id	sid	tid	token	lemma	pos
ejpam-4463	1	1	european	european	PROPN
ejpam-4463	1	2	journal	journal	PROPN
ejpam-4463	1	3	of	of	ADP
ejpam-4463	1	4	pure	pure	ADJ
ejpam-4463	1	5	and	and	CCONJ
ejpam-4463	1	6	applied	apply	VERB
ejpam-4463	1	7	mathematics	mathematic	NOUN
ejpam-4463	1	8	vol	vol	NOUN
ejpam-4463	1	9	.	.	PROPN
ejpam-4463	2	1	15	15	NUM
ejpam-4463	2	2	,	,	PUNCT
ejpam-4463	2	3	no	no	INTJ
ejpam-4463	2	4	.	.	NOUN
ejpam-4463	2	5	3	3	NUM
ejpam-4463	2	6	,	,	PUNCT
ejpam-4463	2	7	2022	2022	NUM
ejpam-4463	2	8	,	,	PUNCT
ejpam-4463	2	9	1321	1321	NUM
ejpam-4463	2	10	-	-	SYM
ejpam-4463	2	11	1330	1330	NUM
ejpam-4463	2	12	issn	issn	PROPN
ejpam-4463	2	13	1307	1307	NUM
ejpam-4463	2	14	-	-	SYM
ejpam-4463	2	15	5543	5543	NUM
ejpam-4463	2	16	–	–	PUNCT
ejpam-4463	2	17	ejpam.com	ejpam.com	X
ejpam-4463	2	18	published	publish	VERB
ejpam-4463	2	19	by	by	ADP
ejpam-4463	2	20	new	new	PROPN
ejpam-4463	2	21	york	york	PROPN
ejpam-4463	2	22	business	business	PROPN
ejpam-4463	2	23	global	global	PROPN
ejpam-4463	2	24	on	on	ADP
ejpam-4463	2	25	salem	salem	PROPN
ejpam-4463	2	26	formal	formal	ADJ
ejpam-4463	2	27	power	power	NOUN
ejpam-4463	2	28	series	series	PROPN
ejpam-4463	2	29	oussama	oussama	PROPN
ejpam-4463	2	30	dammak1,2	dammak1,2	PROPN
ejpam-4463	2	31	,	,	PUNCT
ejpam-4463	2	32	saber	saber	NOUN
ejpam-4463	2	33	mansour1,3,∗	mansour1,3,∗	VERB
ejpam-4463	2	34	1	1	NUM
ejpam-4463	2	35	department	department	NOUN
ejpam-4463	2	36	of	of	ADP
ejpam-4463	2	37	mathematics	mathematic	NOUN
ejpam-4463	2	38	,	,	PUNCT
ejpam-4463	2	39	umm	umm	INTJ
ejpam-4463	2	40	al	al	PROPN
ejpam-4463	2	41	-	-	PUNCT
ejpam-4463	2	42	qura	qura	PROPN
ejpam-4463	2	43	university	university	PROPN
ejpam-4463	2	44	,	,	PUNCT
ejpam-4463	2	45	college	college	NOUN
ejpam-4463	2	46	of	of	ADP
ejpam-4463	2	47	first	first	ADJ
ejpam-4463	2	48	common	common	ADJ
ejpam-4463	2	49	year	year	NOUN
ejpam-4463	2	50	,	,	PUNCT
ejpam-4463	2	51	p.o	p.o	PROPN
ejpam-4463	2	52	.	.	PROPN
ejpam-4463	2	53	box	box	PROPN
ejpam-4463	2	54	14035	14035	NUM
ejpam-4463	2	55	,	,	PUNCT
ejpam-4463	2	56	holly	holly	PROPN
ejpam-4463	2	57	makkah	makkah	PROPN
ejpam-4463	2	58	21955	21955	NUM
ejpam-4463	2	59	,	,	PUNCT
ejpam-4463	2	60	saudi	saudi	PROPN
ejpam-4463	2	61	arabia	arabia	PROPN
ejpam-4463	2	62	2	2	NUM
ejpam-4463	2	63	university	university	NOUN
ejpam-4463	2	64	of	of	ADP
ejpam-4463	2	65	gabes	gabes	PROPN
ejpam-4463	2	66	,	,	PUNCT
ejpam-4463	2	67	science	science	NOUN
ejpam-4463	2	68	faculty	faculty	NOUN
ejpam-4463	2	69	of	of	ADP
ejpam-4463	2	70	gabes	gabes	PROPN
ejpam-4463	2	71	,	,	PUNCT
ejpam-4463	2	72	omar	omar	PROPN
ejpam-4463	2	73	ibn	ibn	PROPN
ejpam-4463	2	74	alkhattab	alkhattab	NOUN
ejpam-4463	2	75	-	-	PUNCT
ejpam-4463	2	76	zrig	zrig	NOUN
ejpam-4463	2	77	road	road	NOUN
ejpam-4463	2	78	,	,	PUNCT
ejpam-4463	2	79	6029	6029	NUM
ejpam-4463	2	80	gabes	gabes	PROPN
ejpam-4463	2	81	,	,	PUNCT
ejpam-4463	2	82	tunisia	tunisia	PROPN
ejpam-4463	2	83	3	3	NUM
ejpam-4463	2	84	sfax	sfax	PROPN
ejpam-4463	2	85	university	university	NOUN
ejpam-4463	2	86	,	,	PUNCT
ejpam-4463	2	87	department	department	NOUN
ejpam-4463	2	88	of	of	ADP
ejpam-4463	2	89	mathematics	mathematic	NOUN
ejpam-4463	2	90	,	,	PUNCT
ejpam-4463	2	91	faculty	faculty	NOUN
ejpam-4463	2	92	of	of	ADP
ejpam-4463	2	93	sciences	science	NOUN
ejpam-4463	2	94	of	of	ADP
ejpam-4463	2	95	sfax	sfax	NOUN
ejpam-4463	2	96	,	,	PUNCT
ejpam-4463	2	97	soukra	soukra	NOUN
ejpam-4463	2	98	road	road	NOUN
ejpam-4463	2	99	,	,	PUNCT
ejpam-4463	2	100	3018	3018	NUM
ejpam-4463	2	101	sfax	sfax	NOUN
ejpam-4463	2	102	,	,	PUNCT
ejpam-4463	2	103	bp	bp	PROPN
ejpam-4463	2	104	802	802	NUM
ejpam-4463	2	105	,	,	PUNCT
ejpam-4463	2	106	tunisia	tunisia	NOUN
ejpam-4463	2	107	abstract	abstract	NOUN
ejpam-4463	2	108	.	.	PUNCT
ejpam-4463	3	1	in	in	ADP
ejpam-4463	3	2	this	this	DET
ejpam-4463	3	3	paper	paper	NOUN
ejpam-4463	3	4	,	,	PUNCT
ejpam-4463	3	5	we	we	PRON
ejpam-4463	3	6	will	will	AUX
ejpam-4463	3	7	take	take	VERB
ejpam-4463	3	8	a	a	DET
ejpam-4463	3	9	look	look	NOUN
ejpam-4463	3	10	at	at	ADP
ejpam-4463	3	11	salem	salem	NOUN
ejpam-4463	3	12	elements	element	NOUN
ejpam-4463	3	13	dealing	deal	VERB
ejpam-4463	3	14	with	with	ADP
ejpam-4463	3	15	formal	formal	ADJ
ejpam-4463	3	16	power	power	NOUN
ejpam-4463	3	17	series	series	NOUN
ejpam-4463	3	18	on	on	ADP
ejpam-4463	3	19	fq	fq	PROPN
ejpam-4463	3	20	,	,	PUNCT
ejpam-4463	3	21	where	where	SCONJ
ejpam-4463	3	22	fq	fq	PROPN
ejpam-4463	3	23	is	be	AUX
ejpam-4463	3	24	a	a	DET
ejpam-4463	3	25	finite	finite	ADJ
ejpam-4463	3	26	field	field	NOUN
ejpam-4463	3	27	.	.	PUNCT
ejpam-4463	4	1	our	our	PRON
ejpam-4463	4	2	main	main	ADJ
ejpam-4463	4	3	result	result	NOUN
ejpam-4463	4	4	,	,	PUNCT
ejpam-4463	4	5	presents	present	VERB
ejpam-4463	4	6	a	a	DET
ejpam-4463	4	7	criteria	criterion	NOUN
ejpam-4463	4	8	for	for	ADP
ejpam-4463	4	9	an	an	DET
ejpam-4463	4	10	element	element	NOUN
ejpam-4463	4	11	to	to	PART
ejpam-4463	4	12	be	be	AUX
ejpam-4463	4	13	the	the	DET
ejpam-4463	4	14	smallest	small	ADJ
ejpam-4463	4	15	salem	salem	NOUN
ejpam-4463	4	16	element	element	NOUN
ejpam-4463	4	17	(	(	PUNCT
ejpam-4463	4	18	sse	sse	PROPN
ejpam-4463	4	19	)	)	PUNCT
ejpam-4463	4	20	via	via	ADP
ejpam-4463	4	21	an	an	DET
ejpam-4463	4	22	order	order	NOUN
ejpam-4463	4	23	extending	extend	VERB
ejpam-4463	4	24	a	a	DET
ejpam-4463	4	25	given	give	VERB
ejpam-4463	4	26	order	order	NOUN
ejpam-4463	4	27	in	in	ADP
ejpam-4463	4	28	fq	fq	PROPN
ejpam-4463	4	29	.	.	PUNCT
ejpam-4463	5	1	moreover	moreover	ADV
ejpam-4463	5	2	,	,	PUNCT
ejpam-4463	5	3	we	we	PRON
ejpam-4463	5	4	provide	provide	VERB
ejpam-4463	5	5	the	the	DET
ejpam-4463	5	6	cfe	cfe	NOUN
ejpam-4463	5	7	of	of	ADP
ejpam-4463	5	8	the	the	DET
ejpam-4463	5	9	(	(	PUNCT
ejpam-4463	5	10	sse	sse	PROPN
ejpam-4463	5	11	)	)	PUNCT
ejpam-4463	5	12	for	for	ADP
ejpam-4463	5	13	each	each	DET
ejpam-4463	5	14	n.	n.	NOUN
ejpam-4463	5	15	2020	2020	NUM
ejpam-4463	5	16	mathematics	mathematic	NOUN
ejpam-4463	5	17	subject	subject	NOUN
ejpam-4463	5	18	classifications	classification	NOUN
ejpam-4463	5	19	:	:	PUNCT
ejpam-4463	5	20	11kxx	11kxx	ADJ
ejpam-4463	5	21	,	,	PUNCT
ejpam-4463	5	22	11k16	11k16	NUM
ejpam-4463	5	23	,	,	PUNCT
ejpam-4463	5	24	11t06	11t06	PRON
ejpam-4463	5	25	key	key	ADJ
ejpam-4463	5	26	words	word	NOUN
ejpam-4463	5	27	and	and	CCONJ
ejpam-4463	5	28	phrases	phrase	NOUN
ejpam-4463	5	29	:	:	PUNCT
ejpam-4463	5	30	finite	finite	PROPN
ejpam-4463	5	31	fields	field	NOUN
ejpam-4463	5	32	,	,	PUNCT
ejpam-4463	5	33	formal	formal	ADJ
ejpam-4463	5	34	power	power	NOUN
ejpam-4463	5	35	series	series	NOUN
ejpam-4463	5	36	,	,	PUNCT
ejpam-4463	5	37	pisot	pisot	ADJ
ejpam-4463	5	38	elements	element	NOUN
ejpam-4463	5	39	,	,	PUNCT
ejpam-4463	5	40	salem	salem	NOUN
ejpam-4463	5	41	elements	element	NOUN
ejpam-4463	5	42	,	,	PUNCT
ejpam-4463	5	43	continued	continued	ADJ
ejpam-4463	5	44	fractions	fraction	NOUN
ejpam-4463	5	45	.	.	PUNCT
ejpam-4463	6	1	1	1	X
ejpam-4463	6	2	.	.	X
ejpam-4463	6	3	introduction	introduction	NOUN
ejpam-4463	6	4	let	let	VERB
ejpam-4463	6	5	α1	α1	PROPN
ejpam-4463	6	6	be	be	AUX
ejpam-4463	6	7	an	an	DET
ejpam-4463	6	8	algebraic	algebraic	ADJ
ejpam-4463	6	9	integer	integer	NOUN
ejpam-4463	6	10	of	of	ADP
ejpam-4463	6	11	degree	degree	NOUN
ejpam-4463	6	12	n	n	PROPN
ejpam-4463	6	13	with	with	SCONJ
ejpam-4463	6	14	galois	galois	PROPN
ejpam-4463	6	15	conjugates	conjugate	NOUN
ejpam-4463	6	16	α2	α2	ADJ
ejpam-4463	6	17	,	,	PUNCT
ejpam-4463	6	18	α3	α3	NOUN
ejpam-4463	6	19	,	,	PUNCT
ejpam-4463	6	20	·	·	PUNCT
ejpam-4463	6	21	·	·	PUNCT
ejpam-4463	6	22	·	·	PUNCT
ejpam-4463	6	23	,	,	PUNCT
ejpam-4463	6	24	αn	αn	X
ejpam-4463	6	25	.	.	PUNCT
ejpam-4463	7	1	if	if	SCONJ
ejpam-4463	7	2	{	{	PUNCT
ejpam-4463	7	3	|α1|	|α1|	VERB
ejpam-4463	7	4	>	>	X
ejpam-4463	7	5	1	1	NUM
ejpam-4463	7	6	and	and	CCONJ
ejpam-4463	7	7	|αi|	|αi|	PRON
ejpam-4463	7	8	<	<	X
ejpam-4463	7	9	1	1	NUM
ejpam-4463	7	10	,	,	PUNCT
ejpam-4463	7	11	∀2	∀2	VERB
ejpam-4463	7	12	≤	≤	NUM
ejpam-4463	7	13	i	i	PRON
ejpam-4463	7	14	≤	≤	PROPN
ejpam-4463	7	15	n	n	CCONJ
ejpam-4463	7	16	,	,	PUNCT
ejpam-4463	7	17	α1	α1	PROPN
ejpam-4463	7	18	is	be	AUX
ejpam-4463	7	19	called	call	VERB
ejpam-4463	7	20	to	to	PART
ejpam-4463	7	21	be	be	AUX
ejpam-4463	7	22	a	a	DET
ejpam-4463	7	23	pisot	pisot	ADJ
ejpam-4463	7	24	number	number	NOUN
ejpam-4463	7	25	.	.	PUNCT
ejpam-4463	8	1	if	if	PROPN
ejpam-4463	8	2	|α1|	|α1|	NOUN
ejpam-4463	8	3	>	>	ADP
ejpam-4463	8	4	1	1	NUM
ejpam-4463	8	5	and	and	CCONJ
ejpam-4463	8	6	|αi|	|αi|	NOUN
ejpam-4463	8	7	=	=	SYM
ejpam-4463	8	8	1	1	NUM
ejpam-4463	8	9	,	,	PUNCT
ejpam-4463	8	10	for	for	ADP
ejpam-4463	8	11	2	2	NUM
ejpam-4463	8	12	≤	≤	NOUN
ejpam-4463	8	13	i	i	PRON
ejpam-4463	8	14	≤	≤	NOUN
ejpam-4463	8	15	n	n	CCONJ
ejpam-4463	8	16	,	,	PUNCT
ejpam-4463	8	17	and	and	CCONJ
ejpam-4463	8	18	|αj	|αj	NUM
ejpam-4463	8	19	|	|	ADV
ejpam-4463	8	20	≤	≤	NUM
ejpam-4463	8	21	1	1	NUM
ejpam-4463	8	22	,	,	PUNCT
ejpam-4463	8	23	for	for	ADP
ejpam-4463	8	24	2	2	NUM
ejpam-4463	8	25	≤	≤	NUM
ejpam-4463	8	26	j	j	PROPN
ejpam-4463	8	27	≤	≤	NUM
ejpam-4463	8	28	n	n	CCONJ
ejpam-4463	8	29	,	,	PUNCT
ejpam-4463	8	30	j	j	PROPN
ejpam-4463	8	31	̸=	̸=	PROPN
ejpam-4463	8	32	i	i	PROPN
ejpam-4463	8	33	,	,	PUNCT
ejpam-4463	8	34	α1	α1	PROPN
ejpam-4463	8	35	is	be	AUX
ejpam-4463	8	36	called	call	VERB
ejpam-4463	8	37	to	to	PART
ejpam-4463	8	38	be	be	AUX
ejpam-4463	8	39	a	a	DET
ejpam-4463	8	40	salem	salem	NOUN
ejpam-4463	8	41	number	number	NOUN
ejpam-4463	8	42	.	.	PUNCT
ejpam-4463	9	1	the	the	DET
ejpam-4463	9	2	set	set	NOUN
ejpam-4463	9	3	of	of	ADP
ejpam-4463	9	4	the	the	DET
ejpam-4463	9	5	so	so	ADV
ejpam-4463	9	6	called	call	VERB
ejpam-4463	9	7	,	,	PUNCT
ejpam-4463	9	8	pisot	pisot	ADJ
ejpam-4463	9	9	numbers	number	NOUN
ejpam-4463	9	10	,	,	PUNCT
ejpam-4463	9	11	is	be	AUX
ejpam-4463	9	12	usually	usually	ADV
ejpam-4463	9	13	denoted	denote	VERB
ejpam-4463	9	14	by	by	ADP
ejpam-4463	9	15	s	s	PRON
ejpam-4463	9	16	,	,	PUNCT
ejpam-4463	9	17	it	it	PRON
ejpam-4463	9	18	is	be	AUX
ejpam-4463	9	19	denoted	denote	VERB
ejpam-4463	9	20	by	by	ADP
ejpam-4463	9	21	t	t	PROPN
ejpam-4463	9	22	,	,	PUNCT
ejpam-4463	9	23	the	the	DET
ejpam-4463	9	24	set	set	NOUN
ejpam-4463	9	25	of	of	ADP
ejpam-4463	9	26	salem	salem	NOUN
ejpam-4463	9	27	numbers	number	NOUN
ejpam-4463	9	28	.	.	PUNCT
ejpam-4463	10	1	thus	thus	ADV
ejpam-4463	10	2	,	,	PUNCT
ejpam-4463	10	3	pisot	pisot	ADJ
ejpam-4463	10	4	numbers	number	NOUN
ejpam-4463	10	5	are	be	AUX
ejpam-4463	10	6	commonly	commonly	ADV
ejpam-4463	10	7	referred	refer	VERB
ejpam-4463	10	8	to	to	ADP
ejpam-4463	10	9	as	as	ADP
ejpam-4463	10	10	s−numbers	s−number	NOUN
ejpam-4463	10	11	,	,	PUNCT
ejpam-4463	10	12	∗corresponding	∗corresponde	VERB
ejpam-4463	10	13	author	author	NOUN
ejpam-4463	10	14	.	.	PUNCT
ejpam-4463	11	1	doi	doi	NOUN
ejpam-4463	11	2	:	:	PUNCT
ejpam-4463	11	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4463	https://doi.org/10.29020/nybg.ejpam.v15i3.4463	ADJ
ejpam-4463	11	4	email	email	NOUN
ejpam-4463	11	5	addresses	address	NOUN
ejpam-4463	11	6	:	:	PUNCT
ejpam-4463	11	7	omdammak@uqu.edu.sa	omdammak@uqu.edu.sa	PROPN
ejpam-4463	11	8	(	(	PUNCT
ejpam-4463	11	9	o.	o.	PROPN
ejpam-4463	11	10	dammak	dammak	PROPN
ejpam-4463	11	11	)	)	PUNCT
ejpam-4463	11	12	,	,	PUNCT
ejpam-4463	11	13	samansour@uqu.edu.sa	samansour@uqu.edu.sa	PROPN
ejpam-4463	11	14	(	(	PUNCT
ejpam-4463	11	15	s.	s.	PROPN
ejpam-4463	11	16	mansour	mansour	PROPN
ejpam-4463	11	17	)	)	PUNCT
ejpam-4463	11	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4463	11	19	1321	1321	NUM
ejpam-4463	12	1	©	©	PROPN
ejpam-4463	12	2	2022	2022	NUM
ejpam-4463	12	3	ejpam	ejpam	VERB
ejpam-4463	12	4	all	all	DET
ejpam-4463	12	5	rights	right	NOUN
ejpam-4463	12	6	reserved	reserve	VERB
ejpam-4463	12	7	.	.	PUNCT
ejpam-4463	13	1	o.	o.	PROPN
ejpam-4463	13	2	dammak	dammak	PROPN
ejpam-4463	13	3	,	,	PUNCT
ejpam-4463	13	4	s.	s.	PROPN
ejpam-4463	13	5	mansour	mansour	PROPN
ejpam-4463	13	6	/	/	SYM
ejpam-4463	13	7	eur	eur	PROPN
ejpam-4463	13	8	.	.	PUNCT
ejpam-4463	14	1	j.	j.	PROPN
ejpam-4463	14	2	pure	pure	PROPN
ejpam-4463	14	3	appl	appl	PROPN
ejpam-4463	14	4	.	.	PROPN
ejpam-4463	14	5	math	math	PROPN
ejpam-4463	14	6	,	,	PUNCT
ejpam-4463	14	7	15	15	NUM
ejpam-4463	14	8	(	(	PUNCT
ejpam-4463	14	9	3	3	NUM
ejpam-4463	14	10	)	)	PUNCT
ejpam-4463	14	11	(	(	PUNCT
ejpam-4463	14	12	2022	2022	NUM
ejpam-4463	14	13	)	)	PUNCT
ejpam-4463	14	14	,	,	PUNCT
ejpam-4463	14	15	1321	1321	NUM
ejpam-4463	14	16	-	-	SYM
ejpam-4463	14	17	1330	1330	NUM
ejpam-4463	14	18	1322	1322	NUM
ejpam-4463	14	19	while	while	SCONJ
ejpam-4463	14	20	salem	salem	NOUN
ejpam-4463	14	21	numbers	number	NOUN
ejpam-4463	14	22	are	be	AUX
ejpam-4463	14	23	referred	refer	VERB
ejpam-4463	14	24	to	to	ADP
ejpam-4463	14	25	as	as	ADP
ejpam-4463	14	26	t−numbers	t−number	NOUN
ejpam-4463	14	27	.	.	PUNCT
ejpam-4463	15	1	the	the	DET
ejpam-4463	15	2	sets	set	NOUN
ejpam-4463	15	3	s	s	PART
ejpam-4463	15	4	and	and	CCONJ
ejpam-4463	15	5	t	t	PROPN
ejpam-4463	15	6	appears	appear	VERB
ejpam-4463	15	7	in	in	ADP
ejpam-4463	15	8	a	a	DET
ejpam-4463	15	9	variety	variety	NOUN
ejpam-4463	15	10	of	of	ADP
ejpam-4463	15	11	algebraic	algebraic	ADJ
ejpam-4463	15	12	number	number	NOUN
ejpam-4463	15	13	theory	theory	NOUN
ejpam-4463	15	14	problems	problem	NOUN
ejpam-4463	15	15	,	,	PUNCT
ejpam-4463	15	16	diophantine	diophantine	VERB
ejpam-4463	15	17	approximation	approximation	NOUN
ejpam-4463	15	18	,	,	PUNCT
ejpam-4463	15	19	fourier	fourier	ADJ
ejpam-4463	15	20	analysis	analysis	NOUN
ejpam-4463	15	21	,	,	PUNCT
ejpam-4463	15	22	distribution	distribution	NOUN
ejpam-4463	15	23	,	,	PUNCT
ejpam-4463	15	24	the	the	DET
ejpam-4463	15	25	so	so	ADV
ejpam-4463	15	26	-	-	PUNCT
ejpam-4463	15	27	called	call	VERB
ejpam-4463	15	28	β	β	NOUN
ejpam-4463	15	29	-	-	NOUN
ejpam-4463	15	30	expansions	expansion	NOUN
ejpam-4463	15	31	,	,	PUNCT
ejpam-4463	15	32	etc	etc	X
ejpam-4463	15	33	.	.	X
ejpam-4463	16	1	the	the	DET
ejpam-4463	16	2	set	set	NOUN
ejpam-4463	16	3	s	s	VERB
ejpam-4463	16	4	was	be	AUX
ejpam-4463	16	5	defined	define	VERB
ejpam-4463	16	6	approximately	approximately	ADV
ejpam-4463	16	7	simultaneously	simultaneously	ADV
ejpam-4463	16	8	and	and	CCONJ
ejpam-4463	16	9	separately	separately	ADV
ejpam-4463	16	10	by	by	ADP
ejpam-4463	16	11	c.	c.	PROPN
ejpam-4463	16	12	pisot	pisot	NOUN
ejpam-4463	17	1	[	[	X
ejpam-4463	17	2	9	9	NUM
ejpam-4463	17	3	]	]	PUNCT
ejpam-4463	17	4	and	and	CCONJ
ejpam-4463	17	5	vihayaraghavan	vihayaraghavan	X
ejpam-4463	17	6	[	[	X
ejpam-4463	17	7	18	18	NUM
ejpam-4463	17	8	,	,	PUNCT
ejpam-4463	17	9	19	19	NUM
ejpam-4463	17	10	]	]	PUNCT
ejpam-4463	17	11	.	.	PUNCT
ejpam-4463	18	1	r.	r.	PROPN
ejpam-4463	18	2	salem	salem	PROPN
ejpam-4463	19	1	[	[	X
ejpam-4463	19	2	11	11	NUM
ejpam-4463	19	3	]	]	PUNCT
ejpam-4463	19	4	a	a	DET
ejpam-4463	19	5	few	few	ADJ
ejpam-4463	19	6	years	year	NOUN
ejpam-4463	19	7	later	later	ADV
ejpam-4463	19	8	,	,	PUNCT
ejpam-4463	19	9	defined	define	VERB
ejpam-4463	19	10	the	the	DET
ejpam-4463	19	11	set	set	NOUN
ejpam-4463	19	12	t	t	PROPN
ejpam-4463	19	13	.	.	PUNCT
ejpam-4463	20	1	however	however	ADV
ejpam-4463	20	2	,	,	PUNCT
ejpam-4463	20	3	some	some	PRON
ejpam-4463	20	4	of	of	ADP
ejpam-4463	20	5	the	the	DET
ejpam-4463	20	6	first	first	ADJ
ejpam-4463	20	7	research	research	NOUN
ejpam-4463	20	8	in	in	ADP
ejpam-4463	20	9	this	this	DET
ejpam-4463	20	10	approach	approach	NOUN
ejpam-4463	20	11	and	and	CCONJ
ejpam-4463	20	12	related	relate	VERB
ejpam-4463	20	13	to	to	ADP
ejpam-4463	20	14	uniform	uniform	ADJ
ejpam-4463	20	15	distributions	distribution	NOUN
ejpam-4463	20	16	were	be	AUX
ejpam-4463	20	17	published	publish	VERB
ejpam-4463	20	18	earlier	early	ADV
ejpam-4463	20	19	by	by	ADP
ejpam-4463	20	20	thue	thue	PROPN
ejpam-4463	20	21	[	[	X
ejpam-4463	20	22	17	17	NUM
ejpam-4463	20	23	]	]	PUNCT
ejpam-4463	20	24	.	.	PUNCT
ejpam-4463	21	1	in	in	ADP
ejpam-4463	21	2	1919	1919	NUM
ejpam-4463	21	3	,	,	PUNCT
ejpam-4463	21	4	hardy	hardy	NOUN
ejpam-4463	21	5	showed	show	VERB
ejpam-4463	21	6	that	that	SCONJ
ejpam-4463	21	7	if	if	SCONJ
ejpam-4463	21	8	α	α	PRON
ejpam-4463	21	9	is	be	AUX
ejpam-4463	21	10	an	an	DET
ejpam-4463	21	11	algebraic	algebraic	ADJ
ejpam-4463	21	12	integer	integer	NOUN
ejpam-4463	21	13	such	such	ADJ
ejpam-4463	21	14	that	that	DET
ejpam-4463	21	15	αn	αn	NOUN
ejpam-4463	21	16	→	→	SYM
ejpam-4463	21	17	0	0	NUM
ejpam-4463	21	18	(	(	PUNCT
ejpam-4463	21	19	mod	mod	NOUN
ejpam-4463	21	20	1	1	NUM
ejpam-4463	21	21	)	)	PUNCT
ejpam-4463	21	22	as	as	ADP
ejpam-4463	21	23	n	n	PROPN
ejpam-4463	21	24	→	→	SYM
ejpam-4463	21	25	∞	∞	PROPN
ejpam-4463	21	26	,	,	PUNCT
ejpam-4463	21	27	then	then	ADV
ejpam-4463	21	28	α	α	PROPN
ejpam-4463	21	29	is	be	AUX
ejpam-4463	21	30	a	a	DET
ejpam-4463	21	31	pisot	pisot	ADJ
ejpam-4463	21	32	number	number	NOUN
ejpam-4463	21	33	.	.	PUNCT
ejpam-4463	22	1	later	later	ADV
ejpam-4463	22	2	,	,	PUNCT
ejpam-4463	22	3	this	this	DET
ejpam-4463	22	4	concept	concept	NOUN
ejpam-4463	22	5	,	,	PUNCT
ejpam-4463	22	6	was	be	AUX
ejpam-4463	22	7	investigated	investigate	VERB
ejpam-4463	22	8	by	by	ADP
ejpam-4463	22	9	salem	salem	NOUN
ejpam-4463	22	10	,	,	PUNCT
ejpam-4463	22	11	who	who	PRON
ejpam-4463	22	12	proved	prove	VERB
ejpam-4463	22	13	that	that	SCONJ
ejpam-4463	22	14	the	the	DET
ejpam-4463	22	15	only	only	ADJ
ejpam-4463	22	16	algebraic	algebraic	ADJ
ejpam-4463	22	17	numbers	number	NOUN
ejpam-4463	22	18	that	that	PRON
ejpam-4463	22	19	have	have	VERB
ejpam-4463	22	20	this	this	DET
ejpam-4463	22	21	property	property	NOUN
ejpam-4463	22	22	of	of	ADP
ejpam-4463	22	23	being	be	AUX
ejpam-4463	22	24	badly	badly	ADV
ejpam-4463	22	25	distributed	distribute	VERB
ejpam-4463	22	26	modulo	modulo	NOUN
ejpam-4463	22	27	1	1	NUM
ejpam-4463	22	28	are	be	AUX
ejpam-4463	22	29	s	s	NOUN
ejpam-4463	22	30	-	-	PUNCT
ejpam-4463	22	31	numbers	number	NOUN
ejpam-4463	22	32	[	[	X
ejpam-4463	22	33	12	12	NUM
ejpam-4463	22	34	]	]	PUNCT
ejpam-4463	22	35	.	.	PUNCT
ejpam-4463	23	1	in	in	ADP
ejpam-4463	23	2	brief	brief	NOUN
ejpam-4463	23	3	,	,	PUNCT
ejpam-4463	23	4	this	this	PRON
ejpam-4463	23	5	occurs	occur	VERB
ejpam-4463	23	6	because	because	SCONJ
ejpam-4463	23	7	for	for	ADP
ejpam-4463	23	8	all	all	DET
ejpam-4463	23	9	algebraic	algebraic	ADJ
ejpam-4463	23	10	number	number	NOUN
ejpam-4463	23	11	α	α	NOUN
ejpam-4463	23	12	and	and	CCONJ
ejpam-4463	23	13	n	n	DET
ejpam-4463	23	14	∈	∈	PROPN
ejpam-4463	23	15	n∗	n∗	PROPN
ejpam-4463	23	16	,	,	PUNCT
ejpam-4463	23	17	the	the	DET
ejpam-4463	23	18	sum	sum	NOUN
ejpam-4463	23	19	of	of	ADP
ejpam-4463	23	20	the	the	DET
ejpam-4463	23	21	nth	nth	NOUN
ejpam-4463	23	22	powers	power	NOUN
ejpam-4463	23	23	of	of	ADP
ejpam-4463	23	24	α	α	NOUN
ejpam-4463	23	25	and	and	CCONJ
ejpam-4463	23	26	its	its	PRON
ejpam-4463	23	27	conjugates	conjugate	NOUN
ejpam-4463	23	28	is	be	AUX
ejpam-4463	23	29	an	an	DET
ejpam-4463	23	30	integer	integer	NOUN
ejpam-4463	23	31	.	.	PUNCT
ejpam-4463	24	1	when	when	SCONJ
ejpam-4463	24	2	α	α	NOUN
ejpam-4463	24	3	is	be	AUX
ejpam-4463	24	4	an	an	DET
ejpam-4463	24	5	s−number	s−number	NOUN
ejpam-4463	24	6	,	,	PUNCT
ejpam-4463	24	7	the	the	DET
ejpam-4463	24	8	nth	nth	NOUN
ejpam-4463	24	9	powers	power	NOUN
ejpam-4463	24	10	of	of	ADP
ejpam-4463	24	11	the	the	DET
ejpam-4463	24	12	conjugates	conjugate	NOUN
ejpam-4463	24	13	of	of	ADP
ejpam-4463	24	14	α	α	PROPN
ejpam-4463	24	15	tends	tend	VERB
ejpam-4463	24	16	to	to	ADP
ejpam-4463	24	17	0	0	NUM
ejpam-4463	24	18	as	as	SCONJ
ejpam-4463	24	19	n	n	PRON
ejpam-4463	24	20	tends	tend	VERB
ejpam-4463	24	21	to	to	ADP
ejpam-4463	24	22	∞	∞	NUM
ejpam-4463	24	23	,	,	PUNCT
ejpam-4463	24	24	because	because	SCONJ
ejpam-4463	24	25	they	they	PRON
ejpam-4463	24	26	all	all	PRON
ejpam-4463	24	27	have	have	VERB
ejpam-4463	24	28	modulus	modulus	NOUN
ejpam-4463	24	29	strictly	strictly	ADV
ejpam-4463	24	30	less	less	ADJ
ejpam-4463	24	31	than	than	ADP
ejpam-4463	24	32	1	1	NUM
ejpam-4463	24	33	.	.	PUNCT
ejpam-4463	25	1	this	this	DET
ejpam-4463	25	2	fundamental	fundamental	ADJ
ejpam-4463	25	3	property	property	NOUN
ejpam-4463	25	4	of	of	ADP
ejpam-4463	25	5	s	s	NOUN
ejpam-4463	25	6	-	-	PUNCT
ejpam-4463	25	7	numbers	number	NOUN
ejpam-4463	25	8	raises	raise	VERB
ejpam-4463	25	9	the	the	DET
ejpam-4463	25	10	following	follow	VERB
ejpam-4463	25	11	significant	significant	ADJ
ejpam-4463	25	12	unanswered	unanswered	ADJ
ejpam-4463	25	13	question	question	NOUN
ejpam-4463	25	14	about	about	ADP
ejpam-4463	25	15	the	the	DET
ejpam-4463	25	16	characterization	characterization	NOUN
ejpam-4463	25	17	of	of	ADP
ejpam-4463	25	18	the	the	DET
ejpam-4463	25	19	set	set	NOUN
ejpam-4463	25	20	s.	s.	PROPN
ejpam-4463	25	21	asuume	asuume	PROPN
ejpam-4463	25	22	α	α	PROPN
ejpam-4463	25	23	>	>	X
ejpam-4463	25	24	1	1	NUM
ejpam-4463	25	25	is	be	AUX
ejpam-4463	25	26	a	a	DET
ejpam-4463	25	27	real	real	ADJ
ejpam-4463	25	28	number	number	NOUN
ejpam-4463	25	29	with	with	ADP
ejpam-4463	25	30	αn	αn	NOUN
ejpam-4463	25	31	→	→	SYM
ejpam-4463	25	32	0	0	NUM
ejpam-4463	25	33	(	(	PUNCT
ejpam-4463	25	34	mod	mod	NOUN
ejpam-4463	25	35	1	1	NUM
ejpam-4463	25	36	)	)	PUNCT
ejpam-4463	25	37	as	as	ADP
ejpam-4463	25	38	n	n	PROPN
ejpam-4463	25	39	→	→	SYM
ejpam-4463	25	40	∞.	∞.	PROPN
ejpam-4463	25	41	can	can	AUX
ejpam-4463	25	42	we	we	PRON
ejpam-4463	25	43	then	then	ADV
ejpam-4463	25	44	conclude	conclude	VERB
ejpam-4463	25	45	,	,	PUNCT
ejpam-4463	25	46	under	under	ADP
ejpam-4463	25	47	no	no	DET
ejpam-4463	25	48	other	other	ADJ
ejpam-4463	25	49	assumptions	assumption	NOUN
ejpam-4463	25	50	,	,	PUNCT
ejpam-4463	25	51	that	that	SCONJ
ejpam-4463	25	52	θ	θ	PROPN
ejpam-4463	25	53	is	be	AUX
ejpam-4463	25	54	an	an	DET
ejpam-4463	25	55	algebraic	algebraic	ADJ
ejpam-4463	25	56	integer	integer	NOUN
ejpam-4463	25	57	in	in	ADP
ejpam-4463	25	58	the	the	DET
ejpam-4463	25	59	set	set	NOUN
ejpam-4463	25	60	s	s	PART
ejpam-4463	25	61	?	?	PUNCT
ejpam-4463	26	1	this	this	PRON
ejpam-4463	26	2	is	be	AUX
ejpam-4463	26	3	possibly	possibly	ADV
ejpam-4463	26	4	one	one	NUM
ejpam-4463	26	5	of	of	ADP
ejpam-4463	26	6	the	the	DET
ejpam-4463	26	7	oldest	old	ADJ
ejpam-4463	26	8	unsolved	unsolved	ADJ
ejpam-4463	26	9	problems	problem	NOUN
ejpam-4463	26	10	involving	involve	VERB
ejpam-4463	26	11	s	s	NOUN
ejpam-4463	26	12	-	-	NOUN
ejpam-4463	26	13	numbers	number	NOUN
ejpam-4463	26	14	,	,	PUNCT
ejpam-4463	26	15	as	as	SCONJ
ejpam-4463	26	16	it	it	PRON
ejpam-4463	26	17	appears	appear	VERB
ejpam-4463	26	18	in	in	ADP
ejpam-4463	26	19	[	[	X
ejpam-4463	26	20	12	12	NUM
ejpam-4463	26	21	]	]	PUNCT
ejpam-4463	26	22	.	.	PUNCT
ejpam-4463	27	1	the	the	DET
ejpam-4463	27	2	sets	set	NOUN
ejpam-4463	27	3	s	s	PART
ejpam-4463	27	4	and	and	CCONJ
ejpam-4463	27	5	t	t	PROPN
ejpam-4463	27	6	have	have	AUX
ejpam-4463	27	7	been	be	AUX
ejpam-4463	27	8	widely	widely	ADV
ejpam-4463	27	9	investigated	investigate	VERB
ejpam-4463	27	10	,	,	PUNCT
ejpam-4463	27	11	and	and	CCONJ
ejpam-4463	27	12	a	a	DET
ejpam-4463	27	13	large	large	ADJ
ejpam-4463	27	14	number	number	NOUN
ejpam-4463	27	15	of	of	ADP
ejpam-4463	27	16	results	result	NOUN
ejpam-4463	27	17	are	be	AUX
ejpam-4463	27	18	known	know	VERB
ejpam-4463	27	19	about	about	ADP
ejpam-4463	27	20	them	they	PRON
ejpam-4463	27	21	.	.	PUNCT
ejpam-4463	28	1	here	here	ADV
ejpam-4463	28	2	are	be	AUX
ejpam-4463	28	3	a	a	DET
ejpam-4463	28	4	handful	handful	NOUN
ejpam-4463	28	5	of	of	ADP
ejpam-4463	28	6	the	the	DET
ejpam-4463	28	7	more	more	ADV
ejpam-4463	28	8	notable	notable	ADJ
ejpam-4463	28	9	results	result	NOUN
ejpam-4463	28	10	.	.	PUNCT
ejpam-4463	29	1	because	because	SCONJ
ejpam-4463	29	2	they	they	PRON
ejpam-4463	29	3	exclusively	exclusively	ADV
ejpam-4463	29	4	include	include	VERB
ejpam-4463	29	5	algebraic	algebraic	ADJ
ejpam-4463	29	6	numbers	number	NOUN
ejpam-4463	29	7	,	,	PUNCT
ejpam-4463	29	8	both	both	DET
ejpam-4463	29	9	s	s	NOUN
ejpam-4463	29	10	and	and	CCONJ
ejpam-4463	29	11	t	t	PROPN
ejpam-4463	29	12	are	be	AUX
ejpam-4463	29	13	clearly	clearly	ADV
ejpam-4463	29	14	countable	countable	ADJ
ejpam-4463	29	15	sets	set	NOUN
ejpam-4463	29	16	.	.	PUNCT
ejpam-4463	30	1	furthermore	furthermore	ADV
ejpam-4463	30	2	,	,	PUNCT
ejpam-4463	30	3	s	s	NOUN
ejpam-4463	30	4	contains	contain	VERB
ejpam-4463	30	5	infinitely	infinitely	ADV
ejpam-4463	30	6	many	many	ADJ
ejpam-4463	30	7	limit	limit	NOUN
ejpam-4463	30	8	points	point	NOUN
ejpam-4463	30	9	,	,	PUNCT
ejpam-4463	30	10	because	because	SCONJ
ejpam-4463	30	11	it	it	PRON
ejpam-4463	30	12	is	be	AUX
ejpam-4463	30	13	possible	possible	ADJ
ejpam-4463	30	14	to	to	PART
ejpam-4463	30	15	consider	consider	VERB
ejpam-4463	30	16	each	each	DET
ejpam-4463	30	17	integer	integer	NOUN
ejpam-4463	30	18	a	a	DET
ejpam-4463	30	19	≥	≥	NOUN
ejpam-4463	30	20	2	2	NUM
ejpam-4463	30	21	as	as	ADP
ejpam-4463	30	22	a	a	DET
ejpam-4463	30	23	limit	limit	NOUN
ejpam-4463	30	24	of	of	ADP
ejpam-4463	30	25	a	a	DET
ejpam-4463	30	26	sequence	sequence	NOUN
ejpam-4463	30	27	of	of	ADP
ejpam-4463	30	28	elements	element	NOUN
ejpam-4463	30	29	in	in	ADP
ejpam-4463	30	30	s.	s.	PROPN
ejpam-4463	30	31	then	then	ADV
ejpam-4463	30	32	,	,	PUNCT
ejpam-4463	30	33	s	s	PROPN
ejpam-4463	30	34	contains	contain	VERB
ejpam-4463	30	35	an	an	DET
ejpam-4463	30	36	infinity	infinity	NOUN
ejpam-4463	30	37	of	of	ADP
ejpam-4463	30	38	limit	limit	NOUN
ejpam-4463	30	39	points	point	NOUN
ejpam-4463	30	40	.	.	PUNCT
ejpam-4463	31	1	the	the	DET
ejpam-4463	31	2	derived	derive	VERB
ejpam-4463	31	3	set	set	NOUN
ejpam-4463	31	4	of	of	ADP
ejpam-4463	31	5	s	s	PRON
ejpam-4463	31	6	is	be	AUX
ejpam-4463	31	7	denoted	denote	VERB
ejpam-4463	31	8	by	by	ADP
ejpam-4463	31	9	s′	s′	NOUN
ejpam-4463	31	10	and	and	CCONJ
ejpam-4463	31	11	contains	contain	VERB
ejpam-4463	31	12	all	all	PRON
ejpam-4463	31	13	of	of	ADP
ejpam-4463	31	14	s	s	NOUN
ejpam-4463	31	15	’s	’s	PART
ejpam-4463	31	16	limits	limit	NOUN
ejpam-4463	31	17	points	point	NOUN
ejpam-4463	31	18	.	.	PUNCT
ejpam-4463	32	1	equally	equally	ADV
ejpam-4463	32	2	,	,	PUNCT
ejpam-4463	32	3	the	the	DET
ejpam-4463	32	4	derived	derived	ADJ
ejpam-4463	32	5	set	set	NOUN
ejpam-4463	32	6	of	of	ADP
ejpam-4463	32	7	t	t	PROPN
ejpam-4463	32	8	,	,	PUNCT
ejpam-4463	32	9	is	be	AUX
ejpam-4463	32	10	the	the	DET
ejpam-4463	32	11	set	set	NOUN
ejpam-4463	32	12	of	of	ADP
ejpam-4463	32	13	all	all	DET
ejpam-4463	32	14	t	t	PROPN
ejpam-4463	32	15	limits	limit	NOUN
ejpam-4463	32	16	points	point	NOUN
ejpam-4463	32	17	,	,	PUNCT
ejpam-4463	32	18	and	and	CCONJ
ejpam-4463	32	19	it	it	PRON
ejpam-4463	32	20	is	be	AUX
ejpam-4463	32	21	denoted	denote	VERB
ejpam-4463	32	22	by	by	ADP
ejpam-4463	32	23	t	t	PROPN
ejpam-4463	32	24	′.	′.	NOUN
ejpam-4463	32	25	while	while	SCONJ
ejpam-4463	32	26	the	the	DET
ejpam-4463	32	27	product	product	NOUN
ejpam-4463	32	28	of	of	ADP
ejpam-4463	32	29	two	two	NUM
ejpam-4463	32	30	algebraic	algebraic	ADJ
ejpam-4463	32	31	integers	integer	NOUN
ejpam-4463	32	32	is	be	AUX
ejpam-4463	32	33	also	also	ADV
ejpam-4463	32	34	an	an	DET
ejpam-4463	32	35	algebraic	algebraic	ADJ
ejpam-4463	32	36	integer	integer	NOUN
ejpam-4463	32	37	,	,	PUNCT
ejpam-4463	32	38	pisot	pisot	ADJ
ejpam-4463	32	39	numbers	number	NOUN
ejpam-4463	32	40	are	be	AUX
ejpam-4463	32	41	not	not	PART
ejpam-4463	32	42	.	.	PUNCT
ejpam-4463	33	1	for	for	ADP
ejpam-4463	33	2	instance	instance	NOUN
ejpam-4463	33	3	,	,	PUNCT
ejpam-4463	33	4	we	we	PRON
ejpam-4463	33	5	have	have	AUX
ejpam-4463	33	6	just	just	ADV
ejpam-4463	33	7	shown	show	VERB
ejpam-4463	33	8	,	,	PUNCT
ejpam-4463	33	9	that	that	SCONJ
ejpam-4463	33	10	both	both	DET
ejpam-4463	33	11	2	2	NUM
ejpam-4463	33	12	and	and	CCONJ
ejpam-4463	33	13	1	1	NUM
ejpam-4463	33	14	+	+	CCONJ
ejpam-4463	33	15	√	√	NUM
ejpam-4463	33	16	5	5	NUM
ejpam-4463	33	17	2	2	NUM
ejpam-4463	33	18	are	be	AUX
ejpam-4463	33	19	pisot	pisot	ADJ
ejpam-4463	33	20	;	;	PUNCT
ejpam-4463	33	21	however	however	ADV
ejpam-4463	33	22	,	,	PUNCT
ejpam-4463	33	23	their	their	PRON
ejpam-4463	33	24	product	product	NOUN
ejpam-4463	33	25	1	1	NUM
ejpam-4463	33	26	+	+	CCONJ
ejpam-4463	33	27	√	√	NUM
ejpam-4463	33	28	5	5	NUM
ejpam-4463	33	29	with	with	ADP
ejpam-4463	33	30	conjugate	conjugate	ADJ
ejpam-4463	33	31	equals	equal	VERB
ejpam-4463	33	32	to	to	ADP
ejpam-4463	33	33	1−	1−	NUM
ejpam-4463	33	34	√	√	NUM
ejpam-4463	33	35	5	5	NUM
ejpam-4463	33	36	clearly	clearly	ADV
ejpam-4463	33	37	is	be	AUX
ejpam-4463	33	38	not	not	PART
ejpam-4463	33	39	a	a	DET
ejpam-4463	33	40	pisot	pisot	ADJ
ejpam-4463	33	41	number	number	NOUN
ejpam-4463	33	42	.	.	PUNCT
ejpam-4463	34	1	if	if	SCONJ
ejpam-4463	34	2	the	the	DET
ejpam-4463	34	3	two	two	NUM
ejpam-4463	34	4	pisot	pisot	ADJ
ejpam-4463	34	5	numbers	number	NOUN
ejpam-4463	34	6	are	be	AUX
ejpam-4463	34	7	equal	equal	ADJ
ejpam-4463	34	8	,	,	PUNCT
ejpam-4463	34	9	their	their	PRON
ejpam-4463	34	10	product	product	NOUN
ejpam-4463	34	11	is	be	AUX
ejpam-4463	34	12	a	a	DET
ejpam-4463	34	13	pisot	pisot	ADJ
ejpam-4463	34	14	number	number	NOUN
ejpam-4463	34	15	as	as	ADV
ejpam-4463	34	16	well	well	ADV
ejpam-4463	34	17	.	.	PUNCT
ejpam-4463	35	1	the	the	DET
ejpam-4463	35	2	sets	set	NOUN
ejpam-4463	35	3	s	s	PART
ejpam-4463	35	4	and	and	CCONJ
ejpam-4463	35	5	t	t	PROPN
ejpam-4463	35	6	are	be	AUX
ejpam-4463	35	7	tightly	tightly	ADV
ejpam-4463	35	8	connected	connect	VERB
ejpam-4463	35	9	and	and	CCONJ
ejpam-4463	35	10	contain	contain	VERB
ejpam-4463	35	11	fascinating	fascinating	ADJ
ejpam-4463	35	12	linkages	linkage	NOUN
ejpam-4463	35	13	,	,	PUNCT
ejpam-4463	35	14	as	as	SCONJ
ejpam-4463	35	15	one	one	PRON
ejpam-4463	35	16	might	might	AUX
ejpam-4463	35	17	expect	expect	VERB
ejpam-4463	35	18	given	give	VERB
ejpam-4463	35	19	their	their	PRON
ejpam-4463	35	20	comparable	comparable	ADJ
ejpam-4463	35	21	definitions	definition	NOUN
ejpam-4463	35	22	.	.	PUNCT
ejpam-4463	36	1	in	in	ADP
ejpam-4463	36	2	[	[	X
ejpam-4463	36	3	10	10	NUM
ejpam-4463	36	4	]	]	PUNCT
ejpam-4463	36	5	it	it	PRON
ejpam-4463	36	6	was	be	AUX
ejpam-4463	36	7	proved	prove	VERB
ejpam-4463	36	8	,	,	PUNCT
ejpam-4463	36	9	by	by	ADP
ejpam-4463	36	10	salem	salem	NOUN
ejpam-4463	36	11	,	,	PUNCT
ejpam-4463	36	12	that	that	SCONJ
ejpam-4463	36	13	s′	s′	VERB
ejpam-4463	36	14	⊂	⊂	ADJ
ejpam-4463	36	15	s	s	X
ejpam-4463	36	16	is	be	AUX
ejpam-4463	36	17	closed	closed	ADJ
ejpam-4463	36	18	.	.	PUNCT
ejpam-4463	37	1	so	so	ADV
ejpam-4463	37	2	,	,	PUNCT
ejpam-4463	37	3	it	it	PRON
ejpam-4463	37	4	must	must	AUX
ejpam-4463	37	5	have	have	VERB
ejpam-4463	37	6	a	a	DET
ejpam-4463	37	7	smallest	small	ADJ
ejpam-4463	37	8	element	element	NOUN
ejpam-4463	37	9	because	because	SCONJ
ejpam-4463	37	10	it	it	PRON
ejpam-4463	37	11	is	be	AUX
ejpam-4463	37	12	bounded	bound	VERB
ejpam-4463	37	13	below	below	ADV
ejpam-4463	37	14	.	.	PUNCT
ejpam-4463	38	1	according	accord	VERB
ejpam-4463	38	2	to	to	ADP
ejpam-4463	38	3	siegel	siegel	PROPN
ejpam-4463	38	4	[	[	X
ejpam-4463	38	5	14	14	NUM
ejpam-4463	38	6	]	]	PUNCT
ejpam-4463	38	7	,	,	PUNCT
ejpam-4463	38	8	the	the	DET
ejpam-4463	38	9	smallest	smallest	ADV
ejpam-4463	38	10	known	know	VERB
ejpam-4463	38	11	pisot	pisot	ADJ
ejpam-4463	38	12	number	number	NOUN
ejpam-4463	38	13	is	be	AUX
ejpam-4463	38	14	equal	equal	ADJ
ejpam-4463	38	15	to	to	ADP
ejpam-4463	38	16	the	the	DET
ejpam-4463	38	17	largest	large	ADJ
ejpam-4463	38	18	root	root	NOUN
ejpam-4463	38	19	of	of	ADP
ejpam-4463	38	20	x3	x3	NOUN
ejpam-4463	38	21	=	=	PUNCT
ejpam-4463	38	22	x	x	SYM
ejpam-4463	39	1	+	+	NUM
ejpam-4463	39	2	1	1	NUM
ejpam-4463	39	3	,	,	PUNCT
ejpam-4463	39	4	which	which	PRON
ejpam-4463	39	5	is	be	AUX
ejpam-4463	39	6	around	around	ADP
ejpam-4463	39	7	1.3247179	1.3247179	NUM
ejpam-4463	39	8	.	.	PUNCT
ejpam-4463	40	1	the	the	DET
ejpam-4463	40	2	smallest	small	ADJ
ejpam-4463	40	3	pisot	pisot	ADJ
ejpam-4463	40	4	number	number	NOUN
ejpam-4463	40	5	of	of	ADP
ejpam-4463	40	6	degree	degree	NOUN
ejpam-4463	40	7	n	n	PRON
ejpam-4463	40	8	≥	≥	NOUN
ejpam-4463	40	9	3	3	NUM
ejpam-4463	40	10	was	be	AUX
ejpam-4463	40	11	identified	identify	VERB
ejpam-4463	40	12	by	by	ADP
ejpam-4463	40	13	dufresnoy	dufresnoy	ADJ
ejpam-4463	40	14	and	and	CCONJ
ejpam-4463	40	15	pisot	pisot	ADJ
ejpam-4463	40	16	[	[	X
ejpam-4463	40	17	5	5	NUM
ejpam-4463	40	18	]	]	PUNCT
ejpam-4463	40	19	.	.	PUNCT
ejpam-4463	41	1	they	they	PRON
ejpam-4463	41	2	arrived	arrive	VERB
ejpam-4463	41	3	to	to	ADP
ejpam-4463	41	4	the	the	DET
ejpam-4463	41	5	following	follow	VERB
ejpam-4463	41	6	theorem	theorem	NOUN
ejpam-4463	41	7	:	:	PUNCT
ejpam-4463	41	8	theorem	theorem	NOUN
ejpam-4463	41	9	1	1	X
ejpam-4463	41	10	.	.	PUNCT
ejpam-4463	42	1	let	let	VERB
ejpam-4463	42	2	an	an	DET
ejpam-4463	42	3	be	be	AUX
ejpam-4463	42	4	the	the	DET
ejpam-4463	42	5	smallest	small	ADJ
ejpam-4463	42	6	pisot	pisot	ADJ
ejpam-4463	42	7	number	number	NOUN
ejpam-4463	42	8	of	of	ADP
ejpam-4463	42	9	degree	degree	NOUN
ejpam-4463	42	10	n	n	PRON
ejpam-4463	42	11	≥	≥	NOUN
ejpam-4463	42	12	3	3	NUM
ejpam-4463	42	13	,	,	PUNCT
ejpam-4463	42	14	then	then	ADV
ejpam-4463	42	15	the	the	DET
ejpam-4463	42	16	following	follow	VERB
ejpam-4463	42	17	assertions	assertion	NOUN
ejpam-4463	42	18	holds	hold	VERB
ejpam-4463	42	19	i	i	PRON
ejpam-4463	42	20	)	)	PUNCT
ejpam-4463	42	21	pn(z	pn(z	PUNCT
ejpam-4463	42	22	)	)	PUNCT
ejpam-4463	43	1	=	=	SYM
ejpam-4463	43	2	zn	zn	X
ejpam-4463	43	3	−	−	PROPN
ejpam-4463	44	1	zn−1	zn−1	PROPN
ejpam-4463	44	2	−	−	PROPN
ejpam-4463	45	1	zn−2	zn−2	PROPN
ejpam-4463	45	2	+	+	PROPN
ejpam-4463	45	3	z2	z2	NOUN
ejpam-4463	45	4	−	−	NOUN
ejpam-4463	45	5	1	1	NUM
ejpam-4463	45	6	is	be	AUX
ejpam-4463	45	7	the	the	DET
ejpam-4463	45	8	minimal	minimal	ADJ
ejpam-4463	45	9	polynomial	polynomial	NOUN
ejpam-4463	45	10	of	of	ADP
ejpam-4463	45	11	an	an	DET
ejpam-4463	45	12	ii	ii	NOUN
ejpam-4463	45	13	)	)	PUNCT
ejpam-4463	45	14	the	the	DET
ejpam-4463	45	15	sequence	sequence	NOUN
ejpam-4463	45	16	(	(	PUNCT
ejpam-4463	45	17	an)n≥1	an)n≥1	NOUN
ejpam-4463	45	18	is	be	AUX
ejpam-4463	45	19	increasing	increase	VERB
ejpam-4463	45	20	and	and	CCONJ
ejpam-4463	45	21	eventually	eventually	ADV
ejpam-4463	45	22	converges	converge	VERB
ejpam-4463	45	23	to	to	ADP
ejpam-4463	45	24	1	1	NUM
ejpam-4463	45	25	+	+	CCONJ
ejpam-4463	45	26	√	√	NUM
ejpam-4463	45	27	5	5	NUM
ejpam-4463	45	28	2	2	NUM
ejpam-4463	45	29	≈	≈	PROPN
ejpam-4463	45	30	1.61803	1.61803	NUM
ejpam-4463	45	31	,	,	PUNCT
ejpam-4463	45	32	a	a	DET
ejpam-4463	45	33	o.	o.	PROPN
ejpam-4463	45	34	dammak	dammak	PROPN
ejpam-4463	45	35	,	,	PUNCT
ejpam-4463	45	36	s.	s.	PROPN
ejpam-4463	45	37	mansour	mansour	PROPN
ejpam-4463	45	38	/	/	SYM
ejpam-4463	45	39	eur	eur	PROPN
ejpam-4463	45	40	.	.	PUNCT
ejpam-4463	46	1	j.	j.	PROPN
ejpam-4463	46	2	pure	pure	PROPN
ejpam-4463	46	3	appl	appl	PROPN
ejpam-4463	46	4	.	.	PROPN
ejpam-4463	46	5	math	math	PROPN
ejpam-4463	46	6	,	,	PUNCT
ejpam-4463	46	7	15	15	NUM
ejpam-4463	46	8	(	(	PUNCT
ejpam-4463	46	9	3	3	NUM
ejpam-4463	46	10	)	)	PUNCT
ejpam-4463	46	11	(	(	PUNCT
ejpam-4463	46	12	2022	2022	NUM
ejpam-4463	46	13	)	)	PUNCT
ejpam-4463	46	14	,	,	PUNCT
ejpam-4463	46	15	1321	1321	NUM
ejpam-4463	46	16	-	-	SYM
ejpam-4463	46	17	1330	1330	NUM
ejpam-4463	46	18	1323	1323	NUM
ejpam-4463	46	19	root	root	NOUN
ejpam-4463	46	20	of	of	ADP
ejpam-4463	46	21	x2	x2	PROPN
ejpam-4463	46	22	=	=	PUNCT
ejpam-4463	46	23	x+	x+	PROPN
ejpam-4463	47	1	1	1	X
ejpam-4463	47	2	.	.	X
ejpam-4463	48	1	it	it	PRON
ejpam-4463	48	2	’s	’	VERB
ejpam-4463	48	3	worth	worth	ADJ
ejpam-4463	48	4	noting	note	VERB
ejpam-4463	48	5	that	that	SCONJ
ejpam-4463	48	6	similar	similar	ADJ
ejpam-4463	48	7	claims	claim	NOUN
ejpam-4463	48	8	concerning	concern	VERB
ejpam-4463	48	9	the	the	DET
ejpam-4463	48	10	set	set	NOUN
ejpam-4463	48	11	t	t	NOUN
ejpam-4463	48	12	have	have	VERB
ejpam-4463	48	13	yet	yet	ADV
ejpam-4463	48	14	to	to	PART
ejpam-4463	48	15	be	be	AUX
ejpam-4463	48	16	discovered	discover	VERB
ejpam-4463	48	17	.	.	PUNCT
ejpam-4463	49	1	there	there	PRON
ejpam-4463	49	2	are	be	VERB
ejpam-4463	49	3	,	,	PUNCT
ejpam-4463	49	4	indeed	indeed	ADV
ejpam-4463	49	5	,	,	PUNCT
ejpam-4463	49	6	two	two	NUM
ejpam-4463	49	7	of	of	ADP
ejpam-4463	49	8	the	the	DET
ejpam-4463	49	9	most	most	ADV
ejpam-4463	49	10	well	well	ADV
ejpam-4463	49	11	-	-	PUNCT
ejpam-4463	49	12	known	know	VERB
ejpam-4463	49	13	unanswered	unanswered	ADJ
ejpam-4463	49	14	questions	question	NOUN
ejpam-4463	49	15	about	about	ADP
ejpam-4463	49	16	s	s	PRON
ejpam-4463	49	17	and	and	CCONJ
ejpam-4463	49	18	t	t	NOUN
ejpam-4463	49	19	numbers	number	NOUN
ejpam-4463	49	20	.	.	PUNCT
ejpam-4463	50	1	the	the	DET
ejpam-4463	50	2	first	first	ADJ
ejpam-4463	50	3	question	question	NOUN
ejpam-4463	50	4	concerns	concern	NOUN
ejpam-4463	50	5	t	t	PROPN
ejpam-4463	50	6	’s	’s	PART
ejpam-4463	50	7	limit	limit	NOUN
ejpam-4463	50	8	point	point	NOUN
ejpam-4463	50	9	.	.	PUNCT
ejpam-4463	51	1	the	the	DET
ejpam-4463	51	2	set	set	NOUN
ejpam-4463	51	3	s	s	PART
ejpam-4463	51	4	is	be	AUX
ejpam-4463	51	5	known	know	VERB
ejpam-4463	51	6	to	to	PART
ejpam-4463	51	7	be	be	AUX
ejpam-4463	51	8	contained	contain	VERB
ejpam-4463	51	9	in	in	ADP
ejpam-4463	51	10	t	t	PROPN
ejpam-4463	51	11	′	′	NUM
ejpam-4463	51	12	,	,	PUNCT
ejpam-4463	51	13	or	or	CCONJ
ejpam-4463	51	14	,	,	PUNCT
ejpam-4463	51	15	to	to	PART
ejpam-4463	51	16	put	put	VERB
ejpam-4463	51	17	it	it	PRON
ejpam-4463	51	18	another	another	DET
ejpam-4463	51	19	way	way	NOUN
ejpam-4463	51	20	,	,	PUNCT
ejpam-4463	51	21	any	any	DET
ejpam-4463	51	22	point	point	NOUN
ejpam-4463	51	23	of	of	ADP
ejpam-4463	51	24	s	s	NOUN
ejpam-4463	51	25	is	be	AUX
ejpam-4463	51	26	a	a	DET
ejpam-4463	51	27	limit	limit	NOUN
ejpam-4463	51	28	point	point	NOUN
ejpam-4463	51	29	of	of	ADP
ejpam-4463	51	30	t	t	PROPN
ejpam-4463	51	31	,	,	PUNCT
ejpam-4463	51	32	on	on	ADP
ejpam-4463	51	33	both	both	DET
ejpam-4463	51	34	sides	side	NOUN
ejpam-4463	51	35	.	.	PUNCT
ejpam-4463	52	1	salem	salem	PROPN
ejpam-4463	52	2	[	[	X
ejpam-4463	52	3	11	11	NUM
ejpam-4463	52	4	]	]	PUNCT
ejpam-4463	52	5	was	be	AUX
ejpam-4463	52	6	the	the	DET
ejpam-4463	52	7	first	first	ADJ
ejpam-4463	52	8	to	to	PART
ejpam-4463	52	9	demonstrate	demonstrate	VERB
ejpam-4463	52	10	this	this	DET
ejpam-4463	52	11	astounding	astounding	ADJ
ejpam-4463	52	12	fact	fact	NOUN
ejpam-4463	52	13	by	by	ADP
ejpam-4463	52	14	creating	create	VERB
ejpam-4463	52	15	polynomial	polynomial	ADJ
ejpam-4463	52	16	sequences	sequence	NOUN
ejpam-4463	52	17	that	that	PRON
ejpam-4463	52	18	provided	provide	VERB
ejpam-4463	52	19	the	the	DET
ejpam-4463	52	20	needed	need	VERB
ejpam-4463	52	21	t−numbers	t−number	NOUN
ejpam-4463	52	22	.	.	PUNCT
ejpam-4463	53	1	although	although	SCONJ
ejpam-4463	53	2	it	it	PRON
ejpam-4463	53	3	is	be	AUX
ejpam-4463	53	4	known	know	VERB
ejpam-4463	53	5	that	that	SCONJ
ejpam-4463	53	6	s	s	VERB
ejpam-4463	53	7	⊆	⊆	NUM
ejpam-4463	53	8	t	t	NOUN
ejpam-4463	53	9	′	′	NOUN
ejpam-4463	53	10	,	,	PUNCT
ejpam-4463	53	11	there	there	PRON
ejpam-4463	53	12	’s	’	VERB
ejpam-4463	53	13	no	no	DET
ejpam-4463	53	14	way	way	NOUN
ejpam-4463	53	15	of	of	ADP
ejpam-4463	53	16	knowing	know	VERB
ejpam-4463	53	17	if	if	SCONJ
ejpam-4463	53	18	the	the	DET
ejpam-4463	53	19	set	set	NOUN
ejpam-4463	53	20	t	t	NOUN
ejpam-4463	53	21	has	have	VERB
ejpam-4463	53	22	any	any	DET
ejpam-4463	53	23	limit	limit	NOUN
ejpam-4463	53	24	points	point	NOUN
ejpam-4463	53	25	other	other	ADJ
ejpam-4463	53	26	than	than	ADP
ejpam-4463	53	27	the	the	DET
ejpam-4463	53	28	ones	one	NOUN
ejpam-4463	53	29	identified	identify	VERB
ejpam-4463	53	30	in	in	ADP
ejpam-4463	53	31	s	s	PROPN
ejpam-4463	53	32	;	;	PUNCT
ejpam-4463	53	33	this	this	PRON
ejpam-4463	53	34	is	be	AUX
ejpam-4463	53	35	an	an	DET
ejpam-4463	53	36	inquiry	inquiry	NOUN
ejpam-4463	53	37	that	that	PRON
ejpam-4463	53	38	is	be	AUX
ejpam-4463	53	39	addressed	address	VERB
ejpam-4463	53	40	in	in	ADP
ejpam-4463	53	41	[	[	X
ejpam-4463	53	42	12	12	NUM
ejpam-4463	53	43	]	]	PUNCT
ejpam-4463	53	44	,	,	PUNCT
ejpam-4463	53	45	but	but	CCONJ
ejpam-4463	53	46	it	it	PRON
ejpam-4463	53	47	is	be	AUX
ejpam-4463	53	48	yet	yet	ADV
ejpam-4463	53	49	unsolved	unsolved	ADJ
ejpam-4463	53	50	.	.	PUNCT
ejpam-4463	54	1	small	small	ADJ
ejpam-4463	54	2	t−numbers	t−number	NOUN
ejpam-4463	54	3	are	be	AUX
ejpam-4463	54	4	the	the	DET
ejpam-4463	54	5	subject	subject	NOUN
ejpam-4463	54	6	of	of	ADP
ejpam-4463	54	7	the	the	DET
ejpam-4463	54	8	second	second	ADJ
ejpam-4463	54	9	open	open	ADJ
ejpam-4463	54	10	question	question	NOUN
ejpam-4463	54	11	.	.	PUNCT
ejpam-4463	55	1	we	we	PRON
ejpam-4463	55	2	ca	can	AUX
ejpam-4463	55	3	n’t	not	PART
ejpam-4463	55	4	assume	assume	VERB
ejpam-4463	55	5	the	the	DET
ejpam-4463	55	6	existence	existence	NOUN
ejpam-4463	55	7	of	of	ADP
ejpam-4463	55	8	a	a	DET
ejpam-4463	55	9	lowest	low	ADJ
ejpam-4463	55	10	salem	salem	NOUN
ejpam-4463	55	11	number	number	NOUN
ejpam-4463	55	12	because	because	SCONJ
ejpam-4463	55	13	t	t	PROPN
ejpam-4463	55	14	is	be	AUX
ejpam-4463	55	15	n’t	not	PART
ejpam-4463	55	16	closed	closed	ADJ
ejpam-4463	55	17	.	.	PUNCT
ejpam-4463	56	1	while	while	SCONJ
ejpam-4463	56	2	we	we	PRON
ejpam-4463	56	3	ca	can	AUX
ejpam-4463	56	4	n’t	not	PART
ejpam-4463	56	5	assume	assume	VERB
ejpam-4463	56	6	that	that	SCONJ
ejpam-4463	56	7	t	t	PROPN
ejpam-4463	56	8	contains	contain	VERB
ejpam-4463	56	9	a	a	DET
ejpam-4463	56	10	smallest	small	ADJ
ejpam-4463	56	11	element	element	NOUN
ejpam-4463	56	12	,	,	PUNCT
ejpam-4463	56	13	there	there	PRON
ejpam-4463	56	14	is	be	VERB
ejpam-4463	56	15	a	a	DET
ejpam-4463	56	16	possibility	possibility	NOUN
ejpam-4463	56	17	.	.	PUNCT
ejpam-4463	57	1	it	it	PRON
ejpam-4463	57	2	is	be	AUX
ejpam-4463	57	3	conjectured	conjecture	VERB
ejpam-4463	57	4	that	that	SCONJ
ejpam-4463	57	5	1.1762808	1.1762808	NUM
ejpam-4463	57	6	...	...	PUNCT
ejpam-4463	57	7	,	,	PUNCT
ejpam-4463	57	8	a	a	DET
ejpam-4463	57	9	root	root	NOUN
ejpam-4463	57	10	of	of	ADP
ejpam-4463	57	11	the	the	DET
ejpam-4463	57	12	10th	10th	ADJ
ejpam-4463	57	13	degree	degree	NOUN
ejpam-4463	57	14	polynomial	polynomial	ADJ
ejpam-4463	57	15	x10	x10	PROPN
ejpam-4463	57	16	+	+	CCONJ
ejpam-4463	57	17	x9	x9	NOUN
ejpam-4463	57	18	−	−	ADP
ejpam-4463	57	19	x7	x7	NOUN
ejpam-4463	57	20	−	−	PROPN
ejpam-4463	57	21	x6	x6	NOUN
ejpam-4463	57	22	−	−	PROPN
ejpam-4463	57	23	x5	x5	PROPN
ejpam-4463	57	24	−	−	PROPN
ejpam-4463	57	25	x4	x4	PROPN
ejpam-4463	57	26	−	−	PROPN
ejpam-4463	57	27	x3	x3	PROPN
ejpam-4463	58	1	+	+	CCONJ
ejpam-4463	58	2	x+	x+	ADJ
ejpam-4463	58	3	1	1	NUM
ejpam-4463	58	4	,	,	PUNCT
ejpam-4463	58	5	discovered	discover	VERB
ejpam-4463	58	6	by	by	ADP
ejpam-4463	58	7	lehmer	lehmer	NOUN
ejpam-4463	58	8	[	[	X
ejpam-4463	58	9	7	7	NUM
ejpam-4463	58	10	]	]	PUNCT
ejpam-4463	58	11	in	in	ADP
ejpam-4463	58	12	1933	1933	NUM
ejpam-4463	58	13	,	,	PUNCT
ejpam-4463	58	14	is	be	AUX
ejpam-4463	58	15	the	the	DET
ejpam-4463	58	16	smallest	small	ADJ
ejpam-4463	58	17	salem	salem	NOUN
ejpam-4463	58	18	number	number	NOUN
ejpam-4463	58	19	.	.	PUNCT
ejpam-4463	59	1	there	there	PRON
ejpam-4463	59	2	has	have	AUX
ejpam-4463	59	3	n’t	not	PART
ejpam-4463	59	4	been	be	AUX
ejpam-4463	59	5	a	a	DET
ejpam-4463	59	6	smaller	small	ADJ
ejpam-4463	59	7	salem	salem	NOUN
ejpam-4463	59	8	number	number	NOUN
ejpam-4463	59	9	in	in	ADP
ejpam-4463	59	10	almost	almost	ADV
ejpam-4463	59	11	eighty	eighty	NUM
ejpam-4463	59	12	years	year	NOUN
ejpam-4463	59	13	.	.	PUNCT
ejpam-4463	60	1	all	all	DET
ejpam-4463	60	2	salem	salem	NOUN
ejpam-4463	60	3	numbers	number	NOUN
ejpam-4463	60	4	<	<	X
ejpam-4463	60	5	1.3	1.3	NUM
ejpam-4463	60	6	of	of	ADP
ejpam-4463	60	7	degree	degree	NOUN
ejpam-4463	60	8	20	20	NUM
ejpam-4463	60	9	over	over	ADP
ejpam-4463	60	10	[	[	X
ejpam-4463	60	11	3	3	NUM
ejpam-4463	60	12	]	]	PUNCT
ejpam-4463	60	13	,	,	PUNCT
ejpam-4463	60	14	are	be	AUX
ejpam-4463	60	15	included	include	VERB
ejpam-4463	60	16	in	in	ADP
ejpam-4463	60	17	the	the	DET
ejpam-4463	60	18	list	list	NOUN
ejpam-4463	60	19	of	of	ADP
ejpam-4463	60	20	39	39	NUM
ejpam-4463	60	21	salem	salem	NOUN
ejpam-4463	60	22	numbers	number	NOUN
ejpam-4463	60	23	given	give	VERB
ejpam-4463	60	24	in	in	ADP
ejpam-4463	60	25	[	[	X
ejpam-4463	60	26	2	2	NUM
ejpam-4463	60	27	]	]	PUNCT
ejpam-4463	60	28	;	;	PUNCT
ejpam-4463	60	29	it	it	PRON
ejpam-4463	60	30	will	will	AUX
ejpam-4463	60	31	enough	enough	ADJ
ejpam-4463	60	32	for	for	ADP
ejpam-4463	60	33	the	the	DET
ejpam-4463	60	34	applications	application	NOUN
ejpam-4463	60	35	below	below	ADV
ejpam-4463	60	36	.	.	PUNCT
ejpam-4463	61	1	there	there	PRON
ejpam-4463	61	2	are	be	VERB
ejpam-4463	61	3	currently	currently	ADV
ejpam-4463	61	4	around	around	ADP
ejpam-4463	61	5	47	47	NUM
ejpam-4463	61	6	salem	salem	NOUN
ejpam-4463	61	7	numbers	number	NOUN
ejpam-4463	61	8	<	<	X
ejpam-4463	61	9	1.3	1.3	NUM
ejpam-4463	61	10	are	be	AUX
ejpam-4463	61	11	known	know	VERB
ejpam-4463	61	12	and	and	CCONJ
ejpam-4463	61	13	the	the	DET
ejpam-4463	61	14	list	list	NOUN
ejpam-4463	61	15	is	be	AUX
ejpam-4463	61	16	believed	believe	VERB
ejpam-4463	61	17	to	to	PART
ejpam-4463	61	18	be	be	AUX
ejpam-4463	61	19	comprehensive	comprehensive	ADJ
ejpam-4463	61	20	up	up	ADP
ejpam-4463	61	21	to	to	PART
ejpam-4463	61	22	degree	degree	VERB
ejpam-4463	61	23	44	44	NUM
ejpam-4463	61	24	..	..	PUNCT
ejpam-4463	61	25	although	although	SCONJ
ejpam-4463	61	26	this	this	PRON
ejpam-4463	61	27	has	have	AUX
ejpam-4463	61	28	not	not	PART
ejpam-4463	61	29	been	be	AUX
ejpam-4463	61	30	proven	prove	VERB
ejpam-4463	61	31	,	,	PUNCT
ejpam-4463	61	32	it	it	PRON
ejpam-4463	61	33	is	be	AUX
ejpam-4463	61	34	widely	widely	ADV
ejpam-4463	61	35	assumed	assume	VERB
ejpam-4463	61	36	that	that	SCONJ
ejpam-4463	61	37	lehmer	lehmer	NOUN
ejpam-4463	61	38	’s	’s	PART
ejpam-4463	61	39	salem	salem	PROPN
ejpam-4463	61	40	number	number	NOUN
ejpam-4463	61	41	1.1762808	1.1762808	NUM
ejpam-4463	61	42	...	...	PUNCT
ejpam-4463	61	43	is	be	AUX
ejpam-4463	61	44	an	an	DET
ejpam-4463	61	45	isolated	isolated	ADJ
ejpam-4463	61	46	point	point	NOUN
ejpam-4463	61	47	of	of	ADP
ejpam-4463	61	48	t.	t.	NOUN
ejpam-4463	61	49	it	it	PRON
ejpam-4463	61	50	was	be	AUX
ejpam-4463	61	51	stated	state	VERB
ejpam-4463	61	52	and	and	CCONJ
ejpam-4463	61	53	proven	prove	VERB
ejpam-4463	61	54	some	some	DET
ejpam-4463	61	55	basic	basic	ADJ
ejpam-4463	61	56	results	result	NOUN
ejpam-4463	61	57	about	about	ADP
ejpam-4463	61	58	salem	salem	NOUN
ejpam-4463	61	59	numbers	number	NOUN
ejpam-4463	61	60	in	in	ADP
ejpam-4463	61	61	[	[	X
ejpam-4463	61	62	15	15	NUM
ejpam-4463	61	63	]	]	PUNCT
ejpam-4463	61	64	,	,	PUNCT
ejpam-4463	61	65	and	and	CCONJ
ejpam-4463	61	66	then	then	ADV
ejpam-4463	61	67	a	a	DET
ejpam-4463	61	68	survey	survey	NOUN
ejpam-4463	61	69	of	of	ADP
ejpam-4463	61	70	the	the	DET
ejpam-4463	61	71	literature	literature	NOUN
ejpam-4463	61	72	about	about	ADP
ejpam-4463	61	73	them	they	PRON
ejpam-4463	61	74	was	be	AUX
ejpam-4463	61	75	conducted	conduct	VERB
ejpam-4463	61	76	.	.	PUNCT
ejpam-4463	62	1	chris	chris	PROPN
ejpam-4463	62	2	smyth	smyth	PROPN
ejpam-4463	62	3	’s	’s	PART
ejpam-4463	62	4	intention	intention	NOUN
ejpam-4463	62	5	was	be	AUX
ejpam-4463	62	6	to	to	PART
ejpam-4463	62	7	supplement	supplement	VERB
ejpam-4463	62	8	rather	rather	ADV
ejpam-4463	62	9	than	than	ADP
ejpam-4463	62	10	duplicate	duplicate	VERB
ejpam-4463	62	11	other	other	ADJ
ejpam-4463	62	12	general	general	ADJ
ejpam-4463	62	13	treatises	treatise	NOUN
ejpam-4463	62	14	on	on	ADP
ejpam-4463	62	15	these	these	DET
ejpam-4463	62	16	numbers	number	NOUN
ejpam-4463	62	17	.	.	PUNCT
ejpam-4463	63	1	this	this	PRON
ejpam-4463	63	2	is	be	AUX
ejpam-4463	63	3	especially	especially	ADV
ejpam-4463	63	4	true	true	ADJ
ejpam-4463	63	5	of	of	ADP
ejpam-4463	63	6	bertin	bertin	PROPN
ejpam-4463	63	7	and	and	CCONJ
ejpam-4463	63	8	her	her	PRON
ejpam-4463	63	9	coauthors	coauthor	NOUN
ejpam-4463	63	10	’	'	PUNCT
ejpam-4463	63	11	work	work	NOUN
ejpam-4463	63	12	[	[	X
ejpam-4463	63	13	1	1	NUM
ejpam-4463	63	14	]	]	PUNCT
ejpam-4463	63	15	,	,	PUNCT
ejpam-4463	63	16	as	as	ADV
ejpam-4463	63	17	well	well	ADV
ejpam-4463	63	18	as	as	ADP
ejpam-4463	63	19	ghate	ghate	NOUN
ejpam-4463	63	20	and	and	CCONJ
ejpam-4463	63	21	hironaka	hironaka	PROPN
ejpam-4463	63	22	’s	’s	PART
ejpam-4463	63	23	applicationrich	applicationrich	PROPN
ejpam-4463	63	24	salem	salem	NOUN
ejpam-4463	63	25	number	number	NOUN
ejpam-4463	63	26	survey	survey	NOUN
ejpam-4463	63	27	[	[	X
ejpam-4463	63	28	6	6	NUM
ejpam-4463	63	29	]	]	PUNCT
ejpam-4463	63	30	.	.	PUNCT
ejpam-4463	64	1	he	he	PRON
ejpam-4463	64	2	did	do	AUX
ejpam-4463	64	3	,	,	PUNCT
ejpam-4463	64	4	however	however	ADV
ejpam-4463	64	5	,	,	PUNCT
ejpam-4463	64	6	cite	cite	VERB
ejpam-4463	64	7	some	some	DET
ejpam-4463	64	8	findings	finding	NOUN
ejpam-4463	64	9	from	from	ADP
ejpam-4463	64	10	salem	salem	PROPN
ejpam-4463	64	11	’s	’s	PART
ejpam-4463	64	12	classic	classic	ADJ
ejpam-4463	64	13	monograph	monograph	NOUN
ejpam-4463	65	1	[	[	X
ejpam-4463	65	2	13	13	NUM
ejpam-4463	65	3	]	]	PUNCT
ejpam-4463	65	4	.	.	PUNCT
ejpam-4463	66	1	moreover	moreover	ADV
ejpam-4463	66	2	,	,	PUNCT
ejpam-4463	66	3	the	the	DET
ejpam-4463	66	4	concept	concept	NOUN
ejpam-4463	66	5	of	of	ADP
ejpam-4463	66	6	the	the	DET
ejpam-4463	66	7	mahler	mahler	PROPN
ejpam-4463	66	8	measure	measure	NOUN
ejpam-4463	66	9	of	of	ADP
ejpam-4463	66	10	a	a	DET
ejpam-4463	66	11	matrix	matrix	NOUN
ejpam-4463	66	12	arose	arise	VERB
ejpam-4463	66	13	from	from	ADP
ejpam-4463	66	14	the	the	DET
ejpam-4463	66	15	investigation	investigation	NOUN
ejpam-4463	66	16	of	of	ADP
ejpam-4463	66	17	salem	salem	NOUN
ejpam-4463	66	18	numbers	number	NOUN
ejpam-4463	66	19	,	,	PUNCT
ejpam-4463	66	20	which	which	PRON
ejpam-4463	66	21	appeared	appear	VERB
ejpam-4463	66	22	as	as	ADP
ejpam-4463	66	23	mahler	mahler	NOUN
ejpam-4463	66	24	measures	measure	NOUN
ejpam-4463	66	25	of	of	ADP
ejpam-4463	66	26	graphs	graph	NOUN
ejpam-4463	66	27	.	.	PUNCT
ejpam-4463	67	1	it	it	PRON
ejpam-4463	67	2	was	be	AUX
ejpam-4463	67	3	demonstrated	demonstrate	VERB
ejpam-4463	67	4	that	that	SCONJ
ejpam-4463	67	5	certain	certain	ADJ
ejpam-4463	67	6	limit	limit	NOUN
ejpam-4463	67	7	points	point	NOUN
ejpam-4463	67	8	of	of	ADP
ejpam-4463	67	9	these	these	DET
ejpam-4463	67	10	salem	salem	NOUN
ejpam-4463	67	11	numbers	number	NOUN
ejpam-4463	67	12	are	be	AUX
ejpam-4463	67	13	pisot	pisot	ADJ
ejpam-4463	67	14	numbers	number	NOUN
ejpam-4463	67	15	,	,	PUNCT
ejpam-4463	67	16	providing	provide	VERB
ejpam-4463	67	17	yet	yet	ADV
ejpam-4463	67	18	another	another	DET
ejpam-4463	67	19	example	example	NOUN
ejpam-4463	67	20	of	of	ADP
ejpam-4463	67	21	a	a	DET
ejpam-4463	67	22	more	more	ADV
ejpam-4463	67	23	general	general	ADJ
ejpam-4463	67	24	result	result	NOUN
ejpam-4463	67	25	.	.	PUNCT
ejpam-4463	68	1	it	it	PRON
ejpam-4463	68	2	was	be	AUX
ejpam-4463	68	3	focused	focus	VERB
ejpam-4463	68	4	on	on	ADP
ejpam-4463	68	5	an	an	DET
ejpam-4463	68	6	interlacing	interlace	VERB
ejpam-4463	68	7	construction	construction	NOUN
ejpam-4463	68	8	for	for	ADP
ejpam-4463	68	9	salem	salem	NOUN
ejpam-4463	68	10	numbers	number	NOUN
ejpam-4463	68	11	,	,	PUNCT
ejpam-4463	68	12	which	which	PRON
ejpam-4463	68	13	evolved	evolve	VERB
ejpam-4463	68	14	historically	historically	ADV
ejpam-4463	68	15	from	from	ADP
ejpam-4463	68	16	the	the	DET
ejpam-4463	68	17	graph	graph	NOUN
ejpam-4463	68	18	construction	construction	NOUN
ejpam-4463	68	19	but	but	CCONJ
ejpam-4463	68	20	is	be	AUX
ejpam-4463	68	21	far	far	ADV
ejpam-4463	68	22	more	more	ADV
ejpam-4463	68	23	general	general	ADJ
ejpam-4463	68	24	(	(	PUNCT
ejpam-4463	68	25	for	for	ADP
ejpam-4463	68	26	more	more	ADJ
ejpam-4463	68	27	details	detail	NOUN
ejpam-4463	68	28	one	one	PRON
ejpam-4463	68	29	can	can	AUX
ejpam-4463	68	30	see	see	VERB
ejpam-4463	68	31	[	[	X
ejpam-4463	68	32	8	8	NUM
ejpam-4463	68	33	]	]	NUM
ejpam-4463	68	34	)	)	PUNCT
ejpam-4463	68	35	.	.	PUNCT
ejpam-4463	69	1	chandoul	chandoul	PROPN
ejpam-4463	69	2	et	et	PROPN
ejpam-4463	69	3	al	al	PROPN
ejpam-4463	69	4	.	.	PUNCT
ejpam-4463	70	1	[	[	X
ejpam-4463	70	2	4	4	NUM
ejpam-4463	70	3	]	]	PUNCT
ejpam-4463	70	4	,	,	PUNCT
ejpam-4463	70	5	established	establish	VERB
ejpam-4463	70	6	that	that	SCONJ
ejpam-4463	70	7	the	the	DET
ejpam-4463	70	8	minimal	minimal	ADJ
ejpam-4463	70	9	polynomial	polynomial	NOUN
ejpam-4463	70	10	of	of	ADP
ejpam-4463	70	11	the	the	DET
ejpam-4463	70	12	so	so	ADV
ejpam-4463	70	13	-	-	PUNCT
ejpam-4463	70	14	called	call	VERB
ejpam-4463	70	15	,	,	PUNCT
ejpam-4463	70	16	smallest	small	ADJ
ejpam-4463	70	17	pisot	pisot	ADJ
ejpam-4463	70	18	element	element	NOUN
ejpam-4463	70	19	(	(	PUNCT
ejpam-4463	70	20	spe	spe	PROPN
ejpam-4463	70	21	)	)	PUNCT
ejpam-4463	70	22	of	of	ADP
ejpam-4463	70	23	degree	degree	NOUN
ejpam-4463	70	24	n	n	CCONJ
ejpam-4463	70	25	in	in	ADV
ejpam-4463	70	26	in	in	ADP
ejpam-4463	70	27	fq((x	fq((x	NOUN
ejpam-4463	70	28	−1	−1	NOUN
ejpam-4463	70	29	)	)	PUNCT
ejpam-4463	70	30	)	)	PUNCT
ejpam-4463	70	31	is	be	AUX
ejpam-4463	70	32	p	p	X
ejpam-4463	70	33	(	(	PUNCT
ejpam-4463	70	34	y	y	PROPN
ejpam-4463	70	35	)	)	PUNCT
ejpam-4463	71	1	=	=	SYM
ejpam-4463	71	2	y	y	PROPN
ejpam-4463	71	3	n	n	CCONJ
ejpam-4463	71	4	−	−	PROPN
ejpam-4463	71	5	axy	axy	PROPN
ejpam-4463	71	6	n−1	n−1	PROPN
ejpam-4463	71	7	−	−	PROPN
ejpam-4463	72	1	an	an	PROPN
ejpam-4463	72	2	,	,	PUNCT
ejpam-4463	72	3	where	where	SCONJ
ejpam-4463	72	4	a	a	PRON
ejpam-4463	72	5	is	be	AUX
ejpam-4463	72	6	the	the	DET
ejpam-4463	72	7	least	least	ADJ
ejpam-4463	72	8	element	element	NOUN
ejpam-4463	72	9	of	of	ADP
ejpam-4463	72	10	the	the	DET
ejpam-4463	72	11	finite	finite	ADJ
ejpam-4463	72	12	field	field	NOUN
ejpam-4463	72	13	fq	fq	PROPN
ejpam-4463	72	14	\	\	PROPN
ejpam-4463	72	15	{	{	PUNCT
ejpam-4463	72	16	0	0	NUM
ejpam-4463	72	17	}	}	PUNCT
ejpam-4463	72	18	(	(	PUNCT
ejpam-4463	72	19	as	as	ADP
ejpam-4463	72	20	a	a	DET
ejpam-4463	72	21	finite	finite	ADJ
ejpam-4463	72	22	total	total	NOUN
ejpam-4463	72	23	ordered	order	VERB
ejpam-4463	72	24	set	set	NOUN
ejpam-4463	72	25	)	)	PUNCT
ejpam-4463	72	26	.	.	PUNCT
ejpam-4463	73	1	it	it	PRON
ejpam-4463	73	2	was	be	AUX
ejpam-4463	73	3	shown	show	VERB
ejpam-4463	73	4	that	that	SCONJ
ejpam-4463	73	5	the	the	DET
ejpam-4463	73	6	sequence	sequence	NOUN
ejpam-4463	73	7	of	of	ADP
ejpam-4463	73	8	spes	spe	NOUN
ejpam-4463	73	9	in	in	ADP
ejpam-4463	73	10	the	the	DET
ejpam-4463	73	11	case	case	NOUN
ejpam-4463	73	12	of	of	ADP
ejpam-4463	73	13	degree	degree	NOUN
ejpam-4463	73	14	n	n	AUX
ejpam-4463	73	15	is	be	AUX
ejpam-4463	73	16	decreasing	decrease	VERB
ejpam-4463	73	17	.	.	PUNCT
ejpam-4463	74	1	moreover	moreover	ADV
ejpam-4463	74	2	it	it	PRON
ejpam-4463	74	3	converges	converge	VERB
ejpam-4463	74	4	to	to	AUX
ejpam-4463	74	5	ax	ax	NOUN
ejpam-4463	74	6	.	.	PUNCT
ejpam-4463	75	1	but	but	CCONJ
ejpam-4463	75	2	why	why	SCONJ
ejpam-4463	75	3	is	be	AUX
ejpam-4463	75	4	finding	find	VERB
ejpam-4463	75	5	the	the	DET
ejpam-4463	75	6	smallest	small	ADJ
ejpam-4463	75	7	element	element	NOUN
ejpam-4463	75	8	of	of	ADP
ejpam-4463	75	9	a	a	DET
ejpam-4463	75	10	set	set	NOUN
ejpam-4463	75	11	so	so	ADV
ejpam-4463	75	12	important	important	ADJ
ejpam-4463	75	13	?	?	PUNCT
ejpam-4463	76	1	the	the	DET
ejpam-4463	76	2	answer	answer	NOUN
ejpam-4463	76	3	is	be	AUX
ejpam-4463	76	4	summed	sum	VERB
ejpam-4463	76	5	up	up	ADP
ejpam-4463	76	6	in	in	ADP
ejpam-4463	76	7	the	the	DET
ejpam-4463	76	8	possibility	possibility	NOUN
ejpam-4463	76	9	of	of	ADP
ejpam-4463	76	10	discovering	discover	VERB
ejpam-4463	76	11	a	a	DET
ejpam-4463	76	12	total	total	ADJ
ejpam-4463	76	13	order	order	NOUN
ejpam-4463	76	14	and	and	CCONJ
ejpam-4463	76	15	a	a	DET
ejpam-4463	76	16	point	point	NOUN
ejpam-4463	76	17	that	that	PRON
ejpam-4463	76	18	reduces	reduce	VERB
ejpam-4463	76	19	all	all	DET
ejpam-4463	76	20	the	the	DET
ejpam-4463	76	21	properties	property	NOUN
ejpam-4463	76	22	of	of	ADP
ejpam-4463	76	23	the	the	DET
ejpam-4463	76	24	set	set	NOUN
ejpam-4463	76	25	which	which	PRON
ejpam-4463	76	26	is	be	AUX
ejpam-4463	76	27	the	the	DET
ejpam-4463	76	28	smallest	small	ADJ
ejpam-4463	76	29	according	accord	VERB
ejpam-4463	76	30	to	to	ADP
ejpam-4463	76	31	this	this	DET
ejpam-4463	76	32	order	order	NOUN
ejpam-4463	76	33	.	.	PUNCT
ejpam-4463	77	1	o.	o.	PROPN
ejpam-4463	77	2	dammak	dammak	PROPN
ejpam-4463	77	3	,	,	PUNCT
ejpam-4463	77	4	s.	s.	PROPN
ejpam-4463	77	5	mansour	mansour	PROPN
ejpam-4463	77	6	/	/	SYM
ejpam-4463	77	7	eur	eur	PROPN
ejpam-4463	77	8	.	.	PUNCT
ejpam-4463	78	1	j.	j.	PROPN
ejpam-4463	78	2	pure	pure	PROPN
ejpam-4463	78	3	appl	appl	PROPN
ejpam-4463	78	4	.	.	PROPN
ejpam-4463	78	5	math	math	PROPN
ejpam-4463	78	6	,	,	PUNCT
ejpam-4463	78	7	15	15	NUM
ejpam-4463	78	8	(	(	PUNCT
ejpam-4463	78	9	3	3	NUM
ejpam-4463	78	10	)	)	PUNCT
ejpam-4463	78	11	(	(	PUNCT
ejpam-4463	78	12	2022	2022	NUM
ejpam-4463	78	13	)	)	PUNCT
ejpam-4463	78	14	,	,	PUNCT
ejpam-4463	78	15	1321	1321	NUM
ejpam-4463	78	16	-	-	SYM
ejpam-4463	78	17	1330	1330	NUM
ejpam-4463	78	18	1324	1324	NUM
ejpam-4463	78	19	the	the	DET
ejpam-4463	78	20	smallest	small	ADJ
ejpam-4463	78	21	salem	salem	NOUN
ejpam-4463	78	22	element	element	NOUN
ejpam-4463	78	23	(	(	PUNCT
ejpam-4463	78	24	sse	sse	PROPN
ejpam-4463	78	25	)	)	PUNCT
ejpam-4463	78	26	of	of	ADP
ejpam-4463	78	27	a	a	DET
ejpam-4463	78	28	given	give	VERB
ejpam-4463	78	29	degree	degree	NOUN
ejpam-4463	78	30	n	n	NOUN
ejpam-4463	78	31	in	in	ADP
ejpam-4463	78	32	fq((x	fq((x	NOUN
ejpam-4463	78	33	−	−	PROPN
ejpam-4463	78	34	1	1	NUM
ejpam-4463	78	35	)	)	PUNCT
ejpam-4463	78	36	)	)	PUNCT
ejpam-4463	78	37	is	be	AUX
ejpam-4463	78	38	presented	present	VERB
ejpam-4463	78	39	in	in	ADP
ejpam-4463	78	40	this	this	DET
ejpam-4463	78	41	work	work	NOUN
ejpam-4463	78	42	.	.	PUNCT
ejpam-4463	79	1	the	the	DET
ejpam-4463	79	2	following	follow	VERB
ejpam-4463	79	3	is	be	AUX
ejpam-4463	79	4	how	how	SCONJ
ejpam-4463	79	5	the	the	DET
ejpam-4463	79	6	paper	paper	NOUN
ejpam-4463	79	7	is	be	AUX
ejpam-4463	79	8	structured	structure	VERB
ejpam-4463	79	9	:	:	PUNCT
ejpam-4463	79	10	in	in	ADP
ejpam-4463	79	11	section	section	NOUN
ejpam-4463	79	12	2	2	NUM
ejpam-4463	79	13	,	,	PUNCT
ejpam-4463	79	14	we	we	PRON
ejpam-4463	79	15	define	define	VERB
ejpam-4463	79	16	the	the	DET
ejpam-4463	79	17	lexicographic	lexicographic	ADJ
ejpam-4463	79	18	order	order	NOUN
ejpam-4463	79	19	on	on	ADP
ejpam-4463	79	20	in	in	ADP
ejpam-4463	79	21	fq((x	fq((x	NOUN
ejpam-4463	79	22	−1	−1	NOUN
ejpam-4463	79	23	)	)	PUNCT
ejpam-4463	79	24	)	)	PUNCT
ejpam-4463	79	25	and	and	CCONJ
ejpam-4463	79	26	provide	provide	VERB
ejpam-4463	79	27	some	some	DET
ejpam-4463	79	28	early	early	ADJ
ejpam-4463	79	29	definitions	definition	NOUN
ejpam-4463	79	30	.	.	PUNCT
ejpam-4463	80	1	we	we	PRON
ejpam-4463	80	2	offer	offer	VERB
ejpam-4463	80	3	the	the	DET
ejpam-4463	80	4	(	(	PUNCT
ejpam-4463	80	5	sse	sse	PROPN
ejpam-4463	80	6	)	)	PUNCT
ejpam-4463	80	7	of	of	ADP
ejpam-4463	80	8	degree	degree	NOUN
ejpam-4463	80	9	n	n	CCONJ
ejpam-4463	80	10	in	in	ADV
ejpam-4463	80	11	in	in	ADP
ejpam-4463	80	12	fq((x	fq((x	NOUN
ejpam-4463	80	13	−1	−1	NOUN
ejpam-4463	80	14	)	)	PUNCT
ejpam-4463	80	15	)	)	PUNCT
ejpam-4463	80	16	in	in	ADP
ejpam-4463	80	17	section	section	NOUN
ejpam-4463	80	18	3	3	NUM
ejpam-4463	80	19	.	.	PUNCT
ejpam-4463	80	20	section	section	NOUN
ejpam-4463	80	21	4	4	NUM
ejpam-4463	80	22	investigates	investigate	VERB
ejpam-4463	80	23	the	the	DET
ejpam-4463	80	24	(	(	PUNCT
ejpam-4463	80	25	sse	sse	PROPN
ejpam-4463	80	26	)	)	PUNCT
ejpam-4463	80	27	’s	’s	PART
ejpam-4463	80	28	cfe	cfe	NOUN
ejpam-4463	80	29	over	over	ADV
ejpam-4463	80	30	in	in	ADV
ejpam-4463	80	31	in	in	ADP
ejpam-4463	80	32	fq((x	fq((x	NOUN
ejpam-4463	80	33	−1	−1	NOUN
ejpam-4463	80	34	)	)	PUNCT
ejpam-4463	80	35	)	)	PUNCT
ejpam-4463	80	36	.	.	PUNCT
ejpam-4463	81	1	2	2	X
ejpam-4463	81	2	.	.	X
ejpam-4463	81	3	formal	formal	ADJ
ejpam-4463	81	4	power	power	NOUN
ejpam-4463	81	5	series	series	PROPN
ejpam-4463	81	6	let	let	VERB
ejpam-4463	81	7	fq	fq	PRON
ejpam-4463	81	8	be	be	AUX
ejpam-4463	81	9	a	a	DET
ejpam-4463	81	10	field	field	NOUN
ejpam-4463	81	11	with	with	ADP
ejpam-4463	81	12	q	q	ADJ
ejpam-4463	81	13	elements	element	NOUN
ejpam-4463	81	14	of	of	ADP
ejpam-4463	81	15	characteristic	characteristic	ADJ
ejpam-4463	81	16	p	p	X
ejpam-4463	81	17	,	,	PUNCT
ejpam-4463	81	18	fq[x	fq[x	PROPN
ejpam-4463	81	19	]	]	PUNCT
ejpam-4463	81	20	the	the	DET
ejpam-4463	81	21	set	set	NOUN
ejpam-4463	81	22	of	of	ADP
ejpam-4463	81	23	polynomials	polynomial	NOUN
ejpam-4463	81	24	of	of	ADP
ejpam-4463	81	25	coefficients	coefficient	NOUN
ejpam-4463	81	26	in	in	ADP
ejpam-4463	81	27	fq	fq	PROPN
ejpam-4463	81	28	and	and	CCONJ
ejpam-4463	81	29	fq(x	fq(x	NOUN
ejpam-4463	81	30	)	)	PUNCT
ejpam-4463	81	31	its	its	PRON
ejpam-4463	81	32	field	field	NOUN
ejpam-4463	81	33	of	of	ADP
ejpam-4463	81	34	fractions	fraction	NOUN
ejpam-4463	81	35	.	.	PUNCT
ejpam-4463	82	1	the	the	DET
ejpam-4463	82	2	set	set	ADJ
ejpam-4463	82	3	fq((x	fq((x	NOUN
ejpam-4463	82	4	−1	−1	NOUN
ejpam-4463	82	5	)	)	PUNCT
ejpam-4463	82	6	)	)	PUNCT
ejpam-4463	82	7	of	of	ADP
ejpam-4463	82	8	formal	formal	ADJ
ejpam-4463	82	9	power	power	NOUN
ejpam-4463	82	10	series	series	NOUN
ejpam-4463	82	11	over	over	ADP
ejpam-4463	82	12	fq	fq	PROPN
ejpam-4463	82	13	is	be	AUX
ejpam-4463	82	14	defined	define	VERB
ejpam-4463	82	15	as	as	SCONJ
ejpam-4463	82	16	follows	follow	VERB
ejpam-4463	82	17	fq((x	fq((x	NOUN
ejpam-4463	82	18	−1	−1	NOUN
ejpam-4463	82	19	)	)	PUNCT
ejpam-4463	82	20	)	)	PUNCT
ejpam-4463	83	1	=	=	PRON
ejpam-4463	83	2	{	{	PUNCT
ejpam-4463	84	1	+	+	ADV
ejpam-4463	84	2	∞∑	∞∑	NUM
ejpam-4463	84	3	j	j	NOUN
ejpam-4463	84	4	=	=	NOUN
ejpam-4463	84	5	s	s	NOUN
ejpam-4463	84	6	ajx	ajx	NOUN
ejpam-4463	84	7	−j	−j	NOUN
ejpam-4463	84	8	:	:	PUNCT
ejpam-4463	84	9	aj	aj	PROPN
ejpam-4463	84	10	∈	∈	PROPN
ejpam-4463	84	11	fq	fq	PROPN
ejpam-4463	84	12	,	,	PUNCT
ejpam-4463	84	13	as	as	ADP
ejpam-4463	84	14	̸=	̸=	PROPN
ejpam-4463	84	15	0	0	NUM
ejpam-4463	84	16	with	with	ADP
ejpam-4463	84	17	s	s	X
ejpam-4463	84	18	∈	∈	PROPN
ejpam-4463	84	19	z	z	NOUN
ejpam-4463	84	20	}	}	PUNCT
ejpam-4463	84	21	.	.	PUNCT
ejpam-4463	85	1	let	let	VERB
ejpam-4463	85	2	ω	ω	NOUN
ejpam-4463	85	3	=	=	PUNCT
ejpam-4463	86	1	+	+	ADJ
ejpam-4463	86	2	∞∑	∞∑	NUM
ejpam-4463	86	3	j	j	NOUN
ejpam-4463	86	4	=	=	NOUN
ejpam-4463	86	5	s	s	NOUN
ejpam-4463	86	6	ajx	ajx	NOUN
ejpam-4463	86	7	−j	−j	NOUN
ejpam-4463	86	8	∈	∈	PROPN
ejpam-4463	86	9	fq((x	fq((x	NOUN
ejpam-4463	86	10	−1	−1	NOUN
ejpam-4463	86	11	)	)	PUNCT
ejpam-4463	86	12	)	)	PUNCT
ejpam-4463	86	13	.	.	PUNCT
ejpam-4463	87	1	the	the	DET
ejpam-4463	87	2	polynomial	polynomial	ADJ
ejpam-4463	87	3	part	part	NOUN
ejpam-4463	87	4	of	of	ADP
ejpam-4463	87	5	ω	ω	PROPN
ejpam-4463	87	6	is	be	AUX
ejpam-4463	87	7	denoted	denote	VERB
ejpam-4463	87	8	by	by	ADP
ejpam-4463	87	9	[	[	X
ejpam-4463	87	10	ω	ω	X
ejpam-4463	87	11	]	]	X
ejpam-4463	87	12	and	and	CCONJ
ejpam-4463	87	13	its	its	PRON
ejpam-4463	87	14	fractional	fractional	ADJ
ejpam-4463	87	15	part	part	NOUN
ejpam-4463	87	16	is	be	AUX
ejpam-4463	87	17	denoted	denote	VERB
ejpam-4463	87	18	by	by	ADP
ejpam-4463	87	19	{	{	PUNCT
ejpam-4463	87	20	ω	ω	NOUN
ejpam-4463	87	21	}	}	PUNCT
ejpam-4463	87	22	.	.	PUNCT
ejpam-4463	88	1	we	we	PRON
ejpam-4463	88	2	remark	remark	VERB
ejpam-4463	88	3	that	that	SCONJ
ejpam-4463	88	4	ω	ω	X
ejpam-4463	88	5	=	=	PUNCT
ejpam-4463	89	1	[	[	X
ejpam-4463	89	2	ω	ω	X
ejpam-4463	89	3	]	]	X
ejpam-4463	89	4	+	+	CCONJ
ejpam-4463	89	5	{	{	PUNCT
ejpam-4463	89	6	ω	ω	NOUN
ejpam-4463	89	7	}	}	PUNCT
ejpam-4463	89	8	.	.	PUNCT
ejpam-4463	90	1	as	as	ADP
ejpam-4463	90	2	in	in	ADP
ejpam-4463	90	3	sprindz̃uk	sprindz̃uk	PROPN
ejpam-4463	90	4	[	[	X
ejpam-4463	90	5	16	16	NUM
ejpam-4463	90	6	]	]	X
ejpam-4463	90	7	a	a	DET
ejpam-4463	90	8	non	non	X
ejpam-4463	90	9	archimedean	archimedean	ADJ
ejpam-4463	90	10	absolute	absolute	ADJ
ejpam-4463	90	11	value	value	NOUN
ejpam-4463	90	12	on	on	ADP
ejpam-4463	90	13	fq((x	fq((x	NOUN
ejpam-4463	90	14	−1	−1	NOUN
ejpam-4463	90	15	)	)	PUNCT
ejpam-4463	90	16	)	)	PUNCT
ejpam-4463	90	17	is	be	AUX
ejpam-4463	90	18	definied	definie	VERB
ejpam-4463	90	19	by	by	ADP
ejpam-4463	90	20	|	|	ADV
ejpam-4463	90	21	ω	ω	NUM
ejpam-4463	90	22	|=	|=	X
ejpam-4463	90	23	e−s	e−s	PROPN
ejpam-4463	90	24	.	.	PUNCT
ejpam-4463	91	1	clearly	clearly	ADV
ejpam-4463	91	2	,	,	PUNCT
ejpam-4463	91	3	we	we	PRON
ejpam-4463	91	4	have	have	VERB
ejpam-4463	91	5	,	,	PUNCT
ejpam-4463	91	6	|	|	ADV
ejpam-4463	91	7	p	p	ADJ
ejpam-4463	91	8	|=	|=	PUNCT
ejpam-4463	91	9	edegp	edegp	ADJ
ejpam-4463	91	10	,	,	PUNCT
ejpam-4463	91	11	for	for	ADP
ejpam-4463	91	12	all	all	DET
ejpam-4463	91	13	p	p	PROPN
ejpam-4463	91	14	∈	∈	PROPN
ejpam-4463	91	15	fq[x	fq[x	NOUN
ejpam-4463	91	16	]	]	PUNCT
ejpam-4463	91	17	,	,	PUNCT
ejpam-4463	91	18	and	and	CCONJ
ejpam-4463	91	19	,	,	PUNCT
ejpam-4463	91	20	|	|	ADV
ejpam-4463	91	21	p	p	X
ejpam-4463	91	22	q	q	X
ejpam-4463	91	23	|=	|=	NOUN
ejpam-4463	91	24	edegp	edegp	ADJ
ejpam-4463	91	25	−	−	PROPN
ejpam-4463	91	26	degq	degq	NOUN
ejpam-4463	91	27	,	,	PUNCT
ejpam-4463	91	28	for	for	ADP
ejpam-4463	91	29	all	all	DET
ejpam-4463	91	30	q	q	PROPN
ejpam-4463	91	31	∈	∈	PROPN
ejpam-4463	91	32	fq[x	fq[x	PROPN
ejpam-4463	91	33	]	]	PUNCT
ejpam-4463	91	34	,	,	PUNCT
ejpam-4463	91	35	such	such	ADJ
ejpam-4463	91	36	that	that	DET
ejpam-4463	91	37	q	q	PROPN
ejpam-4463	91	38	̸=	̸=	PROPN
ejpam-4463	91	39	0	0	NUM
ejpam-4463	91	40	.	.	PUNCT
ejpam-4463	92	1	it	it	PRON
ejpam-4463	92	2	is	be	AUX
ejpam-4463	92	3	well	well	ADV
ejpam-4463	92	4	known	know	VERB
ejpam-4463	92	5	that	that	SCONJ
ejpam-4463	92	6	fq((x	fq((x	NOUN
ejpam-4463	92	7	−1	−1	NOUN
ejpam-4463	92	8	)	)	PUNCT
ejpam-4463	92	9	)	)	PUNCT
ejpam-4463	93	1	is	be	AUX
ejpam-4463	93	2	complete	complete	ADJ
ejpam-4463	93	3	.	.	PUNCT
ejpam-4463	94	1	in	in	ADP
ejpam-4463	94	2	terms	term	NOUN
ejpam-4463	94	3	of	of	ADP
ejpam-4463	94	4	the	the	DET
ejpam-4463	94	5	metric	metric	NOUN
ejpam-4463	94	6	provided	provide	VERB
ejpam-4463	94	7	by	by	ADP
ejpam-4463	94	8	this	this	DET
ejpam-4463	94	9	absolute	absolute	ADJ
ejpam-4463	94	10	value	value	NOUN
ejpam-4463	94	11	,	,	PUNCT
ejpam-4463	94	12	fq((x	fq((x	NOUN
ejpam-4463	94	13	−1	−1	NOUN
ejpam-4463	94	14	)	)	PUNCT
ejpam-4463	94	15	)	)	PUNCT
ejpam-4463	94	16	is	be	AUX
ejpam-4463	94	17	locally	locally	ADV
ejpam-4463	94	18	compact	compact	ADJ
ejpam-4463	94	19	.	.	PUNCT
ejpam-4463	95	1	an	an	DET
ejpam-4463	95	2	algebraic	algebraic	ADJ
ejpam-4463	95	3	closure	closure	NOUN
ejpam-4463	95	4	of	of	ADP
ejpam-4463	95	5	fq((x	fq((x	NOUN
ejpam-4463	95	6	−1	−1	NOUN
ejpam-4463	95	7	)	)	PUNCT
ejpam-4463	95	8	)	)	PUNCT
ejpam-4463	95	9	is	be	AUX
ejpam-4463	95	10	denoted	denote	VERB
ejpam-4463	95	11	by	by	ADP
ejpam-4463	95	12	fq((x	fq((x	NOUN
ejpam-4463	95	13	−1	−1	NOUN
ejpam-4463	95	14	)	)	PUNCT
ejpam-4463	95	15	)	)	PUNCT
ejpam-4463	95	16	.	.	PUNCT
ejpam-4463	96	1	it	it	PRON
ejpam-4463	96	2	is	be	AUX
ejpam-4463	96	3	worth	worth	ADJ
ejpam-4463	96	4	noting	note	VERB
ejpam-4463	96	5	that	that	SCONJ
ejpam-4463	96	6	the	the	DET
ejpam-4463	96	7	absolute	absolute	ADJ
ejpam-4463	96	8	value	value	NOUN
ejpam-4463	96	9	has	have	VERB
ejpam-4463	96	10	a	a	DET
ejpam-4463	96	11	distinct	distinct	ADJ
ejpam-4463	96	12	extension	extension	NOUN
ejpam-4463	96	13	to	to	ADP
ejpam-4463	96	14	fq((x	fq((x	NOUN
ejpam-4463	96	15	−1	−1	NOUN
ejpam-4463	96	16	)	)	PUNCT
ejpam-4463	96	17	)	)	PUNCT
ejpam-4463	96	18	.	.	PUNCT
ejpam-4463	97	1	we	we	PRON
ejpam-4463	97	2	will	will	AUX
ejpam-4463	97	3	use	use	VERB
ejpam-4463	97	4	the	the	DET
ejpam-4463	97	5	same	same	ADJ
ejpam-4463	97	6	symbol	symbol	NOUN
ejpam-4463	97	7	|	|	ADV
ejpam-4463	97	8	·	·	PUNCT
ejpam-4463	97	9	|	|	ADV
ejpam-4463	97	10	for	for	ADP
ejpam-4463	97	11	the	the	DET
ejpam-4463	97	12	two	two	NUM
ejpam-4463	97	13	absolute	absolute	ADJ
ejpam-4463	97	14	values	value	NOUN
ejpam-4463	97	15	,	,	PUNCT
ejpam-4463	97	16	slightly	slightly	ADV
ejpam-4463	97	17	abusing	abuse	VERB
ejpam-4463	97	18	the	the	DET
ejpam-4463	97	19	notations	notation	NOUN
ejpam-4463	97	20	.	.	PUNCT
ejpam-4463	98	1	as	as	SCONJ
ejpam-4463	98	2	fq	fq	PROPN
ejpam-4463	98	3	is	be	AUX
ejpam-4463	98	4	a	a	DET
ejpam-4463	98	5	finite	finite	ADJ
ejpam-4463	98	6	total	total	ADJ
ejpam-4463	98	7	order	order	NOUN
ejpam-4463	98	8	set	set	NOUN
ejpam-4463	98	9	,	,	PUNCT
ejpam-4463	98	10	we	we	PRON
ejpam-4463	98	11	denote	denote	VERB
ejpam-4463	98	12	by	by	ADP
ejpam-4463	98	13	⪯	⪯	NOUN
ejpam-4463	98	14	a	a	DET
ejpam-4463	98	15	totally	totally	ADV
ejpam-4463	98	16	order	order	NOUN
ejpam-4463	98	17	on	on	ADP
ejpam-4463	98	18	fq	fq	PROPN
ejpam-4463	98	19	.	.	PUNCT
ejpam-4463	99	1	now	now	ADV
ejpam-4463	99	2	,	,	PUNCT
ejpam-4463	99	3	we	we	PRON
ejpam-4463	99	4	extend	extend	VERB
ejpam-4463	99	5	⪯	⪯	NOUN
ejpam-4463	99	6	to	to	ADP
ejpam-4463	99	7	the	the	DET
ejpam-4463	99	8	field	field	NOUN
ejpam-4463	99	9	of	of	ADP
ejpam-4463	99	10	formal	formal	ADJ
ejpam-4463	99	11	power	power	NOUN
ejpam-4463	99	12	series	series	NOUN
ejpam-4463	99	13	as	as	SCONJ
ejpam-4463	99	14	follows	follow	VERB
ejpam-4463	99	15	:	:	PUNCT
ejpam-4463	99	16	let	let	VERB
ejpam-4463	99	17	w	w	VERB
ejpam-4463	99	18	=	=	PUNCT
ejpam-4463	100	1	+	+	ADP
ejpam-4463	100	2	∞∑	∞∑	NUM
ejpam-4463	100	3	i	i	PRON
ejpam-4463	100	4	=	=	NOUN
ejpam-4463	100	5	m	m	PROPN
ejpam-4463	100	6	wix	wix	NOUN
ejpam-4463	100	7	−i	−i	PROPN
ejpam-4463	100	8	and	and	CCONJ
ejpam-4463	100	9	v	v	NOUN
ejpam-4463	100	10	=	=	SYM
ejpam-4463	101	1	+	+	ADP
ejpam-4463	101	2	∞∑	∞∑	NUM
ejpam-4463	101	3	i	i	PROPN
ejpam-4463	101	4	=	=	PROPN
ejpam-4463	101	5	k	k	PROPN
ejpam-4463	101	6	vix	vix	PROPN
ejpam-4463	101	7	−i	−i	PROPN
ejpam-4463	101	8	with	with	ADP
ejpam-4463	101	9	wmvk	wmvk	NOUN
ejpam-4463	101	10	̸=	̸=	PROPN
ejpam-4463	101	11	0	0	NUM
ejpam-4463	101	12	,	,	PUNCT
ejpam-4463	101	13	then	then	ADV
ejpam-4463	101	14	,	,	PUNCT
ejpam-4463	101	15	w	w	PROPN
ejpam-4463	101	16	⪯	⪯	NOUN
ejpam-4463	101	17	v	v	X
ejpam-4463	101	18	if	if	SCONJ
ejpam-4463	102	1	and	and	CCONJ
ejpam-4463	102	2	only	only	ADV
ejpam-4463	102	3	if	if	SCONJ
ejpam-4463	102	4	m	m	VERB
ejpam-4463	102	5	>	>	X
ejpam-4463	102	6	k	k	PROPN
ejpam-4463	102	7	or	or	CCONJ
ejpam-4463	102	8	w	w	PROPN
ejpam-4463	102	9	=	=	PUNCT
ejpam-4463	102	10	v	v	NOUN
ejpam-4463	102	11	or	or	CCONJ
ejpam-4463	102	12	m	m	PROPN
ejpam-4463	102	13	=	=	SYM
ejpam-4463	102	14	k	k	PROPN
ejpam-4463	102	15	and	and	CCONJ
ejpam-4463	102	16	there	there	PRON
ejpam-4463	102	17	exists	exist	VERB
ejpam-4463	102	18	j	j	PROPN
ejpam-4463	102	19	≥	≥	PROPN
ejpam-4463	102	20	m	m	PROPN
ejpam-4463	102	21	,	,	PUNCT
ejpam-4463	102	22	such	such	ADJ
ejpam-4463	102	23	that	that	SCONJ
ejpam-4463	102	24	wi	wi	PROPN
ejpam-4463	102	25	=	=	SYM
ejpam-4463	102	26	vi	vi	PROPN
ejpam-4463	102	27	,	,	PUNCT
ejpam-4463	102	28	for	for	SCONJ
ejpam-4463	102	29	i	i	PRON
ejpam-4463	102	30	<	<	X
ejpam-4463	102	31	j	j	PROPN
ejpam-4463	102	32	and	and	CCONJ
ejpam-4463	102	33	wj	wj	PROPN
ejpam-4463	102	34	⪯	⪯	PROPN
ejpam-4463	102	35	vj	vj	INTJ
ejpam-4463	102	36	.	.	PUNCT
ejpam-4463	103	1	let	let	VERB
ejpam-4463	103	2	w	w	PROPN
ejpam-4463	103	3	∈q	∈q	NOUN
ejpam-4463	103	4	(	(	PUNCT
ejpam-4463	103	5	(	(	PUNCT
ejpam-4463	103	6	x−1	x−1	NOUN
ejpam-4463	103	7	)	)	PUNCT
ejpam-4463	103	8	)	)	PUNCT
ejpam-4463	103	9	,	,	PUNCT
ejpam-4463	103	10	with	with	SCONJ
ejpam-4463	103	11	|w|	|w|	PROPN
ejpam-4463	103	12	>	>	SYM
ejpam-4463	103	13	1	1	NUM
ejpam-4463	103	14	is	be	AUX
ejpam-4463	103	15	called	call	VERB
ejpam-4463	103	16	to	to	PART
ejpam-4463	103	17	be	be	AUX
ejpam-4463	103	18	a	a	DET
ejpam-4463	103	19	salem	salem	NOUN
ejpam-4463	103	20	element	element	NOUN
ejpam-4463	103	21	if	if	SCONJ
ejpam-4463	103	22	it	it	PRON
ejpam-4463	103	23	is	be	AUX
ejpam-4463	103	24	algebraic	algebraic	ADJ
ejpam-4463	103	25	over	over	ADP
ejpam-4463	103	26	q[x	q[x	PROPN
ejpam-4463	103	27	]	]	PUNCT
ejpam-4463	103	28	whose	whose	DET
ejpam-4463	103	29	conjugates	conjugate	NOUN
ejpam-4463	103	30	wi	wi	PROPN
ejpam-4463	103	31	in	in	ADP
ejpam-4463	103	32	fq((x	fq((x	NOUN
ejpam-4463	103	33	−1	−1	NOUN
ejpam-4463	103	34	)	)	PUNCT
ejpam-4463	103	35	)	)	PUNCT
ejpam-4463	103	36	have	have	VERB
ejpam-4463	103	37	modulus	modulus	NOUN
ejpam-4463	103	38	|	|	ADV
ejpam-4463	103	39	wi	wi	PROPN
ejpam-4463	103	40	|≤	|≤	PROPN
ejpam-4463	103	41	1	1	NUM
ejpam-4463	103	42	,	,	PUNCT
ejpam-4463	103	43	with	with	ADP
ejpam-4463	103	44	at	at	ADV
ejpam-4463	103	45	least	least	ADV
ejpam-4463	103	46	one	one	NUM
ejpam-4463	103	47	case	case	NOUN
ejpam-4463	103	48	of	of	ADP
ejpam-4463	103	49	equality	equality	NOUN
ejpam-4463	103	50	.	.	PUNCT
ejpam-4463	104	1	theorem	theorem	NOUN
ejpam-4463	104	2	2	2	NUM
ejpam-4463	104	3	.	.	PUNCT
ejpam-4463	105	1	let	let	VERB
ejpam-4463	105	2	w	w	ADP
ejpam-4463	105	3	such	such	ADJ
ejpam-4463	105	4	that	that	PRON
ejpam-4463	105	5	|w|	|w|	VERB
ejpam-4463	105	6	>	>	ADP
ejpam-4463	105	7	1	1	NUM
ejpam-4463	105	8	,	,	PUNCT
ejpam-4463	105	9	be	be	AUX
ejpam-4463	105	10	an	an	DET
ejpam-4463	105	11	element	element	NOUN
ejpam-4463	105	12	of	of	ADP
ejpam-4463	105	13	q((x	q((x	NOUN
ejpam-4463	105	14	−1	−1	NOUN
ejpam-4463	105	15	)	)	PUNCT
ejpam-4463	105	16	)	)	PUNCT
ejpam-4463	105	17	,	,	PUNCT
ejpam-4463	105	18	these	these	DET
ejpam-4463	105	19	two	two	NUM
ejpam-4463	105	20	affirmations	affirmation	NOUN
ejpam-4463	105	21	are	be	AUX
ejpam-4463	105	22	equivalent	equivalent	ADJ
ejpam-4463	105	23	:	:	PUNCT
ejpam-4463	105	24	1	1	X
ejpam-4463	105	25	)	)	PUNCT
ejpam-4463	105	26	w	w	NOUN
ejpam-4463	105	27	is	be	AUX
ejpam-4463	105	28	a	a	DET
ejpam-4463	105	29	salem	salem	NOUN
ejpam-4463	105	30	element	element	NOUN
ejpam-4463	105	31	.	.	PUNCT
ejpam-4463	106	1	o.	o.	PROPN
ejpam-4463	106	2	dammak	dammak	PROPN
ejpam-4463	106	3	,	,	PUNCT
ejpam-4463	106	4	s.	s.	PROPN
ejpam-4463	106	5	mansour	mansour	PROPN
ejpam-4463	106	6	/	/	SYM
ejpam-4463	106	7	eur	eur	PROPN
ejpam-4463	106	8	.	.	PUNCT
ejpam-4463	107	1	j.	j.	PROPN
ejpam-4463	107	2	pure	pure	PROPN
ejpam-4463	107	3	appl	appl	PROPN
ejpam-4463	107	4	.	.	PROPN
ejpam-4463	107	5	math	math	PROPN
ejpam-4463	107	6	,	,	PUNCT
ejpam-4463	107	7	15	15	NUM
ejpam-4463	107	8	(	(	PUNCT
ejpam-4463	107	9	3	3	NUM
ejpam-4463	107	10	)	)	PUNCT
ejpam-4463	107	11	(	(	PUNCT
ejpam-4463	107	12	2022	2022	NUM
ejpam-4463	107	13	)	)	PUNCT
ejpam-4463	107	14	,	,	PUNCT
ejpam-4463	107	15	1321	1321	NUM
ejpam-4463	107	16	-	-	SYM
ejpam-4463	107	17	1330	1330	NUM
ejpam-4463	107	18	1325	1325	NUM
ejpam-4463	107	19	2	2	NUM
ejpam-4463	107	20	)	)	PUNCT
ejpam-4463	107	21	the	the	DET
ejpam-4463	107	22	minimal	minimal	ADJ
ejpam-4463	107	23	polynomial	polynomial	ADJ
ejpam-4463	107	24	p	p	NOUN
ejpam-4463	107	25	of	of	ADP
ejpam-4463	107	26	w	w	PROPN
ejpam-4463	107	27	can	can	AUX
ejpam-4463	107	28	be	be	AUX
ejpam-4463	107	29	written	write	VERB
ejpam-4463	107	30	as	as	ADP
ejpam-4463	107	31	p	p	PROPN
ejpam-4463	107	32	(	(	PUNCT
ejpam-4463	107	33	y	y	PROPN
ejpam-4463	107	34	)	)	PUNCT
ejpam-4463	108	1	=	=	PUNCT
ejpam-4463	109	1	y	y	PROPN
ejpam-4463	109	2	s	s	PART
ejpam-4463	109	3	+	+	NUM
ejpam-4463	109	4	as−1y	as−1y	ADJ
ejpam-4463	109	5	s−1	s−1	PROPN
ejpam-4463	109	6	+	+	CCONJ
ejpam-4463	109	7	·	·	PUNCT
ejpam-4463	109	8	·	·	PUNCT
ejpam-4463	109	9	·	·	PUNCT
ejpam-4463	110	1	+	+	NUM
ejpam-4463	110	2	a0	a0	PROPN
ejpam-4463	110	3	,	,	PUNCT
ejpam-4463	110	4	with	with	ADP
ejpam-4463	110	5	ai	ai	PRON
ejpam-4463	110	6	∈q	∈q	NOUN
ejpam-4463	110	7	[	[	X
ejpam-4463	110	8	x	x	X
ejpam-4463	110	9	]	]	X
ejpam-4463	110	10	\	\	X
ejpam-4463	110	11	{	{	PUNCT
ejpam-4463	110	12	0	0	NUM
ejpam-4463	110	13	}	}	PUNCT
ejpam-4463	110	14	,	,	PUNCT
ejpam-4463	110	15	ai	ai	VERB
ejpam-4463	110	16	∈q	∈q	NOUN
ejpam-4463	110	17	[	[	X
ejpam-4463	110	18	x	x	X
ejpam-4463	110	19	]	]	X
ejpam-4463	110	20	for	for	ADP
ejpam-4463	110	21	i	i	PROPN
ejpam-4463	110	22	=	=	NOUN
ejpam-4463	110	23	0	0	NUM
ejpam-4463	110	24	,	,	PUNCT
ejpam-4463	110	25	.	.	PUNCT
ejpam-4463	110	26	.	.	PUNCT
ejpam-4463	111	1	.	.	PUNCT
ejpam-4463	112	1	,	,	PUNCT
ejpam-4463	112	2	s−	s−	PROPN
ejpam-4463	112	3	1	1	NUM
ejpam-4463	112	4	,	,	PUNCT
ejpam-4463	112	5	and	and	CCONJ
ejpam-4463	112	6	|as−1|	|as−1|	X
ejpam-4463	112	7	=	=	SYM
ejpam-4463	112	8	max	max	PROPN
ejpam-4463	112	9	i	i	PROPN
ejpam-4463	112	10	̸=s−1	̸=s−1	NOUN
ejpam-4463	112	11	|ai|	|ai|	PROPN
ejpam-4463	112	12	.	.	PUNCT
ejpam-4463	113	1	now	now	ADV
ejpam-4463	113	2	,	,	PUNCT
ejpam-4463	113	3	we	we	PRON
ejpam-4463	113	4	will	will	AUX
ejpam-4463	113	5	go	go	VERB
ejpam-4463	113	6	over	over	ADP
ejpam-4463	113	7	the	the	DET
ejpam-4463	113	8	main	main	ADJ
ejpam-4463	113	9	results	result	NOUN
ejpam-4463	113	10	.	.	PUNCT
ejpam-4463	114	1	3	3	X
ejpam-4463	114	2	.	.	X
ejpam-4463	114	3	main	main	ADJ
ejpam-4463	114	4	result	result	NOUN
ejpam-4463	114	5	theorem	theorem	VERB
ejpam-4463	114	6	3	3	X
ejpam-4463	114	7	.	.	PUNCT
ejpam-4463	114	8	let	let	VERB
ejpam-4463	114	9	s(n	s(n	NOUN
ejpam-4463	114	10	)	)	PUNCT
ejpam-4463	114	11	=	=	PRON
ejpam-4463	114	12	{	{	PUNCT
ejpam-4463	114	13	salem	salem	NOUN
ejpam-4463	114	14	elements	element	NOUN
ejpam-4463	114	15	of	of	ADP
ejpam-4463	114	16	degree	degree	NOUN
ejpam-4463	114	17	n	n	CCONJ
ejpam-4463	114	18	}	}	PUNCT
ejpam-4463	114	19	,	,	PUNCT
ejpam-4463	114	20	n	n	X
ejpam-4463	114	21	≥	≥	NOUN
ejpam-4463	114	22	2	2	NUM
ejpam-4463	114	23	and	and	CCONJ
ejpam-4463	114	24	a	a	PRON
ejpam-4463	114	25	is	be	AUX
ejpam-4463	114	26	the	the	DET
ejpam-4463	114	27	least	least	ADJ
ejpam-4463	114	28	element	element	NOUN
ejpam-4463	114	29	of	of	ADP
ejpam-4463	114	30	fq\{0	fq\{0	NOUN
ejpam-4463	114	31	}	}	PUNCT
ejpam-4463	114	32	,	,	PUNCT
ejpam-4463	114	33	then	then	ADV
ejpam-4463	114	34	wn	wn	PROPN
ejpam-4463	114	35	=	=	PROPN
ejpam-4463	114	36	inf	inf	PROPN
ejpam-4463	114	37	s(n	s(n	PROPN
ejpam-4463	114	38	)	)	PUNCT
ejpam-4463	114	39	is	be	AUX
ejpam-4463	114	40	a	a	DET
ejpam-4463	114	41	salem	salem	NOUN
ejpam-4463	114	42	element	element	NOUN
ejpam-4463	114	43	of	of	ADP
ejpam-4463	114	44	minimal	minimal	ADJ
ejpam-4463	114	45	polynomial	polynomial	ADJ
ejpam-4463	114	46	pn(y	pn(y	NOUN
ejpam-4463	114	47	)	)	PUNCT
ejpam-4463	115	1	=	=	PUNCT
ejpam-4463	115	2	y	y	PROPN
ejpam-4463	115	3	n	n	CCONJ
ejpam-4463	115	4	−	−	PROPN
ejpam-4463	115	5	axy	axy	PROPN
ejpam-4463	115	6	n−1	n−1	PROPN
ejpam-4463	115	7	−	−	PROPN
ejpam-4463	116	1	ay	ay	NOUN
ejpam-4463	117	1	+	+	CCONJ
ejpam-4463	117	2	ax	ax	NOUN
ejpam-4463	117	3	−	−	PROPN
ejpam-4463	117	4	a	a	PRON
ejpam-4463	117	5	in	in	ADP
ejpam-4463	117	6	addition	addition	NOUN
ejpam-4463	117	7	,	,	PUNCT
ejpam-4463	117	8	the	the	DET
ejpam-4463	117	9	sequence	sequence	NOUN
ejpam-4463	117	10	(	(	PUNCT
ejpam-4463	117	11	wn)n≥1	wn)n≥1	NOUN
ejpam-4463	117	12	of	of	ADP
ejpam-4463	117	13	wn	wn	PROPN
ejpam-4463	117	14	=	=	PROPN
ejpam-4463	117	15	inf	inf	PROPN
ejpam-4463	117	16	s(n	s(n	PROPN
ejpam-4463	117	17	)	)	PUNCT
ejpam-4463	117	18	is	be	AUX
ejpam-4463	117	19	decreasing	decrease	VERB
ejpam-4463	117	20	one	one	NUM
ejpam-4463	117	21	and	and	CCONJ
ejpam-4463	117	22	converges	converge	VERB
ejpam-4463	117	23	to	to	PART
ejpam-4463	117	24	ax	ax	NOUN
ejpam-4463	117	25	.	.	PUNCT
ejpam-4463	118	1	the	the	DET
ejpam-4463	118	2	following	follow	VERB
ejpam-4463	118	3	lemmas	lemma	NOUN
ejpam-4463	118	4	are	be	AUX
ejpam-4463	118	5	needed	need	VERB
ejpam-4463	118	6	to	to	PART
ejpam-4463	118	7	prove	prove	VERB
ejpam-4463	118	8	this	this	DET
ejpam-4463	118	9	theorem	theorem	NOUN
ejpam-4463	118	10	.	.	PUNCT
ejpam-4463	119	1	lemma	lemma	PROPN
ejpam-4463	119	2	1	1	X
ejpam-4463	119	3	.	.	PUNCT
ejpam-4463	120	1	let	let	VERB
ejpam-4463	120	2	p	p	NOUN
ejpam-4463	120	3	(	(	PUNCT
ejpam-4463	120	4	y	y	PROPN
ejpam-4463	120	5	)	)	PUNCT
ejpam-4463	121	1	=	=	PUNCT
ejpam-4463	121	2	ady	ady	PROPN
ejpam-4463	122	1	d	d	PROPN
ejpam-4463	122	2	+	+	PROPN
ejpam-4463	122	3	·	·	PUNCT
ejpam-4463	122	4	·	·	PUNCT
ejpam-4463	122	5	·	·	PUNCT
ejpam-4463	123	1	+	+	CCONJ
ejpam-4463	123	2	a0	a0	PROPN
ejpam-4463	123	3	with	with	ADP
ejpam-4463	123	4	ai	ai	PROPN
ejpam-4463	123	5	∈q	∈q	NOUN
ejpam-4463	123	6	[	[	X
ejpam-4463	123	7	x	x	X
ejpam-4463	123	8	]	]	X
ejpam-4463	123	9	,	,	PUNCT
ejpam-4463	123	10	ad	ad	NOUN
ejpam-4463	123	11	̸=	̸=	PROPN
ejpam-4463	123	12	0	0	NUM
ejpam-4463	123	13	and	and	CCONJ
ejpam-4463	123	14	|an−1|	|an−1|	ADP
ejpam-4463	123	15	>	>	X
ejpam-4463	123	16	|ai|	|ai|	PROPN
ejpam-4463	123	17	,	,	PUNCT
ejpam-4463	123	18	for	for	ADP
ejpam-4463	123	19	all	all	DET
ejpam-4463	123	20	i	i	PRON
ejpam-4463	123	21	̸=	̸=	PROPN
ejpam-4463	123	22	n−	n−	NOUN
ejpam-4463	123	23	1	1	NUM
ejpam-4463	123	24	.	.	PUNCT
ejpam-4463	124	1	then	then	ADV
ejpam-4463	124	2	p	p	X
ejpam-4463	124	3	has	have	VERB
ejpam-4463	124	4	exactly	exactly	ADV
ejpam-4463	124	5	one	one	NUM
ejpam-4463	124	6	root	root	NOUN
ejpam-4463	124	7	w	w	ADP
ejpam-4463	124	8	∈q	∈q	NOUN
ejpam-4463	124	9	(	(	PUNCT
ejpam-4463	124	10	(	(	PUNCT
ejpam-4463	124	11	x	x	NOUN
ejpam-4463	124	12	−1	−1	NOUN
ejpam-4463	124	13	)	)	PUNCT
ejpam-4463	124	14	)	)	PUNCT
ejpam-4463	124	15	such	such	ADJ
ejpam-4463	124	16	that	that	PRON
ejpam-4463	124	17	|w|	|w|	VERB
ejpam-4463	124	18	>	>	ADP
ejpam-4463	124	19	1	1	NUM
ejpam-4463	124	20	.	.	PUNCT
ejpam-4463	125	1	furthermore	furthermore	ADV
ejpam-4463	125	2	[	[	X
ejpam-4463	125	3	w	w	X
ejpam-4463	125	4	]	]	X
ejpam-4463	125	5	=	=	SYM
ejpam-4463	125	6	−	−	PROPN
ejpam-4463	125	7	[	[	PUNCT
ejpam-4463	125	8	an−1	an−1	ADV
ejpam-4463	125	9	an	an	PRON
ejpam-4463	125	10	]	]	PUNCT
ejpam-4463	125	11	.	.	PUNCT
ejpam-4463	126	1	lemma	lemma	PROPN
ejpam-4463	126	2	2	2	X
ejpam-4463	126	3	.	.	PUNCT
ejpam-4463	127	1	let	let	VERB
ejpam-4463	127	2	h(y	h(y	ADV
ejpam-4463	127	3	)	)	PUNCT
ejpam-4463	128	1	=	=	PUNCT
ejpam-4463	128	2	y	y	PROPN
ejpam-4463	128	3	d	d	PROPN
ejpam-4463	128	4	−ay	−ay	PROPN
ejpam-4463	128	5	d−1	d−1	PROPN
ejpam-4463	128	6	−b	−b	ADJ
ejpam-4463	128	7	,	,	PUNCT
ejpam-4463	128	8	a	a	DET
ejpam-4463	128	9	,	,	PUNCT
ejpam-4463	128	10	b	b	PROPN
ejpam-4463	128	11	∈	∈	PROPN
ejpam-4463	128	12	fq[x	fq[x	PROPN
ejpam-4463	128	13	]	]	PUNCT
ejpam-4463	128	14	\	\	PUNCT
ejpam-4463	128	15	{	{	PUNCT
ejpam-4463	128	16	0	0	NUM
ejpam-4463	128	17	}	}	PUNCT
ejpam-4463	128	18	,	,	PUNCT
ejpam-4463	128	19	dega	dega	PROPN
ejpam-4463	128	20	≥	≥	NUM
ejpam-4463	128	21	degb	degb	PROPN
ejpam-4463	128	22	.	.	PUNCT
ejpam-4463	129	1	then	then	ADV
ejpam-4463	129	2	h	h	PROPN
ejpam-4463	129	3	is	be	AUX
ejpam-4463	129	4	irreducible	irreducible	ADJ
ejpam-4463	129	5	over	over	ADP
ejpam-4463	129	6	fq[x	fq[x	PROPN
ejpam-4463	129	7	]	]	PUNCT
ejpam-4463	129	8	.	.	PUNCT
ejpam-4463	130	1	proof	proof	NOUN
ejpam-4463	130	2	.	.	PUNCT
ejpam-4463	131	1	according	accord	VERB
ejpam-4463	131	2	to	to	ADP
ejpam-4463	131	3	lemma	lemma	PROPN
ejpam-4463	131	4	1	1	NUM
ejpam-4463	131	5	,	,	PUNCT
ejpam-4463	131	6	h	h	NOUN
ejpam-4463	131	7	has	have	VERB
ejpam-4463	131	8	exactly	exactly	ADV
ejpam-4463	131	9	one	one	NUM
ejpam-4463	131	10	root	root	NOUN
ejpam-4463	131	11	w	w	ADP
ejpam-4463	131	12	such	such	ADJ
ejpam-4463	131	13	that	that	PRON
ejpam-4463	131	14	|	|	INTJ
ejpam-4463	131	15	w	w	PROPN
ejpam-4463	131	16	|	|	ADV
ejpam-4463	131	17	>	>	X
ejpam-4463	131	18	1	1	NUM
ejpam-4463	132	1	and	and	CCONJ
ejpam-4463	132	2	[	[	X
ejpam-4463	132	3	w	w	X
ejpam-4463	132	4	]	]	X
ejpam-4463	132	5	=	=	PUNCT
ejpam-4463	132	6	a.	a.	NOUN
ejpam-4463	132	7	let	let	VERB
ejpam-4463	132	8	wi	wi	PROPN
ejpam-4463	132	9	be	be	AUX
ejpam-4463	132	10	the	the	DET
ejpam-4463	132	11	other	other	ADJ
ejpam-4463	132	12	roots	root	NOUN
ejpam-4463	132	13	of	of	ADP
ejpam-4463	132	14	h	h	NOUN
ejpam-4463	132	15	,	,	PUNCT
ejpam-4463	132	16	2	2	NUM
ejpam-4463	132	17	≤	≤	NUM
ejpam-4463	133	1	i	i	NOUN
ejpam-4463	134	1	≤	≤	NUM
ejpam-4463	135	1	d	d	NOUN
ejpam-4463	136	1	and	and	CCONJ
ejpam-4463	136	2	w	w	PROPN
ejpam-4463	136	3	=	=	NOUN
ejpam-4463	136	4	w1	w1	NOUN
ejpam-4463	136	5	.	.	PUNCT
ejpam-4463	137	1	because	because	SCONJ
ejpam-4463	137	2	h	h	NOUN
ejpam-4463	137	3	is	be	AUX
ejpam-4463	137	4	a	a	DET
ejpam-4463	137	5	monic	monic	ADJ
ejpam-4463	137	6	polynomial	polynomial	NOUN
ejpam-4463	137	7	,	,	PUNCT
ejpam-4463	137	8	then	then	ADV
ejpam-4463	137	9	,	,	PUNCT
ejpam-4463	137	10	we	we	PRON
ejpam-4463	137	11	have	have	VERB
ejpam-4463	137	12	d∑	d∑	PROPN
ejpam-4463	138	1	k=1	k=1	NOUN
ejpam-4463	138	2	wk	wk	INTJ
ejpam-4463	139	1	i	i	PRON
ejpam-4463	139	2	∈	∈	PROPN
ejpam-4463	139	3	fq[x	fq[x	PROPN
ejpam-4463	139	4	]	]	PUNCT
ejpam-4463	139	5	,	,	PUNCT
ejpam-4463	139	6	for	for	ADP
ejpam-4463	139	7	every	every	DET
ejpam-4463	139	8	k	k	PROPN
ejpam-4463	139	9	∈	∈	PROPN
ejpam-4463	139	10	n	n	CCONJ
ejpam-4463	139	11	,	,	PUNCT
ejpam-4463	139	12	which	which	PRON
ejpam-4463	139	13	implies	imply	VERB
ejpam-4463	139	14	lim	lim	PROPN
ejpam-4463	139	15	m→+∞	m→+∞	PROPN
ejpam-4463	139	16	{	{	PUNCT
ejpam-4463	139	17	wm	wm	PROPN
ejpam-4463	139	18	}	}	PUNCT
ejpam-4463	139	19	=	=	SYM
ejpam-4463	139	20	0	0	X
ejpam-4463	139	21	.	.	PUNCT
ejpam-4463	140	1	let	let	VERB
ejpam-4463	140	2	p	p	NOUN
ejpam-4463	140	3	(	(	PUNCT
ejpam-4463	140	4	y	y	PROPN
ejpam-4463	140	5	)	)	PUNCT
ejpam-4463	141	1	=	=	PUNCT
ejpam-4463	142	1	y	y	PROPN
ejpam-4463	142	2	n	n	PROPN
ejpam-4463	142	3	+	+	ADJ
ejpam-4463	142	4	an−1y	an−1y	PROPN
ejpam-4463	142	5	n−1	n−1	PROPN
ejpam-4463	142	6	+	+	PROPN
ejpam-4463	142	7	·	·	PUNCT
ejpam-4463	142	8	·	·	PUNCT
ejpam-4463	142	9	·	·	PUNCT
ejpam-4463	143	1	+	+	NUM
ejpam-4463	143	2	a0	a0	PROPN
ejpam-4463	143	3	be	be	VERB
ejpam-4463	143	4	the	the	DET
ejpam-4463	143	5	minimal	minimal	ADJ
ejpam-4463	143	6	polynomial	polynomial	NOUN
ejpam-4463	143	7	of	of	ADP
ejpam-4463	143	8	w	w	PROPN
ejpam-4463	143	9	,	,	PUNCT
ejpam-4463	143	10	it	it	PRON
ejpam-4463	143	11	is	be	AUX
ejpam-4463	143	12	obvious	obvious	ADJ
ejpam-4463	143	13	that	that	SCONJ
ejpam-4463	143	14	an−1	an−1	ADV
ejpam-4463	143	15	=	=	SYM
ejpam-4463	143	16	−a	−a	NOUN
ejpam-4463	143	17	,	,	PUNCT
ejpam-4463	143	18	since	since	SCONJ
ejpam-4463	143	19	[	[	X
ejpam-4463	143	20	w	w	X
ejpam-4463	143	21	]	]	X
ejpam-4463	143	22	=	=	PUNCT
ejpam-4463	143	23	a.	a.	NOUN
ejpam-4463	143	24	from	from	ADP
ejpam-4463	143	25	theorem	theorem	NOUN
ejpam-4463	143	26	2	2	NUM
ejpam-4463	143	27	,	,	PUNCT
ejpam-4463	143	28	the	the	DET
ejpam-4463	143	29	polynomial	polynomial	ADJ
ejpam-4463	143	30	p	p	PROPN
ejpam-4463	143	31	satisfies	satisfy	VERB
ejpam-4463	143	32	degan−1	degan−1	NUM
ejpam-4463	143	33	≥	≥	NUM
ejpam-4463	143	34	max	max	NOUN
ejpam-4463	144	1	i	i	PRON
ejpam-4463	144	2	̸=n−1	̸=n−1	VERB
ejpam-4463	144	3	degai	degai	VERB
ejpam-4463	144	4	.	.	PUNCT
ejpam-4463	145	1	let	let	VERB
ejpam-4463	145	2	now	now	ADV
ejpam-4463	145	3	h(y	h(y	ADV
ejpam-4463	145	4	)	)	PUNCT
ejpam-4463	146	1	=	=	SYM
ejpam-4463	146	2	p	p	X
ejpam-4463	146	3	(	(	PUNCT
ejpam-4463	146	4	y	y	NOUN
ejpam-4463	146	5	)	)	PUNCT
ejpam-4463	146	6	q(y	q(y	PROPN
ejpam-4463	146	7	)	)	PUNCT
ejpam-4463	146	8	,	,	PUNCT
ejpam-4463	146	9	with	with	ADP
ejpam-4463	146	10	q(y	q(y	PROPN
ejpam-4463	146	11	)	)	PUNCT
ejpam-4463	147	1	=	=	SYM
ejpam-4463	148	1	y	y	PROPN
ejpam-4463	148	2	m+bm−1y	m+bm−1y	NOUN
ejpam-4463	148	3	m−1	m−1	PROPN
ejpam-4463	148	4	+	+	CCONJ
ejpam-4463	148	5	·	·	PUNCT
ejpam-4463	148	6	·	·	PUNCT
ejpam-4463	148	7	·	·	PUNCT
ejpam-4463	148	8	+	+	NUM
ejpam-4463	148	9	b0	b0	NOUN
ejpam-4463	148	10	.	.	PUNCT
ejpam-4463	148	11	suppose	suppose	VERB
ejpam-4463	148	12	that	that	SCONJ
ejpam-4463	148	13	m	m	PROPN
ejpam-4463	148	14	≥	≥	NUM
ejpam-4463	148	15	1	1	NUM
ejpam-4463	148	16	,	,	PUNCT
ejpam-4463	148	17	then	then	ADV
ejpam-4463	148	18	bm−1	bm−1	PROPN
ejpam-4463	148	19	+	+	PROPN
ejpam-4463	148	20	an−1	an−1	ADJ
ejpam-4463	148	21	=	=	SYM
ejpam-4463	148	22	−a	−a	NOUN
ejpam-4463	148	23	and	and	CCONJ
ejpam-4463	148	24	a0b0	a0b0	NOUN
ejpam-4463	148	25	=	=	SYM
ejpam-4463	148	26	−b	−b	ADJ
ejpam-4463	148	27	(	(	PUNCT
ejpam-4463	148	28	1	1	NUM
ejpam-4463	148	29	)	)	PUNCT
ejpam-4463	148	30	∑	∑	NOUN
ejpam-4463	148	31	i+	i+	NOUN
ejpam-4463	148	32	j	j	PROPN
ejpam-4463	148	33	=	=	SYM
ejpam-4463	148	34	s	s	PART
ejpam-4463	148	35	0	0	NUM
ejpam-4463	148	36	≤	≤	NUM
ejpam-4463	148	37	i	i	PRON
ejpam-4463	148	38	≤	≤	NOUN
ejpam-4463	148	39	n	n	CCONJ
ejpam-4463	148	40	0	0	NUM
ejpam-4463	148	41	≤	≤	NUM
ejpam-4463	148	42	j	j	PROPN
ejpam-4463	148	43	≤	≤	NOUN
ejpam-4463	148	44	m	m	AUX
ejpam-4463	148	45	aibj	aibj	NOUN
ejpam-4463	149	1	=	=	PUNCT
ejpam-4463	149	2	0	0	NUM
ejpam-4463	149	3	;	;	PUNCT
ejpam-4463	149	4	s	s	X
ejpam-4463	149	5	∈	∈	NOUN
ejpam-4463	149	6	{	{	PUNCT
ejpam-4463	149	7	1	1	NUM
ejpam-4463	149	8	,	,	PUNCT
ejpam-4463	149	9	2	2	NUM
ejpam-4463	149	10	,	,	PUNCT
ejpam-4463	149	11	·	·	PUNCT
ejpam-4463	149	12	·	·	PUNCT
ejpam-4463	149	13	·	·	PUNCT
ejpam-4463	149	14	,	,	PUNCT
ejpam-4463	149	15	d−	d−	PROPN
ejpam-4463	149	16	2	2	NUM
ejpam-4463	149	17	}	}	PUNCT
ejpam-4463	149	18	.	.	PUNCT
ejpam-4463	150	1	(	(	PUNCT
ejpam-4463	150	2	2	2	X
ejpam-4463	150	3	)	)	PUNCT
ejpam-4463	150	4	since	since	SCONJ
ejpam-4463	150	5	an−1	an−1	PROPN
ejpam-4463	150	6	=	=	SYM
ejpam-4463	150	7	−a	−a	NOUN
ejpam-4463	150	8	,	,	PUNCT
ejpam-4463	150	9	then	then	ADV
ejpam-4463	150	10	from	from	ADP
ejpam-4463	150	11	(	(	PUNCT
ejpam-4463	150	12	1	1	NUM
ejpam-4463	150	13	)	)	PUNCT
ejpam-4463	150	14	bm−1	bm−1	NOUN
ejpam-4463	150	15	=	=	SYM
ejpam-4463	150	16	0	0	X
ejpam-4463	150	17	.	.	PUNCT
ejpam-4463	151	1	let	let	VERB
ejpam-4463	151	2	i0	i0	PROPN
ejpam-4463	151	3	∈	∈	PROPN
ejpam-4463	151	4	{	{	PUNCT
ejpam-4463	151	5	0	0	NUM
ejpam-4463	151	6	,	,	PUNCT
ejpam-4463	151	7	1	1	NUM
ejpam-4463	151	8	,	,	PUNCT
ejpam-4463	151	9	·	·	PUNCT
ejpam-4463	151	10	·	·	PUNCT
ejpam-4463	151	11	·	·	PUNCT
ejpam-4463	151	12	,	,	PUNCT
ejpam-4463	151	13	m	m	VERB
ejpam-4463	151	14	}	}	PUNCT
ejpam-4463	151	15	such	such	ADJ
ejpam-4463	151	16	that	that	SCONJ
ejpam-4463	151	17	degbi0	degbi0	NOUN
ejpam-4463	152	1	=	=	PUNCT
ejpam-4463	152	2	max	max	PROPN
ejpam-4463	152	3	0≤i≤m	0≤i≤m	NUM
ejpam-4463	152	4	degbi	degbi	PROPN
ejpam-4463	152	5	.	.	PUNCT
ejpam-4463	153	1	o.	o.	PROPN
ejpam-4463	153	2	dammak	dammak	PROPN
ejpam-4463	153	3	,	,	PUNCT
ejpam-4463	153	4	s.	s.	PROPN
ejpam-4463	153	5	mansour	mansour	PROPN
ejpam-4463	153	6	/	/	SYM
ejpam-4463	153	7	eur	eur	PROPN
ejpam-4463	153	8	.	.	PUNCT
ejpam-4463	154	1	j.	j.	PROPN
ejpam-4463	154	2	pure	pure	PROPN
ejpam-4463	154	3	appl	appl	PROPN
ejpam-4463	154	4	.	.	PROPN
ejpam-4463	154	5	math	math	PROPN
ejpam-4463	154	6	,	,	PUNCT
ejpam-4463	154	7	15	15	NUM
ejpam-4463	154	8	(	(	PUNCT
ejpam-4463	154	9	3	3	NUM
ejpam-4463	154	10	)	)	PUNCT
ejpam-4463	154	11	(	(	PUNCT
ejpam-4463	154	12	2022	2022	NUM
ejpam-4463	154	13	)	)	PUNCT
ejpam-4463	154	14	,	,	PUNCT
ejpam-4463	154	15	1321	1321	NUM
ejpam-4463	154	16	-	-	SYM
ejpam-4463	154	17	1330	1330	NUM
ejpam-4463	154	18	1326	1326	NUM
ejpam-4463	154	19	if	if	SCONJ
ejpam-4463	154	20	bi0	bi0	VERB
ejpam-4463	154	21	̸=	̸=	PROPN
ejpam-4463	154	22	0	0	NUM
ejpam-4463	154	23	,	,	PUNCT
ejpam-4463	154	24	then	then	ADV
ejpam-4463	154	25	deg(an−1bi0	deg(an−1bi0	PROPN
ejpam-4463	154	26	)	)	PUNCT
ejpam-4463	154	27	>	>	PUNCT
ejpam-4463	154	28	deg(aibj	deg(aibj	X
ejpam-4463	154	29	)	)	PUNCT
ejpam-4463	154	30	,	,	PUNCT
ejpam-4463	154	31	(	(	PUNCT
ejpam-4463	154	32	i	i	PROPN
ejpam-4463	154	33	,	,	PUNCT
ejpam-4463	154	34	j	j	PROPN
ejpam-4463	154	35	)	)	PUNCT
ejpam-4463	154	36	̸=	̸=	PROPN
ejpam-4463	154	37	(	(	PUNCT
ejpam-4463	154	38	n−	n−	NOUN
ejpam-4463	154	39	1	1	NUM
ejpam-4463	154	40	,	,	PUNCT
ejpam-4463	154	41	i0	i0	PROPN
ejpam-4463	154	42	)	)	PUNCT
ejpam-4463	154	43	.	.	PUNCT
ejpam-4463	155	1	consequently	consequently	ADV
ejpam-4463	155	2	deg	deg	VERB
ejpam-4463	155	3			PROPN
ejpam-4463	155	4	∑	∑	PROPN
ejpam-4463	155	5	i+	i+	PROPN
ejpam-4463	155	6	j	j	PROPN
ejpam-4463	155	7	=	=	PUNCT
ejpam-4463	155	8	n+	n+	PUNCT
ejpam-4463	155	9	i0	i0	PROPN
ejpam-4463	155	10	−	−	PROPN
ejpam-4463	156	1	1	1	NUM
ejpam-4463	156	2	0	0	NUM
ejpam-4463	156	3	≤	≤	NUM
ejpam-4463	156	4	i	i	PRON
ejpam-4463	156	5	≤	≤	NOUN
ejpam-4463	156	6	n	n	CCONJ
ejpam-4463	156	7	0	0	NUM
ejpam-4463	156	8	≤	≤	NUM
ejpam-4463	157	1	j	j	PROPN
ejpam-4463	158	1	≤	≤	NOUN
ejpam-4463	158	2	m	m	AUX
ejpam-4463	158	3	aibj	aibj	NOUN
ejpam-4463	158	4			PUNCT
ejpam-4463	159	1	=	=	SYM
ejpam-4463	159	2	deg(an−1bi0	deg(an−1bi0	PROPN
ejpam-4463	159	3	)	)	PUNCT
ejpam-4463	159	4	,	,	PUNCT
ejpam-4463	159	5	there	there	PRON
ejpam-4463	159	6	is	be	VERB
ejpam-4463	159	7	a	a	DET
ejpam-4463	159	8	contradiction	contradiction	NOUN
ejpam-4463	159	9	with	with	ADP
ejpam-4463	159	10	(	(	PUNCT
ejpam-4463	159	11	2	2	NUM
ejpam-4463	159	12	)	)	PUNCT
ejpam-4463	159	13	.	.	PUNCT
ejpam-4463	160	1	finally	finally	ADV
ejpam-4463	160	2	,	,	PUNCT
ejpam-4463	160	3	we	we	PRON
ejpam-4463	160	4	arrive	arrive	VERB
ejpam-4463	160	5	to	to	ADP
ejpam-4463	160	6	h(y	h(y	PROPN
ejpam-4463	160	7	)	)	PUNCT
ejpam-4463	161	1	=	=	PUNCT
ejpam-4463	161	2	y	y	PROPN
ejpam-4463	161	3	mp	mp	PROPN
ejpam-4463	161	4	(	(	PUNCT
ejpam-4463	161	5	y	y	PROPN
ejpam-4463	161	6	)	)	PUNCT
ejpam-4463	161	7	,	,	PUNCT
ejpam-4463	161	8	if	if	SCONJ
ejpam-4463	161	9	m	m	PROPN
ejpam-4463	161	10	≥	≥	NOUN
ejpam-4463	161	11	1	1	NUM
ejpam-4463	161	12	,	,	PUNCT
ejpam-4463	161	13	which	which	PRON
ejpam-4463	161	14	leads	lead	VERB
ejpam-4463	161	15	to	to	ADP
ejpam-4463	161	16	a	a	DET
ejpam-4463	161	17	contradiction	contradiction	NOUN
ejpam-4463	161	18	(	(	PUNCT
ejpam-4463	161	19	due	due	ADP
ejpam-4463	161	20	to	to	ADP
ejpam-4463	161	21	the	the	DET
ejpam-4463	161	22	fact	fact	NOUN
ejpam-4463	161	23	that	that	SCONJ
ejpam-4463	161	24	b	b	X
ejpam-4463	161	25	̸=	̸=	PROPN
ejpam-4463	161	26	0	0	NUM
ejpam-4463	161	27	)	)	PUNCT
ejpam-4463	161	28	and	and	CCONJ
ejpam-4463	161	29	arising	arise	VERB
ejpam-4463	161	30	h(y	h(y	ADV
ejpam-4463	161	31	)	)	PUNCT
ejpam-4463	161	32	=	=	SYM
ejpam-4463	162	1	p	p	X
ejpam-4463	162	2	(	(	PUNCT
ejpam-4463	162	3	y	y	PROPN
ejpam-4463	162	4	)	)	PUNCT
ejpam-4463	162	5	.	.	PUNCT
ejpam-4463	163	1	proof	proof	NOUN
ejpam-4463	163	2	.	.	PUNCT
ejpam-4463	164	1	of	of	ADP
ejpam-4463	164	2	theorem	theorem	NOUN
ejpam-4463	164	3	3	3	X
ejpam-4463	164	4	.	.	PUNCT
ejpam-4463	164	5	consider	consider	VERB
ejpam-4463	164	6	the	the	DET
ejpam-4463	164	7	polynomial	polynomial	ADJ
ejpam-4463	164	8	pn(y	pn(y	NOUN
ejpam-4463	164	9	)	)	PUNCT
ejpam-4463	165	1	=	=	SYM
ejpam-4463	165	2	y	y	PROPN
ejpam-4463	165	3	n−axy	n−axy	NOUN
ejpam-4463	165	4	n−1−ay	n−1−ay	PROPN
ejpam-4463	165	5	+	+	PROPN
ejpam-4463	165	6	ax−a	ax−a	PROPN
ejpam-4463	165	7	,	,	PUNCT
ejpam-4463	165	8	such	such	ADJ
ejpam-4463	165	9	that	that	SCONJ
ejpam-4463	165	10	a	a	PRON
ejpam-4463	165	11	is	be	AUX
ejpam-4463	165	12	the	the	DET
ejpam-4463	165	13	least	least	ADJ
ejpam-4463	165	14	element	element	NOUN
ejpam-4463	165	15	of	of	ADP
ejpam-4463	165	16	fq\{0	fq\{0	NOUN
ejpam-4463	165	17	}	}	PUNCT
ejpam-4463	165	18	,	,	PUNCT
ejpam-4463	165	19	.	.	PUNCT
ejpam-4463	166	1	it	it	PRON
ejpam-4463	166	2	follows	follow	VERB
ejpam-4463	166	3	from	from	ADP
ejpam-4463	166	4	lemma	lemma	PROPN
ejpam-4463	166	5	2	2	NUM
ejpam-4463	166	6	that	that	PRON
ejpam-4463	166	7	p	p	NOUN
ejpam-4463	166	8	is	be	AUX
ejpam-4463	166	9	irreducible	irreducible	ADJ
ejpam-4463	166	10	.	.	PUNCT
ejpam-4463	167	1	moreover	moreover	ADV
ejpam-4463	167	2	,	,	PUNCT
ejpam-4463	167	3	p	p	PROPN
ejpam-4463	167	4	has	have	VERB
ejpam-4463	167	5	exactly	exactly	ADV
ejpam-4463	167	6	one	one	NUM
ejpam-4463	167	7	root	root	NOUN
ejpam-4463	167	8	wn	wn	NOUN
ejpam-4463	167	9	satisfying	satisfy	VERB
ejpam-4463	167	10	|	|	ADV
ejpam-4463	167	11	wn	wn	NOUN
ejpam-4463	167	12	|	|	ADV
ejpam-4463	167	13	>	>	X
ejpam-4463	167	14	1	1	NUM
ejpam-4463	168	1	and	and	CCONJ
ejpam-4463	168	2	[	[	X
ejpam-4463	168	3	wn	wn	X
ejpam-4463	168	4	]	]	X
ejpam-4463	168	5	=	=	SYM
ejpam-4463	168	6	ax	ax	NOUN
ejpam-4463	168	7	,	,	PUNCT
ejpam-4463	168	8	all	all	PRON
ejpam-4463	168	9	of	of	ADP
ejpam-4463	168	10	whose	whose	DET
ejpam-4463	168	11	other	other	ADJ
ejpam-4463	168	12	conjugates	conjugate	NOUN
ejpam-4463	168	13	wi	wi	PROPN
ejpam-4463	168	14	satisfy	satisfy	VERB
ejpam-4463	168	15	|	|	ADV
ejpam-4463	168	16	wi	wi	PROPN
ejpam-4463	168	17	|≤	|≤	PROPN
ejpam-4463	168	18	1	1	NUM
ejpam-4463	168	19	with	with	ADP
ejpam-4463	168	20	at	at	ADV
ejpam-4463	168	21	least	least	ADV
ejpam-4463	168	22	one	one	NUM
ejpam-4463	168	23	case	case	NOUN
ejpam-4463	168	24	of	of	ADP
ejpam-4463	168	25	equality	equality	NOUN
ejpam-4463	168	26	.	.	PUNCT
ejpam-4463	169	1	because	because	SCONJ
ejpam-4463	169	2	p	p	NOUN
ejpam-4463	169	3	is	be	AUX
ejpam-4463	169	4	a	a	DET
ejpam-4463	169	5	monic	monic	ADJ
ejpam-4463	169	6	polynomial	polynomial	NOUN
ejpam-4463	169	7	,	,	PUNCT
ejpam-4463	169	8	wn	wn	PROPN
ejpam-4463	169	9	is	be	AUX
ejpam-4463	169	10	a	a	DET
ejpam-4463	169	11	salem	salem	NOUN
ejpam-4463	169	12	element	element	NOUN
ejpam-4463	169	13	of	of	ADP
ejpam-4463	169	14	degree	degree	NOUN
ejpam-4463	169	15	n.	n.	NOUN
ejpam-4463	169	16	additionally	additionally	ADV
ejpam-4463	169	17	,	,	PUNCT
ejpam-4463	169	18	if	if	SCONJ
ejpam-4463	169	19	wn	wn	PROPN
ejpam-4463	169	20	=	=	NOUN
ejpam-4463	169	21	ax	ax	NOUN
ejpam-4463	169	22	+	+	CCONJ
ejpam-4463	169	23	1	1	NUM
ejpam-4463	169	24	h	h	NOUN
ejpam-4463	169	25	,	,	PUNCT
ejpam-4463	169	26	then	then	ADV
ejpam-4463	169	27	h	h	NOUN
ejpam-4463	169	28	is	be	AUX
ejpam-4463	169	29	an	an	DET
ejpam-4463	169	30	algebraic	algebraic	ADJ
ejpam-4463	169	31	formal	formal	ADJ
ejpam-4463	169	32	power	power	NOUN
ejpam-4463	169	33	series	series	NOUN
ejpam-4463	169	34	satisfying	satisfy	VERB
ejpam-4463	169	35	anhn	anhn	PROPN
ejpam-4463	169	36	−	−	PROPN
ejpam-4463	170	1	(	(	PUNCT
ejpam-4463	170	2	ax)n−1hn−1	ax)n−1hn−1	PROPN
ejpam-4463	170	3	−	−	PROPN
ejpam-4463	170	4	n−2∑	n−2∑	NUM
ejpam-4463	170	5	k=0	k=0	PROPN
ejpam-4463	171	1	(	(	PUNCT
ejpam-4463	171	2	n−	n−	NOUN
ejpam-4463	171	3	1	1	NUM
ejpam-4463	171	4	k	k	NOUN
ejpam-4463	171	5	)	)	PUNCT
ejpam-4463	171	6	(	(	PUNCT
ejpam-4463	171	7	ax)khk	ax)khk	X
ejpam-4463	171	8	=	=	SYM
ejpam-4463	171	9	0	0	PUNCT
ejpam-4463	171	10	and	and	CCONJ
ejpam-4463	171	11	using	use	VERB
ejpam-4463	171	12	lemma	lemma	PROPN
ejpam-4463	171	13	1	1	NUM
ejpam-4463	171	14	,	,	PUNCT
ejpam-4463	171	15	we	we	PRON
ejpam-4463	171	16	have	have	VERB
ejpam-4463	171	17	[	[	X
ejpam-4463	171	18	h	h	X
ejpam-4463	171	19	]	]	X
ejpam-4463	171	20	=	=	PUNCT
ejpam-4463	171	21	xn−1	xn−1	PROPN
ejpam-4463	171	22	a	a	X
ejpam-4463	171	23	.	.	PUNCT
ejpam-4463	172	1	(	(	PUNCT
ejpam-4463	172	2	3	3	X
ejpam-4463	172	3	)	)	PUNCT
ejpam-4463	172	4	now	now	ADV
ejpam-4463	172	5	,	,	PUNCT
ejpam-4463	172	6	we	we	PRON
ejpam-4463	172	7	consider	consider	VERB
ejpam-4463	172	8	an	an	DET
ejpam-4463	172	9	other	other	ADJ
ejpam-4463	172	10	salem	salem	NOUN
ejpam-4463	172	11	element	element	NOUN
ejpam-4463	172	12	vn	vn	PROPN
ejpam-4463	172	13	̸=	̸=	PROPN
ejpam-4463	172	14	wn	wn	PROPN
ejpam-4463	172	15	of	of	ADP
ejpam-4463	172	16	degree	degree	NOUN
ejpam-4463	172	17	n	n	PRON
ejpam-4463	172	18	such	such	ADJ
ejpam-4463	172	19	that	that	SCONJ
ejpam-4463	173	1	[	[	X
ejpam-4463	173	2	vn	vn	X
ejpam-4463	173	3	]	]	X
ejpam-4463	173	4	=	=	SYM
ejpam-4463	173	5	ax	ax	NOUN
ejpam-4463	173	6	,	,	PUNCT
ejpam-4463	173	7	then	then	ADV
ejpam-4463	173	8	from	from	ADP
ejpam-4463	173	9	theorem	theorem	NOUN
ejpam-4463	173	10	2	2	NUM
ejpam-4463	173	11	the	the	DET
ejpam-4463	173	12	minimal	minimal	ADJ
ejpam-4463	173	13	polynomial	polynomial	NOUN
ejpam-4463	173	14	of	of	ADP
ejpam-4463	173	15	vn	vn	PROPN
ejpam-4463	173	16	can	can	AUX
ejpam-4463	173	17	be	be	AUX
ejpam-4463	173	18	written	write	VERB
ejpam-4463	173	19	as	as	ADP
ejpam-4463	173	20	f	f	PROPN
ejpam-4463	173	21	(	(	PUNCT
ejpam-4463	173	22	y	y	PROPN
ejpam-4463	173	23	)	)	PUNCT
ejpam-4463	174	1	=	=	SYM
ejpam-4463	174	2	y	y	PROPN
ejpam-4463	174	3	n	n	CCONJ
ejpam-4463	174	4	−	−	PROPN
ejpam-4463	174	5	axy	axy	PROPN
ejpam-4463	174	6	n−1−	n−1−	PROPN
ejpam-4463	174	7	n−2∑	n−2∑	NUM
ejpam-4463	174	8	i=0	i=0	PROPN
ejpam-4463	174	9	aiy	aiy	NOUN
ejpam-4463	175	1	i	i	PRON
ejpam-4463	175	2	where	where	SCONJ
ejpam-4463	175	3	degai	degai	VERB
ejpam-4463	175	4	≤	≤	NOUN
ejpam-4463	175	5	1	1	NUM
ejpam-4463	175	6	,	,	PUNCT
ejpam-4463	175	7	with	with	ADP
ejpam-4463	175	8	at	at	ADV
ejpam-4463	175	9	least	least	ADV
ejpam-4463	175	10	one	one	NUM
ejpam-4463	175	11	case	case	NOUN
ejpam-4463	175	12	of	of	ADP
ejpam-4463	175	13	equality	equality	NOUN
ejpam-4463	175	14	.	.	PUNCT
ejpam-4463	176	1	let	let	VERB
ejpam-4463	176	2	vn	vn	VERB
ejpam-4463	176	3	=	=	PUNCT
ejpam-4463	176	4	ax+	ax+	NOUN
ejpam-4463	176	5	1	1	NUM
ejpam-4463	176	6	g	g	NOUN
ejpam-4463	176	7	,	,	PUNCT
ejpam-4463	176	8	then	then	ADV
ejpam-4463	176	9	f	f	X
ejpam-4463	176	10	(	(	PUNCT
ejpam-4463	176	11	ax	ax	NOUN
ejpam-4463	176	12	+	+	NOUN
ejpam-4463	176	13	1	1	NUM
ejpam-4463	176	14	g	g	NOUN
ejpam-4463	176	15	)	)	PUNCT
ejpam-4463	177	1	=	=	SYM
ejpam-4463	177	2	(	(	PUNCT
ejpam-4463	177	3	ax	ax	NOUN
ejpam-4463	177	4	+	+	NOUN
ejpam-4463	177	5	1	1	NUM
ejpam-4463	177	6	g	g	NOUN
ejpam-4463	177	7	)	)	PUNCT
ejpam-4463	177	8	n	n	NOUN
ejpam-4463	177	9	−	−	PROPN
ejpam-4463	178	1	(	(	PUNCT
ejpam-4463	178	2	ax	ax	NOUN
ejpam-4463	178	3	+	+	NOUN
ejpam-4463	178	4	1	1	NUM
ejpam-4463	178	5	g	g	NOUN
ejpam-4463	178	6	)	)	PUNCT
ejpam-4463	178	7	n−1	n−1	PROPN
ejpam-4463	178	8	−	−	PROPN
ejpam-4463	178	9	n−2∑	n−2∑	NUM
ejpam-4463	178	10	j=0	j=0	PROPN
ejpam-4463	178	11	aj	aj	PROPN
ejpam-4463	178	12	(	(	PUNCT
ejpam-4463	178	13	ax	ax	X
ejpam-4463	178	14	+	+	NOUN
ejpam-4463	178	15	1	1	NUM
ejpam-4463	178	16	g	g	NOUN
ejpam-4463	178	17	)	)	PUNCT
ejpam-4463	178	18	j	j	PROPN
ejpam-4463	179	1	=	=	SYM
ejpam-4463	179	2	n∑	n∑	PROPN
ejpam-4463	179	3	j=0	j=0	PROPN
ejpam-4463	179	4	aj	aj	PROPN
ejpam-4463	179	5	j∑	j∑	PROPN
ejpam-4463	179	6	k=0	k=0	PROPN
ejpam-4463	179	7	(	(	PUNCT
ejpam-4463	179	8	j	j	PROPN
ejpam-4463	179	9	k	k	PROPN
ejpam-4463	179	10	)	)	PUNCT
ejpam-4463	179	11	(	(	PUNCT
ejpam-4463	179	12	ax)j−kg−k	ax)j−kg−k	PUNCT
ejpam-4463	179	13	;	;	PUNCT
ejpam-4463	179	14	an	an	DET
ejpam-4463	179	15	=	=	NOUN
ejpam-4463	179	16	1	1	NUM
ejpam-4463	179	17	,	,	PUNCT
ejpam-4463	179	18	an−1	an−1	ADJ
ejpam-4463	179	19	=	=	NOUN
ejpam-4463	179	20	ax	ax	NOUN
ejpam-4463	179	21	=	=	PUNCT
ejpam-4463	179	22	n∑	n∑	NOUN
ejpam-4463	179	23	k=0	k=0	PROPN
ejpam-4463	179	24			PROPN
ejpam-4463	179	25	n∑	n∑	PROPN
ejpam-4463	179	26	j	j	PROPN
ejpam-4463	180	1	=	=	NOUN
ejpam-4463	180	2	n−k	n−k	NOUN
ejpam-4463	180	3	aj	aj	PROPN
ejpam-4463	180	4	(	(	PUNCT
ejpam-4463	180	5	j	j	PROPN
ejpam-4463	180	6	n−	n−	PROPN
ejpam-4463	180	7	k	k	PROPN
ejpam-4463	180	8	)	)	PUNCT
ejpam-4463	180	9	(	(	PUNCT
ejpam-4463	180	10	ax)j+k−n	ax)j+k−n	X
ejpam-4463	180	11			PROPN
ejpam-4463	180	12	gk	gk	NOUN
ejpam-4463	180	13	=	=	NOUN
ejpam-4463	180	14	0	0	PROPN
ejpam-4463	180	15	.	.	PUNCT
ejpam-4463	181	1	o.	o.	PROPN
ejpam-4463	181	2	dammak	dammak	PROPN
ejpam-4463	181	3	,	,	PUNCT
ejpam-4463	181	4	s.	s.	PROPN
ejpam-4463	181	5	mansour	mansour	PROPN
ejpam-4463	181	6	/	/	SYM
ejpam-4463	181	7	eur	eur	PROPN
ejpam-4463	181	8	.	.	PUNCT
ejpam-4463	182	1	j.	j.	PROPN
ejpam-4463	182	2	pure	pure	PROPN
ejpam-4463	182	3	appl	appl	PROPN
ejpam-4463	182	4	.	.	PROPN
ejpam-4463	182	5	math	math	PROPN
ejpam-4463	182	6	,	,	PUNCT
ejpam-4463	182	7	15	15	NUM
ejpam-4463	182	8	(	(	PUNCT
ejpam-4463	182	9	3	3	NUM
ejpam-4463	182	10	)	)	PUNCT
ejpam-4463	182	11	(	(	PUNCT
ejpam-4463	182	12	2022	2022	NUM
ejpam-4463	182	13	)	)	PUNCT
ejpam-4463	182	14	,	,	PUNCT
ejpam-4463	182	15	1321	1321	NUM
ejpam-4463	182	16	-	-	SYM
ejpam-4463	182	17	1330	1330	NUM
ejpam-4463	182	18	1327	1327	NUM
ejpam-4463	182	19	let	let	VERB
ejpam-4463	182	20	bk	bk	VERB
ejpam-4463	182	21	=	=	PUNCT
ejpam-4463	182	22	n∑	n∑	PROPN
ejpam-4463	182	23	j	j	PROPN
ejpam-4463	183	1	=	=	NOUN
ejpam-4463	183	2	n−k	n−k	NOUN
ejpam-4463	183	3	aj	aj	PROPN
ejpam-4463	183	4	(	(	PUNCT
ejpam-4463	183	5	j	j	PROPN
ejpam-4463	183	6	n−	n−	PROPN
ejpam-4463	183	7	k	k	PROPN
ejpam-4463	183	8	)	)	PUNCT
ejpam-4463	183	9	(	(	PUNCT
ejpam-4463	183	10	ax)j+k−n	ax)j+k−n	NOUN
ejpam-4463	183	11	.	.	PROPN
ejpam-4463	183	12	(	(	PUNCT
ejpam-4463	183	13	4	4	NUM
ejpam-4463	183	14	)	)	PUNCT
ejpam-4463	183	15	then	then	ADV
ejpam-4463	183	16	n∑	n∑	PROPN
ejpam-4463	183	17	k=0	k=0	PROPN
ejpam-4463	183	18	bkg	bkg	PROPN
ejpam-4463	183	19	k	k	X
ejpam-4463	183	20	=	=	PUNCT
ejpam-4463	183	21	0	0	X
ejpam-4463	183	22	.	.	PUNCT
ejpam-4463	184	1	we	we	PRON
ejpam-4463	184	2	have	have	VERB
ejpam-4463	184	3	,	,	PUNCT
ejpam-4463	184	4	by	by	ADP
ejpam-4463	184	5	using	use	VERB
ejpam-4463	184	6	lemma	lemma	PROPN
ejpam-4463	184	7	1	1	NUM
ejpam-4463	184	8	and	and	CCONJ
ejpam-4463	184	9	the	the	DET
ejpam-4463	184	10	equation	equation	NOUN
ejpam-4463	184	11	(	(	PUNCT
ejpam-4463	184	12	4	4	NUM
ejpam-4463	184	13	)	)	PUNCT
ejpam-4463	185	1	[	[	X
ejpam-4463	185	2	g	g	X
ejpam-4463	185	3	]	]	X
ejpam-4463	185	4	=	=	SYM
ejpam-4463	185	5			NOUN
ejpam-4463	185	6	(	(	PUNCT
ejpam-4463	185	7	ax)n−1	ax)n−1	PROPN
ejpam-4463	185	8	−	−	NUM
ejpam-4463	185	9	n−2∑	n−2∑	NUM
ejpam-4463	185	10	i=1	i=1	PROPN
ejpam-4463	185	11	iai(ax)i−1	iai(ax)i−1	PROPN
ejpam-4463	185	12	n−2∑	n−2∑	PROPN
ejpam-4463	185	13	i=0	i=0	PROPN
ejpam-4463	185	14	ai(ax)i	ai(ax)i	X
ejpam-4463	185	15			NOUN
ejpam-4463	185	16	,	,	PUNCT
ejpam-4463	185	17	•	•	ADP
ejpam-4463	185	18	if	if	SCONJ
ejpam-4463	185	19	(	(	PUNCT
ejpam-4463	185	20	a1	a1	NOUN
ejpam-4463	185	21	,	,	PUNCT
ejpam-4463	185	22	.	.	PUNCT
ejpam-4463	185	23	.	.	PUNCT
ejpam-4463	186	1	.	.	PUNCT
ejpam-4463	187	1	,	,	PUNCT
ejpam-4463	187	2	an−2	an−2	PROPN
ejpam-4463	187	3	)	)	PUNCT
ejpam-4463	187	4	̸=	̸=	PROPN
ejpam-4463	187	5	(	(	PUNCT
ejpam-4463	187	6	0	0	NUM
ejpam-4463	187	7	,	,	PUNCT
ejpam-4463	187	8	.	.	PUNCT
ejpam-4463	187	9	.	.	PUNCT
ejpam-4463	188	1	.	.	PUNCT
ejpam-4463	189	1	,	,	PUNCT
ejpam-4463	189	2	0	0	NUM
ejpam-4463	189	3	)	)	PUNCT
ejpam-4463	189	4	,	,	PUNCT
ejpam-4463	189	5	we	we	PRON
ejpam-4463	189	6	have	have	AUX
ejpam-4463	189	7	deg[g	deg[g	VERB
ejpam-4463	189	8	]	]	PUNCT
ejpam-4463	189	9	<	<	X
ejpam-4463	190	1	n−	n−	NOUN
ejpam-4463	190	2	1	1	NUM
ejpam-4463	190	3	=	=	SYM
ejpam-4463	190	4	deg[h	deg[h	PROPN
ejpam-4463	190	5	]	]	PUNCT
ejpam-4463	190	6	then	then	ADV
ejpam-4463	190	7	1	1	NUM
ejpam-4463	190	8	h	h	NOUN
ejpam-4463	190	9	⪯	⪯	NOUN
ejpam-4463	190	10	1	1	NUM
ejpam-4463	190	11	g	g	NOUN
ejpam-4463	190	12	,	,	PUNCT
ejpam-4463	190	13	•	•	INTJ
ejpam-4463	190	14	if	if	SCONJ
ejpam-4463	190	15	(	(	PUNCT
ejpam-4463	190	16	a1	a1	NOUN
ejpam-4463	190	17	,	,	PUNCT
ejpam-4463	190	18	.	.	PUNCT
ejpam-4463	190	19	.	.	PUNCT
ejpam-4463	191	1	.	.	PUNCT
ejpam-4463	192	1	,	,	PUNCT
ejpam-4463	192	2	an−2	an−2	PROPN
ejpam-4463	192	3	)	)	PUNCT
ejpam-4463	192	4	=	=	PUNCT
ejpam-4463	192	5	(	(	PUNCT
ejpam-4463	192	6	0	0	NUM
ejpam-4463	192	7	,	,	PUNCT
ejpam-4463	192	8	.	.	PUNCT
ejpam-4463	192	9	.	.	PUNCT
ejpam-4463	193	1	.	.	PUNCT
ejpam-4463	194	1	,	,	PUNCT
ejpam-4463	194	2	0	0	NUM
ejpam-4463	194	3	)	)	PUNCT
ejpam-4463	194	4	,	,	PUNCT
ejpam-4463	194	5	we	we	PRON
ejpam-4463	194	6	have	have	VERB
ejpam-4463	194	7	[	[	X
ejpam-4463	194	8	g	g	X
ejpam-4463	194	9	]	]	X
ejpam-4463	194	10	=	=	PUNCT
ejpam-4463	194	11	an−1	an−1	PROPN
ejpam-4463	194	12	a0	a0	NOUN
ejpam-4463	194	13	xn−1	xn−1	PROPN
ejpam-4463	194	14	and	and	CCONJ
ejpam-4463	194	15	from	from	ADP
ejpam-4463	194	16	(	(	PUNCT
ejpam-4463	194	17	3	3	NUM
ejpam-4463	194	18	)	)	PUNCT
ejpam-4463	194	19	,	,	PUNCT
ejpam-4463	194	20	we	we	PRON
ejpam-4463	194	21	obtain	obtain	VERB
ejpam-4463	194	22	1	1	NUM
ejpam-4463	194	23	h	h	NOUN
ejpam-4463	194	24	=	=	SYM
ejpam-4463	194	25	ax−(n−1	ax−(n−1	NOUN
ejpam-4463	194	26	)	)	PUNCT
ejpam-4463	194	27	+	+	CCONJ
ejpam-4463	194	28	·	·	PUNCT
ejpam-4463	194	29	·	·	PUNCT
ejpam-4463	194	30	·	·	PUNCT
ejpam-4463	195	1	⪯	⪯	PROPN
ejpam-4463	195	2	a0	a0	PROPN
ejpam-4463	195	3	an−1x	an−1x	PROPN
ejpam-4463	195	4	−(n−1	−(n−1	PROPN
ejpam-4463	195	5	)	)	PUNCT
ejpam-4463	195	6	+	+	CCONJ
ejpam-4463	195	7	·	·	PUNCT
ejpam-4463	195	8	·	·	PUNCT
ejpam-4463	195	9	·	·	PUNCT
ejpam-4463	196	1	=	=	SYM
ejpam-4463	196	2	1	1	NUM
ejpam-4463	196	3	g	g	NOUN
ejpam-4463	196	4	(	(	PUNCT
ejpam-4463	196	5	a0	a0	PROPN
ejpam-4463	196	6	̸=	̸=	PROPN
ejpam-4463	196	7	an	an	DET
ejpam-4463	196	8	if	if	SCONJ
ejpam-4463	196	9	not	not	PART
ejpam-4463	196	10	vn	vn	NOUN
ejpam-4463	196	11	is	be	AUX
ejpam-4463	196	12	not	not	PART
ejpam-4463	196	13	a	a	DET
ejpam-4463	196	14	salem	salem	NOUN
ejpam-4463	196	15	element	element	NOUN
ejpam-4463	196	16	.	.	PUNCT
ejpam-4463	197	1	hence	hence	ADV
ejpam-4463	197	2	,	,	PUNCT
ejpam-4463	197	3	we	we	PRON
ejpam-4463	197	4	get	get	VERB
ejpam-4463	197	5	in	in	ADP
ejpam-4463	197	6	the	the	DET
ejpam-4463	197	7	two	two	NUM
ejpam-4463	197	8	cases	case	NOUN
ejpam-4463	197	9	1	1	NUM
ejpam-4463	197	10	h	h	NOUN
ejpam-4463	197	11	⪯	⪯	NOUN
ejpam-4463	197	12	1	1	NUM
ejpam-4463	197	13	g	g	NOUN
ejpam-4463	197	14	,	,	PUNCT
ejpam-4463	197	15	which	which	PRON
ejpam-4463	197	16	implies	imply	VERB
ejpam-4463	197	17	that	that	SCONJ
ejpam-4463	197	18	wn	wn	PROPN
ejpam-4463	197	19	⪯	⪯	PROPN
ejpam-4463	197	20	fn	fn	PROPN
ejpam-4463	197	21	,	,	PUNCT
ejpam-4463	197	22	and	and	CCONJ
ejpam-4463	197	23	consequently	consequently	ADV
ejpam-4463	197	24	wn	wn	PROPN
ejpam-4463	197	25	is	be	AUX
ejpam-4463	197	26	the	the	DET
ejpam-4463	197	27	(	(	PUNCT
ejpam-4463	197	28	sse	sse	NOUN
ejpam-4463	197	29	)	)	PUNCT
ejpam-4463	197	30	of	of	ADP
ejpam-4463	197	31	degree	degree	NOUN
ejpam-4463	197	32	n.	n.	NOUN
ejpam-4463	197	33	since	since	SCONJ
ejpam-4463	197	34	wn	wn	PROPN
ejpam-4463	197	35	=	=	NOUN
ejpam-4463	197	36	ax	ax	NOUN
ejpam-4463	197	37	+	+	CCONJ
ejpam-4463	197	38	1	1	NUM
ejpam-4463	197	39	h	h	NOUN
ejpam-4463	197	40	,	,	PUNCT
ejpam-4463	197	41	then	then	ADV
ejpam-4463	197	42	from	from	ADP
ejpam-4463	197	43	(	(	PUNCT
ejpam-4463	197	44	3	3	NUM
ejpam-4463	197	45	)	)	PUNCT
ejpam-4463	197	46	|wn−ax|	|wn−ax|	NOUN
ejpam-4463	198	1	=	=	SYM
ejpam-4463	198	2	|1	|1	NUM
ejpam-4463	198	3	h	h	NOUN
ejpam-4463	199	1	|	|	ADV
ejpam-4463	199	2	=	=	PUNCT
ejpam-4463	200	1	|	|	ADV
ejpam-4463	200	2	a	a	DET
ejpam-4463	200	3	xn−1	xn−1	PROPN
ejpam-4463	201	1	|	|	ADV
ejpam-4463	201	2	=	=	SYM
ejpam-4463	201	3	e−(n−1	e−(n−1	ADJ
ejpam-4463	201	4	)	)	PUNCT
ejpam-4463	201	5	,	,	PUNCT
ejpam-4463	201	6	consequently	consequently	ADV
ejpam-4463	201	7	lim	lim	PROPN
ejpam-4463	201	8	n→+∞	n→+∞	VERB
ejpam-4463	201	9	wn	wn	PROPN
ejpam-4463	201	10	=	=	NOUN
ejpam-4463	201	11	ax	ax	NOUN
ejpam-4463	201	12	.	.	PUNCT
ejpam-4463	202	1	4	4	X
ejpam-4463	202	2	.	.	X
ejpam-4463	202	3	cfe	cfe	NOUN
ejpam-4463	202	4	of	of	ADP
ejpam-4463	202	5	the	the	DET
ejpam-4463	202	6	sse	sse	NOUN
ejpam-4463	202	7	let	let	VERB
ejpam-4463	202	8	j	j	PROPN
ejpam-4463	202	9	=	=	PRON
ejpam-4463	202	10	{	{	PUNCT
ejpam-4463	202	11	f	f	PROPN
ejpam-4463	202	12	∈q	∈q	NOUN
ejpam-4463	202	13	(	(	PUNCT
ejpam-4463	202	14	(	(	PUNCT
ejpam-4463	202	15	x	x	SYM
ejpam-4463	202	16	−1))/	−1))/	NOUN
ejpam-4463	203	1	|	|	ADV
ejpam-4463	203	2	f	f	NOUN
ejpam-4463	204	1	|	|	ADV
ejpam-4463	204	2	<	<	X
ejpam-4463	204	3	1	1	NUM
ejpam-4463	204	4	}	}	PUNCT
ejpam-4463	204	5	and	and	CCONJ
ejpam-4463	204	6	let	let	VERB
ejpam-4463	204	7	t	t	NOUN
ejpam-4463	204	8	:	:	PUNCT
ejpam-4463	204	9	j	j	PROPN
ejpam-4463	204	10	→	→	PUNCT
ejpam-4463	204	11	j	j	PROPN
ejpam-4463	204	12	be	be	AUX
ejpam-4463	204	13	the	the	DET
ejpam-4463	204	14	map	map	NOUN
ejpam-4463	204	15	given	give	VERB
ejpam-4463	204	16	by	by	ADP
ejpam-4463	204	17	t	t	PROPN
ejpam-4463	204	18	(	(	PUNCT
ejpam-4463	204	19	ω	ω	PROPN
ejpam-4463	204	20	)	)	PUNCT
ejpam-4463	204	21	:	:	PUNCT
ejpam-4463	205	1	=	=	SYM
ejpam-4463	205	2	1	1	NUM
ejpam-4463	205	3	ω	ω	NUM
ejpam-4463	205	4	−	−	PROPN
ejpam-4463	206	1	[	[	PUNCT
ejpam-4463	206	2	1	1	NUM
ejpam-4463	206	3	ω	ω	NUM
ejpam-4463	206	4	]	]	PUNCT
ejpam-4463	206	5	,	,	PUNCT
ejpam-4463	206	6	ω	ω	NUM
ejpam-4463	206	7	̸=	̸=	PROPN
ejpam-4463	206	8	0	0	NUM
ejpam-4463	206	9	,	,	PUNCT
ejpam-4463	206	10	t	t	PROPN
ejpam-4463	206	11	(	(	PUNCT
ejpam-4463	206	12	0	0	NUM
ejpam-4463	206	13	)	)	PUNCT
ejpam-4463	206	14	=	=	SYM
ejpam-4463	206	15	0	0	NUM
ejpam-4463	206	16	,	,	PUNCT
ejpam-4463	206	17	recall	recall	VERB
ejpam-4463	206	18	that	that	SCONJ
ejpam-4463	206	19	the	the	DET
ejpam-4463	206	20	map	map	NOUN
ejpam-4463	206	21	t	t	NOUN
ejpam-4463	206	22	generate	generate	VERB
ejpam-4463	206	23	the	the	DET
ejpam-4463	206	24	continued	continue	VERB
ejpam-4463	206	25	fraction	fraction	NOUN
ejpam-4463	206	26	expansion	expansion	NOUN
ejpam-4463	206	27	of	of	ADP
ejpam-4463	206	28	ω	ω	NUM
ejpam-4463	206	29	of	of	ADP
ejpam-4463	206	30	the	the	DET
ejpam-4463	206	31	form	form	NOUN
ejpam-4463	206	32	ω	ω	NOUN
ejpam-4463	206	33	=	=	PROPN
ejpam-4463	206	34	a0	a0	PROPN
ejpam-4463	206	35	+	+	CCONJ
ejpam-4463	206	36	1	1	NUM
ejpam-4463	206	37	a1	a1	NOUN
ejpam-4463	206	38	+	+	CCONJ
ejpam-4463	206	39	1	1	NUM
ejpam-4463	206	40	a2	a2	NOUN
ejpam-4463	206	41	+	+	CCONJ
ejpam-4463	206	42	1	1	NUM
ejpam-4463	206	43	a3	a3	NOUN
ejpam-4463	206	44	+	+	X
ejpam-4463	206	45	..	..	PUNCT
ejpam-4463	206	46	.	.	PUNCT
ejpam-4463	207	1	+	+	CCONJ
ejpam-4463	207	2	1	1	NUM
ejpam-4463	207	3	an	an	PRON
ejpam-4463	207	4	+	+	X
ejpam-4463	207	5	..	..	PUNCT
ejpam-4463	207	6	.	.	PUNCT
ejpam-4463	208	1	,	,	PUNCT
ejpam-4463	208	2	(	(	PUNCT
ejpam-4463	208	3	5	5	X
ejpam-4463	208	4	)	)	PUNCT
ejpam-4463	208	5	o.	o.	PROPN
ejpam-4463	208	6	dammak	dammak	PROPN
ejpam-4463	208	7	,	,	PUNCT
ejpam-4463	208	8	s.	s.	PROPN
ejpam-4463	208	9	mansour	mansour	PROPN
ejpam-4463	208	10	/	/	SYM
ejpam-4463	208	11	eur	eur	PROPN
ejpam-4463	208	12	.	.	PUNCT
ejpam-4463	209	1	j.	j.	PROPN
ejpam-4463	209	2	pure	pure	PROPN
ejpam-4463	209	3	appl	appl	PROPN
ejpam-4463	209	4	.	.	PROPN
ejpam-4463	209	5	math	math	PROPN
ejpam-4463	209	6	,	,	PUNCT
ejpam-4463	209	7	15	15	NUM
ejpam-4463	209	8	(	(	PUNCT
ejpam-4463	209	9	3	3	NUM
ejpam-4463	209	10	)	)	PUNCT
ejpam-4463	209	11	(	(	PUNCT
ejpam-4463	209	12	2022	2022	NUM
ejpam-4463	209	13	)	)	PUNCT
ejpam-4463	209	14	,	,	PUNCT
ejpam-4463	209	15	1321	1321	NUM
ejpam-4463	209	16	-	-	SYM
ejpam-4463	209	17	1330	1330	NUM
ejpam-4463	209	18	1328	1328	NUM
ejpam-4463	209	19	where	where	SCONJ
ejpam-4463	209	20	an	an	PRON
ejpam-4463	209	21	=	=	X
ejpam-4463	209	22	[	[	PUNCT
ejpam-4463	209	23	1	1	NUM
ejpam-4463	209	24	tn−1(w	tn−1(w	NOUN
ejpam-4463	209	25	)	)	PUNCT
ejpam-4463	209	26	]	]	PUNCT
ejpam-4463	209	27	.	.	PUNCT
ejpam-4463	210	1	when	when	SCONJ
ejpam-4463	210	2	used	use	VERB
ejpam-4463	210	3	as	as	ADP
ejpam-4463	210	4	a	a	DET
ejpam-4463	210	5	shorthand	shorthand	NOUN
ejpam-4463	210	6	for	for	ADP
ejpam-4463	210	7	(	(	PUNCT
ejpam-4463	210	8	5	5	X
ejpam-4463	210	9	)	)	PUNCT
ejpam-4463	210	10	we	we	PRON
ejpam-4463	210	11	can	can	AUX
ejpam-4463	210	12	write	write	VERB
ejpam-4463	210	13	ω	ω	PROPN
ejpam-4463	211	1	=	=	PUNCT
ejpam-4463	212	1	[	[	X
ejpam-4463	212	2	a0;a1	a0;a1	PROPN
ejpam-4463	212	3	,	,	PUNCT
ejpam-4463	212	4	a2	a2	PROPN
ejpam-4463	212	5	,	,	PUNCT
ejpam-4463	212	6	.	.	PUNCT
ejpam-4463	212	7	.	.	PUNCT
ejpam-4463	212	8	.	.	PUNCT
ejpam-4463	213	1	]	]	PUNCT
ejpam-4463	213	2	.	.	PUNCT
ejpam-4463	214	1	let	let	VERB
ejpam-4463	214	2	ω	ω	PUNCT
ejpam-4463	214	3	the	the	DET
ejpam-4463	214	4	(	(	PUNCT
ejpam-4463	214	5	sse	sse	PROPN
ejpam-4463	214	6	)	)	PUNCT
ejpam-4463	214	7	of	of	ADP
ejpam-4463	214	8	degree	degree	NOUN
ejpam-4463	214	9	qn	qn	NOUN
ejpam-4463	214	10	+	+	NOUN
ejpam-4463	214	11	1	1	NUM
ejpam-4463	214	12	,	,	PUNCT
ejpam-4463	214	13	with	with	ADP
ejpam-4463	214	14	n	n	PRON
ejpam-4463	214	15	∈	∈	PROPN
ejpam-4463	214	16	n	n	CCONJ
ejpam-4463	214	17	,	,	PUNCT
ejpam-4463	214	18	then	then	ADV
ejpam-4463	214	19	ω	ω	X
ejpam-4463	214	20	=	=	PUNCT
ejpam-4463	215	1	[	[	X
ejpam-4463	215	2	a0	a0	NOUN
ejpam-4463	215	3	,	,	PUNCT
ejpam-4463	215	4	a1	a1	NOUN
ejpam-4463	215	5	,	,	PUNCT
ejpam-4463	215	6	.	.	PUNCT
ejpam-4463	215	7	.	.	PUNCT
ejpam-4463	215	8	.	.	PUNCT
ejpam-4463	216	1	,	,	PUNCT
ejpam-4463	216	2	as	as	ADP
ejpam-4463	216	3	,	,	PUNCT
ejpam-4463	216	4	.	.	PUNCT
ejpam-4463	216	5	.	.	PUNCT
ejpam-4463	217	1	.	.	PUNCT
ejpam-4463	218	1	]	]	X
ejpam-4463	218	2	,	,	PUNCT
ejpam-4463	218	3	where	where	SCONJ
ejpam-4463	218	4	a0	a0	NOUN
ejpam-4463	218	5	=	=	NOUN
ejpam-4463	218	6	ax	ax	NOUN
ejpam-4463	218	7	,	,	PUNCT
ejpam-4463	218	8	a1	a1	NOUN
ejpam-4463	218	9	=	=	SYM
ejpam-4463	218	10	xqn−1	xqn−1	PROPN
ejpam-4463	218	11	a2s	a2s	NOUN
ejpam-4463	218	12	=	=	PUNCT
ejpam-4463	218	13	axxq(2s)n−q(2s−1)n	axxq(2s)n−q(2s−1)n	PROPN
ejpam-4463	218	14	and	and	CCONJ
ejpam-4463	218	15	a2s+1	a2s+1	PROPN
ejpam-4463	218	16	=	=	PUNCT
ejpam-4463	218	17	xqn−1xq(2s+1)n−q(2s)n	xqn−1xq(2s+1)n−q(2s)n	PROPN
ejpam-4463	218	18	.	.	PUNCT
ejpam-4463	219	1	proof	proof	NOUN
ejpam-4463	219	2	.	.	PUNCT
ejpam-4463	220	1	let	let	VERB
ejpam-4463	220	2	p	p	NOUN
ejpam-4463	220	3	(	(	PUNCT
ejpam-4463	220	4	y	y	PROPN
ejpam-4463	220	5	)	)	PUNCT
ejpam-4463	221	1	=	=	SYM
ejpam-4463	221	2	y	y	PROPN
ejpam-4463	221	3	qn+1−axy	qn+1−axy	PROPN
ejpam-4463	221	4	qn−ax	qn−ax	VERB
ejpam-4463	221	5	the	the	DET
ejpam-4463	221	6	minimal	minimal	ADJ
ejpam-4463	221	7	polynomial	polynomial	NOUN
ejpam-4463	221	8	of	of	ADP
ejpam-4463	221	9	(	(	PUNCT
ejpam-4463	221	10	spe	spe	PROPN
ejpam-4463	221	11	)	)	PUNCT
ejpam-4463	221	12	w	w	NOUN
ejpam-4463	221	13	=	=	SYM
ejpam-4463	221	14	wqn+1	wqn+1	PROPN
ejpam-4463	221	15	.	.	PUNCT
ejpam-4463	222	1	let	let	VERB
ejpam-4463	222	2	z0	z0	PROPN
ejpam-4463	222	3	=	=	SYM
ejpam-4463	222	4	ω	ω	PROPN
ejpam-4463	222	5	,	,	PUNCT
ejpam-4463	222	6	a0	a0	NOUN
ejpam-4463	222	7	=	=	PUNCT
ejpam-4463	223	1	[	[	X
ejpam-4463	223	2	z0	z0	X
ejpam-4463	223	3	]	]	X
ejpam-4463	223	4	=	=	SYM
ejpam-4463	223	5	ax	ax	NOUN
ejpam-4463	223	6	,	,	PUNCT
ejpam-4463	223	7	u0	u0	ADJ
ejpam-4463	223	8	=	=	ADJ
ejpam-4463	223	9	1	1	NUM
ejpam-4463	223	10	,	,	PUNCT
ejpam-4463	223	11	v0	v0	NOUN
ejpam-4463	223	12	=	=	SYM
ejpam-4463	223	13	−ax	−ax	PROPN
ejpam-4463	223	14	,	,	PUNCT
ejpam-4463	223	15	r0	r0	NOUN
ejpam-4463	223	16	=	=	SYM
ejpam-4463	223	17	0	0	NUM
ejpam-4463	223	18	,	,	PUNCT
ejpam-4463	223	19	t0	t0	X
ejpam-4463	223	20	=	=	SYM
ejpam-4463	224	1	−ax	−ax	NOUN
ejpam-4463	224	2	and	and	CCONJ
ejpam-4463	224	3	zs+1	zs+1	NUM
ejpam-4463	224	4	=	=	SYM
ejpam-4463	224	5	1	1	NUM
ejpam-4463	224	6	zs	zs	NUM
ejpam-4463	224	7	−	−	PROPN
ejpam-4463	225	1	[	[	X
ejpam-4463	225	2	zs	zs	X
ejpam-4463	225	3	]	]	X
ejpam-4463	225	4	,	,	PUNCT
ejpam-4463	225	5	then	then	ADV
ejpam-4463	225	6	from	from	ADP
ejpam-4463	225	7	lemma	lemma	PROPN
ejpam-4463	225	8	1	1	NUM
ejpam-4463	225	9	and	and	CCONJ
ejpam-4463	225	10	lemma	lemma	PROPN
ejpam-4463	225	11	2	2	NUM
ejpam-4463	225	12	we	we	PRON
ejpam-4463	225	13	know	know	VERB
ejpam-4463	225	14	that	that	SCONJ
ejpam-4463	225	15	zs	zs	PROPN
ejpam-4463	225	16	satisfies	satisfy	VERB
ejpam-4463	225	17	the	the	DET
ejpam-4463	225	18	equation	equation	NOUN
ejpam-4463	225	19	usz	usz	ADV
ejpam-4463	225	20	qn+1	qn+1	PROPN
ejpam-4463	225	21	s	s	NOUN
ejpam-4463	225	22	+	+	NUM
ejpam-4463	225	23	vsz	vsz	PROPN
ejpam-4463	225	24	qn	qn	NOUN
ejpam-4463	225	25	s	s	PART
ejpam-4463	225	26	+	+	NOUN
ejpam-4463	225	27	rszs	rszs	ADJ
ejpam-4463	225	28	+	+	CCONJ
ejpam-4463	225	29	ts	ts	X
ejpam-4463	225	30	=	=	NOUN
ejpam-4463	225	31	0	0	NUM
ejpam-4463	225	32	with	with	ADP
ejpam-4463	225	33	deg	deg	PROPN
ejpam-4463	225	34	vs	vs	ADP
ejpam-4463	225	35	>	>	X
ejpam-4463	225	36	max(degus	max(degus	X
ejpam-4463	225	37	,	,	PUNCT
ejpam-4463	225	38	degrs	degrs	PROPN
ejpam-4463	225	39	,	,	PUNCT
ejpam-4463	225	40	deg	deg	NOUN
ejpam-4463	225	41	ts	ts	NOUN
ejpam-4463	225	42	)	)	PUNCT
ejpam-4463	225	43	for	for	ADP
ejpam-4463	225	44	all	all	DET
ejpam-4463	225	45	s	s	PART
ejpam-4463	225	46	≥	≥	NOUN
ejpam-4463	225	47	1	1	NUM
ejpam-4463	225	48	and	and	CCONJ
ejpam-4463	225	49	us+1	us+1	PROPN
ejpam-4463	225	50	=	=	SYM
ejpam-4463	225	51	usa	usa	PROPN
ejpam-4463	225	52	qn+1	qn+1	PROPN
ejpam-4463	225	53	s	s	PART
ejpam-4463	225	54	+	+	X
ejpam-4463	225	55	vsa	vsa	PROPN
ejpam-4463	225	56	qn	qn	NOUN
ejpam-4463	225	57	s	s	PART
ejpam-4463	225	58	+	+	NOUN
ejpam-4463	225	59	rsas	rsa	NOUN
ejpam-4463	225	60	+	+	CCONJ
ejpam-4463	225	61	ts	ts	NOUN
ejpam-4463	225	62	,	,	PUNCT
ejpam-4463	225	63	vs+1	vs+1	PROPN
ejpam-4463	225	64	=	=	SYM
ejpam-4463	225	65	usa	usa	PROPN
ejpam-4463	225	66	qn	qn	PROPN
ejpam-4463	225	67	s	s	X
ejpam-4463	225	68	,	,	PUNCT
ejpam-4463	225	69	rs+1	rs+1	PROPN
ejpam-4463	225	70	=	=	PUNCT
ejpam-4463	225	71	vs	vs	ADP
ejpam-4463	225	72	+	+	PROPN
ejpam-4463	225	73	asus	asus	NOUN
ejpam-4463	225	74	,	,	PUNCT
ejpam-4463	225	75	ts+1	ts+1	PROPN
ejpam-4463	225	76	=	=	SYM
ejpam-4463	225	77	us	us	PROPN
ejpam-4463	225	78	,	,	PUNCT
ejpam-4463	225	79	as+1	as+1	PROPN
ejpam-4463	225	80	=	=	SYM
ejpam-4463	226	1	−	−	PROPN
ejpam-4463	227	1	[	[	PUNCT
ejpam-4463	227	2	vs+1	vs+1	X
ejpam-4463	227	3	us+1	us+1	PROPN
ejpam-4463	227	4	]	]	PUNCT
ejpam-4463	227	5	now	now	ADV
ejpam-4463	227	6	one	one	NUM
ejpam-4463	227	7	shows	show	NOUN
ejpam-4463	227	8	,	,	PUNCT
ejpam-4463	227	9	using	use	VERB
ejpam-4463	227	10	a	a	DET
ejpam-4463	227	11	simple	simple	ADJ
ejpam-4463	227	12	recurrence	recurrence	NOUN
ejpam-4463	227	13	on	on	ADP
ejpam-4463	227	14	s	s	PRON
ejpam-4463	227	15	,	,	PUNCT
ejpam-4463	227	16	that	that	DET
ejpam-4463	227	17	u2s	u2s	NOUN
ejpam-4463	227	18	=	=	SYM
ejpam-4463	227	19	1	1	NUM
ejpam-4463	227	20	,	,	PUNCT
ejpam-4463	227	21	u2s+1	u2s+1	PROPN
ejpam-4463	227	22	=	=	SYM
ejpam-4463	227	23	−ax	−ax	PROPN
ejpam-4463	227	24	,	,	PUNCT
ejpam-4463	227	25	v2s	v2s	PROPN
ejpam-4463	227	26	=	=	SYM
ejpam-4463	227	27	−(ax)xqn−1xq(2s−1)n−q(2s−2)nq	−(ax)xqn−1xq(2s−1)n−q(2s−2)nq	PROPN
ejpam-4463	227	28	n	n	NOUN
ejpam-4463	227	29	,	,	PUNCT
ejpam-4463	227	30	v2s+1	v2s+1	PROPN
ejpam-4463	227	31	=	=	SYM
ejpam-4463	227	32	a(xxq(2s)n−q(2s−1)n	a(xxq(2s)n−q(2s−1)n	NOUN
ejpam-4463	227	33	)	)	PUNCT
ejpam-4463	227	34	q	q	PROPN
ejpam-4463	227	35	n	n	NOUN
ejpam-4463	227	36	,	,	PUNCT
ejpam-4463	227	37	rs	rs	NOUN
ejpam-4463	227	38	=	=	SYM
ejpam-4463	227	39	0	0	NUM
ejpam-4463	227	40	,	,	PUNCT
ejpam-4463	227	41	t2s	t2s	NOUN
ejpam-4463	227	42	=	=	SYM
ejpam-4463	227	43	−ax	−ax	PROPN
ejpam-4463	227	44	,	,	PUNCT
ejpam-4463	227	45	t2s+1	t2s+1	PROPN
ejpam-4463	227	46	=	=	NOUN
ejpam-4463	227	47	1	1	NUM
ejpam-4463	227	48	,	,	PUNCT
ejpam-4463	227	49	a2s	a2s	NOUN
ejpam-4463	227	50	=	=	PUNCT
ejpam-4463	227	51	axxq(2s)n−q(2s−1)n	axxq(2s)n−q(2s−1)n	NOUN
ejpam-4463	227	52	and	and	CCONJ
ejpam-4463	227	53	a2s+1	a2s+1	PROPN
ejpam-4463	227	54	=	=	PUNCT
ejpam-4463	227	55	xqn−1xq(2s+1)n−q(2s)n	xqn−1xq(2s+1)n−q(2s)n	PROPN
ejpam-4463	227	56	.	.	PUNCT
ejpam-4463	228	1	example	example	NOUN
ejpam-4463	229	1	1	1	NUM
ejpam-4463	229	2	.	.	PUNCT
ejpam-4463	230	1	the	the	DET
ejpam-4463	230	2	minimal	minimal	ADJ
ejpam-4463	230	3	polynomial	polynomial	NOUN
ejpam-4463	230	4	of	of	ADP
ejpam-4463	230	5	the	the	DET
ejpam-4463	230	6	(	(	PUNCT
ejpam-4463	230	7	sse	sse	PROPN
ejpam-4463	230	8	)	)	PUNCT
ejpam-4463	230	9	w	w	NOUN
ejpam-4463	230	10	of	of	ADP
ejpam-4463	230	11	degree	degree	NOUN
ejpam-4463	230	12	2	2	NUM
ejpam-4463	230	13	over	over	ADP
ejpam-4463	230	14	2((x	2((x	NUM
ejpam-4463	230	15	−1	−1	NOUN
ejpam-4463	230	16	)	)	PUNCT
ejpam-4463	230	17	)	)	PUNCT
ejpam-4463	230	18	is	be	AUX
ejpam-4463	230	19	p	p	X
ejpam-4463	230	20	(	(	PUNCT
ejpam-4463	230	21	y	y	PROPN
ejpam-4463	230	22	)	)	PUNCT
ejpam-4463	231	1	=	=	SYM
ejpam-4463	231	2	y	y	PROPN
ejpam-4463	231	3	2	2	NUM
ejpam-4463	231	4	−xy	−xy	PROPN
ejpam-4463	231	5	−x	−x	NOUN
ejpam-4463	231	6	,	,	PUNCT
ejpam-4463	231	7	so	so	SCONJ
ejpam-4463	231	8	w	w	NOUN
ejpam-4463	231	9	=	=	PUNCT
ejpam-4463	231	10	∞∑	∞∑	NUM
ejpam-4463	231	11	i=−1	i=−1	NUM
ejpam-4463	231	12	wix	wix	NOUN
ejpam-4463	231	13	−i	−i	PROPN
ejpam-4463	231	14	is	be	AUX
ejpam-4463	231	15	defined	define	VERB
ejpam-4463	231	16	by	by	NOUN
ejpam-4463	231	17	w−1	w−1	PROPN
ejpam-4463	231	18	=	=	SYM
ejpam-4463	231	19	w0	w0	PROPN
ejpam-4463	231	20	=	=	PROPN
ejpam-4463	231	21	w1	w1	NOUN
ejpam-4463	231	22	=	=	SYM
ejpam-4463	231	23	1	1	NUM
ejpam-4463	231	24	,	,	PUNCT
ejpam-4463	231	25	w2n	w2n	PRON
ejpam-4463	231	26	=	=	SYM
ejpam-4463	231	27	0	0	NUM
ejpam-4463	231	28	w2n+1	w2n+1	PROPN
ejpam-4463	231	29	=	=	SYM
ejpam-4463	231	30	wn	wn	PROPN
ejpam-4463	231	31	,	,	PUNCT
ejpam-4463	231	32	for	for	ADP
ejpam-4463	231	33	all	all	DET
ejpam-4463	231	34	n	n	PRON
ejpam-4463	231	35	≥	≥	NOUN
ejpam-4463	231	36	0	0	NUM
ejpam-4463	231	37	.	.	PUNCT
ejpam-4463	232	1	the	the	DET
ejpam-4463	232	2	continued	continue	VERB
ejpam-4463	232	3	fraction	fraction	NOUN
ejpam-4463	232	4	of	of	ADP
ejpam-4463	232	5	w	w	PROPN
ejpam-4463	232	6	is	be	AUX
ejpam-4463	232	7	w	w	NOUN
ejpam-4463	232	8	=	=	PUNCT
ejpam-4463	232	9	[	[	X
ejpam-4463	232	10	x	x	X
ejpam-4463	232	11	,	,	PUNCT
ejpam-4463	232	12	x3	x3	ADJ
ejpam-4463	232	13	,	,	PUNCT
ejpam-4463	232	14	x11	x11	PROPN
ejpam-4463	232	15	,	,	PUNCT
ejpam-4463	232	16	x48	x48	NUM
ejpam-4463	232	17	,	,	PUNCT
ejpam-4463	232	18	·	·	PUNCT
ejpam-4463	232	19	·	·	PUNCT
ejpam-4463	232	20	·	·	PUNCT
ejpam-4463	233	1	]	]	PUNCT
ejpam-4463	233	2	.	.	PUNCT
ejpam-4463	234	1	references	reference	NOUN
ejpam-4463	234	2	1329	1329	NUM
ejpam-4463	234	3	acknowledgements	acknowledgement	NOUN
ejpam-4463	234	4	the	the	DET
ejpam-4463	234	5	authors	author	NOUN
ejpam-4463	234	6	would	would	AUX
ejpam-4463	234	7	like	like	VERB
ejpam-4463	234	8	to	to	PART
ejpam-4463	234	9	thank	thank	VERB
ejpam-4463	234	10	the	the	DET
ejpam-4463	234	11	deanship	deanship	NOUN
ejpam-4463	234	12	of	of	ADP
ejpam-4463	234	13	scientific	scientific	ADJ
ejpam-4463	234	14	research	research	NOUN
ejpam-4463	234	15	at	at	ADP
ejpam-4463	234	16	umm	umm	INTJ
ejpam-4463	234	17	al	al	PROPN
ejpam-4463	234	18	-	-	PUNCT
ejpam-4463	234	19	qura	qura	PROPN
ejpam-4463	234	20	university	university	NOUN
ejpam-4463	234	21	for	for	ADP
ejpam-4463	234	22	supporting	support	VERB
ejpam-4463	234	23	this	this	DET
ejpam-4463	234	24	work	work	NOUN
ejpam-4463	234	25	grant	grant	NOUN
ejpam-4463	234	26	code	code	NOUN
ejpam-4463	234	27	:	:	PUNCT
ejpam-4463	234	28	22uqu4340610dsr02	22uqu4340610dsr02	PROPN
ejpam-4463	234	29	.	.	PUNCT
ejpam-4463	235	1	references	reference	NOUN
ejpam-4463	235	2	[	[	X
ejpam-4463	235	3	1	1	NUM
ejpam-4463	235	4	]	]	X
ejpam-4463	235	5	mj	mj	PROPN
ejpam-4463	235	6	bertin	bertin	PROPN
ejpam-4463	235	7	.	.	PUNCT
ejpam-4463	236	1	quelques	quelques	PROPN
ejpam-4463	236	2	nouveaux	nouveaux	PROPN
ejpam-4463	236	3	résultats	résultats	ADP
ejpam-4463	236	4	sur	sur	PROPN
ejpam-4463	236	5	les	les	X
ejpam-4463	236	6	nombres	nombres	X
ejpam-4463	236	7	de	de	X
ejpam-4463	236	8	pisot	pisot	PROPN
ejpam-4463	236	9	et	et	PROPN
ejpam-4463	236	10	de	de	PROPN
ejpam-4463	236	11	salem	salem	PROPN
ejpam-4463	236	12	.	.	PUNCT
ejpam-4463	237	1	number	number	NOUN
ejpam-4463	237	2	theory	theory	NOUN
ejpam-4463	237	3	in	in	ADP
ejpam-4463	237	4	progress	progress	NOUN
ejpam-4463	237	5	,	,	PUNCT
ejpam-4463	237	6	1:1–9	1:1–9	NUM
ejpam-4463	237	7	,	,	PUNCT
ejpam-4463	237	8	2012	2012	NUM
ejpam-4463	237	9	.	.	PUNCT
ejpam-4463	238	1	[	[	X
ejpam-4463	238	2	2	2	X
ejpam-4463	238	3	]	]	X
ejpam-4463	238	4	david	david	PROPN
ejpam-4463	238	5	w	w	PROPN
ejpam-4463	238	6	boyd	boyd	PROPN
ejpam-4463	238	7	.	.	PUNCT
ejpam-4463	239	1	small	small	ADJ
ejpam-4463	239	2	salem	salem	NOUN
ejpam-4463	239	3	numbers	number	NOUN
ejpam-4463	239	4	.	.	PUNCT
ejpam-4463	240	1	duke	duke	PROPN
ejpam-4463	240	2	mathematical	mathematical	PROPN
ejpam-4463	240	3	journal	journal	PROPN
ejpam-4463	240	4	,	,	PUNCT
ejpam-4463	240	5	44(2):315–328	44(2):315–328	PROPN
ejpam-4463	240	6	,	,	PUNCT
ejpam-4463	240	7	1977	1977	NUM
ejpam-4463	240	8	.	.	PUNCT
ejpam-4463	241	1	[	[	X
ejpam-4463	241	2	3	3	X
ejpam-4463	241	3	]	]	X
ejpam-4463	241	4	david	david	PROPN
ejpam-4463	241	5	w	w	PROPN
ejpam-4463	241	6	boyd	boyd	PROPN
ejpam-4463	241	7	.	.	PUNCT
ejpam-4463	242	1	reciprocal	reciprocal	ADJ
ejpam-4463	242	2	polynomials	polynomial	NOUN
ejpam-4463	242	3	having	have	VERB
ejpam-4463	242	4	small	small	ADJ
ejpam-4463	242	5	measure	measure	NOUN
ejpam-4463	242	6	.	.	PUNCT
ejpam-4463	243	1	ii	ii	X
ejpam-4463	243	2	.	.	PUNCT
ejpam-4463	244	1	mathematics	mathematic	NOUN
ejpam-4463	244	2	of	of	ADP
ejpam-4463	244	3	computation	computation	NOUN
ejpam-4463	244	4	,	,	PUNCT
ejpam-4463	244	5	53(187):355–357	53(187):355–357	PROPN
ejpam-4463	244	6	,	,	PUNCT
ejpam-4463	244	7	1989	1989	NUM
ejpam-4463	244	8	.	.	PUNCT
ejpam-4463	245	1	[	[	X
ejpam-4463	245	2	4	4	X
ejpam-4463	245	3	]	]	X
ejpam-4463	245	4	a	a	DET
ejpam-4463	245	5	chandoul	chandoul	PROPN
ejpam-4463	245	6	,	,	PUNCT
ejpam-4463	245	7	manel	manel	PROPN
ejpam-4463	245	8	jellali	jellali	PROPN
ejpam-4463	245	9	,	,	PUNCT
ejpam-4463	245	10	and	and	CCONJ
ejpam-4463	245	11	mohamed	mohamed	PROPN
ejpam-4463	245	12	mkaouar	mkaouar	PROPN
ejpam-4463	245	13	.	.	PUNCT
ejpam-4463	246	1	the	the	DET
ejpam-4463	246	2	smallest	small	ADJ
ejpam-4463	246	3	pisot	pisot	ADJ
ejpam-4463	246	4	element	element	NOUN
ejpam-4463	246	5	in	in	ADP
ejpam-4463	246	6	the	the	DET
ejpam-4463	246	7	field	field	NOUN
ejpam-4463	246	8	of	of	ADP
ejpam-4463	246	9	formal	formal	ADJ
ejpam-4463	246	10	power	power	NOUN
ejpam-4463	246	11	series	series	NOUN
ejpam-4463	246	12	over	over	ADP
ejpam-4463	246	13	a	a	DET
ejpam-4463	246	14	finite	finite	ADJ
ejpam-4463	246	15	field	field	NOUN
ejpam-4463	246	16	.	.	PUNCT
ejpam-4463	247	1	canadian	canadian	ADJ
ejpam-4463	247	2	mathematical	mathematical	ADJ
ejpam-4463	247	3	bulletin	bulletin	NOUN
ejpam-4463	247	4	,	,	PUNCT
ejpam-4463	247	5	56(2):258–264	56(2):258–264	PROPN
ejpam-4463	247	6	,	,	PUNCT
ejpam-4463	247	7	2013	2013	NUM
ejpam-4463	247	8	.	.	PUNCT
ejpam-4463	248	1	[	[	X
ejpam-4463	248	2	5	5	X
ejpam-4463	248	3	]	]	X
ejpam-4463	248	4	jacques	jacque	NOUN
ejpam-4463	248	5	dufresnoy	dufresnoy	VERB
ejpam-4463	248	6	and	and	CCONJ
ejpam-4463	248	7	ch	ch	NOUN
ejpam-4463	248	8	pisot	pisot	NOUN
ejpam-4463	248	9	.	.	PUNCT
ejpam-4463	249	1	étude	étude	VERB
ejpam-4463	249	2	de	de	X
ejpam-4463	249	3	certaines	certaines	X
ejpam-4463	249	4	fonctions	fonction	NOUN
ejpam-4463	249	5	méromorphes	méromorphes	X
ejpam-4463	249	6	bornées	bornée	VERB
ejpam-4463	249	7	sur	sur	PROPN
ejpam-4463	249	8	le	le	X
ejpam-4463	249	9	cercle	cercle	PROPN
ejpam-4463	249	10	unité.	unité.	PROPN
ejpam-4463	249	11	application	application	NOUN
ejpam-4463	249	12	à	à	PROPN
ejpam-4463	249	13	un	un	PROPN
ejpam-4463	249	14	ensemble	ensemble	PROPN
ejpam-4463	249	15	fermé	fermé	PROPN
ejpam-4463	249	16	d’entiers	d’entiers	PROPN
ejpam-4463	249	17	algébriques	algébriques	PROPN
ejpam-4463	249	18	.	.	PUNCT
ejpam-4463	250	1	in	in	ADP
ejpam-4463	250	2	annales	annale	NOUN
ejpam-4463	250	3	scientifiques	scientifique	NOUN
ejpam-4463	250	4	de	de	ADP
ejpam-4463	250	5	l’école	l’école	ADJ
ejpam-4463	250	6	normale	normale	PROPN
ejpam-4463	250	7	supérieure	supérieure	PROPN
ejpam-4463	250	8	,	,	PUNCT
ejpam-4463	250	9	volume	volume	NOUN
ejpam-4463	250	10	72	72	NUM
ejpam-4463	250	11	,	,	PUNCT
ejpam-4463	250	12	pages	page	VERB
ejpam-4463	250	13	69–92	69–92	NUM
ejpam-4463	250	14	,	,	PUNCT
ejpam-4463	250	15	1955	1955	NUM
ejpam-4463	250	16	.	.	PUNCT
ejpam-4463	251	1	[	[	X
ejpam-4463	251	2	6	6	NUM
ejpam-4463	251	3	]	]	PUNCT
ejpam-4463	251	4	eknath	eknath	NOUN
ejpam-4463	251	5	ghate	ghate	NOUN
ejpam-4463	251	6	and	and	CCONJ
ejpam-4463	251	7	eriko	eriko	PROPN
ejpam-4463	251	8	hironaka	hironaka	PROPN
ejpam-4463	251	9	.	.	PUNCT
ejpam-4463	252	1	the	the	DET
ejpam-4463	252	2	arithmetic	arithmetic	NOUN
ejpam-4463	252	3	and	and	CCONJ
ejpam-4463	252	4	geometry	geometry	NOUN
ejpam-4463	252	5	of	of	ADP
ejpam-4463	252	6	salem	salem	NOUN
ejpam-4463	252	7	numbers	number	NOUN
ejpam-4463	252	8	.	.	PUNCT
ejpam-4463	253	1	bulletin	bulletin	NOUN
ejpam-4463	253	2	of	of	ADP
ejpam-4463	253	3	the	the	DET
ejpam-4463	253	4	american	american	PROPN
ejpam-4463	253	5	mathematical	mathematical	PROPN
ejpam-4463	253	6	society	society	NOUN
ejpam-4463	253	7	,	,	PUNCT
ejpam-4463	253	8	38(3):293–314	38(3):293–314	PROPN
ejpam-4463	253	9	,	,	PUNCT
ejpam-4463	253	10	2001	2001	NUM
ejpam-4463	253	11	.	.	PUNCT
ejpam-4463	254	1	[	[	X
ejpam-4463	254	2	7	7	X
ejpam-4463	254	3	]	]	X
ejpam-4463	254	4	derrick	derrick	PROPN
ejpam-4463	254	5	h	h	PROPN
ejpam-4463	254	6	lehmer	lehmer	PROPN
ejpam-4463	254	7	.	.	PUNCT
ejpam-4463	255	1	factorization	factorization	NOUN
ejpam-4463	255	2	of	of	ADP
ejpam-4463	255	3	certain	certain	ADJ
ejpam-4463	255	4	cyclotomic	cyclotomic	ADJ
ejpam-4463	255	5	functions	function	NOUN
ejpam-4463	255	6	.	.	PUNCT
ejpam-4463	256	1	annals	annal	NOUN
ejpam-4463	256	2	of	of	ADP
ejpam-4463	256	3	mathematics	mathematic	NOUN
ejpam-4463	256	4	,	,	PUNCT
ejpam-4463	256	5	pages	page	NOUN
ejpam-4463	256	6	461–479	461–479	NUM
ejpam-4463	256	7	,	,	PUNCT
ejpam-4463	256	8	1933	1933	NUM
ejpam-4463	256	9	.	.	PUNCT
ejpam-4463	257	1	[	[	X
ejpam-4463	257	2	8	8	NUM
ejpam-4463	257	3	]	]	X
ejpam-4463	257	4	james	james	PROPN
ejpam-4463	257	5	mckee	mckee	PROPN
ejpam-4463	257	6	and	and	CCONJ
ejpam-4463	257	7	chris	chris	PROPN
ejpam-4463	257	8	smyth	smyth	PROPN
ejpam-4463	257	9	.	.	PUNCT
ejpam-4463	258	1	salem	salem	PROPN
ejpam-4463	258	2	numbers	number	NOUN
ejpam-4463	258	3	from	from	ADP
ejpam-4463	258	4	graphs	graph	NOUN
ejpam-4463	258	5	and	and	CCONJ
ejpam-4463	258	6	interlacing	interlace	VERB
ejpam-4463	258	7	quotients	quotient	NOUN
ejpam-4463	258	8	.	.	PUNCT
ejpam-4463	259	1	in	in	ADP
ejpam-4463	259	2	around	around	ADP
ejpam-4463	259	3	the	the	DET
ejpam-4463	259	4	unit	unit	NOUN
ejpam-4463	259	5	circle	circle	NOUN
ejpam-4463	259	6	,	,	PUNCT
ejpam-4463	259	7	pages	page	NOUN
ejpam-4463	259	8	343–359	343–359	NUM
ejpam-4463	259	9	.	.	PUNCT
ejpam-4463	259	10	springer	springer	NOUN
ejpam-4463	259	11	,	,	PUNCT
ejpam-4463	259	12	2021	2021	NUM
ejpam-4463	259	13	.	.	PUNCT
ejpam-4463	260	1	[	[	X
ejpam-4463	260	2	9	9	NUM
ejpam-4463	260	3	]	]	X
ejpam-4463	260	4	charles	charles	PROPN
ejpam-4463	260	5	pisot	pisot	ADJ
ejpam-4463	260	6	.	.	PUNCT
ejpam-4463	261	1	la	la	PRON
ejpam-4463	261	2	répartition	répartition	PROPN
ejpam-4463	261	3	modulo	modulo	NOUN
ejpam-4463	261	4	1	1	NUM
ejpam-4463	261	5	et	et	NOUN
ejpam-4463	261	6	les	les	PROPN
ejpam-4463	261	7	nombres	nombres	PROPN
ejpam-4463	261	8	algébriques	algébriques	PROPN
ejpam-4463	261	9	.	.	PUNCT
ejpam-4463	262	1	annali	annali	PROPN
ejpam-4463	262	2	della	della	PROPN
ejpam-4463	262	3	scuola	scuola	PROPN
ejpam-4463	262	4	normale	normale	PROPN
ejpam-4463	262	5	superiore	superiore	PROPN
ejpam-4463	262	6	di	di	PROPN
ejpam-4463	262	7	pisa	pisa	PROPN
ejpam-4463	262	8	-	-	PROPN
ejpam-4463	262	9	classe	classe	PROPN
ejpam-4463	262	10	di	di	X
ejpam-4463	262	11	scienze	scienze	PROPN
ejpam-4463	262	12	,	,	PUNCT
ejpam-4463	262	13	7(3	7(3	NUM
ejpam-4463	262	14	-	-	SYM
ejpam-4463	262	15	4):205–248	4):205–248	NUM
ejpam-4463	262	16	,	,	PUNCT
ejpam-4463	262	17	1938	1938	NUM
ejpam-4463	262	18	.	.	PUNCT
ejpam-4463	263	1	[	[	X
ejpam-4463	263	2	10	10	NUM
ejpam-4463	263	3	]	]	X
ejpam-4463	263	4	raphael	raphael	PROPN
ejpam-4463	263	5	salem	salem	PROPN
ejpam-4463	263	6	.	.	PUNCT
ejpam-4463	264	1	a	a	DET
ejpam-4463	264	2	remarkable	remarkable	ADJ
ejpam-4463	264	3	class	class	NOUN
ejpam-4463	264	4	of	of	ADP
ejpam-4463	264	5	algebraic	algebraic	ADJ
ejpam-4463	264	6	integers	integer	NOUN
ejpam-4463	264	7	.	.	PUNCT
ejpam-4463	265	1	proof	proof	NOUN
ejpam-4463	265	2	of	of	ADP
ejpam-4463	265	3	a	a	DET
ejpam-4463	265	4	conjecture	conjecture	NOUN
ejpam-4463	265	5	of	of	ADP
ejpam-4463	265	6	vijayaraghavan	vijayaraghavan	NOUN
ejpam-4463	265	7	.	.	PUNCT
ejpam-4463	266	1	duke	duke	PROPN
ejpam-4463	266	2	mathematical	mathematical	PROPN
ejpam-4463	266	3	journal	journal	PROPN
ejpam-4463	266	4	,	,	PUNCT
ejpam-4463	266	5	11(1):103–108	11(1):103–108	PROPN
ejpam-4463	266	6	,	,	PUNCT
ejpam-4463	266	7	1944	1944	NUM
ejpam-4463	266	8	.	.	PUNCT
ejpam-4463	267	1	[	[	X
ejpam-4463	267	2	11	11	NUM
ejpam-4463	267	3	]	]	X
ejpam-4463	267	4	raphael	raphael	PROPN
ejpam-4463	267	5	salem	salem	PROPN
ejpam-4463	267	6	.	.	PUNCT
ejpam-4463	268	1	power	power	NOUN
ejpam-4463	268	2	series	series	PROPN
ejpam-4463	268	3	with	with	ADP
ejpam-4463	268	4	integral	integral	ADJ
ejpam-4463	268	5	coefficients	coefficient	NOUN
ejpam-4463	268	6	.	.	PUNCT
ejpam-4463	269	1	duke	duke	PROPN
ejpam-4463	269	2	mathematical	mathematical	PROPN
ejpam-4463	269	3	journal	journal	PROPN
ejpam-4463	269	4	,	,	PUNCT
ejpam-4463	269	5	12(1):153–172	12(1):153–172	PROPN
ejpam-4463	269	6	,	,	PUNCT
ejpam-4463	269	7	1945	1945	NUM
ejpam-4463	269	8	.	.	PUNCT
ejpam-4463	270	1	[	[	X
ejpam-4463	270	2	12	12	NUM
ejpam-4463	270	3	]	]	PUNCT
ejpam-4463	270	4	raphaël	raphaël	PROPN
ejpam-4463	270	5	salem	salem	NOUN
ejpam-4463	270	6	.	.	PUNCT
ejpam-4463	271	1	algebraic	algebraic	ADJ
ejpam-4463	271	2	numbers	number	NOUN
ejpam-4463	271	3	and	and	CCONJ
ejpam-4463	271	4	fourier	fouri	ADJ
ejpam-4463	271	5	analysis	analysis	NOUN
ejpam-4463	271	6	,	,	PUNCT
ejpam-4463	271	7	dc	dc	PROPN
ejpam-4463	271	8	heath	heath	PROPN
ejpam-4463	271	9	and	and	CCONJ
ejpam-4463	271	10	co.	co.	PROPN
ejpam-4463	271	11	boston	boston	PROPN
ejpam-4463	271	12	,	,	PUNCT
ejpam-4463	271	13	mass	mass	PROPN
ejpam-4463	271	14	,	,	PUNCT
ejpam-4463	271	15	1963	1963	NUM
ejpam-4463	271	16	.	.	PUNCT
ejpam-4463	272	1	[	[	X
ejpam-4463	272	2	13	13	NUM
ejpam-4463	272	3	]	]	PUNCT
ejpam-4463	272	4	raphaël	raphaël	PROPN
ejpam-4463	272	5	salem	salem	NOUN
ejpam-4463	272	6	.	.	PUNCT
ejpam-4463	273	1	algebraic	algebraic	ADJ
ejpam-4463	273	2	numbers	number	NOUN
ejpam-4463	273	3	and	and	CCONJ
ejpam-4463	273	4	fourier	fouri	ADJ
ejpam-4463	273	5	analysis	analysis	NOUN
ejpam-4463	273	6	,	,	PUNCT
ejpam-4463	273	7	dc	dc	PROPN
ejpam-4463	273	8	heath	heath	PROPN
ejpam-4463	273	9	and	and	CCONJ
ejpam-4463	273	10	co.	co.	PROPN
ejpam-4463	273	11	boston	boston	PROPN
ejpam-4463	273	12	,	,	PUNCT
ejpam-4463	273	13	mass	mass	PROPN
ejpam-4463	273	14	,	,	PUNCT
ejpam-4463	273	15	1963	1963	NUM
ejpam-4463	273	16	.	.	PUNCT
ejpam-4463	274	1	references	reference	NOUN
ejpam-4463	274	2	1330	1330	NUM
ejpam-4463	274	3	[	[	X
ejpam-4463	274	4	14	14	NUM
ejpam-4463	274	5	]	]	PUNCT
ejpam-4463	274	6	carl	carl	PROPN
ejpam-4463	274	7	ludwig	ludwig	PROPN
ejpam-4463	274	8	siegel	siegel	PROPN
ejpam-4463	274	9	.	.	PUNCT
ejpam-4463	275	1	algebraic	algebraic	PROPN
ejpam-4463	275	2	integers	integer	NOUN
ejpam-4463	275	3	whose	whose	DET
ejpam-4463	275	4	conjugates	conjugate	NOUN
ejpam-4463	275	5	lie	lie	VERB
ejpam-4463	275	6	in	in	ADP
ejpam-4463	275	7	the	the	DET
ejpam-4463	275	8	unit	unit	NOUN
ejpam-4463	275	9	circle	circle	NOUN
ejpam-4463	275	10	.	.	PUNCT
ejpam-4463	276	1	duke	duke	PROPN
ejpam-4463	276	2	mathematical	mathematical	PROPN
ejpam-4463	276	3	journal	journal	PROPN
ejpam-4463	276	4	,	,	PUNCT
ejpam-4463	276	5	11(3):597–602	11(3):597–602	NUM
ejpam-4463	276	6	,	,	PUNCT
ejpam-4463	276	7	1944	1944	NUM
ejpam-4463	276	8	.	.	PUNCT
ejpam-4463	277	1	[	[	X
ejpam-4463	277	2	15	15	NUM
ejpam-4463	277	3	]	]	X
ejpam-4463	277	4	chris	chris	PROPN
ejpam-4463	277	5	smyth	smyth	PROPN
ejpam-4463	277	6	.	.	PUNCT
ejpam-4463	278	1	survey	survey	NOUN
ejpam-4463	278	2	article	article	NOUN
ejpam-4463	278	3	:	:	PUNCT
ejpam-4463	278	4	seventy	seventy	NUM
ejpam-4463	278	5	years	year	NOUN
ejpam-4463	278	6	of	of	ADP
ejpam-4463	278	7	salem	salem	NOUN
ejpam-4463	278	8	numbers	number	NOUN
ejpam-4463	278	9	.	.	PUNCT
ejpam-4463	279	1	arxiv	arxiv	PROPN
ejpam-4463	279	2	preprint	preprint	VERB
ejpam-4463	279	3	arxiv:1408.0195	arxiv:1408.0195	PROPN
ejpam-4463	279	4	,	,	PUNCT
ejpam-4463	279	5	2014	2014	NUM
ejpam-4463	279	6	.	.	PUNCT
ejpam-4463	280	1	[	[	X
ejpam-4463	280	2	16	16	NUM
ejpam-4463	280	3	]	]	X
ejpam-4463	280	4	vladimir	vladimir	PROPN
ejpam-4463	280	5	gennadievich	gennadievich	PROPN
ejpam-4463	280	6	sprindzhuk	sprindzhuk	NOUN
ejpam-4463	280	7	.	.	PUNCT
ejpam-4463	281	1	mahler	mahler	PROPN
ejpam-4463	281	2	’s	’s	PART
ejpam-4463	281	3	problem	problem	NOUN
ejpam-4463	281	4	in	in	ADP
ejpam-4463	281	5	metric	metric	ADJ
ejpam-4463	281	6	number	number	NOUN
ejpam-4463	281	7	theory	theory	NOUN
ejpam-4463	281	8	,	,	PUNCT
ejpam-4463	281	9	volume	volume	NOUN
ejpam-4463	281	10	25	25	NUM
ejpam-4463	281	11	.	.	PUNCT
ejpam-4463	282	1	american	american	PROPN
ejpam-4463	282	2	mathematical	mathematical	PROPN
ejpam-4463	282	3	soc	soc	PROPN
ejpam-4463	282	4	.	.	PUNCT
ejpam-4463	282	5	,	,	PUNCT
ejpam-4463	282	6	1969	1969	NUM
ejpam-4463	282	7	.	.	PUNCT
ejpam-4463	283	1	[	[	X
ejpam-4463	283	2	17	17	NUM
ejpam-4463	283	3	]	]	X
ejpam-4463	283	4	axel	axel	PROPN
ejpam-4463	283	5	thue	thue	PROPN
ejpam-4463	283	6	.	.	PUNCT
ejpam-4463	284	1	über	über	PROPN
ejpam-4463	284	2	eine	eine	PROPN
ejpam-4463	284	3	eigenschaft	eigenschaft	PROPN
ejpam-4463	284	4	die	die	VERB
ejpam-4463	284	5	keine	keine	PROPN
ejpam-4463	284	6	transcendente	transcendente	PROPN
ejpam-4463	284	7	grösse	grösse	PROPN
ejpam-4463	284	8	haben	haben	VERB
ejpam-4463	284	9	kann	kann	PROPN
ejpam-4463	284	10	.	.	PUNCT
ejpam-4463	285	1	na	na	NOUN
ejpam-4463	285	2	,	,	PUNCT
ejpam-4463	285	3	1912	1912	NUM
ejpam-4463	285	4	.	.	PUNCT
ejpam-4463	286	1	[	[	X
ejpam-4463	286	2	18	18	NUM
ejpam-4463	286	3	]	]	PUNCT
ejpam-4463	286	4	t	t	NOUN
ejpam-4463	286	5	vijayaraghavan	vijayaraghavan	NOUN
ejpam-4463	286	6	.	.	PUNCT
ejpam-4463	287	1	on	on	ADP
ejpam-4463	287	2	the	the	DET
ejpam-4463	287	3	fractional	fractional	ADJ
ejpam-4463	287	4	parts	part	NOUN
ejpam-4463	287	5	of	of	ADP
ejpam-4463	287	6	the	the	DET
ejpam-4463	287	7	powers	power	NOUN
ejpam-4463	287	8	of	of	ADP
ejpam-4463	287	9	a	a	DET
ejpam-4463	287	10	number	number	NOUN
ejpam-4463	287	11	(	(	PUNCT
ejpam-4463	287	12	ii	ii	NOUN
ejpam-4463	287	13	)	)	PUNCT
ejpam-4463	287	14	.	.	PUNCT
ejpam-4463	288	1	in	in	ADP
ejpam-4463	288	2	mathematical	mathematical	ADJ
ejpam-4463	288	3	proceedings	proceeding	NOUN
ejpam-4463	288	4	of	of	ADP
ejpam-4463	288	5	the	the	DET
ejpam-4463	288	6	cambridge	cambridge	PROPN
ejpam-4463	288	7	philosophical	philosophical	ADJ
ejpam-4463	288	8	society	society	NOUN
ejpam-4463	288	9	,	,	PUNCT
ejpam-4463	288	10	volume	volume	NOUN
ejpam-4463	288	11	37	37	NUM
ejpam-4463	288	12	,	,	PUNCT
ejpam-4463	288	13	pages	page	NOUN
ejpam-4463	288	14	349	349	NUM
ejpam-4463	288	15	–	–	PUNCT
ejpam-4463	288	16	357	357	NUM
ejpam-4463	288	17	.	.	PUNCT
ejpam-4463	289	1	cambridge	cambridge	PROPN
ejpam-4463	289	2	university	university	PROPN
ejpam-4463	289	3	press	press	NOUN
ejpam-4463	289	4	,	,	PUNCT
ejpam-4463	289	5	1941	1941	NUM
ejpam-4463	289	6	.	.	PUNCT
ejpam-4463	290	1	[	[	X
ejpam-4463	290	2	19	19	NUM
ejpam-4463	290	3	]	]	PUNCT
ejpam-4463	290	4	t	t	NOUN
ejpam-4463	290	5	vijayaraghavan	vijayaraghavan	NOUN
ejpam-4463	290	6	.	.	PUNCT
ejpam-4463	291	1	on	on	ADP
ejpam-4463	291	2	the	the	DET
ejpam-4463	291	3	fractional	fractional	ADJ
ejpam-4463	291	4	parts	part	NOUN
ejpam-4463	291	5	of	of	ADP
ejpam-4463	291	6	the	the	DET
ejpam-4463	291	7	powers	power	NOUN
ejpam-4463	291	8	of	of	ADP
ejpam-4463	291	9	a	a	DET
ejpam-4463	291	10	number	number	NOUN
ejpam-4463	291	11	(	(	PUNCT
ejpam-4463	291	12	iii	iii	NOUN
ejpam-4463	291	13	)	)	PUNCT
ejpam-4463	291	14	.	.	PUNCT
ejpam-4463	292	1	journal	journal	PROPN
ejpam-4463	292	2	of	of	ADP
ejpam-4463	292	3	the	the	DET
ejpam-4463	292	4	london	london	PROPN
ejpam-4463	292	5	mathematical	mathematical	ADJ
ejpam-4463	292	6	society	society	NOUN
ejpam-4463	292	7	,	,	PUNCT
ejpam-4463	292	8	1(3):137–138	1(3):137–138	NUM
ejpam-4463	292	9	,	,	PUNCT
ejpam-4463	292	10	1942	1942	NUM
ejpam-4463	292	11	.	.	PUNCT