id	sid	tid	token	lemma	pos
ejpam-4989	1	1	european	european	PROPN
ejpam-4989	1	2	journal	journal	PROPN
ejpam-4989	1	3	of	of	ADP
ejpam-4989	1	4	pure	pure	ADJ
ejpam-4989	1	5	and	and	CCONJ
ejpam-4989	1	6	applied	apply	VERB
ejpam-4989	1	7	mathematics	mathematic	NOUN
ejpam-4989	1	8	vol	vol	NOUN
ejpam-4989	1	9	.	.	PROPN
ejpam-4989	2	1	17	17	NUM
ejpam-4989	2	2	,	,	PUNCT
ejpam-4989	2	3	no	no	INTJ
ejpam-4989	2	4	.	.	NOUN
ejpam-4989	2	5	1	1	NUM
ejpam-4989	2	6	,	,	PUNCT
ejpam-4989	2	7	2024	2024	NUM
ejpam-4989	2	8	,	,	PUNCT
ejpam-4989	2	9	135	135	NUM
ejpam-4989	2	10	-	-	SYM
ejpam-4989	2	11	146	146	NUM
ejpam-4989	2	12	issn	issn	PROPN
ejpam-4989	2	13	1307	1307	NUM
ejpam-4989	2	14	-	-	SYM
ejpam-4989	2	15	5543	5543	NUM
ejpam-4989	2	16	–	–	PUNCT
ejpam-4989	2	17	ejpam.com	ejpam.com	X
ejpam-4989	2	18	published	publish	VERB
ejpam-4989	2	19	by	by	ADP
ejpam-4989	2	20	new	new	PROPN
ejpam-4989	2	21	york	york	PROPN
ejpam-4989	2	22	business	business	PROPN
ejpam-4989	2	23	global	global	ADJ
ejpam-4989	2	24	common	common	ADJ
ejpam-4989	2	25	terms	term	NOUN
ejpam-4989	2	26	of	of	ADP
ejpam-4989	2	27	k	k	NOUN
ejpam-4989	2	28	-	-	NOUN
ejpam-4989	2	29	pell	pell	PROPN
ejpam-4989	2	30	and	and	CCONJ
ejpam-4989	3	1	tribonacci	tribonacci	NUM
ejpam-4989	3	2	numbers	number	NOUN
ejpam-4989	3	3	hunar	hunar	VERB
ejpam-4989	3	4	sherzad	sherzad	PROPN
ejpam-4989	3	5	taher1	taher1	PROPN
ejpam-4989	3	6	,	,	PUNCT
ejpam-4989	3	7	saroj	saroj	PROPN
ejpam-4989	3	8	kumar	kumar	PROPN
ejpam-4989	3	9	dash2,∗	dash2,∗	PROPN
ejpam-4989	3	10	1	1	NUM
ejpam-4989	3	11	mathematics	mathematic	NOUN
ejpam-4989	3	12	division	division	NOUN
ejpam-4989	3	13	,	,	PUNCT
ejpam-4989	3	14	school	school	NOUN
ejpam-4989	3	15	of	of	ADP
ejpam-4989	3	16	advanced	advanced	ADJ
ejpam-4989	3	17	science	science	NOUN
ejpam-4989	3	18	,	,	PUNCT
ejpam-4989	3	19	vellore	vellore	PROPN
ejpam-4989	3	20	institute	institute	PROPN
ejpam-4989	3	21	of	of	ADP
ejpam-4989	3	22	technology	technology	PROPN
ejpam-4989	3	23	,	,	PUNCT
ejpam-4989	3	24	chennai	chennai	NOUN
ejpam-4989	3	25	campus	campus	PROPN
ejpam-4989	3	26	,	,	PUNCT
ejpam-4989	3	27	chennai	chennai	PROPN
ejpam-4989	3	28	600127	600127	NUM
ejpam-4989	3	29	,	,	PUNCT
ejpam-4989	3	30	india	india	PROPN
ejpam-4989	3	31	abstract	abstract	NOUN
ejpam-4989	3	32	.	.	PUNCT
ejpam-4989	4	1	let	let	VERB
ejpam-4989	4	2	tm	tm	NOUN
ejpam-4989	4	3	be	be	AUX
ejpam-4989	4	4	a	a	DET
ejpam-4989	4	5	tribonacci	tribonacci	NOUN
ejpam-4989	4	6	sequence	sequence	NOUN
ejpam-4989	4	7	,	,	PUNCT
ejpam-4989	4	8	and	and	CCONJ
ejpam-4989	4	9	let	let	VERB
ejpam-4989	4	10	the	the	DET
ejpam-4989	4	11	k	k	NOUN
ejpam-4989	4	12	-	-	PUNCT
ejpam-4989	4	13	pell	pell	ADJ
ejpam-4989	4	14	sequence	sequence	NOUN
ejpam-4989	4	15	be	be	AUX
ejpam-4989	4	16	a	a	DET
ejpam-4989	4	17	generalization	generalization	NOUN
ejpam-4989	4	18	of	of	ADP
ejpam-4989	4	19	the	the	DET
ejpam-4989	4	20	pell	pell	NOUN
ejpam-4989	4	21	sequence	sequence	NOUN
ejpam-4989	4	22	for	for	ADP
ejpam-4989	4	23	k	k	PROPN
ejpam-4989	4	24	≥	≥	PROPN
ejpam-4989	4	25	2	2	NUM
ejpam-4989	4	26	.	.	PUNCT
ejpam-4989	5	1	the	the	DET
ejpam-4989	5	2	first	first	ADJ
ejpam-4989	5	3	k	k	PROPN
ejpam-4989	5	4	terms	term	NOUN
ejpam-4989	5	5	are	be	AUX
ejpam-4989	5	6	0	0	NUM
ejpam-4989	5	7	,	,	PUNCT
ejpam-4989	5	8	0	0	NUM
ejpam-4989	5	9	,	,	PUNCT
ejpam-4989	5	10	...	...	PUNCT
ejpam-4989	5	11	,	,	PUNCT
ejpam-4989	5	12	0	0	NUM
ejpam-4989	5	13	,	,	PUNCT
ejpam-4989	5	14	1	1	NUM
ejpam-4989	5	15	,	,	PUNCT
ejpam-4989	5	16	and	and	CCONJ
ejpam-4989	5	17	each	each	DET
ejpam-4989	5	18	term	term	NOUN
ejpam-4989	5	19	after	after	SCONJ
ejpam-4989	5	20	the	the	DET
ejpam-4989	5	21	forewords	foreword	NOUN
ejpam-4989	5	22	is	be	AUX
ejpam-4989	5	23	defined	define	VERB
ejpam-4989	5	24	by	by	ADP
ejpam-4989	5	25	linear	linear	PROPN
ejpam-4989	5	26	recurrence	recurrence	NOUN
ejpam-4989	5	27	p	p	PROPN
ejpam-4989	5	28	(	(	PUNCT
ejpam-4989	5	29	k	k	NOUN
ejpam-4989	5	30	)	)	PUNCT
ejpam-4989	5	31	n	n	NOUN
ejpam-4989	5	32	=	=	SYM
ejpam-4989	5	33	2p	2p	NOUN
ejpam-4989	5	34	(	(	PUNCT
ejpam-4989	5	35	k	k	NOUN
ejpam-4989	5	36	)	)	PUNCT
ejpam-4989	5	37	n−1	n−1	PROPN
ejpam-4989	6	1	+	+	CCONJ
ejpam-4989	6	2	p	p	X
ejpam-4989	6	3	(	(	PUNCT
ejpam-4989	6	4	k	k	NOUN
ejpam-4989	6	5	)	)	PUNCT
ejpam-4989	6	6	n−2	n−2	PROPN
ejpam-4989	6	7	+	+	CCONJ
ejpam-4989	6	8	...	...	PUNCT
ejpam-4989	7	1	+	+	CCONJ
ejpam-4989	7	2	p	p	X
ejpam-4989	7	3	(	(	PUNCT
ejpam-4989	7	4	k	k	NOUN
ejpam-4989	7	5	)	)	PUNCT
ejpam-4989	7	6	n−k	n−k	NOUN
ejpam-4989	7	7	.	.	PUNCT
ejpam-4989	8	1	we	we	PRON
ejpam-4989	8	2	study	study	VERB
ejpam-4989	8	3	the	the	DET
ejpam-4989	8	4	solution	solution	NOUN
ejpam-4989	8	5	of	of	ADP
ejpam-4989	8	6	the	the	DET
ejpam-4989	8	7	diophantine	diophantine	NOUN
ejpam-4989	8	8	equation	equation	NOUN
ejpam-4989	8	9	p	p	X
ejpam-4989	8	10	(	(	PUNCT
ejpam-4989	8	11	k	k	NOUN
ejpam-4989	8	12	)	)	PUNCT
ejpam-4989	8	13	n	n	NOUN
ejpam-4989	8	14	=	=	NOUN
ejpam-4989	8	15	tm	tm	PROPN
ejpam-4989	8	16	for	for	ADP
ejpam-4989	8	17	the	the	DET
ejpam-4989	8	18	positive	positive	ADJ
ejpam-4989	8	19	integer	integer	NOUN
ejpam-4989	8	20	(	(	PUNCT
ejpam-4989	8	21	n	n	CCONJ
ejpam-4989	8	22	,	,	PUNCT
ejpam-4989	8	23	k	k	PROPN
ejpam-4989	8	24	,	,	PUNCT
ejpam-4989	8	25	m	m	NOUN
ejpam-4989	8	26	)	)	PUNCT
ejpam-4989	8	27	with	with	ADP
ejpam-4989	8	28	k	k	PROPN
ejpam-4989	8	29	≥	≥	NUM
ejpam-4989	8	30	2	2	NUM
ejpam-4989	8	31	.	.	PUNCT
ejpam-4989	9	1	we	we	PRON
ejpam-4989	9	2	use	use	VERB
ejpam-4989	9	3	the	the	DET
ejpam-4989	9	4	lower	lower	ADV
ejpam-4989	9	5	bound	bind	VERB
ejpam-4989	9	6	for	for	ADP
ejpam-4989	9	7	linear	linear	ADJ
ejpam-4989	9	8	forms	form	NOUN
ejpam-4989	9	9	in	in	ADP
ejpam-4989	9	10	logarithms	logarithm	NOUN
ejpam-4989	9	11	of	of	ADP
ejpam-4989	9	12	algebraic	algebraic	ADJ
ejpam-4989	9	13	numbers	number	NOUN
ejpam-4989	9	14	with	with	ADP
ejpam-4989	9	15	the	the	DET
ejpam-4989	9	16	theory	theory	NOUN
ejpam-4989	9	17	of	of	ADP
ejpam-4989	9	18	the	the	DET
ejpam-4989	9	19	continued	continue	VERB
ejpam-4989	9	20	fraction	fraction	NOUN
ejpam-4989	9	21	.	.	PUNCT
ejpam-4989	10	1	2020	2020	NUM
ejpam-4989	10	2	mathematics	mathematic	NOUN
ejpam-4989	10	3	subject	subject	NOUN
ejpam-4989	10	4	classifications	classification	NOUN
ejpam-4989	10	5	:	:	PUNCT
ejpam-4989	10	6	11d61	11d61	NUM
ejpam-4989	10	7	,	,	PUNCT
ejpam-4989	10	8	11j86	11j86	NUM
ejpam-4989	10	9	,	,	PUNCT
ejpam-4989	10	10	11j70	11j70	NUM
ejpam-4989	10	11	,	,	PUNCT
ejpam-4989	10	12	11b83	11b83	NUM
ejpam-4989	10	13	key	key	ADJ
ejpam-4989	10	14	words	word	NOUN
ejpam-4989	10	15	and	and	CCONJ
ejpam-4989	10	16	phrases	phrase	NOUN
ejpam-4989	10	17	:	:	PUNCT
ejpam-4989	10	18	exponential	exponential	ADJ
ejpam-4989	10	19	diophantine	diophantine	NOUN
ejpam-4989	10	20	equation	equation	NOUN
ejpam-4989	10	21	,	,	PUNCT
ejpam-4989	10	22	linear	linear	ADJ
ejpam-4989	10	23	forms	form	NOUN
ejpam-4989	10	24	in	in	ADP
ejpam-4989	10	25	logarithms	logarithm	NOUN
ejpam-4989	10	26	,	,	PUNCT
ejpam-4989	10	27	k	k	ADJ
ejpam-4989	10	28	-	-	PUNCT
ejpam-4989	10	29	pell	pell	NOUN
ejpam-4989	10	30	numbers	number	NOUN
ejpam-4989	10	31	,	,	PUNCT
ejpam-4989	10	32	tribonacci	tribonacci	DET
ejpam-4989	10	33	numbers	number	NOUN
ejpam-4989	10	34	.	.	PUNCT
ejpam-4989	11	1	1	1	X
ejpam-4989	11	2	.	.	X
ejpam-4989	11	3	introduction	introduction	NOUN
ejpam-4989	11	4	the	the	DET
ejpam-4989	11	5	pell	pell	NOUN
ejpam-4989	11	6	sequence	sequence	NOUN
ejpam-4989	11	7	is	be	AUX
ejpam-4989	11	8	defined	define	VERB
ejpam-4989	11	9	by	by	ADP
ejpam-4989	11	10	pn	pn	PROPN
ejpam-4989	11	11	=	=	SYM
ejpam-4989	11	12	2pn−1	2pn−1	PROPN
ejpam-4989	11	13	+	+	CCONJ
ejpam-4989	11	14	pn−2	pn−2	PROPN
ejpam-4989	11	15	,	,	PUNCT
ejpam-4989	11	16	for	for	ADP
ejpam-4989	11	17	all	all	DET
ejpam-4989	11	18	n	n	PRON
ejpam-4989	11	19	≥	≥	NOUN
ejpam-4989	11	20	3	3	NUM
ejpam-4989	11	21	,	,	PUNCT
ejpam-4989	11	22	where	where	SCONJ
ejpam-4989	11	23	p0	p0	NOUN
ejpam-4989	11	24	=	=	SYM
ejpam-4989	11	25	0	0	PUNCT
ejpam-4989	11	26	and	and	CCONJ
ejpam-4989	11	27	p1	p1	PROPN
ejpam-4989	11	28	=	=	SYM
ejpam-4989	11	29	1	1	X
ejpam-4989	11	30	.	.	PUNCT
ejpam-4989	12	1	let	let	VERB
ejpam-4989	12	2	an	an	DET
ejpam-4989	12	3	integer	integer	NOUN
ejpam-4989	12	4	k	k	PROPN
ejpam-4989	12	5	≥	≥	NUM
ejpam-4989	12	6	2	2	NUM
ejpam-4989	12	7	.	.	PUNCT
ejpam-4989	13	1	the	the	DET
ejpam-4989	13	2	generalization	generalization	NOUN
ejpam-4989	13	3	of	of	ADP
ejpam-4989	13	4	the	the	DET
ejpam-4989	13	5	pell	pell	NOUN
ejpam-4989	13	6	sequence	sequence	NOUN
ejpam-4989	13	7	is	be	AUX
ejpam-4989	13	8	a	a	DET
ejpam-4989	13	9	k	k	NOUN
ejpam-4989	13	10	-	-	PUNCT
ejpam-4989	13	11	pell	pell	ADJ
ejpam-4989	13	12	sequence	sequence	NOUN
ejpam-4989	13	13	,	,	PUNCT
ejpam-4989	13	14	denoted	denote	VERB
ejpam-4989	13	15	by	by	ADP
ejpam-4989	13	16	{	{	PUNCT
ejpam-4989	13	17	p	p	X
ejpam-4989	13	18	(	(	PUNCT
ejpam-4989	13	19	k	k	NOUN
ejpam-4989	13	20	)	)	PUNCT
ejpam-4989	13	21	n	n	CCONJ
ejpam-4989	13	22	}	}	PUNCT
ejpam-4989	13	23	n≥−(k−2	n≥−(k−2	PROPN
ejpam-4989	13	24	)	)	PUNCT
ejpam-4989	13	25	given	give	VERB
ejpam-4989	13	26	linear	linear	NOUN
ejpam-4989	13	27	recurrence	recurrence	NOUN
ejpam-4989	13	28	as	as	ADP
ejpam-4989	13	29	:	:	PUNCT
ejpam-4989	13	30	p	p	X
ejpam-4989	13	31	(	(	PUNCT
ejpam-4989	13	32	k	k	NOUN
ejpam-4989	13	33	)	)	PUNCT
ejpam-4989	13	34	n	n	NOUN
ejpam-4989	13	35	=	=	SYM
ejpam-4989	13	36	2p	2p	NOUN
ejpam-4989	13	37	(	(	PUNCT
ejpam-4989	13	38	k	k	NOUN
ejpam-4989	13	39	)	)	PUNCT
ejpam-4989	13	40	n−1	n−1	PROPN
ejpam-4989	14	1	+	+	CCONJ
ejpam-4989	14	2	p	p	X
ejpam-4989	14	3	(	(	PUNCT
ejpam-4989	14	4	k	k	NOUN
ejpam-4989	14	5	)	)	PUNCT
ejpam-4989	14	6	n−2	n−2	PROPN
ejpam-4989	14	7	+	+	CCONJ
ejpam-4989	14	8	...	...	PUNCT
ejpam-4989	15	1	+	+	CCONJ
ejpam-4989	15	2	p	p	X
ejpam-4989	15	3	(	(	PUNCT
ejpam-4989	15	4	k	k	NOUN
ejpam-4989	15	5	)	)	PUNCT
ejpam-4989	15	6	n−k	n−k	NOUN
ejpam-4989	15	7	for	for	ADP
ejpam-4989	15	8	all	all	DET
ejpam-4989	15	9	n	n	PRON
ejpam-4989	15	10	≥	≥	NOUN
ejpam-4989	15	11	2	2	NUM
ejpam-4989	15	12	,	,	PUNCT
ejpam-4989	15	13	(	(	PUNCT
ejpam-4989	15	14	1	1	X
ejpam-4989	15	15	)	)	PUNCT
ejpam-4989	15	16	with	with	ADP
ejpam-4989	15	17	the	the	DET
ejpam-4989	15	18	initial	initial	ADJ
ejpam-4989	15	19	conditions	condition	NOUN
ejpam-4989	15	20	p	p	X
ejpam-4989	15	21	(	(	PUNCT
ejpam-4989	15	22	k	k	NOUN
ejpam-4989	15	23	)	)	PUNCT
ejpam-4989	15	24	−(k−2	−(k−2	PROPN
ejpam-4989	15	25	)	)	PUNCT
ejpam-4989	16	1	=	=	SYM
ejpam-4989	16	2	p	p	X
ejpam-4989	16	3	(	(	PUNCT
ejpam-4989	16	4	k	k	NOUN
ejpam-4989	16	5	)	)	PUNCT
ejpam-4989	16	6	−(k−3	−(k−3	NOUN
ejpam-4989	16	7	)	)	PUNCT
ejpam-4989	17	1	=	=	PUNCT
ejpam-4989	17	2	...	...	PUNCT
ejpam-4989	18	1	=	=	PUNCT
ejpam-4989	18	2	p	p	X
ejpam-4989	18	3	(	(	PUNCT
ejpam-4989	18	4	k	k	NOUN
ejpam-4989	18	5	)	)	PUNCT
ejpam-4989	18	6	0	0	NUM
ejpam-4989	19	1	=	=	SYM
ejpam-4989	19	2	0	0	NUM
ejpam-4989	19	3	and	and	CCONJ
ejpam-4989	19	4	p	p	X
ejpam-4989	19	5	(	(	PUNCT
ejpam-4989	19	6	k	k	NOUN
ejpam-4989	19	7	)	)	PUNCT
ejpam-4989	19	8	1	1	NUM
ejpam-4989	19	9	=	=	SYM
ejpam-4989	19	10	1	1	X
ejpam-4989	19	11	.	.	PUNCT
ejpam-4989	20	1	if	if	SCONJ
ejpam-4989	20	2	k	k	PROPN
ejpam-4989	20	3	=	=	SYM
ejpam-4989	20	4	2	2	NUM
ejpam-4989	20	5	in	in	ADP
ejpam-4989	20	6	equation	equation	NOUN
ejpam-4989	20	7	(	(	PUNCT
ejpam-4989	20	8	1	1	NUM
ejpam-4989	20	9	)	)	PUNCT
ejpam-4989	20	10	,	,	PUNCT
ejpam-4989	20	11	it	it	PRON
ejpam-4989	20	12	becomes	become	VERB
ejpam-4989	20	13	a	a	DET
ejpam-4989	20	14	linear	linear	ADJ
ejpam-4989	20	15	recurrence	recurrence	NOUN
ejpam-4989	20	16	of	of	ADP
ejpam-4989	20	17	the	the	DET
ejpam-4989	20	18	pell	pell	NOUN
ejpam-4989	20	19	sequence	sequence	NOUN
ejpam-4989	20	20	.	.	PUNCT
ejpam-4989	21	1	the	the	DET
ejpam-4989	21	2	tribonacci	tribonacci	PROPN
ejpam-4989	21	3	sequence	sequence	NOUN
ejpam-4989	21	4	tm	tm	NOUN
ejpam-4989	21	5	is	be	AUX
ejpam-4989	21	6	defined	define	VERB
ejpam-4989	21	7	by	by	ADP
ejpam-4989	21	8	tm	tm	NOUN
ejpam-4989	21	9	=	=	PROPN
ejpam-4989	21	10	tm−1	tm−1	NOUN
ejpam-4989	21	11	+	+	CCONJ
ejpam-4989	21	12	tm−2	tm−2	ADJ
ejpam-4989	21	13	+	+	CCONJ
ejpam-4989	21	14	tm−3	tm−3	NOUN
ejpam-4989	21	15	for	for	ADP
ejpam-4989	21	16	each	each	DET
ejpam-4989	21	17	m	m	PROPN
ejpam-4989	21	18	≥	≥	NOUN
ejpam-4989	21	19	3	3	NUM
ejpam-4989	21	20	(	(	PUNCT
ejpam-4989	21	21	2	2	NUM
ejpam-4989	21	22	)	)	PUNCT
ejpam-4989	21	23	∗corresponding	∗corresponde	VERB
ejpam-4989	21	24	author	author	NOUN
ejpam-4989	21	25	.	.	PUNCT
ejpam-4989	22	1	doi	doi	NOUN
ejpam-4989	22	2	:	:	PUNCT
ejpam-4989	22	3	https://doi.org/10.29020/nybg.ejpam.v17i1.4989	https://doi.org/10.29020/nybg.ejpam.v17i1.4989	ADJ
ejpam-4989	22	4	email	email	NOUN
ejpam-4989	22	5	addresses	address	NOUN
ejpam-4989	22	6	:	:	PUNCT
ejpam-4989	22	7	sarojkumar.dash@vit.ac.in	sarojkumar.dash@vit.ac.in	NOUN
ejpam-4989	22	8	(	(	PUNCT
ejpam-4989	22	9	s.	s.	PROPN
ejpam-4989	22	10	k.	k.	PROPN
ejpam-4989	22	11	dash	dash	PROPN
ejpam-4989	22	12	)	)	PUNCT
ejpam-4989	22	13	,	,	PUNCT
ejpam-4989	22	14	hunarsherzad.taher2022@vitstudent.ac.in	hunarsherzad.taher2022@vitstudent.ac.in	PROPN
ejpam-4989	22	15	(	(	PUNCT
ejpam-4989	22	16	h.	h.	PROPN
ejpam-4989	22	17	s.	s.	PROPN
ejpam-4989	22	18	taher	taher	PROPN
ejpam-4989	22	19	)	)	PUNCT
ejpam-4989	22	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4989	22	21	135	135	NUM
ejpam-4989	22	22	©	©	PROPN
ejpam-4989	22	23	2024	2024	NUM
ejpam-4989	22	24	ejpam	ejpam	NOUN
ejpam-4989	22	25	all	all	DET
ejpam-4989	22	26	rights	right	NOUN
ejpam-4989	22	27	reserved	reserve	VERB
ejpam-4989	22	28	.	.	PUNCT
ejpam-4989	23	1	h.	h.	PROPN
ejpam-4989	23	2	s.	s.	PROPN
ejpam-4989	23	3	taher	taher	PROPN
ejpam-4989	23	4	,	,	PUNCT
ejpam-4989	23	5	s.	s.	PROPN
ejpam-4989	23	6	k.	k.	PROPN
ejpam-4989	23	7	dash	dash	NOUN
ejpam-4989	23	8	/	/	SYM
ejpam-4989	23	9	eur	eur	NOUN
ejpam-4989	23	10	.	.	PUNCT
ejpam-4989	24	1	j.	j.	PROPN
ejpam-4989	24	2	pure	pure	PROPN
ejpam-4989	24	3	appl	appl	PROPN
ejpam-4989	24	4	.	.	PROPN
ejpam-4989	24	5	math	math	PROPN
ejpam-4989	24	6	,	,	PUNCT
ejpam-4989	24	7	17	17	NUM
ejpam-4989	24	8	(	(	PUNCT
ejpam-4989	24	9	1	1	NUM
ejpam-4989	24	10	)	)	PUNCT
ejpam-4989	24	11	(	(	PUNCT
ejpam-4989	24	12	2024	2024	NUM
ejpam-4989	24	13	)	)	PUNCT
ejpam-4989	24	14	,	,	PUNCT
ejpam-4989	24	15	135	135	NUM
ejpam-4989	24	16	-	-	SYM
ejpam-4989	24	17	146	146	NUM
ejpam-4989	24	18	136	136	NUM
ejpam-4989	24	19	with	with	ADP
ejpam-4989	24	20	initial	initial	ADJ
ejpam-4989	24	21	conditions	condition	NOUN
ejpam-4989	24	22	t0	t0	NOUN
ejpam-4989	24	23	=	=	SYM
ejpam-4989	24	24	0	0	NUM
ejpam-4989	24	25	,	,	PUNCT
ejpam-4989	24	26	t1	t1	NOUN
ejpam-4989	24	27	=	=	SYM
ejpam-4989	24	28	t2	t2	NOUN
ejpam-4989	24	29	=	=	SYM
ejpam-4989	25	1	1	1	X
ejpam-4989	25	2	.	.	PUNCT
ejpam-4989	26	1	it	it	PRON
ejpam-4989	26	2	's	be	AUX
ejpam-4989	26	3	first	first	ADJ
ejpam-4989	26	4	few	few	ADJ
ejpam-4989	26	5	terms	term	NOUN
ejpam-4989	26	6	are	be	AUX
ejpam-4989	26	7	0	0	NUM
ejpam-4989	26	8	,	,	PUNCT
ejpam-4989	26	9	1	1	NUM
ejpam-4989	26	10	,	,	PUNCT
ejpam-4989	26	11	1	1	NUM
ejpam-4989	26	12	,	,	PUNCT
ejpam-4989	26	13	2	2	NUM
ejpam-4989	26	14	,	,	PUNCT
ejpam-4989	26	15	4	4	NUM
ejpam-4989	26	16	,	,	PUNCT
ejpam-4989	26	17	7	7	NUM
ejpam-4989	26	18	,	,	PUNCT
ejpam-4989	26	19	13	13	NUM
ejpam-4989	26	20	,	,	PUNCT
ejpam-4989	26	21	24	24	NUM
ejpam-4989	26	22	,	,	PUNCT
ejpam-4989	26	23	44	44	NUM
ejpam-4989	26	24	,	,	PUNCT
ejpam-4989	26	25	81	81	NUM
ejpam-4989	26	26	,	,	PUNCT
ejpam-4989	26	27	149	149	NUM
ejpam-4989	26	28	,	,	PUNCT
ejpam-4989	26	29	274	274	NUM
ejpam-4989	26	30	,	,	PUNCT
ejpam-4989	26	31	504	504	NUM
ejpam-4989	26	32	,	,	PUNCT
ejpam-4989	26	33	927	927	NUM
ejpam-4989	26	34	,	,	PUNCT
ejpam-4989	26	35	1705	1705	NUM
ejpam-4989	26	36	,	,	PUNCT
ejpam-4989	26	37	3136	3136	NUM
ejpam-4989	26	38	,	,	PUNCT
ejpam-4989	26	39	...	...	PUNCT
ejpam-4989	26	40	the	the	DET
ejpam-4989	26	41	online	online	ADJ
ejpam-4989	26	42	encyclopedia	encyclopedia	NOUN
ejpam-4989	26	43	of	of	ADP
ejpam-4989	26	44	integer	integer	NOUN
ejpam-4989	26	45	(	(	PUNCT
ejpam-4989	26	46	oeis	oeis	PROPN
ejpam-4989	26	47	)	)	PUNCT
ejpam-4989	26	48	of	of	ADP
ejpam-4989	26	49	pell	pell	NOUN
ejpam-4989	26	50	and	and	CCONJ
ejpam-4989	27	1	tribonacci	tribonacci	PROPN
ejpam-4989	27	2	sequences	sequence	NOUN
ejpam-4989	27	3	are	be	AUX
ejpam-4989	27	4	a000129	a000129	ADJ
ejpam-4989	27	5	and	and	CCONJ
ejpam-4989	27	6	a000073	a000073	NOUN
ejpam-4989	27	7	,	,	PUNCT
ejpam-4989	27	8	respectively	respectively	ADV
ejpam-4989	27	9	.	.	PUNCT
ejpam-4989	28	1	presently	presently	ADV
ejpam-4989	28	2	,	,	PUNCT
ejpam-4989	28	3	researchers	researcher	NOUN
ejpam-4989	28	4	are	be	AUX
ejpam-4989	28	5	finding	find	VERB
ejpam-4989	28	6	the	the	DET
ejpam-4989	28	7	intersection	intersection	NOUN
ejpam-4989	28	8	between	between	ADP
ejpam-4989	28	9	two	two	NUM
ejpam-4989	28	10	recurrences	recurrence	NOUN
ejpam-4989	28	11	,	,	PUNCT
ejpam-4989	28	12	and	and	CCONJ
ejpam-4989	28	13	several	several	ADJ
ejpam-4989	28	14	studies	study	NOUN
ejpam-4989	28	15	have	have	AUX
ejpam-4989	28	16	been	be	AUX
ejpam-4989	28	17	published	publish	VERB
ejpam-4989	28	18	on	on	ADP
ejpam-4989	28	19	k	k	PROPN
ejpam-4989	28	20	-	-	NOUN
ejpam-4989	28	21	fibonacci	fibonacci	NOUN
ejpam-4989	28	22	,	,	PUNCT
ejpam-4989	28	23	k	k	X
ejpam-4989	28	24	-	-	PUNCT
ejpam-4989	28	25	pell	pell	PROPN
ejpam-4989	28	26	,	,	PUNCT
ejpam-4989	28	27	tribonacci	tribonacci	PROPN
ejpam-4989	28	28	,	,	PUNCT
ejpam-4989	28	29	padovan	padovan	NOUN
ejpam-4989	28	30	,	,	PUNCT
ejpam-4989	28	31	and	and	CCONJ
ejpam-4989	28	32	perrin	perrin	NOUN
ejpam-4989	28	33	sequences	sequence	NOUN
ejpam-4989	28	34	related	relate	VERB
ejpam-4989	28	35	to	to	ADP
ejpam-4989	28	36	other	other	ADJ
ejpam-4989	28	37	sequences	sequence	NOUN
ejpam-4989	28	38	.	.	PUNCT
ejpam-4989	29	1	one	one	PRON
ejpam-4989	29	2	can	can	AUX
ejpam-4989	29	3	cite	cite	VERB
ejpam-4989	29	4	[	[	X
ejpam-4989	29	5	1	1	NUM
ejpam-4989	29	6	,	,	PUNCT
ejpam-4989	29	7	3	3	NUM
ejpam-4989	29	8	,	,	PUNCT
ejpam-4989	29	9	7	7	NUM
ejpam-4989	29	10	,	,	PUNCT
ejpam-4989	29	11	9	9	NUM
ejpam-4989	29	12	,	,	PUNCT
ejpam-4989	29	13	10	10	NUM
ejpam-4989	29	14	,	,	PUNCT
ejpam-4989	29	15	13	13	NUM
ejpam-4989	29	16	]	]	PUNCT
ejpam-4989	29	17	.	.	PUNCT
ejpam-4989	30	1	our	our	PRON
ejpam-4989	30	2	aim	aim	NOUN
ejpam-4989	30	3	is	be	AUX
ejpam-4989	30	4	to	to	PART
ejpam-4989	30	5	show	show	VERB
ejpam-4989	30	6	that	that	SCONJ
ejpam-4989	30	7	there	there	PRON
ejpam-4989	30	8	are	be	VERB
ejpam-4989	30	9	common	common	ADJ
ejpam-4989	30	10	terms	term	NOUN
ejpam-4989	30	11	between	between	ADP
ejpam-4989	30	12	k	k	ADV
ejpam-4989	30	13	-	-	ADJ
ejpam-4989	30	14	generalized	generalize	VERB
ejpam-4989	30	15	pell	pell	NOUN
ejpam-4989	30	16	numbers	number	NOUN
ejpam-4989	30	17	and	and	CCONJ
ejpam-4989	30	18	tribonacci	tribonacci	NUM
ejpam-4989	30	19	numbers	number	NOUN
ejpam-4989	30	20	.	.	PUNCT
ejpam-4989	31	1	the	the	DET
ejpam-4989	31	2	earlier	early	ADJ
ejpam-4989	31	3	findings	finding	NOUN
ejpam-4989	31	4	guided	guide	VERB
ejpam-4989	31	5	our	our	PRON
ejpam-4989	31	6	completion	completion	NOUN
ejpam-4989	31	7	of	of	ADP
ejpam-4989	31	8	the	the	DET
ejpam-4989	31	9	investigation	investigation	NOUN
ejpam-4989	31	10	.	.	PUNCT
ejpam-4989	32	1	2	2	X
ejpam-4989	32	2	.	.	X
ejpam-4989	32	3	auxiliary	auxiliary	NOUN
ejpam-4989	32	4	results	result	VERB
ejpam-4989	32	5	2.1	2.1	NUM
ejpam-4989	32	6	.	.	PUNCT
ejpam-4989	33	1	properties	property	NOUN
ejpam-4989	33	2	of	of	ADP
ejpam-4989	33	3	tribonacci	tribonacci	NUM
ejpam-4989	33	4	sequence	sequence	NOUN
ejpam-4989	33	5	the	the	DET
ejpam-4989	33	6	characteristic	characteristic	ADJ
ejpam-4989	33	7	polynomial	polynomial	NOUN
ejpam-4989	33	8	of	of	ADP
ejpam-4989	33	9	the	the	DET
ejpam-4989	33	10	tibonacci	tibonacci	ADJ
ejpam-4989	33	11	sequence	sequence	NOUN
ejpam-4989	33	12	is	be	AUX
ejpam-4989	33	13	f(x	f(x	PROPN
ejpam-4989	33	14	)	)	PUNCT
ejpam-4989	33	15	=	=	PUNCT
ejpam-4989	34	1	x3	x3	ADJ
ejpam-4989	34	2	−	−	PROPN
ejpam-4989	35	1	x2	x2	INTJ
ejpam-4989	35	2	−	−	PROPN
ejpam-4989	35	3	x−	x−	PROPN
ejpam-4989	35	4	1	1	NUM
ejpam-4989	35	5	.	.	PUNCT
ejpam-4989	36	1	the	the	DET
ejpam-4989	36	2	tribonacci	tribonacci	PROPN
ejpam-4989	36	3	sequence	sequence	NOUN
ejpam-4989	36	4	has	have	VERB
ejpam-4989	36	5	one	one	NUM
ejpam-4989	36	6	real	real	ADJ
ejpam-4989	36	7	root	root	NOUN
ejpam-4989	36	8	η1	η1	NOUN
ejpam-4989	36	9	with	with	ADP
ejpam-4989	36	10	two	two	NUM
ejpam-4989	36	11	complex	complex	ADJ
ejpam-4989	36	12	roots	root	NOUN
ejpam-4989	36	13	η2	η2	NOUN
ejpam-4989	36	14	and	and	CCONJ
ejpam-4989	36	15	η3	η3	NOUN
ejpam-4989	36	16	.	.	PUNCT
ejpam-4989	37	1	η1	η1	NOUN
ejpam-4989	37	2	=	=	SYM
ejpam-4989	37	3	1	1	NUM
ejpam-4989	37	4	+	+	CCONJ
ejpam-4989	37	5	3	3	NUM
ejpam-4989	37	6	√	√	NUM
ejpam-4989	37	7	19	19	NUM
ejpam-4989	37	8	+	+	CCONJ
ejpam-4989	37	9	3	3	NUM
ejpam-4989	37	10	√	√	NUM
ejpam-4989	37	11	33	33	NUM
ejpam-4989	37	12	+	+	CCONJ
ejpam-4989	37	13	3	3	NUM
ejpam-4989	37	14	√	√	NUM
ejpam-4989	37	15	19−	19−	NUM
ejpam-4989	37	16	3	3	NUM
ejpam-4989	37	17	√	√	PROPN
ejpam-4989	37	18	33	33	NUM
ejpam-4989	37	19	3	3	NUM
ejpam-4989	37	20	,	,	PUNCT
ejpam-4989	37	21	η2	η2	ADJ
ejpam-4989	37	22	=	=	SYM
ejpam-4989	37	23	1	1	NUM
ejpam-4989	37	24	+	+	NUM
ejpam-4989	37	25	ω	ω	NUM
ejpam-4989	37	26	3	3	NUM
ejpam-4989	37	27	√	√	PROPN
ejpam-4989	37	28	19	19	NUM
ejpam-4989	37	29	+	+	CCONJ
ejpam-4989	37	30	3	3	NUM
ejpam-4989	37	31	√	√	NUM
ejpam-4989	37	32	33	33	NUM
ejpam-4989	37	33	+	+	CCONJ
ejpam-4989	37	34	ω2	ω2	ADJ
ejpam-4989	37	35	3	3	NUM
ejpam-4989	37	36	√	√	NOUN
ejpam-4989	37	37	19−	19−	NUM
ejpam-4989	37	38	3	3	NUM
ejpam-4989	37	39	√	√	PROPN
ejpam-4989	37	40	33	33	NUM
ejpam-4989	37	41	3	3	NUM
ejpam-4989	37	42	,	,	PUNCT
ejpam-4989	37	43	η3	η3	NOUN
ejpam-4989	37	44	=	=	PUNCT
ejpam-4989	37	45	1	1	NUM
ejpam-4989	37	46	+	+	CCONJ
ejpam-4989	37	47	ω2	ω2	ADJ
ejpam-4989	37	48	3	3	NUM
ejpam-4989	37	49	√	√	NUM
ejpam-4989	37	50	19	19	NUM
ejpam-4989	37	51	+	+	CCONJ
ejpam-4989	37	52	3	3	NUM
ejpam-4989	37	53	√	√	NUM
ejpam-4989	37	54	33	33	NUM
ejpam-4989	37	55	+	+	NUM
ejpam-4989	37	56	ω	ω	NUM
ejpam-4989	37	57	3	3	NUM
ejpam-4989	37	58	√	√	PROPN
ejpam-4989	37	59	19−	19−	NUM
ejpam-4989	37	60	3	3	NUM
ejpam-4989	37	61	√	√	PROPN
ejpam-4989	37	62	33	33	NUM
ejpam-4989	37	63	3	3	NUM
ejpam-4989	37	64	,	,	PUNCT
ejpam-4989	37	65	where	where	SCONJ
ejpam-4989	37	66	ω	ω	NOUN
ejpam-4989	37	67	=	=	SYM
ejpam-4989	37	68	−1+i	−1+i	NOUN
ejpam-4989	37	69	√	√	NOUN
ejpam-4989	37	70	3	3	NUM
ejpam-4989	37	71	2	2	NUM
ejpam-4989	37	72	.	.	PUNCT
ejpam-4989	38	1	spickerman	spickerman	ADJ
ejpam-4989	38	2	[	[	X
ejpam-4989	38	3	12	12	NUM
ejpam-4989	38	4	]	]	PUNCT
ejpam-4989	38	5	found	find	VERB
ejpam-4989	38	6	the	the	DET
ejpam-4989	38	7	binet	binet	NOUN
ejpam-4989	38	8	formula	formula	NOUN
ejpam-4989	38	9	of	of	ADP
ejpam-4989	38	10	the	the	DET
ejpam-4989	38	11	tribonacci	tribonacci	PROPN
ejpam-4989	38	12	numbers	number	NOUN
ejpam-4989	38	13	as	as	ADP
ejpam-4989	38	14	tm	tm	NOUN
ejpam-4989	38	15	=	=	NOUN
ejpam-4989	38	16	ηm+1	ηm+1	PROPN
ejpam-4989	38	17	1	1	NUM
ejpam-4989	38	18	(	(	PUNCT
ejpam-4989	38	19	η1	η1	NOUN
ejpam-4989	38	20	−	−	PROPN
ejpam-4989	38	21	η2)(η1	η2)(η1	NOUN
ejpam-4989	39	1	−	−	PROPN
ejpam-4989	39	2	η3	η3	NOUN
ejpam-4989	39	3	)	)	PUNCT
ejpam-4989	40	1	+	+	CCONJ
ejpam-4989	40	2	ηm+1	ηm+1	PRON
ejpam-4989	40	3	2	2	NUM
ejpam-4989	40	4	(	(	PUNCT
ejpam-4989	40	5	η2	η2	ADJ
ejpam-4989	40	6	−	−	PROPN
ejpam-4989	40	7	η1)(η2	η1)(η2	NOUN
ejpam-4989	40	8	−	−	PROPN
ejpam-4989	40	9	η3	η3	PROPN
ejpam-4989	40	10	)	)	PUNCT
ejpam-4989	41	1	+	+	CCONJ
ejpam-4989	41	2	ηm+1	ηm+1	PRON
ejpam-4989	41	3	3	3	NUM
ejpam-4989	41	4	(	(	PUNCT
ejpam-4989	41	5	η3	η3	PROPN
ejpam-4989	41	6	−	−	PROPN
ejpam-4989	41	7	η1)(η3	η1)(η3	NOUN
ejpam-4989	41	8	−	−	PROPN
ejpam-4989	41	9	η2	η2	PROPN
ejpam-4989	41	10	)	)	PUNCT
ejpam-4989	41	11	,	,	PUNCT
ejpam-4989	41	12	for	for	ADP
ejpam-4989	41	13	all	all	DET
ejpam-4989	41	14	m	m	NOUN
ejpam-4989	41	15	≥	≥	NOUN
ejpam-4989	41	16	0	0	NUM
ejpam-4989	41	17	.	.	PUNCT
ejpam-4989	42	1	(	(	PUNCT
ejpam-4989	42	2	3	3	X
ejpam-4989	42	3	)	)	PUNCT
ejpam-4989	42	4	the	the	DET
ejpam-4989	42	5	generating	generate	VERB
ejpam-4989	42	6	function	function	NOUN
ejpam-4989	42	7	of	of	ADP
ejpam-4989	42	8	the	the	DET
ejpam-4989	42	9	tribonacci	tribonacci	PROPN
ejpam-4989	42	10	sequence	sequence	NOUN
ejpam-4989	42	11	is	be	AUX
ejpam-4989	42	12	:	:	PUNCT
ejpam-4989	42	13	g(x	g(x	X
ejpam-4989	42	14	)	)	PUNCT
ejpam-4989	43	1	=	=	PUNCT
ejpam-4989	43	2	x	x	SYM
ejpam-4989	43	3	1−	1−	NUM
ejpam-4989	43	4	x−	x−	PROPN
ejpam-4989	43	5	x2	x2	PROPN
ejpam-4989	44	1	−	−	NOUN
ejpam-4989	44	2	x3	x3	NOUN
ejpam-4989	44	3	=	=	SYM
ejpam-4989	45	1	∞∑	∞∑	NUM
ejpam-4989	45	2	m=0	m=0	PROPN
ejpam-4989	45	3	tmx	tmx	PROPN
ejpam-4989	45	4	m.	m.	NOUN
ejpam-4989	45	5	note	note	NOUN
ejpam-4989	45	6	that	that	SCONJ
ejpam-4989	45	7	we	we	PRON
ejpam-4989	45	8	have	have	VERB
ejpam-4989	45	9	the	the	DET
ejpam-4989	45	10	following	follow	VERB
ejpam-4989	45	11	identities	identity	NOUN
ejpam-4989	45	12	η1	η1	NOUN
ejpam-4989	45	13	+	+	CCONJ
ejpam-4989	45	14	η2	η2	ADJ
ejpam-4989	45	15	+	+	CCONJ
ejpam-4989	45	16	η3	η3	NOUN
ejpam-4989	45	17	=	=	SYM
ejpam-4989	45	18	1	1	NUM
ejpam-4989	45	19	,	,	PUNCT
ejpam-4989	45	20	η1η2	η1η2	VERB
ejpam-4989	45	21	+	+	PUNCT
ejpam-4989	45	22	η2η3	η2η3	ADJ
ejpam-4989	45	23	+	+	X
ejpam-4989	45	24	η1η3	η1η3	NOUN
ejpam-4989	45	25	=	=	SYM
ejpam-4989	45	26	−1	−1	NOUN
ejpam-4989	45	27	,	,	PUNCT
ejpam-4989	45	28	η1η2η3	η1η2η3	NOUN
ejpam-4989	45	29	=	=	SYM
ejpam-4989	45	30	1	1	X
ejpam-4989	45	31	.	.	PUNCT
ejpam-4989	45	32	h.	h.	PROPN
ejpam-4989	45	33	s.	s.	PROPN
ejpam-4989	45	34	taher	taher	PROPN
ejpam-4989	45	35	,	,	PUNCT
ejpam-4989	45	36	s.	s.	PROPN
ejpam-4989	45	37	k.	k.	PROPN
ejpam-4989	45	38	dash	dash	NOUN
ejpam-4989	45	39	/	/	SYM
ejpam-4989	45	40	eur	eur	NOUN
ejpam-4989	45	41	.	.	PUNCT
ejpam-4989	46	1	j.	j.	PROPN
ejpam-4989	46	2	pure	pure	PROPN
ejpam-4989	46	3	appl	appl	PROPN
ejpam-4989	46	4	.	.	PROPN
ejpam-4989	46	5	math	math	PROPN
ejpam-4989	46	6	,	,	PUNCT
ejpam-4989	46	7	17	17	NUM
ejpam-4989	46	8	(	(	PUNCT
ejpam-4989	46	9	1	1	NUM
ejpam-4989	46	10	)	)	PUNCT
ejpam-4989	46	11	(	(	PUNCT
ejpam-4989	46	12	2024	2024	NUM
ejpam-4989	46	13	)	)	PUNCT
ejpam-4989	46	14	,	,	PUNCT
ejpam-4989	46	15	135	135	NUM
ejpam-4989	46	16	-	-	SYM
ejpam-4989	46	17	146	146	NUM
ejpam-4989	46	18	137	137	NUM
ejpam-4989	46	19	furthermore	furthermore	ADV
ejpam-4989	46	20	,	,	PUNCT
ejpam-4989	46	21	dresden	dresden	PROPN
ejpam-4989	46	22	and	and	CCONJ
ejpam-4989	46	23	du	du	PROPN
ejpam-4989	47	1	[	[	X
ejpam-4989	47	2	6	6	NUM
ejpam-4989	47	3	]	]	PUNCT
ejpam-4989	47	4	presented	present	VERB
ejpam-4989	47	5	a	a	DET
ejpam-4989	47	6	binet	binet	NOUN
ejpam-4989	47	7	-	-	PUNCT
ejpam-4989	47	8	style	style	NOUN
ejpam-4989	47	9	formula	formula	NOUN
ejpam-4989	47	10	for	for	ADP
ejpam-4989	47	11	generating	generate	VERB
ejpam-4989	47	12	k	k	ADJ
ejpam-4989	47	13	-	-	ADJ
ejpam-4989	47	14	generalized	generalize	VERB
ejpam-4989	47	15	fibonacci	fibonacci	NOUN
ejpam-4989	47	16	numbers	number	NOUN
ejpam-4989	47	17	.	.	PUNCT
ejpam-4989	48	1	if	if	SCONJ
ejpam-4989	48	2	k	k	PROPN
ejpam-4989	48	3	=	=	SYM
ejpam-4989	48	4	3	3	NUM
ejpam-4989	48	5	,	,	PUNCT
ejpam-4989	48	6	it	it	PRON
ejpam-4989	48	7	follows	follow	VERB
ejpam-4989	48	8	that	that	SCONJ
ejpam-4989	48	9	:	:	PUNCT
ejpam-4989	48	10	tm	tm	NOUN
ejpam-4989	48	11	=	=	SYM
ejpam-4989	48	12	(	(	PUNCT
ejpam-4989	48	13	η1	η1	NOUN
ejpam-4989	48	14	−	−	PROPN
ejpam-4989	48	15	1)ηm−1	1)ηm−1	PROPN
ejpam-4989	48	16	1	1	NUM
ejpam-4989	48	17	2	2	NUM
ejpam-4989	48	18	+	+	NUM
ejpam-4989	48	19	4(η1	4(η1	NOUN
ejpam-4989	48	20	−	−	NOUN
ejpam-4989	48	21	2	2	NUM
ejpam-4989	48	22	)	)	PUNCT
ejpam-4989	48	23	+	+	CCONJ
ejpam-4989	48	24	(	(	PUNCT
ejpam-4989	48	25	η2	η2	ADJ
ejpam-4989	48	26	−	−	PROPN
ejpam-4989	48	27	1)ηm−1	1)ηm−1	PROPN
ejpam-4989	48	28	2	2	NUM
ejpam-4989	48	29	2	2	NUM
ejpam-4989	48	30	+	+	NUM
ejpam-4989	48	31	4(η2	4(η2	NUM
ejpam-4989	48	32	−	−	NOUN
ejpam-4989	48	33	2	2	NUM
ejpam-4989	48	34	)	)	PUNCT
ejpam-4989	49	1	+	+	CCONJ
ejpam-4989	49	2	(	(	PUNCT
ejpam-4989	49	3	η3	η3	NOUN
ejpam-4989	49	4	−	−	PROPN
ejpam-4989	49	5	1)ηm−1	1)ηm−1	PROPN
ejpam-4989	49	6	3	3	NUM
ejpam-4989	49	7	2	2	NUM
ejpam-4989	49	8	+	+	CCONJ
ejpam-4989	49	9	4(η3	4(η3	NUM
ejpam-4989	49	10	−	−	NOUN
ejpam-4989	49	11	2	2	NUM
ejpam-4989	49	12	)	)	PUNCT
ejpam-4989	49	13	,	,	PUNCT
ejpam-4989	49	14	for	for	ADP
ejpam-4989	49	15	all	all	DET
ejpam-4989	49	16	m	m	NOUN
ejpam-4989	49	17	≥	≥	NOUN
ejpam-4989	49	18	0	0	NUM
ejpam-4989	49	19	.	.	PUNCT
ejpam-4989	50	1	(	(	PUNCT
ejpam-4989	50	2	4	4	X
ejpam-4989	50	3	)	)	PUNCT
ejpam-4989	50	4	moreover	moreover	ADV
ejpam-4989	50	5	,	,	PUNCT
ejpam-4989	50	6	dresden	dresden	PROPN
ejpam-4989	50	7	and	and	CCONJ
ejpam-4989	50	8	du	du	PROPN
ejpam-4989	51	1	[	[	X
ejpam-4989	51	2	6	6	NUM
ejpam-4989	51	3	,	,	PUNCT
ejpam-4989	51	4	lemma	lemma	PROPN
ejpam-4989	51	5	5	5	NUM
ejpam-4989	51	6	]	]	PUNCT
ejpam-4989	51	7	found	find	VERB
ejpam-4989	51	8	that	that	SCONJ
ejpam-4989	51	9	the	the	DET
ejpam-4989	51	10	tribonacci	tribonacci	PROPN
ejpam-4989	51	11	numbers	number	NOUN
ejpam-4989	51	12	can	can	AUX
ejpam-4989	51	13	be	be	AUX
ejpam-4989	51	14	written	write	VERB
ejpam-4989	51	15	as	as	ADP
ejpam-4989	51	16	tm	tm	PROPN
ejpam-4989	51	17	=	=	PROPN
ejpam-4989	51	18	cηm−1	cηm−1	PROPN
ejpam-4989	51	19	1	1	NUM
ejpam-4989	51	20	+	+	CCONJ
ejpam-4989	51	21	dm	dm	VERB
ejpam-4989	51	22	with	with	ADP
ejpam-4989	51	23	|dm|	|dm|	NOUN
ejpam-4989	51	24	<	<	X
ejpam-4989	51	25	1	1	NUM
ejpam-4989	51	26	2	2	NUM
ejpam-4989	51	27	,	,	PUNCT
ejpam-4989	51	28	for	for	ADP
ejpam-4989	51	29	all	all	DET
ejpam-4989	51	30	m	m	PROPN
ejpam-4989	51	31	≥	≥	NOUN
ejpam-4989	51	32	1	1	NUM
ejpam-4989	51	33	,	,	PUNCT
ejpam-4989	51	34	(	(	PUNCT
ejpam-4989	51	35	5	5	NUM
ejpam-4989	51	36	)	)	PUNCT
ejpam-4989	51	37	where	where	SCONJ
ejpam-4989	51	38	c	c	NOUN
ejpam-4989	51	39	=	=	SYM
ejpam-4989	51	40	(	(	PUNCT
ejpam-4989	51	41	η1	η1	NOUN
ejpam-4989	51	42	−	−	PROPN
ejpam-4989	51	43	1)/(4η1	1)/(4η1	NUM
ejpam-4989	51	44	−	−	NOUN
ejpam-4989	51	45	6	6	NUM
ejpam-4989	51	46	)	)	PUNCT
ejpam-4989	51	47	≈	≈	PROPN
ejpam-4989	51	48	0.61	0.61	NUM
ejpam-4989	51	49	.	.	PUNCT
ejpam-4989	52	1	for	for	ADP
ejpam-4989	52	2	m	m	PROPN
ejpam-4989	52	3	≥	≥	NOUN
ejpam-4989	52	4	1	1	NUM
ejpam-4989	52	5	,	,	PUNCT
ejpam-4989	52	6	the	the	DET
ejpam-4989	52	7	inequality	inequality	NOUN
ejpam-4989	52	8	ηm−2	ηm−2	ADJ
ejpam-4989	52	9	1	1	NUM
ejpam-4989	52	10	≤	≤	NUM
ejpam-4989	52	11	tm	tm	PRON
ejpam-4989	52	12	≤	≤	ADJ
ejpam-4989	52	13	ηm−1	ηm−1	PROPN
ejpam-4989	52	14	1	1	NUM
ejpam-4989	52	15	,	,	PUNCT
ejpam-4989	52	16	(	(	PUNCT
ejpam-4989	52	17	6	6	X
ejpam-4989	52	18	)	)	PUNCT
ejpam-4989	52	19	hold	hold	NOUN
ejpam-4989	52	20	.	.	PUNCT
ejpam-4989	53	1	2.2	2.2	NUM
ejpam-4989	53	2	.	.	PUNCT
ejpam-4989	53	3	properties	property	NOUN
ejpam-4989	53	4	of	of	ADP
ejpam-4989	53	5	k−generalized	k−generalize	VERB
ejpam-4989	53	6	pell	pell	NOUN
ejpam-4989	53	7	sequence	sequence	NOUN
ejpam-4989	53	8	we	we	PRON
ejpam-4989	53	9	are	be	AUX
ejpam-4989	53	10	aware	aware	ADJ
ejpam-4989	53	11	that	that	SCONJ
ejpam-4989	53	12	the	the	DET
ejpam-4989	53	13	characteristic	characteristic	ADJ
ejpam-4989	53	14	polynomial	polynomial	NOUN
ejpam-4989	53	15	of	of	ADP
ejpam-4989	53	16	the	the	DET
ejpam-4989	53	17	k	k	ADV
ejpam-4989	53	18	-	-	ADJ
ejpam-4989	53	19	generalized	generalize	VERB
ejpam-4989	53	20	pell	pell	NOUN
ejpam-4989	53	21	sequence	sequence	NOUN
ejpam-4989	53	22	is	be	AUX
ejpam-4989	53	23	ψk(x	ψk(x	NOUN
ejpam-4989	53	24	)	)	PUNCT
ejpam-4989	54	1	=	=	SYM
ejpam-4989	54	2	xk	xk	PROPN
ejpam-4989	55	1	−	−	PROPN
ejpam-4989	55	2	2xk−1	2xk−1	PROPN
ejpam-4989	55	3	−	−	PROPN
ejpam-4989	56	1	xk−2	xk−2	PROPN
ejpam-4989	56	2	−	−	PROPN
ejpam-4989	56	3	...	...	PUNCT
ejpam-4989	56	4	−	−	PROPN
ejpam-4989	56	5	x−	x−	PROPN
ejpam-4989	56	6	1	1	X
ejpam-4989	56	7	.	.	X
ejpam-4989	57	1	bravo	bravo	PROPN
ejpam-4989	57	2	,	,	PUNCT
ejpam-4989	57	3	herrera	herrera	NOUN
ejpam-4989	57	4	and	and	CCONJ
ejpam-4989	57	5	luca	luca	PROPN
ejpam-4989	58	1	[	[	X
ejpam-4989	58	2	4	4	NUM
ejpam-4989	58	3	]	]	PUNCT
ejpam-4989	58	4	showed	show	VERB
ejpam-4989	58	5	that	that	SCONJ
ejpam-4989	58	6	ψk(x	ψk(x	NOUN
ejpam-4989	58	7	)	)	PUNCT
ejpam-4989	58	8	is	be	AUX
ejpam-4989	58	9	irreducible	irreducible	ADJ
ejpam-4989	58	10	over	over	ADP
ejpam-4989	58	11	q[x	q[x	PROPN
ejpam-4989	58	12	]	]	PUNCT
ejpam-4989	58	13	and	and	CCONJ
ejpam-4989	58	14	has	have	VERB
ejpam-4989	58	15	one	one	NUM
ejpam-4989	58	16	positive	positive	ADJ
ejpam-4989	58	17	real	real	ADJ
ejpam-4989	58	18	root	root	NOUN
ejpam-4989	58	19	α(k	α(k	NOUN
ejpam-4989	58	20	)	)	PUNCT
ejpam-4989	58	21	outside	outside	ADP
ejpam-4989	58	22	the	the	DET
ejpam-4989	58	23	unit	unit	NOUN
ejpam-4989	58	24	circle	circle	NOUN
ejpam-4989	58	25	.	.	PUNCT
ejpam-4989	59	1	the	the	DET
ejpam-4989	59	2	other	other	ADJ
ejpam-4989	59	3	roots	root	NOUN
ejpam-4989	59	4	were	be	AUX
ejpam-4989	59	5	inside	inside	ADP
ejpam-4989	59	6	the	the	DET
ejpam-4989	59	7	unit	unit	NOUN
ejpam-4989	59	8	circle	circle	NOUN
ejpam-4989	59	9	.	.	PUNCT
ejpam-4989	60	1	moreover	moreover	ADV
ejpam-4989	60	2	,	,	PUNCT
ejpam-4989	60	3	they	they	PRON
ejpam-4989	60	4	showed	show	VERB
ejpam-4989	60	5	the	the	DET
ejpam-4989	60	6	following	following	NOUN
ejpam-4989	60	7	:	:	PUNCT
ejpam-4989	60	8	ϕ2(1−	ϕ2(1−	PROPN
ejpam-4989	60	9	ϕ−k	ϕ−k	PROPN
ejpam-4989	60	10	)	)	PUNCT
ejpam-4989	60	11	<	<	X
ejpam-4989	60	12	α(k	α(k	NOUN
ejpam-4989	60	13	)	)	PUNCT
ejpam-4989	60	14	<	<	X
ejpam-4989	60	15	ϕ2	ϕ2	ADV
ejpam-4989	60	16	,	,	PUNCT
ejpam-4989	60	17	for	for	ADP
ejpam-4989	60	18	all	all	DET
ejpam-4989	60	19	k	k	PROPN
ejpam-4989	60	20	≥	≥	NUM
ejpam-4989	60	21	2	2	NUM
ejpam-4989	60	22	,	,	PUNCT
ejpam-4989	60	23	(	(	PUNCT
ejpam-4989	60	24	7	7	X
ejpam-4989	60	25	)	)	PUNCT
ejpam-4989	60	26	where	where	SCONJ
ejpam-4989	60	27	ϕ	ϕ	NOUN
ejpam-4989	60	28	=	=	X
ejpam-4989	60	29	(	(	PUNCT
ejpam-4989	60	30	(	(	PUNCT
ejpam-4989	60	31	1	1	NUM
ejpam-4989	60	32	+	+	CCONJ
ejpam-4989	60	33	√	√	NUM
ejpam-4989	60	34	5)/2	5)/2	NUM
ejpam-4989	60	35	)	)	PUNCT
ejpam-4989	60	36	.	.	PUNCT
ejpam-4989	61	1	to	to	PART
ejpam-4989	61	2	simplify	simplify	VERB
ejpam-4989	61	3	the	the	DET
ejpam-4989	61	4	notation	notation	NOUN
ejpam-4989	61	5	,	,	PUNCT
ejpam-4989	61	6	we	we	PRON
ejpam-4989	61	7	omit	omit	VERB
ejpam-4989	61	8	the	the	DET
ejpam-4989	61	9	dependence	dependence	NOUN
ejpam-4989	61	10	on	on	ADP
ejpam-4989	61	11	k	k	PROPN
ejpam-4989	61	12	of	of	ADP
ejpam-4989	61	13	α	α	PROPN
ejpam-4989	61	14	.	.	PUNCT
ejpam-4989	62	1	the	the	DET
ejpam-4989	62	2	authors	author	NOUN
ejpam-4989	62	3	found	find	VERB
ejpam-4989	62	4	that	that	SCONJ
ejpam-4989	62	5	the	the	DET
ejpam-4989	62	6	binet	binet	NOUN
ejpam-4989	62	7	formula	formula	NOUN
ejpam-4989	62	8	for	for	ADP
ejpam-4989	62	9	p	p	PROPN
ejpam-4989	62	10	(	(	PUNCT
ejpam-4989	62	11	k	k	NOUN
ejpam-4989	62	12	)	)	PUNCT
ejpam-4989	62	13	n	n	PRON
ejpam-4989	62	14	is	be	AUX
ejpam-4989	62	15	p	p	X
ejpam-4989	62	16	(	(	PUNCT
ejpam-4989	62	17	k	k	NOUN
ejpam-4989	62	18	)	)	PUNCT
ejpam-4989	63	1	n	n	NOUN
ejpam-4989	63	2	=	=	SYM
ejpam-4989	63	3	k∑	k∑	PROPN
ejpam-4989	63	4	i=1	i=1	PROPN
ejpam-4989	63	5	gk(αi)(αi	gk(αi)(αi	NOUN
ejpam-4989	63	6	)	)	PUNCT
ejpam-4989	63	7	n	n	CCONJ
ejpam-4989	63	8	,	,	PUNCT
ejpam-4989	63	9	(	(	PUNCT
ejpam-4989	63	10	8)	8)	NUM
ejpam-4989	63	11	where	where	SCONJ
ejpam-4989	63	12	ai	ai	NOUN
ejpam-4989	63	13	represents	represent	VERB
ejpam-4989	63	14	the	the	DET
ejpam-4989	63	15	root	root	NOUN
ejpam-4989	63	16	of	of	ADP
ejpam-4989	63	17	the	the	DET
ejpam-4989	63	18	characteristic	characteristic	ADJ
ejpam-4989	63	19	polynomial	polynomial	ADJ
ejpam-4989	63	20	ψk(x	ψk(x	NOUN
ejpam-4989	63	21	)	)	PUNCT
ejpam-4989	63	22	and	and	CCONJ
ejpam-4989	63	23	gk	gk	PROPN
ejpam-4989	63	24	is	be	AUX
ejpam-4989	63	25	given	give	VERB
ejpam-4989	63	26	by	by	ADP
ejpam-4989	63	27	gk(x	gk(x	PROPN
ejpam-4989	63	28	)	)	PUNCT
ejpam-4989	63	29	=	=	SYM
ejpam-4989	63	30	x−	x−	PROPN
ejpam-4989	63	31	1	1	NUM
ejpam-4989	63	32	(	(	PUNCT
ejpam-4989	63	33	k	k	PROPN
ejpam-4989	64	1	+	+	PUNCT
ejpam-4989	64	2	1)x2	1)x2	NUM
ejpam-4989	64	3	−	−	PROPN
ejpam-4989	64	4	3kx+	3kx+	NUM
ejpam-4989	64	5	k	k	NOUN
ejpam-4989	64	6	−	−	PROPN
ejpam-4989	64	7	1	1	NUM
ejpam-4989	64	8	,	,	PUNCT
ejpam-4989	64	9	for	for	ADP
ejpam-4989	64	10	all	all	DET
ejpam-4989	64	11	k	k	PROPN
ejpam-4989	64	12	≥	≥	NUM
ejpam-4989	64	13	2	2	NUM
ejpam-4989	64	14	.	.	X
ejpam-4989	64	15	bravo	bravo	PROPN
ejpam-4989	64	16	and	and	CCONJ
ejpam-4989	64	17	herrera	herrera	NOUN
ejpam-4989	64	18	[	[	X
ejpam-4989	64	19	2	2	NUM
ejpam-4989	64	20	,	,	PUNCT
ejpam-4989	64	21	lemma	lemma	PROPN
ejpam-4989	64	22	1	1	NUM
ejpam-4989	64	23	]	]	PUNCT
ejpam-4989	64	24	proved	prove	VERB
ejpam-4989	64	25	that	that	SCONJ
ejpam-4989	64	26	0.276	0.276	NUM
ejpam-4989	64	27	<	<	X
ejpam-4989	64	28	gk(α	gk(α	PUNCT
ejpam-4989	64	29	)	)	PUNCT
ejpam-4989	64	30	<	<	X
ejpam-4989	64	31	0.5	0.5	NUM
ejpam-4989	64	32	and	and	CCONJ
ejpam-4989	64	33	|gk(αi)|	|gk(αi)|	NOUN
ejpam-4989	64	34	<	<	X
ejpam-4989	64	35	1	1	NUM
ejpam-4989	64	36	,	,	PUNCT
ejpam-4989	64	37	2	2	NUM
ejpam-4989	64	38	≤	≤	NUM
ejpam-4989	64	39	i	i	NOUN
ejpam-4989	64	40	≤	≤	PUNCT
ejpam-4989	65	1	k	k	NOUN
ejpam-4989	65	2	,	,	PUNCT
ejpam-4989	65	3	where	where	SCONJ
ejpam-4989	65	4	gk(α	gk(α	PUNCT
ejpam-4989	65	5	)	)	PUNCT
ejpam-4989	65	6	is	be	AUX
ejpam-4989	65	7	not	not	PART
ejpam-4989	65	8	an	an	DET
ejpam-4989	65	9	algebraic	algebraic	ADJ
ejpam-4989	65	10	integer	integer	NOUN
ejpam-4989	65	11	.	.	PUNCT
ejpam-4989	66	1	furthermore	furthermore	ADV
ejpam-4989	66	2	,	,	PUNCT
ejpam-4989	66	3	they	they	PRON
ejpam-4989	66	4	proved	prove	VERB
ejpam-4989	66	5	that	that	SCONJ
ejpam-4989	66	6	the	the	DET
ejpam-4989	66	7	logarithmic	logarithmic	ADJ
ejpam-4989	66	8	height	height	NOUN
ejpam-4989	66	9	of	of	ADP
ejpam-4989	66	10	gk	gk	PROPN
ejpam-4989	66	11	is	be	AUX
ejpam-4989	66	12	h(gk	h(gk	NOUN
ejpam-4989	66	13	)	)	PUNCT
ejpam-4989	66	14	<	<	X
ejpam-4989	66	15	4k	4k	X
ejpam-4989	66	16	log(ϕ	log(ϕ	X
ejpam-4989	66	17	)	)	PUNCT
ejpam-4989	66	18	+	+	CCONJ
ejpam-4989	67	1	k	k	PROPN
ejpam-4989	67	2	log(k	log(k	PROPN
ejpam-4989	67	3	+	+	PROPN
ejpam-4989	67	4	1	1	NUM
ejpam-4989	67	5	)	)	PUNCT
ejpam-4989	67	6	,	,	PUNCT
ejpam-4989	67	7	for	for	ADP
ejpam-4989	67	8	all	all	DET
ejpam-4989	67	9	k	k	PROPN
ejpam-4989	67	10	≥	≥	NUM
ejpam-4989	67	11	2	2	NUM
ejpam-4989	67	12	.	.	PUNCT
ejpam-4989	68	1	(	(	PUNCT
ejpam-4989	68	2	9	9	X
ejpam-4989	68	3	)	)	PUNCT
ejpam-4989	68	4	h.	h.	PROPN
ejpam-4989	68	5	s.	s.	PROPN
ejpam-4989	68	6	taher	taher	PROPN
ejpam-4989	68	7	,	,	PUNCT
ejpam-4989	68	8	s.	s.	PROPN
ejpam-4989	68	9	k.	k.	PROPN
ejpam-4989	68	10	dash	dash	NOUN
ejpam-4989	68	11	/	/	SYM
ejpam-4989	68	12	eur	eur	NOUN
ejpam-4989	68	13	.	.	PUNCT
ejpam-4989	69	1	j.	j.	PROPN
ejpam-4989	69	2	pure	pure	PROPN
ejpam-4989	69	3	appl	appl	PROPN
ejpam-4989	69	4	.	.	PROPN
ejpam-4989	69	5	math	math	PROPN
ejpam-4989	69	6	,	,	PUNCT
ejpam-4989	69	7	17	17	NUM
ejpam-4989	69	8	(	(	PUNCT
ejpam-4989	69	9	1	1	NUM
ejpam-4989	69	10	)	)	PUNCT
ejpam-4989	69	11	(	(	PUNCT
ejpam-4989	69	12	2024	2024	NUM
ejpam-4989	69	13	)	)	PUNCT
ejpam-4989	69	14	,	,	PUNCT
ejpam-4989	69	15	135	135	NUM
ejpam-4989	69	16	-	-	SYM
ejpam-4989	69	17	146	146	NUM
ejpam-4989	69	18	138	138	NUM
ejpam-4989	69	19	according	accord	VERB
ejpam-4989	69	20	to	to	ADP
ejpam-4989	69	21	the	the	DET
ejpam-4989	69	22	above	above	ADJ
ejpam-4989	69	23	notation	notation	NOUN
ejpam-4989	69	24	,	,	PUNCT
ejpam-4989	69	25	bravo	bravo	NOUN
ejpam-4989	69	26	,	,	PUNCT
ejpam-4989	69	27	herrera	herrera	NOUN
ejpam-4989	69	28	and	and	CCONJ
ejpam-4989	69	29	luca	luca	PROPN
ejpam-4989	70	1	[	[	X
ejpam-4989	70	2	4	4	NUM
ejpam-4989	70	3	]	]	PUNCT
ejpam-4989	70	4	showed	show	VERB
ejpam-4989	70	5	that	that	SCONJ
ejpam-4989	70	6	formula	formula	NOUN
ejpam-4989	70	7	(	(	PUNCT
ejpam-4989	70	8	8)	8)	NUM
ejpam-4989	70	9	,	,	PUNCT
ejpam-4989	70	10	given	give	VERB
ejpam-4989	70	11	by	by	ADP
ejpam-4989	70	12	the	the	DET
ejpam-4989	70	13	approximation∣∣∣p	approximation∣∣∣p	PROPN
ejpam-4989	70	14	(	(	PUNCT
ejpam-4989	70	15	k	k	NOUN
ejpam-4989	70	16	)	)	PUNCT
ejpam-4989	70	17	n	n	CCONJ
ejpam-4989	70	18	−	−	PROPN
ejpam-4989	70	19	gk(α)α	gk(α)α	ADP
ejpam-4989	70	20	n	n	CCONJ
ejpam-4989	70	21	∣∣∣	∣∣∣	NOUN
ejpam-4989	70	22	<	<	X
ejpam-4989	70	23	1	1	NUM
ejpam-4989	70	24	2	2	NUM
ejpam-4989	70	25	,	,	PUNCT
ejpam-4989	70	26	for	for	ADP
ejpam-4989	70	27	all	all	DET
ejpam-4989	70	28	n	n	DET
ejpam-4989	70	29	≥	≥	NOUN
ejpam-4989	70	30	2−	2−	NUM
ejpam-4989	70	31	k.	k.	NOUN
ejpam-4989	70	32	therefore	therefore	ADV
ejpam-4989	70	33	,	,	PUNCT
ejpam-4989	70	34	for	for	ADP
ejpam-4989	70	35	n	n	PRON
ejpam-4989	70	36	≥	≥	NOUN
ejpam-4989	70	37	1	1	NUM
ejpam-4989	70	38	and	and	CCONJ
ejpam-4989	70	39	k	k	PROPN
ejpam-4989	70	40	≥	≥	NUM
ejpam-4989	70	41	2	2	NUM
ejpam-4989	70	42	,	,	PUNCT
ejpam-4989	70	43	we	we	PRON
ejpam-4989	70	44	have	have	VERB
ejpam-4989	70	45	p	p	NOUN
ejpam-4989	70	46	(	(	PUNCT
ejpam-4989	70	47	k	k	NOUN
ejpam-4989	70	48	)	)	PUNCT
ejpam-4989	70	49	n	n	NOUN
ejpam-4989	70	50	=	=	SYM
ejpam-4989	70	51	gk(α)α	gk(α)α	PROPN
ejpam-4989	70	52	n	n	PROPN
ejpam-4989	70	53	+	+	NUM
ejpam-4989	70	54	ek(n	ek(n	NOUN
ejpam-4989	70	55	)	)	PUNCT
ejpam-4989	70	56	,	,	PUNCT
ejpam-4989	70	57	where	where	SCONJ
ejpam-4989	70	58	|ek(n)|	|ek(n)|	NOUN
ejpam-4989	70	59	≤	≤	NOUN
ejpam-4989	70	60	1	1	NUM
ejpam-4989	70	61	2	2	NUM
ejpam-4989	70	62	.	.	PUNCT
ejpam-4989	71	1	(	(	PUNCT
ejpam-4989	71	2	10	10	NUM
ejpam-4989	71	3	)	)	PUNCT
ejpam-4989	71	4	moreover	moreover	ADV
ejpam-4989	71	5	,	,	PUNCT
ejpam-4989	71	6	the	the	DET
ejpam-4989	71	7	inequality	inequality	NOUN
ejpam-4989	71	8	αn−2	αn−2	NOUN
ejpam-4989	71	9	≤	≤	ADJ
ejpam-4989	72	1	p	p	NOUN
ejpam-4989	72	2	(	(	PUNCT
ejpam-4989	72	3	k	k	NOUN
ejpam-4989	72	4	)	)	PUNCT
ejpam-4989	72	5	n	n	PRON
ejpam-4989	72	6	≤	≤	NOUN
ejpam-4989	72	7	αn−1	αn−1	ADJ
ejpam-4989	72	8	(	(	PUNCT
ejpam-4989	72	9	11	11	NUM
ejpam-4989	72	10	)	)	PUNCT
ejpam-4989	72	11	holds	hold	VERB
ejpam-4989	72	12	for	for	ADP
ejpam-4989	72	13	all	all	PRON
ejpam-4989	72	14	n	n	PRON
ejpam-4989	72	15	≥	≥	NOUN
ejpam-4989	72	16	1	1	NUM
ejpam-4989	72	17	and	and	CCONJ
ejpam-4989	72	18	k	k	PROPN
ejpam-4989	72	19	≥	≥	NUM
ejpam-4989	72	20	2	2	NUM
ejpam-4989	72	21	.	.	PUNCT
ejpam-4989	73	1	lemma	lemma	PROPN
ejpam-4989	73	2	1	1	NUM
ejpam-4989	73	3	.	.	PUNCT
ejpam-4989	74	1	(	(	PUNCT
ejpam-4989	74	2	[	[	X
ejpam-4989	74	3	2	2	NUM
ejpam-4989	74	4	,	,	PUNCT
ejpam-4989	74	5	lemma	lemma	PROPN
ejpam-4989	74	6	2	2	NUM
ejpam-4989	74	7	]	]	PUNCT
ejpam-4989	74	8	)	)	PUNCT
ejpam-4989	74	9	if	if	SCONJ
ejpam-4989	74	10	k	k	PROPN
ejpam-4989	74	11	≥	≥	VERB
ejpam-4989	74	12	30	30	NUM
ejpam-4989	74	13	and	and	CCONJ
ejpam-4989	74	14	n	n	PRON
ejpam-4989	74	15	≥	≥	NOUN
ejpam-4989	74	16	1	1	NUM
ejpam-4989	74	17	are	be	AUX
ejpam-4989	74	18	integers	integer	NOUN
ejpam-4989	74	19	satisfying	satisfy	VERB
ejpam-4989	74	20	n	n	CCONJ
ejpam-4989	74	21	<	<	X
ejpam-4989	74	22	ϕk/2	ϕk/2	X
ejpam-4989	74	23	,	,	PUNCT
ejpam-4989	74	24	then	then	ADV
ejpam-4989	74	25	gk(α)α	gk(α)α	ADP
ejpam-4989	74	26	n	n	PROPN
ejpam-4989	75	1	=	=	SYM
ejpam-4989	75	2	ϕ2n	ϕ2n	PROPN
ejpam-4989	76	1	ϕ+	ϕ+	INTJ
ejpam-4989	76	2	2	2	NUM
ejpam-4989	76	3	(	(	PUNCT
ejpam-4989	76	4	1	1	NUM
ejpam-4989	76	5	+	+	NUM
ejpam-4989	76	6	ζ	ζ	NOUN
ejpam-4989	76	7	)	)	PUNCT
ejpam-4989	76	8	,	,	PUNCT
ejpam-4989	76	9	where	where	SCONJ
ejpam-4989	76	10	|ζ|	|ζ|	NOUN
ejpam-4989	76	11	<	<	X
ejpam-4989	76	12	4	4	NUM
ejpam-4989	76	13	ϕk/2	ϕk/2	NOUN
ejpam-4989	76	14	,	,	PUNCT
ejpam-4989	76	15	ϕ	ϕ	X
ejpam-4989	76	16	=	=	SYM
ejpam-4989	76	17	1	1	NUM
ejpam-4989	76	18	+	+	CCONJ
ejpam-4989	76	19	√	√	NUM
ejpam-4989	76	20	5	5	NUM
ejpam-4989	76	21	2	2	NUM
ejpam-4989	76	22	.	.	PUNCT
ejpam-4989	77	1	(	(	PUNCT
ejpam-4989	77	2	12	12	NUM
ejpam-4989	77	3	)	)	PUNCT
ejpam-4989	77	4	lemma	lemma	PROPN
ejpam-4989	77	5	2	2	NUM
ejpam-4989	77	6	.	.	PUNCT
ejpam-4989	78	1	(	(	PUNCT
ejpam-4989	78	2	[	[	X
ejpam-4989	78	3	14	14	NUM
ejpam-4989	78	4	,	,	PUNCT
ejpam-4989	78	5	lemma	lemma	PROPN
ejpam-4989	78	6	2.2	2.2	NUM
ejpam-4989	78	7	]	]	PUNCT
ejpam-4989	78	8	)	)	PUNCT
ejpam-4989	78	9	let	let	VERB
ejpam-4989	78	10	v	v	NOUN
ejpam-4989	78	11	,	,	PUNCT
ejpam-4989	78	12	x	x	SYM
ejpam-4989	78	13	∈	∈	NOUN
ejpam-4989	78	14	r	r	NOUN
ejpam-4989	78	15	and	and	CCONJ
ejpam-4989	78	16	0	0	NUM
ejpam-4989	78	17	<	<	X
ejpam-4989	78	18	v	v	X
ejpam-4989	78	19	<	<	X
ejpam-4989	78	20	1	1	NUM
ejpam-4989	78	21	.	.	PUNCT
ejpam-4989	79	1	if	if	SCONJ
ejpam-4989	79	2	|x|	|x|	PROPN
ejpam-4989	79	3	<	<	X
ejpam-4989	79	4	v	v	PROPN
ejpam-4989	79	5	,	,	PUNCT
ejpam-4989	79	6	then	then	ADV
ejpam-4989	79	7	|	|	ADV
ejpam-4989	79	8	log(1	log(1	VERB
ejpam-4989	79	9	+	+	CCONJ
ejpam-4989	80	1	x)|	x)|	X
ejpam-4989	80	2	<	<	X
ejpam-4989	80	3	−	−	X
ejpam-4989	80	4	log(1−	log(1−	PROPN
ejpam-4989	80	5	v	v	NOUN
ejpam-4989	80	6	)	)	PUNCT
ejpam-4989	80	7	v	v	ADP
ejpam-4989	80	8	|x|	|x|	PROPN
ejpam-4989	80	9	.	.	PROPN
ejpam-4989	81	1	2.3	2.3	NUM
ejpam-4989	81	2	.	.	PUNCT
ejpam-4989	82	1	linear	linear	ADJ
ejpam-4989	82	2	forms	form	NOUN
ejpam-4989	82	3	in	in	ADP
ejpam-4989	82	4	logarithms	logarithm	NOUN
ejpam-4989	82	5	let	let	VERB
ejpam-4989	82	6	γ	γ	NOUN
ejpam-4989	82	7	be	be	AUX
ejpam-4989	82	8	an	an	DET
ejpam-4989	82	9	algebraic	algebraic	ADJ
ejpam-4989	82	10	number	number	NOUN
ejpam-4989	82	11	of	of	ADP
ejpam-4989	82	12	degree	degree	NOUN
ejpam-4989	82	13	d	d	NOUN
ejpam-4989	82	14	with	with	ADP
ejpam-4989	82	15	minimal	minimal	ADJ
ejpam-4989	82	16	polynomial	polynomial	ADJ
ejpam-4989	82	17	c0x	c0x	NOUN
ejpam-4989	83	1	d	d	PROPN
ejpam-4989	83	2	+	+	CCONJ
ejpam-4989	83	3	c1x	c1x	NOUN
ejpam-4989	83	4	d−1	d−1	PROPN
ejpam-4989	83	5	+	+	PROPN
ejpam-4989	83	6	.	.	PUNCT
ejpam-4989	83	7	.	.	PUNCT
ejpam-4989	84	1	.+	.+	NOUN
ejpam-4989	84	2	cd	cd	PROPN
ejpam-4989	84	3	=	=	SYM
ejpam-4989	84	4	c0	c0	PROPN
ejpam-4989	84	5	d∏	d∏	PROPN
ejpam-4989	84	6	i=1	i=1	PROPN
ejpam-4989	85	1	(	(	PUNCT
ejpam-4989	85	2	x−	x−	PROPN
ejpam-4989	85	3	γ(i	γ(i	NOUN
ejpam-4989	85	4	)	)	PUNCT
ejpam-4989	85	5	)	)	PUNCT
ejpam-4989	86	1	∈	∈	PROPN
ejpam-4989	86	2	z[x	z[x	NOUN
ejpam-4989	86	3	]	]	X
ejpam-4989	86	4	,	,	PUNCT
ejpam-4989	86	5	where	where	SCONJ
ejpam-4989	86	6	the	the	DET
ejpam-4989	86	7	γ(i	γ(i	NOUN
ejpam-4989	86	8	)	)	PUNCT
ejpam-4989	86	9	’s	’	VERB
ejpam-4989	86	10	are	be	AUX
ejpam-4989	86	11	conjugates	conjugate	NOUN
ejpam-4989	86	12	of	of	ADP
ejpam-4989	86	13	γ	γ	NOUN
ejpam-4989	86	14	,	,	PUNCT
ejpam-4989	86	15	and	and	CCONJ
ejpam-4989	86	16	the	the	DET
ejpam-4989	86	17	ci	ci	NOUN
ejpam-4989	86	18	’s	’s	PART
ejpam-4989	86	19	are	be	AUX
ejpam-4989	86	20	relative	relative	ADJ
ejpam-4989	86	21	primes	prime	NOUN
ejpam-4989	86	22	to	to	ADP
ejpam-4989	86	23	each	each	DET
ejpam-4989	86	24	other	other	ADJ
ejpam-4989	86	25	with	with	ADP
ejpam-4989	86	26	c0	c0	PROPN
ejpam-4989	86	27	>	>	X
ejpam-4989	87	1	0	0	X
ejpam-4989	87	2	.	.	PUNCT
ejpam-4989	88	1	then	then	ADV
ejpam-4989	88	2	the	the	DET
ejpam-4989	88	3	logarithmic	logarithmic	ADJ
ejpam-4989	88	4	height	height	NOUN
ejpam-4989	88	5	of	of	ADP
ejpam-4989	88	6	γ	γ	PROPN
ejpam-4989	88	7	is	be	AUX
ejpam-4989	88	8	given	give	VERB
ejpam-4989	88	9	by	by	ADP
ejpam-4989	88	10	h(γ	h(γ	NOUN
ejpam-4989	88	11	)	)	PUNCT
ejpam-4989	88	12	=	=	SYM
ejpam-4989	88	13	1	1	NUM
ejpam-4989	88	14	d	d	NOUN
ejpam-4989	88	15	(	(	PUNCT
ejpam-4989	88	16	log	log	NOUN
ejpam-4989	88	17	c0	c0	NOUN
ejpam-4989	88	18	+	+	CCONJ
ejpam-4989	88	19	d∑	d∑	PROPN
ejpam-4989	88	20	i=1	i=1	PROPN
ejpam-4989	88	21	log	log	NOUN
ejpam-4989	88	22	(	(	PUNCT
ejpam-4989	88	23	max	max	PROPN
ejpam-4989	88	24	{	{	PUNCT
ejpam-4989	88	25	∣∣∣γ(i)∣∣∣	∣∣∣γ(i)∣∣∣	NOUN
ejpam-4989	88	26	,	,	PUNCT
ejpam-4989	88	27	1	1	NUM
ejpam-4989	88	28	}	}	PUNCT
ejpam-4989	88	29	)	)	PUNCT
ejpam-4989	88	30	)	)	PUNCT
ejpam-4989	88	31	.	.	PUNCT
ejpam-4989	89	1	(	(	PUNCT
ejpam-4989	89	2	13	13	NUM
ejpam-4989	89	3	)	)	PUNCT
ejpam-4989	89	4	if	if	SCONJ
ejpam-4989	89	5	γ	γ	X
ejpam-4989	89	6	=	=	VERB
ejpam-4989	89	7	a	a	DET
ejpam-4989	89	8	b	b	NOUN
ejpam-4989	89	9	is	be	AUX
ejpam-4989	89	10	rational	rational	ADJ
ejpam-4989	89	11	number	number	NOUN
ejpam-4989	89	12	with	with	ADP
ejpam-4989	89	13	gcd(a	gcd(a	PROPN
ejpam-4989	89	14	,	,	PUNCT
ejpam-4989	89	15	b	b	NOUN
ejpam-4989	89	16	)	)	PUNCT
ejpam-4989	89	17	=	=	SYM
ejpam-4989	89	18	1	1	NUM
ejpam-4989	89	19	and	and	CCONJ
ejpam-4989	89	20	b	b	NOUN
ejpam-4989	89	21	>	>	X
ejpam-4989	89	22	0	0	NUM
ejpam-4989	89	23	,	,	PUNCT
ejpam-4989	89	24	then	then	ADV
ejpam-4989	89	25	h(γ	h(γ	PROPN
ejpam-4989	89	26	)	)	PUNCT
ejpam-4989	90	1	=	=	SYM
ejpam-4989	90	2	log(max{|a|	log(max{|a|	PROPN
ejpam-4989	90	3	,	,	PUNCT
ejpam-4989	90	4	b	b	NOUN
ejpam-4989	90	5	}	}	PUNCT
ejpam-4989	90	6	)	)	PUNCT
ejpam-4989	90	7	.	.	PUNCT
ejpam-4989	91	1	some	some	DET
ejpam-4989	91	2	properties	property	NOUN
ejpam-4989	91	3	of	of	ADP
ejpam-4989	91	4	the	the	DET
ejpam-4989	91	5	logarithmic	logarithmic	ADJ
ejpam-4989	91	6	height	height	NOUN
ejpam-4989	91	7	function	function	NOUN
ejpam-4989	91	8	are	be	AUX
ejpam-4989	91	9	listed	list	VERB
ejpam-4989	91	10	below	below	ADP
ejpam-4989	91	11	,	,	PUNCT
ejpam-4989	91	12	which	which	PRON
ejpam-4989	91	13	will	will	AUX
ejpam-4989	91	14	be	be	AUX
ejpam-4989	91	15	used	use	VERB
ejpam-4989	91	16	in	in	ADP
ejpam-4989	91	17	the	the	DET
ejpam-4989	91	18	next	next	ADJ
ejpam-4989	91	19	parts	part	NOUN
ejpam-4989	91	20	of	of	ADP
ejpam-4989	91	21	this	this	DET
ejpam-4989	91	22	paper	paper	NOUN
ejpam-4989	91	23	:	:	PUNCT
ejpam-4989	92	1	h(η	h(η	PROPN
ejpam-4989	92	2	±	±	X
ejpam-4989	92	3	γ	γ	NOUN
ejpam-4989	92	4	)	)	PUNCT
ejpam-4989	92	5	≤	≤	NOUN
ejpam-4989	92	6	h(η	h(η	NOUN
ejpam-4989	92	7	)	)	PUNCT
ejpam-4989	93	1	+	+	CCONJ
ejpam-4989	93	2	h(γ	h(γ	NOUN
ejpam-4989	93	3	)	)	PUNCT
ejpam-4989	94	1	+	+	CCONJ
ejpam-4989	94	2	log	log	NOUN
ejpam-4989	94	3	2	2	NUM
ejpam-4989	94	4	,	,	PUNCT
ejpam-4989	94	5	(	(	PUNCT
ejpam-4989	94	6	14	14	NUM
ejpam-4989	94	7	)	)	PUNCT
ejpam-4989	94	8	h	h	NOUN
ejpam-4989	94	9	(	(	PUNCT
ejpam-4989	94	10	ηγ±1	ηγ±1	PROPN
ejpam-4989	94	11	)	)	PUNCT
ejpam-4989	94	12	≤	≤	NOUN
ejpam-4989	94	13	h(η	h(η	NOUN
ejpam-4989	94	14	)	)	PUNCT
ejpam-4989	95	1	+	+	CCONJ
ejpam-4989	95	2	h(γ	h(γ	NOUN
ejpam-4989	95	3	)	)	PUNCT
ejpam-4989	95	4	,	,	PUNCT
ejpam-4989	95	5	(	(	PUNCT
ejpam-4989	95	6	15	15	X
ejpam-4989	95	7	)	)	PUNCT
ejpam-4989	95	8	h	h	NOUN
ejpam-4989	95	9	(	(	PUNCT
ejpam-4989	95	10	ηk	ηk	PROPN
ejpam-4989	95	11	)	)	PUNCT
ejpam-4989	95	12	=	=	SYM
ejpam-4989	96	1	|k|h(η	|k|h(η	PROPN
ejpam-4989	96	2	)	)	PUNCT
ejpam-4989	96	3	.	.	PUNCT
ejpam-4989	97	1	(	(	PUNCT
ejpam-4989	97	2	16	16	NUM
ejpam-4989	97	3	)	)	PUNCT
ejpam-4989	97	4	we	we	PRON
ejpam-4989	97	5	use	use	VERB
ejpam-4989	97	6	the	the	DET
ejpam-4989	97	7	following	following	NOUN
ejpam-4989	97	8	[	[	X
ejpam-4989	97	9	5	5	NUM
ejpam-4989	97	10	,	,	PUNCT
ejpam-4989	97	11	theorem	theorem	VERB
ejpam-4989	97	12	9.4	9.4	NUM
ejpam-4989	97	13	]	]	PUNCT
ejpam-4989	97	14	,	,	PUNCT
ejpam-4989	97	15	which	which	PRON
ejpam-4989	97	16	is	be	AUX
ejpam-4989	97	17	a	a	DET
ejpam-4989	97	18	modified	modify	VERB
ejpam-4989	97	19	version	version	NOUN
ejpam-4989	97	20	of	of	ADP
ejpam-4989	97	21	the	the	DET
ejpam-4989	97	22	matveev	matveev	NOUN
ejpam-4989	97	23	result	result	VERB
ejpam-4989	97	24	[	[	X
ejpam-4989	97	25	8	8	X
ejpam-4989	97	26	]	]	PUNCT
ejpam-4989	97	27	h.	h.	PROPN
ejpam-4989	97	28	s.	s.	PROPN
ejpam-4989	97	29	taher	taher	PROPN
ejpam-4989	97	30	,	,	PUNCT
ejpam-4989	97	31	s.	s.	PROPN
ejpam-4989	97	32	k.	k.	PROPN
ejpam-4989	97	33	dash	dash	NOUN
ejpam-4989	97	34	/	/	SYM
ejpam-4989	97	35	eur	eur	NOUN
ejpam-4989	97	36	.	.	PUNCT
ejpam-4989	98	1	j.	j.	PROPN
ejpam-4989	98	2	pure	pure	PROPN
ejpam-4989	98	3	appl	appl	PROPN
ejpam-4989	98	4	.	.	PROPN
ejpam-4989	98	5	math	math	PROPN
ejpam-4989	98	6	,	,	PUNCT
ejpam-4989	98	7	17	17	NUM
ejpam-4989	98	8	(	(	PUNCT
ejpam-4989	98	9	1	1	NUM
ejpam-4989	98	10	)	)	PUNCT
ejpam-4989	98	11	(	(	PUNCT
ejpam-4989	98	12	2024	2024	NUM
ejpam-4989	98	13	)	)	PUNCT
ejpam-4989	98	14	,	,	PUNCT
ejpam-4989	98	15	135	135	NUM
ejpam-4989	98	16	-	-	SYM
ejpam-4989	98	17	146	146	NUM
ejpam-4989	98	18	139	139	NUM
ejpam-4989	98	19	theorem	theorem	NOUN
ejpam-4989	98	20	1	1	NUM
ejpam-4989	98	21	.	.	PUNCT
ejpam-4989	99	1	let	let	VERB
ejpam-4989	99	2	l	l	NOUN
ejpam-4989	99	3	be	be	AUX
ejpam-4989	99	4	a	a	DET
ejpam-4989	99	5	real	real	ADJ
ejpam-4989	99	6	algebraic	algebraic	ADJ
ejpam-4989	99	7	number	number	NOUN
ejpam-4989	99	8	field	field	NOUN
ejpam-4989	99	9	of	of	ADP
ejpam-4989	99	10	degree	degree	NOUN
ejpam-4989	99	11	d	d	PROPN
ejpam-4989	99	12	over	over	ADP
ejpam-4989	99	13	q.	q.	PROPN
ejpam-4989	99	14	let	let	VERB
ejpam-4989	99	15	γ1	γ1	NOUN
ejpam-4989	99	16	,	,	PUNCT
ejpam-4989	99	17	.	.	PUNCT
ejpam-4989	99	18	.	.	PUNCT
ejpam-4989	100	1	.	.	PUNCT
ejpam-4989	101	1	,	,	PUNCT
ejpam-4989	101	2	γt	γt	PROPN
ejpam-4989	101	3	∈	∈	PROPN
ejpam-4989	101	4	l	l	NOUN
ejpam-4989	101	5	be	be	AUX
ejpam-4989	101	6	a	a	DET
ejpam-4989	101	7	positive	positive	ADJ
ejpam-4989	101	8	real	real	ADJ
ejpam-4989	101	9	algebraic	algebraic	ADJ
ejpam-4989	101	10	number	number	NOUN
ejpam-4989	101	11	,	,	PUNCT
ejpam-4989	101	12	and	and	CCONJ
ejpam-4989	101	13	b1	b1	NOUN
ejpam-4989	101	14	,	,	PUNCT
ejpam-4989	101	15	b2	b2	NOUN
ejpam-4989	101	16	,	,	PUNCT
ejpam-4989	101	17	.	.	PUNCT
ejpam-4989	101	18	.	.	PUNCT
ejpam-4989	102	1	.	.	PUNCT
ejpam-4989	103	1	,	,	PUNCT
ejpam-4989	103	2	bt	bt	PROPN
ejpam-4989	103	3	be	be	AUX
ejpam-4989	103	4	nonzero	nonzero	NOUN
ejpam-4989	103	5	integers	integer	NOUN
ejpam-4989	103	6	such	such	ADJ
ejpam-4989	103	7	that	that	DET
ejpam-4989	103	8	λ	λ	X
ejpam-4989	103	9	:	:	PUNCT
ejpam-4989	104	1	=	=	SYM
ejpam-4989	104	2	γb11	γb11	PROPN
ejpam-4989	104	3	·	·	PUNCT
ejpam-4989	104	4	·	·	PUNCT
ejpam-4989	104	5	·	·	PUNCT
ejpam-4989	104	6	γbtt	γbtt	PROPN
ejpam-4989	104	7	−	−	PROPN
ejpam-4989	104	8	1	1	NUM
ejpam-4989	104	9	,	,	PUNCT
ejpam-4989	104	10	is	be	AUX
ejpam-4989	104	11	not	not	PART
ejpam-4989	104	12	zero	zero	NUM
ejpam-4989	104	13	.	.	PUNCT
ejpam-4989	105	1	then	then	ADV
ejpam-4989	105	2	log	log	VERB
ejpam-4989	105	3	|λ|	|λ|	PROPN
ejpam-4989	105	4	>	>	X
ejpam-4989	105	5	(	(	PUNCT
ejpam-4989	105	6	−1.4	−1.4	NOUN
ejpam-4989	105	7	)	)	PUNCT
ejpam-4989	105	8	(	(	PUNCT
ejpam-4989	105	9	30t+3	30t+3	NUM
ejpam-4989	105	10	)	)	PUNCT
ejpam-4989	105	11	(	(	PUNCT
ejpam-4989	105	12	t4.5	t4.5	PROPN
ejpam-4989	105	13	)	)	PUNCT
ejpam-4989	105	14	(	(	PUNCT
ejpam-4989	105	15	d2	d2	PROPN
ejpam-4989	105	16	)	)	PUNCT
ejpam-4989	105	17	(	(	PUNCT
ejpam-4989	105	18	a1	a1	NOUN
ejpam-4989	105	19	.	.	PUNCT
ejpam-4989	105	20	.	.	PUNCT
ejpam-4989	105	21	.	.	PUNCT
ejpam-4989	106	1	at	at	ADP
ejpam-4989	106	2	)	)	PUNCT
ejpam-4989	106	3	(	(	PUNCT
ejpam-4989	106	4	1	1	NUM
ejpam-4989	106	5	+	+	NUM
ejpam-4989	106	6	logd)(1	logd)(1	PROPN
ejpam-4989	106	7	+	+	CCONJ
ejpam-4989	106	8	logb	logb	ADV
ejpam-4989	106	9	)	)	PUNCT
ejpam-4989	106	10	,	,	PUNCT
ejpam-4989	106	11	where	where	SCONJ
ejpam-4989	106	12	b	b	X
ejpam-4989	106	13	≥	≥	X
ejpam-4989	106	14	max	max	PROPN
ejpam-4989	106	15	{	{	PUNCT
ejpam-4989	106	16	|b1|	|b1|	NOUN
ejpam-4989	106	17	,	,	PUNCT
ejpam-4989	106	18	.	.	PUNCT
ejpam-4989	106	19	.	.	PUNCT
ejpam-4989	106	20	.	.	PUNCT
ejpam-4989	107	1	,	,	PUNCT
ejpam-4989	107	2	|bt|	|bt|	NOUN
ejpam-4989	107	3	}	}	PUNCT
ejpam-4989	107	4	,	,	PUNCT
ejpam-4989	107	5	and	and	CCONJ
ejpam-4989	107	6	ai	ai	VERB
ejpam-4989	107	7	≥	≥	PROPN
ejpam-4989	107	8	max	max	PROPN
ejpam-4989	107	9	{	{	PUNCT
ejpam-4989	107	10	dh	dh	PROPN
ejpam-4989	107	11	(	(	PUNCT
ejpam-4989	107	12	γi	γi	NOUN
ejpam-4989	107	13	)	)	PUNCT
ejpam-4989	107	14	,	,	PUNCT
ejpam-4989	107	15	|log	|log	X
ejpam-4989	107	16	(	(	PUNCT
ejpam-4989	107	17	γi)|	γi)|	INTJ
ejpam-4989	107	18	,	,	PUNCT
ejpam-4989	107	19	0.16	0.16	NUM
ejpam-4989	107	20	}	}	PUNCT
ejpam-4989	107	21	,	,	PUNCT
ejpam-4989	107	22	1	1	NUM
ejpam-4989	107	23	≤	≤	NUM
ejpam-4989	107	24	i	i	PRON
ejpam-4989	108	1	≤	≤	ADJ
ejpam-4989	108	2	t.	t.	PROPN
ejpam-4989	108	3	2.4	2.4	NUM
ejpam-4989	108	4	.	.	PUNCT
ejpam-4989	109	1	de	de	X
ejpam-4989	109	2	weger	weger	NOUN
ejpam-4989	109	3	reduction	reduction	NOUN
ejpam-4989	109	4	method	method	NOUN
ejpam-4989	109	5	to	to	PART
ejpam-4989	109	6	reduce	reduce	VERB
ejpam-4989	109	7	the	the	DET
ejpam-4989	109	8	upper	upper	ADJ
ejpam-4989	109	9	bound	bind	VERB
ejpam-4989	109	10	,	,	PUNCT
ejpam-4989	109	11	we	we	PRON
ejpam-4989	109	12	present	present	VERB
ejpam-4989	109	13	a	a	DET
ejpam-4989	109	14	variant	variant	NOUN
ejpam-4989	109	15	of	of	ADP
ejpam-4989	109	16	baker	baker	PROPN
ejpam-4989	109	17	and	and	CCONJ
ejpam-4989	109	18	davenport	davenport	PROPN
ejpam-4989	109	19	’s	’s	PART
ejpam-4989	109	20	reduction	reduction	NOUN
ejpam-4989	109	21	method	method	NOUN
ejpam-4989	109	22	[	[	X
ejpam-4989	109	23	14	14	NUM
ejpam-4989	109	24	]	]	PUNCT
ejpam-4989	109	25	.	.	PUNCT
ejpam-4989	110	1	let	let	VERB
ejpam-4989	110	2	ϑ1	ϑ1	NOUN
ejpam-4989	110	3	,	,	PUNCT
ejpam-4989	110	4	ϑ2	ϑ2	PROPN
ejpam-4989	110	5	,	,	PUNCT
ejpam-4989	110	6	β	β	X
ejpam-4989	110	7	∈	∈	NOUN
ejpam-4989	110	8	r	r	NOUN
ejpam-4989	110	9	be	be	AUX
ejpam-4989	110	10	given	give	VERB
ejpam-4989	110	11	,	,	PUNCT
ejpam-4989	110	12	and	and	CCONJ
ejpam-4989	110	13	let	let	VERB
ejpam-4989	110	14	x1	x1	NUM
ejpam-4989	110	15	,	,	PUNCT
ejpam-4989	110	16	x2	x2	PROPN
ejpam-4989	110	17	∈	∈	PROPN
ejpam-4989	110	18	z	z	AUX
ejpam-4989	110	19	be	be	VERB
ejpam-4989	110	20	unknowns	unknown	NOUN
ejpam-4989	110	21	.	.	PUNCT
ejpam-4989	111	1	let	let	VERB
ejpam-4989	111	2	λ	λ	X
ejpam-4989	111	3	=	=	PRON
ejpam-4989	111	4	β	β	X
ejpam-4989	111	5	+	+	X
ejpam-4989	111	6	x1ϑ1	x1ϑ1	PUNCT
ejpam-4989	112	1	+	+	NUM
ejpam-4989	112	2	x2ϑ2	x2ϑ2	NOUN
ejpam-4989	112	3	.	.	PUNCT
ejpam-4989	113	1	(	(	PUNCT
ejpam-4989	113	2	17	17	NUM
ejpam-4989	113	3	)	)	PUNCT
ejpam-4989	113	4	let	let	VERB
ejpam-4989	113	5	c	c	X
ejpam-4989	113	6	,	,	PUNCT
ejpam-4989	113	7	δ	δ	PROPN
ejpam-4989	113	8	be	be	VERB
ejpam-4989	113	9	positive	positive	ADJ
ejpam-4989	113	10	constants	constant	NOUN
ejpam-4989	113	11	.	.	PUNCT
ejpam-4989	114	1	set	set	VERB
ejpam-4989	114	2	x	x	X
ejpam-4989	114	3	=	=	SYM
ejpam-4989	114	4	max	max	PROPN
ejpam-4989	114	5	{	{	PUNCT
ejpam-4989	114	6	|x1|	|x1|	PROPN
ejpam-4989	114	7	,	,	PUNCT
ejpam-4989	114	8	|x2|	|x2|	PROPN
ejpam-4989	114	9	}	}	PUNCT
ejpam-4989	114	10	.	.	PUNCT
ejpam-4989	115	1	let	let	VERB
ejpam-4989	115	2	x0	x0	PROPN
ejpam-4989	115	3	,	,	PUNCT
ejpam-4989	115	4	y	y	PROPN
ejpam-4989	115	5	be	be	VERB
ejpam-4989	115	6	positive	positive	ADJ
ejpam-4989	115	7	.	.	PUNCT
ejpam-4989	116	1	assume	assume	VERB
ejpam-4989	116	2	that	that	SCONJ
ejpam-4989	116	3	|λ|	|λ|	NOUN
ejpam-4989	116	4	<	<	X
ejpam-4989	116	5	c	c	X
ejpam-4989	116	6	·	·	PUNCT
ejpam-4989	116	7	exp(−δ	exp(−δ	PROPN
ejpam-4989	116	8	·	·	PUNCT
ejpam-4989	116	9	y	y	PROPN
ejpam-4989	116	10	)	)	PUNCT
ejpam-4989	116	11	,	,	PUNCT
ejpam-4989	116	12	(	(	PUNCT
ejpam-4989	116	13	18	18	NUM
ejpam-4989	116	14	)	)	PUNCT
ejpam-4989	116	15	y	y	PROPN
ejpam-4989	116	16	≤	≤	NUM
ejpam-4989	116	17	x	x	PUNCT
ejpam-4989	116	18	≤	≤	ADJ
ejpam-4989	116	19	x0	x0	PROPN
ejpam-4989	116	20	.	.	PUNCT
ejpam-4989	117	1	(	(	PUNCT
ejpam-4989	117	2	19	19	NUM
ejpam-4989	117	3	)	)	PUNCT
ejpam-4989	117	4	when	when	SCONJ
ejpam-4989	117	5	β	β	X
ejpam-4989	117	6	=	=	NOUN
ejpam-4989	117	7	0	0	PUNCT
ejpam-4989	117	8	in	in	ADP
ejpam-4989	117	9	(	(	PUNCT
ejpam-4989	117	10	17	17	NUM
ejpam-4989	117	11	)	)	PUNCT
ejpam-4989	117	12	,	,	PUNCT
ejpam-4989	117	13	we	we	PRON
ejpam-4989	117	14	get	get	VERB
ejpam-4989	117	15	λ	λ	X
ejpam-4989	117	16	=	=	PUNCT
ejpam-4989	117	17	x1ϑ1	x1ϑ1	PROPN
ejpam-4989	118	1	+	+	NUM
ejpam-4989	118	2	x2ϑ2	x2ϑ2	X
ejpam-4989	118	3	.	.	PUNCT
ejpam-4989	118	4	put	put	VERB
ejpam-4989	118	5	ϑ	ϑ	NOUN
ejpam-4989	118	6	=	=	X
ejpam-4989	118	7	−ϑ1/ϑ2	−ϑ1/ϑ2	NOUN
ejpam-4989	118	8	.	.	PUNCT
ejpam-4989	119	1	we	we	PRON
ejpam-4989	119	2	assume	assume	VERB
ejpam-4989	119	3	that	that	SCONJ
ejpam-4989	119	4	x1	x1	PROPN
ejpam-4989	119	5	and	and	CCONJ
ejpam-4989	119	6	x2	x2	PROPN
ejpam-4989	119	7	are	be	AUX
ejpam-4989	119	8	coprime	coprime	ADJ
ejpam-4989	119	9	.	.	PUNCT
ejpam-4989	120	1	let	let	VERB
ejpam-4989	120	2	the	the	DET
ejpam-4989	120	3	continued	continue	VERB
ejpam-4989	120	4	fraction	fraction	NOUN
ejpam-4989	120	5	expansion	expansion	NOUN
ejpam-4989	120	6	of	of	ADP
ejpam-4989	120	7	ϑ	ϑ	AUX
ejpam-4989	120	8	be	be	AUX
ejpam-4989	120	9	given	give	VERB
ejpam-4989	120	10	by	by	ADP
ejpam-4989	120	11	[	[	X
ejpam-4989	120	12	a0	a0	PROPN
ejpam-4989	120	13	,	,	PUNCT
ejpam-4989	120	14	a1	a1	NOUN
ejpam-4989	120	15	,	,	PUNCT
ejpam-4989	120	16	a2	a2	PROPN
ejpam-4989	120	17	,	,	PUNCT
ejpam-4989	120	18	.	.	PUNCT
ejpam-4989	120	19	.	.	PUNCT
ejpam-4989	121	1	.	.	PUNCT
ejpam-4989	121	2	]	]	PUNCT
ejpam-4989	122	1	,	,	PUNCT
ejpam-4989	122	2	and	and	CCONJ
ejpam-4989	122	3	let	let	VERB
ejpam-4989	122	4	the	the	DET
ejpam-4989	122	5	k	k	NOUN
ejpam-4989	122	6	-	-	PUNCT
ejpam-4989	122	7	th	th	VERB
ejpam-4989	122	8	convergent	convergent	NOUN
ejpam-4989	122	9	of	of	ADP
ejpam-4989	122	10	ϑ	ϑ	X
ejpam-4989	122	11	be	be	AUX
ejpam-4989	122	12	pk	pk	NOUN
ejpam-4989	122	13	/	/	SYM
ejpam-4989	122	14	qk	qk	NOUN
ejpam-4989	122	15	for	for	ADP
ejpam-4989	122	16	k	k	PROPN
ejpam-4989	122	17	=	=	SYM
ejpam-4989	122	18	0	0	NUM
ejpam-4989	122	19	,	,	PUNCT
ejpam-4989	122	20	1	1	NUM
ejpam-4989	122	21	,	,	PUNCT
ejpam-4989	122	22	2	2	NUM
ejpam-4989	122	23	,	,	PUNCT
ejpam-4989	122	24	.	.	PUNCT
ejpam-4989	122	25	.	.	PUNCT
ejpam-4989	123	1	.	.	PUNCT
ejpam-4989	124	1	we	we	PRON
ejpam-4989	124	2	may	may	AUX
ejpam-4989	124	3	assume	assume	VERB
ejpam-4989	124	4	without	without	ADP
ejpam-4989	124	5	loss	loss	NOUN
ejpam-4989	124	6	of	of	ADP
ejpam-4989	124	7	generality	generality	NOUN
ejpam-4989	124	8	that	that	SCONJ
ejpam-4989	124	9	|ϑ1|	|ϑ1|	NOUN
ejpam-4989	124	10	<	<	X
ejpam-4989	124	11	|ϑ2|	|ϑ2|	NOUN
ejpam-4989	124	12	and	and	CCONJ
ejpam-4989	124	13	that	that	SCONJ
ejpam-4989	125	1	x1	x1	PRON
ejpam-4989	125	2	>	>	X
ejpam-4989	125	3	0	0	X
ejpam-4989	125	4	.	.	PUNCT
ejpam-4989	126	1	we	we	PRON
ejpam-4989	126	2	obtain	obtain	VERB
ejpam-4989	126	3	the	the	DET
ejpam-4989	126	4	following	follow	VERB
ejpam-4989	126	5	results	result	NOUN
ejpam-4989	126	6	.	.	PUNCT
ejpam-4989	127	1	lemma	lemma	PROPN
ejpam-4989	127	2	3	3	NUM
ejpam-4989	127	3	.	.	PUNCT
ejpam-4989	128	1	(	(	PUNCT
ejpam-4989	128	2	[	[	X
ejpam-4989	128	3	14	14	NUM
ejpam-4989	128	4	,	,	PUNCT
ejpam-4989	128	5	lemma	lemma	PROPN
ejpam-4989	128	6	3.2	3.2	NUM
ejpam-4989	128	7	]	]	PUNCT
ejpam-4989	128	8	)	)	PUNCT
ejpam-4989	128	9	let	let	VERB
ejpam-4989	128	10	a	a	DET
ejpam-4989	128	11	=	=	SYM
ejpam-4989	128	12	max	max	PROPN
ejpam-4989	128	13	0≤k≤y0	0≤k≤y0	NUM
ejpam-4989	128	14	ak+1	ak+1	NOUN
ejpam-4989	128	15	,	,	PUNCT
ejpam-4989	128	16	where	where	SCONJ
ejpam-4989	128	17	y0	y0	NOUN
ejpam-4989	128	18	=	=	SYM
ejpam-4989	128	19	−1	−1	NOUN
ejpam-4989	128	20	+	+	X
ejpam-4989	128	21	log	log	NOUN
ejpam-4989	128	22	(	(	PUNCT
ejpam-4989	128	23	√	√	NUM
ejpam-4989	128	24	5x0	5x0	NUM
ejpam-4989	128	25	+	+	CCONJ
ejpam-4989	128	26	1	1	X
ejpam-4989	128	27	)	)	PUNCT
ejpam-4989	128	28	log	log	NOUN
ejpam-4989	128	29	(	(	PUNCT
ejpam-4989	128	30	1	1	NUM
ejpam-4989	128	31	+	+	NUM
ejpam-4989	128	32	√	√	NUM
ejpam-4989	128	33	5	5	NUM
ejpam-4989	128	34	2	2	NUM
ejpam-4989	128	35	)	)	PUNCT
ejpam-4989	128	36	.	.	PUNCT
ejpam-4989	129	1	if	if	SCONJ
ejpam-4989	129	2	(	(	PUNCT
ejpam-4989	129	3	18	18	NUM
ejpam-4989	129	4	)	)	PUNCT
ejpam-4989	129	5	and	and	CCONJ
ejpam-4989	129	6	(	(	PUNCT
ejpam-4989	129	7	19	19	NUM
ejpam-4989	129	8	)	)	PUNCT
ejpam-4989	129	9	hold	hold	VERB
ejpam-4989	129	10	for	for	ADP
ejpam-4989	129	11	x1	x1	PROPN
ejpam-4989	129	12	,	,	PUNCT
ejpam-4989	129	13	x2	x2	PROPN
ejpam-4989	129	14	and	and	CCONJ
ejpam-4989	129	15	β	β	X
ejpam-4989	129	16	=	=	SYM
ejpam-4989	129	17	0	0	NUM
ejpam-4989	129	18	,	,	PUNCT
ejpam-4989	129	19	then	then	ADV
ejpam-4989	129	20	y	y	X
ejpam-4989	129	21	<	<	X
ejpam-4989	129	22	1	1	NUM
ejpam-4989	129	23	δ	δ	NOUN
ejpam-4989	129	24	log	log	NOUN
ejpam-4989	129	25	(	(	PUNCT
ejpam-4989	129	26	c(a+	c(a+	PROPN
ejpam-4989	129	27	2)x0	2)x0	NUM
ejpam-4989	129	28	|ϑ2|	|ϑ2|	NOUN
ejpam-4989	129	29	)	)	PUNCT
ejpam-4989	129	30	.	.	PUNCT
ejpam-4989	130	1	(	(	PUNCT
ejpam-4989	130	2	20	20	X
ejpam-4989	130	3	)	)	PUNCT
ejpam-4989	130	4	h.	h.	PROPN
ejpam-4989	130	5	s.	s.	PROPN
ejpam-4989	130	6	taher	taher	PROPN
ejpam-4989	130	7	,	,	PUNCT
ejpam-4989	130	8	s.	s.	PROPN
ejpam-4989	130	9	k.	k.	PROPN
ejpam-4989	130	10	dash	dash	NOUN
ejpam-4989	130	11	/	/	SYM
ejpam-4989	130	12	eur	eur	NOUN
ejpam-4989	130	13	.	.	PUNCT
ejpam-4989	131	1	j.	j.	PROPN
ejpam-4989	131	2	pure	pure	PROPN
ejpam-4989	131	3	appl	appl	PROPN
ejpam-4989	131	4	.	.	PROPN
ejpam-4989	131	5	math	math	PROPN
ejpam-4989	131	6	,	,	PUNCT
ejpam-4989	131	7	17	17	NUM
ejpam-4989	131	8	(	(	PUNCT
ejpam-4989	131	9	1	1	NUM
ejpam-4989	131	10	)	)	PUNCT
ejpam-4989	131	11	(	(	PUNCT
ejpam-4989	131	12	2024	2024	NUM
ejpam-4989	131	13	)	)	PUNCT
ejpam-4989	131	14	,	,	PUNCT
ejpam-4989	131	15	135	135	NUM
ejpam-4989	131	16	-	-	SYM
ejpam-4989	131	17	146	146	NUM
ejpam-4989	131	18	140	140	NUM
ejpam-4989	131	19	when	when	SCONJ
ejpam-4989	131	20	β	β	X
ejpam-4989	131	21	̸=	̸=	PROPN
ejpam-4989	131	22	0	0	NUM
ejpam-4989	131	23	in	in	ADP
ejpam-4989	131	24	(	(	PUNCT
ejpam-4989	131	25	17	17	NUM
ejpam-4989	131	26	)	)	PUNCT
ejpam-4989	131	27	,	,	PUNCT
ejpam-4989	131	28	put	put	VERB
ejpam-4989	131	29	ϑ	ϑ	NOUN
ejpam-4989	131	30	=	=	X
ejpam-4989	131	31	−ϑ1/ϑ2	−ϑ1/ϑ2	NOUN
ejpam-4989	131	32	and	and	CCONJ
ejpam-4989	131	33	ψ	ψ	X
ejpam-4989	131	34	=	=	NOUN
ejpam-4989	131	35	β/ϑ2	β/ϑ2	NOUN
ejpam-4989	131	36	.	.	PUNCT
ejpam-4989	132	1	then	then	ADV
ejpam-4989	132	2	we	we	PRON
ejpam-4989	132	3	have	have	VERB
ejpam-4989	132	4	λ	λ	NOUN
ejpam-4989	132	5	ϑ2	ϑ2	NOUN
ejpam-4989	132	6	=	=	SYM
ejpam-4989	132	7	ψ	ψ	X
ejpam-4989	132	8	−	−	NOUN
ejpam-4989	132	9	x1ϑ	x1ϑ	PROPN
ejpam-4989	133	1	+	+	CCONJ
ejpam-4989	133	2	x2	x2	PROPN
ejpam-4989	133	3	.	.	PUNCT
ejpam-4989	134	1	let	let	VERB
ejpam-4989	134	2	p	p	X
ejpam-4989	134	3	/	/	SYM
ejpam-4989	134	4	q	q	AUX
ejpam-4989	134	5	be	be	AUX
ejpam-4989	134	6	a	a	DET
ejpam-4989	134	7	convergent	convergent	NOUN
ejpam-4989	134	8	of	of	ADP
ejpam-4989	134	9	ϑ	ϑ	NOUN
ejpam-4989	134	10	with	with	ADP
ejpam-4989	134	11	q	q	PROPN
ejpam-4989	134	12	>	>	X
ejpam-4989	134	13	x0	x0	PROPN
ejpam-4989	134	14	.	.	PUNCT
ejpam-4989	135	1	tthe	tthe	DET
ejpam-4989	135	2	distance	distance	NOUN
ejpam-4989	135	3	between	between	ADP
ejpam-4989	135	4	real	real	ADJ
ejpam-4989	135	5	number	number	NOUN
ejpam-4989	135	6	t	t	PROPN
ejpam-4989	135	7	and	and	CCONJ
ejpam-4989	135	8	the	the	DET
ejpam-4989	135	9	closest	close	ADJ
ejpam-4989	135	10	integer	integer	NOUN
ejpam-4989	135	11	is	be	AUX
ejpam-4989	135	12	expressed	express	VERB
ejpam-4989	135	13	as	as	ADP
ejpam-4989	135	14	∥t∥	∥t∥	ADP
ejpam-4989	135	15	=	=	SYM
ejpam-4989	135	16	min{|t	min{|t	PROPN
ejpam-4989	135	17	−n|	−n|	X
ejpam-4989	135	18	:	:	PUNCT
ejpam-4989	135	19	n	n	X
ejpam-4989	135	20	∈	∈	PROPN
ejpam-4989	135	21	z	z	NOUN
ejpam-4989	135	22	}	}	PUNCT
ejpam-4989	135	23	.	.	PUNCT
ejpam-4989	136	1	we	we	PRON
ejpam-4989	136	2	obtain	obtain	VERB
ejpam-4989	136	3	the	the	DET
ejpam-4989	136	4	following	follow	VERB
ejpam-4989	136	5	result	result	NOUN
ejpam-4989	136	6	.	.	PUNCT
ejpam-4989	137	1	lemma	lemma	PROPN
ejpam-4989	137	2	4	4	NUM
ejpam-4989	137	3	.	.	PUNCT
ejpam-4989	138	1	(	(	PUNCT
ejpam-4989	138	2	[	[	X
ejpam-4989	138	3	14	14	NUM
ejpam-4989	138	4	,	,	PUNCT
ejpam-4989	138	5	lemma	lemma	PROPN
ejpam-4989	138	6	3.3	3.3	NUM
ejpam-4989	138	7	]	]	PUNCT
ejpam-4989	138	8	)	)	PUNCT
ejpam-4989	138	9	suppose	suppose	VERB
ejpam-4989	138	10	that	that	SCONJ
ejpam-4989	138	11	∥qψ∥	∥qψ∥	PROPN
ejpam-4989	138	12	>	>	X
ejpam-4989	138	13	2x0	2x0	NUM
ejpam-4989	138	14	q	q	NOUN
ejpam-4989	138	15	.	.	PUNCT
ejpam-4989	139	1	then	then	ADV
ejpam-4989	139	2	,	,	PUNCT
ejpam-4989	139	3	the	the	DET
ejpam-4989	139	4	solutions	solution	NOUN
ejpam-4989	139	5	of	of	ADP
ejpam-4989	139	6	(	(	PUNCT
ejpam-4989	139	7	18	18	NUM
ejpam-4989	139	8	)	)	PUNCT
ejpam-4989	139	9	and	and	CCONJ
ejpam-4989	139	10	(	(	PUNCT
ejpam-4989	139	11	19	19	NUM
ejpam-4989	139	12	)	)	PUNCT
ejpam-4989	139	13	satisfy	satisfy	NOUN
ejpam-4989	139	14	y	y	PROPN
ejpam-4989	139	15	<	<	X
ejpam-4989	139	16	1	1	NUM
ejpam-4989	139	17	δ	δ	NOUN
ejpam-4989	139	18	log	log	NOUN
ejpam-4989	139	19	(	(	PUNCT
ejpam-4989	139	20	q2c	q2c	X
ejpam-4989	139	21	|ϑ2|x0	|ϑ2|x0	NOUN
ejpam-4989	139	22	)	)	PUNCT
ejpam-4989	139	23	.	.	PUNCT
ejpam-4989	140	1	(	(	PUNCT
ejpam-4989	140	2	21	21	NUM
ejpam-4989	140	3	)	)	PUNCT
ejpam-4989	140	4	we	we	PRON
ejpam-4989	140	5	need	need	VERB
ejpam-4989	140	6	the	the	DET
ejpam-4989	140	7	following	follow	VERB
ejpam-4989	140	8	discovery	discovery	NOUN
ejpam-4989	140	9	to	to	PART
ejpam-4989	140	10	prove	prove	VERB
ejpam-4989	140	11	our	our	PRON
ejpam-4989	140	12	theorem	theorem	NOUN
ejpam-4989	140	13	.	.	PUNCT
ejpam-4989	141	1	lemma	lemma	PROPN
ejpam-4989	141	2	5	5	NUM
ejpam-4989	141	3	.	.	PUNCT
ejpam-4989	142	1	(	(	PUNCT
ejpam-4989	142	2	[	[	X
ejpam-4989	142	3	11	11	NUM
ejpam-4989	142	4	,	,	PUNCT
ejpam-4989	142	5	lemma	lemma	PROPN
ejpam-4989	142	6	7	7	NUM
ejpam-4989	142	7	]	]	PUNCT
ejpam-4989	142	8	)	)	PUNCT
ejpam-4989	142	9	if	if	SCONJ
ejpam-4989	142	10	r	r	NOUN
ejpam-4989	142	11	≥	≥	NOUN
ejpam-4989	142	12	1	1	NUM
ejpam-4989	142	13	and	and	CCONJ
ejpam-4989	142	14	s	s	PRON
ejpam-4989	142	15	≥	≥	X
ejpam-4989	142	16	(	(	PUNCT
ejpam-4989	142	17	4r2)r	4r2)r	NUM
ejpam-4989	142	18	,	,	PUNCT
ejpam-4989	142	19	and	and	CCONJ
ejpam-4989	142	20	l	l	NOUN
ejpam-4989	142	21	(	(	PUNCT
ejpam-4989	142	22	logl)r	logl)r	VERB
ejpam-4989	142	23	<	<	X
ejpam-4989	142	24	s	s	X
ejpam-4989	142	25	,	,	PUNCT
ejpam-4989	142	26	then	then	ADV
ejpam-4989	142	27	l	l	NOUN
ejpam-4989	142	28	<	<	X
ejpam-4989	142	29	2rs(logs)r	2rs(logs)r	NOUN
ejpam-4989	142	30	.	.	PUNCT
ejpam-4989	143	1	3	3	X
ejpam-4989	143	2	.	.	X
ejpam-4989	143	3	main	main	ADJ
ejpam-4989	143	4	results	result	NOUN
ejpam-4989	143	5	theorem	theorem	VERB
ejpam-4989	143	6	2	2	NUM
ejpam-4989	143	7	.	.	PUNCT
ejpam-4989	144	1	the	the	DET
ejpam-4989	144	2	positive	positive	ADJ
ejpam-4989	144	3	integer	integer	NOUN
ejpam-4989	144	4	solutions	solution	NOUN
ejpam-4989	144	5	of	of	ADP
ejpam-4989	144	6	the	the	DET
ejpam-4989	144	7	diophantine	diophantine	NOUN
ejpam-4989	144	8	equation	equation	NOUN
ejpam-4989	144	9	p	p	X
ejpam-4989	144	10	(	(	PUNCT
ejpam-4989	144	11	k	k	NOUN
ejpam-4989	144	12	)	)	PUNCT
ejpam-4989	144	13	n	n	NOUN
ejpam-4989	144	14	=	=	SYM
ejpam-4989	144	15	tm	tm	NOUN
ejpam-4989	144	16	,	,	PUNCT
ejpam-4989	144	17	(	(	PUNCT
ejpam-4989	144	18	22	22	NUM
ejpam-4989	144	19	)	)	PUNCT
ejpam-4989	144	20	where	where	SCONJ
ejpam-4989	144	21	k	k	PROPN
ejpam-4989	144	22	≥	≥	NUM
ejpam-4989	144	23	2	2	NUM
ejpam-4989	144	24	are	be	AUX
ejpam-4989	144	25	p	p	X
ejpam-4989	144	26	(	(	PUNCT
ejpam-4989	144	27	k	k	NOUN
ejpam-4989	144	28	)	)	PUNCT
ejpam-4989	144	29	1	1	NUM
ejpam-4989	144	30	=	=	SYM
ejpam-4989	144	31	t1	t1	NOUN
ejpam-4989	144	32	=	=	SYM
ejpam-4989	144	33	t2	t2	PROPN
ejpam-4989	144	34	,	,	PUNCT
ejpam-4989	144	35	p	p	X
ejpam-4989	144	36	(	(	PUNCT
ejpam-4989	144	37	k	k	NOUN
ejpam-4989	144	38	)	)	PUNCT
ejpam-4989	144	39	2	2	NUM
ejpam-4989	144	40	=	=	SYM
ejpam-4989	144	41	t3	t3	PROPN
ejpam-4989	144	42	,	,	PUNCT
ejpam-4989	144	43	and	and	CCONJ
ejpam-4989	144	44	p	p	NOUN
ejpam-4989	144	45	(	(	PUNCT
ejpam-4989	144	46	k	k	NOUN
ejpam-4989	144	47	)	)	PUNCT
ejpam-4989	144	48	4	4	NUM
ejpam-4989	144	49	=	=	SYM
ejpam-4989	144	50	t6	t6	PROPN
ejpam-4989	144	51	.	.	PUNCT
ejpam-4989	145	1	to	to	PART
ejpam-4989	145	2	prove	prove	VERB
ejpam-4989	145	3	theorem	theorem	ADJ
ejpam-4989	145	4	2	2	NUM
ejpam-4989	145	5	will	will	AUX
ejpam-4989	145	6	be	be	AUX
ejpam-4989	145	7	done	do	VERB
ejpam-4989	145	8	in	in	ADP
ejpam-4989	145	9	four	four	NUM
ejpam-4989	145	10	steps	step	NOUN
ejpam-4989	145	11	.	.	PUNCT
ejpam-4989	146	1	3.1	3.1	NUM
ejpam-4989	146	2	.	.	PUNCT
ejpam-4989	146	3	relation	relation	NOUN
ejpam-4989	146	4	between	between	ADP
ejpam-4989	146	5	n	n	PROPN
ejpam-4989	146	6	and	and	CCONJ
ejpam-4989	146	7	m	m	VERB
ejpam-4989	146	8	for	for	ADP
ejpam-4989	146	9	the	the	DET
ejpam-4989	146	10	diophantine	diophantine	NOUN
ejpam-4989	146	11	equation	equation	NOUN
ejpam-4989	146	12	(	(	PUNCT
ejpam-4989	146	13	22	22	NUM
ejpam-4989	146	14	)	)	PUNCT
ejpam-4989	146	15	in	in	ADP
ejpam-4989	146	16	the	the	DET
ejpam-4989	146	17	range	range	NOUN
ejpam-4989	146	18	1	1	NUM
ejpam-4989	146	19	≤	≤	NUM
ejpam-4989	146	20	n	n	PRON
ejpam-4989	146	21	≤	≤	NOUN
ejpam-4989	146	22	k	k	NOUN
ejpam-4989	147	1	+	+	NOUN
ejpam-4989	147	2	1	1	NUM
ejpam-4989	147	3	,	,	PUNCT
ejpam-4989	147	4	we	we	PRON
ejpam-4989	147	5	have	have	VERB
ejpam-4989	147	6	p	p	NOUN
ejpam-4989	147	7	(	(	PUNCT
ejpam-4989	147	8	k	k	NOUN
ejpam-4989	147	9	)	)	PUNCT
ejpam-4989	147	10	n	n	NOUN
ejpam-4989	147	11	=	=	SYM
ejpam-4989	147	12	f2n−1	f2n−1	PROPN
ejpam-4989	147	13	,	,	PUNCT
ejpam-4989	147	14	where	where	SCONJ
ejpam-4989	147	15	fn	fn	NOUN
ejpam-4989	147	16	is	be	AUX
ejpam-4989	147	17	a	a	DET
ejpam-4989	147	18	fibonacci	fibonacci	NOUN
ejpam-4989	147	19	number	number	NOUN
ejpam-4989	147	20	,	,	PUNCT
ejpam-4989	147	21	and	and	CCONJ
ejpam-4989	147	22	we	we	PRON
ejpam-4989	147	23	obtain	obtain	VERB
ejpam-4989	147	24	the	the	DET
ejpam-4989	147	25	set	set	NOUN
ejpam-4989	147	26	of	of	ADP
ejpam-4989	147	27	solutions	solution	NOUN
ejpam-4989	147	28	in	in	ADP
ejpam-4989	147	29	theorem	theorem	NOUN
ejpam-4989	147	30	2	2	NUM
ejpam-4989	147	31	.	.	X
ejpam-4989	147	32	for	for	ADP
ejpam-4989	147	33	the	the	DET
ejpam-4989	147	34	remaining	remain	VERB
ejpam-4989	147	35	possibility	possibility	NOUN
ejpam-4989	147	36	,	,	PUNCT
ejpam-4989	147	37	we	we	PRON
ejpam-4989	147	38	assumed	assume	VERB
ejpam-4989	147	39	that	that	SCONJ
ejpam-4989	147	40	n	n	PROPN
ejpam-4989	147	41	≥	≥	NOUN
ejpam-4989	147	42	k	k	NOUN
ejpam-4989	148	1	+	+	CCONJ
ejpam-4989	148	2	2	2	NUM
ejpam-4989	148	3	and	and	CCONJ
ejpam-4989	148	4	k	k	PROPN
ejpam-4989	148	5	≥	≥	NUM
ejpam-4989	148	6	2	2	NUM
ejpam-4989	148	7	.	.	PUNCT
ejpam-4989	148	8	by	by	ADP
ejpam-4989	148	9	combining	combine	VERB
ejpam-4989	148	10	inequalities	inequality	NOUN
ejpam-4989	148	11	(	(	PUNCT
ejpam-4989	148	12	6	6	NUM
ejpam-4989	148	13	)	)	PUNCT
ejpam-4989	148	14	and	and	CCONJ
ejpam-4989	148	15	(	(	PUNCT
ejpam-4989	148	16	11	11	NUM
ejpam-4989	148	17	)	)	PUNCT
ejpam-4989	148	18	with	with	ADP
ejpam-4989	148	19	equation	equation	NOUN
ejpam-4989	148	20	(	(	PUNCT
ejpam-4989	148	21	22	22	NUM
ejpam-4989	148	22	)	)	PUNCT
ejpam-4989	148	23	,	,	PUNCT
ejpam-4989	148	24	we	we	PRON
ejpam-4989	148	25	obtain	obtain	VERB
ejpam-4989	148	26	:	:	PUNCT
ejpam-4989	148	27	αn−2	αn−2	VERB
ejpam-4989	148	28	≤	≤	ADJ
ejpam-4989	149	1	p	p	NOUN
ejpam-4989	149	2	(	(	PUNCT
ejpam-4989	149	3	k	k	NOUN
ejpam-4989	149	4	)	)	PUNCT
ejpam-4989	149	5	n	n	NOUN
ejpam-4989	149	6	=	=	PUNCT
ejpam-4989	149	7	tm	tm	PROPN
ejpam-4989	149	8	≤	≤	PROPN
ejpam-4989	149	9	ηm−1	ηm−1	NOUN
ejpam-4989	149	10	1	1	NUM
ejpam-4989	149	11	and	and	CCONJ
ejpam-4989	149	12	ηm−2	ηm−2	ADJ
ejpam-4989	149	13	1	1	NUM
ejpam-4989	149	14	≤	≤	NOUN
ejpam-4989	149	15	tm	tm	NOUN
ejpam-4989	149	16	=	=	SYM
ejpam-4989	149	17	p	p	X
ejpam-4989	149	18	(	(	PUNCT
ejpam-4989	149	19	k	k	NOUN
ejpam-4989	149	20	)	)	PUNCT
ejpam-4989	149	21	n	n	PRON
ejpam-4989	149	22	≤	≤	PROPN
ejpam-4989	149	23	αn−1	αn−1	ADJ
ejpam-4989	149	24	,	,	PUNCT
ejpam-4989	149	25	we	we	PRON
ejpam-4989	149	26	conclude	conclude	VERB
ejpam-4989	149	27	that	that	SCONJ
ejpam-4989	149	28	(	(	PUNCT
ejpam-4989	149	29	n−	n−	NOUN
ejpam-4989	149	30	2	2	NUM
ejpam-4989	149	31	)	)	PUNCT
ejpam-4989	149	32	log(α	log(α	PROPN
ejpam-4989	149	33	)	)	PUNCT
ejpam-4989	149	34	log(η1	log(η1	NOUN
ejpam-4989	149	35	)	)	PUNCT
ejpam-4989	149	36	≤	≤	NOUN
ejpam-4989	149	37	m−	m−	PROPN
ejpam-4989	149	38	1	1	NUM
ejpam-4989	149	39	and	and	CCONJ
ejpam-4989	149	40	m	m	PRON
ejpam-4989	149	41	≤	≤	NOUN
ejpam-4989	149	42	(	(	PUNCT
ejpam-4989	149	43	n−	n−	NOUN
ejpam-4989	149	44	1	1	NUM
ejpam-4989	149	45	)	)	PUNCT
ejpam-4989	149	46	log(α	log(α	PROPN
ejpam-4989	149	47	)	)	PUNCT
ejpam-4989	149	48	log(η1	log(η1	NOUN
ejpam-4989	149	49	)	)	PUNCT
ejpam-4989	150	1	+	+	CCONJ
ejpam-4989	150	2	2	2	NUM
ejpam-4989	150	3	,	,	PUNCT
ejpam-4989	150	4	we	we	PRON
ejpam-4989	150	5	obtain	obtain	VERB
ejpam-4989	150	6	0.79n−	0.79n−	X
ejpam-4989	150	7	1.58	1.58	NUM
ejpam-4989	150	8	<	<	X
ejpam-4989	151	1	m−	m−	PROPN
ejpam-4989	152	1	1	1	NUM
ejpam-4989	152	2	<	<	X
ejpam-4989	152	3	m	m	X
ejpam-4989	152	4	<	<	X
ejpam-4989	152	5	1.58n+	1.58n+	NUM
ejpam-4989	152	6	0.42	0.42	NUM
ejpam-4989	152	7	,	,	PUNCT
ejpam-4989	152	8	because	because	SCONJ
ejpam-4989	152	9	ϕ2(1−	ϕ2(1−	PROPN
ejpam-4989	152	10	ϕ−k	ϕ−k	PROPN
ejpam-4989	152	11	)	)	PUNCT
ejpam-4989	152	12	<	<	X
ejpam-4989	152	13	α(k	α(k	NOUN
ejpam-4989	152	14	)	)	PUNCT
ejpam-4989	152	15	<	<	X
ejpam-4989	152	16	ϕ2	ϕ2	ADV
ejpam-4989	152	17	for	for	ADP
ejpam-4989	152	18	all	all	DET
ejpam-4989	152	19	k	k	PROPN
ejpam-4989	152	20	≥	≥	NUM
ejpam-4989	152	21	2	2	NUM
ejpam-4989	152	22	.	.	PUNCT
ejpam-4989	153	1	we	we	PRON
ejpam-4989	153	2	consider	consider	VERB
ejpam-4989	153	3	the	the	DET
ejpam-4989	153	4	following	following	NOUN
ejpam-4989	153	5	0.79n−	0.79n−	X
ejpam-4989	153	6	1.58	1.58	NUM
ejpam-4989	153	7	<	<	X
ejpam-4989	153	8	m−	m−	PROPN
ejpam-4989	153	9	1	1	NUM
ejpam-4989	153	10	<	<	X
ejpam-4989	153	11	m	m	X
ejpam-4989	153	12	<	<	X
ejpam-4989	153	13	2n	2n	NUM
ejpam-4989	153	14	.	.	PUNCT
ejpam-4989	154	1	(	(	PUNCT
ejpam-4989	154	2	23	23	NUM
ejpam-4989	154	3	)	)	PUNCT
ejpam-4989	154	4	h.	h.	PROPN
ejpam-4989	154	5	s.	s.	PROPN
ejpam-4989	154	6	taher	taher	PROPN
ejpam-4989	154	7	,	,	PUNCT
ejpam-4989	154	8	s.	s.	PROPN
ejpam-4989	154	9	k.	k.	PROPN
ejpam-4989	154	10	dash	dash	NOUN
ejpam-4989	154	11	/	/	SYM
ejpam-4989	154	12	eur	eur	NOUN
ejpam-4989	154	13	.	.	PUNCT
ejpam-4989	155	1	j.	j.	PROPN
ejpam-4989	155	2	pure	pure	PROPN
ejpam-4989	155	3	appl	appl	PROPN
ejpam-4989	155	4	.	.	PROPN
ejpam-4989	155	5	math	math	PROPN
ejpam-4989	155	6	,	,	PUNCT
ejpam-4989	155	7	17	17	NUM
ejpam-4989	155	8	(	(	PUNCT
ejpam-4989	155	9	1	1	NUM
ejpam-4989	155	10	)	)	PUNCT
ejpam-4989	155	11	(	(	PUNCT
ejpam-4989	155	12	2024	2024	NUM
ejpam-4989	155	13	)	)	PUNCT
ejpam-4989	155	14	,	,	PUNCT
ejpam-4989	155	15	135	135	NUM
ejpam-4989	155	16	-	-	SYM
ejpam-4989	155	17	146	146	NUM
ejpam-4989	155	18	141	141	NUM
ejpam-4989	155	19	3.2	3.2	NUM
ejpam-4989	155	20	.	.	PUNCT
ejpam-4989	156	1	bounding	bound	VERB
ejpam-4989	156	2	n	n	NOUN
ejpam-4989	156	3	in	in	ADP
ejpam-4989	156	4	terms	term	NOUN
ejpam-4989	156	5	of	of	ADP
ejpam-4989	156	6	k	k	PROPN
ejpam-4989	156	7	in	in	ADP
ejpam-4989	156	8	this	this	DET
ejpam-4989	156	9	step	step	NOUN
ejpam-4989	156	10	,	,	PUNCT
ejpam-4989	156	11	we	we	PRON
ejpam-4989	156	12	prove	prove	VERB
ejpam-4989	156	13	the	the	DET
ejpam-4989	156	14	following	follow	VERB
ejpam-4989	156	15	lemma	lemma	PROPN
ejpam-4989	156	16	to	to	PART
ejpam-4989	156	17	find	find	VERB
ejpam-4989	156	18	an	an	DET
ejpam-4989	156	19	upper	upper	ADJ
ejpam-4989	156	20	bound	bind	VERB
ejpam-4989	156	21	for	for	ADP
ejpam-4989	156	22	n	n	NOUN
ejpam-4989	156	23	in	in	ADP
ejpam-4989	156	24	terms	term	NOUN
ejpam-4989	156	25	of	of	ADP
ejpam-4989	156	26	k.	k.	PROPN
ejpam-4989	156	27	lemma	lemma	PROPN
ejpam-4989	157	1	6	6	NUM
ejpam-4989	157	2	.	.	PUNCT
ejpam-4989	158	1	if	if	SCONJ
ejpam-4989	158	2	(	(	PUNCT
ejpam-4989	158	3	m	m	NOUN
ejpam-4989	158	4	,	,	PUNCT
ejpam-4989	158	5	n	n	CCONJ
ejpam-4989	158	6	,	,	PUNCT
ejpam-4989	158	7	k	k	NOUN
ejpam-4989	158	8	)	)	PUNCT
ejpam-4989	158	9	is	be	AUX
ejpam-4989	158	10	a	a	DET
ejpam-4989	158	11	positive	positive	ADJ
ejpam-4989	158	12	integers	integer	NOUN
ejpam-4989	158	13	solution	solution	NOUN
ejpam-4989	158	14	of	of	ADP
ejpam-4989	158	15	equation	equation	NOUN
ejpam-4989	158	16	(	(	PUNCT
ejpam-4989	158	17	22	22	NUM
ejpam-4989	158	18	)	)	PUNCT
ejpam-4989	158	19	with	with	ADP
ejpam-4989	158	20	k	k	PROPN
ejpam-4989	158	21	≥	≥	NUM
ejpam-4989	158	22	2	2	NUM
ejpam-4989	158	23	and	and	CCONJ
ejpam-4989	158	24	n	n	PRON
ejpam-4989	158	25	≥	≥	NOUN
ejpam-4989	158	26	k	k	NOUN
ejpam-4989	159	1	+	+	CCONJ
ejpam-4989	159	2	2	2	NUM
ejpam-4989	159	3	,	,	PUNCT
ejpam-4989	159	4	then	then	ADV
ejpam-4989	159	5	the	the	DET
ejpam-4989	159	6	inequalities	inequality	NOUN
ejpam-4989	159	7	0.63	0.63	NUM
ejpam-4989	159	8	m	m	NOUN
ejpam-4989	159	9	<	<	X
ejpam-4989	159	10	n	n	X
ejpam-4989	159	11	<	<	X
ejpam-4989	159	12	7.6	7.6	NUM
ejpam-4989	159	13	·	·	SYM
ejpam-4989	159	14	1016k5(log(k))3	1016k5(log(k))3	NUM
ejpam-4989	159	15	hold	hold	VERB
ejpam-4989	159	16	.	.	PUNCT
ejpam-4989	160	1	proof	proof	NOUN
ejpam-4989	160	2	.	.	PUNCT
ejpam-4989	161	1	combining	combine	VERB
ejpam-4989	161	2	equation	equation	NOUN
ejpam-4989	161	3	(	(	PUNCT
ejpam-4989	161	4	22	22	NUM
ejpam-4989	161	5	)	)	PUNCT
ejpam-4989	161	6	,	,	PUNCT
ejpam-4989	161	7	(	(	PUNCT
ejpam-4989	161	8	5	5	NUM
ejpam-4989	161	9	)	)	PUNCT
ejpam-4989	161	10	,	,	PUNCT
ejpam-4989	161	11	and	and	CCONJ
ejpam-4989	161	12	(	(	PUNCT
ejpam-4989	161	13	10	10	NUM
ejpam-4989	161	14	)	)	PUNCT
ejpam-4989	161	15	,	,	PUNCT
ejpam-4989	161	16	we	we	PRON
ejpam-4989	161	17	obtain	obtain	VERB
ejpam-4989	161	18	:	:	PUNCT
ejpam-4989	161	19	gk(α)α	gk(α)α	ADP
ejpam-4989	161	20	n	n	PROPN
ejpam-4989	161	21	+	+	NUM
ejpam-4989	161	22	ek(n	ek(n	NOUN
ejpam-4989	161	23	)	)	PUNCT
ejpam-4989	162	1	=	=	SYM
ejpam-4989	162	2	cηm−1	cηm−1	PROPN
ejpam-4989	162	3	1	1	NUM
ejpam-4989	163	1	+	+	CCONJ
ejpam-4989	163	2	dm	dm	NOUN
ejpam-4989	163	3	.	.	PUNCT
ejpam-4989	164	1	taking	take	VERB
ejpam-4989	164	2	absolute	absolute	ADJ
ejpam-4989	164	3	values	value	NOUN
ejpam-4989	164	4	for	for	ADP
ejpam-4989	164	5	both	both	DET
ejpam-4989	164	6	sides	side	NOUN
ejpam-4989	164	7	,	,	PUNCT
ejpam-4989	164	8	we	we	PRON
ejpam-4989	164	9	get∣∣gk(α)αn	get∣∣gk(α)αn	VERB
ejpam-4989	164	10	−	−	NOUN
ejpam-4989	165	1	cηm−1	cηm−1	PROPN
ejpam-4989	165	2	1	1	NUM
ejpam-4989	165	3	∣∣	∣∣	X
ejpam-4989	165	4	<	<	X
ejpam-4989	165	5	1	1	NUM
ejpam-4989	165	6	2	2	NUM
ejpam-4989	165	7	+	+	CCONJ
ejpam-4989	165	8	|dm|	|dm|	X
ejpam-4989	165	9	<	<	X
ejpam-4989	165	10	1	1	NUM
ejpam-4989	165	11	.	.	PUNCT
ejpam-4989	165	12	(	(	PUNCT
ejpam-4989	165	13	24	24	NUM
ejpam-4989	165	14	)	)	PUNCT
ejpam-4989	165	15	dividing	divide	VERB
ejpam-4989	165	16	both	both	DET
ejpam-4989	165	17	sides	side	NOUN
ejpam-4989	165	18	by	by	ADP
ejpam-4989	165	19	cηm−1	cηm−1	PROPN
ejpam-4989	165	20	1	1	NUM
ejpam-4989	165	21	,	,	PUNCT
ejpam-4989	165	22	we	we	PRON
ejpam-4989	165	23	deduce	deduce	VERB
ejpam-4989	165	24	that∣∣∣(c−1gk(α))α	that∣∣∣(c−1gk(α))α	NOUN
ejpam-4989	165	25	nη	nη	ADP
ejpam-4989	165	26	−(m−1	−(m−1	PROPN
ejpam-4989	165	27	)	)	PUNCT
ejpam-4989	165	28	1	1	NUM
ejpam-4989	165	29	−	−	NOUN
ejpam-4989	165	30	1	1	NUM
ejpam-4989	165	31	∣∣∣	∣∣∣	NOUN
ejpam-4989	165	32	<	<	X
ejpam-4989	165	33	1.6	1.6	NUM
ejpam-4989	165	34	ηm−1	ηm−1	PROPN
ejpam-4989	165	35	1	1	NUM
ejpam-4989	165	36	.	.	PUNCT
ejpam-4989	166	1	(	(	PUNCT
ejpam-4989	166	2	25	25	NUM
ejpam-4989	166	3	)	)	PUNCT
ejpam-4989	166	4	we	we	PRON
ejpam-4989	166	5	apply	apply	VERB
ejpam-4989	166	6	theorem	theorem	VERB
ejpam-4989	166	7	1	1	NUM
ejpam-4989	166	8	to	to	ADP
ejpam-4989	166	9	the	the	DET
ejpam-4989	166	10	left	left	ADJ
ejpam-4989	166	11	-	-	PUNCT
ejpam-4989	166	12	hand	hand	NOUN
ejpam-4989	166	13	side	side	NOUN
ejpam-4989	166	14	inequality	inequality	NOUN
ejpam-4989	166	15	(	(	PUNCT
ejpam-4989	166	16	25	25	NUM
ejpam-4989	166	17	)	)	PUNCT
ejpam-4989	166	18	with	with	ADP
ejpam-4989	166	19	parameters	parameter	NOUN
ejpam-4989	166	20	t	t	NOUN
ejpam-4989	166	21	:	:	PUNCT
ejpam-4989	166	22	=	=	SYM
ejpam-4989	166	23	3	3	NUM
ejpam-4989	166	24	,	,	PUNCT
ejpam-4989	166	25	where	where	SCONJ
ejpam-4989	166	26	γ1	γ1	NOUN
ejpam-4989	166	27	:	:	PUNCT
ejpam-4989	166	28	=	=	SYM
ejpam-4989	166	29	c−1gk(α	c−1gk(α	PROPN
ejpam-4989	166	30	)	)	PUNCT
ejpam-4989	166	31	,	,	PUNCT
ejpam-4989	166	32	γ2	γ2	NOUN
ejpam-4989	166	33	:	:	PUNCT
ejpam-4989	166	34	=	=	SYM
ejpam-4989	166	35	α	α	PROPN
ejpam-4989	166	36	,	,	PUNCT
ejpam-4989	166	37	γ3	γ3	NOUN
ejpam-4989	166	38	:	:	PUNCT
ejpam-4989	166	39	=	=	SYM
ejpam-4989	166	40	η1	η1	NOUN
ejpam-4989	166	41	,	,	PUNCT
ejpam-4989	166	42	and	and	CCONJ
ejpam-4989	166	43	b1	b1	NOUN
ejpam-4989	166	44	:	:	PUNCT
ejpam-4989	166	45	=	=	SYM
ejpam-4989	166	46	1	1	NUM
ejpam-4989	166	47	,	,	PUNCT
ejpam-4989	166	48	b2	b2	NOUN
ejpam-4989	166	49	:	:	PUNCT
ejpam-4989	166	50	=	=	SYM
ejpam-4989	166	51	n	n	CCONJ
ejpam-4989	166	52	,	,	PUNCT
ejpam-4989	166	53	b3	b3	PROPN
ejpam-4989	166	54	=	=	SYM
ejpam-4989	166	55	−(m	−(m	PROPN
ejpam-4989	166	56	−	−	NOUN
ejpam-4989	166	57	1	1	NUM
ejpam-4989	166	58	)	)	PUNCT
ejpam-4989	166	59	.	.	PUNCT
ejpam-4989	167	1	so	so	ADV
ejpam-4989	167	2	l	l	NOUN
ejpam-4989	167	3	:	:	PUNCT
ejpam-4989	167	4	=	=	NOUN
ejpam-4989	167	5	q(γ1	q(γ1	NOUN
ejpam-4989	167	6	,	,	PUNCT
ejpam-4989	167	7	γ2	γ2	ADJ
ejpam-4989	167	8	,	,	PUNCT
ejpam-4989	167	9	γ3	γ3	NOUN
ejpam-4989	167	10	)	)	PUNCT
ejpam-4989	167	11	.	.	PUNCT
ejpam-4989	168	1	thus	thus	ADV
ejpam-4989	168	2	,	,	PUNCT
ejpam-4989	168	3	d	d	X
ejpam-4989	168	4	:	:	PUNCT
ejpam-4989	168	5	=	=	PUNCT
ejpam-4989	169	1	[	[	X
ejpam-4989	169	2	l	l	NOUN
ejpam-4989	169	3	,	,	PUNCT
ejpam-4989	169	4	q	q	X
ejpam-4989	169	5	]	]	X
ejpam-4989	169	6	=	=	SYM
ejpam-4989	169	7	3k	3k	X
ejpam-4989	169	8	.	.	PUNCT
ejpam-4989	170	1	to	to	PART
ejpam-4989	170	2	show	show	VERB
ejpam-4989	170	3	that	that	SCONJ
ejpam-4989	170	4	λ	λ	PROPN
ejpam-4989	170	5	is	be	AUX
ejpam-4989	170	6	nonzero	nonzero	ADJ
ejpam-4989	170	7	,	,	PUNCT
ejpam-4989	170	8	it	it	PRON
ejpam-4989	170	9	is	be	AUX
ejpam-4989	170	10	assumed	assume	VERB
ejpam-4989	170	11	that	that	SCONJ
ejpam-4989	170	12	λ	λ	PROPN
ejpam-4989	170	13	=	=	SYM
ejpam-4989	170	14	0	0	PROPN
ejpam-4989	170	15	,	,	PUNCT
ejpam-4989	170	16	which	which	PRON
ejpam-4989	170	17	implies	imply	VERB
ejpam-4989	170	18	that	that	PRON
ejpam-4989	170	19	gk(α	gk(α	PUNCT
ejpam-4989	170	20	)	)	PUNCT
ejpam-4989	171	1	=	=	SYM
ejpam-4989	171	2	cη	cη	PROPN
ejpam-4989	171	3	(	(	PUNCT
ejpam-4989	171	4	m−1	m−1	PROPN
ejpam-4989	171	5	)	)	PUNCT
ejpam-4989	171	6	1	1	NUM
ejpam-4989	171	7	θ−n	θ−n	PROPN
ejpam-4989	171	8	1	1	NUM
ejpam-4989	171	9	,	,	PUNCT
ejpam-4989	171	10	we	we	PRON
ejpam-4989	171	11	obtain	obtain	VERB
ejpam-4989	171	12	gk(α	gk(α	PUNCT
ejpam-4989	171	13	)	)	PUNCT
ejpam-4989	171	14	as	as	ADP
ejpam-4989	171	15	an	an	DET
ejpam-4989	171	16	algebraic	algebraic	ADJ
ejpam-4989	171	17	integer	integer	NOUN
ejpam-4989	171	18	,	,	PUNCT
ejpam-4989	171	19	which	which	PRON
ejpam-4989	171	20	is	be	AUX
ejpam-4989	171	21	a	a	DET
ejpam-4989	171	22	contradiction	contradiction	NOUN
ejpam-4989	171	23	.	.	PUNCT
ejpam-4989	172	1	hence	hence	ADV
ejpam-4989	172	2	λ	λ	X
ejpam-4989	172	3	̸=	̸=	PROPN
ejpam-4989	172	4	0	0	NUM
ejpam-4989	172	5	.	.	PUNCT
ejpam-4989	173	1	not	not	PART
ejpam-4989	173	2	that	that	SCONJ
ejpam-4989	173	3	h	h	NOUN
ejpam-4989	173	4	(	(	PUNCT
ejpam-4989	173	5	γ1	γ1	PROPN
ejpam-4989	173	6	)	)	PUNCT
ejpam-4989	173	7	<	<	X
ejpam-4989	173	8	h(c	h(c	PROPN
ejpam-4989	173	9	)	)	PUNCT
ejpam-4989	174	1	+	+	CCONJ
ejpam-4989	174	2	h(gk(α	h(gk(α	NOUN
ejpam-4989	174	3	)	)	PUNCT
ejpam-4989	174	4	)	)	PUNCT
ejpam-4989	175	1	<	<	X
ejpam-4989	175	2	log(44	log(44	PROPN
ejpam-4989	175	3	)	)	PUNCT
ejpam-4989	175	4	3	3	NUM
ejpam-4989	175	5	+	+	SYM
ejpam-4989	175	6	4k	4k	NUM
ejpam-4989	175	7	log(ϕ	log(ϕ	NOUN
ejpam-4989	175	8	)	)	PUNCT
ejpam-4989	175	9	+	+	CCONJ
ejpam-4989	175	10	k	k	PROPN
ejpam-4989	175	11	log(k	log(k	PROPN
ejpam-4989	176	1	+	+	NOUN
ejpam-4989	176	2	1	1	NUM
ejpam-4989	176	3	)	)	PUNCT
ejpam-4989	176	4	<	<	X
ejpam-4989	176	5	5.3k	5.3k	NUM
ejpam-4989	176	6	log(k	log(k	NOUN
ejpam-4989	176	7	)	)	PUNCT
ejpam-4989	176	8	,	,	PUNCT
ejpam-4989	176	9	which	which	PRON
ejpam-4989	176	10	holds	hold	VERB
ejpam-4989	176	11	for	for	ADP
ejpam-4989	176	12	all	all	DET
ejpam-4989	176	13	k	k	PROPN
ejpam-4989	176	14	≥	≥	NUM
ejpam-4989	176	15	2	2	NUM
ejpam-4989	176	16	and	and	CCONJ
ejpam-4989	176	17	a	a	DET
ejpam-4989	176	18	minimal	minimal	ADJ
ejpam-4989	176	19	polynomial	polynomial	ADJ
ejpam-4989	176	20	44x3−	44x3−	NOUN
ejpam-4989	177	1	44x2	44x2	NUM
ejpam-4989	178	1	+	+	ADJ
ejpam-4989	178	2	12x−	12x−	NUM
ejpam-4989	178	3	1	1	NUM
ejpam-4989	178	4	of	of	ADP
ejpam-4989	178	5	c.	c.	PROPN
ejpam-4989	178	6	therefore	therefore	ADV
ejpam-4989	178	7	,	,	PUNCT
ejpam-4989	178	8	h	h	PROPN
ejpam-4989	178	9	(	(	PUNCT
ejpam-4989	178	10	γ2	γ2	ADJ
ejpam-4989	178	11	)	)	PUNCT
ejpam-4989	178	12	=	=	SYM
ejpam-4989	178	13	log(α	log(α	X
ejpam-4989	178	14	)	)	PUNCT
ejpam-4989	178	15	k	k	X
ejpam-4989	178	16	<	<	X
ejpam-4989	178	17	2	2	NUM
ejpam-4989	178	18	log(ϕ	log(ϕ	X
ejpam-4989	178	19	)	)	PUNCT
ejpam-4989	178	20	k	k	NOUN
ejpam-4989	178	21	and	and	CCONJ
ejpam-4989	178	22	h	h	PROPN
ejpam-4989	178	23	(	(	PUNCT
ejpam-4989	178	24	γ3	γ3	NOUN
ejpam-4989	178	25	)	)	PUNCT
ejpam-4989	178	26	=	=	PUNCT
ejpam-4989	179	1	log(η1	log(η1	PROPN
ejpam-4989	179	2	)	)	PUNCT
ejpam-4989	179	3	3	3	NUM
ejpam-4989	179	4	.	.	PUNCT
ejpam-4989	180	1	thus	thus	ADV
ejpam-4989	180	2	,	,	PUNCT
ejpam-4989	180	3	we	we	PRON
ejpam-4989	180	4	obtained	obtain	VERB
ejpam-4989	180	5	a1	a1	NOUN
ejpam-4989	180	6	:	:	PUNCT
ejpam-4989	180	7	=	=	SYM
ejpam-4989	180	8	15.9k2	15.9k2	NUM
ejpam-4989	180	9	log(k	log(k	NOUN
ejpam-4989	180	10	)	)	PUNCT
ejpam-4989	180	11	,	,	PUNCT
ejpam-4989	180	12	a2	a2	PROPN
ejpam-4989	180	13	:	:	PUNCT
ejpam-4989	180	14	=	=	SYM
ejpam-4989	180	15	6	6	NUM
ejpam-4989	180	16	log(ϕ	log(ϕ	NOUN
ejpam-4989	180	17	)	)	PUNCT
ejpam-4989	180	18	,	,	PUNCT
ejpam-4989	180	19	and	and	CCONJ
ejpam-4989	180	20	a3	a3	VERB
ejpam-4989	180	21	:	:	PUNCT
ejpam-4989	181	1	=	=	SYM
ejpam-4989	181	2	k	k	X
ejpam-4989	181	3	log(η1	log(η1	PROPN
ejpam-4989	181	4	)	)	PUNCT
ejpam-4989	181	5	.	.	PUNCT
ejpam-4989	182	1	in	in	ADP
ejpam-4989	182	2	addition	addition	NOUN
ejpam-4989	182	3	,	,	PUNCT
ejpam-4989	182	4	taking	take	VERB
ejpam-4989	182	5	b	b	NOUN
ejpam-4989	182	6	:	:	PUNCT
ejpam-4989	182	7	=	=	SYM
ejpam-4989	182	8	2n	2n	NUM
ejpam-4989	182	9	,	,	PUNCT
ejpam-4989	182	10	since	since	SCONJ
ejpam-4989	182	11	max{|1|	max{|1|	NOUN
ejpam-4989	182	12	,	,	PUNCT
ejpam-4989	182	13	|n|	|n|	NOUN
ejpam-4989	182	14	,	,	PUNCT
ejpam-4989	182	15	|−(m−1)|	|−(m−1)|	PRON
ejpam-4989	182	16	}	}	PUNCT
ejpam-4989	182	17	≤	≤	NUM
ejpam-4989	182	18	2n	2n	NUM
ejpam-4989	182	19	.	.	PUNCT
ejpam-4989	183	1	thus	thus	ADV
ejpam-4989	183	2	,	,	PUNCT
ejpam-4989	183	3	by	by	ADP
ejpam-4989	183	4	theorem	theorem	NOUN
ejpam-4989	183	5	1	1	NUM
ejpam-4989	183	6	,	,	PUNCT
ejpam-4989	183	7	we	we	PRON
ejpam-4989	183	8	get	get	VERB
ejpam-4989	183	9	that	that	PRON
ejpam-4989	183	10	1.6	1.6	NUM
ejpam-4989	183	11	ηm−1	ηm−1	NOUN
ejpam-4989	183	12	1	1	NUM
ejpam-4989	183	13	>	>	PUNCT
ejpam-4989	183	14	|λ|	|λ|	X
ejpam-4989	183	15	>	>	X
ejpam-4989	183	16	exp{−g(1	exp{−g(1	PROPN
ejpam-4989	183	17	+	+	CCONJ
ejpam-4989	183	18	log(2n))(15.9k2	log(2n))(15.9k2	NUM
ejpam-4989	183	19	log(k))(6	log(k))(6	NOUN
ejpam-4989	183	20	log(ϕ))(k	log(ϕ))(k	PROPN
ejpam-4989	183	21	log(η1	log(η1	PROPN
ejpam-4989	183	22	)	)	PUNCT
ejpam-4989	183	23	)	)	PUNCT
ejpam-4989	183	24	}	}	PUNCT
ejpam-4989	183	25	,	,	PUNCT
ejpam-4989	183	26	where	where	SCONJ
ejpam-4989	183	27	g	g	NOUN
ejpam-4989	183	28	=	=	SYM
ejpam-4989	183	29	(	(	PUNCT
ejpam-4989	183	30	1.4	1.4	NUM
ejpam-4989	183	31	)	)	PUNCT
ejpam-4989	183	32	(	(	PUNCT
ejpam-4989	183	33	306	306	NUM
ejpam-4989	183	34	)	)	PUNCT
ejpam-4989	183	35	(	(	PUNCT
ejpam-4989	183	36	34.5	34.5	NUM
ejpam-4989	183	37	)	)	PUNCT
ejpam-4989	183	38	(	(	PUNCT
ejpam-4989	183	39	3k)2(1	3k)2(1	NUM
ejpam-4989	183	40	+	+	CCONJ
ejpam-4989	183	41	log(3k	log(3k	ADJ
ejpam-4989	183	42	)	)	PUNCT
ejpam-4989	183	43	)	)	PUNCT
ejpam-4989	183	44	.	.	PUNCT
ejpam-4989	184	1	we	we	PRON
ejpam-4989	184	2	get	get	VERB
ejpam-4989	184	3	(	(	PUNCT
ejpam-4989	184	4	m−	m−	PROPN
ejpam-4989	184	5	1	1	NUM
ejpam-4989	184	6	)	)	PUNCT
ejpam-4989	184	7	log(η1)−	log(η1)−	NOUN
ejpam-4989	184	8	log(1.6	log(1.6	NOUN
ejpam-4989	184	9	)	)	PUNCT
ejpam-4989	184	10	<	<	X
ejpam-4989	185	1	3.61	3.61	NUM
ejpam-4989	185	2	·	·	PUNCT
ejpam-4989	185	3	1013k5	1013k5	NUM
ejpam-4989	185	4	log(k)(1	log(k)(1	NOUN
ejpam-4989	186	1	+	+	CCONJ
ejpam-4989	186	2	log(3k))(1	log(3k))(1	PRON
ejpam-4989	186	3	+	+	NUM
ejpam-4989	186	4	log(2n	log(2n	NOUN
ejpam-4989	186	5	)	)	PUNCT
ejpam-4989	186	6	)	)	PUNCT
ejpam-4989	186	7	.	.	PUNCT
ejpam-4989	187	1	(	(	PUNCT
ejpam-4989	187	2	26	26	NUM
ejpam-4989	187	3	)	)	PUNCT
ejpam-4989	187	4	using	use	VERB
ejpam-4989	187	5	the	the	DET
ejpam-4989	187	6	facts	fact	NOUN
ejpam-4989	187	7	that	that	SCONJ
ejpam-4989	187	8	(	(	PUNCT
ejpam-4989	187	9	1	1	NUM
ejpam-4989	187	10	+	+	CCONJ
ejpam-4989	187	11	log(3k	log(3k	ADJ
ejpam-4989	187	12	)	)	PUNCT
ejpam-4989	187	13	)	)	PUNCT
ejpam-4989	188	1	<	<	X
ejpam-4989	188	2	4.1	4.1	NUM
ejpam-4989	188	3	log(k	log(k	NOUN
ejpam-4989	188	4	)	)	PUNCT
ejpam-4989	188	5	for	for	ADP
ejpam-4989	188	6	all	all	DET
ejpam-4989	188	7	k	k	PROPN
ejpam-4989	188	8	≥	≥	NUM
ejpam-4989	188	9	2	2	NUM
ejpam-4989	188	10	and	and	CCONJ
ejpam-4989	188	11	(	(	PUNCT
ejpam-4989	188	12	1	1	NUM
ejpam-4989	188	13	+	+	NUM
ejpam-4989	188	14	log(2n	log(2n	NOUN
ejpam-4989	188	15	)	)	PUNCT
ejpam-4989	188	16	)	)	PUNCT
ejpam-4989	189	1	<	<	X
ejpam-4989	189	2	2.3	2.3	NUM
ejpam-4989	189	3	log(n	log(n	NOUN
ejpam-4989	189	4	)	)	PUNCT
ejpam-4989	189	5	for	for	ADP
ejpam-4989	189	6	all	all	DET
ejpam-4989	189	7	n	n	PRON
ejpam-4989	189	8	≥	≥	NOUN
ejpam-4989	189	9	4	4	NUM
ejpam-4989	189	10	.	.	PUNCT
ejpam-4989	190	1	simplifying	simplify	VERB
ejpam-4989	190	2	the	the	DET
ejpam-4989	190	3	calculation	calculation	NOUN
ejpam-4989	190	4	,	,	PUNCT
ejpam-4989	190	5	we	we	PRON
ejpam-4989	190	6	obtain	obtain	VERB
ejpam-4989	190	7	m−	m−	PROPN
ejpam-4989	190	8	1	1	NUM
ejpam-4989	190	9	<	<	X
ejpam-4989	190	10	5.6	5.6	NUM
ejpam-4989	190	11	·	·	SYM
ejpam-4989	190	12	1014k5(log(k))2	1014k5(log(k))2	NUM
ejpam-4989	190	13	log(n	log(n	NOUN
ejpam-4989	190	14	)	)	PUNCT
ejpam-4989	190	15	,	,	PUNCT
ejpam-4989	190	16	h.	h.	PROPN
ejpam-4989	190	17	s.	s.	PROPN
ejpam-4989	190	18	taher	taher	PROPN
ejpam-4989	190	19	,	,	PUNCT
ejpam-4989	190	20	s.	s.	PROPN
ejpam-4989	190	21	k.	k.	PROPN
ejpam-4989	190	22	dash	dash	NOUN
ejpam-4989	190	23	/	/	SYM
ejpam-4989	190	24	eur	eur	NOUN
ejpam-4989	190	25	.	.	PUNCT
ejpam-4989	191	1	j.	j.	PROPN
ejpam-4989	191	2	pure	pure	PROPN
ejpam-4989	191	3	appl	appl	PROPN
ejpam-4989	191	4	.	.	PROPN
ejpam-4989	191	5	math	math	PROPN
ejpam-4989	191	6	,	,	PUNCT
ejpam-4989	191	7	17	17	NUM
ejpam-4989	191	8	(	(	PUNCT
ejpam-4989	191	9	1	1	NUM
ejpam-4989	191	10	)	)	PUNCT
ejpam-4989	191	11	(	(	PUNCT
ejpam-4989	191	12	2024	2024	NUM
ejpam-4989	191	13	)	)	PUNCT
ejpam-4989	191	14	,	,	PUNCT
ejpam-4989	191	15	135	135	NUM
ejpam-4989	191	16	-	-	SYM
ejpam-4989	191	17	146	146	NUM
ejpam-4989	191	18	142	142	NUM
ejpam-4989	191	19	by	by	ADP
ejpam-4989	191	20	inequality	inequality	NOUN
ejpam-4989	191	21	(	(	PUNCT
ejpam-4989	191	22	23	23	NUM
ejpam-4989	191	23	)	)	PUNCT
ejpam-4989	191	24	,	,	PUNCT
ejpam-4989	191	25	we	we	PRON
ejpam-4989	191	26	deduce	deduce	VERB
ejpam-4989	191	27	that	that	SCONJ
ejpam-4989	191	28	n	n	PRON
ejpam-4989	191	29	log(n	log(n	NOUN
ejpam-4989	191	30	)	)	PUNCT
ejpam-4989	191	31	<	<	X
ejpam-4989	191	32	7.1	7.1	NUM
ejpam-4989	191	33	·	·	SYM
ejpam-4989	191	34	1014k5(log(k))2	1014k5(log(k))2	NUM
ejpam-4989	191	35	,	,	PUNCT
ejpam-4989	191	36	now	now	ADV
ejpam-4989	191	37	we	we	PRON
ejpam-4989	191	38	apply	apply	VERB
ejpam-4989	191	39	lemma	lemma	PROPN
ejpam-4989	191	40	5	5	NUM
ejpam-4989	191	41	take	take	NOUN
ejpam-4989	191	42	s	s	PART
ejpam-4989	191	43	:	:	PUNCT
ejpam-4989	191	44	=	=	NOUN
ejpam-4989	191	45	7.1·1014k5(log(k))2	7.1·1014k5(log(k))2	NUM
ejpam-4989	191	46	,	,	PUNCT
ejpam-4989	191	47	l	l	NOUN
ejpam-4989	191	48	:	:	PUNCT
ejpam-4989	191	49	=	=	SYM
ejpam-4989	191	50	n	n	CCONJ
ejpam-4989	191	51	,	,	PUNCT
ejpam-4989	191	52	r	r	NOUN
ejpam-4989	191	53	:	:	PUNCT
ejpam-4989	191	54	=	=	SYM
ejpam-4989	191	55	1	1	NUM
ejpam-4989	191	56	with	with	ADP
ejpam-4989	191	57	34.2	34.2	NUM
ejpam-4989	191	58	+	+	NUM
ejpam-4989	191	59	5	5	NUM
ejpam-4989	191	60	log(k)+	log(k)+	PROPN
ejpam-4989	191	61	2	2	NUM
ejpam-4989	191	62	log(log(k	log(log(k	NOUN
ejpam-4989	191	63	)	)	PUNCT
ejpam-4989	191	64	)	)	PUNCT
ejpam-4989	192	1	<	<	X
ejpam-4989	192	2	53.5	53.5	NUM
ejpam-4989	192	3	log(k	log(k	NOUN
ejpam-4989	192	4	)	)	PUNCT
ejpam-4989	192	5	for	for	ADP
ejpam-4989	192	6	all	all	DET
ejpam-4989	192	7	k	k	PROPN
ejpam-4989	192	8	≥	≥	NUM
ejpam-4989	192	9	2	2	NUM
ejpam-4989	192	10	,	,	PUNCT
ejpam-4989	192	11	we	we	PRON
ejpam-4989	192	12	get	get	VERB
ejpam-4989	192	13	n	n	PRON
ejpam-4989	192	14	<	<	X
ejpam-4989	192	15	2(7.1	2(7.1	NUM
ejpam-4989	192	16	·	·	PUNCT
ejpam-4989	192	17	1014k5(log(k))2)(log(7.1	1014k5(log(k))2)(log(7.1	NUM
ejpam-4989	192	18	·	·	SYM
ejpam-4989	192	19	1014k5(log(k))2	1014k5(log(k))2	NUM
ejpam-4989	192	20	)	)	PUNCT
ejpam-4989	192	21	)	)	PUNCT
ejpam-4989	193	1	<	<	X
ejpam-4989	193	2	(	(	PUNCT
ejpam-4989	193	3	1.42	1.42	NUM
ejpam-4989	193	4	·	·	PUNCT
ejpam-4989	193	5	1015k5(log(k))2)(34.2	1015k5(log(k))2)(34.2	NOUN
ejpam-4989	194	1	+	+	CCONJ
ejpam-4989	194	2	5	5	NUM
ejpam-4989	194	3	log(k	log(k	NOUN
ejpam-4989	194	4	)	)	PUNCT
ejpam-4989	195	1	+	+	CCONJ
ejpam-4989	195	2	2	2	NUM
ejpam-4989	195	3	log(log(k	log(log(k	NOUN
ejpam-4989	195	4	)	)	PUNCT
ejpam-4989	195	5	)	)	PUNCT
ejpam-4989	195	6	)	)	PUNCT
ejpam-4989	196	1	<	<	X
ejpam-4989	196	2	7.6	7.6	NUM
ejpam-4989	196	3	·	·	PUNCT
ejpam-4989	196	4	1016k5(log(k))3	1016k5(log(k))3	NUM
ejpam-4989	196	5	.	.	PUNCT
ejpam-4989	197	1	(	(	PUNCT
ejpam-4989	197	2	27	27	NUM
ejpam-4989	197	3	)	)	PUNCT
ejpam-4989	197	4	3.3	3.3	NUM
ejpam-4989	197	5	.	.	PUNCT
ejpam-4989	198	1	the	the	DET
ejpam-4989	198	2	case	case	NOUN
ejpam-4989	198	3	2	2	NUM
ejpam-4989	198	4	≤	≤	NUM
ejpam-4989	198	5	k	k	NOUN
ejpam-4989	198	6	≤	≤	ADV
ejpam-4989	198	7	350	350	NUM
ejpam-4989	198	8	in	in	ADP
ejpam-4989	198	9	the	the	DET
ejpam-4989	198	10	previous	previous	NOUN
ejpam-4989	198	11	,	,	PUNCT
ejpam-4989	198	12	we	we	PRON
ejpam-4989	198	13	obtained	obtain	VERB
ejpam-4989	198	14	a	a	DET
ejpam-4989	198	15	very	very	ADV
ejpam-4989	198	16	large	large	ADJ
ejpam-4989	198	17	upper	upper	ADJ
ejpam-4989	198	18	bound	bind	VERB
ejpam-4989	198	19	of	of	ADP
ejpam-4989	198	20	n.	n.	NOUN
ejpam-4989	198	21	we	we	PRON
ejpam-4989	198	22	apply	apply	VERB
ejpam-4989	198	23	lemma	lemma	PROPN
ejpam-4989	198	24	4	4	NUM
ejpam-4989	198	25	to	to	PART
ejpam-4989	198	26	reduce	reduce	VERB
ejpam-4989	198	27	the	the	DET
ejpam-4989	198	28	upper	upper	ADJ
ejpam-4989	198	29	bound	bind	VERB
ejpam-4989	198	30	.	.	PUNCT
ejpam-4989	199	1	in	in	ADP
ejpam-4989	199	2	this	this	DET
ejpam-4989	199	3	case	case	NOUN
ejpam-4989	199	4	,	,	PUNCT
ejpam-4989	199	5	we	we	PRON
ejpam-4989	199	6	will	will	AUX
ejpam-4989	199	7	prove	prove	VERB
ejpam-4989	199	8	the	the	DET
ejpam-4989	199	9	following	follow	VERB
ejpam-4989	199	10	lemma	lemma	PROPN
ejpam-4989	199	11	.	.	PUNCT
ejpam-4989	200	1	lemma	lemma	PROPN
ejpam-4989	200	2	7	7	NUM
ejpam-4989	200	3	.	.	PUNCT
ejpam-4989	201	1	the	the	DET
ejpam-4989	201	2	only	only	ADJ
ejpam-4989	201	3	solution	solution	NOUN
ejpam-4989	201	4	of	of	ADP
ejpam-4989	201	5	the	the	DET
ejpam-4989	201	6	diophantine	diophantine	NOUN
ejpam-4989	201	7	equation	equation	NOUN
ejpam-4989	201	8	(	(	PUNCT
ejpam-4989	201	9	22	22	NUM
ejpam-4989	201	10	)	)	PUNCT
ejpam-4989	201	11	is	be	AUX
ejpam-4989	201	12	p	p	X
ejpam-4989	201	13	(	(	PUNCT
ejpam-4989	201	14	k	k	NOUN
ejpam-4989	201	15	)	)	PUNCT
ejpam-4989	201	16	4	4	NUM
ejpam-4989	201	17	=	=	SYM
ejpam-4989	201	18	t6	t6	PROPN
ejpam-4989	201	19	where	where	SCONJ
ejpam-4989	201	20	n	n	PRON
ejpam-4989	201	21	≥	≥	X
ejpam-4989	201	22	k+2	k+2	NUM
ejpam-4989	201	23	and	and	CCONJ
ejpam-4989	201	24	2	2	NUM
ejpam-4989	201	25	≤	≤	NUM
ejpam-4989	201	26	k	k	X
ejpam-4989	201	27	≤	≤	ADJ
ejpam-4989	201	28	350	350	NUM
ejpam-4989	201	29	proof	proof	NOUN
ejpam-4989	201	30	.	.	PUNCT
ejpam-4989	202	1	to	to	PART
ejpam-4989	202	2	apply	apply	VERB
ejpam-4989	202	3	lemma	lemma	PROPN
ejpam-4989	202	4	4	4	NUM
ejpam-4989	202	5	,	,	PUNCT
ejpam-4989	202	6	let	let	VERB
ejpam-4989	202	7	v1	v1	VERB
ejpam-4989	202	8	:	:	PUNCT
ejpam-4989	202	9	=	=	SYM
ejpam-4989	202	10	n	n	CCONJ
ejpam-4989	202	11	log(α)−	log(α)−	PROPN
ejpam-4989	202	12	(	(	PUNCT
ejpam-4989	202	13	m−	m−	PROPN
ejpam-4989	202	14	1	1	NUM
ejpam-4989	202	15	)	)	PUNCT
ejpam-4989	202	16	log(η1	log(η1	PROPN
ejpam-4989	202	17	)	)	PUNCT
ejpam-4989	203	1	+	+	CCONJ
ejpam-4989	203	2	log(c−1gk(α	log(c−1gk(α	PROPN
ejpam-4989	203	3	)	)	PUNCT
ejpam-4989	203	4	)	)	PUNCT
ejpam-4989	203	5	.	.	PUNCT
ejpam-4989	204	1	then	then	ADV
ejpam-4989	204	2	we	we	PRON
ejpam-4989	204	3	have	have	AUX
ejpam-4989	204	4	,	,	PUNCT
ejpam-4989	204	5	by	by	ADP
ejpam-4989	204	6	inequality	inequality	NOUN
ejpam-4989	204	7	(	(	PUNCT
ejpam-4989	204	8	25	25	NUM
ejpam-4989	204	9	)	)	PUNCT
ejpam-4989	204	10	,	,	PUNCT
ejpam-4989	204	11	|ev1	|ev1	PROPN
ejpam-4989	204	12	−	−	NOUN
ejpam-4989	204	13	1|	1|	PRON
ejpam-4989	204	14	<	<	X
ejpam-4989	204	15	1.6	1.6	NUM
ejpam-4989	204	16	ηm−1	ηm−1	NOUN
ejpam-4989	204	17	1	1	NUM
ejpam-4989	204	18	.	.	PUNCT
ejpam-4989	205	1	we	we	PRON
ejpam-4989	205	2	know	know	VERB
ejpam-4989	205	3	v1	v1	VERB
ejpam-4989	205	4	̸=	̸=	PROPN
ejpam-4989	205	5	0	0	NUM
ejpam-4989	205	6	,	,	PUNCT
ejpam-4989	205	7	since	since	SCONJ
ejpam-4989	205	8	λ	λ	PROPN
ejpam-4989	205	9	̸=	̸=	PROPN
ejpam-4989	205	10	0	0	NUM
ejpam-4989	205	11	.	.	PUNCT
ejpam-4989	206	1	if	if	SCONJ
ejpam-4989	206	2	m	m	PROPN
ejpam-4989	206	3	≥	≥	NOUN
ejpam-4989	206	4	2	2	NUM
ejpam-4989	206	5	,	,	PUNCT
ejpam-4989	206	6	we	we	PRON
ejpam-4989	206	7	have	have	VERB
ejpam-4989	206	8	1.6	1.6	NUM
ejpam-4989	206	9	ηm−1	ηm−1	NOUN
ejpam-4989	206	10	1	1	NUM
ejpam-4989	206	11	<	<	X
ejpam-4989	206	12	0.87	0.87	NUM
ejpam-4989	206	13	.	.	PUNCT
ejpam-4989	207	1	by	by	ADP
ejpam-4989	207	2	lemma	lemma	PROPN
ejpam-4989	207	3	2	2	NUM
ejpam-4989	207	4	,	,	PUNCT
ejpam-4989	207	5	we	we	PRON
ejpam-4989	207	6	get	get	VERB
ejpam-4989	207	7	|v1|	|v1|	NOUN
ejpam-4989	207	8	=	=	PUNCT
ejpam-4989	208	1	|	|	ADV
ejpam-4989	208	2	log(λ	log(λ	PROPN
ejpam-4989	209	1	+	+	CCONJ
ejpam-4989	209	2	1)|	1)|	NUM
ejpam-4989	209	3	=	=	SYM
ejpam-4989	209	4	−	−	PROPN
ejpam-4989	209	5	log(1−	log(1−	PROPN
ejpam-4989	209	6	0.87	0.87	NUM
ejpam-4989	209	7	)	)	PUNCT
ejpam-4989	209	8	0.87	0.87	NUM
ejpam-4989	209	9	·	·	PUNCT
ejpam-4989	209	10	1.6	1.6	NUM
ejpam-4989	209	11	ηm−1	ηm−1	NOUN
ejpam-4989	209	12	1	1	NUM
ejpam-4989	209	13	<	<	X
ejpam-4989	209	14	3.75	3.75	NUM
ejpam-4989	209	15	ηm−1	ηm−1	PROPN
ejpam-4989	209	16	1	1	NUM
ejpam-4989	209	17	,	,	PUNCT
ejpam-4989	209	18	and	and	CCONJ
ejpam-4989	209	19	0	0	NUM
ejpam-4989	209	20	<	<	X
ejpam-4989	209	21	∣∣(m−	∣∣(m−	NUM
ejpam-4989	209	22	1)(−	1)(−	NUM
ejpam-4989	209	23	log(η1	log(η1	NOUN
ejpam-4989	209	24	)	)	PUNCT
ejpam-4989	209	25	)	)	PUNCT
ejpam-4989	210	1	+	+	CCONJ
ejpam-4989	210	2	n	n	PRON
ejpam-4989	210	3	log(α	log(α	PROPN
ejpam-4989	210	4	)	)	PUNCT
ejpam-4989	210	5	+	+	CCONJ
ejpam-4989	210	6	log(c−1gk(α	log(c−1gk(α	PROPN
ejpam-4989	210	7	)	)	PUNCT
ejpam-4989	210	8	)	)	PUNCT
ejpam-4989	211	1	∣∣	∣∣	X
ejpam-4989	211	2	<	<	X
ejpam-4989	211	3	3.75	3.75	NUM
ejpam-4989	211	4	·	·	PUNCT
ejpam-4989	211	5	exp(−(m−	exp(−(m−	ADJ
ejpam-4989	211	6	1	1	NUM
ejpam-4989	211	7	)	)	PUNCT
ejpam-4989	211	8	log(η1	log(η1	PROPN
ejpam-4989	211	9	)	)	PUNCT
ejpam-4989	211	10	)	)	PUNCT
ejpam-4989	211	11	.	.	PUNCT
ejpam-4989	212	1	(	(	PUNCT
ejpam-4989	212	2	28	28	NUM
ejpam-4989	212	3	)	)	PUNCT
ejpam-4989	212	4	according	accord	VERB
ejpam-4989	212	5	to	to	ADP
ejpam-4989	212	6	lemma	lemma	PROPN
ejpam-4989	212	7	4	4	NUM
ejpam-4989	212	8	,	,	PUNCT
ejpam-4989	212	9	we	we	PRON
ejpam-4989	212	10	obtain	obtain	VERB
ejpam-4989	212	11	c	c	NOUN
ejpam-4989	212	12	:	:	PUNCT
ejpam-4989	212	13	=	=	SYM
ejpam-4989	212	14	3.75	3.75	NUM
ejpam-4989	212	15	,	,	PUNCT
ejpam-4989	212	16	δ	δ	X
ejpam-4989	212	17	:	:	PUNCT
ejpam-4989	212	18	=	=	SYM
ejpam-4989	212	19	log(η1	log(η1	PROPN
ejpam-4989	212	20	)	)	PUNCT
ejpam-4989	212	21	,	,	PUNCT
ejpam-4989	212	22	ψ	ψ	X
ejpam-4989	212	23	:	:	PUNCT
ejpam-4989	212	24	=	=	SYM
ejpam-4989	212	25	log(c−1gk(α	log(c−1gk(α	PROPN
ejpam-4989	212	26	)	)	PUNCT
ejpam-4989	212	27	)	)	PUNCT
ejpam-4989	213	1	log(α	log(α	PROPN
ejpam-4989	213	2	)	)	PUNCT
ejpam-4989	213	3	,	,	PUNCT
ejpam-4989	213	4	h.	h.	PROPN
ejpam-4989	213	5	s.	s.	PROPN
ejpam-4989	213	6	taher	taher	PROPN
ejpam-4989	213	7	,	,	PUNCT
ejpam-4989	213	8	s.	s.	PROPN
ejpam-4989	213	9	k.	k.	PROPN
ejpam-4989	213	10	dash	dash	NOUN
ejpam-4989	213	11	/	/	SYM
ejpam-4989	213	12	eur	eur	NOUN
ejpam-4989	213	13	.	.	PUNCT
ejpam-4989	214	1	j.	j.	PROPN
ejpam-4989	214	2	pure	pure	PROPN
ejpam-4989	214	3	appl	appl	PROPN
ejpam-4989	214	4	.	.	PROPN
ejpam-4989	214	5	math	math	PROPN
ejpam-4989	214	6	,	,	PUNCT
ejpam-4989	214	7	17	17	NUM
ejpam-4989	214	8	(	(	PUNCT
ejpam-4989	214	9	1	1	NUM
ejpam-4989	214	10	)	)	PUNCT
ejpam-4989	214	11	(	(	PUNCT
ejpam-4989	214	12	2024	2024	NUM
ejpam-4989	214	13	)	)	PUNCT
ejpam-4989	214	14	,	,	PUNCT
ejpam-4989	214	15	135	135	NUM
ejpam-4989	214	16	-	-	SYM
ejpam-4989	214	17	146	146	NUM
ejpam-4989	214	18	143	143	NUM
ejpam-4989	214	19	ϑ	ϑ	X
ejpam-4989	214	20	:	:	PUNCT
ejpam-4989	214	21	=	=	SYM
ejpam-4989	214	22	log(η1	log(η1	X
ejpam-4989	214	23	)	)	PUNCT
ejpam-4989	214	24	log(α	log(α	PROPN
ejpam-4989	214	25	)	)	PUNCT
ejpam-4989	214	26	,	,	PUNCT
ejpam-4989	214	27	ϑ1	ϑ1	NOUN
ejpam-4989	214	28	:	:	PUNCT
ejpam-4989	214	29	=	=	PUNCT
ejpam-4989	215	1	−	−	PROPN
ejpam-4989	215	2	log(η1	log(η1	NOUN
ejpam-4989	215	3	)	)	PUNCT
ejpam-4989	215	4	,	,	PUNCT
ejpam-4989	215	5	ϑ2	ϑ2	PROPN
ejpam-4989	215	6	:	:	PUNCT
ejpam-4989	215	7	=	=	SYM
ejpam-4989	215	8	log(α	log(α	PROPN
ejpam-4989	215	9	)	)	PUNCT
ejpam-4989	215	10	,	,	PUNCT
ejpam-4989	215	11	β	β	X
ejpam-4989	215	12	:	:	PUNCT
ejpam-4989	215	13	=	=	SYM
ejpam-4989	215	14	log(c−1gk(α	log(c−1gk(α	PROPN
ejpam-4989	215	15	)	)	PUNCT
ejpam-4989	215	16	)	)	PUNCT
ejpam-4989	215	17	.	.	PUNCT
ejpam-4989	216	1	we	we	PRON
ejpam-4989	216	2	are	be	AUX
ejpam-4989	216	3	aware	aware	ADJ
ejpam-4989	216	4	that	that	SCONJ
ejpam-4989	216	5	ϑ	ϑ	NOUN
ejpam-4989	216	6	is	be	AUX
ejpam-4989	216	7	an	an	DET
ejpam-4989	216	8	irrational	irrational	ADJ
ejpam-4989	216	9	number	number	NOUN
ejpam-4989	216	10	.	.	PUNCT
ejpam-4989	217	1	taking	take	VERB
ejpam-4989	217	2	x0	x0	PROPN
ejpam-4989	217	3	:	:	PUNCT
ejpam-4989	217	4	=	=	SYM
ejpam-4989	217	5	1.5	1.5	NUM
ejpam-4989	217	6	·	·	SYM
ejpam-4989	217	7	1017k5(log(k))3	1017k5(log(k))3	NUM
ejpam-4989	217	8	,	,	PUNCT
ejpam-4989	217	9	which	which	PRON
ejpam-4989	217	10	is	be	AUX
ejpam-4989	217	11	an	an	DET
ejpam-4989	217	12	upper	upper	ADJ
ejpam-4989	217	13	bound	bound	NOUN
ejpam-4989	217	14	of	of	ADP
ejpam-4989	217	15	m−	m−	PROPN
ejpam-4989	217	16	1	1	NUM
ejpam-4989	217	17	and	and	CCONJ
ejpam-4989	217	18	n.	n.	NOUN
ejpam-4989	217	19	using	use	VERB
ejpam-4989	217	20	maple	maple	NOUN
ejpam-4989	217	21	program	program	NOUN
ejpam-4989	217	22	inspection	inspection	NOUN
ejpam-4989	217	23	,	,	PUNCT
ejpam-4989	217	24	the	the	DET
ejpam-4989	217	25	maximum	maximum	ADJ
ejpam-4989	217	26	value	value	NOUN
ejpam-4989	217	27	of	of	ADP
ejpam-4989	217	28	1	1	NUM
ejpam-4989	217	29	δ	δ	NOUN
ejpam-4989	217	30	log	log	NOUN
ejpam-4989	217	31	(	(	PUNCT
ejpam-4989	217	32	q2c	q2c	X
ejpam-4989	217	33	|ϑ2|x0	|ϑ2|x0	NOUN
ejpam-4989	217	34	)	)	PUNCT
ejpam-4989	217	35	for	for	ADP
ejpam-4989	217	36	k	k	PROPN
ejpam-4989	217	37	∈	∈	PROPN
ejpam-4989	218	1	[	[	X
ejpam-4989	218	2	2	2	NUM
ejpam-4989	218	3	,	,	PUNCT
ejpam-4989	218	4	350	350	NUM
ejpam-4989	218	5	]	]	PUNCT
ejpam-4989	218	6	is	be	AUX
ejpam-4989	218	7	143	143	NUM
ejpam-4989	218	8	.	.	PUNCT
ejpam-4989	219	1	we	we	PRON
ejpam-4989	219	2	get	get	VERB
ejpam-4989	219	3	1	1	NUM
ejpam-4989	219	4	≤	≤	NUM
ejpam-4989	219	5	m	m	VERB
ejpam-4989	219	6	−	−	PROPN
ejpam-4989	219	7	1	1	NUM
ejpam-4989	219	8	≤	≤	NOUN
ejpam-4989	219	9	143	143	NUM
ejpam-4989	219	10	and	and	CCONJ
ejpam-4989	219	11	discover	discover	VERB
ejpam-4989	219	12	the	the	DET
ejpam-4989	219	13	possible	possible	ADJ
ejpam-4989	219	14	values	value	NOUN
ejpam-4989	219	15	of	of	ADP
ejpam-4989	219	16	the	the	DET
ejpam-4989	219	17	diophantine	diophantine	NOUN
ejpam-4989	219	18	equation	equation	NOUN
ejpam-4989	219	19	(	(	PUNCT
ejpam-4989	219	20	22	22	NUM
ejpam-4989	219	21	)	)	PUNCT
ejpam-4989	219	22	for	for	ADP
ejpam-4989	219	23	which	which	PRON
ejpam-4989	219	24	k	k	PROPN
ejpam-4989	219	25	∈	∈	PROPN
ejpam-4989	220	1	[	[	X
ejpam-4989	220	2	2	2	NUM
ejpam-4989	220	3	,	,	PUNCT
ejpam-4989	220	4	350	350	NUM
ejpam-4989	220	5	]	]	PUNCT
ejpam-4989	220	6	have	have	VERB
ejpam-4989	220	7	2	2	NUM
ejpam-4989	220	8	≤	≤	NUM
ejpam-4989	220	9	m	m	VERB
ejpam-4989	220	10	≤	≤	NOUN
ejpam-4989	220	11	144	144	NUM
ejpam-4989	220	12	,	,	PUNCT
ejpam-4989	220	13	and	and	CCONJ
ejpam-4989	220	14	by	by	ADP
ejpam-4989	220	15	inequality	inequality	NOUN
ejpam-4989	220	16	(	(	PUNCT
ejpam-4989	220	17	23	23	NUM
ejpam-4989	220	18	)	)	PUNCT
ejpam-4989	220	19	,	,	PUNCT
ejpam-4989	220	20	we	we	PRON
ejpam-4989	220	21	obtain	obtain	VERB
ejpam-4989	220	22	4	4	NUM
ejpam-4989	220	23	≤	≤	NOUN
ejpam-4989	220	24	n	n	PRON
ejpam-4989	220	25	≤	≤	NOUN
ejpam-4989	220	26	181	181	NUM
ejpam-4989	220	27	.	.	PUNCT
ejpam-4989	221	1	the	the	DET
ejpam-4989	221	2	only	only	ADJ
ejpam-4989	221	3	possible	possible	ADJ
ejpam-4989	221	4	solution	solution	NOUN
ejpam-4989	221	5	in	in	ADP
ejpam-4989	221	6	this	this	DET
ejpam-4989	221	7	range	range	NOUN
ejpam-4989	221	8	was	be	AUX
ejpam-4989	221	9	p	p	X
ejpam-4989	221	10	(	(	PUNCT
ejpam-4989	221	11	k	k	NOUN
ejpam-4989	221	12	)	)	PUNCT
ejpam-4989	221	13	4	4	NUM
ejpam-4989	221	14	=	=	SYM
ejpam-4989	221	15	t6	t6	PROPN
ejpam-4989	221	16	.	.	PUNCT
ejpam-4989	222	1	3.4	3.4	NUM
ejpam-4989	222	2	.	.	PUNCT
ejpam-4989	223	1	the	the	DET
ejpam-4989	223	2	case	case	NOUN
ejpam-4989	223	3	k	k	PROPN
ejpam-4989	223	4	>	>	X
ejpam-4989	223	5	350	350	NUM
ejpam-4989	223	6	in	in	ADP
ejpam-4989	223	7	this	this	DET
ejpam-4989	223	8	case	case	NOUN
ejpam-4989	223	9	,	,	PUNCT
ejpam-4989	223	10	we	we	PRON
ejpam-4989	223	11	prove	prove	VERB
ejpam-4989	223	12	the	the	DET
ejpam-4989	223	13	following	follow	VERB
ejpam-4989	223	14	lemma	lemma	PROPN
ejpam-4989	223	15	lemma	lemma	PROPN
ejpam-4989	223	16	8	8	NUM
ejpam-4989	223	17	.	.	PUNCT
ejpam-4989	224	1	the	the	DET
ejpam-4989	224	2	diophantine	diophantine	NOUN
ejpam-4989	224	3	equation	equation	NOUN
ejpam-4989	224	4	(	(	PUNCT
ejpam-4989	224	5	22	22	NUM
ejpam-4989	224	6	)	)	PUNCT
ejpam-4989	224	7	has	have	VERB
ejpam-4989	224	8	no	no	DET
ejpam-4989	224	9	solution	solution	NOUN
ejpam-4989	224	10	for	for	ADP
ejpam-4989	224	11	n	n	DET
ejpam-4989	224	12	≥	≥	NOUN
ejpam-4989	224	13	k	k	NOUN
ejpam-4989	225	1	+	+	CCONJ
ejpam-4989	225	2	2	2	NUM
ejpam-4989	225	3	and	and	CCONJ
ejpam-4989	225	4	k	k	X
ejpam-4989	225	5	>	>	X
ejpam-4989	225	6	350	350	NUM
ejpam-4989	225	7	proof	proof	NOUN
ejpam-4989	225	8	.	.	PUNCT
ejpam-4989	226	1	for	for	ADP
ejpam-4989	226	2	k	k	PROPN
ejpam-4989	226	3	>	>	X
ejpam-4989	226	4	350	350	NUM
ejpam-4989	226	5	,	,	PUNCT
ejpam-4989	226	6	as	as	ADP
ejpam-4989	226	7	a	a	DET
ejpam-4989	226	8	result	result	NOUN
ejpam-4989	226	9	of	of	ADP
ejpam-4989	226	10	lemma	lemma	PROPN
ejpam-4989	226	11	1	1	NUM
ejpam-4989	226	12	,	,	PUNCT
ejpam-4989	226	13	we	we	PRON
ejpam-4989	226	14	have	have	VERB
ejpam-4989	226	15	n	n	ADV
ejpam-4989	226	16	<	<	X
ejpam-4989	226	17	7.6	7.6	NUM
ejpam-4989	226	18	·	·	PUNCT
ejpam-4989	226	19	1016k5(log(k))3	1016k5(log(k))3	NUM
ejpam-4989	226	20	<	<	X
ejpam-4989	226	21	ϕk/2	ϕk/2	X
ejpam-4989	226	22	.	.	PUNCT
ejpam-4989	227	1	from	from	ADP
ejpam-4989	227	2	(	(	PUNCT
ejpam-4989	227	3	12),(22	12),(22	NUM
ejpam-4989	227	4	)	)	PUNCT
ejpam-4989	227	5	and	and	CCONJ
ejpam-4989	227	6	(	(	PUNCT
ejpam-4989	227	7	24	24	NUM
ejpam-4989	227	8	)	)	PUNCT
ejpam-4989	227	9	,	,	PUNCT
ejpam-4989	227	10	we	we	PRON
ejpam-4989	227	11	get∣∣∣∣	get∣∣∣∣	VERB
ejpam-4989	227	12	ϕ2nϕ+	ϕ2nϕ+	NUM
ejpam-4989	227	13	2	2	NUM
ejpam-4989	227	14	−	−	NOUN
ejpam-4989	227	15	cηm−1	cηm−1	PROPN
ejpam-4989	227	16	1	1	NUM
ejpam-4989	227	17	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4989	227	18	<	<	X
ejpam-4989	227	19	∣∣gk(α)αn	∣∣gk(α)αn	NOUN
ejpam-4989	227	20	−	−	PROPN
ejpam-4989	227	21	cηm−1	cηm−1	PROPN
ejpam-4989	227	22	1	1	NUM
ejpam-4989	227	23	∣∣+	∣∣+	PROPN
ejpam-4989	228	1	ϕ2n	ϕ2n	PROPN
ejpam-4989	228	2	ϕ+	ϕ+	PUNCT
ejpam-4989	228	3	2	2	NUM
ejpam-4989	228	4	|ζ|	|ζ|	PROPN
ejpam-4989	228	5	<	<	X
ejpam-4989	228	6	1	1	NUM
ejpam-4989	228	7	+	+	NUM
ejpam-4989	228	8	4ϕ2n	4ϕ2n	NOUN
ejpam-4989	228	9	(	(	PUNCT
ejpam-4989	228	10	ϕ+	ϕ+	ADP
ejpam-4989	228	11	2)ϕk/2	2)ϕk/2	INTJ
ejpam-4989	228	12	.	.	PUNCT
ejpam-4989	229	1	dividing	divide	VERB
ejpam-4989	229	2	both	both	DET
ejpam-4989	229	3	sides	side	NOUN
ejpam-4989	229	4	by	by	ADP
ejpam-4989	229	5	ϕ2n	ϕ2n	PROPN
ejpam-4989	229	6	ϕ+2	ϕ+2	X
ejpam-4989	229	7	,	,	PUNCT
ejpam-4989	229	8	it	it	PRON
ejpam-4989	229	9	becomes	become	VERB
ejpam-4989	229	10	|λ1|	|λ1|	ADP
ejpam-4989	229	11	<	<	X
ejpam-4989	229	12	7.6	7.6	NUM
ejpam-4989	229	13	ϕk/2	ϕk/2	NOUN
ejpam-4989	229	14	,	,	PUNCT
ejpam-4989	229	15	where	where	SCONJ
ejpam-4989	229	16	λ1	λ1	ADJ
ejpam-4989	229	17	:	:	PUNCT
ejpam-4989	229	18	=	=	NOUN
ejpam-4989	229	19	c(ϕ+	c(ϕ+	X
ejpam-4989	229	20	2)ϕ−2nηm−1	2)ϕ−2nηm−1	NUM
ejpam-4989	229	21	1	1	NUM
ejpam-4989	229	22	−	−	NOUN
ejpam-4989	229	23	1	1	NUM
ejpam-4989	229	24	.	.	PUNCT
ejpam-4989	230	1	(	(	PUNCT
ejpam-4989	230	2	29	29	NUM
ejpam-4989	230	3	)	)	PUNCT
ejpam-4989	230	4	using	use	VERB
ejpam-4989	230	5	the	the	DET
ejpam-4989	230	6	fact	fact	NOUN
ejpam-4989	230	7	that	that	SCONJ
ejpam-4989	230	8	1	1	NUM
ejpam-4989	230	9	ϕ2n	ϕ2n	ADJ
ejpam-4989	230	10	<	<	X
ejpam-4989	230	11	1	1	NUM
ejpam-4989	230	12	ϕk/2	ϕk/2	NOUN
ejpam-4989	230	13	yield	yield	NOUN
ejpam-4989	230	14	for	for	ADP
ejpam-4989	230	15	n	n	DET
ejpam-4989	230	16	≥	≥	NOUN
ejpam-4989	230	17	k	k	NOUN
ejpam-4989	231	1	+	+	CCONJ
ejpam-4989	231	2	2	2	X
ejpam-4989	231	3	.	.	X
ejpam-4989	231	4	it	it	PRON
ejpam-4989	231	5	is	be	AUX
ejpam-4989	231	6	known	know	VERB
ejpam-4989	231	7	that	that	SCONJ
ejpam-4989	231	8	λ1	λ1	PROPN
ejpam-4989	231	9	is	be	AUX
ejpam-4989	231	10	nonzero	nonzero	NOUN
ejpam-4989	231	11	.	.	PUNCT
ejpam-4989	232	1	if	if	SCONJ
ejpam-4989	232	2	λ1	λ1	PROPN
ejpam-4989	232	3	is	be	AUX
ejpam-4989	232	4	zero	zero	NUM
ejpam-4989	232	5	,	,	PUNCT
ejpam-4989	232	6	then	then	ADV
ejpam-4989	232	7	ϕ2n	ϕ2n	PROPN
ejpam-4989	232	8	ηm−1	ηm−1	PROPN
ejpam-4989	232	9	1	1	NUM
ejpam-4989	232	10	=	=	SYM
ejpam-4989	232	11	c(ϕ	c(ϕ	PROPN
ejpam-4989	232	12	+	+	CCONJ
ejpam-4989	232	13	2	2	NUM
ejpam-4989	232	14	)	)	PUNCT
ejpam-4989	232	15	,	,	PUNCT
ejpam-4989	232	16	and	and	CCONJ
ejpam-4989	232	17	we	we	PRON
ejpam-4989	232	18	get	get	VERB
ejpam-4989	232	19	the	the	DET
ejpam-4989	232	20	left	left	ADJ
ejpam-4989	232	21	-	-	PUNCT
ejpam-4989	232	22	hand	hand	NOUN
ejpam-4989	232	23	side	side	NOUN
ejpam-4989	232	24	as	as	ADP
ejpam-4989	232	25	an	an	DET
ejpam-4989	232	26	algebraic	algebraic	ADJ
ejpam-4989	232	27	integer	integer	NOUN
ejpam-4989	232	28	,	,	PUNCT
ejpam-4989	232	29	but	but	CCONJ
ejpam-4989	232	30	the	the	DET
ejpam-4989	232	31	right	right	ADJ
ejpam-4989	232	32	-	-	PUNCT
ejpam-4989	232	33	hand	hand	NOUN
ejpam-4989	232	34	side	side	NOUN
ejpam-4989	232	35	is	be	AUX
ejpam-4989	232	36	not	not	PART
ejpam-4989	232	37	an	an	DET
ejpam-4989	232	38	algebraic	algebraic	ADJ
ejpam-4989	232	39	integer	integer	NOUN
ejpam-4989	232	40	,	,	PUNCT
ejpam-4989	232	41	which	which	PRON
ejpam-4989	232	42	is	be	AUX
ejpam-4989	232	43	impossible	impossible	ADJ
ejpam-4989	232	44	,	,	PUNCT
ejpam-4989	232	45	hence	hence	ADV
ejpam-4989	232	46	,	,	PUNCT
ejpam-4989	232	47	λ1	λ1	PROPN
ejpam-4989	232	48	̸=	̸=	PROPN
ejpam-4989	232	49	0	0	NUM
ejpam-4989	232	50	.	.	PUNCT
ejpam-4989	233	1	we	we	PRON
ejpam-4989	233	2	apply	apply	VERB
ejpam-4989	233	3	theorem	theorem	NOUN
ejpam-4989	233	4	1	1	NUM
ejpam-4989	233	5	,	,	PUNCT
ejpam-4989	233	6	we	we	PRON
ejpam-4989	233	7	take	take	VERB
ejpam-4989	233	8	parameters	parameter	NOUN
ejpam-4989	233	9	t	t	NOUN
ejpam-4989	233	10	:	:	PUNCT
ejpam-4989	233	11	=	=	SYM
ejpam-4989	233	12	3	3	NUM
ejpam-4989	233	13	,	,	PUNCT
ejpam-4989	233	14	and	and	CCONJ
ejpam-4989	233	15	γ1	γ1	PROPN
ejpam-4989	233	16	:	:	PUNCT
ejpam-4989	233	17	=	=	SYM
ejpam-4989	233	18	c(ϕ	c(ϕ	PROPN
ejpam-4989	233	19	+	+	CCONJ
ejpam-4989	233	20	2	2	NUM
ejpam-4989	233	21	)	)	PUNCT
ejpam-4989	233	22	,	,	PUNCT
ejpam-4989	233	23	γ2	γ2	NOUN
ejpam-4989	233	24	:	:	PUNCT
ejpam-4989	233	25	=	=	SYM
ejpam-4989	233	26	ϕ	ϕ	NOUN
ejpam-4989	233	27	,	,	PUNCT
ejpam-4989	233	28	γ3	γ3	NOUN
ejpam-4989	233	29	:	:	PUNCT
ejpam-4989	233	30	=	=	SYM
ejpam-4989	233	31	η1	η1	NOUN
ejpam-4989	233	32	,	,	PUNCT
ejpam-4989	233	33	and	and	CCONJ
ejpam-4989	233	34	b1	b1	NOUN
ejpam-4989	233	35	:	:	PUNCT
ejpam-4989	233	36	=	=	SYM
ejpam-4989	233	37	1	1	NUM
ejpam-4989	233	38	,	,	PUNCT
ejpam-4989	233	39	b2	b2	NOUN
ejpam-4989	233	40	:	:	PUNCT
ejpam-4989	233	41	=	=	SYM
ejpam-4989	233	42	−2n	−2n	PROPN
ejpam-4989	233	43	,	,	PUNCT
ejpam-4989	233	44	b3	b3	PROPN
ejpam-4989	233	45	=	=	SYM
ejpam-4989	233	46	(	(	PUNCT
ejpam-4989	233	47	m−	m−	PROPN
ejpam-4989	233	48	1	1	NUM
ejpam-4989	233	49	)	)	PUNCT
ejpam-4989	233	50	.	.	PUNCT
ejpam-4989	234	1	so	so	ADV
ejpam-4989	234	2	l	l	NOUN
ejpam-4989	234	3	:	:	PUNCT
ejpam-4989	234	4	=	=	NOUN
ejpam-4989	234	5	q(γ1	q(γ1	NOUN
ejpam-4989	234	6	,	,	PUNCT
ejpam-4989	234	7	γ2	γ2	ADJ
ejpam-4989	234	8	,	,	PUNCT
ejpam-4989	234	9	γ3	γ3	NOUN
ejpam-4989	234	10	)	)	PUNCT
ejpam-4989	234	11	.	.	PUNCT
ejpam-4989	235	1	thus	thus	ADV
ejpam-4989	235	2	d	d	ADP
ejpam-4989	235	3	:	:	PUNCT
ejpam-4989	235	4	=	=	PUNCT
ejpam-4989	236	1	[	[	X
ejpam-4989	236	2	l	l	NOUN
ejpam-4989	236	3	,	,	PUNCT
ejpam-4989	236	4	q	q	X
ejpam-4989	236	5	]	]	X
ejpam-4989	236	6	=	=	SYM
ejpam-4989	236	7	6	6	X
ejpam-4989	236	8	.	.	PUNCT
ejpam-4989	237	1	moreover	moreover	ADV
ejpam-4989	237	2	,	,	PUNCT
ejpam-4989	237	3	h(η2	h(η2	ADJ
ejpam-4989	237	4	)	)	PUNCT
ejpam-4989	237	5	=	=	PUNCT
ejpam-4989	238	1	log(ϕ	log(ϕ	X
ejpam-4989	238	2	)	)	PUNCT
ejpam-4989	238	3	2	2	NUM
ejpam-4989	238	4	,	,	PUNCT
ejpam-4989	238	5	h(η3	h(η3	NOUN
ejpam-4989	238	6	)	)	PUNCT
ejpam-4989	238	7	=	=	SYM
ejpam-4989	239	1	log(η1	log(η1	PROPN
ejpam-4989	239	2	)	)	PUNCT
ejpam-4989	239	3	3	3	NUM
ejpam-4989	239	4	and	and	CCONJ
ejpam-4989	239	5	h(η1	h(η1	NUM
ejpam-4989	239	6	)	)	PUNCT
ejpam-4989	240	1	≤	≤	NOUN
ejpam-4989	240	2	h(c	h(c	PROPN
ejpam-4989	240	3	)	)	PUNCT
ejpam-4989	240	4	+	+	NUM
ejpam-4989	240	5	h(ϕ	h(ϕ	NOUN
ejpam-4989	240	6	)	)	PUNCT
ejpam-4989	241	1	+	+	CCONJ
ejpam-4989	241	2	2	2	NUM
ejpam-4989	241	3	log(2	log(2	NOUN
ejpam-4989	241	4	)	)	PUNCT
ejpam-4989	242	1	<	<	X
ejpam-4989	242	2	2.9	2.9	NUM
ejpam-4989	242	3	,	,	PUNCT
ejpam-4989	242	4	it	it	PRON
ejpam-4989	242	5	follows	follow	VERB
ejpam-4989	242	6	that	that	SCONJ
ejpam-4989	242	7	a1	a1	NOUN
ejpam-4989	242	8	:	:	PUNCT
ejpam-4989	242	9	=	=	SYM
ejpam-4989	242	10	17.4	17.4	NUM
ejpam-4989	242	11	,	,	PUNCT
ejpam-4989	242	12	a2	a2	PROPN
ejpam-4989	242	13	:	:	PUNCT
ejpam-4989	242	14	=	=	SYM
ejpam-4989	242	15	1.45	1.45	NUM
ejpam-4989	242	16	and	and	CCONJ
ejpam-4989	242	17	a3	a3	NOUN
ejpam-4989	242	18	:	:	PUNCT
ejpam-4989	243	1	=	=	NOUN
ejpam-4989	243	2	1.22	1.22	NUM
ejpam-4989	243	3	.	.	PUNCT
ejpam-4989	244	1	since	since	SCONJ
ejpam-4989	244	2	max{|1|	max{|1|	NOUN
ejpam-4989	244	3	,	,	PUNCT
ejpam-4989	244	4	|	|	ADV
ejpam-4989	244	5	−	−	ADP
ejpam-4989	244	6	2n|	2n|	NUM
ejpam-4989	244	7	,	,	PUNCT
ejpam-4989	244	8	|(m−	|(m−	X
ejpam-4989	244	9	1)|	1)|	NUM
ejpam-4989	244	10	}	}	PUNCT
ejpam-4989	244	11	≤	≤	NUM
ejpam-4989	244	12	2n	2n	NUM
ejpam-4989	244	13	,	,	PUNCT
ejpam-4989	244	14	we	we	PRON
ejpam-4989	244	15	can	can	AUX
ejpam-4989	244	16	take	take	VERB
ejpam-4989	244	17	b	b	NOUN
ejpam-4989	244	18	:	:	PUNCT
ejpam-4989	244	19	=	=	SYM
ejpam-4989	244	20	2n	2n	NUM
ejpam-4989	244	21	.	.	PUNCT
ejpam-4989	245	1	thus	thus	ADV
ejpam-4989	245	2	,	,	PUNCT
ejpam-4989	245	3	by	by	ADP
ejpam-4989	245	4	theorem	theorem	NOUN
ejpam-4989	245	5	6	6	NUM
ejpam-4989	245	6	,	,	PUNCT
ejpam-4989	245	7	we	we	PRON
ejpam-4989	245	8	get	get	VERB
ejpam-4989	245	9	k	k	PROPN
ejpam-4989	245	10	2	2	NUM
ejpam-4989	245	11	log(ϕ)−	log(ϕ)−	NOUN
ejpam-4989	245	12	log(7.6	log(7.6	NUM
ejpam-4989	245	13	)	)	PUNCT
ejpam-4989	245	14	<	<	X
ejpam-4989	245	15	4.43	4.43	NUM
ejpam-4989	245	16	·	·	SYM
ejpam-4989	245	17	1014	1014	NUM
ejpam-4989	245	18	·	·	PUNCT
ejpam-4989	245	19	(	(	PUNCT
ejpam-4989	245	20	1	1	NUM
ejpam-4989	245	21	+	+	NUM
ejpam-4989	245	22	log(2n	log(2n	NOUN
ejpam-4989	245	23	)	)	PUNCT
ejpam-4989	245	24	)	)	PUNCT
ejpam-4989	245	25	.	.	PUNCT
ejpam-4989	246	1	h.	h.	PROPN
ejpam-4989	246	2	s.	s.	PROPN
ejpam-4989	246	3	taher	taher	PROPN
ejpam-4989	246	4	,	,	PUNCT
ejpam-4989	246	5	s.	s.	PROPN
ejpam-4989	246	6	k.	k.	PROPN
ejpam-4989	246	7	dash	dash	NOUN
ejpam-4989	246	8	/	/	SYM
ejpam-4989	246	9	eur	eur	NOUN
ejpam-4989	246	10	.	.	PUNCT
ejpam-4989	247	1	j.	j.	PROPN
ejpam-4989	247	2	pure	pure	PROPN
ejpam-4989	247	3	appl	appl	PROPN
ejpam-4989	247	4	.	.	PROPN
ejpam-4989	247	5	math	math	PROPN
ejpam-4989	247	6	,	,	PUNCT
ejpam-4989	247	7	17	17	NUM
ejpam-4989	247	8	(	(	PUNCT
ejpam-4989	247	9	1	1	NUM
ejpam-4989	247	10	)	)	PUNCT
ejpam-4989	247	11	(	(	PUNCT
ejpam-4989	247	12	2024	2024	NUM
ejpam-4989	247	13	)	)	PUNCT
ejpam-4989	247	14	,	,	PUNCT
ejpam-4989	247	15	135	135	NUM
ejpam-4989	247	16	-	-	SYM
ejpam-4989	247	17	146	146	NUM
ejpam-4989	247	18	144	144	NUM
ejpam-4989	247	19	using	use	VERB
ejpam-4989	247	20	fact	fact	NOUN
ejpam-4989	247	21	that	that	SCONJ
ejpam-4989	247	22	1	1	NUM
ejpam-4989	247	23	+	+	NUM
ejpam-4989	247	24	log(2n	log(2n	NOUN
ejpam-4989	247	25	)	)	PUNCT
ejpam-4989	247	26	<	<	X
ejpam-4989	247	27	1.3	1.3	NUM
ejpam-4989	247	28	log(n	log(n	NOUN
ejpam-4989	247	29	)	)	PUNCT
ejpam-4989	247	30	for	for	ADP
ejpam-4989	247	31	all	all	DET
ejpam-4989	247	32	n	n	DET
ejpam-4989	247	33	≥	≥	NOUN
ejpam-4989	247	34	k	k	NOUN
ejpam-4989	248	1	+	+	CCONJ
ejpam-4989	248	2	2	2	NUM
ejpam-4989	248	3	>	>	SYM
ejpam-4989	248	4	352	352	NUM
ejpam-4989	248	5	,	,	PUNCT
ejpam-4989	248	6	which	which	PRON
ejpam-4989	248	7	implies	imply	VERB
ejpam-4989	248	8	that	that	SCONJ
ejpam-4989	248	9	k	k	PROPN
ejpam-4989	248	10	<	<	X
ejpam-4989	248	11	2.4	2.4	NUM
ejpam-4989	248	12	·	·	SYM
ejpam-4989	248	13	1015	1015	NUM
ejpam-4989	248	14	log(n	log(n	NOUN
ejpam-4989	248	15	)	)	PUNCT
ejpam-4989	248	16	.	.	PUNCT
ejpam-4989	249	1	we	we	PRON
ejpam-4989	249	2	have	have	VERB
ejpam-4989	249	3	an	an	DET
ejpam-4989	249	4	upper	upper	ADJ
ejpam-4989	249	5	bound	bound	NOUN
ejpam-4989	249	6	of	of	ADP
ejpam-4989	249	7	n	n	PROPN
ejpam-4989	249	8	in	in	ADP
ejpam-4989	249	9	inequality(27	inequality(27	NOUN
ejpam-4989	249	10	)	)	PUNCT
ejpam-4989	249	11	,	,	PUNCT
ejpam-4989	249	12	then	then	ADV
ejpam-4989	249	13	38.87	38.87	NUM
ejpam-4989	249	14	+	+	SYM
ejpam-4989	249	15	5	5	NUM
ejpam-4989	249	16	log(k	log(k	NOUN
ejpam-4989	249	17	)	)	PUNCT
ejpam-4989	250	1	+	+	CCONJ
ejpam-4989	250	2	3	3	NUM
ejpam-4989	250	3	log(log(k	log(log(k	NOUN
ejpam-4989	250	4	)	)	PUNCT
ejpam-4989	250	5	)	)	PUNCT
ejpam-4989	251	1	<	<	X
ejpam-4989	251	2	13	13	NUM
ejpam-4989	251	3	log(k	log(k	NOUN
ejpam-4989	251	4	)	)	PUNCT
ejpam-4989	251	5	for	for	ADP
ejpam-4989	251	6	all	all	PRON
ejpam-4989	251	7	k	k	PROPN
ejpam-4989	251	8	>	>	X
ejpam-4989	251	9	350	350	NUM
ejpam-4989	251	10	,	,	PUNCT
ejpam-4989	251	11	we	we	PRON
ejpam-4989	251	12	get	get	VERB
ejpam-4989	251	13	k	k	X
ejpam-4989	251	14	<	<	X
ejpam-4989	251	15	2.4	2.4	NUM
ejpam-4989	251	16	·	·	SYM
ejpam-4989	251	17	1015	1015	NUM
ejpam-4989	251	18	log(7.6	log(7.6	NUM
ejpam-4989	251	19	·	·	PUNCT
ejpam-4989	251	20	1016k5(log(k))3	1016k5(log(k))3	NUM
ejpam-4989	251	21	)	)	PUNCT
ejpam-4989	251	22	<	<	X
ejpam-4989	252	1	2.4	2.4	NUM
ejpam-4989	252	2	·	·	PUNCT
ejpam-4989	253	1	1015(38.87	1015(38.87	NUM
ejpam-4989	253	2	+	+	NUM
ejpam-4989	253	3	5	5	NUM
ejpam-4989	253	4	log(k	log(k	NOUN
ejpam-4989	253	5	)	)	PUNCT
ejpam-4989	254	1	+	+	CCONJ
ejpam-4989	254	2	3	3	NUM
ejpam-4989	254	3	log(log(k	log(log(k	NOUN
ejpam-4989	254	4	)	)	PUNCT
ejpam-4989	254	5	)	)	PUNCT
ejpam-4989	254	6	)	)	PUNCT
ejpam-4989	255	1	<	<	X
ejpam-4989	255	2	3.12	3.12	NUM
ejpam-4989	255	3	·	·	SYM
ejpam-4989	255	4	1016	1016	NUM
ejpam-4989	255	5	log(k	log(k	PROPN
ejpam-4989	255	6	)	)	PUNCT
ejpam-4989	255	7	.	.	PUNCT
ejpam-4989	256	1	the	the	DET
ejpam-4989	256	2	above	above	ADJ
ejpam-4989	256	3	inequality	inequality	NOUN
ejpam-4989	256	4	gives	give	VERB
ejpam-4989	256	5	k	k	PROPN
ejpam-4989	256	6	<	<	X
ejpam-4989	256	7	1.3	1.3	NUM
ejpam-4989	256	8	·	·	SYM
ejpam-4989	256	9	1018	1018	NUM
ejpam-4989	256	10	.	.	PUNCT
ejpam-4989	257	1	thus	thus	ADV
ejpam-4989	257	2	,	,	PUNCT
ejpam-4989	257	3	we	we	PRON
ejpam-4989	257	4	get	get	VERB
ejpam-4989	257	5	n	n	PRON
ejpam-4989	257	6	<	<	X
ejpam-4989	257	7	7.6	7.6	NUM
ejpam-4989	257	8	·	·	PUNCT
ejpam-4989	257	9	1016(1.3	1016(1.3	NUM
ejpam-4989	257	10	·	·	PUNCT
ejpam-4989	257	11	1018)5(log(1.3	1018)5(log(1.3	NUM
ejpam-4989	257	12	·	·	SYM
ejpam-4989	257	13	1018))3	1018))3	X
ejpam-4989	257	14	<	<	X
ejpam-4989	257	15	2.1	2.1	NUM
ejpam-4989	257	16	·	·	SYM
ejpam-4989	257	17	10112	10112	NUM
ejpam-4989	257	18	m	m	VERB
ejpam-4989	257	19	<	<	X
ejpam-4989	257	20	2(2.1	2(2.1	NUM
ejpam-4989	257	21	·	·	SYM
ejpam-4989	257	22	10112	10112	NUM
ejpam-4989	257	23	)	)	PUNCT
ejpam-4989	257	24	<	<	X
ejpam-4989	257	25	4.2	4.2	NUM
ejpam-4989	257	26	·	·	SYM
ejpam-4989	257	27	10112	10112	NUM
ejpam-4989	257	28	.	.	PUNCT
ejpam-4989	258	1	let	let	VERB
ejpam-4989	258	2	v2	v2	VERB
ejpam-4989	258	3	:	:	PUNCT
ejpam-4989	258	4	=	=	SYM
ejpam-4989	258	5	(	(	PUNCT
ejpam-4989	258	6	m−	m−	PROPN
ejpam-4989	258	7	1	1	NUM
ejpam-4989	258	8	)	)	PUNCT
ejpam-4989	258	9	log(η1)−	log(η1)−	NOUN
ejpam-4989	258	10	(	(	PUNCT
ejpam-4989	258	11	2n	2n	NUM
ejpam-4989	258	12	)	)	PUNCT
ejpam-4989	258	13	log(α	log(α	PROPN
ejpam-4989	258	14	)	)	PUNCT
ejpam-4989	259	1	+	+	CCONJ
ejpam-4989	260	1	log(c(ϕ+	log(c(ϕ+	ADJ
ejpam-4989	260	2	2	2	NUM
ejpam-4989	260	3	)	)	PUNCT
ejpam-4989	260	4	)	)	PUNCT
ejpam-4989	260	5	.	.	PUNCT
ejpam-4989	261	1	then	then	ADV
ejpam-4989	261	2	we	we	PRON
ejpam-4989	261	3	have	have	AUX
ejpam-4989	261	4	,	,	PUNCT
ejpam-4989	261	5	by	by	ADP
ejpam-4989	261	6	inequality	inequality	NOUN
ejpam-4989	261	7	(	(	PUNCT
ejpam-4989	261	8	29	29	NUM
ejpam-4989	261	9	)	)	PUNCT
ejpam-4989	261	10	,	,	PUNCT
ejpam-4989	261	11	|ev2	|ev2	VERB
ejpam-4989	261	12	−	−	PROPN
ejpam-4989	261	13	1|	1|	NUM
ejpam-4989	261	14	<	<	X
ejpam-4989	261	15	7.6	7.6	NUM
ejpam-4989	261	16	ϕk/2	ϕk/2	NOUN
ejpam-4989	261	17	.	.	PUNCT
ejpam-4989	262	1	we	we	PRON
ejpam-4989	262	2	know	know	VERB
ejpam-4989	262	3	v2	v2	PROPN
ejpam-4989	262	4	̸=	̸=	PROPN
ejpam-4989	262	5	0	0	NUM
ejpam-4989	262	6	,	,	PUNCT
ejpam-4989	262	7	since	since	SCONJ
ejpam-4989	262	8	λ1	λ1	PROPN
ejpam-4989	262	9	̸=	̸=	PROPN
ejpam-4989	262	10	0	0	NUM
ejpam-4989	262	11	.	.	PUNCT
ejpam-4989	263	1	if	if	SCONJ
ejpam-4989	263	2	k	k	PROPN
ejpam-4989	263	3	≥	≥	VERB
ejpam-4989	263	4	350	350	NUM
ejpam-4989	263	5	,	,	PUNCT
ejpam-4989	263	6	we	we	PRON
ejpam-4989	263	7	get	get	VERB
ejpam-4989	263	8	7.6	7.6	NUM
ejpam-4989	263	9	ϕk/2	ϕk/2	NOUN
ejpam-4989	263	10	<	<	X
ejpam-4989	263	11	0.1	0.1	NUM
ejpam-4989	263	12	.	.	PUNCT
ejpam-4989	264	1	by	by	ADP
ejpam-4989	264	2	lemma	lemma	PROPN
ejpam-4989	264	3	2	2	NUM
ejpam-4989	264	4	,	,	PUNCT
ejpam-4989	264	5	we	we	PRON
ejpam-4989	264	6	obtain	obtain	VERB
ejpam-4989	264	7	the	the	DET
ejpam-4989	264	8	inequality	inequality	NOUN
ejpam-4989	264	9	|v2|	|v2|	NOUN
ejpam-4989	264	10	=	=	SYM
ejpam-4989	265	1	|	|	ADV
ejpam-4989	265	2	log(λ1	log(λ1	NOUN
ejpam-4989	265	3	+	+	CCONJ
ejpam-4989	265	4	1)|	1)|	NUM
ejpam-4989	265	5	=	=	SYM
ejpam-4989	265	6	−	−	PROPN
ejpam-4989	265	7	log(1−	log(1−	PROPN
ejpam-4989	265	8	0.1	0.1	NUM
ejpam-4989	265	9	)	)	PUNCT
ejpam-4989	265	10	0.1	0.1	NUM
ejpam-4989	265	11	·	·	PUNCT
ejpam-4989	265	12	7.6	7.6	NUM
ejpam-4989	265	13	ϕk/2	ϕk/2	NOUN
ejpam-4989	265	14	<	<	X
ejpam-4989	265	15	8.1	8.1	NUM
ejpam-4989	265	16	ϕk/2	ϕk/2	NOUN
ejpam-4989	265	17	.	.	PUNCT
ejpam-4989	266	1	thus	thus	ADV
ejpam-4989	266	2	,	,	PUNCT
ejpam-4989	266	3	we	we	PRON
ejpam-4989	266	4	get	get	VERB
ejpam-4989	266	5	0	0	NUM
ejpam-4989	266	6	<	<	X
ejpam-4989	266	7	|(m−	|(m−	PRON
ejpam-4989	266	8	1	1	X
ejpam-4989	266	9	)	)	PUNCT
ejpam-4989	266	10	log(η1)−	log(η1)−	NOUN
ejpam-4989	266	11	2n	2n	NUM
ejpam-4989	266	12	log(ϕ	log(ϕ	NOUN
ejpam-4989	266	13	)	)	PUNCT
ejpam-4989	266	14	+	+	PUNCT
ejpam-4989	267	1	log(c(ϕ+	log(c(ϕ+	NUM
ejpam-4989	267	2	2))|	2))|	NOUN
ejpam-4989	267	3	<	<	X
ejpam-4989	267	4	8.1	8.1	NUM
ejpam-4989	267	5	·	·	PUNCT
ejpam-4989	267	6	exp(−0.24	exp(−0.24	X
ejpam-4989	267	7	·	·	PUNCT
ejpam-4989	267	8	k	k	X
ejpam-4989	267	9	)	)	PUNCT
ejpam-4989	267	10	.	.	PUNCT
ejpam-4989	268	1	(	(	PUNCT
ejpam-4989	268	2	30	30	X
ejpam-4989	268	3	)	)	PUNCT
ejpam-4989	268	4	applying	apply	VERB
ejpam-4989	268	5	lemma	lemma	PROPN
ejpam-4989	268	6	4	4	NUM
ejpam-4989	268	7	,	,	PUNCT
ejpam-4989	268	8	we	we	PRON
ejpam-4989	268	9	can	can	AUX
ejpam-4989	268	10	take	take	VERB
ejpam-4989	268	11	c	c	NOUN
ejpam-4989	268	12	:	:	PUNCT
ejpam-4989	268	13	=	=	SYM
ejpam-4989	268	14	8.1	8.1	NUM
ejpam-4989	268	15	,	,	PUNCT
ejpam-4989	268	16	δ	δ	X
ejpam-4989	268	17	:	:	PUNCT
ejpam-4989	269	1	=	=	NOUN
ejpam-4989	269	2	0.24	0.24	NUM
ejpam-4989	269	3	,	,	PUNCT
ejpam-4989	269	4	ψ	ψ	X
ejpam-4989	269	5	:	:	PUNCT
ejpam-4989	269	6	=	=	SYM
ejpam-4989	269	7	−	−	PROPN
ejpam-4989	270	1	log(c(ϕ+	log(c(ϕ+	ADJ
ejpam-4989	270	2	2	2	NUM
ejpam-4989	270	3	)	)	PUNCT
ejpam-4989	270	4	)	)	PUNCT
ejpam-4989	271	1	log(ϕ	log(ϕ	PROPN
ejpam-4989	271	2	)	)	PUNCT
ejpam-4989	271	3	,	,	PUNCT
ejpam-4989	271	4	ϑ	ϑ	X
ejpam-4989	271	5	:	:	PUNCT
ejpam-4989	271	6	=	=	SYM
ejpam-4989	271	7	log(η1	log(η1	X
ejpam-4989	271	8	)	)	PUNCT
ejpam-4989	271	9	log(ϕ	log(ϕ	NOUN
ejpam-4989	271	10	)	)	PUNCT
ejpam-4989	271	11	,	,	PUNCT
ejpam-4989	271	12	ϑ1	ϑ1	NOUN
ejpam-4989	271	13	:	:	PUNCT
ejpam-4989	271	14	=	=	SYM
ejpam-4989	271	15	log(η1	log(η1	NOUN
ejpam-4989	271	16	)	)	PUNCT
ejpam-4989	271	17	,	,	PUNCT
ejpam-4989	271	18	ϑ2	ϑ2	PROPN
ejpam-4989	271	19	:	:	PUNCT
ejpam-4989	271	20	=	=	SYM
ejpam-4989	271	21	−	−	PROPN
ejpam-4989	271	22	log(ϕ	log(ϕ	NOUN
ejpam-4989	271	23	)	)	PUNCT
ejpam-4989	271	24	,	,	PUNCT
ejpam-4989	271	25	β	β	X
ejpam-4989	271	26	:	:	PUNCT
ejpam-4989	271	27	=	=	SYM
ejpam-4989	272	1	log(c(ϕ+	log(c(ϕ+	NOUN
ejpam-4989	272	2	2	2	NUM
ejpam-4989	272	3	)	)	PUNCT
ejpam-4989	272	4	)	)	PUNCT
ejpam-4989	272	5	.	.	PUNCT
ejpam-4989	273	1	references	reference	NOUN
ejpam-4989	273	2	145	145	NUM
ejpam-4989	273	3	we	we	PRON
ejpam-4989	273	4	take	take	VERB
ejpam-4989	273	5	m	m	VERB
ejpam-4989	273	6	:	:	PUNCT
ejpam-4989	273	7	=	=	SYM
ejpam-4989	273	8	4.2	4.2	NUM
ejpam-4989	273	9	·	·	SYM
ejpam-4989	273	10	10112	10112	NUM
ejpam-4989	273	11	,	,	PUNCT
ejpam-4989	273	12	which	which	PRON
ejpam-4989	273	13	is	be	AUX
ejpam-4989	273	14	the	the	DET
ejpam-4989	273	15	upper	upper	ADJ
ejpam-4989	273	16	bound	bind	VERB
ejpam-4989	273	17	for	for	ADP
ejpam-4989	273	18	m−1	m−1	PROPN
ejpam-4989	273	19	.	.	PUNCT
ejpam-4989	274	1	a	a	DET
ejpam-4989	274	2	quick	quick	ADJ
ejpam-4989	274	3	inspection	inspection	NOUN
ejpam-4989	274	4	with	with	ADP
ejpam-4989	274	5	the	the	DET
ejpam-4989	274	6	help	help	NOUN
ejpam-4989	274	7	of	of	ADP
ejpam-4989	274	8	maple	maple	NOUN
ejpam-4989	274	9	programming	programming	NOUN
ejpam-4989	274	10	found	find	VERB
ejpam-4989	274	11	that	that	SCONJ
ejpam-4989	274	12	q211	q211	PROPN
ejpam-4989	274	13	is	be	AUX
ejpam-4989	274	14	convergent	convergent	NOUN
ejpam-4989	274	15	of	of	ADP
ejpam-4989	274	16	ϑ.	ϑ.	NOUN
ejpam-4989	274	17	by	by	ADP
ejpam-4989	274	18	lemma	lemma	PROPN
ejpam-4989	274	19	4	4	NUM
ejpam-4989	274	20	,	,	PUNCT
ejpam-4989	274	21	we	we	PRON
ejpam-4989	274	22	obtain	obtain	VERB
ejpam-4989	274	23	k	k	NOUN
ejpam-4989	274	24	<	<	X
ejpam-4989	274	25	1	1	NUM
ejpam-4989	274	26	0.24	0.24	NUM
ejpam-4989	274	27	(	(	PUNCT
ejpam-4989	274	28	q2211	q2211	NUM
ejpam-4989	274	29	·	·	PUNCT
ejpam-4989	274	30	8.1	8.1	NUM
ejpam-4989	274	31	4.2	4.2	NUM
ejpam-4989	274	32	·	·	SYM
ejpam-4989	274	33	10122	10122	NUM
ejpam-4989	274	34	·	·	PUNCT
ejpam-4989	275	1	|	|	ADV
ejpam-4989	275	2	−	−	PROPN
ejpam-4989	275	3	log(ϕ)|	log(ϕ)|	PROPN
ejpam-4989	275	4	)	)	PUNCT
ejpam-4989	275	5	<	<	X
ejpam-4989	275	6	1105	1105	NUM
ejpam-4989	275	7	.	.	PUNCT
ejpam-4989	276	1	(	(	PUNCT
ejpam-4989	276	2	31	31	NUM
ejpam-4989	276	3	)	)	PUNCT
ejpam-4989	276	4	by	by	ADP
ejpam-4989	276	5	inequalities	inequality	NOUN
ejpam-4989	276	6	of	of	ADP
ejpam-4989	276	7	(	(	PUNCT
ejpam-4989	276	8	27	27	NUM
ejpam-4989	276	9	)	)	PUNCT
ejpam-4989	276	10	and	and	CCONJ
ejpam-4989	276	11	(	(	PUNCT
ejpam-4989	276	12	23	23	NUM
ejpam-4989	276	13	)	)	PUNCT
ejpam-4989	276	14	we	we	PRON
ejpam-4989	276	15	have	have	VERB
ejpam-4989	276	16	n	n	ADV
ejpam-4989	276	17	<	<	X
ejpam-4989	276	18	4.3	4.3	NUM
ejpam-4989	276	19	·	·	SYM
ejpam-4989	276	20	1034	1034	NUM
ejpam-4989	276	21	and	and	CCONJ
ejpam-4989	276	22	m	m	VERB
ejpam-4989	276	23	<	<	X
ejpam-4989	276	24	8.6	8.6	NUM
ejpam-4989	276	25	·	·	SYM
ejpam-4989	276	26	1034	1034	NUM
ejpam-4989	276	27	.	.	PUNCT
ejpam-4989	277	1	again	again	ADV
ejpam-4989	277	2	we	we	PRON
ejpam-4989	277	3	apply	apply	VERB
ejpam-4989	277	4	lemma	lemma	PROPN
ejpam-4989	277	5	4	4	NUM
ejpam-4989	277	6	for	for	ADP
ejpam-4989	277	7	(	(	PUNCT
ejpam-4989	277	8	30	30	NUM
ejpam-4989	277	9	)	)	PUNCT
ejpam-4989	277	10	with	with	ADP
ejpam-4989	277	11	m	m	PRON
ejpam-4989	277	12	:	:	PUNCT
ejpam-4989	277	13	=	=	SYM
ejpam-4989	277	14	8.6	8.6	NUM
ejpam-4989	277	15	·	·	SYM
ejpam-4989	277	16	1034	1034	NUM
ejpam-4989	277	17	,	,	PUNCT
ejpam-4989	277	18	we	we	PRON
ejpam-4989	277	19	found	find	VERB
ejpam-4989	277	20	that	that	SCONJ
ejpam-4989	277	21	q72	q72	PROPN
ejpam-4989	277	22	is	be	AUX
ejpam-4989	277	23	a	a	DET
ejpam-4989	277	24	convergent	convergent	NOUN
ejpam-4989	277	25	of	of	ADP
ejpam-4989	277	26	ϑ	ϑ	NOUN
ejpam-4989	277	27	,	,	PUNCT
ejpam-4989	277	28	and	and	CCONJ
ejpam-4989	277	29	k	k	X
ejpam-4989	277	30	<	<	X
ejpam-4989	277	31	389	389	NUM
ejpam-4989	277	32	.	.	PUNCT
ejpam-4989	278	1	hence	hence	ADV
ejpam-4989	278	2	n	n	CCONJ
ejpam-4989	278	3	<	<	X
ejpam-4989	278	4	1.4	1.4	NUM
ejpam-4989	278	5	·	·	SYM
ejpam-4989	278	6	1032	1032	NUM
ejpam-4989	278	7	and	and	CCONJ
ejpam-4989	278	8	m	m	VERB
ejpam-4989	278	9	<	<	X
ejpam-4989	278	10	2.8	2.8	NUM
ejpam-4989	278	11	·	·	SYM
ejpam-4989	278	12	1032	1032	NUM
ejpam-4989	278	13	.	.	PUNCT
ejpam-4989	279	1	third	third	ADJ
ejpam-4989	279	2	time	time	NOUN
ejpam-4989	279	3	applying	apply	VERB
ejpam-4989	279	4	lemma	lemma	PROPN
ejpam-4989	279	5	4	4	NUM
ejpam-4989	279	6	for	for	ADP
ejpam-4989	279	7	(	(	PUNCT
ejpam-4989	279	8	30	30	NUM
ejpam-4989	279	9	)	)	PUNCT
ejpam-4989	279	10	with	with	ADP
ejpam-4989	279	11	m	m	PRON
ejpam-4989	279	12	:	:	PUNCT
ejpam-4989	279	13	=	=	SYM
ejpam-4989	279	14	2.8	2.8	NUM
ejpam-4989	279	15	·	·	SYM
ejpam-4989	279	16	1032	1032	NUM
ejpam-4989	279	17	,	,	PUNCT
ejpam-4989	279	18	we	we	PRON
ejpam-4989	279	19	found	find	VERB
ejpam-4989	279	20	that	that	DET
ejpam-4989	279	21	q65	q65	NOUN
ejpam-4989	279	22	is	be	AUX
ejpam-4989	279	23	a	a	DET
ejpam-4989	279	24	convergent	convergent	NOUN
ejpam-4989	279	25	of	of	ADP
ejpam-4989	279	26	ϑ	ϑ	NOUN
ejpam-4989	279	27	,	,	PUNCT
ejpam-4989	279	28	and	and	CCONJ
ejpam-4989	279	29	k	k	X
ejpam-4989	279	30	<	<	X
ejpam-4989	279	31	342	342	NUM
ejpam-4989	279	32	,	,	PUNCT
ejpam-4989	279	33	we	we	PRON
ejpam-4989	279	34	get	get	VERB
ejpam-4989	279	35	contradiction	contradiction	NOUN
ejpam-4989	279	36	by	by	ADP
ejpam-4989	279	37	our	our	PRON
ejpam-4989	279	38	assumption	assumption	NOUN
ejpam-4989	279	39	that	that	SCONJ
ejpam-4989	279	40	k	k	PROPN
ejpam-4989	279	41	>	>	X
ejpam-4989	279	42	350	350	NUM
ejpam-4989	279	43	.	.	PUNCT
ejpam-4989	280	1	theorem	theorem	NOUN
ejpam-4989	280	2	2	2	NUM
ejpam-4989	280	3	is	be	AUX
ejpam-4989	280	4	proved	prove	VERB
ejpam-4989	280	5	.	.	PUNCT
ejpam-4989	281	1	4	4	X
ejpam-4989	281	2	.	.	X
ejpam-4989	281	3	conclusion	conclusion	NOUN
ejpam-4989	281	4	we	we	PRON
ejpam-4989	281	5	found	find	VERB
ejpam-4989	281	6	all	all	DET
ejpam-4989	281	7	solutions	solution	NOUN
ejpam-4989	281	8	of	of	ADP
ejpam-4989	281	9	the	the	DET
ejpam-4989	281	10	diophantine	diophantine	NOUN
ejpam-4989	281	11	equation	equation	NOUN
ejpam-4989	281	12	(	(	PUNCT
ejpam-4989	281	13	22	22	NUM
ejpam-4989	281	14	)	)	PUNCT
ejpam-4989	281	15	,	,	PUNCT
ejpam-4989	281	16	where	where	SCONJ
ejpam-4989	281	17	p	p	PROPN
ejpam-4989	281	18	(	(	PUNCT
ejpam-4989	281	19	k	k	NOUN
ejpam-4989	281	20	)	)	PUNCT
ejpam-4989	281	21	n	n	PRON
ejpam-4989	281	22	is	be	AUX
ejpam-4989	281	23	a	a	DET
ejpam-4989	281	24	k	k	ADV
ejpam-4989	281	25	-	-	ADJ
ejpam-4989	281	26	generalized	generalize	VERB
ejpam-4989	281	27	pell	pell	NOUN
ejpam-4989	281	28	number	number	NOUN
ejpam-4989	281	29	and	and	CCONJ
ejpam-4989	281	30	tm	tm	NOUN
ejpam-4989	281	31	is	be	AUX
ejpam-4989	281	32	a	a	DET
ejpam-4989	281	33	tribonacci	tribonacci	ADJ
ejpam-4989	281	34	number	number	NOUN
ejpam-4989	281	35	,	,	PUNCT
ejpam-4989	281	36	for	for	ADP
ejpam-4989	281	37	each	each	DET
ejpam-4989	281	38	positive	positive	ADJ
ejpam-4989	281	39	integer	integer	NOUN
ejpam-4989	281	40	n	n	CCONJ
ejpam-4989	281	41	,	,	PUNCT
ejpam-4989	281	42	m	m	PRON
ejpam-4989	281	43	and	and	CCONJ
ejpam-4989	281	44	k.	k.	PROPN
ejpam-4989	282	1	we	we	PRON
ejpam-4989	282	2	used	use	VERB
ejpam-4989	282	3	a	a	DET
ejpam-4989	282	4	lower	lower	ADV
ejpam-4989	282	5	bound	bind	VERB
ejpam-4989	282	6	for	for	ADP
ejpam-4989	282	7	linear	linear	ADJ
ejpam-4989	282	8	forms	form	NOUN
ejpam-4989	282	9	in	in	ADP
ejpam-4989	282	10	logarithms	logarithm	NOUN
ejpam-4989	282	11	of	of	ADP
ejpam-4989	282	12	algebraic	algebraic	ADJ
ejpam-4989	282	13	numbers	number	NOUN
ejpam-4989	282	14	to	to	PART
ejpam-4989	282	15	get	get	VERB
ejpam-4989	282	16	an	an	DET
ejpam-4989	282	17	upper	upper	ADJ
ejpam-4989	282	18	bound	bind	VERB
ejpam-4989	282	19	for	for	ADP
ejpam-4989	282	20	n.	n.	NOUN
ejpam-4989	282	21	then	then	ADV
ejpam-4989	282	22	,	,	PUNCT
ejpam-4989	282	23	we	we	PRON
ejpam-4989	282	24	used	use	VERB
ejpam-4989	282	25	a	a	DET
ejpam-4989	282	26	variation	variation	NOUN
ejpam-4989	282	27	of	of	ADP
ejpam-4989	282	28	the	the	DET
ejpam-4989	282	29	baker	baker	PROPN
ejpam-4989	282	30	-	-	PUNCT
ejpam-4989	282	31	davenport	davenport	PROPN
ejpam-4989	282	32	reduction	reduction	NOUN
ejpam-4989	282	33	method	method	NOUN
ejpam-4989	282	34	called	call	VERB
ejpam-4989	282	35	the	the	DET
ejpam-4989	282	36	de	de	X
ejpam-4989	282	37	weger	weger	NOUN
ejpam-4989	282	38	reduction	reduction	NOUN
ejpam-4989	282	39	method	method	NOUN
ejpam-4989	282	40	to	to	PART
ejpam-4989	282	41	reduce	reduce	VERB
ejpam-4989	282	42	the	the	DET
ejpam-4989	282	43	upper	upper	ADJ
ejpam-4989	282	44	bound	bind	VERB
ejpam-4989	282	45	.	.	PUNCT
ejpam-4989	283	1	acknowledgements	acknowledgement	NOUN
ejpam-4989	283	2	the	the	DET
ejpam-4989	283	3	authors	author	NOUN
ejpam-4989	283	4	express	express	VERB
ejpam-4989	283	5	their	their	PRON
ejpam-4989	283	6	gratitude	gratitude	NOUN
ejpam-4989	283	7	to	to	ADP
ejpam-4989	283	8	the	the	DET
ejpam-4989	283	9	anonymous	anonymous	ADJ
ejpam-4989	283	10	reviewers	reviewer	NOUN
ejpam-4989	283	11	for	for	ADP
ejpam-4989	283	12	the	the	DET
ejpam-4989	283	13	instructive	instructive	ADJ
ejpam-4989	283	14	suggestions	suggestion	NOUN
ejpam-4989	283	15	.	.	PUNCT
ejpam-4989	284	1	references	reference	NOUN
ejpam-4989	284	2	[	[	X
ejpam-4989	284	3	1	1	NUM
ejpam-4989	284	4	]	]	PUNCT
ejpam-4989	284	5	a.	a.	NOUN
ejpam-4989	284	6	acikel	acikel	NOUN
ejpam-4989	284	7	and	and	CCONJ
ejpam-4989	284	8	n.	n.	PROPN
ejpam-4989	284	9	irmak	irmak	PROPN
ejpam-4989	284	10	.	.	PUNCT
ejpam-4989	285	1	common	common	ADJ
ejpam-4989	285	2	terms	term	NOUN
ejpam-4989	285	3	of	of	ADP
ejpam-4989	285	4	tribonacci	tribonacci	NOUN
ejpam-4989	285	5	and	and	CCONJ
ejpam-4989	285	6	perrin	perrin	NOUN
ejpam-4989	285	7	sequences	sequence	NOUN
ejpam-4989	285	8	.	.	PUNCT
ejpam-4989	286	1	miskolc	miskolc	ADJ
ejpam-4989	286	2	mathematical	mathematical	ADJ
ejpam-4989	286	3	notes	note	NOUN
ejpam-4989	286	4	,	,	PUNCT
ejpam-4989	286	5	23(1):5–11	23(1):5–11	NOUN
ejpam-4989	286	6	,	,	PUNCT
ejpam-4989	286	7	2022	2022	NUM
ejpam-4989	286	8	.	.	PUNCT
ejpam-4989	287	1	[	[	X
ejpam-4989	287	2	2	2	X
ejpam-4989	287	3	]	]	PUNCT
ejpam-4989	287	4	j.	j.	PROPN
ejpam-4989	287	5	j.	j.	PROPN
ejpam-4989	287	6	bravo	bravo	PROPN
ejpam-4989	287	7	and	and	CCONJ
ejpam-4989	287	8	j.	j.	PROPN
ejpam-4989	287	9	l.	l.	PROPN
ejpam-4989	287	10	herrera	herrera	PROPN
ejpam-4989	287	11	.	.	PUNCT
ejpam-4989	288	1	repdigits	repdigit	NOUN
ejpam-4989	288	2	in	in	ADP
ejpam-4989	288	3	generalized	generalized	ADJ
ejpam-4989	288	4	pell	pell	NOUN
ejpam-4989	288	5	sequences	sequence	NOUN
ejpam-4989	288	6	.	.	PUNCT
ejpam-4989	289	1	archivum	archivum	PROPN
ejpam-4989	289	2	mathematicum	mathematicum	PROPN
ejpam-4989	289	3	,	,	PUNCT
ejpam-4989	289	4	56(4):249–262	56(4):249–262	PROPN
ejpam-4989	289	5	,	,	PUNCT
ejpam-4989	289	6	2020	2020	NUM
ejpam-4989	289	7	.	.	PUNCT
ejpam-4989	290	1	[	[	X
ejpam-4989	290	2	3	3	X
ejpam-4989	290	3	]	]	X
ejpam-4989	290	4	j.	j.	PROPN
ejpam-4989	290	5	j.	j.	PROPN
ejpam-4989	290	6	bravo	bravo	PROPN
ejpam-4989	290	7	,	,	PUNCT
ejpam-4989	290	8	j.	j.	PROPN
ejpam-4989	290	9	l.	l.	PROPN
ejpam-4989	290	10	herrera	herrera	PROPN
ejpam-4989	290	11	,	,	PUNCT
ejpam-4989	290	12	and	and	CCONJ
ejpam-4989	290	13	f.	f.	PROPN
ejpam-4989	290	14	luca	luca	PROPN
ejpam-4989	290	15	.	.	PUNCT
ejpam-4989	291	1	common	common	ADJ
ejpam-4989	291	2	values	value	NOUN
ejpam-4989	291	3	of	of	ADP
ejpam-4989	291	4	generalized	generalized	ADJ
ejpam-4989	291	5	fibonacci	fibonacci	NOUN
ejpam-4989	291	6	and	and	CCONJ
ejpam-4989	291	7	pell	pell	VERB
ejpam-4989	291	8	sequences	sequence	NOUN
ejpam-4989	291	9	.	.	PUNCT
ejpam-4989	292	1	journal	journal	PROPN
ejpam-4989	292	2	of	of	ADP
ejpam-4989	292	3	number	number	NOUN
ejpam-4989	292	4	theory	theory	NOUN
ejpam-4989	292	5	,	,	PUNCT
ejpam-4989	292	6	226:51–71	226:51–71	PROPN
ejpam-4989	292	7	,	,	PUNCT
ejpam-4989	292	8	9	9	NUM
ejpam-4989	292	9	2021	2021	NUM
ejpam-4989	292	10	.	.	PUNCT
ejpam-4989	293	1	[	[	X
ejpam-4989	293	2	4	4	X
ejpam-4989	293	3	]	]	PUNCT
ejpam-4989	293	4	j.	j.	PROPN
ejpam-4989	293	5	j.	j.	PROPN
ejpam-4989	293	6	bravo	bravo	PROPN
ejpam-4989	293	7	,	,	PUNCT
ejpam-4989	293	8	j.	j.	PROPN
ejpam-4989	293	9	l.	l.	PROPN
ejpam-4989	293	10	herrera	herrera	PROPN
ejpam-4989	293	11	,	,	PUNCT
ejpam-4989	293	12	and	and	CCONJ
ejpam-4989	293	13	f.	f.	PROPN
ejpam-4989	293	14	luca	luca	PROPN
ejpam-4989	293	15	.	.	PUNCT
ejpam-4989	294	1	on	on	ADP
ejpam-4989	294	2	a	a	DET
ejpam-4989	294	3	generalization	generalization	NOUN
ejpam-4989	294	4	of	of	ADP
ejpam-4989	294	5	the	the	DET
ejpam-4989	294	6	pell	pell	NOUN
ejpam-4989	294	7	sequence	sequence	NOUN
ejpam-4989	294	8	.	.	PUNCT
ejpam-4989	295	1	mathematica	mathematica	PROPN
ejpam-4989	295	2	bohemica	bohemica	PROPN
ejpam-4989	295	3	,	,	PUNCT
ejpam-4989	295	4	146(2):199–213	146(2):199–213	NUM
ejpam-4989	295	5	,	,	PUNCT
ejpam-4989	295	6	2021	2021	NUM
ejpam-4989	295	7	.	.	PUNCT
ejpam-4989	296	1	references	reference	NOUN
ejpam-4989	296	2	146	146	NUM
ejpam-4989	296	3	[	[	X
ejpam-4989	296	4	5	5	NUM
ejpam-4989	296	5	]	]	X
ejpam-4989	296	6	y.	y.	PROPN
ejpam-4989	296	7	bugeaud	bugeaud	PROPN
ejpam-4989	296	8	,	,	PUNCT
ejpam-4989	296	9	m.	m.	NOUN
ejpam-4989	296	10	mignotte	mignotte	PROPN
ejpam-4989	296	11	,	,	PUNCT
ejpam-4989	296	12	and	and	CCONJ
ejpam-4989	296	13	s.	s.	PROPN
ejpam-4989	296	14	siksek	siksek	PROPN
ejpam-4989	296	15	.	.	PUNCT
ejpam-4989	297	1	classical	classical	ADJ
ejpam-4989	297	2	and	and	CCONJ
ejpam-4989	297	3	modular	modular	ADJ
ejpam-4989	297	4	approaches	approach	NOUN
ejpam-4989	297	5	to	to	ADP
ejpam-4989	297	6	exponential	exponential	ADJ
ejpam-4989	297	7	diophantine	diophantine	NOUN
ejpam-4989	297	8	equations	equation	NOUN
ejpam-4989	297	9	i.	i.	PROPN
ejpam-4989	297	10	fibonacci	fibonacci	PROPN
ejpam-4989	297	11	and	and	CCONJ
ejpam-4989	297	12	lucas	lucas	PROPN
ejpam-4989	297	13	perfect	perfect	ADJ
ejpam-4989	297	14	powers	power	NOUN
ejpam-4989	297	15	.	.	PUNCT
ejpam-4989	298	1	annals	annal	NOUN
ejpam-4989	298	2	of	of	ADP
ejpam-4989	298	3	mathematics	mathematic	NOUN
ejpam-4989	298	4	,	,	PUNCT
ejpam-4989	298	5	163(3):969–1018	163(3):969–1018	PROPN
ejpam-4989	298	6	,	,	PUNCT
ejpam-4989	298	7	2006	2006	NUM
ejpam-4989	298	8	.	.	PUNCT
ejpam-4989	299	1	[	[	X
ejpam-4989	299	2	6	6	NUM
ejpam-4989	299	3	]	]	PUNCT
ejpam-4989	299	4	g.	g.	PROPN
ejpam-4989	299	5	p.	p.	PROPN
ejpam-4989	299	6	b.	b.	PROPN
ejpam-4989	299	7	dresden	dresden	PROPN
ejpam-4989	299	8	and	and	CCONJ
ejpam-4989	299	9	z.	z.	PROPN
ejpam-4989	299	10	du	du	PROPN
ejpam-4989	299	11	.	.	PUNCT
ejpam-4989	300	1	a	a	DET
ejpam-4989	300	2	simplified	simplified	ADJ
ejpam-4989	300	3	binet	binet	NOUN
ejpam-4989	300	4	formula	formula	NOUN
ejpam-4989	300	5	for	for	ADP
ejpam-4989	300	6	k	k	ADV
ejpam-4989	300	7	-	-	ADJ
ejpam-4989	300	8	generalized	generalize	VERB
ejpam-4989	300	9	fibonacci	fibonacci	NOUN
ejpam-4989	300	10	numbers	number	NOUN
ejpam-4989	300	11	.	.	PUNCT
ejpam-4989	301	1	journal	journal	NOUN
ejpam-4989	301	2	of	of	ADP
ejpam-4989	301	3	integer	integer	PROPN
ejpam-4989	301	4	sequences	sequence	NOUN
ejpam-4989	301	5	,	,	PUNCT
ejpam-4989	301	6	17	17	NUM
ejpam-4989	301	7	:	:	PUNCT
ejpam-4989	301	8	article	article	NOUN
ejpam-4989	301	9	14.4.7	14.4.7	NOUN
ejpam-4989	301	10	,	,	PUNCT
ejpam-4989	301	11	2014	2014	NUM
ejpam-4989	301	12	.	.	PUNCT
ejpam-4989	302	1	[	[	X
ejpam-4989	302	2	7	7	X
ejpam-4989	302	3	]	]	X
ejpam-4989	302	4	b.	b.	PROPN
ejpam-4989	302	5	kafle	kafle	PROPN
ejpam-4989	302	6	,	,	PUNCT
ejpam-4989	302	7	s.	s.	PROPN
ejpam-4989	302	8	e.	e.	PROPN
ejpam-4989	302	9	rihane	rihane	PROPN
ejpam-4989	302	10	,	,	PUNCT
ejpam-4989	302	11	and	and	CCONJ
ejpam-4989	302	12	a.	a.	PROPN
ejpam-4989	302	13	togbé.	togbé.	PROPN
ejpam-4989	302	14	a	a	DET
ejpam-4989	302	15	note	note	NOUN
ejpam-4989	302	16	on	on	ADP
ejpam-4989	302	17	mersenne	mersenne	PROPN
ejpam-4989	302	18	padovan	padovan	PROPN
ejpam-4989	302	19	and	and	CCONJ
ejpam-4989	302	20	perrin	perrin	NOUN
ejpam-4989	302	21	numbers	number	NOUN
ejpam-4989	302	22	.	.	PUNCT
ejpam-4989	303	1	notes	note	NOUN
ejpam-4989	303	2	on	on	ADP
ejpam-4989	303	3	number	number	NOUN
ejpam-4989	303	4	theory	theory	NOUN
ejpam-4989	303	5	and	and	CCONJ
ejpam-4989	303	6	discrete	discrete	ADJ
ejpam-4989	303	7	mathematics	mathematic	NOUN
ejpam-4989	303	8	,	,	PUNCT
ejpam-4989	303	9	27(1):161–170	27(1):161–170	PROPN
ejpam-4989	303	10	,	,	PUNCT
ejpam-4989	303	11	2021	2021	NUM
ejpam-4989	303	12	.	.	PUNCT
ejpam-4989	304	1	[	[	X
ejpam-4989	304	2	8	8	NUM
ejpam-4989	304	3	]	]	PUNCT
ejpam-4989	304	4	em	em	PRON
ejpam-4989	304	5	.	.	PUNCT
ejpam-4989	305	1	matveev	matveev	PROPN
ejpam-4989	305	2	.	.	PUNCT
ejpam-4989	306	1	an	an	DET
ejpam-4989	306	2	explicit	explicit	ADJ
ejpam-4989	306	3	lower	lower	ADV
ejpam-4989	306	4	bound	bind	VERB
ejpam-4989	306	5	for	for	ADP
ejpam-4989	306	6	a	a	DET
ejpam-4989	306	7	homogeneous	homogeneous	ADJ
ejpam-4989	306	8	rational	rational	ADJ
ejpam-4989	306	9	linear	linear	NOUN
ejpam-4989	306	10	form	form	NOUN
ejpam-4989	306	11	in	in	ADP
ejpam-4989	306	12	the	the	DET
ejpam-4989	306	13	logarithms	logarithm	NOUN
ejpam-4989	306	14	of	of	ADP
ejpam-4989	306	15	algebraic	algebraic	ADJ
ejpam-4989	306	16	numbers	number	NOUN
ejpam-4989	306	17	.	.	PUNCT
ejpam-4989	307	1	izv	izv	PROPN
ejpam-4989	307	2	.	.	PROPN
ejpam-4989	307	3	math	math	PROPN
ejpam-4989	307	4	,	,	PUNCT
ejpam-4989	307	5	64(6):1217–1269	64(6):1217–1269	NUM
ejpam-4989	307	6	,	,	PUNCT
ejpam-4989	307	7	2000	2000	NUM
ejpam-4989	307	8	.	.	PUNCT
ejpam-4989	308	1	[	[	X
ejpam-4989	308	2	9	9	NUM
ejpam-4989	308	3	]	]	X
ejpam-4989	308	4	b.	b.	PROPN
ejpam-4989	308	5	v.	v.	PROPN
ejpam-4989	308	6	normenyo	normenyo	PROPN
ejpam-4989	308	7	,	,	PUNCT
ejpam-4989	308	8	s.	s.	PROPN
ejpam-4989	308	9	e.	e.	PROPN
ejpam-4989	308	10	rihane	rihane	PROPN
ejpam-4989	308	11	,	,	PUNCT
ejpam-4989	308	12	and	and	CCONJ
ejpam-4989	308	13	a.	a.	NOUN
ejpam-4989	308	14	togbe	togbe	NOUN
ejpam-4989	308	15	.	.	PUNCT
ejpam-4989	309	1	fermat	fermat	PROPN
ejpam-4989	309	2	and	and	CCONJ
ejpam-4989	309	3	mersenne	mersenne	NOUN
ejpam-4989	309	4	numbers	number	NOUN
ejpam-4989	309	5	in	in	ADP
ejpam-4989	309	6	k	k	NOUN
ejpam-4989	309	7	-	-	PUNCT
ejpam-4989	309	8	pell	pell	ADJ
ejpam-4989	309	9	sequence	sequence	NOUN
ejpam-4989	309	10	.	.	PUNCT
ejpam-4989	310	1	matematychni	matematychni	PROPN
ejpam-4989	310	2	studii	studii	PROPN
ejpam-4989	310	3	,	,	PUNCT
ejpam-4989	310	4	56(2):115–123	56(2):115–123	PROPN
ejpam-4989	310	5	,	,	PUNCT
ejpam-4989	310	6	2021	2021	NUM
ejpam-4989	310	7	.	.	PUNCT
ejpam-4989	311	1	[	[	X
ejpam-4989	311	2	10	10	NUM
ejpam-4989	311	3	]	]	X
ejpam-4989	311	4	b.	b.	PROPN
ejpam-4989	312	1	v.	v.	PROPN
ejpam-4989	313	1	normenyo	normenyo	PROPN
ejpam-4989	314	1	,	,	PUNCT
ejpam-4989	314	2	s.	s.	PROPN
ejpam-4989	314	3	e.	e.	PROPN
ejpam-4989	314	4	rihane	rihane	PROPN
ejpam-4989	314	5	,	,	PUNCT
ejpam-4989	314	6	and	and	CCONJ
ejpam-4989	314	7	a.	a.	NOUN
ejpam-4989	314	8	togbé.	togbé.	PROPN
ejpam-4989	314	9	common	common	ADJ
ejpam-4989	314	10	terms	term	NOUN
ejpam-4989	314	11	of	of	ADP
ejpam-4989	314	12	k	k	NOUN
ejpam-4989	314	13	-	-	PUNCT
ejpam-4989	314	14	pell	pell	ADJ
ejpam-4989	314	15	numbers	number	NOUN
ejpam-4989	314	16	and	and	CCONJ
ejpam-4989	314	17	padovan	padovan	NOUN
ejpam-4989	314	18	or	or	CCONJ
ejpam-4989	314	19	perrin	perrin	NOUN
ejpam-4989	314	20	numbers	number	NOUN
ejpam-4989	314	21	.	.	PUNCT
ejpam-4989	315	1	arabian	arabian	ADJ
ejpam-4989	315	2	journal	journal	PROPN
ejpam-4989	315	3	of	of	ADP
ejpam-4989	315	4	mathematics	mathematic	NOUN
ejpam-4989	315	5	,	,	PUNCT
ejpam-4989	315	6	12(1):219–232	12(1):219–232	PROPN
ejpam-4989	315	7	,	,	PUNCT
ejpam-4989	315	8	2023	2023	NUM
ejpam-4989	315	9	.	.	PUNCT
ejpam-4989	316	1	[	[	X
ejpam-4989	316	2	11	11	NUM
ejpam-4989	316	3	]	]	PUNCT
ejpam-4989	316	4	s.	s.	PROPN
ejpam-4989	316	5	g.	g.	PROPN
ejpam-4989	316	6	sanchez	sanchez	PROPN
ejpam-4989	316	7	and	and	CCONJ
ejpam-4989	316	8	f.	f.	PROPN
ejpam-4989	316	9	luca	luca	PROPN
ejpam-4989	316	10	.	.	PUNCT
ejpam-4989	317	1	linear	linear	ADJ
ejpam-4989	317	2	combinations	combination	NOUN
ejpam-4989	317	3	of	of	ADP
ejpam-4989	317	4	factorials	factorial	NOUN
ejpam-4989	317	5	and	and	CCONJ
ejpam-4989	317	6	s	s	NOUN
ejpam-4989	317	7	-	-	NOUN
ejpam-4989	317	8	units	unit	NOUN
ejpam-4989	317	9	in	in	ADP
ejpam-4989	317	10	a	a	DET
ejpam-4989	317	11	binary	binary	ADJ
ejpam-4989	317	12	recurrence	recurrence	NOUN
ejpam-4989	317	13	sequence	sequence	NOUN
ejpam-4989	317	14	.	.	PUNCT
ejpam-4989	318	1	annales	annales	PROPN
ejpam-4989	318	2	mathematiques	mathematiques	ADP
ejpam-4989	318	3	du	du	PROPN
ejpam-4989	318	4	quebec	quebec	PROPN
ejpam-4989	318	5	,	,	PUNCT
ejpam-4989	318	6	38(2):169–188	38(2):169–188	PROPN
ejpam-4989	318	7	,	,	PUNCT
ejpam-4989	318	8	2014	2014	NUM
ejpam-4989	318	9	.	.	PUNCT
ejpam-4989	319	1	[	[	X
ejpam-4989	319	2	12	12	NUM
ejpam-4989	319	3	]	]	PUNCT
ejpam-4989	319	4	w.	w.	PROPN
ejpam-4989	319	5	r.	r.	PROPN
ejpam-4989	319	6	spickerman	spickerman	PROPN
ejpam-4989	319	7	.	.	PUNCT
ejpam-4989	320	1	binet	binet	PROPN
ejpam-4989	320	2	’s	’s	PART
ejpam-4989	320	3	formula	formula	NOUN
ejpam-4989	320	4	the	the	DET
ejpam-4989	320	5	tribonacci	tribonacci	PROPN
ejpam-4989	320	6	sequence	sequence	NOUN
ejpam-4989	320	7	.	.	PUNCT
ejpam-4989	321	1	fibonacci	fibonacci	PROPN
ejpam-4989	321	2	quart	quart	PROPN
ejpam-4989	321	3	,	,	PUNCT
ejpam-4989	321	4	20:118	20:118	NUM
ejpam-4989	321	5	–	–	PUNCT
ejpam-4989	321	6	120	120	NUM
ejpam-4989	321	7	,	,	PUNCT
ejpam-4989	321	8	1982	1982	NUM
ejpam-4989	321	9	.	.	PUNCT
ejpam-4989	322	1	[	[	X
ejpam-4989	322	2	13	13	NUM
ejpam-4989	322	3	]	]	PUNCT
ejpam-4989	322	4	b.	b.	PROPN
ejpam-4989	323	1	p.	p.	PROPN
ejpam-4989	323	2	tripathy	tripathy	PROPN
ejpam-4989	323	3	and	and	CCONJ
ejpam-4989	323	4	b.	b.	PROPN
ejpam-4989	323	5	k.	k.	PROPN
ejpam-4989	323	6	patel	patel	PROPN
ejpam-4989	323	7	.	.	PUNCT
ejpam-4989	324	1	common	common	ADJ
ejpam-4989	324	2	values	value	NOUN
ejpam-4989	324	3	of	of	ADP
ejpam-4989	324	4	generalized	generalized	ADJ
ejpam-4989	324	5	fibonacci	fibonacci	NOUN
ejpam-4989	324	6	and	and	CCONJ
ejpam-4989	324	7	leonardo	leonardo	PROPN
ejpam-4989	324	8	sequences	sequences	PROPN
ejpam-4989	324	9	.	.	PUNCT
ejpam-4989	325	1	journal	journal	PROPN
ejpam-4989	325	2	of	of	ADP
ejpam-4989	325	3	integer	integer	PROPN
ejpam-4989	325	4	sequences	sequence	NOUN
ejpam-4989	325	5	,	,	PUNCT
ejpam-4989	325	6	26	26	NUM
ejpam-4989	325	7	:	:	PUNCT
ejpam-4989	325	8	article	article	NOUN
ejpam-4989	325	9	23.6.2	23.6.2	NUM
ejpam-4989	325	10	,	,	PUNCT
ejpam-4989	325	11	2023	2023	NUM
ejpam-4989	325	12	.	.	PUNCT
ejpam-4989	326	1	[	[	X
ejpam-4989	326	2	14	14	NUM
ejpam-4989	326	3	]	]	X
ejpam-4989	326	4	b.	b.	PROPN
ejpam-4989	326	5	m.	m.	PROPN
ejpam-4989	326	6	m.	m.	PROPN
ejpam-4989	326	7	de	de	PROPN
ejpam-4989	326	8	weger	weger	PROPN
ejpam-4989	326	9	.	.	PUNCT
ejpam-4989	327	1	algorithms	algorithm	NOUN
ejpam-4989	327	2	for	for	ADP
ejpam-4989	327	3	diophantine	diophantine	NOUN
ejpam-4989	327	4	equations	equation	NOUN
ejpam-4989	327	5	.	.	PUNCT
ejpam-4989	328	1	centrum	centrum	PROPN
ejpam-4989	328	2	voor	voor	PROPN
ejpam-4989	328	3	wiskunde	wiskunde	PROPN
ejpam-4989	328	4	en	en	PROPN
ejpam-4989	328	5	informatica	informatica	PROPN
ejpam-4989	328	6	,	,	PUNCT
ejpam-4989	328	7	amsterdam	amsterdam	PROPN
ejpam-4989	328	8	,	,	PUNCT
ejpam-4989	328	9	netherlands	netherlands	PROPN
ejpam-4989	328	10	,	,	PUNCT
ejpam-4989	328	11	1989	1989	NUM
ejpam-4989	328	12	.	.	PUNCT