROPN
ejpam-4940	115	10	p	p	PROPN
ejpam-4940	115	11	(	(	PUNCT
ejpam-4940	115	12	t	t	PROPN
ejpam-4940	115	13	)	)	PUNCT
ejpam-4940	115	14	.	.	PUNCT
ejpam-4940	116	1	then	then	ADV
ejpam-4940	116	2	(	(	PUNCT
ejpam-4940	116	3	1	1	X
ejpam-4940	116	4	)	)	PUNCT
ejpam-4940	116	5	the	the	DET
ejpam-4940	116	6	fundamental	fundamental	ADJ
ejpam-4940	116	7	solution	solution	NOUN
ejpam-4940	116	8	of	of	ADP
ejpam-4940	116	9	the	the	DET
ejpam-4940	116	10	pell	pell	NOUN
ejpam-4940	116	11	equation	equation	NOUN
ejpam-4940	116	12	ẽ	ẽ	PROPN
ejpam-4940	116	13	in	in	ADP
ejpam-4940	116	14	(	(	PUNCT
ejpam-4940	116	15	3	3	NUM
ejpam-4940	116	16	)	)	PUNCT
ejpam-4940	116	17	is	be	AUX
ejpam-4940	116	18	(	(	PUNCT
ejpam-4940	116	19	u1	u1	NOUN
ejpam-4940	116	20	,	,	PUNCT
ejpam-4940	116	21	v1	v1	NOUN
ejpam-4940	116	22	)	)	PUNCT
ejpam-4940	116	23	,	,	PUNCT
ejpam-4940	116	24	such	such	ADJ
ejpam-4940	116	25	that	that	NUM
ejpam-4940	116	26	u1	u1	NOUN
ejpam-4940	116	27	=	=	SYM
ejpam-4940	116	28	pl−1	pl−1	NOUN
ejpam-4940	116	29	,	,	PUNCT
ejpam-4940	116	30	if	if	SCONJ
ejpam-4940	116	31	l	l	NOUN
ejpam-4940	116	32	is	be	AUX
ejpam-4940	116	33	even	even	ADV
ejpam-4940	116	34	,	,	PUNCT
ejpam-4940	116	35	v1	v1	NOUN
ejpam-4940	116	36	=	=	SYM
ejpam-4940	116	37	ql−1	ql−1	NOUN
ejpam-4940	116	38	and	and	CCONJ
ejpam-4940	116	39			NUM
ejpam-4940	116	40	u1	u1	NOUN
ejpam-4940	116	41	=	=	SYM
ejpam-4940	116	42	p2l−1	p2l−1	PROPN
ejpam-4940	116	43	,	,	PUNCT
ejpam-4940	116	44	if	if	SCONJ
ejpam-4940	116	45	l	l	NOUN
ejpam-4940	116	46	is	be	AUX
ejpam-4940	116	47	even	even	ADV
ejpam-4940	116	48	v1	v1	VERB
ejpam-4940	116	49	=	=	SYM
ejpam-4940	116	50	q2l−1	q2l−1	PROPN
ejpam-4940	116	51	set	set	NOUN
ejpam-4940	116	52	{	{	PUNCT
ejpam-4940	116	53	(	(	PUNCT
ejpam-4940	116	54	uk	uk	PROPN
ejpam-4940	116	55	,	,	PUNCT
ejpam-4940	116	56	vk	vk	NOUN
ejpam-4940	116	57	)	)	PUNCT
ejpam-4940	116	58	}	}	PUNCT
ejpam-4940	116	59	=	=	SYM
ejpam-4940	116	60	{	{	PUNCT
ejpam-4940	116	61	(	(	PUNCT
ejpam-4940	116	62	pkl−1	pkl−1	PROPN
ejpam-4940	116	63	,	,	PUNCT
ejpam-4940	116	64	qkl−1	qkl−1	NOUN
ejpam-4940	116	65	)	)	PUNCT
ejpam-4940	116	66	}	}	PUNCT
ejpam-4940	116	67	where	where	SCONJ
ejpam-4940	116	68	pkl−1	pkl−1	NOUN
ejpam-4940	116	69	qkl−1	qkl−1	PROPN
ejpam-4940	116	70	=	=	SYM
ejpam-4940	116	71	a0	a0	NUM
ejpam-4940	116	72	;	;	PUNCT
ejpam-4940	116	73	a1	a1	NOUN
ejpam-4940	116	74	,	,	PUNCT
ejpam-4940	116	75	a2	a2	PROPN
ejpam-4940	116	76	,	,	PUNCT
ejpam-4940	116	77	·	·	PUNCT
ejpam-4940	116	78	·	·	PUNCT
ejpam-4940	116	79	·	·	PUNCT
ejpam-4940	116	80	,	,	PUNCT
ejpam-4940	116	81	al	al	PROPN
ejpam-4940	116	82	,	,	PUNCT
ejpam-4940	116	83	︸	︸	SYM
ejpam-4940	116	84	︷︷	︷︷	NOUN
ejpam-4940	116	85	︸	︸	X
ejpam-4940	117	1	l−1	l−1	PROPN
ejpam-4940	117	2	2a0	2a0	NUM
ejpam-4940	117	3	,	,	PUNCT
ejpam-4940	117	4	a1	a1	NOUN
ejpam-4940	117	5	,	,	PUNCT
ejpam-4940	117	6	a2	a2	PROPN
ejpam-4940	117	7	,	,	PUNCT
ejpam-4940	117	8	·	·	PUNCT
ejpam-4940	117	9	·	·	PUNCT
ejpam-4940	117	10	·	·	PUNCT
ejpam-4940	117	11	,	,	PUNCT
ejpam-4940	117	12	al	al	PROPN
ejpam-4940	117	13	,	,	PUNCT
ejpam-4940	117	14	2a0	2a0	NUM
ejpam-4940	117	15	,	,	PUNCT
ejpam-4940	117	16	a1	a1	NOUN
ejpam-4940	117	17	,	,	PUNCT
ejpam-4940	117	18	a2	a2	PROPN
ejpam-4940	117	19	,	,	PUNCT
ejpam-4940	117	20	·	·	PUNCT
ejpam-4940	117	21	·	·	PUNCT
ejpam-4940	117	22	·	·	PUNCT
ejpam-4940	117	23	,	,	PUNCT
ejpam-4940	117	24	al︸	al︸	PROPN
ejpam-4940	117	25	︷︷	︷︷	PROPN
ejpam-4940	117	26	︸	︸	X
ejpam-4940	117	27	(	(	PUNCT
ejpam-4940	117	28	k−1)l−1	k−1)l−1	PROPN
ejpam-4940	117	29			VERB
ejpam-4940	117	30	,	,	PUNCT
ejpam-4940	117	31	if	if	SCONJ
ejpam-4940	117	32	l	l	NOUN
ejpam-4940	117	33	is	be	AUX
ejpam-4940	117	34	even	even	ADV
ejpam-4940	117	35	.	.	PUNCT
ejpam-4940	118	1	and	and	CCONJ
ejpam-4940	118	2	p2kl−1	p2kl−1	NOUN
ejpam-4940	118	3	q2kl−1	q2kl−1	NUM
ejpam-4940	118	4	=	=	SYM
ejpam-4940	118	5	a0	a0	X
ejpam-4940	118	6	;	;	PUNCT
ejpam-4940	118	7	a1	a1	NOUN
ejpam-4940	118	8	,	,	PUNCT
ejpam-4940	118	9	·	·	PUNCT
ejpam-4940	118	10	·	·	PUNCT
ejpam-4940	118	11	·	·	PUNCT
ejpam-4940	118	12	,	,	PUNCT
ejpam-4940	118	13	al	al	PROPN
ejpam-4940	118	14	,	,	PUNCT
ejpam-4940	118	15	2a0	2a0	NUM
ejpam-4940	118	16	,	,	PUNCT
ejpam-4940	118	17	a1	a1	NOUN
ejpam-4940	118	18	,	,	PUNCT
ejpam-4940	118	19	·	·	PUNCT
ejpam-4940	118	20	·	·	PUNCT
ejpam-4940	118	21	·	·	PUNCT
ejpam-4940	118	22	,	,	PUNCT
ejpam-4940	118	23	al︸	al︸	PROPN
ejpam-4940	118	24	︷︷	︷︷	PROPN
ejpam-4940	118	25	︸	︸	ADP
ejpam-4940	118	26	2l−1	2l−1	NUM
ejpam-4940	118	27	,	,	PUNCT
ejpam-4940	118	28	2a0	2a0	NUM
ejpam-4940	118	29	,	,	PUNCT
ejpam-4940	118	30	a1	a1	PROPN
ejpam-4940	118	31	,	,	PUNCT
ejpam-4940	118	32	·	·	PUNCT
ejpam-4940	118	33	·	·	PUNCT
ejpam-4940	118	34	·	·	PUNCT
ejpam-4940	118	35	,	,	PUNCT
ejpam-4940	118	36	al	al	PROPN
ejpam-4940	118	37	,	,	PUNCT
ejpam-4940	118	38	2a0	2a0	NUM
ejpam-4940	118	39	,	,	PUNCT
ejpam-4940	118	40	·	·	PUNCT
ejpam-4940	118	41	·	·	PUNCT
ejpam-4940	118	42	·	·	PUNCT
ejpam-4940	118	43	,	,	PUNCT
ejpam-4940	118	44	a1	a1	PROPN
ejpam-4940	118	45	,	,	PUNCT
ejpam-4940	118	46	·	·	PUNCT
ejpam-4940	118	47	·	·	PUNCT
ejpam-4940	118	48	·	·	PUNCT
ejpam-4940	118	49	,	,	PUNCT
ejpam-4940	118	50	al	al	PROPN
ejpam-4940	118	51	,	,	PUNCT
ejpam-4940	118	52	︸	︸	SYM
ejpam-4940	118	53	︷︷	︷︷	NOUN
ejpam-4940	118	54	︸	︸	X
ejpam-4940	118	55	(	(	PUNCT
ejpam-4940	118	56	2k−2)l−1	2k−2)l−1	NUM
ejpam-4940	118	57			NOUN
ejpam-4940	118	58	,	,	PUNCT
ejpam-4940	118	59	if	if	SCONJ
ejpam-4940	118	60	l	l	NOUN
ejpam-4940	118	61	is	be	AUX
ejpam-4940	118	62	odd	odd	ADJ
ejpam-4940	118	63	.	.	PUNCT
ejpam-4940	119	1	then	then	ADV
ejpam-4940	119	2	(	(	PUNCT
ejpam-4940	119	3	uk	uk	PROPN
ejpam-4940	119	4	,	,	PUNCT
ejpam-4940	119	5	vk	vk	PROPN
ejpam-4940	119	6	)	)	PUNCT
ejpam-4940	119	7	is	be	AUX
ejpam-4940	119	8	a	a	DET
ejpam-4940	119	9	solution	solution	NOUN
ejpam-4940	119	10	of	of	ADP
ejpam-4940	119	11	ẽ.	ẽ.	PROPN
ejpam-4940	119	12	(	(	PUNCT
ejpam-4940	119	13	2	2	NUM
ejpam-4940	119	14	)	)	PUNCT
ejpam-4940	119	15	the	the	DET
ejpam-4940	119	16	consecutive	consecutive	ADJ
ejpam-4940	119	17	solutions	solution	NOUN
ejpam-4940	119	18	(	(	PUNCT
ejpam-4940	119	19	uk−1	uk−1	PROPN
ejpam-4940	119	20	,	,	PUNCT
ejpam-4940	119	21	vk−1	vk−1	NOUN
ejpam-4940	119	22	)	)	PUNCT
ejpam-4940	119	23	and	and	CCONJ
ejpam-4940	119	24	(	(	PUNCT
ejpam-4940	119	25	uk	uk	PROPN
ejpam-4940	119	26	,	,	PUNCT
ejpam-4940	119	27	vk	vk	PROPN
ejpam-4940	119	28	)	)	PUNCT
ejpam-4940	119	29	the	the	DET
ejpam-4940	119	30	pell	pell	NOUN
ejpam-4940	119	31	equation	equation	NOUN
ejpam-4940	119	32	ẽ	ẽ	PROPN
ejpam-4940	119	33	in	in	ADP
ejpam-4940	119	34	(	(	PUNCT
ejpam-4940	119	35	3	3	NUM
ejpam-4940	119	36	)	)	PUNCT
ejpam-4940	119	37	satisfy	satisfy	NOUN
ejpam-4940	119	38			PUNCT
ejpam-4940	119	39	uk	uk	PROPN
ejpam-4940	119	40	=	=	PUNCT
ejpam-4940	119	41	u1uk−1	u1uk−1	X
ejpam-4940	119	42	+	+	PUNCT
ejpam-4940	119	43	(	(	PUNCT
ejpam-4940	119	44	a0u1	a0u1	X
ejpam-4940	119	45	+	+	CCONJ
ejpam-4940	119	46	α)vk−1	α)vk−1	ADV
ejpam-4940	119	47	,	,	PUNCT
ejpam-4940	119	48	forall	forall	PROPN
ejpam-4940	119	49	k	k	X
ejpam-4940	119	50	≥	≥	NUM
ejpam-4940	119	51	2	2	NUM
ejpam-4940	119	52	,	,	PUNCT
ejpam-4940	119	53	if	if	SCONJ
ejpam-4940	119	54	l	l	NOUN
ejpam-4940	119	55	is	be	AUX
ejpam-4940	119	56	even	even	ADV
ejpam-4940	119	57	vk	vk	ADP
ejpam-4940	119	58	=	=	SYM
ejpam-4940	119	59	v1uk−1	v1uk−1	NUM
ejpam-4940	119	60	+	+	CCONJ
ejpam-4940	119	61	(	(	PUNCT
ejpam-4940	119	62	a0v1	a0v1	NOUN
ejpam-4940	119	63	+	+	CCONJ
ejpam-4940	119	64	β)vk−1	β)vk−1	ADJ
ejpam-4940	119	65	where	where	SCONJ
ejpam-4940	119	66	α	α	PROPN
ejpam-4940	119	67	=	=	SYM
ejpam-4940	119	68	xl−2	xl−2	PROPN
ejpam-4940	119	69	and	and	CCONJ
ejpam-4940	119	70	β	β	X
ejpam-4940	119	71	=	=	SYM
ejpam-4940	119	72	xl−2	xl−2	PROPN
ejpam-4940	119	73	.	.	PUNCT
ejpam-4940	120	1	and	and	CCONJ
ejpam-4940	120	2			PUNCT
ejpam-4940	120	3	uk	uk	PROPN
ejpam-4940	120	4	=	=	PUNCT
ejpam-4940	120	5	u1uk−1	u1uk−1	X
ejpam-4940	120	6	+	+	PUNCT
ejpam-4940	120	7	(	(	PUNCT
ejpam-4940	120	8	a0u1	a0u1	SYM
ejpam-4940	120	9	+	+	PUNCT
ejpam-4940	120	10	η)vk−1	η)vk−1	PROPN
ejpam-4940	120	11	,	,	PUNCT
ejpam-4940	120	12	forall	forall	PROPN
ejpam-4940	120	13	k	k	PROPN
ejpam-4940	120	14	≥	≥	NUM
ejpam-4940	120	15	2	2	NUM
ejpam-4940	120	16	,	,	PUNCT
ejpam-4940	120	17	if	if	SCONJ
ejpam-4940	120	18	l	l	NOUN
ejpam-4940	120	19	is	be	AUX
ejpam-4940	120	20	odd	odd	ADJ
ejpam-4940	120	21	vk	vk	X
ejpam-4940	120	22	=	=	SYM
ejpam-4940	120	23	v1uk−1	v1uk−1	NUM
ejpam-4940	120	24	+	+	CCONJ
ejpam-4940	120	25	(	(	PUNCT
ejpam-4940	120	26	a0v1	a0v1	SYM
ejpam-4940	120	27	+	+	NUM
ejpam-4940	120	28	δ)vk−1	δ)vk−1	PROPN
ejpam-4940	120	29	a.	a.	NOUN
ejpam-4940	120	30	m.	m.	PROPN
ejpam-4940	120	31	sibih	sibih	PROPN
ejpam-4940	120	32	/	/	SYM
ejpam-4940	120	33	eur	eur	PROPN
ejpam-4940	120	34	.	.	PUNCT
ejpam-4940	121	1	j.	j.	PROPN
ejpam-4940	121	2	pure	pure	PROPN
ejpam-4940	121	3	appl	appl	PROPN
ejpam-4940	121	4	.	.	PROPN
ejpam-4940	121	5	math	math	PROPN
ejpam-4940	121	6	,	,	PUNCT
ejpam-4940	121	7	16	16	NUM
ejpam-4940	121	8	(	(	PUNCT
ejpam-4940	121	9	4	4	NUM
ejpam-4940	121	10	)	)	PUNCT
ejpam-4940	121	11	(	(	PUNCT
ejpam-4940	121	12	2023	2023	NUM
ejpam-4940	121	13	)	)	PUNCT
ejpam-4940	121	14	,	,	PUNCT
ejpam-4940	121	15	2693	2693	NUM
ejpam-4940	121	16	-	-	SYM
ejpam-4940	121	17	2702	2702	NUM
ejpam-4940	121	18	2698	2698	NUM
ejpam-4940	121	19	where	where	SCONJ
ejpam-4940	121	20	η	η	X
ejpam-4940	121	21	=	=	SYM
ejpam-4940	121	22	x2l−2	x2l−2	PROPN
ejpam-4940	121	23	and	and	CCONJ
ejpam-4940	121	24	δ	δ	PROPN
ejpam-4940	121	25	=	=	PUNCT
ejpam-4940	122	1	x2l−2	x2l−2	PROPN
ejpam-4940	122	2	.	.	PUNCT
ejpam-4940	123	1	to	to	PART
ejpam-4940	123	2	prove	prove	VERB
ejpam-4940	123	3	this	this	DET
ejpam-4940	123	4	theorem	theorem	NOUN
ejpam-4940	123	5	,	,	PUNCT
ejpam-4940	123	6	we	we	PRON
ejpam-4940	123	7	need	need	VERB
ejpam-4940	123	8	the	the	DET
ejpam-4940	123	9	following	follow	VERB
ejpam-4940	123	10	lemma	lemma	PROPN
ejpam-4940	123	11	lemma	lemma	PROPN
ejpam-4940	123	12	1	1	X
ejpam-4940	123	13	.	.	PUNCT
ejpam-4940	124	1	let	let	VERB
ejpam-4940	124	2	√	√	VERB
ejpam-4940	125	1	p	p	NOUN
ejpam-4940	125	2	(	(	PUNCT
ejpam-4940	125	3	t	t	NOUN
ejpam-4940	125	4	)	)	PUNCT
ejpam-4940	125	5	=	=	PUNCT
ejpam-4940	125	6	[	[	PUNCT
ejpam-4940	125	7	a0	a0	NOUN
ejpam-4940	125	8	;	;	PUNCT
ejpam-4940	125	9	a1	a1	PROPN
ejpam-4940	125	10	,	,	PUNCT
ejpam-4940	125	11	a2	a2	PROPN
ejpam-4940	125	12	,	,	PUNCT
ejpam-4940	125	13	·	·	PUNCT
ejpam-4940	125	14	·	·	PUNCT
ejpam-4940	125	15	·	·	PUNCT
ejpam-4940	125	16	,	,	PUNCT
ejpam-4940	125	17	al	al	PROPN
ejpam-4940	125	18	,	,	PUNCT
ejpam-4940	125	19	2a0	2a0	NUM
ejpam-4940	125	20	]	]	PUNCT
ejpam-4940	125	21	denote	denote	VERB
ejpam-4940	125	22	the	the	DET
ejpam-4940	125	23	continued	continue	VERB
ejpam-4940	125	24	fraction	fraction	NOUN
ejpam-4940	125	25	expansion	expansion	NOUN
ejpam-4940	125	26	of	of	ADP
ejpam-4940	125	27	period	period	NOUN
ejpam-4940	125	28	lenght	lenght	PROPN
ejpam-4940	125	29	l.	l.	PROPN
ejpam-4940	126	1	then	then	ADV
ejpam-4940	126	2	{	{	PUNCT
ejpam-4940	126	3	a0xkl−1	a0xkl−1	NOUN
ejpam-4940	126	4	+	+	PRON
ejpam-4940	126	5	xkl−2	xkl−2	NOUN
ejpam-4940	126	6	=	=	SYM
ejpam-4940	126	7	p	p	X
ejpam-4940	126	8	(	(	PUNCT
ejpam-4940	126	9	t)ykl−1	t)ykl−1	NOUN
ejpam-4940	126	10	a0ykl−1	a0ykl−1	NOUN
ejpam-4940	126	11	+	+	CCONJ
ejpam-4940	126	12	ykl−2	ykl−2	NOUN
ejpam-4940	126	13	=	=	SYM
ejpam-4940	126	14	xkl−1	xkl−1	PROPN
ejpam-4940	126	15	for	for	ADP
ejpam-4940	126	16	all	all	DET
ejpam-4940	126	17	k	k	PROPN
ejpam-4940	126	18	≥	≥	NUM
ejpam-4940	126	19	2	2	NUM
ejpam-4940	126	20	.	.	PUNCT
ejpam-4940	126	21	proof	proof	NOUN
ejpam-4940	126	22	.	.	PUNCT
ejpam-4940	127	1	(	(	PUNCT
ejpam-4940	127	2	lemma	lemma	PROPN
ejpam-4940	127	3	1	1	X
ejpam-4940	127	4	)	)	PUNCT
ejpam-4940	127	5	we	we	PRON
ejpam-4940	127	6	have	have	VERB
ejpam-4940	127	7	√	√	NUM
ejpam-4940	127	8	p	p	NOUN
ejpam-4940	127	9	(	(	PUNCT
ejpam-4940	127	10	t	t	NOUN
ejpam-4940	127	11	)	)	PUNCT
ejpam-4940	128	1	=	=	PUNCT
ejpam-4940	128	2	[	[	PUNCT
ejpam-4940	128	3	a0	a0	NOUN
ejpam-4940	128	4	;	;	PUNCT
ejpam-4940	128	5	a1	a1	PROPN
ejpam-4940	128	6	,	,	PUNCT
ejpam-4940	128	7	a2	a2	PROPN
ejpam-4940	128	8	,	,	PUNCT
ejpam-4940	128	9	·	·	PUNCT
ejpam-4940	128	10	·	·	PUNCT
ejpam-4940	128	11	·	·	PUNCT
ejpam-4940	128	12	,	,	PUNCT
ejpam-4940	128	13	a1	a1	PROPN
ejpam-4940	128	14	,	,	PUNCT
ejpam-4940	128	15	2a0	2a0	NUM
ejpam-4940	128	16	]	]	PUNCT
ejpam-4940	128	17	.	.	PUNCT
ejpam-4940	129	1	thus	thus	ADV
ejpam-4940	129	2	,	,	PUNCT
ejpam-4940	129	3	we	we	PRON
ejpam-4940	129	4	may	may	AUX
ejpam-4940	129	5	write	write	VERB
ejpam-4940	129	6	√	√	PROPN
ejpam-4940	130	1	p	p	PROPN
ejpam-4940	130	2	(	(	PUNCT
ejpam-4940	130	3	t	t	NOUN
ejpam-4940	130	4	)	)	PUNCT
ejpam-4940	130	5	=	=	PUNCT
ejpam-4940	130	6	[	[	PUNCT
ejpam-4940	130	7	a0	a0	NOUN
ejpam-4940	130	8	;	;	PUNCT
ejpam-4940	130	9	a1	a1	PROPN
ejpam-4940	130	10	,	,	PUNCT
ejpam-4940	130	11	a2	a2	PROPN
ejpam-4940	130	12	,	,	PUNCT
ejpam-4940	130	13	·	·	PUNCT
ejpam-4940	130	14	·	·	PUNCT
ejpam-4940	130	15	·	·	PUNCT
ejpam-4940	130	16	,	,	PUNCT
ejpam-4940	130	17	akl−1	akl−1	NOUN
ejpam-4940	130	18	,	,	PUNCT
ejpam-4940	130	19	a0	a0	NOUN
ejpam-4940	130	20	+	+	CCONJ
ejpam-4940	130	21	√	√	PROPN
ejpam-4940	130	22	p	p	NOUN
ejpam-4940	130	23	(	(	PUNCT
ejpam-4940	130	24	t	t	PROPN
ejpam-4940	130	25	)	)	PUNCT
ejpam-4940	130	26	]	]	PUNCT
ejpam-4940	130	27	,	,	PUNCT
ejpam-4940	130	28	then	then	ADV
ejpam-4940	130	29	√	√	VERB
ejpam-4940	130	30	p	p	PROPN
ejpam-4940	130	31	(	(	PUNCT
ejpam-4940	130	32	t	t	NOUN
ejpam-4940	130	33	)	)	PUNCT
ejpam-4940	130	34	=	=	PUNCT
ejpam-4940	130	35	(	(	PUNCT
ejpam-4940	130	36	a0	a0	NOUN
ejpam-4940	130	37	+	+	CCONJ
ejpam-4940	130	38	√	√	PROPN
ejpam-4940	130	39	p	p	NOUN
ejpam-4940	130	40	(	(	PUNCT
ejpam-4940	130	41	t))xkl−1	t))xkl−1	NOUN
ejpam-4940	130	42	+	+	X
ejpam-4940	130	43	xkl−2	xkl−2	PROPN
ejpam-4940	130	44	(	(	PUNCT
ejpam-4940	130	45	a0	a0	NOUN
ejpam-4940	130	46	+	+	CCONJ
ejpam-4940	130	47	√	√	PROPN
ejpam-4940	130	48	p	p	NOUN
ejpam-4940	130	49	(	(	PUNCT
ejpam-4940	130	50	t))ykl−1	t))ykl−1	NOUN
ejpam-4940	130	51	+	+	CCONJ
ejpam-4940	130	52	ykl−2	ykl−2	NOUN
ejpam-4940	130	53	,	,	PUNCT
ejpam-4940	130	54	which	which	PRON
ejpam-4940	130	55	gives	give	VERB
ejpam-4940	130	56	rise	rise	NOUN
ejpam-4940	130	57	to	to	ADP
ejpam-4940	130	58	the	the	DET
ejpam-4940	130	59	equation	equation	NOUN
ejpam-4940	130	60	p	p	NOUN
ejpam-4940	130	61	(	(	PUNCT
ejpam-4940	130	62	t)ykl−1	t)ykl−1	X
ejpam-4940	130	63	+	+	NOUN
ejpam-4940	130	64	√	√	PROPN
ejpam-4940	130	65	p	p	NOUN
ejpam-4940	130	66	(	(	PUNCT
ejpam-4940	130	67	t)(a0ykl−1	t)(a0ykl−1	X
ejpam-4940	130	68	+	+	CCONJ
ejpam-4940	130	69	ykl−2	ykl−2	NOUN
ejpam-4940	130	70	)	)	PUNCT
ejpam-4940	130	71	=	=	NOUN
ejpam-4940	130	72	(	(	PUNCT
ejpam-4940	130	73	a0xkl−1	a0xkl−1	NOUN
ejpam-4940	130	74	+	+	CCONJ
ejpam-4940	130	75	xkl−2	xkl−2	NOUN
ejpam-4940	130	76	)	)	PUNCT
ejpam-4940	131	1	+	+	CCONJ
ejpam-4940	131	2	√	√	ADV
ejpam-4940	131	3	p	p	X
ejpam-4940	131	4	(	(	PUNCT
ejpam-4940	131	5	t)xkl−1	t)xkl−1	PROPN
ejpam-4940	131	6	.	.	NOUN
ejpam-4940	131	7	which	which	PRON
ejpam-4940	131	8	yields	yield	VERB
ejpam-4940	131	9	,	,	PUNCT
ejpam-4940	131	10	a0xkl−1	a0xkl−1	NOUN
ejpam-4940	131	11	+	+	X
ejpam-4940	131	12	xkl−2	xkl−2	NOUN
ejpam-4940	131	13	=	=	SYM
ejpam-4940	131	14	p	p	X
ejpam-4940	131	15	(	(	PUNCT
ejpam-4940	131	16	t)ykl−1	t)ykl−1	NOUN
ejpam-4940	131	17	and	and	CCONJ
ejpam-4940	131	18	a0ykl−1	a0ykl−1	NOUN
ejpam-4940	131	19	+	+	CCONJ
ejpam-4940	131	20	ykl−2	ykl−2	NOUN
ejpam-4940	131	21	=	=	SYM
ejpam-4940	131	22	xkl−1	xkl−1	PROPN
ejpam-4940	131	23	.	.	PUNCT
ejpam-4940	131	24	proof	proof	NOUN
ejpam-4940	131	25	.	.	PUNCT
ejpam-4940	132	1	(	(	PUNCT
ejpam-4940	132	2	theorem	theorem	NOUN
ejpam-4940	132	3	4	4	NUM
ejpam-4940	132	4	)	)	PUNCT
ejpam-4940	132	5	(	(	PUNCT
ejpam-4940	132	6	1	1	X
ejpam-4940	132	7	)	)	PUNCT
ejpam-4940	132	8	we	we	PRON
ejpam-4940	132	9	prove	prove	VERB
ejpam-4940	132	10	the	the	DET
ejpam-4940	132	11	theorem	theorem	NOUN
ejpam-4940	132	12	only	only	ADV
ejpam-4940	132	13	for	for	ADP
ejpam-4940	132	14	even	even	ADV
ejpam-4940	132	15	number	number	NOUN
ejpam-4940	132	16	l.	l.	NOUN
ejpam-4940	132	17	it	it	PRON
ejpam-4940	132	18	is	be	AUX
ejpam-4940	132	19	easily	easily	ADV
ejpam-4940	132	20	seen	see	VERB
ejpam-4940	132	21	that	that	SCONJ
ejpam-4940	132	22	x2kl−1−p	x2kl−1−p	PROPN
ejpam-4940	132	23	(	(	PUNCT
ejpam-4940	132	24	t)y2kl−1	t)y2kl−1	NOUN
ejpam-4940	132	25	=	=	SYM
ejpam-4940	132	26	xkl−1ykl−1	xkl−1ykl−1	PROPN
ejpam-4940	132	27	−	−	PROPN
ejpam-4940	132	28	ykl−1xkl−2	ykl−1xkl−2	PROPN
ejpam-4940	132	29	.	.	PUNCT
ejpam-4940	133	1	then	then	ADV
ejpam-4940	133	2	x2kl−1	x2kl−1	PROPN
ejpam-4940	133	3	−	−	PROPN
ejpam-4940	134	1	p	p	X
ejpam-4940	134	2	(	(	PUNCT
ejpam-4940	134	3	t)y2kl−1	t)y2kl−1	NOUN
ejpam-4940	134	4	=	=	SYM
ejpam-4940	134	5	(	(	PUNCT
ejpam-4940	134	6	−1)kl	−1)kl	PROPN
ejpam-4940	134	7	.	.	PUNCT
ejpam-4940	135	1	thus	thus	ADV
ejpam-4940	135	2	,	,	PUNCT
ejpam-4940	135	3	if	if	SCONJ
ejpam-4940	135	4	l	l	NOUN
ejpam-4940	135	5	is	be	AUX
ejpam-4940	135	6	even	even	ADV
ejpam-4940	135	7	x2kl−1	x2kl−1	X
ejpam-4940	135	8	−	−	PROPN
ejpam-4940	136	1	p	p	NOUN
ejpam-4940	136	2	(	(	PUNCT
ejpam-4940	136	3	t)y2kl−1	t)y2kl−1	NOUN
ejpam-4940	136	4	=	=	SYM
ejpam-4940	136	5	1	1	NUM
ejpam-4940	136	6	which	which	DET
ejpam-4940	136	7	yields	yield	VERB
ejpam-4940	136	8	(	(	PUNCT
ejpam-4940	136	9	uk	uk	PROPN
ejpam-4940	136	10	,	,	PUNCT
ejpam-4940	136	11	vk	vk	NOUN
ejpam-4940	136	12	)	)	PUNCT
ejpam-4940	136	13	are	be	AUX
ejpam-4940	136	14	solutions	solution	NOUN
ejpam-4940	136	15	of	of	ADP
ejpam-4940	136	16	ẽ	ẽ	PROPN
ejpam-4940	136	17	for	for	ADP
ejpam-4940	136	18	all	all	PRON
ejpam-4940	136	19	k	k	PROPN
ejpam-4940	136	20	≥	≥	NUM
ejpam-4940	136	21	1	1	NUM
ejpam-4940	136	22	and	and	CCONJ
ejpam-4940	136	23	(	(	PUNCT
ejpam-4940	136	24	u1	u1	NOUN
ejpam-4940	136	25	,	,	PUNCT
ejpam-4940	136	26	v1	v1	NOUN
ejpam-4940	136	27	)	)	PUNCT
ejpam-4940	136	28	is	be	AUX
ejpam-4940	136	29	the	the	DET
ejpam-4940	136	30	fundamental	fundamental	ADJ
ejpam-4940	136	31	solution	solution	NOUN
ejpam-4940	136	32	.	.	PUNCT
ejpam-4940	137	1	we	we	PRON
ejpam-4940	137	2	can	can	AUX
ejpam-4940	137	3	also	also	ADV
ejpam-4940	137	4	prove	prove	VERB
ejpam-4940	137	5	it	it	PRON
ejpam-4940	137	6	using	use	VERB
ejpam-4940	137	7	the	the	DET
ejpam-4940	137	8	method	method	NOUN
ejpam-4940	137	9	of	of	ADP
ejpam-4940	137	10	mathematical	mathematical	ADJ
ejpam-4940	137	11	induction	induction	NOUN
ejpam-4940	137	12	.	.	PUNCT
ejpam-4940	138	1	in	in	ADP
ejpam-4940	138	2	fact	fact	NOUN
ejpam-4940	138	3	,	,	PUNCT
ejpam-4940	138	4	if	if	SCONJ
ejpam-4940	138	5	l	l	NOUN
ejpam-4940	138	6	is	be	AUX
ejpam-4940	138	7	even	even	ADV
ejpam-4940	138	8	,	,	PUNCT
ejpam-4940	138	9	we	we	PRON
ejpam-4940	138	10	have	have	VERB
ejpam-4940	138	11	a.	a.	NOUN
ejpam-4940	138	12	m.	m.	NOUN
ejpam-4940	138	13	sibih	sibih	PROPN
ejpam-4940	138	14	/	/	SYM
ejpam-4940	138	15	eur	eur	PROPN
ejpam-4940	138	16	.	.	PUNCT
ejpam-4940	139	1	j.	j.	PROPN
ejpam-4940	139	2	pure	pure	PROPN
ejpam-4940	139	3	appl	appl	PROPN
ejpam-4940	139	4	.	.	PROPN
ejpam-4940	139	5	math	math	PROPN
ejpam-4940	139	6	,	,	PUNCT
ejpam-4940	139	7	16	16	NUM
ejpam-4940	139	8	(	(	PUNCT
ejpam-4940	139	9	4	4	NUM
ejpam-4940	139	10	)	)	PUNCT
ejpam-4940	139	11	(	(	PUNCT
ejpam-4940	139	12	2023	2023	NUM
ejpam-4940	139	13	)	)	PUNCT
ejpam-4940	139	14	,	,	PUNCT
ejpam-4940	139	15	2693	2693	NUM
ejpam-4940	139	16	-	-	SYM
ejpam-4940	139	17	2702	2702	NUM
ejpam-4940	139	18	2699	2699	NUM
ejpam-4940	139	19	uk	uk	PROPN
ejpam-4940	139	20	vk	vk	NOUN
ejpam-4940	139	21	=	=	SYM
ejpam-4940	139	22	xkl−1	xkl−1	PROPN
ejpam-4940	139	23	ykl−1	ykl−1	PROPN
ejpam-4940	139	24	=	=	SYM
ejpam-4940	139	25	a0	a0	PROPN
ejpam-4940	139	26	;	;	PUNCT
ejpam-4940	139	27	a1	a1	NOUN
ejpam-4940	139	28	,	,	PUNCT
ejpam-4940	139	29	a2	a2	PROPN
ejpam-4940	139	30	,	,	PUNCT
ejpam-4940	139	31	·	·	PUNCT
ejpam-4940	139	32	·	·	PUNCT
ejpam-4940	139	33	·	·	PUNCT
ejpam-4940	139	34	,	,	PUNCT
ejpam-4940	139	35	a1,︸	a1,︸	ADP
ejpam-4940	139	36	︷︷	︷︷	NOUN
ejpam-4940	139	37	︸	︸	X
ejpam-4940	140	1	l−1	l−1	PROPN
ejpam-4940	140	2	2a0	2a0	NUM
ejpam-4940	140	3	,	,	PUNCT
ejpam-4940	140	4	a1	a1	NOUN
ejpam-4940	140	5	,	,	PUNCT
ejpam-4940	140	6	a2	a2	PROPN
ejpam-4940	140	7	,	,	PUNCT
ejpam-4940	140	8	·	·	PUNCT
ejpam-4940	140	9	·	·	PUNCT
ejpam-4940	140	10	·	·	PUNCT
ejpam-4940	140	11	,	,	PUNCT
ejpam-4940	140	12	a1	a1	PROPN
ejpam-4940	140	13	,	,	PUNCT
ejpam-4940	140	14	2a0	2a0	NUM
ejpam-4940	140	15	,	,	PUNCT
ejpam-4940	140	16	·	·	PUNCT
ejpam-4940	140	17	·	·	PUNCT
ejpam-4940	140	18	·	·	PUNCT
ejpam-4940	140	19	,	,	PUNCT
ejpam-4940	140	20	a1	a1	PROPN
ejpam-4940	140	21	,	,	PUNCT
ejpam-4940	140	22	a2	a2	PROPN
ejpam-4940	140	23	,	,	PUNCT
ejpam-4940	140	24	·	·	PUNCT
ejpam-4940	140	25	·	·	PUNCT
ejpam-4940	140	26	·	·	PUNCT
ejpam-4940	140	27	,	,	PUNCT
ejpam-4940	140	28	a1︸	a1︸	PROPN
ejpam-4940	140	29	︷︷	︷︷	PROPN
ejpam-4940	140	30	︸	︸	X
ejpam-4940	140	31	(	(	PUNCT
ejpam-4940	140	32	k−1)l−1	k−1)l−1	PROPN
ejpam-4940	140	33			NUM
ejpam-4940	140	34	=	=	NOUN
ejpam-4940	140	35	a0	a0	X
ejpam-4940	140	36	;	;	PUNCT
ejpam-4940	140	37	a1	a1	NOUN
ejpam-4940	140	38	,	,	PUNCT
ejpam-4940	140	39	a2	a2	PROPN
ejpam-4940	140	40	,	,	PUNCT
ejpam-4940	140	41	·	·	PUNCT
ejpam-4940	140	42	·	·	PUNCT
ejpam-4940	140	43	·	·	PUNCT
ejpam-4940	140	44	,	,	PUNCT
ejpam-4940	140	45	a1,︸	a1,︸	ADP
ejpam-4940	140	46	︷︷	︷︷	NOUN
ejpam-4940	140	47	︸	︸	X
ejpam-4940	140	48	l−1	l−1	PROPN
ejpam-4940	140	49	a0	a0	PROPN
ejpam-4940	140	50	+	+	CCONJ
ejpam-4940	140	51	a0	a0	PROPN
ejpam-4940	140	52	,	,	PUNCT
ejpam-4940	140	53	a1	a1	NOUN
ejpam-4940	140	54	,	,	PUNCT
ejpam-4940	140	55	a2	a2	PROPN
ejpam-4940	140	56	,	,	PUNCT
ejpam-4940	140	57	·	·	PUNCT
ejpam-4940	140	58	·	·	PUNCT
ejpam-4940	140	59	·	·	PUNCT
ejpam-4940	140	60	,	,	PUNCT
ejpam-4940	140	61	a1	a1	PROPN
ejpam-4940	140	62	,	,	PUNCT
ejpam-4940	140	63	2a0	2a0	NUM
ejpam-4940	140	64	,	,	PUNCT
ejpam-4940	140	65	·	·	PUNCT
ejpam-4940	140	66	·	·	PUNCT
ejpam-4940	140	67	·	·	PUNCT
ejpam-4940	140	68	,	,	PUNCT
ejpam-4940	140	69	a1	a1	PROPN
ejpam-4940	140	70	,	,	PUNCT
ejpam-4940	140	71	·	·	PUNCT
ejpam-4940	140	72	·	·	PUNCT
ejpam-4940	140	73	·	·	PUNCT
ejpam-4940	140	74	,	,	PUNCT
ejpam-4940	140	75	a1︸	a1︸	PROPN
ejpam-4940	140	76	︷︷	︷︷	PROPN
ejpam-4940	140	77	︸	︸	X
ejpam-4940	140	78	(	(	PUNCT
ejpam-4940	140	79	k−1)l−1	k−1)l−1	PROPN
ejpam-4940	140	80			NUM
ejpam-4940	140	81	=	=	NOUN
ejpam-4940	140	82	a0	a0	NOUN
ejpam-4940	140	83	;	;	PUNCT
ejpam-4940	140	84	a1	a1	NOUN
ejpam-4940	140	85	,	,	PUNCT
ejpam-4940	140	86	a2	a2	PROPN
ejpam-4940	140	87	,	,	PUNCT
ejpam-4940	140	88	·	·	PUNCT
ejpam-4940	140	89	·	·	PUNCT
ejpam-4940	140	90	·	·	PUNCT
ejpam-4940	140	91	,	,	PUNCT
ejpam-4940	140	92	a1,︸	a1,︸	ADP
ejpam-4940	140	93	︷︷	︷︷	NOUN
ejpam-4940	140	94	︸	︸	X
ejpam-4940	140	95	l−1	l−1	PROPN
ejpam-4940	140	96	a0	a0	NOUN
ejpam-4940	140	97	+	+	CCONJ
ejpam-4940	140	98	x(k−1)l−1	x(k−1)l−1	NOUN
ejpam-4940	140	99	y(k−1)l−1	y(k−1)l−1	NOUN
ejpam-4940	140	100			NOUN
ejpam-4940	140	101	=	=	SYM
ejpam-4940	140	102	(	(	PUNCT
ejpam-4940	140	103	a0	a0	NOUN
ejpam-4940	140	104	+	+	CCONJ
ejpam-4940	140	105	x(k−1)l−1	x(k−1)l−1	PROPN
ejpam-4940	140	106	y(k−1)l−1	y(k−1)l−1	NOUN
ejpam-4940	140	107	)	)	PUNCT
ejpam-4940	140	108	xl−1	xl−1	NOUN
ejpam-4940	141	1	+	+	X
ejpam-4940	141	2	xl−2	xl−2	PROPN
ejpam-4940	141	3	(	(	PUNCT
ejpam-4940	141	4	a0	a0	NOUN
ejpam-4940	141	5	+	+	CCONJ
ejpam-4940	141	6	x(k−1)l−1	x(k−1)l−1	PROPN
ejpam-4940	141	7	y(k−1)l−1	y(k−1)l−1	NOUN
ejpam-4940	141	8	)	)	PUNCT
ejpam-4940	141	9	yl−1	yl−1	PROPN
ejpam-4940	141	10	+	+	CCONJ
ejpam-4940	141	11	yl−2	yl−2	X
ejpam-4940	141	12	=	=	SYM
ejpam-4940	141	13	a0y(k−1)l−1xl−1	a0y(k−1)l−1xl−1	PROPN
ejpam-4940	141	14	+	+	CCONJ
ejpam-4940	141	15	x(k−1)l−1xl−1	x(k−1)l−1xl−1	X
ejpam-4940	142	1	+	+	PUNCT
ejpam-4940	143	1	y(k−1)l−1xl−2	y(k−1)l−1xl−2	ADJ
ejpam-4940	143	2	a0y(k−1)l−1yl−1	a0y(k−1)l−1yl−1	NOUN
ejpam-4940	143	3	+	+	CCONJ
ejpam-4940	143	4	x(k−1)l−1yl−1	x(k−1)l−1yl−1	PROPN
ejpam-4940	143	5	+	+	CCONJ
ejpam-4940	143	6	y(k−1)l−1yl−2	y(k−1)l−1yl−2	PROPN
ejpam-4940	143	7	.	.	PUNCT
ejpam-4940	144	1	then	then	ADV
ejpam-4940	144	2	u2k	u2k	VERB
ejpam-4940	144	3	−	−	PROPN
ejpam-4940	144	4	p	p	NOUN
ejpam-4940	144	5	(	(	PUNCT
ejpam-4940	144	6	t)v2k	t)v2k	NOUN
ejpam-4940	144	7	=	=	SYM
ejpam-4940	144	8	(	(	PUNCT
ejpam-4940	144	9	a0y(k−1)l−1xl−1	a0y(k−1)l−1xl−1	PROPN
ejpam-4940	144	10	+	+	CCONJ
ejpam-4940	144	11	x(k−1)l−1xl−1	x(k−1)l−1xl−1	PROPN
ejpam-4940	144	12	+	+	CCONJ
ejpam-4940	145	1	y(k−1)l−1xl−2	y(k−1)l−1xl−2	ADJ
ejpam-4940	145	2	)	)	PUNCT
ejpam-4940	145	3	2	2	NUM
ejpam-4940	145	4	−p	−p	NOUN
ejpam-4940	145	5	(	(	PUNCT
ejpam-4940	145	6	t)(a0y(k−1)l−1yl−1	t)(a0y(k−1)l−1yl−1	NOUN
ejpam-4940	145	7	+	+	CCONJ
ejpam-4940	145	8	x(k−1)l−1yl−1	x(k−1)l−1yl−1	PROPN
ejpam-4940	145	9	+	+	CCONJ
ejpam-4940	145	10	y(k−1)l−1yl−2	y(k−1)l−1yl−2	PROPN
ejpam-4940	145	11	)	)	PUNCT
ejpam-4940	145	12	2	2	NUM
ejpam-4940	145	13	=	=	SYM
ejpam-4940	145	14	(	(	PUNCT
ejpam-4940	145	15	u1uk−1	u1uk−1	X
ejpam-4940	145	16	+	+	PUNCT
ejpam-4940	145	17	(	(	PUNCT
ejpam-4940	145	18	a0u1	a0u1	SYM
ejpam-4940	145	19	+	+	PUNCT
ejpam-4940	145	20	α)vk−1	α)vk−1	ADJ
ejpam-4940	145	21	)	)	PUNCT
ejpam-4940	145	22	2	2	NUM
ejpam-4940	145	23	−	−	NOUN
ejpam-4940	145	24	p	p	NOUN
ejpam-4940	145	25	(	(	PUNCT
ejpam-4940	145	26	t)(v1uk−1	t)(v1uk−1	NUM
ejpam-4940	145	27	+	+	CCONJ
ejpam-4940	145	28	(	(	PUNCT
ejpam-4940	145	29	a0v1	a0v1	ADP
ejpam-4940	145	30	+	+	SYM
ejpam-4940	145	31	β)vk−1	β)vk−1	ADJ
ejpam-4940	145	32	)	)	PUNCT
ejpam-4940	145	33	2	2	NUM
ejpam-4940	145	34	=	=	SYM
ejpam-4940	145	35	u21u	u21u	NOUN
ejpam-4940	145	36	2	2	NUM
ejpam-4940	145	37	k−1	k−1	PROPN
ejpam-4940	145	38	+	+	CCONJ
ejpam-4940	145	39	2u1(a0u1	2u1(a0u1	NUM
ejpam-4940	145	40	+	+	NUM
ejpam-4940	145	41	α)uk−1vk−1	α)uk−1vk−1	PROPN
ejpam-4940	145	42	+	+	CCONJ
ejpam-4940	145	43	(	(	PUNCT
ejpam-4940	145	44	a0u1	a0u1	PROPN
ejpam-4940	145	45	+	+	CCONJ
ejpam-4940	145	46	α)2v2k−1	α)2v2k−1	ADJ
ejpam-4940	145	47	−p	−p	NOUN
ejpam-4940	145	48	(	(	PUNCT
ejpam-4940	145	49	t)v21u	t)v21u	NOUN
ejpam-4940	145	50	2	2	NUM
ejpam-4940	145	51	k−1	k−1	PROPN
ejpam-4940	145	52	−	−	PROPN
ejpam-4940	145	53	2p	2p	NOUN
ejpam-4940	145	54	(	(	PUNCT
ejpam-4940	145	55	t)(a0v1	t)(a0v1	NOUN
ejpam-4940	145	56	+	+	CCONJ
ejpam-4940	145	57	β)v1uk−1vk−1	β)v1uk−1vk−1	ADP
ejpam-4940	145	58	−	−	PROPN
ejpam-4940	145	59	p	p	X
ejpam-4940	145	60	(	(	PUNCT
ejpam-4940	145	61	t)(a0v1	t)(a0v1	NOUN
ejpam-4940	145	62	+	+	X
ejpam-4940	145	63	β)2v2k−1	β)2v2k−1	PUNCT
ejpam-4940	145	64	=	=	SYM
ejpam-4940	145	65	(	(	PUNCT
ejpam-4940	145	66	u21	u21	PROPN
ejpam-4940	145	67	−	−	PROPN
ejpam-4940	145	68	p	p	NOUN
ejpam-4940	145	69	(	(	PUNCT
ejpam-4940	145	70	t)v21)u	t)v21)u	PROPN
ejpam-4940	145	71	2	2	NUM
ejpam-4940	145	72	k−1	k−1	PROPN
ejpam-4940	145	73	−	−	PROPN
ejpam-4940	145	74	[	[	PUNCT
ejpam-4940	145	75	(	(	PUNCT
ejpam-4940	145	76	p	p	X
ejpam-4940	145	77	(	(	PUNCT
ejpam-4940	145	78	t)(a0v1	t)(a0v1	NOUN
ejpam-4940	145	79	+	+	CCONJ
ejpam-4940	145	80	β)2	β)2	ADV
ejpam-4940	145	81	−	−	PROPN
ejpam-4940	145	82	(	(	PUNCT
ejpam-4940	145	83	a0u1	a0u1	PROPN
ejpam-4940	145	84	+	+	PUNCT
ejpam-4940	145	85	α)2	α)2	NOUN
ejpam-4940	145	86	]	]	PUNCT
ejpam-4940	145	87	v2k−1	v2k−1	INTJ
ejpam-4940	145	88	+2	+2	PRON
ejpam-4940	146	1	[	[	X
ejpam-4940	146	2	u1(a0u1	u1(a0u1	X
ejpam-4940	146	3	+	+	X
ejpam-4940	146	4	α)−	α)−	ADJ
ejpam-4940	146	5	p	p	NOUN
ejpam-4940	146	6	(	(	PUNCT
ejpam-4940	146	7	t)v1(a0v1	t)v1(a0v1	NOUN
ejpam-4940	146	8	+	+	CCONJ
ejpam-4940	146	9	β)]uk−1vk−1	β)]uk−1vk−1	NOUN
ejpam-4940	146	10	using	use	VERB
ejpam-4940	146	11	the	the	DET
ejpam-4940	146	12	above	above	ADJ
ejpam-4940	146	13	lemma	lemma	PROPN
ejpam-4940	146	14	,	,	PUNCT
ejpam-4940	146	15	we	we	PRON
ejpam-4940	146	16	have	have	VERB
ejpam-4940	146	17	(	(	PUNCT
ejpam-4940	146	18	p	p	X
ejpam-4940	146	19	(	(	PUNCT
ejpam-4940	146	20	t)(a0v1	t)(a0v1	NOUN
ejpam-4940	146	21	+	+	CCONJ
ejpam-4940	146	22	β)2	β)2	ADV
ejpam-4940	146	23	−	−	PROPN
ejpam-4940	146	24	(	(	PUNCT
ejpam-4940	146	25	a0u1	a0u1	PROPN
ejpam-4940	146	26	+	+	NUM
ejpam-4940	146	27	α)2	α)2	X
ejpam-4940	146	28	=	=	SYM
ejpam-4940	147	1	p	p	X
ejpam-4940	147	2	(	(	PUNCT
ejpam-4940	147	3	t)u21	t)u21	X
ejpam-4940	147	4	−	−	PROPN
ejpam-4940	147	5	p	p	X
ejpam-4940	147	6	(	(	PUNCT
ejpam-4940	147	7	t)2v21	t)2v21	PROPN
ejpam-4940	147	8	=	=	SYM
ejpam-4940	147	9	p	p	X
ejpam-4940	147	10	(	(	PUNCT
ejpam-4940	147	11	t)(u21	t)(u21	PROPN
ejpam-4940	147	12	−	−	PROPN
ejpam-4940	147	13	p	p	X
ejpam-4940	147	14	(	(	PUNCT
ejpam-4940	147	15	t)v21	t)v21	PROPN
ejpam-4940	147	16	)	)	PUNCT
ejpam-4940	148	1	=	=	SYM
ejpam-4940	148	2	p	p	X
ejpam-4940	148	3	(	(	PUNCT
ejpam-4940	148	4	t	t	PROPN
ejpam-4940	148	5	)	)	PUNCT
ejpam-4940	148	6	and	and	CCONJ
ejpam-4940	148	7	u1(a0u1	u1(a0u1	ADV
ejpam-4940	149	1	+	+	X
ejpam-4940	149	2	α)−	α)−	ADJ
ejpam-4940	149	3	p	p	NOUN
ejpam-4940	149	4	(	(	PUNCT
ejpam-4940	149	5	t)v1(a0v1	t)v1(a0v1	NOUN
ejpam-4940	149	6	+	+	CCONJ
ejpam-4940	149	7	β	β	X
ejpam-4940	149	8	)	)	PUNCT
ejpam-4940	149	9	=	=	SYM
ejpam-4940	150	1	0	0	X
ejpam-4940	150	2	.	.	PUNCT
ejpam-4940	151	1	hence	hence	ADV
ejpam-4940	151	2	,	,	PUNCT
ejpam-4940	151	3	we	we	PRON
ejpam-4940	151	4	conclude	conclude	VERB
ejpam-4940	151	5	that	that	SCONJ
ejpam-4940	151	6	u2k	u2k	VERB
ejpam-4940	151	7	−	−	PROPN
ejpam-4940	151	8	p	p	NOUN
ejpam-4940	151	9	(	(	PUNCT
ejpam-4940	151	10	t)v2k	t)v2k	NOUN
ejpam-4940	151	11	=	=	PUNCT
ejpam-4940	151	12	u2k−1	u2k−1	PROPN
ejpam-4940	151	13	−	−	PROPN
ejpam-4940	152	1	p	p	NOUN
ejpam-4940	153	1	(	(	PUNCT
ejpam-4940	153	2	t)v2k−1	t)v2k−1	NOUN
ejpam-4940	153	3	=	=	SYM
ejpam-4940	153	4	1	1	NUM
ejpam-4940	153	5	so	so	ADV
ejpam-4940	153	6	(	(	PUNCT
ejpam-4940	153	7	uk	uk	PROPN
ejpam-4940	153	8	,	,	PUNCT
ejpam-4940	153	9	vk	vk	NOUN
ejpam-4940	153	10	)	)	PUNCT
ejpam-4940	153	11	is	be	AUX
ejpam-4940	153	12	also	also	ADV
ejpam-4940	153	13	solution	solution	NOUN
ejpam-4940	153	14	of	of	ADP
ejpam-4940	153	15	ẽ.	ẽ.	PROPN
ejpam-4940	153	16	completing	complete	VERB
ejpam-4940	153	17	the	the	DET
ejpam-4940	153	18	proof	proof	NOUN
ejpam-4940	153	19	.	.	PUNCT
ejpam-4940	154	1	(	(	PUNCT
ejpam-4940	154	2	2	2	X
ejpam-4940	154	3	)	)	PUNCT
ejpam-4940	154	4	this	this	DET
ejpam-4940	154	5	assertion	assertion	NOUN
ejpam-4940	154	6	is	be	AUX
ejpam-4940	154	7	clear	clear	ADJ
ejpam-4940	154	8	by	by	ADP
ejpam-4940	154	9	the	the	DET
ejpam-4940	154	10	above	above	ADJ
ejpam-4940	154	11	.	.	PUNCT
ejpam-4940	155	1	as	as	SCONJ
ejpam-4940	155	2	we	we	PRON
ejpam-4940	155	3	reported	report	VERB
ejpam-4940	155	4	above	above	ADV
ejpam-4940	155	5	,	,	PUNCT
ejpam-4940	155	6	the	the	DET
ejpam-4940	155	7	diophantine	diophantine	NOUN
ejpam-4940	155	8	equation	equation	NOUN
ejpam-4940	155	9	e	e	NOUN
ejpam-4940	155	10	could	could	AUX
ejpam-4940	155	11	be	be	AUX
ejpam-4940	155	12	transformed	transform	VERB
ejpam-4940	155	13	into	into	ADP
ejpam-4940	155	14	the	the	DET
ejpam-4940	155	15	diophantine	diophantine	NOUN
ejpam-4940	155	16	equation	equation	NOUN
ejpam-4940	155	17	ẽ	ẽ	PROPN
ejpam-4940	155	18	via	via	ADP
ejpam-4940	155	19	the	the	DET
ejpam-4940	155	20	transformation	transformation	NOUN
ejpam-4940	155	21	t.	t.	PROPN
ejpam-4940	155	22	also	also	ADV
ejpam-4940	155	23	,	,	PUNCT
ejpam-4940	155	24	we	we	PRON
ejpam-4940	155	25	showed	show	VERB
ejpam-4940	155	26	that	that	SCONJ
ejpam-4940	155	27	x	x	NOUN
ejpam-4940	155	28	=	=	PUNCT
ejpam-4940	155	29	u	u	NOUN
ejpam-4940	155	30	+	+	X
ejpam-4940	155	31	p	p	NOUN
ejpam-4940	155	32	′(t	′(t	NOUN
ejpam-4940	155	33	)	)	PUNCT
ejpam-4940	155	34	and	and	CCONJ
ejpam-4940	155	35	y	y	PROPN
ejpam-4940	155	36	=	=	SYM
ejpam-4940	155	37	v	v	PROPN
ejpam-4940	155	38	+	+	NOUN
ejpam-4940	155	39	2	2	NUM
ejpam-4940	155	40	.	.	PUNCT
ejpam-4940	156	1	so	so	ADV
ejpam-4940	156	2	,	,	PUNCT
ejpam-4940	156	3	we	we	PRON
ejpam-4940	156	4	can	can	AUX
ejpam-4940	156	5	retransfer	retransfer	VERB
ejpam-4940	156	6	all	all	DET
ejpam-4940	156	7	results	result	NOUN
ejpam-4940	156	8	from	from	ADP
ejpam-4940	156	9	ẽ	ẽ	PROPN
ejpam-4940	156	10	to	to	ADP
ejpam-4940	156	11	e	e	NOUN
ejpam-4940	156	12	by	by	ADP
ejpam-4940	156	13	applying	apply	VERB
ejpam-4940	156	14	the	the	DET
ejpam-4940	156	15	inverse	inverse	NOUN
ejpam-4940	156	16	of	of	ADP
ejpam-4940	156	17	t.	t.	PROPN
ejpam-4940	156	18	thus	thus	ADV
ejpam-4940	156	19	,	,	PUNCT
ejpam-4940	156	20	we	we	PRON
ejpam-4940	156	21	can	can	AUX
ejpam-4940	156	22	give	give	VERB
ejpam-4940	156	23	the	the	DET
ejpam-4940	156	24	following	follow	VERB
ejpam-4940	156	25	main	main	ADJ
ejpam-4940	156	26	theorem	theorem	NOUN
ejpam-4940	156	27	theorem	theorem	NOUN
ejpam-4940	156	28	6	6	NUM
ejpam-4940	156	29	.	.	PUNCT
ejpam-4940	157	1	let	let	VERB
ejpam-4940	157	2	d	d	PRON
ejpam-4940	157	3	be	be	AUX
ejpam-4940	157	4	the	the	DET
ejpam-4940	157	5	diophantine	diophantine	NOUN
ejpam-4940	157	6	equation	equation	NOUN
ejpam-4940	157	7	in	in	ADP
ejpam-4940	157	8	(	(	PUNCT
ejpam-4940	157	9	1	1	NUM
ejpam-4940	157	10	)	)	PUNCT
ejpam-4940	157	11	.	.	PUNCT
ejpam-4940	158	1	then	then	ADV
ejpam-4940	158	2	(	(	PUNCT
ejpam-4940	158	3	1	1	X
ejpam-4940	158	4	)	)	PUNCT
ejpam-4940	158	5	the	the	DET
ejpam-4940	158	6	fundamental	fundamental	ADJ
ejpam-4940	158	7	(	(	PUNCT
ejpam-4940	158	8	minimal	minimal	ADJ
ejpam-4940	158	9	)	)	PUNCT
ejpam-4940	158	10	solution	solution	NOUN
ejpam-4940	158	11	of	of	ADP
ejpam-4940	158	12	e	e	PROPN
ejpam-4940	158	13	is	be	AUX
ejpam-4940	158	14	(	(	PUNCT
ejpam-4940	158	15	x1	x1	PROPN
ejpam-4940	158	16	,	,	PUNCT
ejpam-4940	158	17	y1	y1	NOUN
ejpam-4940	158	18	)	)	PUNCT
ejpam-4940	158	19	=	=	SYM
ejpam-4940	158	20	(	(	PUNCT
ejpam-4940	158	21	u1	u1	NOUN
ejpam-4940	158	22	+	+	CCONJ
ejpam-4940	158	23	p	p	NOUN
ejpam-4940	158	24	′(t	′(t	NOUN
ejpam-4940	158	25	)	)	PUNCT
ejpam-4940	158	26	,	,	PUNCT
ejpam-4940	158	27	v1	v1	VERB
ejpam-4940	158	28	+	+	CCONJ
ejpam-4940	158	29	2	2	NUM
ejpam-4940	158	30	)	)	PUNCT
ejpam-4940	158	31	a.	a.	NOUN
ejpam-4940	158	32	m.	m.	NOUN
ejpam-4940	158	33	sibih	sibih	PROPN
ejpam-4940	158	34	/	/	SYM
ejpam-4940	158	35	eur	eur	PROPN
ejpam-4940	158	36	.	.	PUNCT
ejpam-4940	159	1	j.	j.	PROPN
ejpam-4940	159	2	pure	pure	PROPN
ejpam-4940	159	3	appl	appl	PROPN
ejpam-4940	159	4	.	.	PROPN
ejpam-4940	159	5	math	math	PROPN
ejpam-4940	159	6	,	,	PUNCT
ejpam-4940	159	7	16	16	NUM
ejpam-4940	159	8	(	(	PUNCT
ejpam-4940	159	9	4	4	NUM
ejpam-4940	159	10	)	)	PUNCT
ejpam-4940	159	11	(	(	PUNCT
ejpam-4940	159	12	2023	2023	NUM
ejpam-4940	159	13	)	)	PUNCT
ejpam-4940	159	14	,	,	PUNCT
ejpam-4940	159	15	2693	2693	NUM
ejpam-4940	159	16	-	-	SYM
ejpam-4940	159	17	2702	2702	NUM
ejpam-4940	159	18	2700	2700	NUM
ejpam-4940	159	19	(	(	PUNCT
ejpam-4940	159	20	2	2	NUM
ejpam-4940	159	21	)	)	PUNCT
ejpam-4940	159	22	define	define	VERB
ejpam-4940	159	23	the	the	DET
ejpam-4940	159	24	sequence	sequence	NOUN
ejpam-4940	159	25	{	{	PUNCT
ejpam-4940	159	26	(	(	PUNCT
ejpam-4940	159	27	xn	xn	PROPN
ejpam-4940	159	28	,	,	PUNCT
ejpam-4940	159	29	yn)}n≥1	yn)}n≥1	NOUN
ejpam-4940	159	30	=	=	PRON
ejpam-4940	159	31	{	{	PUNCT
ejpam-4940	159	32	(	(	PUNCT
ejpam-4940	159	33	un	un	PROPN
ejpam-4940	159	34	+	+	CCONJ
ejpam-4940	159	35	p	p	NOUN
ejpam-4940	159	36	′(t	′(t	NOUN
ejpam-4940	159	37	)	)	PUNCT
ejpam-4940	159	38	,	,	PUNCT
ejpam-4940	159	39	vn	vn	X
ejpam-4940	159	40	+	+	NOUN
ejpam-4940	159	41	2	2	NUM
ejpam-4940	159	42	)	)	PUNCT
ejpam-4940	159	43	}	}	PUNCT
ejpam-4940	159	44	,	,	PUNCT
ejpam-4940	159	45	where	where	SCONJ
ejpam-4940	159	46	{	{	PUNCT
ejpam-4940	159	47	(	(	PUNCT
ejpam-4940	159	48	xn	xn	PROPN
ejpam-4940	159	49	,	,	PUNCT
ejpam-4940	159	50	yn	yn	PROPN
ejpam-4940	159	51	)	)	PUNCT
ejpam-4940	159	52	}	}	PUNCT
ejpam-4940	159	53	defined	define	VERB
ejpam-4940	159	54	in	in	ADP
ejpam-4940	159	55	(	(	PUNCT
ejpam-4940	159	56	3	3	NUM
ejpam-4940	159	57	)	)	PUNCT
ejpam-4940	159	58	.	.	PUNCT
ejpam-4940	160	1	then	then	ADV
ejpam-4940	160	2	(	(	PUNCT
ejpam-4940	160	3	xn	xn	PROPN
ejpam-4940	160	4	,	,	PUNCT
ejpam-4940	160	5	yn	yn	PROPN
ejpam-4940	160	6	)	)	PUNCT
ejpam-4940	160	7	is	be	AUX
ejpam-4940	160	8	a	a	DET
ejpam-4940	160	9	solution	solution	NOUN
ejpam-4940	160	10	of	of	ADP
ejpam-4940	160	11	e.	e.	PROPN
ejpam-4940	161	1	so	so	SCONJ
ejpam-4940	161	2	it	it	PRON
ejpam-4940	161	3	has	have	VERB
ejpam-4940	161	4	infinitely	infinitely	ADV
ejpam-4940	161	5	many	many	ADJ
ejpam-4940	161	6	integer	integer	NOUN
ejpam-4940	161	7	solutions	solution	NOUN
ejpam-4940	161	8	(	(	PUNCT
ejpam-4940	161	9	xn	xn	PROPN
ejpam-4940	161	10	,	,	PUNCT
ejpam-4940	161	11	yn	yn	NOUN
ejpam-4940	161	12	)	)	PUNCT
ejpam-4940	161	13	∈	∈	PROPN
ejpam-4940	161	14	z×	z×	NUM
ejpam-4940	161	15	z.	z.	X
ejpam-4940	161	16	(	(	PUNCT
ejpam-4940	161	17	3	3	X
ejpam-4940	161	18	)	)	PUNCT
ejpam-4940	161	19	the	the	DET
ejpam-4940	161	20	solutions	solution	NOUN
ejpam-4940	161	21	(	(	PUNCT
ejpam-4940	161	22	xn	xn	PROPN
ejpam-4940	161	23	,	,	PUNCT
ejpam-4940	161	24	yn	yn	NOUN
ejpam-4940	161	25	)	)	PUNCT
ejpam-4940	161	26	satisfy	satisfy	VERB
ejpam-4940	161	27	the	the	DET
ejpam-4940	161	28	recurrence	recurrence	NOUN
ejpam-4940	161	29	relations	relations	PUNCT
ejpam-4940	161	30	xk	xk	PROPN
ejpam-4940	161	31	=	=	SYM
ejpam-4940	161	32	u1xk−1	u1xk−1	PROPN
ejpam-4940	162	1	+	+	CCONJ
ejpam-4940	162	2	(	(	PUNCT
ejpam-4940	162	3	a0u1	a0u1	PROPN
ejpam-4940	162	4	+	+	NUM
ejpam-4940	162	5	α)yn−1	α)yn−1	ADJ
ejpam-4940	162	6	−	−	PROPN
ejpam-4940	162	7	u1(2a0	u1(2a0	PRON
ejpam-4940	162	8	+	+	X
ejpam-4940	163	1	p	p	X
ejpam-4940	163	2	′(t))−	′(t))−	VERB
ejpam-4940	163	3	2α+	2α+	NUM
ejpam-4940	163	4	p	p	NOUN
ejpam-4940	163	5	′(t	′(t	NOUN
ejpam-4940	163	6	)	)	PUNCT
ejpam-4940	163	7	,	,	PUNCT
ejpam-4940	163	8	if	if	SCONJ
ejpam-4940	163	9	l	l	NOUN
ejpam-4940	163	10	is	be	AUX
ejpam-4940	163	11	even	even	ADV
ejpam-4940	163	12	yk	yk	NOUN
ejpam-4940	163	13	=	=	PUNCT
ejpam-4940	163	14	v1xk−1	v1xk−1	X
ejpam-4940	163	15	+	+	CCONJ
ejpam-4940	163	16	(	(	PUNCT
ejpam-4940	163	17	a0v1	a0v1	NOUN
ejpam-4940	163	18	+	+	CCONJ
ejpam-4940	163	19	β)yn−1	β)yn−1	PROPN
ejpam-4940	163	20	−	−	PROPN
ejpam-4940	163	21	v1(2a0	v1(2a0	NOUN
ejpam-4940	164	1	+	+	CCONJ
ejpam-4940	164	2	p	p	X
ejpam-4940	164	3	′(t))−	′(t))−	ADJ
ejpam-4940	164	4	2β	2β	NOUN
ejpam-4940	164	5	+	+	CCONJ
ejpam-4940	164	6	2	2	NUM
ejpam-4940	164	7	for	for	ADP
ejpam-4940	164	8	k	k	PROPN
ejpam-4940	164	9	≥	≥	NUM
ejpam-4940	164	10	2,and	2,and	NUM
ejpam-4940	164	11	xk	xk	X
ejpam-4940	164	12	=	=	PUNCT
ejpam-4940	164	13	u1xk−1	u1xk−1	PROPN
ejpam-4940	164	14	+	+	CCONJ
ejpam-4940	164	15	(	(	PUNCT
ejpam-4940	164	16	a0u1	a0u1	X
ejpam-4940	164	17	+	+	PUNCT
ejpam-4940	164	18	η)yn−1	η)yn−1	ADJ
ejpam-4940	164	19	−	−	PUNCT
ejpam-4940	164	20	u1(2a0	u1(2a0	PRON
ejpam-4940	165	1	+	+	X
ejpam-4940	165	2	p	p	X
ejpam-4940	165	3	′(t))−	′(t))−	X
ejpam-4940	165	4	2η	2η	NOUN
ejpam-4940	166	1	+	+	CCONJ
ejpam-4940	166	2	p	p	NOUN
ejpam-4940	166	3	′(t	′(t	NOUN
ejpam-4940	166	4	)	)	PUNCT
ejpam-4940	166	5	,	,	PUNCT
ejpam-4940	166	6	if	if	SCONJ
ejpam-4940	166	7	l	l	NOUN
ejpam-4940	166	8	is	be	AUX
ejpam-4940	166	9	odd	odd	ADJ
ejpam-4940	166	10	yk	yk	NOUN
ejpam-4940	166	11	=	=	PUNCT
ejpam-4940	166	12	v1xk−1	v1xk−1	PROPN
ejpam-4940	166	13	+	+	CCONJ
ejpam-4940	166	14	(	(	PUNCT
ejpam-4940	166	15	a0v1	a0v1	ADP
ejpam-4940	167	1	+	+	CCONJ
ejpam-4940	167	2	δ)yn−1	δ)yn−1	PROPN
ejpam-4940	167	3	−	−	PROPN
ejpam-4940	167	4	v1(2a0	v1(2a0	PROPN
ejpam-4940	167	5	+	+	CCONJ
ejpam-4940	167	6	p	p	X
ejpam-4940	167	7	′(t))−	′(t))−	ADJ
ejpam-4940	167	8	2δ	2δ	NOUN
ejpam-4940	167	9	+	+	CCONJ
ejpam-4940	167	10	2	2	NUM
ejpam-4940	167	11	for	for	ADP
ejpam-4940	167	12	k	k	PROPN
ejpam-4940	167	13	≥	≥	NUM
ejpam-4940	167	14	2	2	NUM
ejpam-4940	167	15	.	.	PUNCT
ejpam-4940	168	1	as	as	ADP
ejpam-4940	168	2	an	an	DET
ejpam-4940	168	3	application	application	NOUN
ejpam-4940	168	4	,	,	PUNCT
ejpam-4940	168	5	we	we	PRON
ejpam-4940	168	6	can	can	AUX
ejpam-4940	168	7	give	give	VERB
ejpam-4940	168	8	the	the	DET
ejpam-4940	168	9	following	follow	VERB
ejpam-4940	168	10	examples	example	NOUN
ejpam-4940	168	11	:	:	PUNCT
ejpam-4940	168	12	example	example	NOUN
ejpam-4940	169	1	1	1	X
ejpam-4940	169	2	.	.	PUNCT
ejpam-4940	170	1	let	let	VERB
ejpam-4940	170	2	p	p	PROPN
ejpam-4940	170	3	(	(	PUNCT
ejpam-4940	170	4	t	t	PROPN
ejpam-4940	170	5	)	)	PUNCT
ejpam-4940	170	6	=	=	SYM
ejpam-4940	171	1	t4	t4	PROPN
ejpam-4940	171	2	+	+	NUM
ejpam-4940	171	3	4t3	4t3	NUM
ejpam-4940	171	4	+	+	CCONJ
ejpam-4940	171	5	6t2	6t2	NUM
ejpam-4940	171	6	+	+	CCONJ
ejpam-4940	171	7	4t+	4t+	NUM
ejpam-4940	171	8	2	2	NUM
ejpam-4940	171	9	,	,	PUNCT
ejpam-4940	171	10	then√	then√	NOUN
ejpam-4940	171	11	p	p	PROPN
ejpam-4940	171	12	(	(	PUNCT
ejpam-4940	171	13	t	t	PROPN
ejpam-4940	171	14	)	)	PUNCT
ejpam-4940	171	15	=	=	PUNCT
ejpam-4940	172	1	[	[	PUNCT
ejpam-4940	172	2	t2	t2	NOUN
ejpam-4940	172	3	+	+	CCONJ
ejpam-4940	172	4	2t+	2t+	NUM
ejpam-4940	172	5	1	1	NUM
ejpam-4940	172	6	;	;	PUNCT
ejpam-4940	172	7	2t2	2t2	NUM
ejpam-4940	172	8	+	+	CCONJ
ejpam-4940	172	9	4t+	4t+	NUM
ejpam-4940	172	10	2	2	NUM
ejpam-4940	172	11	]	]	PUNCT
ejpam-4940	172	12	.	.	PUNCT
ejpam-4940	173	1	so	so	ADV
ejpam-4940	173	2	,	,	PUNCT
ejpam-4940	173	3	(	(	PUNCT
ejpam-4940	173	4	u1	u1	NOUN
ejpam-4940	173	5	,	,	PUNCT
ejpam-4940	173	6	v1	v1	NOUN
ejpam-4940	173	7	)	)	PUNCT
ejpam-4940	173	8	=	=	SYM
ejpam-4940	174	1	(	(	PUNCT
ejpam-4940	174	2	2t4	2t4	NUM
ejpam-4940	174	3	+	+	SYM
ejpam-4940	174	4	8t3	8t3	NUM
ejpam-4940	175	1	+	+	SYM
ejpam-4940	175	2	4t2	4t2	NUM
ejpam-4940	176	1	+	+	CCONJ
ejpam-4940	176	2	3	3	NUM
ejpam-4940	176	3	,	,	PUNCT
ejpam-4940	176	4	2t2	2t2	NUM
ejpam-4940	177	1	+	+	CCONJ
ejpam-4940	177	2	4t+	4t+	NUM
ejpam-4940	177	3	2	2	NUM
ejpam-4940	177	4	)	)	PUNCT
ejpam-4940	177	5	is	be	AUX
ejpam-4940	177	6	the	the	DET
ejpam-4940	177	7	fundamental	fundamental	ADJ
ejpam-4940	177	8	solution	solution	NOUN
ejpam-4940	177	9	of	of	ADP
ejpam-4940	177	10	ẽ1	ẽ1	NOUN
ejpam-4940	177	11	:	:	PUNCT
ejpam-4940	177	12	u2	u2	PROPN
ejpam-4940	177	13	−	−	PROPN
ejpam-4940	177	14	(	(	PUNCT
ejpam-4940	177	15	t4	t4	PROPN
ejpam-4940	177	16	+	+	PROPN
ejpam-4940	177	17	4t3	4t3	NUM
ejpam-4940	178	1	+	+	CCONJ
ejpam-4940	178	2	2t2	2t2	NUM
ejpam-4940	179	1	+	+	CCONJ
ejpam-4940	179	2	2)v2	2)v2	NUM
ejpam-4940	179	3	=	=	SYM
ejpam-4940	179	4	1	1	NUM
ejpam-4940	179	5	and	and	CCONJ
ejpam-4940	179	6	the	the	DET
ejpam-4940	179	7	other	other	ADJ
ejpam-4940	179	8	solutions	solution	NOUN
ejpam-4940	179	9	are	be	AUX
ejpam-4940	179	10	given	give	VERB
ejpam-4940	179	11	by	by	ADP
ejpam-4940	179	12			PROPN
ejpam-4940	179	13	uk	uk	PROPN
ejpam-4940	179	14	=	=	SYM
ejpam-4940	179	15	(	(	PUNCT
ejpam-4940	179	16	2t4	2t4	NUM
ejpam-4940	179	17	+	+	SYM
ejpam-4940	179	18	8t3	8t3	NUM
ejpam-4940	180	1	+	+	SYM
ejpam-4940	180	2	4t2	4t2	NUM
ejpam-4940	181	1	+	+	CCONJ
ejpam-4940	181	2	3)uk−1	3)uk−1	NUM
ejpam-4940	181	3	+	+	CCONJ
ejpam-4940	181	4	(	(	PUNCT
ejpam-4940	181	5	2t6	2t6	NUM
ejpam-4940	181	6	+	+	SYM
ejpam-4940	181	7	12t5	12t5	NUM
ejpam-4940	182	1	+	+	SYM
ejpam-4940	182	2	30t4	30t4	NUM
ejpam-4940	182	3	+	+	CCONJ
ejpam-4940	182	4	40t3	40t3	NUM
ejpam-4940	183	1	+	+	NUM
ejpam-4940	183	2	32t2	32t2	NUM
ejpam-4940	183	3	+	+	CCONJ
ejpam-4940	183	4	16t+	16t+	NUM
ejpam-4940	183	5	4)vk−1	4)vk−1	NUM
ejpam-4940	183	6	vk	vk	NOUN
ejpam-4940	183	7	=	=	SYM
ejpam-4940	183	8	(	(	PUNCT
ejpam-4940	183	9	2t2	2t2	NUM
ejpam-4940	183	10	+	+	CCONJ
ejpam-4940	183	11	4t+	4t+	NUM
ejpam-4940	183	12	2)uk−1	2)uk−1	NUM
ejpam-4940	184	1	+	+	CCONJ
ejpam-4940	184	2	(	(	PUNCT
ejpam-4940	184	3	2t4	2t4	NUM
ejpam-4940	184	4	+	+	SYM
ejpam-4940	184	5	8t3	8t3	NUM
ejpam-4940	185	1	+	+	SYM
ejpam-4940	185	2	4t2	4t2	NUM
ejpam-4940	186	1	+	+	CCONJ
ejpam-4940	186	2	3)vk−1	3)vk−1	NUM
ejpam-4940	186	3	for	for	ADP
ejpam-4940	186	4	k	k	PROPN
ejpam-4940	186	5	≥	≥	PROPN
ejpam-4940	186	6	2	2	NUM
ejpam-4940	186	7	.	.	PUNCT
ejpam-4940	187	1	morover	morover	PROPN
ejpam-4940	187	2	,	,	PUNCT
ejpam-4940	187	3	let	let	VERB
ejpam-4940	187	4	n	n	PRON
ejpam-4940	187	5	=	=	PROPN
ejpam-4940	187	6	t2	t2	PROPN
ejpam-4940	187	7	+	+	CCONJ
ejpam-4940	187	8	2t+	2t+	NUM
ejpam-4940	187	9	1	1	NUM
ejpam-4940	187	10	,	,	PUNCT
ejpam-4940	187	11	then	then	ADV
ejpam-4940	187	12	p	p	X
ejpam-4940	187	13	(	(	PUNCT
ejpam-4940	187	14	t	t	NOUN
ejpam-4940	187	15	)	)	PUNCT
ejpam-4940	187	16	become	become	VERB
ejpam-4940	187	17	d(n	d(n	NOUN
ejpam-4940	187	18	)	)	PUNCT
ejpam-4940	187	19	=	=	SYM
ejpam-4940	187	20	n2	n2	NOUN
ejpam-4940	187	21	+	+	CCONJ
ejpam-4940	187	22	1	1	X
ejpam-4940	187	23	.	.	X
ejpam-4940	187	24	then√	then√	PROPN
ejpam-4940	187	25	d(n	d(n	PROPN
ejpam-4940	187	26	)	)	PUNCT
ejpam-4940	187	27	=	=	SYM
ejpam-4940	187	28	[	[	PUNCT
ejpam-4940	187	29	n	n	CCONJ
ejpam-4940	187	30	;	;	PUNCT
ejpam-4940	187	31	2n	2n	NUM
ejpam-4940	187	32	]	]	PUNCT
ejpam-4940	187	33	.	.	PUNCT
ejpam-4940	188	1	so	so	ADV
ejpam-4940	188	2	,	,	PUNCT
ejpam-4940	188	3	(	(	PUNCT
ejpam-4940	188	4	u1	u1	NOUN
ejpam-4940	188	5	,	,	PUNCT
ejpam-4940	188	6	v1	v1	NOUN
ejpam-4940	188	7	)	)	PUNCT
ejpam-4940	188	8	=	=	PUNCT
ejpam-4940	189	1	(	(	PUNCT
ejpam-4940	189	2	2n2	2n2	NUM
ejpam-4940	189	3	+	+	CCONJ
ejpam-4940	189	4	1	1	NUM
ejpam-4940	189	5	,	,	PUNCT
ejpam-4940	189	6	2n	2n	NUM
ejpam-4940	189	7	)	)	PUNCT
ejpam-4940	189	8	is	be	AUX
ejpam-4940	189	9	the	the	DET
ejpam-4940	189	10	fundamental	fundamental	ADJ
ejpam-4940	189	11	solution	solution	NOUN
ejpam-4940	189	12	of	of	ADP
ejpam-4940	189	13	ẽ1	ẽ1	NOUN
ejpam-4940	189	14	:	:	PUNCT
ejpam-4940	189	15	u2	u2	PROPN
ejpam-4940	189	16	−	−	PROPN
ejpam-4940	189	17	(	(	PUNCT
ejpam-4940	189	18	n2	n2	NOUN
ejpam-4940	189	19	+	+	X
ejpam-4940	189	20	1)v2	1)v2	NUM
ejpam-4940	189	21	=	=	SYM
ejpam-4940	189	22	1	1	NUM
ejpam-4940	189	23	and	and	CCONJ
ejpam-4940	189	24	the	the	DET
ejpam-4940	189	25	other	other	ADJ
ejpam-4940	189	26	solutions	solution	NOUN
ejpam-4940	189	27	are	be	AUX
ejpam-4940	189	28	given	give	VERB
ejpam-4940	189	29	by	by	ADP
ejpam-4940	189	30	a.	a.	NOUN
ejpam-4940	189	31	m.	m.	NOUN
ejpam-4940	189	32	sibih	sibih	PROPN
ejpam-4940	189	33	/	/	SYM
ejpam-4940	189	34	eur	eur	PROPN
ejpam-4940	189	35	.	.	PUNCT
ejpam-4940	190	1	j.	j.	PROPN
ejpam-4940	190	2	pure	pure	PROPN
ejpam-4940	190	3	appl	appl	PROPN
ejpam-4940	190	4	.	.	PROPN
ejpam-4940	190	5	math	math	PROPN
ejpam-4940	190	6	,	,	PUNCT
ejpam-4940	190	7	16	16	NUM
ejpam-4940	190	8	(	(	PUNCT
ejpam-4940	190	9	4	4	NUM
ejpam-4940	190	10	)	)	PUNCT
ejpam-4940	190	11	(	(	PUNCT
ejpam-4940	190	12	2023	2023	NUM
ejpam-4940	190	13	)	)	PUNCT
ejpam-4940	190	14	,	,	PUNCT
ejpam-4940	190	15	2693	2693	NUM
ejpam-4940	190	16	-	-	SYM
ejpam-4940	190	17	2702	2702	NUM
ejpam-4940	190	18	2701	2701	NUM
ejpam-4940	190	19			PUNCT
ejpam-4940	190	20	uk	uk	PROPN
ejpam-4940	190	21	=	=	PUNCT
ejpam-4940	190	22	(	(	PUNCT
ejpam-4940	190	23	2n2	2n2	NUM
ejpam-4940	190	24	+	+	CCONJ
ejpam-4940	190	25	1)uk−1	1)uk−1	NUM
ejpam-4940	190	26	+	+	CCONJ
ejpam-4940	190	27	(	(	PUNCT
ejpam-4940	190	28	2n3	2n3	NUM
ejpam-4940	190	29	+	+	CCONJ
ejpam-4940	190	30	2n)vk−1	2n)vk−1	PRON
ejpam-4940	190	31	vk	vk	ADJ
ejpam-4940	190	32	=	=	SYM
ejpam-4940	190	33	2nuk−1	2nuk−1	NUM
ejpam-4940	190	34	+	+	CCONJ
ejpam-4940	190	35	(	(	PUNCT
ejpam-4940	190	36	2n2	2n2	NUM
ejpam-4940	190	37	+	+	CCONJ
ejpam-4940	190	38	1)vk−1	1)vk−1	NUM
ejpam-4940	190	39	for	for	ADP
ejpam-4940	190	40	k	k	PROPN
ejpam-4940	190	41	≥	≥	NUM
ejpam-4940	190	42	2	2	NUM
ejpam-4940	190	43	.	.	PUNCT
ejpam-4940	191	1	then	then	ADV
ejpam-4940	191	2	the	the	DET
ejpam-4940	191	3	fundamental	fundamental	ADJ
ejpam-4940	191	4	solution	solution	NOUN
ejpam-4940	191	5	of	of	ADP
ejpam-4940	191	6	e1	e1	PROPN
ejpam-4940	191	7	:	:	PUNCT
ejpam-4940	191	8	x2	x2	PROPN
ejpam-4940	191	9	−	−	PROPN
ejpam-4940	191	10	(	(	PUNCT
ejpam-4940	191	11	n2	n2	NOUN
ejpam-4940	191	12	+	+	CCONJ
ejpam-4940	191	13	1)y2	1)y2	NUM
ejpam-4940	191	14	−	−	NOUN
ejpam-4940	191	15	4nx+	4nx+	NUM
ejpam-4940	191	16	(	(	PUNCT
ejpam-4940	191	17	4n2	4n2	NUM
ejpam-4940	192	1	+	+	CCONJ
ejpam-4940	193	1	4)y	4)y	NUM
ejpam-4940	193	2	−	−	NOUN
ejpam-4940	193	3	2	2	NUM
ejpam-4940	193	4	=	=	SYM
ejpam-4940	193	5	0	0	NUM
ejpam-4940	193	6	is	be	AUX
ejpam-4940	193	7	(	(	PUNCT
ejpam-4940	193	8	x1	x1	PROPN
ejpam-4940	193	9	,	,	PUNCT
ejpam-4940	193	10	y1	y1	NOUN
ejpam-4940	193	11	)	)	PUNCT
ejpam-4940	193	12	=	=	PUNCT
ejpam-4940	193	13	(	(	PUNCT
ejpam-4940	193	14	2n2	2n2	NUM
ejpam-4940	193	15	+	+	CCONJ
ejpam-4940	193	16	2n+	2n+	NUM
ejpam-4940	193	17	1	1	NUM
ejpam-4940	193	18	,	,	PUNCT
ejpam-4940	193	19	2n+	2n+	NUM
ejpam-4940	193	20	2	2	NUM
ejpam-4940	193	21	)	)	PUNCT
ejpam-4940	193	22	and	and	CCONJ
ejpam-4940	193	23	the	the	DET
ejpam-4940	193	24	other	other	ADJ
ejpam-4940	193	25	solutions	solution	NOUN
ejpam-4940	193	26	are	be	AUX
ejpam-4940	193	27	given	give	VERB
ejpam-4940	193	28	,	,	PUNCT
ejpam-4940	193	29	for	for	ADP
ejpam-4940	193	30	k	k	PROPN
ejpam-4940	193	31	≥	≥	NUM
ejpam-4940	193	32	2	2	NUM
ejpam-4940	193	33	,	,	PUNCT
ejpam-4940	193	34	by	by	NOUN
ejpam-4940	193	35	xk	xk	PROPN
ejpam-4940	193	36	=	=	X
ejpam-4940	193	37	(	(	PUNCT
ejpam-4940	193	38	2n2	2n2	NUM
ejpam-4940	193	39	+	+	CCONJ
ejpam-4940	193	40	1)xk−1	1)xk−1	NUM
ejpam-4940	193	41	+	+	CCONJ
ejpam-4940	193	42	(	(	PUNCT
ejpam-4940	193	43	2n3	2n3	NUM
ejpam-4940	194	1	+	+	CCONJ
ejpam-4940	194	2	2n)yk−1	2n)yk−1	NUM
ejpam-4940	194	3	−	−	PROPN
ejpam-4940	194	4	8n3	8n3	NOUN
ejpam-4940	194	5	−	−	ADP
ejpam-4940	194	6	4n	4n	PROPN
ejpam-4940	194	7	yk	yk	NOUN
ejpam-4940	194	8	=	=	PUNCT
ejpam-4940	194	9	2nxk−1	2nxk−1	PROPN
ejpam-4940	194	10	+	+	CCONJ
ejpam-4940	194	11	(	(	PUNCT
ejpam-4940	194	12	2n2	2n2	NUM
ejpam-4940	194	13	+	+	CCONJ
ejpam-4940	194	14	1)yk−1	1)yk−1	NUM
ejpam-4940	194	15	−	−	NOUN
ejpam-4940	194	16	8n2	8n2	NUM
ejpam-4940	195	1	+	+	CCONJ
ejpam-4940	195	2	2n−	2n−	NUM
ejpam-4940	195	3	2	2	NUM
ejpam-4940	195	4	.	.	PUNCT
ejpam-4940	195	5	further	far	ADV
ejpam-4940	195	6	,	,	PUNCT
ejpam-4940	195	7	for	for	ADP
ejpam-4940	195	8	t	t	NOUN
ejpam-4940	195	9	=	=	SYM
ejpam-4940	195	10	1	1	NUM
ejpam-4940	195	11	,	,	PUNCT
ejpam-4940	195	12	p	p	X
ejpam-4940	195	13	(	(	PUNCT
ejpam-4940	195	14	t	t	NOUN
ejpam-4940	195	15	)	)	PUNCT
ejpam-4940	195	16	=	=	SYM
ejpam-4940	196	1	17	17	NUM
ejpam-4940	196	2	.	.	PUNCT
ejpam-4940	197	1	then	then	ADV
ejpam-4940	197	2	√	√	VERB
ejpam-4940	197	3	p	p	PROPN
ejpam-4940	197	4	(	(	PUNCT
ejpam-4940	197	5	t	t	NOUN
ejpam-4940	197	6	)	)	PUNCT
ejpam-4940	197	7	=	=	PUNCT
ejpam-4940	198	1	[	[	PUNCT
ejpam-4940	198	2	4	4	NUM
ejpam-4940	198	3	;	;	PUNCT
ejpam-4940	198	4	8	8	NUM
ejpam-4940	198	5	]	]	PUNCT
ejpam-4940	198	6	.	.	PUNCT
ejpam-4940	199	1	so	so	ADV
ejpam-4940	199	2	,	,	PUNCT
ejpam-4940	199	3	(	(	PUNCT
ejpam-4940	199	4	u1	u1	NOUN
ejpam-4940	199	5	,	,	PUNCT
ejpam-4940	199	6	v1	v1	NOUN
ejpam-4940	199	7	)	)	PUNCT
ejpam-4940	200	1	=	=	PUNCT
ejpam-4940	200	2	(	(	PUNCT
ejpam-4940	200	3	33	33	NUM
ejpam-4940	200	4	,	,	PUNCT
ejpam-4940	200	5	8)	8)	NUM
ejpam-4940	200	6	is	be	AUX
ejpam-4940	200	7	the	the	DET
ejpam-4940	200	8	fundamental	fundamental	ADJ
ejpam-4940	200	9	solution	solution	NOUN
ejpam-4940	200	10	of	of	ADP
ejpam-4940	200	11	ẽ1	ẽ1	NOUN
ejpam-4940	200	12	:	:	PUNCT
ejpam-4940	200	13	u2	u2	PROPN
ejpam-4940	200	14	−	−	PROPN
ejpam-4940	200	15	17v2	17v2	NUM
ejpam-4940	200	16	=	=	SYM
ejpam-4940	200	17	1	1	NUM
ejpam-4940	200	18	and	and	CCONJ
ejpam-4940	200	19	the	the	DET
ejpam-4940	200	20	other	other	ADJ
ejpam-4940	200	21	solutions	solution	NOUN
ejpam-4940	200	22	are	be	AUX
ejpam-4940	200	23	given	give	VERB
ejpam-4940	200	24	by	by	NOUN
ejpam-4940	200	25	uk	uk	PROPN
ejpam-4940	200	26	=	=	SYM
ejpam-4940	200	27	33uk−1	33uk−1	NUM
ejpam-4940	200	28	+	+	NUM
ejpam-4940	200	29	136vk−1	136vk−1	NUM
ejpam-4940	200	30	vk	vk	NOUN
ejpam-4940	200	31	=	=	VERB
ejpam-4940	200	32	8uk−1	8uk−1	NOUN
ejpam-4940	200	33	+	+	CCONJ
ejpam-4940	200	34	33vk−1	33vk−1	NUM
ejpam-4940	200	35	for	for	ADP
ejpam-4940	200	36	k	k	PROPN
ejpam-4940	200	37	≥	≥	NUM
ejpam-4940	200	38	2	2	NUM
ejpam-4940	200	39	.	.	PUNCT
ejpam-4940	201	1	then	then	ADV
ejpam-4940	201	2	the	the	DET
ejpam-4940	201	3	fundamental	fundamental	ADJ
ejpam-4940	201	4	solution	solution	NOUN
ejpam-4940	201	5	of	of	ADP
ejpam-4940	201	6	e1	e1	PROPN
ejpam-4940	201	7	:	:	PUNCT
ejpam-4940	201	8	x2	x2	PROPN
ejpam-4940	202	1	−	−	PROPN
ejpam-4940	203	1	17y2	17y2	NUM
ejpam-4940	203	2	−	−	NOUN
ejpam-4940	203	3	64x+	64x+	NUM
ejpam-4940	203	4	68y	68y	NUM
ejpam-4940	203	5	+	+	CCONJ
ejpam-4940	203	6	955	955	NUM
ejpam-4940	203	7	=	=	SYM
ejpam-4940	203	8	0	0	NUM
ejpam-4940	203	9	is	be	AUX
ejpam-4940	203	10	(	(	PUNCT
ejpam-4940	203	11	x1	x1	PROPN
ejpam-4940	203	12	,	,	PUNCT
ejpam-4940	203	13	y1	y1	NOUN
ejpam-4940	203	14	)	)	PUNCT
ejpam-4940	203	15	=	=	SYM
ejpam-4940	203	16	(	(	PUNCT
ejpam-4940	203	17	65	65	NUM
ejpam-4940	203	18	,	,	PUNCT
ejpam-4940	203	19	10	10	NUM
ejpam-4940	203	20	)	)	PUNCT
ejpam-4940	203	21	and	and	CCONJ
ejpam-4940	203	22	the	the	DET
ejpam-4940	203	23	other	other	ADJ
ejpam-4940	203	24	solutions	solution	NOUN
ejpam-4940	203	25	are	be	AUX
ejpam-4940	203	26	given	give	VERB
ejpam-4940	203	27	,	,	PUNCT
ejpam-4940	203	28	for	for	ADP
ejpam-4940	203	29	k	k	PROPN
ejpam-4940	203	30	≥	≥	NUM
ejpam-4940	203	31	2	2	NUM
ejpam-4940	203	32	,	,	PUNCT
ejpam-4940	203	33	by	by	NOUN
ejpam-4940	203	34	xk	xk	PROPN
ejpam-4940	203	35	=	=	PUNCT
ejpam-4940	203	36	33xk−1	33xk−1	NUM
ejpam-4940	203	37	+	+	NUM
ejpam-4940	203	38	136yk−1	136yk−1	NUM
ejpam-4940	203	39	−	−	PROPN
ejpam-4940	203	40	1296	1296	NUM
ejpam-4940	203	41	yk	yk	PROPN
ejpam-4940	203	42	=	=	PUNCT
ejpam-4940	203	43	8xk−1	8xk−1	PROPN
ejpam-4940	203	44	+	+	NUM
ejpam-4940	203	45	33yk−1	33yk−1	NUM
ejpam-4940	203	46	−	−	PROPN
ejpam-4940	203	47	320	320	NUM
ejpam-4940	203	48	.	.	PUNCT
ejpam-4940	203	49	example	example	NOUN
ejpam-4940	204	1	2	2	NUM
ejpam-4940	204	2	.	.	PUNCT
ejpam-4940	204	3	in	in	ADP
ejpam-4940	204	4	this	this	DET
ejpam-4940	204	5	example	example	NOUN
ejpam-4940	204	6	,	,	PUNCT
ejpam-4940	204	7	we	we	PRON
ejpam-4940	204	8	consider	consider	VERB
ejpam-4940	204	9	the	the	DET
ejpam-4940	204	10	number	number	NOUN
ejpam-4940	204	11	of	of	ADP
ejpam-4940	204	12	integer	integer	NOUN
ejpam-4940	204	13	solutions	solution	NOUN
ejpam-4940	204	14	of	of	ADP
ejpam-4940	204	15	the	the	DET
ejpam-4940	204	16	diophantine	diophantine	NOUN
ejpam-4940	204	17	equation	equation	NOUN
ejpam-4940	204	18	e	e	NOUN
ejpam-4940	204	19	:	:	PUNCT
ejpam-4940	205	1	x2	x2	INTJ
ejpam-4940	205	2	−	−	PROPN
ejpam-4940	205	3	(	(	PUNCT
ejpam-4940	205	4	t2	t2	NOUN
ejpam-4940	205	5	+	+	CCONJ
ejpam-4940	205	6	t)y2	t)y2	PROPN
ejpam-4940	205	7	−	−	NOUN
ejpam-4940	205	8	(	(	PUNCT
ejpam-4940	205	9	4t+	4t+	NUM
ejpam-4940	205	10	2)x+	2)x+	NUM
ejpam-4940	205	11	(	(	PUNCT
ejpam-4940	205	12	4t2	4t2	NOUN
ejpam-4940	206	1	+	+	CCONJ
ejpam-4940	206	2	4t)y	4t)y	NUM
ejpam-4940	206	3	=	=	SYM
ejpam-4940	206	4	0	0	NUM
ejpam-4940	207	1	we	we	PRON
ejpam-4940	207	2	have	have	VERB
ejpam-4940	207	3	p	p	PROPN
ejpam-4940	207	4	(	(	PUNCT
ejpam-4940	207	5	t	t	NOUN
ejpam-4940	207	6	)	)	PUNCT
ejpam-4940	207	7	=	=	SYM
ejpam-4940	207	8	t2	t2	PROPN
ejpam-4940	207	9	+	+	X
ejpam-4940	207	10	t	t	PROPN
ejpam-4940	207	11	,	,	PUNCT
ejpam-4940	207	12	thus	thus	ADV
ejpam-4940	207	13	p	p	NOUN
ejpam-4940	207	14	′(t	′(t	NOUN
ejpam-4940	207	15	)	)	PUNCT
ejpam-4940	207	16	=	=	PUNCT
ejpam-4940	208	1	2t+1	2t+1	PROPN
ejpam-4940	208	2	and	and	CCONJ
ejpam-4940	208	3	the	the	DET
ejpam-4940	208	4	continued	continue	VERB
ejpam-4940	208	5	fraction	fraction	NOUN
ejpam-4940	208	6	expansion	expansion	NOUN
ejpam-4940	208	7	of	of	ADP
ejpam-4940	208	8	√	√	PROPN
ejpam-4940	208	9	p	p	PROPN
ejpam-4940	208	10	(	(	PUNCT
ejpam-4940	208	11	t	t	PROPN
ejpam-4940	208	12	)	)	PUNCT
ejpam-4940	208	13	is	be	AUX
ejpam-4940	208	14	references	reference	NOUN
ejpam-4940	208	15	2702	2702	NUM
ejpam-4940	208	16	√	√	PROPN
ejpam-4940	208	17	p	p	PROPN
ejpam-4940	208	18	(	(	PUNCT
ejpam-4940	208	19	t	t	NOUN
ejpam-4940	208	20	)	)	PUNCT
ejpam-4940	208	21	=	=	PROPN
ejpam-4940	209	1	[	[	PUNCT
ejpam-4940	209	2	t	t	PROPN
ejpam-4940	209	3	;	;	PUNCT
ejpam-4940	209	4	2	2	NUM
ejpam-4940	209	5	,	,	PUNCT
ejpam-4940	209	6	2	2	NUM
ejpam-4940	209	7	t	t	NOUN
ejpam-4940	209	8	]	]	PUNCT
ejpam-4940	209	9	which	which	PRON
ejpam-4940	209	10	yields	yield	VERB
ejpam-4940	209	11	,	,	PUNCT
ejpam-4940	209	12	u1	u1	NOUN
ejpam-4940	209	13	v1	v1	NOUN
ejpam-4940	209	14	=	=	PUNCT
ejpam-4940	210	1	[	[	X
ejpam-4940	210	2	t	t	X
ejpam-4940	210	3	;	;	PUNCT
ejpam-4940	210	4	2	2	NUM
ejpam-4940	210	5	]	]	PUNCT
ejpam-4940	210	6	=	=	SYM
ejpam-4940	210	7	2t+	2t+	NUM
ejpam-4940	210	8	1	1	NUM
ejpam-4940	210	9	2	2	NUM
ejpam-4940	210	10	.	.	PUNCT
ejpam-4940	211	1	then	then	ADV
ejpam-4940	211	2	the	the	DET
ejpam-4940	211	3	fundamental	fundamental	ADJ
ejpam-4940	211	4	solution	solution	NOUN
ejpam-4940	211	5	of	of	ADP
ejpam-4940	211	6	e	e	PROPN
ejpam-4940	211	7	is	be	AUX
ejpam-4940	211	8	(	(	PUNCT
ejpam-4940	211	9	x1	x1	PROPN
ejpam-4940	211	10	,	,	PUNCT
ejpam-4940	211	11	y1	y1	NOUN
ejpam-4940	211	12	)	)	PUNCT
ejpam-4940	211	13	=	=	SYM
ejpam-4940	211	14	(	(	PUNCT
ejpam-4940	211	15	2t+	2t+	NUM
ejpam-4940	211	16	1	1	NUM
ejpam-4940	211	17	+	+	CCONJ
ejpam-4940	211	18	p	p	NOUN
ejpam-4940	211	19	′(t	′(t	NOUN
ejpam-4940	211	20	)	)	PUNCT
ejpam-4940	211	21	,	,	PUNCT
ejpam-4940	211	22	2	2	NUM
ejpam-4940	211	23	+	+	SYM
ejpam-4940	211	24	2	2	NUM
ejpam-4940	211	25	)	)	PUNCT
ejpam-4940	211	26	=	=	SYM
ejpam-4940	211	27	(	(	PUNCT
ejpam-4940	211	28	4t+	4t+	NUM
ejpam-4940	211	29	2	2	NUM
ejpam-4940	211	30	,	,	PUNCT
ejpam-4940	211	31	4	4	NUM
ejpam-4940	211	32	)	)	PUNCT
ejpam-4940	211	33	and	and	CCONJ
ejpam-4940	211	34	the	the	DET
ejpam-4940	211	35	other	other	ADJ
ejpam-4940	211	36	solutions	solution	NOUN
ejpam-4940	211	37	are	be	AUX
ejpam-4940	211	38	given	give	VERB
ejpam-4940	211	39	by	by	NOUN
ejpam-4940	211	40	xk	xk	X
ejpam-4940	211	41	=	=	PRON
ejpam-4940	211	42	(	(	PUNCT
ejpam-4940	211	43	2t+	2t+	NUM
ejpam-4940	211	44	1)xk−1	1)xk−1	PROPN
ejpam-4940	211	45	+	+	CCONJ
ejpam-4940	211	46	(	(	PUNCT
ejpam-4940	211	47	2t2	2t2	NUM
ejpam-4940	212	1	+	+	CCONJ
ejpam-4940	212	2	2t)yk−1	2t)yk−1	NUM
ejpam-4940	212	3	−	−	NOUN
ejpam-4940	212	4	8t2	8t2	NUM
ejpam-4940	212	5	−	−	PROPN
ejpam-4940	212	6	6	6	NUM
ejpam-4940	212	7	t	t	NOUN
ejpam-4940	212	8	for	for	ADP
ejpam-4940	212	9	,	,	PUNCT
ejpam-4940	212	10	k	k	PROPN
ejpam-4940	212	11	≥	≥	NUM
ejpam-4940	212	12	2	2	NUM
ejpam-4940	212	13	yk	yk	NOUN
ejpam-4940	212	14	=	=	PUNCT
ejpam-4940	212	15	2xk−1	2xk−1	PROPN
ejpam-4940	212	16	+	+	CCONJ
ejpam-4940	212	17	(	(	PUNCT
ejpam-4940	212	18	2t+	2t+	NUM
ejpam-4940	212	19	1)yk−1	1)yk−1	NUM
ejpam-4940	212	20	−	−	PROPN
ejpam-4940	212	21	8t−	8t−	NUM
ejpam-4940	212	22	2	2	NUM
ejpam-4940	212	23	acknowledgements	acknowledgement	NOUN
ejpam-4940	212	24	the	the	DET
ejpam-4940	212	25	authors	author	NOUN
ejpam-4940	212	26	would	would	AUX
ejpam-4940	212	27	like	like	VERB
ejpam-4940	212	28	to	to	PART
ejpam-4940	212	29	thank	thank	VERB
ejpam-4940	212	30	the	the	DET
ejpam-4940	212	31	deanship	deanship	NOUN
ejpam-4940	212	32	of	of	ADP
ejpam-4940	212	33	scientific	scientific	ADJ
ejpam-4940	212	34	research	research	NOUN
ejpam-4940	212	35	at	at	ADP
ejpam-4940	212	36	umm	umm	INTJ
ejpam-4940	212	37	al	al	PROPN
ejpam-4940	212	38	-	-	PUNCT
ejpam-4940	212	39	qura	qura	PROPN
ejpam-4940	212	40	university	university	NOUN
ejpam-4940	212	41	for	for	ADP
ejpam-4940	212	42	supporting	support	VERB
ejpam-4940	212	43	this	this	DET
ejpam-4940	212	44	work	work	NOUN
ejpam-4940	212	45	by	by	ADP
ejpam-4940	212	46	grant	grant	PROPN
ejpam-4940	212	47	code	code	PROPN
ejpam-4940	212	48	:	:	PUNCT
ejpam-4940	212	49	(	(	PUNCT
ejpam-4940	212	50	22uqu	22uqu	ADJ
ejpam-4940	212	51	4350388dsr01	4350388dsr01	NOUN
ejpam-4940	212	52	)	)	PUNCT
ejpam-4940	212	53	references	reference	NOUN
ejpam-4940	212	54	[	[	X
ejpam-4940	212	55	1	1	NUM
ejpam-4940	212	56	]	]	X
ejpam-4940	212	57	chandoul	chandoul	PROPN
ejpam-4940	212	58	,	,	PUNCT
ejpam-4940	212	59	a.	a.	PROPN
ejpam-4940	212	60	,	,	PUNCT
ejpam-4940	212	61	marques	marques	PROPN
ejpam-4940	212	62	,	,	PUNCT
ejpam-4940	212	63	d.	d.	PROPN
ejpam-4940	212	64	,	,	PUNCT
ejpam-4940	212	65	albrbar	albrbar	PROPN
ejpam-4940	212	66	,	,	PUNCT
ejpam-4940	212	67	s.	s.	PROPN
ejpam-4940	212	68	s	s	PROPN
ejpam-4940	212	69	,	,	PUNCT
ejpam-4940	212	70	the	the	DET
ejpam-4940	212	71	quadratic	quadratic	ADJ
ejpam-4940	212	72	diophantine	diophantine	NOUN
ejpam-4940	212	73	equations	equation	NOUN
ejpam-4940	213	1	x2	x2	INTJ
ejpam-4940	213	2	−	−	PROPN
ejpam-4940	214	1	p	p	X
ejpam-4940	214	2	(	(	PUNCT
ejpam-4940	214	3	t)y2	t)y2	PROPN
ejpam-4940	214	4	−	−	NOUN
ejpam-4940	214	5	2p	2p	NOUN
ejpam-4940	214	6	′(t)x	′(t)x	ADP
ejpam-4940	215	1	+	+	NUM
ejpam-4940	215	2	4p	4p	NOUN
ejpam-4940	215	3	(	(	PUNCT
ejpam-4940	215	4	t)y	t)y	PUNCT
ejpam-4940	215	5	+	+	PUNCT
ejpam-4940	215	6	p	p	X
ejpam-4940	215	7	′(t)2	′(t)2	X
ejpam-4940	215	8	−	−	PROPN
ejpam-4940	215	9	4p	4p	NOUN
ejpam-4940	215	10	(	(	PUNCT
ejpam-4940	215	11	t	t	NOUN
ejpam-4940	215	12	)	)	PUNCT
ejpam-4940	215	13	−	−	PROPN
ejpam-4940	216	1	1	1	NUM
ejpam-4940	216	2	=	=	SYM
ejpam-4940	216	3	0	0	NUM
ejpam-4940	216	4	,	,	PUNCT
ejpam-4940	216	5	journal	journal	NOUN
ejpam-4940	216	6	of	of	ADP
ejpam-4940	216	7	mathematics	mathematics	PROPN
ejpam-4940	216	8	research	research	NOUN
ejpam-4940	216	9	,	,	PUNCT
ejpam-4940	216	10	11(2	11(2	NUM
ejpam-4940	216	11	)	)	PUNCT
ejpam-4940	216	12	,	,	PUNCT
ejpam-4940	216	13	(	(	PUNCT
ejpam-4940	216	14	2019	2019	NUM
ejpam-4940	216	15	)	)	PUNCT
ejpam-4940	216	16	,	,	PUNCT
ejpam-4940	216	17	30	30	NUM
ejpam-4940	216	18	-	-	SYM
ejpam-4940	216	19	38	38	NUM
ejpam-4940	216	20	.	.	PUNCT
ejpam-4940	217	1	[	[	X
ejpam-4940	217	2	2	2	NUM
ejpam-4940	217	3	]	]	PUNCT
ejpam-4940	217	4	a.	a.	NOUN
ejpam-4940	217	5	tekcan	tekcan	PROPN
ejpam-4940	217	6	,	,	PUNCT
ejpam-4940	217	7	quadratic	quadratic	ADJ
ejpam-4940	217	8	diophantine	diophantine	NOUN
ejpam-4940	217	9	equation	equation	NOUN
ejpam-4940	217	10	x2−(t2−t)y2−(4t−2)x+(4t2−4t)y	x2−(t2−t)y2−(4t−2)x+(4t2−4t)y	PUNCT
ejpam-4940	218	1	=	=	SYM
ejpam-4940	218	2	0	0	NUM
ejpam-4940	218	3	,	,	PUNCT
ejpam-4940	218	4	bull	bull	NOUN
ejpam-4940	218	5	.	.	PUNCT
ejpam-4940	219	1	malays	malays	PROPN
ejpam-4940	219	2	.	.	PUNCT
ejpam-4940	220	1	math	math	NOUN
ejpam-4940	220	2	.	.	PUNCT
ejpam-4940	221	1	sci	sci	PROPN
ejpam-4940	221	2	.	.	PROPN
ejpam-4940	221	3	soc	soc	PROPN
ejpam-4940	221	4	,	,	PUNCT
ejpam-4940	221	5	(	(	PUNCT
ejpam-4940	221	6	2)33	2)33	X
ejpam-4940	221	7	(	(	PUNCT
ejpam-4940	221	8	2	2	NUM
ejpam-4940	221	9	)	)	PUNCT
ejpam-4940	221	10	(	(	PUNCT
ejpam-4940	221	11	2010	2010	NUM
ejpam-4940	221	12	)	)	PUNCT
ejpam-4940	221	13	,	,	PUNCT
ejpam-4940	221	14	273	273	NUM
ejpam-4940	221	15	-	-	SYM
ejpam-4940	221	16	280	280	NUM
ejpam-4940	221	17	.	.	PUNCT
ejpam-4940	222	1	[	[	X
ejpam-4940	222	2	3	3	X
ejpam-4940	222	3	]	]	X
ejpam-4940	222	4	y.	y.	NOUN
ejpam-4940	222	5	v.	v.	ADP
ejpam-4940	222	6	matiyasevich	matiyasevich	NOUN
ejpam-4940	222	7	,	,	PUNCT
ejpam-4940	222	8	solution	solution	NOUN
ejpam-4940	222	9	of	of	ADP
ejpam-4940	222	10	the	the	DET
ejpam-4940	222	11	tenth	tenth	ADJ
ejpam-4940	222	12	problem	problem	NOUN
ejpam-4940	222	13	of	of	ADP
ejpam-4940	222	14	hilbert	hilbert	PROPN
ejpam-4940	222	15	,	,	PUNCT
ejpam-4940	222	16	mat	mat	PROPN
ejpam-4940	222	17	.	.	PUNCT
ejpam-4940	222	18	lapok	lapok	NOUN
ejpam-4940	222	19	,	,	PUNCT
ejpam-4940	222	20	21	21	NUM
ejpam-4940	222	21	:	:	PUNCT
ejpam-4940	222	22	(	(	PUNCT
ejpam-4940	222	23	1970	1970	NUM
ejpam-4940	222	24	)	)	PUNCT
ejpam-4940	222	25	83	83	NUM
ejpam-4940	222	26	-	-	SYM
ejpam-4940	222	27	87	87	NUM
ejpam-4940	222	28	.	.	PUNCT
ejpam-4940	223	1	[	[	X
ejpam-4940	223	2	4	4	X
ejpam-4940	223	3	]	]	X
ejpam-4940	223	4	david	david	PROPN
ejpam-4940	223	5	hilbert	hilbert	PROPN
ejpam-4940	223	6	,	,	PUNCT
ejpam-4940	223	7	mathematische	mathematische	NOUN
ejpam-4940	223	8	probleme	probleme	NOUN
ejpam-4940	223	9	.	.	PUNCT
ejpam-4940	224	1	vortrag	vortrag	ADJ
ejpam-4940	224	2	,	,	PUNCT
ejpam-4940	224	3	gehalten	gehalten	VERB
ejpam-4940	224	4	auf	auf	PROPN
ejpam-4940	224	5	dem	dem	PROPN
ejpam-4940	224	6	internationalen	internationalen	ADJ
ejpam-4940	224	7	mathematiker	mathematiker	PROPN
ejpam-4940	224	8	kongress	kongress	PROPN
ejpam-4940	224	9	zu	zu	PROPN
ejpam-4940	224	10	paris	paris	PROPN
ejpam-4940	224	11	1900	1900	NUM
ejpam-4940	224	12	,	,	PUNCT
ejpam-4940	224	13	nachr	nachr	PROPN
ejpam-4940	224	14	.	.	PUNCT
ejpam-4940	225	1	k.	k.	PROPN
ejpam-4940	225	2	ges	ges	PROPN
ejpam-4940	226	1	.	.	PROPN
ejpam-4940	226	2	wiss	wiss	PROPN
ejpam-4940	226	3	.	.	PROPN
ejpam-4940	226	4	,	,	PUNCT
ejpam-4940	227	1	g.	g.	PROPN
ejpam-4940	227	2	ottingen	ottingen	PROPN
ejpam-4940	227	3	,	,	PUNCT
ejpam-4940	227	4	math.phys.kl	math.phys.kl	PROPN
ejpam-4940	227	5	,	,	PUNCT
ejpam-4940	227	6	(	(	PUNCT
ejpam-4940	227	7	1900	1900	NUM
ejpam-4940	227	8	)	)	PUNCT
ejpam-4940	227	9	,	,	PUNCT
ejpam-4940	227	10	253	253	NUM
ejpam-4940	227	11	-	-	SYM
ejpam-4940	227	12	297	297	NUM
ejpam-4940	227	13	.	.	PUNCT