id	sid	tid	token	lemma	pos
ejpam-5095	1	1	european	european	PROPN
ejpam-5095	1	2	journal	journal	PROPN
ejpam-5095	1	3	of	of	ADP
ejpam-5095	1	4	pure	pure	ADJ
ejpam-5095	1	5	and	and	CCONJ
ejpam-5095	1	6	applied	apply	VERB
ejpam-5095	1	7	mathematics	mathematic	NOUN
ejpam-5095	1	8	vol	vol	NOUN
ejpam-5095	1	9	.	.	PROPN
ejpam-5095	2	1	17	17	NUM
ejpam-5095	2	2	,	,	PUNCT
ejpam-5095	2	3	no	no	INTJ
ejpam-5095	2	4	.	.	NOUN
ejpam-5095	2	5	2	2	NUM
ejpam-5095	2	6	,	,	PUNCT
ejpam-5095	2	7	2024	2024	NUM
ejpam-5095	2	8	,	,	PUNCT
ejpam-5095	2	9	721	721	NUM
ejpam-5095	2	10	-	-	SYM
ejpam-5095	2	11	724	724	NUM
ejpam-5095	2	12	issn	issn	PROPN
ejpam-5095	2	13	1307	1307	NUM
ejpam-5095	2	14	-	-	SYM
ejpam-5095	2	15	5543	5543	NUM
ejpam-5095	2	16	–	–	PUNCT
ejpam-5095	3	1	ejpam.com	ejpam.com	X
ejpam-5095	3	2	published	publish	VERB
ejpam-5095	3	3	by	by	ADP
ejpam-5095	3	4	new	new	PROPN
ejpam-5095	3	5	york	york	PROPN
ejpam-5095	3	6	business	business	PROPN
ejpam-5095	3	7	global	global	ADJ
ejpam-5095	3	8	note	note	NOUN
ejpam-5095	3	9	on	on	ADP
ejpam-5095	3	10	irreducible	irreducible	ADJ
ejpam-5095	3	11	polynomials	polynomial	NOUN
ejpam-5095	3	12	over	over	ADP
ejpam-5095	3	13	fq[x	fq[x	PROPN
ejpam-5095	3	14	]	]	PUNCT
ejpam-5095	3	15	alanod	alanod	PROPN
ejpam-5095	3	16	m.	m.	PROPN
ejpam-5095	3	17	sibih	sibih	PROPN
ejpam-5095	3	18	department	department	PROPN
ejpam-5095	3	19	of	of	ADP
ejpam-5095	3	20	mathematics	mathematic	NOUN
ejpam-5095	3	21	,	,	PUNCT
ejpam-5095	3	22	jamoum	jamoum	PROPN
ejpam-5095	3	23	university	university	PROPN
ejpam-5095	3	24	college	college	NOUN
ejpam-5095	3	25	,	,	PUNCT
ejpam-5095	3	26	umm	umm	INTJ
ejpam-5095	3	27	al	al	PROPN
ejpam-5095	3	28	-	-	PUNCT
ejpam-5095	3	29	qura	qura	PROPN
ejpam-5095	3	30	university	university	NOUN
ejpam-5095	3	31	,	,	PUNCT
ejpam-5095	3	32	holly	holly	PROPN
ejpam-5095	3	33	makkah	makkah	PROPN
ejpam-5095	3	34	21955	21955	NUM
ejpam-5095	3	35	,	,	PUNCT
ejpam-5095	3	36	saudi	saudi	PROPN
ejpam-5095	3	37	arabia	arabia	PROPN
ejpam-5095	3	38	abstract	abstract	NOUN
ejpam-5095	3	39	.	.	PUNCT
ejpam-5095	4	1	in	in	ADP
ejpam-5095	4	2	this	this	DET
ejpam-5095	4	3	note	note	NOUN
ejpam-5095	4	4	,	,	PUNCT
ejpam-5095	4	5	we	we	PRON
ejpam-5095	4	6	provide	provide	VERB
ejpam-5095	4	7	a	a	DET
ejpam-5095	4	8	new	new	ADJ
ejpam-5095	4	9	criterion	criterion	NOUN
ejpam-5095	4	10	of	of	ADP
ejpam-5095	4	11	polynomials	polynomial	NOUN
ejpam-5095	4	12	’s	’s	PART
ejpam-5095	4	13	irreducibility	irreducibility	NOUN
ejpam-5095	4	14	over	over	ADP
ejpam-5095	4	15	fq[x	fq[x	PROPN
ejpam-5095	4	16	]	]	PUNCT
ejpam-5095	4	17	,	,	PUNCT
ejpam-5095	4	18	where	where	SCONJ
ejpam-5095	4	19	fq	fq	PROPN
ejpam-5095	4	20	is	be	AUX
ejpam-5095	4	21	a	a	DET
ejpam-5095	4	22	finite	finite	ADJ
ejpam-5095	4	23	field	field	NOUN
ejpam-5095	4	24	.	.	PUNCT
ejpam-5095	5	1	2020	2020	NUM
ejpam-5095	5	2	mathematics	mathematic	NOUN
ejpam-5095	5	3	subject	subject	NOUN
ejpam-5095	5	4	classifications	classification	NOUN
ejpam-5095	5	5	:	:	PUNCT
ejpam-5095	5	6	11txx	11txx	NOUN
ejpam-5095	5	7	,	,	PUNCT
ejpam-5095	5	8	11t55	11t55	NUM
ejpam-5095	5	9	key	key	ADJ
ejpam-5095	5	10	words	word	NOUN
ejpam-5095	5	11	and	and	CCONJ
ejpam-5095	5	12	phrases	phrase	NOUN
ejpam-5095	5	13	:	:	PUNCT
ejpam-5095	5	14	polynomials	polynomial	NOUN
ejpam-5095	5	15	,	,	PUNCT
ejpam-5095	5	16	irreducibility	irreducibility	NOUN
ejpam-5095	5	17	,	,	PUNCT
ejpam-5095	5	18	criterion	criterion	NOUN
ejpam-5095	5	19	,	,	PUNCT
ejpam-5095	5	20	finite	finite	ADJ
ejpam-5095	5	21	fields	field	NOUN
ejpam-5095	5	22	.	.	PUNCT
ejpam-5095	6	1	1	1	X
ejpam-5095	6	2	.	.	X
ejpam-5095	6	3	introduction	introduction	NOUN
ejpam-5095	6	4	a	a	DET
ejpam-5095	6	5	polynomial	polynomial	NOUN
ejpam-5095	6	6	is	be	AUX
ejpam-5095	6	7	reducible	reducible	ADJ
ejpam-5095	6	8	over	over	ADP
ejpam-5095	6	9	a	a	DET
ejpam-5095	6	10	given	give	VERB
ejpam-5095	6	11	field	field	NOUN
ejpam-5095	6	12	if	if	SCONJ
ejpam-5095	6	13	it	it	PRON
ejpam-5095	6	14	can	can	AUX
ejpam-5095	6	15	be	be	AUX
ejpam-5095	6	16	expressed	express	VERB
ejpam-5095	6	17	as	as	ADP
ejpam-5095	6	18	a	a	DET
ejpam-5095	6	19	product	product	NOUN
ejpam-5095	6	20	of	of	ADP
ejpam-5095	6	21	lower	low	ADJ
ejpam-5095	6	22	degree	degree	NOUN
ejpam-5095	6	23	polynomials	polynomial	NOUN
ejpam-5095	6	24	with	with	ADP
ejpam-5095	6	25	coefficients	coefficient	NOUN
ejpam-5095	6	26	in	in	ADP
ejpam-5095	6	27	the	the	DET
ejpam-5095	6	28	same	same	ADJ
ejpam-5095	6	29	field	field	NOUN
ejpam-5095	6	30	.	.	PUNCT
ejpam-5095	7	1	otherwise	otherwise	ADV
ejpam-5095	7	2	,	,	PUNCT
ejpam-5095	7	3	it	it	PRON
ejpam-5095	7	4	is	be	AUX
ejpam-5095	7	5	called	call	VERB
ejpam-5095	7	6	to	to	PART
ejpam-5095	7	7	be	be	AUX
ejpam-5095	7	8	irreducible	irreducible	ADJ
ejpam-5095	7	9	.	.	PUNCT
ejpam-5095	8	1	we	we	PRON
ejpam-5095	8	2	are	be	AUX
ejpam-5095	8	3	interested	interested	ADJ
ejpam-5095	8	4	in	in	ADP
ejpam-5095	8	5	determining	determine	VERB
ejpam-5095	8	6	if	if	SCONJ
ejpam-5095	8	7	a	a	DET
ejpam-5095	8	8	particular	particular	ADJ
ejpam-5095	8	9	polynomial	polynomial	NOUN
ejpam-5095	8	10	is	be	AUX
ejpam-5095	8	11	irreducible	irreducible	ADJ
ejpam-5095	8	12	or	or	CCONJ
ejpam-5095	8	13	not	not	PART
ejpam-5095	8	14	.	.	PUNCT
ejpam-5095	9	1	as	as	ADP
ejpam-5095	9	2	a	a	DET
ejpam-5095	9	3	result	result	NOUN
ejpam-5095	9	4	,	,	PUNCT
ejpam-5095	9	5	a	a	DET
ejpam-5095	9	6	simple	simple	ADJ
ejpam-5095	9	7	test	test	NOUN
ejpam-5095	9	8	or	or	CCONJ
ejpam-5095	9	9	criterion	criterion	NOUN
ejpam-5095	9	10	for	for	ADP
ejpam-5095	9	11	obtaining	obtain	VERB
ejpam-5095	9	12	this	this	DET
ejpam-5095	9	13	information	information	NOUN
ejpam-5095	9	14	is	be	AUX
ejpam-5095	9	15	desirable	desirable	ADJ
ejpam-5095	9	16	.	.	PUNCT
ejpam-5095	10	1	unfortunately	unfortunately	ADV
ejpam-5095	10	2	,	,	PUNCT
ejpam-5095	10	3	no	no	DET
ejpam-5095	10	4	such	such	ADJ
ejpam-5095	10	5	criterion	criterion	NOUN
ejpam-5095	10	6	that	that	PRON
ejpam-5095	10	7	applies	apply	VERB
ejpam-5095	10	8	to	to	ADP
ejpam-5095	10	9	all	all	DET
ejpam-5095	10	10	classes	class	NOUN
ejpam-5095	10	11	of	of	ADP
ejpam-5095	10	12	polynomials	polynomial	NOUN
ejpam-5095	10	13	has	have	AUX
ejpam-5095	10	14	yet	yet	ADV
ejpam-5095	10	15	been	be	AUX
ejpam-5095	10	16	developed	develop	VERB
ejpam-5095	10	17	;	;	PUNCT
ejpam-5095	10	18	nonetheless	nonetheless	ADV
ejpam-5095	10	19	,	,	PUNCT
ejpam-5095	10	20	a	a	DET
ejpam-5095	10	21	number	number	NOUN
ejpam-5095	10	22	of	of	ADP
ejpam-5095	10	23	tests	test	NOUN
ejpam-5095	10	24	,	,	PUNCT
ejpam-5095	10	25	or	or	CCONJ
ejpam-5095	10	26	irreducibility	irreducibility	NOUN
ejpam-5095	10	27	criteria	criterion	NOUN
ejpam-5095	10	28	,	,	PUNCT
ejpam-5095	10	29	have	have	AUX
ejpam-5095	10	30	been	be	AUX
ejpam-5095	10	31	discovered	discover	VERB
ejpam-5095	10	32	so	so	ADV
ejpam-5095	10	33	far	far	ADV
ejpam-5095	10	34	that	that	PRON
ejpam-5095	10	35	provide	provide	VERB
ejpam-5095	10	36	useful	useful	ADJ
ejpam-5095	10	37	information	information	NOUN
ejpam-5095	10	38	for	for	ADP
ejpam-5095	10	39	some	some	DET
ejpam-5095	10	40	specific	specific	ADJ
ejpam-5095	10	41	classes	class	NOUN
ejpam-5095	10	42	of	of	ADP
ejpam-5095	10	43	polynomials	polynomial	NOUN
ejpam-5095	10	44	.	.	PUNCT
ejpam-5095	11	1	this	this	DET
ejpam-5095	11	2	article	article	NOUN
ejpam-5095	11	3	focuses	focus	VERB
ejpam-5095	11	4	on	on	ADP
ejpam-5095	11	5	irreducible	irreducible	ADJ
ejpam-5095	11	6	polynomials	polynomial	NOUN
ejpam-5095	11	7	with	with	ADP
ejpam-5095	11	8	coefficients	coefficient	NOUN
ejpam-5095	11	9	in	in	ADP
ejpam-5095	11	10	fq[x	fq[x	PROPN
ejpam-5095	11	11	]	]	PUNCT
ejpam-5095	11	12	,	,	PUNCT
ejpam-5095	11	13	where	where	SCONJ
ejpam-5095	11	14	over	over	ADP
ejpam-5095	11	15	fq	fq	PROPN
ejpam-5095	11	16	is	be	AUX
ejpam-5095	11	17	a	a	DET
ejpam-5095	11	18	finite	finite	ADJ
ejpam-5095	11	19	field	field	NOUN
ejpam-5095	11	20	.	.	PUNCT
ejpam-5095	12	1	a.	a.	PROPN
ejpam-5095	12	2	chandoul	chandoul	PROPN
ejpam-5095	12	3	et	et	PROPN
ejpam-5095	12	4	al	al	PROPN
ejpam-5095	12	5	.	.	PUNCT
ejpam-5095	13	1	[	[	X
ejpam-5095	13	2	2	2	NUM
ejpam-5095	13	3	]	]	PUNCT
ejpam-5095	13	4	,	,	PUNCT
ejpam-5095	13	5	proved	prove	VERB
ejpam-5095	13	6	a	a	DET
ejpam-5095	13	7	widely	widely	ADV
ejpam-5095	13	8	accepted	accept	VERB
ejpam-5095	13	9	irreducibility	irreducibility	NOUN
ejpam-5095	13	10	criterion	criterion	NOUN
ejpam-5095	13	11	,	,	PUNCT
ejpam-5095	13	12	which	which	PRON
ejpam-5095	13	13	states	state	VERB
ejpam-5095	13	14	that	that	SCONJ
ejpam-5095	13	15	:	:	PUNCT
ejpam-5095	13	16	theorem	theorem	NOUN
ejpam-5095	13	17	1	1	NUM
ejpam-5095	13	18	.	.	PUNCT
ejpam-5095	14	1	if	if	SCONJ
ejpam-5095	14	2	λ(y	λ(y	PROPN
ejpam-5095	14	3	)	)	PUNCT
ejpam-5095	15	1	=	=	PUNCT
ejpam-5095	15	2	y	y	PROPN
ejpam-5095	15	3	d+λd−1y	d+λd−1y	PROPN
ejpam-5095	15	4	d−1	d−1	PROPN
ejpam-5095	15	5	+	+	PROPN
ejpam-5095	15	6	·	·	PUNCT
ejpam-5095	15	7	·	·	PUNCT
ejpam-5095	15	8	·	·	PUNCT
ejpam-5095	15	9	+	+	NOUN
ejpam-5095	15	10	λ0	λ0	NOUN
ejpam-5095	15	11	be	be	VERB
ejpam-5095	15	12	a	a	DET
ejpam-5095	15	13	polynomial	polynomial	NOUN
ejpam-5095	15	14	with	with	ADP
ejpam-5095	15	15	λi	λi	ADP
ejpam-5095	15	16	∈q	∈q	NOUN
ejpam-5095	15	17	[	[	X
ejpam-5095	15	18	x	x	X
ejpam-5095	15	19	]	]	X
ejpam-5095	15	20	,	,	PUNCT
ejpam-5095	15	21	λ0	λ0	NOUN
ejpam-5095	15	22	̸=	̸=	PROPN
ejpam-5095	15	23	0	0	NUM
ejpam-5095	15	24	and	and	CCONJ
ejpam-5095	15	25	deg	deg	PROPN
ejpam-5095	15	26	λd−1	λd−1	PROPN
ejpam-5095	15	27	>	>	X
ejpam-5095	15	28	deg	deg	PROPN
ejpam-5095	15	29	λi	λi	AUX
ejpam-5095	15	30	,	,	PUNCT
ejpam-5095	15	31	for	for	ADP
ejpam-5095	15	32	each	each	DET
ejpam-5095	15	33	i	i	PRON
ejpam-5095	15	34	̸=	̸=	PROPN
ejpam-5095	15	35	d−	d−	PROPN
ejpam-5095	15	36	1	1	NUM
ejpam-5095	15	37	.	.	PUNCT
ejpam-5095	16	1	then	then	ADV
ejpam-5095	16	2	λ	λ	PROPN
ejpam-5095	16	3	is	be	AUX
ejpam-5095	16	4	irreducible	irreducible	ADJ
ejpam-5095	16	5	over	over	ADP
ejpam-5095	16	6	q[x	q[x	PROPN
ejpam-5095	16	7	]	]	PUNCT
ejpam-5095	16	8	.	.	PUNCT
ejpam-5095	17	1	this	this	DET
ejpam-5095	17	2	result	result	NOUN
ejpam-5095	17	3	was	be	AUX
ejpam-5095	17	4	the	the	DET
ejpam-5095	17	5	starting	starting	NOUN
ejpam-5095	17	6	point	point	NOUN
ejpam-5095	17	7	for	for	ADP
ejpam-5095	17	8	many	many	ADJ
ejpam-5095	17	9	researches	research	NOUN
ejpam-5095	17	10	and	and	CCONJ
ejpam-5095	17	11	the	the	DET
ejpam-5095	17	12	exploration	exploration	NOUN
ejpam-5095	17	13	of	of	ADP
ejpam-5095	17	14	new	new	ADJ
ejpam-5095	17	15	criterions	criterion	NOUN
ejpam-5095	17	16	,	,	PUNCT
ejpam-5095	17	17	see	see	VERB
ejpam-5095	17	18	[	[	X
ejpam-5095	17	19	1	1	NUM
ejpam-5095	17	20	,	,	PUNCT
ejpam-5095	17	21	3	3	NUM
ejpam-5095	17	22	]	]	PUNCT
ejpam-5095	17	23	.	.	PUNCT
ejpam-5095	18	1	for	for	ADP
ejpam-5095	18	2	older	old	ADJ
ejpam-5095	18	3	results	result	NOUN
ejpam-5095	18	4	,	,	PUNCT
ejpam-5095	18	5	see	see	VERB
ejpam-5095	18	6	[	[	X
ejpam-5095	18	7	4	4	NUM
ejpam-5095	18	8	,	,	PUNCT
ejpam-5095	18	9	5	5	NUM
ejpam-5095	18	10	]	]	PUNCT
ejpam-5095	18	11	.	.	PUNCT
ejpam-5095	19	1	in	in	ADP
ejpam-5095	19	2	this	this	DET
ejpam-5095	19	3	note	note	NOUN
ejpam-5095	19	4	,	,	PUNCT
ejpam-5095	19	5	we	we	PRON
ejpam-5095	19	6	provide	provide	VERB
ejpam-5095	19	7	a	a	DET
ejpam-5095	19	8	new	new	ADJ
ejpam-5095	19	9	criterion	criterion	NOUN
ejpam-5095	19	10	of	of	ADP
ejpam-5095	19	11	polynomials	polynomial	NOUN
ejpam-5095	19	12	’s	’s	PART
ejpam-5095	19	13	irreducibility	irreducibility	NOUN
ejpam-5095	19	14	over	over	ADP
ejpam-5095	19	15	fq[x	fq[x	PROPN
ejpam-5095	19	16	]	]	PUNCT
ejpam-5095	19	17	.	.	PUNCT
ejpam-5095	20	1	doi	doi	NOUN
ejpam-5095	20	2	:	:	PUNCT
ejpam-5095	20	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5095	https://doi.org/10.29020/nybg.ejpam.v17i2.5095	NUM
ejpam-5095	20	4	email	email	NOUN
ejpam-5095	20	5	address	address	NOUN
ejpam-5095	20	6	:	:	PUNCT
ejpam-5095	20	7	amsibih@uqu.edu.sa	amsibih@uqu.edu.sa	PROPN
ejpam-5095	20	8	(	(	PUNCT
ejpam-5095	20	9	a.	a.	NOUN
ejpam-5095	20	10	m.	m.	NOUN
ejpam-5095	20	11	sibih	sibih	PROPN
ejpam-5095	20	12	)	)	PUNCT
ejpam-5095	20	13	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5095	21	1	721	721	NUM
ejpam-5095	22	1	©	©	ADP
ejpam-5095	22	2	2024	2024	NUM
ejpam-5095	22	3	ejpam	ejpam	NOUN
ejpam-5095	22	4	all	all	DET
ejpam-5095	22	5	rights	right	NOUN
ejpam-5095	22	6	reserved	reserve	VERB
ejpam-5095	22	7	.	.	PUNCT
ejpam-5095	23	1	a.	a.	NOUN
ejpam-5095	23	2	m.	m.	PROPN
ejpam-5095	23	3	sibih	sibih	PROPN
ejpam-5095	23	4	/	/	SYM
ejpam-5095	23	5	eur	eur	PROPN
ejpam-5095	23	6	.	.	PUNCT
ejpam-5095	24	1	j.	j.	PROPN
ejpam-5095	24	2	pure	pure	PROPN
ejpam-5095	24	3	appl	appl	PROPN
ejpam-5095	24	4	.	.	PROPN
ejpam-5095	24	5	math	math	PROPN
ejpam-5095	24	6	,	,	PUNCT
ejpam-5095	24	7	17	17	NUM
ejpam-5095	24	8	(	(	PUNCT
ejpam-5095	24	9	2	2	NUM
ejpam-5095	24	10	)	)	PUNCT
ejpam-5095	24	11	(	(	PUNCT
ejpam-5095	24	12	2024	2024	NUM
ejpam-5095	24	13	)	)	PUNCT
ejpam-5095	24	14	,	,	PUNCT
ejpam-5095	24	15	721	721	NUM
ejpam-5095	24	16	-	-	SYM
ejpam-5095	24	17	724	724	NUM
ejpam-5095	24	18	722	722	NUM
ejpam-5095	24	19	2	2	NUM
ejpam-5095	24	20	.	.	PUNCT
ejpam-5095	25	1	preliminaries	preliminary	NOUN
ejpam-5095	25	2	let	let	VERB
ejpam-5095	25	3	fq	fq	PRON
ejpam-5095	25	4	be	be	AUX
ejpam-5095	25	5	the	the	DET
ejpam-5095	25	6	finite	finite	ADJ
ejpam-5095	25	7	field	field	NOUN
ejpam-5095	25	8	and	and	CCONJ
ejpam-5095	25	9	denote	denote	VERB
ejpam-5095	25	10	by	by	ADP
ejpam-5095	25	11	fq[x	fq[x	PROPN
ejpam-5095	25	12	]	]	X
ejpam-5095	25	13	the	the	DET
ejpam-5095	25	14	ring	ring	NOUN
ejpam-5095	25	15	of	of	ADP
ejpam-5095	25	16	polynomials	polynomial	NOUN
ejpam-5095	25	17	with	with	ADP
ejpam-5095	25	18	coefficients	coefficient	NOUN
ejpam-5095	25	19	in	in	ADP
ejpam-5095	25	20	fq	fq	PROPN
ejpam-5095	25	21	and	and	CCONJ
ejpam-5095	25	22	by	by	ADP
ejpam-5095	25	23	fq(x	fq(x	NOUN
ejpam-5095	25	24	)	)	PUNCT
ejpam-5095	25	25	the	the	DET
ejpam-5095	25	26	quotient	quotient	NOUN
ejpam-5095	25	27	field	field	NOUN
ejpam-5095	25	28	of	of	ADP
ejpam-5095	25	29	fq[x	fq[x	PROPN
ejpam-5095	25	30	]	]	PUNCT
ejpam-5095	25	31	.	.	PUNCT
ejpam-5095	26	1	let	let	VERB
ejpam-5095	26	2	fq((x	fq((x	NOUN
ejpam-5095	26	3	−1	−1	VERB
ejpam-5095	26	4	)	)	PUNCT
ejpam-5095	26	5	)	)	PUNCT
ejpam-5095	27	1	be	be	AUX
ejpam-5095	27	2	the	the	DET
ejpam-5095	27	3	field	field	NOUN
ejpam-5095	27	4	of	of	ADP
ejpam-5095	27	5	laurent	laurent	ADJ
ejpam-5095	27	6	formal	formal	ADJ
ejpam-5095	27	7	power	power	NOUN
ejpam-5095	27	8	series	series	NOUN
ejpam-5095	27	9	defined	define	VERB
ejpam-5095	27	10	as	as	SCONJ
ejpam-5095	27	11	follows	follow	VERB
ejpam-5095	27	12	:	:	PUNCT
ejpam-5095	27	13	fq((x	fq((x	NOUN
ejpam-5095	27	14	−1	−1	NOUN
ejpam-5095	27	15	)	)	PUNCT
ejpam-5095	27	16	)	)	PUNCT
ejpam-5095	28	1	=	=	PRON
ejpam-5095	28	2	{	{	PUNCT
ejpam-5095	28	3	∑	∑	PROPN
ejpam-5095	28	4	n≥n0	n≥n0	PROPN
ejpam-5095	28	5	anx	anx	ADJ
ejpam-5095	28	6	−n	−n	NOUN
ejpam-5095	28	7	,	,	PUNCT
ejpam-5095	28	8	an	an	DET
ejpam-5095	28	9	∈	∈	PROPN
ejpam-5095	28	10	fq	fq	NOUN
ejpam-5095	28	11	and	and	CCONJ
ejpam-5095	28	12	n0	n0	NUM
ejpam-5095	28	13	∈	∈	PROPN
ejpam-5095	28	14	}	}	PUNCT
ejpam-5095	28	15	.	.	PUNCT
ejpam-5095	29	1	for	for	ADP
ejpam-5095	29	2	w	w	NOUN
ejpam-5095	29	3	=	=	SYM
ejpam-5095	29	4	+	+	PROPN
ejpam-5095	29	5	∞∑	∞∑	NUM
ejpam-5095	29	6	n	n	CCONJ
ejpam-5095	29	7	=	=	SYM
ejpam-5095	29	8	n0	n0	X
ejpam-5095	29	9	anx	anx	ADJ
ejpam-5095	29	10	−n	−n	PROPN
ejpam-5095	29	11	∈	∈	PROPN
ejpam-5095	29	12	fq((x	fq((x	NOUN
ejpam-5095	29	13	−1	−1	NOUN
ejpam-5095	29	14	)	)	PUNCT
ejpam-5095	29	15	)	)	PUNCT
ejpam-5095	29	16	,	,	PUNCT
ejpam-5095	29	17	we	we	PRON
ejpam-5095	29	18	define	define	VERB
ejpam-5095	29	19	the	the	DET
ejpam-5095	29	20	integer	integer	NOUN
ejpam-5095	29	21	part	part	NOUN
ejpam-5095	30	1	[	[	X
ejpam-5095	30	2	w	w	X
ejpam-5095	30	3	]	]	X
ejpam-5095	30	4	of	of	ADP
ejpam-5095	30	5	w	w	NOUN
ejpam-5095	30	6	by	by	ADP
ejpam-5095	30	7	[	[	X
ejpam-5095	30	8	w	w	X
ejpam-5095	30	9	]	]	X
ejpam-5095	30	10	=	=	SYM
ejpam-5095	30	11	0∑	0∑	NUM
ejpam-5095	30	12	n	n	CCONJ
ejpam-5095	30	13	=	=	SYM
ejpam-5095	30	14	n0	n0	X
ejpam-5095	30	15	anx	anx	NOUN
ejpam-5095	30	16	−n	−n	PROPN
ejpam-5095	30	17	if	if	SCONJ
ejpam-5095	30	18	n0	n0	ADJ
ejpam-5095	30	19	≤	≤	X
ejpam-5095	30	20	0	0	PUNCT
ejpam-5095	31	1	and	and	CCONJ
ejpam-5095	31	2	[	[	X
ejpam-5095	31	3	w	w	X
ejpam-5095	31	4	]	]	X
ejpam-5095	31	5	=	=	SYM
ejpam-5095	31	6	0	0	PUNCT
ejpam-5095	31	7	if	if	SCONJ
ejpam-5095	31	8	n0	n0	X
ejpam-5095	31	9	>	>	X
ejpam-5095	31	10	0	0	PROPN
ejpam-5095	31	11	,	,	PUNCT
ejpam-5095	31	12	the	the	DET
ejpam-5095	31	13	fractional	fractional	ADJ
ejpam-5095	31	14	part	part	NOUN
ejpam-5095	31	15	of	of	ADP
ejpam-5095	31	16	w	w	NOUN
ejpam-5095	31	17	by	by	ADP
ejpam-5095	31	18	{	{	PUNCT
ejpam-5095	31	19	w	w	NOUN
ejpam-5095	31	20	}	}	PUNCT
ejpam-5095	31	21	=	=	PUNCT
ejpam-5095	31	22	w−	w−	NOUN
ejpam-5095	32	1	[	[	X
ejpam-5095	32	2	w	w	X
ejpam-5095	32	3	]	]	X
ejpam-5095	32	4	=	=	PUNCT
ejpam-5095	33	1	+	+	PUNCT
ejpam-5095	33	2	∞∑	∞∑	NUM
ejpam-5095	33	3	n	n	NOUN
ejpam-5095	33	4	=	=	SYM
ejpam-5095	33	5	1	1	NUM
ejpam-5095	33	6	anx	anx	NOUN
ejpam-5095	33	7	−n	−n	NOUN
ejpam-5095	33	8	.	.	PUNCT
ejpam-5095	34	1	we	we	PRON
ejpam-5095	34	2	have	have	VERB
ejpam-5095	34	3	a	a	DET
ejpam-5095	34	4	non	non	ADJ
ejpam-5095	34	5	-	-	ADJ
ejpam-5095	34	6	archimedean	archimedean	ADJ
ejpam-5095	34	7	absolute	absolute	ADJ
ejpam-5095	34	8	value	value	NOUN
ejpam-5095	34	9	|	|	ADV
ejpam-5095	34	10	·	·	PUNCT
ejpam-5095	34	11	|	|	ADV
ejpam-5095	34	12	on	on	ADP
ejpam-5095	34	13	fq((x	fq((x	NOUN
ejpam-5095	34	14	−1	−1	NOUN
ejpam-5095	34	15	)	)	PUNCT
ejpam-5095	34	16	)	)	PUNCT
ejpam-5095	34	17	,	,	PUNCT
ejpam-5095	34	18	namely	namely	ADV
ejpam-5095	34	19	,	,	PUNCT
ejpam-5095	34	20	for	for	ADP
ejpam-5095	34	21	any	any	DET
ejpam-5095	34	22	element	element	NOUN
ejpam-5095	34	23	w	w	PROPN
ejpam-5095	34	24	∈	∈	PROPN
ejpam-5095	34	25	fq((x	fq((x	NOUN
ejpam-5095	34	26	−1	−1	NOUN
ejpam-5095	34	27	)	)	PUNCT
ejpam-5095	34	28	)	)	PUNCT
ejpam-5095	35	1	having	have	VERB
ejpam-5095	35	2	the	the	DET
ejpam-5095	35	3	form	form	NOUN
ejpam-5095	35	4	w	w	NOUN
ejpam-5095	35	5	=	=	PUNCT
ejpam-5095	36	1	+	+	PROPN
ejpam-5095	36	2	∞∑	∞∑	NUM
ejpam-5095	36	3	n	n	CCONJ
ejpam-5095	36	4	=	=	SYM
ejpam-5095	36	5	n0	n0	X
ejpam-5095	36	6	anx	anx	NOUN
ejpam-5095	36	7	−n	−n	PROPN
ejpam-5095	36	8	(	(	PUNCT
ejpam-5095	36	9	an	an	DET
ejpam-5095	36	10	∈	∈	PROPN
ejpam-5095	36	11	fq	fq	PROPN
ejpam-5095	36	12	)	)	PUNCT
ejpam-5095	36	13	,	,	PUNCT
ejpam-5095	36	14	we	we	PRON
ejpam-5095	36	15	define	define	VERB
ejpam-5095	36	16	|w|	|w|	ADJ
ejpam-5095	36	17	=	=	PUNCT
ejpam-5095	36	18	e−n0	e−n0	NOUN
ejpam-5095	36	19	if	if	SCONJ
ejpam-5095	36	20	w	w	PROPN
ejpam-5095	36	21	̸=	̸=	PROPN
ejpam-5095	36	22	0	0	NUM
ejpam-5095	36	23	,	,	PUNCT
ejpam-5095	36	24	where	where	SCONJ
ejpam-5095	36	25	n0	n0	PROPN
ejpam-5095	36	26	is	be	AUX
ejpam-5095	36	27	the	the	DET
ejpam-5095	36	28	smallest	small	ADJ
ejpam-5095	36	29	index	index	NOUN
ejpam-5095	36	30	verifying	verify	VERB
ejpam-5095	36	31	an0	an0	PROPN
ejpam-5095	36	32	̸=	̸=	PROPN
ejpam-5095	36	33	0	0	NUM
ejpam-5095	36	34	,	,	PUNCT
ejpam-5095	36	35	and	and	CCONJ
ejpam-5095	36	36	|w|	|w|	ADJ
ejpam-5095	36	37	=	=	SYM
ejpam-5095	36	38	0	0	PUNCT
ejpam-5095	37	1	if	if	SCONJ
ejpam-5095	37	2	w	w	PROPN
ejpam-5095	37	3	=	=	NOUN
ejpam-5095	37	4	0	0	X
ejpam-5095	37	5	.	.	PUNCT
ejpam-5095	38	1	we	we	PRON
ejpam-5095	38	2	know	know	VERB
ejpam-5095	38	3	that	that	DET
ejpam-5095	38	4	fq((x	fq((x	NOUN
ejpam-5095	38	5	−1	−1	NOUN
ejpam-5095	38	6	)	)	PUNCT
ejpam-5095	38	7	)	)	PUNCT
ejpam-5095	38	8	is	be	AUX
ejpam-5095	38	9	complete	complete	ADJ
ejpam-5095	38	10	and	and	CCONJ
ejpam-5095	38	11	locally	locally	ADV
ejpam-5095	38	12	compact	compact	ADJ
ejpam-5095	38	13	with	with	ADP
ejpam-5095	38	14	respect	respect	NOUN
ejpam-5095	38	15	to	to	ADP
ejpam-5095	38	16	the	the	DET
ejpam-5095	38	17	metric	metric	NOUN
ejpam-5095	38	18	defined	define	VERB
ejpam-5095	38	19	by	by	ADP
ejpam-5095	38	20	this	this	DET
ejpam-5095	38	21	absolute	absolute	ADJ
ejpam-5095	38	22	value	value	NOUN
ejpam-5095	38	23	.	.	PUNCT
ejpam-5095	39	1	we	we	PRON
ejpam-5095	39	2	denote	denote	VERB
ejpam-5095	39	3	by	by	ADP
ejpam-5095	39	4	fq((x	fq((x	NOUN
ejpam-5095	39	5	−1	−1	NOUN
ejpam-5095	39	6	)	)	PUNCT
ejpam-5095	39	7	)	)	PUNCT
ejpam-5095	40	1	an	an	DET
ejpam-5095	40	2	algebraic	algebraic	ADJ
ejpam-5095	40	3	closure	closure	NOUN
ejpam-5095	40	4	of	of	ADP
ejpam-5095	40	5	fq((x	fq((x	NOUN
ejpam-5095	40	6	−1	−1	NOUN
ejpam-5095	40	7	)	)	PUNCT
ejpam-5095	40	8	)	)	PUNCT
ejpam-5095	40	9	.	.	PUNCT
ejpam-5095	41	1	we	we	PRON
ejpam-5095	41	2	note	note	VERB
ejpam-5095	41	3	that	that	SCONJ
ejpam-5095	41	4	the	the	DET
ejpam-5095	41	5	absolute	absolute	ADJ
ejpam-5095	41	6	value	value	NOUN
ejpam-5095	41	7	has	have	VERB
ejpam-5095	41	8	a	a	DET
ejpam-5095	41	9	unique	unique	ADJ
ejpam-5095	41	10	extension	extension	NOUN
ejpam-5095	41	11	to	to	ADP
ejpam-5095	41	12	fq((x	fq((x	NOUN
ejpam-5095	41	13	−1	−1	NOUN
ejpam-5095	41	14	)	)	PUNCT
ejpam-5095	41	15	)	)	PUNCT
ejpam-5095	41	16	.	.	PUNCT
ejpam-5095	42	1	to	to	PART
ejpam-5095	42	2	denote	denote	VERB
ejpam-5095	42	3	this	this	DET
ejpam-5095	42	4	extended	extended	ADJ
ejpam-5095	42	5	absolute	absolute	ADJ
ejpam-5095	42	6	value	value	NOUN
ejpam-5095	42	7	,	,	PUNCT
ejpam-5095	42	8	we	we	PRON
ejpam-5095	42	9	also	also	ADV
ejpam-5095	42	10	use	use	VERB
ejpam-5095	42	11	the	the	DET
ejpam-5095	42	12	symbol	symbol	NOUN
ejpam-5095	42	13	|	|	ADV
ejpam-5095	42	14	·	·	PUNCT
ejpam-5095	43	1	|	|	INTJ
ejpam-5095	43	2	.	.	PUNCT
ejpam-5095	44	1	3	3	X
ejpam-5095	44	2	.	.	X
ejpam-5095	44	3	main	main	ADJ
ejpam-5095	44	4	results	result	NOUN
ejpam-5095	44	5	theorem	theorem	VERB
ejpam-5095	44	6	2	2	X
ejpam-5095	44	7	.	.	PUNCT
ejpam-5095	45	1	let	let	VERB
ejpam-5095	45	2	fq	fq	PRON
ejpam-5095	45	3	be	be	AUX
ejpam-5095	45	4	a	a	DET
ejpam-5095	45	5	finite	finite	ADJ
ejpam-5095	45	6	field	field	NOUN
ejpam-5095	45	7	of	of	ADP
ejpam-5095	45	8	caracteristic	caracteristic	ADJ
ejpam-5095	45	9	p	p	X
ejpam-5095	45	10	,	,	PUNCT
ejpam-5095	45	11	n	n	X
ejpam-5095	45	12	≥	≥	NOUN
ejpam-5095	45	13	2	2	NUM
ejpam-5095	45	14	and	and	CCONJ
ejpam-5095	45	15	let	let	VERB
ejpam-5095	45	16	p	p	PROPN
ejpam-5095	45	17	(	(	PUNCT
ejpam-5095	45	18	y	y	PROPN
ejpam-5095	45	19	)	)	PUNCT
ejpam-5095	45	20	=	=	PUNCT
ejpam-5095	46	1	asy	asy	PROPN
ejpam-5095	46	2	s	s	PART
ejpam-5095	47	1	+	+	ADJ
ejpam-5095	47	2	as−1y	as−1y	ADJ
ejpam-5095	47	3	s−1	s−1	PROPN
ejpam-5095	47	4	+	+	PROPN
ejpam-5095	47	5	as−2y	as−2y	PROPN
ejpam-5095	47	6	s−2	s−2	PROPN
ejpam-5095	47	7	+	+	CCONJ
ejpam-5095	47	8	·	·	PUNCT
ejpam-5095	47	9	·	·	PUNCT
ejpam-5095	47	10	·	·	PUNCT
ejpam-5095	47	11	+	+	ADJ
ejpam-5095	47	12	a1y	a1y	PROPN
ejpam-5095	47	13	+	+	SYM
ejpam-5095	47	14	a0	a0	NOUN
ejpam-5095	47	15	be	be	VERB
ejpam-5095	47	16	a	a	DET
ejpam-5095	47	17	polynomial	polynomial	NOUN
ejpam-5095	47	18	over	over	ADP
ejpam-5095	47	19	fq[x	fq[x	PROPN
ejpam-5095	47	20	]	]	PUNCT
ejpam-5095	47	21	,	,	PUNCT
ejpam-5095	47	22	such	such	ADJ
ejpam-5095	47	23	that	that	DET
ejpam-5095	47	24	asas−1a0	asas−1a0	NOUN
ejpam-5095	47	25	̸=	̸=	PROPN
ejpam-5095	47	26	0	0	NUM
ejpam-5095	47	27	,	,	PUNCT
ejpam-5095	47	28	as	as	SCONJ
ejpam-5095	47	29	and	and	CCONJ
ejpam-5095	47	30	as−1	as−1	PROPN
ejpam-5095	47	31	has	have	VERB
ejpam-5095	47	32	a	a	DET
ejpam-5095	47	33	same	same	ADJ
ejpam-5095	47	34	irreducible	irreducible	ADJ
ejpam-5095	47	35	factor	factor	NOUN
ejpam-5095	47	36	b	b	NOUN
ejpam-5095	47	37	,	,	PUNCT
ejpam-5095	47	38	with	with	ADP
ejpam-5095	47	39	lcm(as−1	lcm(as−1	PROPN
ejpam-5095	47	40	,	,	PUNCT
ejpam-5095	47	41	b	b	NOUN
ejpam-5095	47	42	)	)	PUNCT
ejpam-5095	47	43	=	=	SYM
ejpam-5095	47	44	bm	bm	PROPN
ejpam-5095	47	45	(	(	PUNCT
ejpam-5095	47	46	as−1	as−1	PROPN
ejpam-5095	47	47	=	=	SYM
ejpam-5095	47	48	bmas−1	bmas−1	NOUN
ejpam-5095	47	49	)	)	PUNCT
ejpam-5095	47	50	and	and	CCONJ
ejpam-5095	47	51	lcm(as	lcm(a	NOUN
ejpam-5095	47	52	,	,	PUNCT
ejpam-5095	47	53	b	b	NOUN
ejpam-5095	47	54	)	)	PUNCT
ejpam-5095	47	55	=	=	SYM
ejpam-5095	47	56	bn	bn	NOUN
ejpam-5095	47	57	(	(	PUNCT
ejpam-5095	47	58	as	as	ADP
ejpam-5095	47	59	=	=	NOUN
ejpam-5095	47	60	bnas	bna	NOUN
ejpam-5095	47	61	)	)	PUNCT
ejpam-5095	47	62	.	.	PUNCT
ejpam-5095	48	1	if	if	SCONJ
ejpam-5095	48	2	n	n	PROPN
ejpam-5095	48	3	>	>	X
ejpam-5095	48	4	ms+	ms+	NOUN
ejpam-5095	48	5	(	(	PUNCT
ejpam-5095	48	6	s−	s−	PROPN
ejpam-5095	48	7	1)(degas	1)(degas	NUM
ejpam-5095	48	8	−mdegb	−mdegb	NOUN
ejpam-5095	48	9	)	)	PUNCT
ejpam-5095	49	1	+	+	NOUN
ejpam-5095	49	2	m	m	NOUN
ejpam-5095	49	3	degb	degb	ADJ
ejpam-5095	49	4	with	with	ADP
ejpam-5095	49	5	m	m	PROPN
ejpam-5095	49	6	=	=	SYM
ejpam-5095	49	7	max(deg	max(deg	NOUN
ejpam-5095	49	8	i	i	PRON
ejpam-5095	49	9	̸=s	̸=s	X
ejpam-5095	49	10	ai	ai	VERB
ejpam-5095	49	11	)	)	PUNCT
ejpam-5095	49	12	,	,	PUNCT
ejpam-5095	49	13	then	then	ADV
ejpam-5095	49	14	p	p	NOUN
ejpam-5095	49	15	is	be	AUX
ejpam-5095	49	16	irreducible	irreducible	ADJ
ejpam-5095	49	17	over	over	ADP
ejpam-5095	49	18	fq[x	fq[x	PROPN
ejpam-5095	49	19	]	]	PUNCT
ejpam-5095	49	20	.	.	PUNCT
ejpam-5095	50	1	proof	proof	NOUN
ejpam-5095	50	2	.	.	PUNCT
ejpam-5095	51	1	suppose	suppose	VERB
ejpam-5095	52	1	that	that	SCONJ
ejpam-5095	52	2	p	p	PROPN
ejpam-5095	52	3	(	(	PUNCT
ejpam-5095	52	4	y	y	PROPN
ejpam-5095	52	5	)	)	PUNCT
ejpam-5095	52	6	=	=	SYM
ejpam-5095	52	7	q(y	q(y	NOUN
ejpam-5095	52	8	)	)	PUNCT
ejpam-5095	52	9	h(y	h(y	ADV
ejpam-5095	52	10	)	)	PUNCT
ejpam-5095	52	11	,	,	PUNCT
ejpam-5095	52	12	where	where	SCONJ
ejpam-5095	52	13	q	q	X
ejpam-5095	52	14	,	,	PUNCT
ejpam-5095	52	15	h	h	PROPN
ejpam-5095	52	16	∈	∈	PROPN
ejpam-5095	52	17	fq[x][y	fq[x][y	NOUN
ejpam-5095	52	18	]	]	PUNCT
ejpam-5095	52	19	.	.	PUNCT
ejpam-5095	53	1	let	let	VERB
ejpam-5095	53	2	a.	a.	NOUN
ejpam-5095	53	3	m.	m.	PROPN
ejpam-5095	53	4	sibih	sibih	PROPN
ejpam-5095	53	5	/	/	SYM
ejpam-5095	53	6	eur	eur	PROPN
ejpam-5095	53	7	.	.	PUNCT
ejpam-5095	54	1	j.	j.	PROPN
ejpam-5095	54	2	pure	pure	PROPN
ejpam-5095	54	3	appl	appl	PROPN
ejpam-5095	54	4	.	.	PROPN
ejpam-5095	54	5	math	math	PROPN
ejpam-5095	54	6	,	,	PUNCT
ejpam-5095	54	7	17	17	NUM
ejpam-5095	54	8	(	(	PUNCT
ejpam-5095	54	9	2	2	NUM
ejpam-5095	54	10	)	)	PUNCT
ejpam-5095	54	11	(	(	PUNCT
ejpam-5095	54	12	2024	2024	NUM
ejpam-5095	54	13	)	)	PUNCT
ejpam-5095	54	14	,	,	PUNCT
ejpam-5095	54	15	721	721	NUM
ejpam-5095	54	16	-	-	SYM
ejpam-5095	54	17	724	724	NUM
ejpam-5095	54	18	723	723	NUM
ejpam-5095	54	19	q(y)=	q(y)=	NOUN
ejpam-5095	54	20	qjy	qjy	NOUN
ejpam-5095	54	21	j	j	NOUN
ejpam-5095	55	1	+	+	NOUN
ejpam-5095	55	2	qj−1y	qj−1y	NOUN
ejpam-5095	55	3	j−1	j−1	PROPN
ejpam-5095	55	4	+	+	NOUN
ejpam-5095	55	5	qj−2y	qj−2y	PROPN
ejpam-5095	55	6	j−2	j−2	PROPN
ejpam-5095	55	7	+	+	CCONJ
ejpam-5095	55	8	·	·	PUNCT
ejpam-5095	55	9	·	·	PUNCT
ejpam-5095	55	10	·	·	PUNCT
ejpam-5095	55	11	+	+	PUNCT
ejpam-5095	55	12	q1y	q1y	ADJ
ejpam-5095	55	13	+	+	ADJ
ejpam-5095	55	14	q0	q0	ADJ
ejpam-5095	55	15	and	and	CCONJ
ejpam-5095	55	16	h(y)=	h(y)=	ADP
ejpam-5095	55	17	hky	hky	PROPN
ejpam-5095	55	18	k	k	PROPN
ejpam-5095	56	1	+	+	PROPN
ejpam-5095	56	2	hk−1y	hk−1y	PROPN
ejpam-5095	56	3	k−1	k−1	PROPN
ejpam-5095	56	4	+	+	PROPN
ejpam-5095	56	5	hk−2y	hk−2y	PROPN
ejpam-5095	56	6	k−2	k−2	PROPN
ejpam-5095	56	7	+	+	CCONJ
ejpam-5095	56	8	·	·	PUNCT
ejpam-5095	56	9	·	·	PUNCT
ejpam-5095	56	10	·	·	PUNCT
ejpam-5095	56	11	+	+	NUM
ejpam-5095	56	12	h1y	h1y	NOUN
ejpam-5095	56	13	+	+	NOUN
ejpam-5095	56	14	h0	h0	PROPN
ejpam-5095	56	15	where	where	SCONJ
ejpam-5095	56	16	j	j	PROPN
ejpam-5095	56	17	+	+	CCONJ
ejpam-5095	56	18	k	k	PROPN
ejpam-5095	56	19	=	=	SYM
ejpam-5095	56	20	s	s	PROPN
ejpam-5095	56	21	,	,	PUNCT
ejpam-5095	56	22	qjhk	qjhk	NOUN
ejpam-5095	56	23	=	=	PUNCT
ejpam-5095	56	24	as	as	ADP
ejpam-5095	56	25	,	,	PUNCT
ejpam-5095	56	26	q0h0	q0h0	NOUN
ejpam-5095	56	27	=	=	SYM
ejpam-5095	56	28	a0	a0	PROPN
ejpam-5095	56	29	and	and	CCONJ
ejpam-5095	56	30	as−1	as−1	PROPN
ejpam-5095	56	31	=	=	SYM
ejpam-5095	56	32	qjhk−1	qjhk−1	X
ejpam-5095	56	33	+	+	CCONJ
ejpam-5095	56	34	hkqj−1	hkqj−1	NOUN
ejpam-5095	56	35	.	.	PUNCT
ejpam-5095	57	1	let	let	VERB
ejpam-5095	57	2	bd	bd	PROPN
ejpam-5095	57	3	=	=	PROPN
ejpam-5095	57	4	lcm(qj	lcm(qj	NOUN
ejpam-5095	57	5	,	,	PUNCT
ejpam-5095	57	6	b	b	NOUN
ejpam-5095	57	7	)	)	PUNCT
ejpam-5095	57	8	,	,	PUNCT
ejpam-5095	57	9	(	(	PUNCT
ejpam-5095	57	10	qj	qj	NOUN
ejpam-5095	57	11	=	=	PUNCT
ejpam-5095	57	12	bdqj	bdqj	NOUN
ejpam-5095	57	13	)	)	PUNCT
ejpam-5095	57	14	,	,	PUNCT
ejpam-5095	57	15	then	then	ADV
ejpam-5095	57	16	bn−d	bn−d	PROPN
ejpam-5095	57	17	=	=	SYM
ejpam-5095	57	18	lcm(hk	lcm(hk	PROPN
ejpam-5095	57	19	,	,	PUNCT
ejpam-5095	57	20	b	b	NOUN
ejpam-5095	57	21	)	)	PUNCT
ejpam-5095	57	22	(	(	PUNCT
ejpam-5095	57	23	hk	hk	NOUN
ejpam-5095	57	24	=	=	PUNCT
ejpam-5095	57	25	bm−dhk	bm−dhk	X
ejpam-5095	57	26	)	)	PUNCT
ejpam-5095	57	27	and	and	CCONJ
ejpam-5095	57	28	we	we	PRON
ejpam-5095	57	29	must	must	AUX
ejpam-5095	57	30	have	have	VERB
ejpam-5095	57	31	m	m	PROPN
ejpam-5095	57	32	≥	≥	PROPN
ejpam-5095	57	33	d.	d.	PROPN
ejpam-5095	57	34	consider	consider	VERB
ejpam-5095	57	35	the	the	DET
ejpam-5095	57	36	factorisation	factorisation	NOUN
ejpam-5095	57	37	of	of	ADP
ejpam-5095	57	38	p	p	NOUN
ejpam-5095	57	39	and	and	CCONJ
ejpam-5095	57	40	q	q	NOUN
ejpam-5095	57	41	in	in	ADP
ejpam-5095	57	42	fq((x−1	fq((x−1	NOUN
ejpam-5095	57	43	)	)	PUNCT
ejpam-5095	57	44	)	)	PUNCT
ejpam-5095	57	45	,	,	PUNCT
ejpam-5095	57	46	we	we	PRON
ejpam-5095	57	47	have	have	VERB
ejpam-5095	57	48	p(y)=as(y	p(y)=as(y	NUM
ejpam-5095	57	49	−	−	PROPN
ejpam-5095	57	50	ω1	ω1	PROPN
ejpam-5095	57	51	)	)	PUNCT
ejpam-5095	57	52	·	·	PUNCT
ejpam-5095	57	53	·	·	PUNCT
ejpam-5095	57	54	·	·	PUNCT
ejpam-5095	57	55	(	(	PUNCT
ejpam-5095	57	56	y	y	NOUN
ejpam-5095	57	57	−	−	PROPN
ejpam-5095	57	58	ωn	ωn	NUM
ejpam-5095	57	59	)	)	PUNCT
ejpam-5095	57	60	and	and	CCONJ
ejpam-5095	57	61	q(y)=qj(y	q(y)=qj(y	NUM
ejpam-5095	57	62	−	−	PROPN
ejpam-5095	57	63	ω1	ω1	PROPN
ejpam-5095	57	64	)	)	PUNCT
ejpam-5095	57	65	·	·	PUNCT
ejpam-5095	57	66	·	·	PUNCT
ejpam-5095	57	67	·	·	PUNCT
ejpam-5095	57	68	(	(	PUNCT
ejpam-5095	57	69	y	y	PROPN
ejpam-5095	57	70	−	−	PROPN
ejpam-5095	57	71	ωj	ωj	ADP
ejpam-5095	57	72	)	)	PUNCT
ejpam-5095	57	73	where	where	SCONJ
ejpam-5095	57	74	ωi	ωi	PROPN
ejpam-5095	57	75	∈	∈	PROPN
ejpam-5095	57	76	fq((x−1	fq((x−1	NOUN
ejpam-5095	57	77	)	)	PUNCT
ejpam-5095	57	78	)	)	PUNCT
ejpam-5095	57	79	,	,	PUNCT
ejpam-5095	57	80	forall	forall	VERB
ejpam-5095	57	81	i	i	PRON
ejpam-5095	57	82	:	:	PUNCT
ejpam-5095	57	83	=	=	SYM
ejpam-5095	57	84	1	1	NUM
ejpam-5095	57	85	,	,	PUNCT
ejpam-5095	57	86	·	·	PUNCT
ejpam-5095	57	87	·	·	PUNCT
ejpam-5095	57	88	·	·	PUNCT
ejpam-5095	57	89	,	,	PUNCT
ejpam-5095	57	90	n.	n.	NOUN
ejpam-5095	57	91	consider	consider	VERB
ejpam-5095	57	92	,	,	PUNCT
ejpam-5095	57	93	now	now	ADV
ejpam-5095	57	94	,	,	PUNCT
ejpam-5095	57	95	the	the	DET
ejpam-5095	57	96	nonarchimedean	nonarchimedean	ADJ
ejpam-5095	57	97	absolute	absolute	ADJ
ejpam-5095	57	98	value	value	NOUN
ejpam-5095	57	99	,	,	PUNCT
ejpam-5095	57	100	and	and	CCONJ
ejpam-5095	57	101	set	set	VERB
ejpam-5095	57	102	a	a	DET
ejpam-5095	57	103	real	real	ADJ
ejpam-5095	57	104	number	number	NOUN
ejpam-5095	57	105	α	α	NOUN
ejpam-5095	57	106	≥	≥	NOUN
ejpam-5095	57	107	0	0	NUM
ejpam-5095	57	108	such	such	ADJ
ejpam-5095	57	109	that	that	SCONJ
ejpam-5095	57	110	|as|	|as|	PROPN
ejpam-5095	57	111	>	>	X
ejpam-5095	57	112	eαmax	eαmax	PROPN
ejpam-5095	57	113	|ai|	|ai|	NOUN
ejpam-5095	57	114	i	i	PRON
ejpam-5095	57	115	̸=s	̸=s	PROPN
ejpam-5095	57	116	then	then	ADV
ejpam-5095	57	117	,	,	PUNCT
ejpam-5095	57	118	using	use	VERB
ejpam-5095	57	119	the	the	DET
ejpam-5095	57	120	viète	viète	NOUN
ejpam-5095	57	121	theorem	theorem	VERB
ejpam-5095	57	122	,	,	PUNCT
ejpam-5095	57	123	we	we	PRON
ejpam-5095	57	124	have	have	VERB
ejpam-5095	57	125	|ω1	|ω1	PRON
ejpam-5095	57	126	·	·	PUNCT
ejpam-5095	57	127	·	·	PUNCT
ejpam-5095	57	128	·	·	PUNCT
ejpam-5095	57	129	ωs|	ωs|	NUM
ejpam-5095	57	130	=	=	PRON
ejpam-5095	57	131	|ω1|	|ω1|	NOUN
ejpam-5095	57	132	·	·	PUNCT
ejpam-5095	57	133	·	·	PUNCT
ejpam-5095	57	134	·	·	PUNCT
ejpam-5095	58	1	|ωs|	|ωs|	NUM
ejpam-5095	58	2	=	=	PUNCT
ejpam-5095	58	3	|a0|	|a0|	NOUN
ejpam-5095	58	4	|as|	|as|	X
ejpam-5095	58	5	<	<	X
ejpam-5095	58	6	|a0|	|a0|	NOUN
ejpam-5095	58	7	eαmax	eαmax	VERB
ejpam-5095	58	8	|ai|	|ai|	NUM
ejpam-5095	58	9	i	i	PRON
ejpam-5095	58	10	̸=s	̸=s	PROPN
ejpam-5095	58	11	<	<	X
ejpam-5095	58	12	1	1	NUM
ejpam-5095	58	13	eα	eα	NOUN
ejpam-5095	58	14	,	,	PUNCT
ejpam-5095	58	15	thus	thus	ADV
ejpam-5095	58	16	,	,	PUNCT
ejpam-5095	58	17	for	for	ADP
ejpam-5095	58	18	any	any	DET
ejpam-5095	58	19	j	j	NOUN
ejpam-5095	58	20	:	:	PUNCT
ejpam-5095	58	21	=	=	SYM
ejpam-5095	58	22	1	1	NUM
ejpam-5095	58	23	,	,	PUNCT
ejpam-5095	58	24	·	·	PUNCT
ejpam-5095	58	25	·	·	PUNCT
ejpam-5095	58	26	·	·	PUNCT
ejpam-5095	58	27	,	,	PUNCT
ejpam-5095	58	28	n	n	CCONJ
ejpam-5095	58	29	,	,	PUNCT
ejpam-5095	58	30	we	we	PRON
ejpam-5095	58	31	must	must	AUX
ejpam-5095	58	32	have	have	VERB
ejpam-5095	58	33	|ωj	|ωj	VERB
ejpam-5095	59	1	|	|	ADV
ejpam-5095	59	2	<	<	X
ejpam-5095	59	3	1	1	NUM
ejpam-5095	59	4	eα	eα	NOUN
ejpam-5095	59	5	/	/	SYM
ejpam-5095	59	6	s	s	NOUN
ejpam-5095	59	7	.	.	PUNCT
ejpam-5095	60	1	so	so	ADV
ejpam-5095	60	2	that	that	SCONJ
ejpam-5095	60	3	,	,	PUNCT
ejpam-5095	60	4	we	we	PRON
ejpam-5095	60	5	get	get	VERB
ejpam-5095	60	6	|ω1	|ω1	PRON
ejpam-5095	60	7	·	·	PUNCT
ejpam-5095	60	8	·	·	PUNCT
ejpam-5095	60	9	·	·	PUNCT
ejpam-5095	60	10	ωj	ωj	ADP
ejpam-5095	60	11	|	|	ADV
ejpam-5095	60	12	<	<	X
ejpam-5095	60	13	1	1	NUM
ejpam-5095	60	14	ejα	ejα	NOUN
ejpam-5095	60	15	/	/	SYM
ejpam-5095	60	16	s	s	NOUN
ejpam-5095	60	17	.	.	PUNCT
ejpam-5095	61	1	on	on	ADP
ejpam-5095	61	2	the	the	DET
ejpam-5095	61	3	other	other	ADJ
ejpam-5095	61	4	hand	hand	NOUN
ejpam-5095	61	5	,	,	PUNCT
ejpam-5095	61	6	we	we	PRON
ejpam-5095	61	7	have	have	VERB
ejpam-5095	61	8	|ω1	|ω1	PRON
ejpam-5095	61	9	·	·	PUNCT
ejpam-5095	61	10	·	·	PUNCT
ejpam-5095	61	11	·	·	PUNCT
ejpam-5095	62	1	ωj	ωj	ADP
ejpam-5095	62	2	|	|	ADV
ejpam-5095	62	3	=	=	SYM
ejpam-5095	62	4	∣∣∣∣q0	∣∣∣∣q0	PROPN
ejpam-5095	62	5	qj	qj	PROPN
ejpam-5095	62	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5095	62	7	=	=	PUNCT
ejpam-5095	62	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5095	62	9	q0	q0	PROPN
ejpam-5095	62	10	bdqj	bdqj	NOUN
ejpam-5095	62	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5095	62	12	≥	≥	NUM
ejpam-5095	62	13	1	1	NUM
ejpam-5095	62	14	|bm|	|bm|	PROPN
ejpam-5095	62	15	|as|	|as|	PROPN
ejpam-5095	62	16	.	.	PUNCT
ejpam-5095	63	1	to	to	PART
ejpam-5095	63	2	reach	reach	VERB
ejpam-5095	63	3	a	a	DET
ejpam-5095	63	4	contraduction	contraduction	NOUN
ejpam-5095	63	5	,	,	PUNCT
ejpam-5095	63	6	it	it	PRON
ejpam-5095	63	7	is	be	AUX
ejpam-5095	63	8	still	still	ADV
ejpam-5095	63	9	necessary	necessary	ADJ
ejpam-5095	63	10	to	to	PART
ejpam-5095	63	11	chose	chose	VERB
ejpam-5095	63	12	α	α	PRON
ejpam-5095	63	13	such	such	ADJ
ejpam-5095	63	14	that	that	SCONJ
ejpam-5095	63	15	1	1	NUM
ejpam-5095	63	16	|bm|	|bm|	PROPN
ejpam-5095	63	17	|as|	|as|	PROPN
ejpam-5095	63	18	≥	≥	NOUN
ejpam-5095	63	19	1	1	NUM
ejpam-5095	63	20	ejα	ejα	NOUN
ejpam-5095	63	21	/	/	SYM
ejpam-5095	63	22	s	s	NOUN
ejpam-5095	63	23	.	.	PUNCT
ejpam-5095	64	1	it	it	PRON
ejpam-5095	64	2	can	can	AUX
ejpam-5095	64	3	be	be	AUX
ejpam-5095	64	4	sufficient	sufficient	ADJ
ejpam-5095	64	5	to	to	PART
ejpam-5095	64	6	choose	choose	VERB
ejpam-5095	64	7	α	α	PRON
ejpam-5095	64	8	such	such	ADJ
ejpam-5095	64	9	that	that	SCONJ
ejpam-5095	64	10	|bm|	|bm|	PROPN
ejpam-5095	64	11	|as|	|as|	PROPN
ejpam-5095	64	12	≤	≤	NUM
ejpam-5095	64	13	eα	eα	PROPN
ejpam-5095	64	14	/	/	SYM
ejpam-5095	64	15	s.	s.	PROPN
ejpam-5095	64	16	or	or	CCONJ
ejpam-5095	64	17	,	,	PUNCT
ejpam-5095	64	18	equivalently	equivalently	ADV
ejpam-5095	64	19	α	α	DET
ejpam-5095	64	20	≥	≥	NOUN
ejpam-5095	64	21	smdegb	smdegb	NOUN
ejpam-5095	64	22	+	+	CCONJ
ejpam-5095	64	23	s(degas	s(degas	NOUN
ejpam-5095	64	24	−	−	NOUN
ejpam-5095	64	25	n	n	PRON
ejpam-5095	64	26	degb	degb	NOUN
ejpam-5095	64	27	)	)	PUNCT
ejpam-5095	64	28	.	.	PUNCT
ejpam-5095	65	1	a	a	DET
ejpam-5095	65	2	conceivable	conceivable	ADJ
ejpam-5095	65	3	value	value	NOUN
ejpam-5095	65	4	for	for	ADP
ejpam-5095	65	5	α	α	PROPN
ejpam-5095	65	6	is	be	AUX
ejpam-5095	65	7	sm	sm	NOUN
ejpam-5095	65	8	degb	degb	NOUN
ejpam-5095	65	9	+	+	CCONJ
ejpam-5095	65	10	s(degas	s(degas	NOUN
ejpam-5095	65	11	−	−	NOUN
ejpam-5095	65	12	n	n	CCONJ
ejpam-5095	65	13	degb	degb	NOUN
ejpam-5095	65	14	)	)	PUNCT
ejpam-5095	65	15	,	,	PUNCT
ejpam-5095	65	16	which	which	PRON
ejpam-5095	65	17	leads	lead	VERB
ejpam-5095	65	18	to	to	ADP
ejpam-5095	65	19	a	a	DET
ejpam-5095	65	20	contradiction	contradiction	NOUN
ejpam-5095	65	21	if	if	SCONJ
ejpam-5095	65	22	n	n	CCONJ
ejpam-5095	65	23	>	>	X
ejpam-5095	65	24	ms+	ms+	NOUN
ejpam-5095	65	25	(	(	PUNCT
ejpam-5095	65	26	s−	s−	PROPN
ejpam-5095	65	27	1)(degas	1)(degas	NUM
ejpam-5095	65	28	−m	−m	ADJ
ejpam-5095	65	29	degb	degb	NOUN
ejpam-5095	65	30	)	)	PUNCT
ejpam-5095	66	1	+	+	NOUN
ejpam-5095	66	2	m	m	NOUN
ejpam-5095	66	3	degb	degb	ADJ
ejpam-5095	66	4	where	where	SCONJ
ejpam-5095	66	5	m	m	VERB
ejpam-5095	66	6	=	=	SYM
ejpam-5095	66	7	max(deg	max(deg	NOUN
ejpam-5095	66	8	i	i	PRON
ejpam-5095	66	9	̸=s	̸=s	X
ejpam-5095	66	10	ai	ai	VERB
ejpam-5095	66	11	)	)	PUNCT
ejpam-5095	66	12	,	,	PUNCT
ejpam-5095	66	13	what	what	PRON
ejpam-5095	66	14	was	be	AUX
ejpam-5095	66	15	to	to	PART
ejpam-5095	66	16	be	be	AUX
ejpam-5095	66	17	proved	prove	VERB
ejpam-5095	66	18	.	.	PUNCT
ejpam-5095	67	1	references	reference	NOUN
ejpam-5095	67	2	724	724	NUM
ejpam-5095	67	3	references	reference	NOUN
ejpam-5095	67	4	[	[	X
ejpam-5095	67	5	1	1	NUM
ejpam-5095	67	6	]	]	X
ejpam-5095	67	7	m	m	VERB
ejpam-5095	67	8	ben	ben	PROPN
ejpam-5095	67	9	nasr	nasr	PROPN
ejpam-5095	67	10	and	and	CCONJ
ejpam-5095	67	11	hassen	hassen	PROPN
ejpam-5095	67	12	kthiri	kthiri	PROPN
ejpam-5095	67	13	.	.	PUNCT
ejpam-5095	68	1	characterization	characterization	NOUN
ejpam-5095	68	2	of	of	ADP
ejpam-5095	68	3	2	2	NUM
ejpam-5095	68	4	-	-	PUNCT
ejpam-5095	68	5	pisot	pisot	ADJ
ejpam-5095	68	6	elements	element	NOUN
ejpam-5095	68	7	in	in	ADP
ejpam-5095	68	8	the	the	DET
ejpam-5095	68	9	field	field	NOUN
ejpam-5095	68	10	of	of	ADP
ejpam-5095	68	11	laurent	laurent	PROPN
ejpam-5095	68	12	series	series	PROPN
ejpam-5095	68	13	over	over	ADP
ejpam-5095	68	14	a	a	DET
ejpam-5095	68	15	finite	finite	ADJ
ejpam-5095	68	16	field	field	NOUN
ejpam-5095	68	17	.	.	PUNCT
ejpam-5095	69	1	mathematical	mathematical	ADJ
ejpam-5095	69	2	notes	note	NOUN
ejpam-5095	69	3	,	,	PUNCT
ejpam-5095	69	4	107:552–558	107:552–558	NUM
ejpam-5095	69	5	,	,	PUNCT
ejpam-5095	69	6	2020	2020	NUM
ejpam-5095	69	7	.	.	PUNCT
ejpam-5095	70	1	[	[	X
ejpam-5095	70	2	2	2	NUM
ejpam-5095	70	3	]	]	PUNCT
ejpam-5095	70	4	a	a	DET
ejpam-5095	70	5	chandoul	chandoul	PROPN
ejpam-5095	70	6	,	,	PUNCT
ejpam-5095	70	7	m	m	PROPN
ejpam-5095	70	8	jellali	jellali	PROPN
ejpam-5095	70	9	,	,	PUNCT
ejpam-5095	70	10	and	and	CCONJ
ejpam-5095	70	11	m	m	PROPN
ejpam-5095	70	12	mkaouar	mkaouar	NOUN
ejpam-5095	70	13	.	.	PUNCT
ejpam-5095	71	1	irreducibility	irreducibility	NOUN
ejpam-5095	71	2	criterion	criterion	NOUN
ejpam-5095	71	3	over	over	ADP
ejpam-5095	71	4	finite	finite	ADJ
ejpam-5095	71	5	fields	field	NOUN
ejpam-5095	71	6	.	.	PUNCT
ejpam-5095	72	1	communications	communication	NOUN
ejpam-5095	72	2	in	in	ADP
ejpam-5095	72	3	algebra	algebra	NOUN
ejpam-5095	72	4	,	,	PUNCT
ejpam-5095	72	5	39(9):3133–3137	39(9):3133–3137	NUM
ejpam-5095	72	6	,	,	PUNCT
ejpam-5095	72	7	2011	2011	NUM
ejpam-5095	72	8	.	.	PUNCT
ejpam-5095	73	1	[	[	X
ejpam-5095	73	2	3	3	X
ejpam-5095	73	3	]	]	X
ejpam-5095	73	4	amara	amara	X
ejpam-5095	73	5	chandoul	chandoul	PROPN
ejpam-5095	73	6	and	and	CCONJ
ejpam-5095	73	7	alanod	alanod	PROPN
ejpam-5095	73	8	m	m	VERB
ejpam-5095	73	9	sibih	sibih	ADJ
ejpam-5095	73	10	.	.	PUNCT
ejpam-5095	74	1	note	note	NOUN
ejpam-5095	74	2	on	on	ADP
ejpam-5095	74	3	irreducible	irreducible	ADJ
ejpam-5095	74	4	polynomials	polynomial	NOUN
ejpam-5095	74	5	over	over	ADP
ejpam-5095	74	6	finite	finite	ADJ
ejpam-5095	74	7	field	field	NOUN
ejpam-5095	74	8	.	.	PUNCT
ejpam-5095	75	1	european	european	ADJ
ejpam-5095	75	2	journal	journal	PROPN
ejpam-5095	75	3	of	of	ADP
ejpam-5095	75	4	pure	pure	ADJ
ejpam-5095	75	5	and	and	CCONJ
ejpam-5095	75	6	applied	applied	ADJ
ejpam-5095	75	7	mathematics	mathematic	NOUN
ejpam-5095	75	8	,	,	PUNCT
ejpam-5095	75	9	14(1):265–267	14(1):265–267	NUM
ejpam-5095	75	10	,	,	PUNCT
ejpam-5095	75	11	2021	2021	NUM
ejpam-5095	75	12	.	.	PUNCT
ejpam-5095	76	1	[	[	X
ejpam-5095	76	2	4	4	NUM
ejpam-5095	76	3	]	]	PUNCT
ejpam-5095	76	4	hl	hl	NOUN
ejpam-5095	76	5	dorwart	dorwart	NOUN
ejpam-5095	76	6	.	.	PUNCT
ejpam-5095	77	1	irreducibility	irreducibility	NOUN
ejpam-5095	77	2	of	of	ADP
ejpam-5095	77	3	polynomials	polynomial	NOUN
ejpam-5095	77	4	.	.	PUNCT
ejpam-5095	78	1	the	the	DET
ejpam-5095	78	2	american	american	PROPN
ejpam-5095	78	3	mathematical	mathematical	PROPN
ejpam-5095	78	4	monthly	monthly	PROPN
ejpam-5095	78	5	,	,	PUNCT
ejpam-5095	78	6	42(6):369–381	42(6):369–381	PROPN
ejpam-5095	78	7	,	,	PUNCT
ejpam-5095	78	8	1935	1935	NUM
ejpam-5095	78	9	.	.	PUNCT
ejpam-5095	79	1	[	[	X
ejpam-5095	79	2	5	5	X
ejpam-5095	79	3	]	]	PUNCT
ejpam-5095	79	4	ravindranathan	ravindranathan	NOUN
ejpam-5095	79	5	thangadurai	thangadurai	ADJ
ejpam-5095	79	6	.	.	PUNCT
ejpam-5095	80	1	irreducibility	irreducibility	NOUN
ejpam-5095	80	2	of	of	ADP
ejpam-5095	80	3	polynomials	polynomial	NOUN
ejpam-5095	80	4	whose	whose	DET
ejpam-5095	80	5	coefficients	coefficient	NOUN
ejpam-5095	80	6	are	be	AUX
ejpam-5095	80	7	integers	integer	NOUN
ejpam-5095	80	8	.	.	PUNCT
ejpam-5095	81	1	mathematics	mathematic	NOUN
ejpam-5095	81	2	newsletter	newsletter	NOUN
ejpam-5095	81	3	,	,	PUNCT
ejpam-5095	81	4	17:29–61	17:29–61	NUM
ejpam-5095	81	5	,	,	PUNCT
ejpam-5095	81	6	2007	2007	NUM
ejpam-5095	81	7	.	.	PUNCT