id	sid	tid	token	lemma	pos
ejpam-2305	1	1	european	european	PROPN
ejpam-2305	1	2	journal	journal	PROPN
ejpam-2305	1	3	of	of	ADP
ejpam-2305	1	4	pure	pure	ADJ
ejpam-2305	1	5	and	and	CCONJ
ejpam-2305	1	6	applied	apply	VERB
ejpam-2305	1	7	mathematics	mathematic	NOUN
ejpam-2305	1	8	vol	vol	NOUN
ejpam-2305	1	9	.	.	PROPN
ejpam-2305	1	10	8	8	NUM
ejpam-2305	1	11	,	,	PUNCT
ejpam-2305	1	12	no	no	INTJ
ejpam-2305	1	13	.	.	NOUN
ejpam-2305	1	14	1	1	NUM
ejpam-2305	1	15	,	,	PUNCT
ejpam-2305	1	16	2015	2015	NUM
ejpam-2305	1	17	,	,	PUNCT
ejpam-2305	1	18	126	126	NUM
ejpam-2305	1	19	-	-	SYM
ejpam-2305	1	20	134	134	NUM
ejpam-2305	1	21	issn	issn	PROPN
ejpam-2305	1	22	1307	1307	NUM
ejpam-2305	1	23	-	-	SYM
ejpam-2305	1	24	5543	5543	NUM
ejpam-2305	1	25	–	–	PUNCT
ejpam-2305	1	26	www.ejpam.com	www.ejpam.com	X
ejpam-2305	1	27	on	on	ADP
ejpam-2305	1	28	the	the	DET
ejpam-2305	1	29	group	group	NOUN
ejpam-2305	1	30	of	of	ADP
ejpam-2305	1	31	the	the	DET
ejpam-2305	1	32	elliptic	elliptic	ADJ
ejpam-2305	1	33	curve	curve	NOUN
ejpam-2305	2	1	y2	y2	PROPN
ejpam-2305	2	2	=	=	SYM
ejpam-2305	3	1	x3	x3	PROPN
ejpam-2305	3	2	+	+	CCONJ
ejpam-2305	3	3	4px	4px	ADJ
ejpam-2305	3	4	naser	naser	PROPN
ejpam-2305	3	5	zamani1	zamani1	PROPN
ejpam-2305	3	6	,	,	PUNCT
ejpam-2305	3	7	⇤	⇤	PROPN
ejpam-2305	3	8	,	,	PUNCT
ejpam-2305	3	9	arman	arman	NOUN
ejpam-2305	3	10	shams2	shams2	NOUN
ejpam-2305	3	11	1	1	NUM
ejpam-2305	3	12	faculty	faculty	NOUN
ejpam-2305	3	13	of	of	ADP
ejpam-2305	3	14	mathematical	mathematical	ADJ
ejpam-2305	3	15	science	science	NOUN
ejpam-2305	3	16	,	,	PUNCT
ejpam-2305	3	17	university	university	NOUN
ejpam-2305	3	18	of	of	ADP
ejpam-2305	3	19	mohaghegh	mohaghegh	PROPN
ejpam-2305	3	20	ardabili	ardabili	PROPN
ejpam-2305	3	21	,	,	PUNCT
ejpam-2305	3	22	ardabil	ardabil	VERB
ejpam-2305	3	23	,	,	PUNCT
ejpam-2305	3	24	iran	iran	PROPN
ejpam-2305	3	25	2	2	NUM
ejpam-2305	3	26	department	department	NOUN
ejpam-2305	3	27	of	of	ADP
ejpam-2305	3	28	mathematics	mathematic	NOUN
ejpam-2305	3	29	,	,	PUNCT
ejpam-2305	3	30	shahid	shahid	PROPN
ejpam-2305	3	31	madani	madani	PROPN
ejpam-2305	3	32	university	university	PROPN
ejpam-2305	3	33	,	,	PUNCT
ejpam-2305	3	34	tabriz	tabriz	NOUN
ejpam-2305	3	35	,	,	PUNCT
ejpam-2305	3	36	iran	iran	PROPN
ejpam-2305	3	37	abstract	abstract	NOUN
ejpam-2305	3	38	.	.	PUNCT
ejpam-2305	4	1	in	in	ADP
ejpam-2305	4	2	this	this	DET
ejpam-2305	4	3	paper	paper	NOUN
ejpam-2305	4	4	we	we	PRON
ejpam-2305	4	5	study	study	VERB
ejpam-2305	4	6	the	the	DET
ejpam-2305	4	7	group	group	NOUN
ejpam-2305	4	8	structure	structure	NOUN
ejpam-2305	4	9	of	of	ADP
ejpam-2305	4	10	the	the	DET
ejpam-2305	4	11	elliptic	elliptic	ADJ
ejpam-2305	4	12	curves	curve	NOUN
ejpam-2305	4	13	e	e	NOUN
ejpam-2305	4	14	:	:	PUNCT
ejpam-2305	4	15	y2	y2	NOUN
ejpam-2305	4	16	=	=	SYM
ejpam-2305	5	1	x3	x3	PROPN
ejpam-2305	5	2	+	+	CCONJ
ejpam-2305	5	3	4px	4px	NOUN
ejpam-2305	5	4	,	,	PUNCT
ejpam-2305	5	5	where	where	SCONJ
ejpam-2305	5	6	p	p	NOUN
ejpam-2305	5	7	is	be	AUX
ejpam-2305	5	8	3	3	NUM
ejpam-2305	5	9	,	,	PUNCT
ejpam-2305	5	10	5	5	NUM
ejpam-2305	5	11	or	or	CCONJ
ejpam-2305	5	12	a	a	DET
ejpam-2305	5	13	prime	prime	NOUN
ejpam-2305	5	14	of	of	ADP
ejpam-2305	5	15	the	the	DET
ejpam-2305	5	16	form	form	NOUN
ejpam-2305	5	17	u4	u4	PROPN
ejpam-2305	5	18	+	+	CCONJ
ejpam-2305	5	19	v4	v4	PROPN
ejpam-2305	5	20	for	for	ADP
ejpam-2305	5	21	positive	positive	ADJ
ejpam-2305	5	22	integers	integer	NOUN
ejpam-2305	5	23	u	u	NOUN
ejpam-2305	5	24	,	,	PUNCT
ejpam-2305	5	25	v.	v.	ADP
ejpam-2305	5	26	2010	2010	NUM
ejpam-2305	5	27	mathematics	mathematic	NOUN
ejpam-2305	5	28	subject	subject	NOUN
ejpam-2305	5	29	classifications	classification	NOUN
ejpam-2305	5	30	:	:	PUNCT
ejpam-2305	5	31	11g05	11g05	NUM
ejpam-2305	5	32	key	key	ADJ
ejpam-2305	5	33	words	word	NOUN
ejpam-2305	5	34	and	and	CCONJ
ejpam-2305	5	35	phrases	phrase	NOUN
ejpam-2305	5	36	:	:	PUNCT
ejpam-2305	5	37	elliptic	elliptic	ADJ
ejpam-2305	5	38	curves	curve	NOUN
ejpam-2305	5	39	,	,	PUNCT
ejpam-2305	5	40	rank	rank	NOUN
ejpam-2305	5	41	,	,	PUNCT
ejpam-2305	5	42	isogenous	isogenous	ADJ
ejpam-2305	5	43	,	,	PUNCT
ejpam-2305	5	44	selmer	selmer	PROPN
ejpam-2305	5	45	group	group	PROPN
ejpam-2305	5	46	1	1	NUM
ejpam-2305	5	47	.	.	PUNCT
ejpam-2305	6	1	introduction	introduction	NOUN
ejpam-2305	6	2	let	let	VERB
ejpam-2305	6	3	e	e	PRON
ejpam-2305	6	4	denote	denote	VERB
ejpam-2305	6	5	an	an	DET
ejpam-2305	6	6	elliptic	elliptic	ADJ
ejpam-2305	6	7	curve	curve	NOUN
ejpam-2305	6	8	over	over	ADP
ejpam-2305	6	9	q	q	NOUN
ejpam-2305	6	10	and	and	CCONJ
ejpam-2305	6	11	�	�	PROPN
ejpam-2305	6	12	=	=	SYM
ejpam-2305	6	13	e(q	e(q	PROPN
ejpam-2305	6	14	)	)	PUNCT
ejpam-2305	6	15	be	be	VERB
ejpam-2305	6	16	the	the	DET
ejpam-2305	6	17	set	set	NOUN
ejpam-2305	6	18	of	of	ADP
ejpam-2305	6	19	all	all	DET
ejpam-2305	6	20	rational	rational	ADJ
ejpam-2305	6	21	points	point	NOUN
ejpam-2305	6	22	on	on	ADP
ejpam-2305	6	23	e.	e.	PROPN
ejpam-2305	6	24	a	a	DET
ejpam-2305	6	25	seminal	seminal	ADJ
ejpam-2305	6	26	theorem	theorem	NOUN
ejpam-2305	6	27	of	of	ADP
ejpam-2305	6	28	mordell	mordell	PROPN
ejpam-2305	6	29	-	-	PUNCT
ejpam-2305	6	30	weil	weil	PROPN
ejpam-2305	6	31	asserts	assert	VERB
ejpam-2305	6	32	that	that	SCONJ
ejpam-2305	6	33	�	�	PROPN
ejpam-2305	6	34	is	be	AUX
ejpam-2305	6	35	a	a	DET
ejpam-2305	6	36	finitely	finitely	ADV
ejpam-2305	6	37	generated	generate	VERB
ejpam-2305	6	38	abelian	abelian	ADJ
ejpam-2305	6	39	group	group	NOUN
ejpam-2305	6	40	in	in	ADP
ejpam-2305	6	41	a	a	DET
ejpam-2305	6	42	natural	natural	ADJ
ejpam-2305	6	43	way	way	NOUN
ejpam-2305	6	44	with	with	ADP
ejpam-2305	6	45	zero	zero	NUM
ejpam-2305	6	46	element	element	NOUN
ejpam-2305	6	47	o	o	NOUN
ejpam-2305	6	48	.	.	PUNCT
ejpam-2305	7	1	we	we	PRON
ejpam-2305	7	2	put	put	VERB
ejpam-2305	7	3	�	�	PROPN
ejpam-2305	7	4	=	=	SYM
ejpam-2305	7	5	t	t	PROPN
ejpam-2305	7	6	�	�	PROPN
ejpam-2305	7	7	f	f	PROPN
ejpam-2305	7	8	where	where	SCONJ
ejpam-2305	7	9	t	t	PROPN
ejpam-2305	7	10	and	and	CCONJ
ejpam-2305	7	11	f	f	PROPN
ejpam-2305	7	12	are	be	AUX
ejpam-2305	7	13	the	the	DET
ejpam-2305	7	14	torsion	torsion	NOUN
ejpam-2305	7	15	and	and	CCONJ
ejpam-2305	7	16	maximal	maximal	ADJ
ejpam-2305	7	17	free	free	ADJ
ejpam-2305	7	18	subgroups	subgroup	NOUN
ejpam-2305	7	19	of	of	ADP
ejpam-2305	7	20	�	�	PROPN
ejpam-2305	7	21	respectively	respectively	ADV
ejpam-2305	7	22	.	.	PUNCT
ejpam-2305	8	1	by	by	ADP
ejpam-2305	8	2	the	the	DET
ejpam-2305	8	3	rank	rank	NOUN
ejpam-2305	8	4	of	of	ADP
ejpam-2305	8	5	e	e	PROPN
ejpam-2305	8	6	,	,	PUNCT
ejpam-2305	8	7	rank(e	rank(e	PROPN
ejpam-2305	8	8	)	)	PUNCT
ejpam-2305	8	9	,	,	PUNCT
ejpam-2305	8	10	we	we	PRON
ejpam-2305	8	11	mean	mean	VERB
ejpam-2305	8	12	the	the	DET
ejpam-2305	8	13	rank	rank	NOUN
ejpam-2305	8	14	of	of	ADP
ejpam-2305	8	15	f	f	PROPN
ejpam-2305	8	16	.	.	PUNCT
ejpam-2305	9	1	hence	hence	ADV
ejpam-2305	9	2	the	the	DET
ejpam-2305	9	3	rank	rank	NOUN
ejpam-2305	9	4	of	of	ADP
ejpam-2305	9	5	e	e	PROPN
ejpam-2305	9	6	is	be	AUX
ejpam-2305	9	7	positive	positive	ADJ
ejpam-2305	9	8	if	if	SCONJ
ejpam-2305	9	9	and	and	CCONJ
ejpam-2305	9	10	only	only	ADV
ejpam-2305	9	11	if	if	SCONJ
ejpam-2305	9	12	e	e	PRON
ejpam-2305	9	13	possesses	possess	VERB
ejpam-2305	9	14	an	an	DET
ejpam-2305	9	15	infinity	infinity	NOUN
ejpam-2305	9	16	of	of	ADP
ejpam-2305	9	17	rational	rational	ADJ
ejpam-2305	9	18	points	point	NOUN
ejpam-2305	9	19	.	.	PUNCT
ejpam-2305	10	1	computational	computational	ADJ
ejpam-2305	10	2	works	work	NOUN
ejpam-2305	10	3	show	show	VERB
ejpam-2305	10	4	that	that	SCONJ
ejpam-2305	10	5	a	a	DET
ejpam-2305	10	6	typical	typical	ADJ
ejpam-2305	10	7	elliptic	elliptic	ADJ
ejpam-2305	10	8	curve	curve	NOUN
ejpam-2305	10	9	has	have	VERB
ejpam-2305	10	10	more	more	ADV
ejpam-2305	10	11	small	small	ADJ
ejpam-2305	10	12	rank	rank	NOUN
ejpam-2305	11	1	[	[	X
ejpam-2305	11	2	1	1	NUM
ejpam-2305	11	3	,	,	PUNCT
ejpam-2305	11	4	9	9	NUM
ejpam-2305	11	5	]	]	PUNCT
ejpam-2305	11	6	.	.	PUNCT
ejpam-2305	12	1	let	let	VERB
ejpam-2305	12	2	p	p	PRON
ejpam-2305	12	3	be	be	AUX
ejpam-2305	12	4	a	a	DET
ejpam-2305	12	5	prime	prime	ADJ
ejpam-2305	12	6	number	number	NOUN
ejpam-2305	12	7	and	and	CCONJ
ejpam-2305	12	8	consider	consider	VERB
ejpam-2305	12	9	the	the	DET
ejpam-2305	12	10	curve	curve	NOUN
ejpam-2305	12	11	e	e	NOUN
ejpam-2305	12	12	=	=	PRON
ejpam-2305	12	13	e4p	e4p	PROPN
ejpam-2305	12	14	:	:	PUNCT
ejpam-2305	13	1	y2	y2	NOUN
ejpam-2305	13	2	=	=	PUNCT
ejpam-2305	14	1	x3	x3	PROPN
ejpam-2305	14	2	+	+	CCONJ
ejpam-2305	14	3	4px	4px	NOUN
ejpam-2305	14	4	.	.	PUNCT
ejpam-2305	15	1	we	we	PRON
ejpam-2305	15	2	study	study	VERB
ejpam-2305	15	3	the	the	DET
ejpam-2305	15	4	group	group	NOUN
ejpam-2305	15	5	�	�	PROPN
ejpam-2305	15	6	and	and	CCONJ
ejpam-2305	15	7	show	show	VERB
ejpam-2305	15	8	that	that	PRON
ejpam-2305	15	9	t	t	NOUN
ejpam-2305	15	10	=	=	SYM
ejpam-2305	15	11	z2	z2	PROPN
ejpam-2305	15	12	.	.	PUNCT
ejpam-2305	16	1	by	by	ADP
ejpam-2305	16	2	combining	combine	VERB
ejpam-2305	16	3	some	some	DET
ejpam-2305	16	4	facts	fact	NOUN
ejpam-2305	16	5	of	of	ADP
ejpam-2305	16	6	[	[	X
ejpam-2305	16	7	4	4	NUM
ejpam-2305	16	8	]	]	PUNCT
ejpam-2305	16	9	,	,	PUNCT
ejpam-2305	16	10	a	a	DET
ejpam-2305	16	11	result	result	NOUN
ejpam-2305	16	12	on	on	ADP
ejpam-2305	16	13	the	the	DET
ejpam-2305	16	14	selmer	selmer	PROPN
ejpam-2305	16	15	group	group	NOUN
ejpam-2305	16	16	of	of	ADP
ejpam-2305	16	17	�	�	PROPN
ejpam-2305	16	18	and	and	CCONJ
ejpam-2305	16	19	that	that	PRON
ejpam-2305	16	20	of	of	ADP
ejpam-2305	16	21	its	its	PRON
ejpam-2305	16	22	isogenous	isogenous	ADJ
ejpam-2305	16	23	�	�	NOUN
ejpam-2305	16	24	̃	̃	PROPN
ejpam-2305	16	25	will	will	AUX
ejpam-2305	16	26	be	be	AUX
ejpam-2305	16	27	given	give	VERB
ejpam-2305	16	28	.	.	PUNCT
ejpam-2305	17	1	next	next	ADV
ejpam-2305	17	2	,	,	PUNCT
ejpam-2305	17	3	when	when	SCONJ
ejpam-2305	17	4	p	p	NOUN
ejpam-2305	17	5	=	=	NOUN
ejpam-2305	17	6	3,5	3,5	NUM
ejpam-2305	17	7	,	,	PUNCT
ejpam-2305	17	8	u4	u4	PROPN
ejpam-2305	17	9	+	+	X
ejpam-2305	17	10	v4	v4	NOUN
ejpam-2305	17	11	for	for	ADP
ejpam-2305	17	12	positive	positive	ADJ
ejpam-2305	17	13	integers	integer	NOUN
ejpam-2305	17	14	u	u	NOUN
ejpam-2305	17	15	,	,	PUNCT
ejpam-2305	17	16	v	v	NOUN
ejpam-2305	17	17	,	,	PUNCT
ejpam-2305	17	18	some	some	DET
ejpam-2305	17	19	results	result	NOUN
ejpam-2305	17	20	on	on	ADP
ejpam-2305	17	21	the	the	DET
ejpam-2305	17	22	rank	rank	NOUN
ejpam-2305	17	23	of	of	ADP
ejpam-2305	17	24	e	e	PROPN
ejpam-2305	17	25	are	be	AUX
ejpam-2305	17	26	presented	present	VERB
ejpam-2305	17	27	.	.	PUNCT
ejpam-2305	18	1	although	although	SCONJ
ejpam-2305	18	2	,	,	PUNCT
ejpam-2305	18	3	it	it	PRON
ejpam-2305	18	4	can	can	AUX
ejpam-2305	18	5	be	be	AUX
ejpam-2305	18	6	find	find	VERB
ejpam-2305	18	7	some	some	DET
ejpam-2305	18	8	similar	similar	ADJ
ejpam-2305	18	9	results	result	NOUN
ejpam-2305	18	10	concerning	concern	VERB
ejpam-2305	18	11	the	the	DET
ejpam-2305	18	12	2	2	NUM
ejpam-2305	18	13	-	-	PUNCT
ejpam-2305	18	14	isogenous	isogenous	ADJ
ejpam-2305	18	15	of	of	ADP
ejpam-2305	18	16	e	e	PROPN
ejpam-2305	18	17	in	in	ADP
ejpam-2305	18	18	the	the	DET
ejpam-2305	18	19	literatures	literature	NOUN
ejpam-2305	18	20	(	(	PUNCT
ejpam-2305	18	21	[	[	X
ejpam-2305	18	22	5	5	NUM
ejpam-2305	18	23	,	,	PUNCT
ejpam-2305	18	24	8	8	NUM
ejpam-2305	18	25	]	]	NUM
ejpam-2305	18	26	)	)	PUNCT
ejpam-2305	18	27	,	,	PUNCT
ejpam-2305	18	28	which	which	PRON
ejpam-2305	18	29	imply	imply	VERB
ejpam-2305	18	30	some	some	PRON
ejpam-2305	18	31	of	of	ADP
ejpam-2305	18	32	our	our	PRON
ejpam-2305	18	33	results	result	NOUN
ejpam-2305	18	34	,	,	PUNCT
ejpam-2305	18	35	our	our	PRON
ejpam-2305	18	36	method	method	NOUN
ejpam-2305	18	37	of	of	ADP
ejpam-2305	18	38	study	study	NOUN
ejpam-2305	18	39	completely	completely	ADV
ejpam-2305	18	40	differs	differ	VERB
ejpam-2305	18	41	from	from	ADP
ejpam-2305	18	42	those	those	PRON
ejpam-2305	18	43	.	.	PUNCT
ejpam-2305	19	1	2	2	X
ejpam-2305	19	2	.	.	X
ejpam-2305	19	3	preliminaries	preliminary	NOUN
ejpam-2305	19	4	we	we	PRON
ejpam-2305	19	5	begin	begin	VERB
ejpam-2305	19	6	with	with	ADP
ejpam-2305	19	7	the	the	DET
ejpam-2305	19	8	following	follow	VERB
ejpam-2305	19	9	proposition	proposition	NOUN
ejpam-2305	19	10	which	which	PRON
ejpam-2305	19	11	shows	show	VERB
ejpam-2305	19	12	some	some	DET
ejpam-2305	19	13	properties	property	NOUN
ejpam-2305	19	14	of	of	ADP
ejpam-2305	19	15	�	�	PROPN
ejpam-2305	19	16	.	.	PUNCT
ejpam-2305	20	1	proposition	proposition	NOUN
ejpam-2305	20	2	1	1	NUM
ejpam-2305	20	3	.	.	PUNCT
ejpam-2305	21	1	let	let	VERB
ejpam-2305	21	2	q	q	NOUN
ejpam-2305	22	1	=	=	PUNCT
ejpam-2305	22	2	(	(	PUNCT
ejpam-2305	22	3	x	x	NOUN
ejpam-2305	22	4	0	0	PROPN
ejpam-2305	22	5	,	,	PUNCT
ejpam-2305	22	6	y	y	PROPN
ejpam-2305	22	7	0	0	NUM
ejpam-2305	22	8	)	)	PUNCT
ejpam-2305	22	9	,	,	PUNCT
ejpam-2305	22	10	p	p	NOUN
ejpam-2305	22	11	=	=	SYM
ejpam-2305	22	12	(	(	PUNCT
ejpam-2305	22	13	x	x	INTJ
ejpam-2305	22	14	,	,	PUNCT
ejpam-2305	22	15	y	y	PROPN
ejpam-2305	22	16	)	)	PUNCT
ejpam-2305	22	17	be	be	VERB
ejpam-2305	22	18	two	two	NUM
ejpam-2305	22	19	points	point	NOUN
ejpam-2305	22	20	of	of	ADP
ejpam-2305	22	21	e	e	NOUN
ejpam-2305	22	22	such	such	ADJ
ejpam-2305	22	23	that	that	SCONJ
ejpam-2305	22	24	x	x	SYM
ejpam-2305	22	25	0	0	NUM
ejpam-2305	22	26	2	2	NUM
ejpam-2305	22	27	z	z	NOUN
ejpam-2305	22	28	and	and	CCONJ
ejpam-2305	22	29	q	q	NOUN
ejpam-2305	23	1	=	=	NOUN
ejpam-2305	23	2	2p	2p	NOUN
ejpam-2305	23	3	.	.	PUNCT
ejpam-2305	24	1	then	then	ADV
ejpam-2305	24	2	x	x	SYM
ejpam-2305	24	3	2	2	NUM
ejpam-2305	24	4	z	z	NOUN
ejpam-2305	24	5	is	be	AUX
ejpam-2305	24	6	even	even	ADV
ejpam-2305	24	7	.	.	PUNCT
ejpam-2305	25	1	⇤	⇤	PROPN
ejpam-2305	25	2	corresponding	corresponding	ADJ
ejpam-2305	25	3	author	author	NOUN
ejpam-2305	25	4	.	.	PUNCT
ejpam-2305	26	1	email	email	NOUN
ejpam-2305	26	2	addresses	address	NOUN
ejpam-2305	26	3	:	:	PUNCT
ejpam-2305	26	4	zamanin@uma.ac.ir	zamanin@uma.ac.ir	PROPN
ejpam-2305	26	5	,	,	PUNCT
ejpam-2305	26	6	naserzaka@yahoo.com	naserzaka@yahoo.com	PROPN
ejpam-2305	26	7	(	(	PUNCT
ejpam-2305	26	8	n.	n.	PROPN
ejpam-2305	26	9	zamani	zamani	PROPN
ejpam-2305	26	10	)	)	PUNCT
ejpam-2305	26	11	,	,	PUNCT
ejpam-2305	26	12	shzarghar.arman@gmail.com	shzarghar.arman@gmail.com	X
ejpam-2305	26	13	(	(	PUNCT
ejpam-2305	26	14	a.	a.	NOUN
ejpam-2305	26	15	shams	sham	NOUN
ejpam-2305	26	16	)	)	PUNCT
ejpam-2305	26	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2305	27	1	126	126	NUM
ejpam-2305	27	2	c	c	X
ejpam-2305	27	3	�	�	PROPN
ejpam-2305	27	4	2015	2015	NUM
ejpam-2305	27	5	ejpam	ejpam	VERB
ejpam-2305	27	6	all	all	DET
ejpam-2305	27	7	rights	right	NOUN
ejpam-2305	27	8	reserved	reserve	VERB
ejpam-2305	27	9	.	.	PUNCT
ejpam-2305	28	1	n.	n.	PROPN
ejpam-2305	28	2	zamani	zamani	PROPN
ejpam-2305	28	3	,	,	PUNCT
ejpam-2305	28	4	a.	a.	NOUN
ejpam-2305	28	5	shams	sham	NOUN
ejpam-2305	28	6	/	/	SYM
ejpam-2305	28	7	eur	eur	PROPN
ejpam-2305	28	8	.	.	PUNCT
ejpam-2305	29	1	j.	j.	PROPN
ejpam-2305	29	2	pure	pure	PROPN
ejpam-2305	29	3	appl	appl	PROPN
ejpam-2305	29	4	.	.	PROPN
ejpam-2305	29	5	math	math	PROPN
ejpam-2305	29	6	,	,	PUNCT
ejpam-2305	29	7	8	8	NUM
ejpam-2305	29	8	(	(	PUNCT
ejpam-2305	29	9	2015	2015	NUM
ejpam-2305	29	10	)	)	PUNCT
ejpam-2305	29	11	,	,	PUNCT
ejpam-2305	29	12	126	126	NUM
ejpam-2305	29	13	-	-	SYM
ejpam-2305	29	14	134	134	NUM
ejpam-2305	29	15	127	127	NUM
ejpam-2305	29	16	proof	proof	NOUN
ejpam-2305	29	17	.	.	PUNCT
ejpam-2305	30	1	let	let	VERB
ejpam-2305	30	2	x	x	PUNCT
ejpam-2305	30	3	=	=	PUNCT
ejpam-2305	30	4	a	a	PROPN
ejpam-2305	30	5	/	/	SYM
ejpam-2305	30	6	b	b	PROPN
ejpam-2305	30	7	,	,	PUNCT
ejpam-2305	30	8	gcd(a	gcd(a	PROPN
ejpam-2305	30	9	,	,	PUNCT
ejpam-2305	30	10	b	b	NOUN
ejpam-2305	30	11	)	)	PUNCT
ejpam-2305	30	12	=	=	SYM
ejpam-2305	30	13	1	1	NUM
ejpam-2305	30	14	and	and	CCONJ
ejpam-2305	30	15	x	x	ADJ
ejpam-2305	30	16	/2	/2	PROPN
ejpam-2305	30	17	z.	z.	PROPN
ejpam-2305	31	1	according	accord	VERB
ejpam-2305	31	2	to	to	ADP
ejpam-2305	31	3	the	the	DET
ejpam-2305	31	4	group	group	NOUN
ejpam-2305	31	5	law	law	NOUN
ejpam-2305	31	6	of	of	ADP
ejpam-2305	31	7	�	�	PROPN
ejpam-2305	31	8	,	,	PUNCT
ejpam-2305	31	9	one	one	PRON
ejpam-2305	31	10	can	can	AUX
ejpam-2305	31	11	see	see	VERB
ejpam-2305	31	12	that	that	SCONJ
ejpam-2305	31	13	x	x	PROPN
ejpam-2305	31	14	0	0	PUNCT
ejpam-2305	31	15	=	=	SYM
ejpam-2305	31	16	(	(	PUNCT
ejpam-2305	31	17	a2	a2	PROPN
ejpam-2305	31	18	�	�	PROPN
ejpam-2305	31	19	4pb2)2	4pb2)2	VERB
ejpam-2305	31	20	4ab(a2	4ab(a2	PROPN
ejpam-2305	31	21	+	+	CCONJ
ejpam-2305	31	22	4pb2	4pb2	NUM
ejpam-2305	31	23	)	)	PUNCT
ejpam-2305	31	24	.	.	PUNCT
ejpam-2305	32	1	hence	hence	ADV
ejpam-2305	32	2	,	,	PUNCT
ejpam-2305	32	3	(	(	PUNCT
ejpam-2305	32	4	a2	a2	PROPN
ejpam-2305	32	5	�	�	PROPN
ejpam-2305	32	6	4pb2)2	4pb2)2	NOUN
ejpam-2305	32	7	�	�	NOUN
ejpam-2305	32	8	4ab(a2	4ab(a2	NOUN
ejpam-2305	32	9	+	+	ADJ
ejpam-2305	32	10	4pb2)x	4pb2)x	NOUN
ejpam-2305	32	11	0	0	PUNCT
ejpam-2305	33	1	=	=	SYM
ejpam-2305	33	2	0	0	NUM
ejpam-2305	33	3	which	which	PRON
ejpam-2305	33	4	gives	give	VERB
ejpam-2305	33	5	that	that	DET
ejpam-2305	33	6	a4	a4	NOUN
ejpam-2305	33	7	⌘	⌘	X
ejpam-2305	33	8	0	0	NUM
ejpam-2305	33	9	(	(	PUNCT
ejpam-2305	33	10	mod	mod	NOUN
ejpam-2305	33	11	4	4	NUM
ejpam-2305	33	12	)	)	PUNCT
ejpam-2305	33	13	and	and	CCONJ
ejpam-2305	33	14	so	so	ADV
ejpam-2305	33	15	a	a	PRON
ejpam-2305	33	16	is	be	AUX
ejpam-2305	33	17	even	even	ADV
ejpam-2305	33	18	.	.	PUNCT
ejpam-2305	34	1	also	also	ADV
ejpam-2305	34	2	,	,	PUNCT
ejpam-2305	34	3	we	we	PRON
ejpam-2305	34	4	have	have	VERB
ejpam-2305	34	5	b	b	NOUN
ejpam-2305	34	6	|	|	NOUN
ejpam-2305	34	7	(	(	PUNCT
ejpam-2305	34	8	a2	a2	PROPN
ejpam-2305	34	9	�	�	PROPN
ejpam-2305	34	10	4pb2)2	4pb2)2	AUX
ejpam-2305	34	11	.	.	PUNCT
ejpam-2305	35	1	thus	thus	ADV
ejpam-2305	35	2	b	b	X
ejpam-2305	35	3	is	be	AUX
ejpam-2305	35	4	either	either	CCONJ
ejpam-2305	35	5	even	even	ADV
ejpam-2305	35	6	or	or	CCONJ
ejpam-2305	35	7	b	b	NOUN
ejpam-2305	35	8	=	=	SYM
ejpam-2305	35	9	±1	±1	VERB
ejpam-2305	35	10	.	.	PUNCT
ejpam-2305	36	1	the	the	DET
ejpam-2305	36	2	first	first	ADJ
ejpam-2305	36	3	case	case	NOUN
ejpam-2305	36	4	contradicts	contradict	VERB
ejpam-2305	36	5	gcd(a	gcd(a	PROPN
ejpam-2305	36	6	,	,	PUNCT
ejpam-2305	36	7	b	b	NOUN
ejpam-2305	36	8	)	)	PUNCT
ejpam-2305	36	9	=	=	SYM
ejpam-2305	36	10	1	1	X
ejpam-2305	36	11	.	.	PUNCT
ejpam-2305	37	1	thus	thus	ADV
ejpam-2305	37	2	we	we	PRON
ejpam-2305	37	3	must	must	AUX
ejpam-2305	37	4	have	have	VERB
ejpam-2305	37	5	b	b	NOUN
ejpam-2305	37	6	=	=	SYM
ejpam-2305	37	7	±1	±1	VERB
ejpam-2305	37	8	and	and	CCONJ
ejpam-2305	37	9	x	x	SYM
ejpam-2305	37	10	2	2	NUM
ejpam-2305	37	11	z	z	NOUN
ejpam-2305	37	12	is	be	AUX
ejpam-2305	37	13	even	even	ADV
ejpam-2305	37	14	.	.	PUNCT
ejpam-2305	38	1	lemma	lemma	PROPN
ejpam-2305	38	2	1	1	NUM
ejpam-2305	38	3	.	.	PUNCT
ejpam-2305	39	1	for	for	ADP
ejpam-2305	39	2	any	any	DET
ejpam-2305	39	3	prime	prime	ADJ
ejpam-2305	39	4	p	p	NOUN
ejpam-2305	39	5	,	,	PUNCT
ejpam-2305	39	6	the	the	DET
ejpam-2305	39	7	point	point	NOUN
ejpam-2305	39	8	0=	0=	PUNCT
ejpam-2305	39	9	(	(	PUNCT
ejpam-2305	39	10	0,0	0,0	NOUN
ejpam-2305	39	11	)	)	PUNCT
ejpam-2305	39	12	is	be	AUX
ejpam-2305	39	13	the	the	DET
ejpam-2305	39	14	only	only	ADJ
ejpam-2305	39	15	element	element	NOUN
ejpam-2305	39	16	of	of	ADP
ejpam-2305	39	17	order	order	NOUN
ejpam-2305	39	18	2	2	NUM
ejpam-2305	39	19	in	in	ADP
ejpam-2305	39	20	�	�	PROPN
ejpam-2305	39	21	.	.	PUNCT
ejpam-2305	40	1	proof	proof	NOUN
ejpam-2305	40	2	.	.	PUNCT
ejpam-2305	41	1	suppose	suppose	VERB
ejpam-2305	41	2	the	the	DET
ejpam-2305	41	3	contrary	contrary	NOUN
ejpam-2305	41	4	,	,	PUNCT
ejpam-2305	41	5	0	0	PUNCT
ejpam-2305	41	6	6=	6=	X
ejpam-2305	41	7	p	p	NOUN
ejpam-2305	41	8	=	=	X
ejpam-2305	41	9	(	(	PUNCT
ejpam-2305	41	10	x	x	INTJ
ejpam-2305	41	11	,	,	PUNCT
ejpam-2305	41	12	y	y	NOUN
ejpam-2305	41	13	)	)	PUNCT
ejpam-2305	41	14	2	2	NUM
ejpam-2305	41	15	�	�	NOUN
ejpam-2305	41	16	is	be	AUX
ejpam-2305	41	17	of	of	ADP
ejpam-2305	41	18	order	order	NOUN
ejpam-2305	41	19	2	2	NUM
ejpam-2305	41	20	.	.	PUNCT
ejpam-2305	42	1	thus	thus	ADV
ejpam-2305	42	2	2p	2p	NUM
ejpam-2305	42	3	=	=	SYM
ejpam-2305	42	4	o	o	NOUN
ejpam-2305	42	5	and	and	CCONJ
ejpam-2305	42	6	hence	hence	ADV
ejpam-2305	42	7	(	(	PUNCT
ejpam-2305	42	8	x	x	X
ejpam-2305	42	9	,	,	PUNCT
ejpam-2305	42	10	y	y	PROPN
ejpam-2305	42	11	)	)	PUNCT
ejpam-2305	43	1	=	=	SYM
ejpam-2305	43	2	(	(	PUNCT
ejpam-2305	43	3	x	x	INTJ
ejpam-2305	43	4	,	,	PUNCT
ejpam-2305	43	5	�	�	PROPN
ejpam-2305	43	6	y	y	NOUN
ejpam-2305	43	7	)	)	PUNCT
ejpam-2305	43	8	.	.	PUNCT
ejpam-2305	44	1	then	then	ADV
ejpam-2305	44	2	x	x	X
ejpam-2305	44	3	6=	6=	PROPN
ejpam-2305	44	4	0	0	NUM
ejpam-2305	44	5	,	,	PUNCT
ejpam-2305	44	6	y	y	PROPN
ejpam-2305	44	7	=	=	SYM
ejpam-2305	44	8	0	0	NUM
ejpam-2305	45	1	and	and	CCONJ
ejpam-2305	45	2	x3	x3	VERB
ejpam-2305	45	3	+	+	CCONJ
ejpam-2305	45	4	4px	4px	NOUN
ejpam-2305	46	1	=	=	SYM
ejpam-2305	46	2	0	0	X
ejpam-2305	46	3	.	.	X
ejpam-2305	47	1	setting	set	VERB
ejpam-2305	47	2	x	x	PUNCT
ejpam-2305	47	3	=	=	PUNCT
ejpam-2305	47	4	a	a	PROPN
ejpam-2305	47	5	/	/	SYM
ejpam-2305	47	6	b	b	PROPN
ejpam-2305	47	7	and	and	CCONJ
ejpam-2305	47	8	gcd(a	gcd(a	PROPN
ejpam-2305	47	9	,	,	PUNCT
ejpam-2305	47	10	b	b	NOUN
ejpam-2305	47	11	)	)	PUNCT
ejpam-2305	47	12	=	=	SYM
ejpam-2305	47	13	1	1	NUM
ejpam-2305	47	14	,	,	PUNCT
ejpam-2305	47	15	we	we	PRON
ejpam-2305	47	16	get	get	VERB
ejpam-2305	47	17	a3	a3	NOUN
ejpam-2305	47	18	+	+	CCONJ
ejpam-2305	48	1	4pab2	4pab2	NUM
ejpam-2305	48	2	=	=	NOUN
ejpam-2305	48	3	0	0	X
ejpam-2305	48	4	.	.	PUNCT
ejpam-2305	48	5	hence	hence	ADV
ejpam-2305	48	6	b2	b2	VERB
ejpam-2305	48	7	|	|	ADJ
ejpam-2305	48	8	a3	a3	NOUN
ejpam-2305	48	9	.	.	PUNCT
ejpam-2305	49	1	since	since	SCONJ
ejpam-2305	49	2	a	a	DET
ejpam-2305	49	3	,	,	PUNCT
ejpam-2305	49	4	b	b	NOUN
ejpam-2305	49	5	are	be	AUX
ejpam-2305	49	6	coprime	coprime	ADJ
ejpam-2305	49	7	,	,	PUNCT
ejpam-2305	49	8	so	so	PROPN
ejpam-2305	49	9	b	b	X
ejpam-2305	49	10	=	=	PUNCT
ejpam-2305	49	11	±1	±1	VERB
ejpam-2305	49	12	,	,	PUNCT
ejpam-2305	49	13	i.e.	i.e.	X
ejpam-2305	49	14	x	x	SYM
ejpam-2305	49	15	2	2	NUM
ejpam-2305	49	16	z.	z.	NOUN
ejpam-2305	50	1	but	but	CCONJ
ejpam-2305	50	2	,	,	PUNCT
ejpam-2305	50	3	we	we	PRON
ejpam-2305	50	4	have	have	VERB
ejpam-2305	50	5	p	p	NOUN
ejpam-2305	50	6	=	=	PROPN
ejpam-2305	50	7	x3/(	x3/(	PROPN
ejpam-2305	50	8	�	�	PROPN
ejpam-2305	50	9	4x	4x	NUM
ejpam-2305	50	10	)	)	PUNCT
ejpam-2305	50	11	=	=	PUNCT
ejpam-2305	51	1	x2/(	x2/(	NUM
ejpam-2305	51	2	�	�	PROPN
ejpam-2305	51	3	4	4	NUM
ejpam-2305	51	4	)	)	PUNCT
ejpam-2305	51	5	<	<	X
ejpam-2305	51	6	0	0	PROPN
ejpam-2305	51	7	,	,	PUNCT
ejpam-2305	51	8	a	a	DET
ejpam-2305	51	9	contradiction	contradiction	NOUN
ejpam-2305	51	10	.	.	PUNCT
ejpam-2305	52	1	proposition	proposition	NOUN
ejpam-2305	52	2	2	2	NUM
ejpam-2305	52	3	.	.	X
ejpam-2305	52	4	for	for	ADP
ejpam-2305	52	5	any	any	DET
ejpam-2305	52	6	prime	prime	NOUN
ejpam-2305	52	7	p	p	NOUN
ejpam-2305	52	8	,	,	PUNCT
ejpam-2305	52	9	there	there	PRON
ejpam-2305	52	10	is	be	VERB
ejpam-2305	52	11	no	no	DET
ejpam-2305	52	12	point	point	NOUN
ejpam-2305	52	13	of	of	ADP
ejpam-2305	52	14	order	order	NOUN
ejpam-2305	52	15	3	3	NUM
ejpam-2305	52	16	in	in	ADP
ejpam-2305	52	17	�	�	PROPN
ejpam-2305	52	18	.	.	PUNCT
ejpam-2305	53	1	proof	proof	NOUN
ejpam-2305	53	2	.	.	PUNCT
ejpam-2305	54	1	on	on	ADP
ejpam-2305	54	2	the	the	DET
ejpam-2305	54	3	contrary	contrary	NOUN
ejpam-2305	54	4	,	,	PUNCT
ejpam-2305	54	5	we	we	PRON
ejpam-2305	54	6	suppose	suppose	VERB
ejpam-2305	54	7	p	p	X
ejpam-2305	54	8	=	=	X
ejpam-2305	54	9	(	(	PUNCT
ejpam-2305	54	10	x	x	INTJ
ejpam-2305	54	11	,	,	PUNCT
ejpam-2305	54	12	y	y	NOUN
ejpam-2305	54	13	)	)	PUNCT
ejpam-2305	54	14	2	2	NUM
ejpam-2305	54	15	�	�	NOUN
ejpam-2305	54	16	is	be	AUX
ejpam-2305	54	17	of	of	ADP
ejpam-2305	54	18	order	order	NOUN
ejpam-2305	54	19	3	3	NUM
ejpam-2305	54	20	,	,	PUNCT
ejpam-2305	54	21	i.e.	i.e.	X
ejpam-2305	54	22	2p	2p	NUM
ejpam-2305	54	23	=	=	SYM
ejpam-2305	55	1	�	�	PROPN
ejpam-2305	55	2	p.	p.	NOUN
ejpam-2305	55	3	let	let	VERB
ejpam-2305	55	4	p	p	NOUN
ejpam-2305	55	5	=	=	X
ejpam-2305	55	6	(	(	PUNCT
ejpam-2305	55	7	x	x	INTJ
ejpam-2305	55	8	,	,	PUNCT
ejpam-2305	55	9	y	y	PROPN
ejpam-2305	55	10	)	)	PUNCT
ejpam-2305	55	11	,	,	PUNCT
ejpam-2305	55	12	2p	2p	NUM
ejpam-2305	55	13	=	=	SYM
ejpam-2305	55	14	(	(	PUNCT
ejpam-2305	55	15	x	x	NOUN
ejpam-2305	55	16	0	0	PROPN
ejpam-2305	55	17	,	,	PUNCT
ejpam-2305	55	18	y	y	PROPN
ejpam-2305	55	19	0	0	NUM
ejpam-2305	55	20	)	)	PUNCT
ejpam-2305	55	21	.	.	PUNCT
ejpam-2305	56	1	hence	hence	ADV
ejpam-2305	56	2	(	(	PUNCT
ejpam-2305	56	3	x	x	X
ejpam-2305	56	4	0	0	PROPN
ejpam-2305	56	5	,	,	PUNCT
ejpam-2305	56	6	y	y	PROPN
ejpam-2305	56	7	0	0	NUM
ejpam-2305	56	8	)	)	PUNCT
ejpam-2305	56	9	=	=	SYM
ejpam-2305	56	10	�	�	PROPN
ejpam-2305	56	11	(	(	PUNCT
ejpam-2305	56	12	x	x	PROPN
ejpam-2305	56	13	,	,	PUNCT
ejpam-2305	56	14	y	y	PROPN
ejpam-2305	56	15	)	)	PUNCT
ejpam-2305	56	16	=	=	SYM
ejpam-2305	56	17	(	(	PUNCT
ejpam-2305	56	18	x	x	INTJ
ejpam-2305	56	19	,	,	PUNCT
ejpam-2305	56	20	�	�	PROPN
ejpam-2305	56	21	y	y	NOUN
ejpam-2305	56	22	)	)	PUNCT
ejpam-2305	56	23	,	,	PUNCT
ejpam-2305	56	24	so	so	ADV
ejpam-2305	56	25	x	x	SYM
ejpam-2305	56	26	0	0	X
ejpam-2305	57	1	=	=	SYM
ejpam-2305	57	2	x	x	X
ejpam-2305	57	3	.	.	PUNCT
ejpam-2305	58	1	on	on	ADP
ejpam-2305	58	2	the	the	DET
ejpam-2305	58	3	other	other	ADJ
ejpam-2305	58	4	hand	hand	NOUN
ejpam-2305	58	5	,	,	PUNCT
ejpam-2305	58	6	from	from	ADP
ejpam-2305	58	7	duplication	duplication	NOUN
ejpam-2305	58	8	formula	formula	NOUN
ejpam-2305	58	9	,	,	PUNCT
ejpam-2305	58	10	we	we	PRON
ejpam-2305	58	11	have	have	VERB
ejpam-2305	58	12	x	x	X
ejpam-2305	58	13	=	=	PUNCT
ejpam-2305	58	14	x	x	SYM
ejpam-2305	58	15	0	0	PUNCT
ejpam-2305	59	1	=	=	SYM
ejpam-2305	59	2	(	(	PUNCT
ejpam-2305	59	3	x2	x2	PROPN
ejpam-2305	59	4	�	�	PROPN
ejpam-2305	59	5	4p)2	4p)2	NUM
ejpam-2305	59	6	4(x3	4(x3	PROPN
ejpam-2305	59	7	+	+	CCONJ
ejpam-2305	59	8	4px	4px	NOUN
ejpam-2305	59	9	)	)	PUNCT
ejpam-2305	59	10	.	.	PUNCT
ejpam-2305	60	1	thus	thus	ADV
ejpam-2305	60	2	,	,	PUNCT
ejpam-2305	60	3	16p2	16p2	NUM
ejpam-2305	60	4	�	�	PROPN
ejpam-2305	60	5	24x2p	24x2p	NUM
ejpam-2305	60	6	�	�	PROPN
ejpam-2305	60	7	3x4	3x4	NUM
ejpam-2305	60	8	=	=	SYM
ejpam-2305	60	9	0	0	NUM
ejpam-2305	60	10	is	be	AUX
ejpam-2305	60	11	a	a	DET
ejpam-2305	60	12	quadratic	quadratic	ADJ
ejpam-2305	60	13	polynomial	polynomial	NOUN
ejpam-2305	60	14	in	in	ADP
ejpam-2305	60	15	variable	variable	ADJ
ejpam-2305	60	16	p.	p.	PROPN
ejpam-2305	61	1	therefore	therefore	ADV
ejpam-2305	61	2	,	,	PUNCT
ejpam-2305	61	3	p	p	NOUN
ejpam-2305	61	4	=	=	SYM
ejpam-2305	61	5	12x2	12x2	NUM
ejpam-2305	61	6	±p	±p	NOUN
ejpam-2305	61	7	�	�	NOUN
ejpam-2305	61	8	0	0	NUM
ejpam-2305	61	9	16	16	NUM
ejpam-2305	61	10	with	with	ADP
ejpam-2305	61	11	�	�	PROPN
ejpam-2305	61	12	0	0	NUM
ejpam-2305	61	13	=	=	SYM
ejpam-2305	61	14	192x4	192x4	NUM
ejpam-2305	61	15	.	.	PUNCT
ejpam-2305	62	1	since	since	SCONJ
ejpam-2305	62	2	�	�	PROPN
ejpam-2305	62	3	0	0	NUM
ejpam-2305	62	4	is	be	AUX
ejpam-2305	62	5	not	not	PART
ejpam-2305	62	6	square	square	ADJ
ejpam-2305	62	7	,	,	PUNCT
ejpam-2305	62	8	then	then	ADV
ejpam-2305	62	9	p	p	X
ejpam-2305	62	10	/2	/2	ADJ
ejpam-2305	62	11	n	n	CCONJ
ejpam-2305	62	12	,	,	PUNCT
ejpam-2305	62	13	a	a	DET
ejpam-2305	62	14	contradiction	contradiction	NOUN
ejpam-2305	62	15	.	.	PUNCT
ejpam-2305	63	1	the	the	DET
ejpam-2305	63	2	following	follow	VERB
ejpam-2305	63	3	is	be	AUX
ejpam-2305	63	4	one	one	NUM
ejpam-2305	63	5	of	of	ADP
ejpam-2305	63	6	our	our	PRON
ejpam-2305	63	7	main	main	ADJ
ejpam-2305	63	8	results	result	NOUN
ejpam-2305	63	9	.	.	PUNCT
ejpam-2305	64	1	theorem	theorem	NOUN
ejpam-2305	64	2	1	1	NUM
ejpam-2305	64	3	.	.	X
ejpam-2305	65	1	for	for	ADP
ejpam-2305	65	2	any	any	DET
ejpam-2305	65	3	prime	prime	ADJ
ejpam-2305	65	4	p	p	NOUN
ejpam-2305	65	5	,	,	PUNCT
ejpam-2305	65	6	t	t	PROPN
ejpam-2305	65	7	⇠	⇠	PROPN
ejpam-2305	65	8	=	=	SYM
ejpam-2305	65	9	z2	z2	PROPN
ejpam-2305	65	10	.	.	PUNCT
ejpam-2305	65	11	proof	proof	NOUN
ejpam-2305	65	12	.	.	PUNCT
ejpam-2305	66	1	by	by	ADP
ejpam-2305	66	2	lemma	lemma	PROPN
ejpam-2305	66	3	1	1	NUM
ejpam-2305	66	4	,	,	PUNCT
ejpam-2305	66	5	{	{	PUNCT
ejpam-2305	66	6	o	o	NOUN
ejpam-2305	66	7	,	,	PUNCT
ejpam-2305	66	8	0	0	NUM
ejpam-2305	66	9	}	}	PUNCT
ejpam-2305	66	10	✓	✓	ADJ
ejpam-2305	66	11	t	t	NOUN
ejpam-2305	66	12	.	.	PUNCT
ejpam-2305	67	1	let	let	VERB
ejpam-2305	67	2	p	p	NOUN
ejpam-2305	67	3	:	:	PUNCT
ejpam-2305	67	4	=	=	SYM
ejpam-2305	67	5	(	(	PUNCT
ejpam-2305	67	6	x	x	INTJ
ejpam-2305	67	7	,	,	PUNCT
ejpam-2305	67	8	y	y	PROPN
ejpam-2305	67	9	)	)	PUNCT
ejpam-2305	67	10	2	2	NUM
ejpam-2305	67	11	t	t	NOUN
ejpam-2305	67	12	\	\	PUNCT
ejpam-2305	67	13	{	{	PUNCT
ejpam-2305	67	14	o	o	NOUN
ejpam-2305	67	15	,	,	PUNCT
ejpam-2305	67	16	0	0	NUM
ejpam-2305	67	17	}	}	PUNCT
ejpam-2305	67	18	.	.	PUNCT
ejpam-2305	68	1	by	by	ADP
ejpam-2305	68	2	lutz	lutz	NOUN
ejpam-2305	68	3	-	-	PUNCT
ejpam-2305	68	4	nagell	nagell	PROPN
ejpam-2305	68	5	theorem	theorem	VERB
ejpam-2305	68	6	,	,	PUNCT
ejpam-2305	68	7	x	x	SYM
ejpam-2305	68	8	and	and	CCONJ
ejpam-2305	68	9	y	y	PROPN
ejpam-2305	68	10	are	be	AUX
ejpam-2305	68	11	integers	integer	NOUN
ejpam-2305	68	12	such	such	ADJ
ejpam-2305	68	13	that	that	SCONJ
ejpam-2305	68	14	y2	y2	PROPN
ejpam-2305	68	15	divides	divide	VERB
ejpam-2305	68	16	the	the	DET
ejpam-2305	68	17	discriminant	discriminant	NOUN
ejpam-2305	68	18	�	�	X
ejpam-2305	68	19	=	=	PROPN
ejpam-2305	68	20	28p3	28p3	NUM
ejpam-2305	68	21	of	of	ADP
ejpam-2305	68	22	the	the	DET
ejpam-2305	68	23	curve	curve	NOUN
ejpam-2305	68	24	e.	e.	PROPN
ejpam-2305	68	25	thus	thus	ADV
ejpam-2305	68	26	y2	y2	PROPN
ejpam-2305	68	27	=	=	PROPN
ejpam-2305	68	28	1,22	1,22	NUM
ejpam-2305	68	29	,	,	PUNCT
ejpam-2305	68	30	24	24	NUM
ejpam-2305	68	31	,	,	PUNCT
ejpam-2305	68	32	26	26	NUM
ejpam-2305	68	33	,	,	PUNCT
ejpam-2305	68	34	28	28	NUM
ejpam-2305	68	35	,	,	PUNCT
ejpam-2305	68	36	p2	p2	NOUN
ejpam-2305	68	37	,	,	PUNCT
ejpam-2305	68	38	22p2	22p2	NUM
ejpam-2305	68	39	,	,	PUNCT
ejpam-2305	68	40	24p2	24p2	NUM
ejpam-2305	68	41	,	,	PUNCT
ejpam-2305	68	42	26p2	26p2	NUM
ejpam-2305	68	43	,	,	PUNCT
ejpam-2305	68	44	28p2	28p2	NUM
ejpam-2305	68	45	.	.	PUNCT
ejpam-2305	69	1	we	we	PRON
ejpam-2305	69	2	list	list	VERB
ejpam-2305	69	3	the	the	DET
ejpam-2305	69	4	computations	computation	NOUN
ejpam-2305	69	5	done	do	VERB
ejpam-2305	69	6	with	with	ADP
ejpam-2305	69	7	2p	2p	NUM
ejpam-2305	69	8	=	=	SYM
ejpam-2305	69	9	(	(	PUNCT
ejpam-2305	69	10	x2	x2	PROPN
ejpam-2305	69	11	,	,	PUNCT
ejpam-2305	69	12	y2	y2	PROPN
ejpam-2305	69	13	)	)	PUNCT
ejpam-2305	70	1	where	where	SCONJ
ejpam-2305	70	2	x2	x2	PROPN
ejpam-2305	70	3	=	=	PRON
ejpam-2305	70	4	(	(	PUNCT
ejpam-2305	70	5	3x2	3x2	NUM
ejpam-2305	70	6	+	+	SYM
ejpam-2305	70	7	4p)2	4p)2	NOUN
ejpam-2305	70	8	4y2	4y2	DET
ejpam-2305	70	9	�	�	NOUN
ejpam-2305	70	10	2x	2x	NUM
ejpam-2305	70	11	=	=	SYM
ejpam-2305	70	12	(	(	PUNCT
ejpam-2305	70	13	x2	x2	PROPN
ejpam-2305	70	14	�	�	PROPN
ejpam-2305	70	15	4p)2	4p)2	NUM
ejpam-2305	70	16	4(x3	4(x3	PROPN
ejpam-2305	70	17	+	+	CCONJ
ejpam-2305	70	18	4px	4px	NOUN
ejpam-2305	70	19	)	)	PUNCT
ejpam-2305	70	20	in	in	ADP
ejpam-2305	70	21	the	the	DET
ejpam-2305	70	22	following	follow	VERB
ejpam-2305	70	23	table	table	NOUN
ejpam-2305	70	24	:	:	PUNCT
ejpam-2305	70	25	n.	n.	PROPN
ejpam-2305	70	26	zamani	zamani	PROPN
ejpam-2305	70	27	,	,	PUNCT
ejpam-2305	70	28	a.	a.	NOUN
ejpam-2305	70	29	shams	sham	NOUN
ejpam-2305	70	30	/	/	SYM
ejpam-2305	70	31	eur	eur	PROPN
ejpam-2305	70	32	.	.	PUNCT
ejpam-2305	71	1	j.	j.	PROPN
ejpam-2305	71	2	pure	pure	PROPN
ejpam-2305	71	3	appl	appl	PROPN
ejpam-2305	71	4	.	.	PROPN
ejpam-2305	71	5	math	math	PROPN
ejpam-2305	71	6	,	,	PUNCT
ejpam-2305	71	7	8	8	NUM
ejpam-2305	71	8	(	(	PUNCT
ejpam-2305	71	9	2015	2015	NUM
ejpam-2305	71	10	)	)	PUNCT
ejpam-2305	71	11	,	,	PUNCT
ejpam-2305	71	12	126	126	NUM
ejpam-2305	71	13	-	-	SYM
ejpam-2305	71	14	134	134	NUM
ejpam-2305	71	15	128	128	NUM
ejpam-2305	71	16	table	table	NOUN
ejpam-2305	71	17	1	1	NUM
ejpam-2305	71	18	:	:	PUNCT
ejpam-2305	71	19	computations	computation	NOUN
ejpam-2305	71	20	with	with	ADP
ejpam-2305	71	21	2p	2p	NUM
ejpam-2305	71	22	=	=	SYM
ejpam-2305	71	23	(	(	PUNCT
ejpam-2305	71	24	x2	x2	PROPN
ejpam-2305	71	25	,	,	PUNCT
ejpam-2305	71	26	y2	y2	NOUN
ejpam-2305	71	27	)	)	PUNCT
ejpam-2305	72	1	y2	y2	NOUN
ejpam-2305	72	2	x	x	SYM
ejpam-2305	73	1	(	(	PUNCT
ejpam-2305	73	2	x	x	X
ejpam-2305	73	3	,	,	PUNCT
ejpam-2305	73	4	y2	y2	PROPN
ejpam-2305	73	5	;	;	PUNCT
ejpam-2305	73	6	p	p	X
ejpam-2305	73	7	)	)	PUNCT
ejpam-2305	73	8	x2	x2	PROPN
ejpam-2305	73	9	1	1	NUM
ejpam-2305	73	10	±1	±1	VERB
ejpam-2305	73	11	–	–	PUNCT
ejpam-2305	73	12	–	–	PUNCT
ejpam-2305	73	13	4	4	NUM
ejpam-2305	73	14	±1,±2,±4	±1,±2,±4	NOUN
ejpam-2305	73	15	–	–	PUNCT
ejpam-2305	73	16	–	–	PUNCT
ejpam-2305	73	17	16	16	NUM
ejpam-2305	73	18	±1,±2,±4,±8,±16	±1,±2,±4,±8,±16	NOUN
ejpam-2305	73	19	–	–	PUNCT
ejpam-2305	73	20	–	–	PUNCT
ejpam-2305	73	21	64	64	NUM
ejpam-2305	73	22	±1,±2,±4,±8,±16,±32,±64	±1,±2,±4,±8,±16,±32,±64	PROPN
ejpam-2305	73	23	(	(	PUNCT
ejpam-2305	73	24	2	2	NUM
ejpam-2305	73	25	,	,	PUNCT
ejpam-2305	73	26	64	64	NUM
ejpam-2305	73	27	;	;	PUNCT
ejpam-2305	73	28	7	7	X
ejpam-2305	73	29	)	)	PUNCT
ejpam-2305	73	30	9	9	NUM
ejpam-2305	73	31	4	4	NUM
ejpam-2305	73	32	256	256	NUM
ejpam-2305	73	33	±1,±2,±4,±8,±16,±32,±64	±1,±2,±4,±8,±16,±32,±64	NOUN
ejpam-2305	73	34	,	,	PUNCT
ejpam-2305	73	35	±128,±256	±128,±256	PROPN
ejpam-2305	73	36	(	(	PUNCT
ejpam-2305	73	37	2	2	NUM
ejpam-2305	73	38	,	,	PUNCT
ejpam-2305	73	39	256;31	256;31	NUM
ejpam-2305	73	40	)	)	PUNCT
ejpam-2305	73	41	225	225	NUM
ejpam-2305	73	42	16	16	NUM
ejpam-2305	73	43	p2	p2	NOUN
ejpam-2305	73	44	±1,±p,±p2	±1,±p,±p2	ADP
ejpam-2305	73	45	–	–	PUNCT
ejpam-2305	73	46	–	–	PUNCT
ejpam-2305	73	47	4p2	4p2	NUM
ejpam-2305	73	48	±1,±2,±4,±p,±2p,±4p,±p2	±1,±2,±4,±p,±2p,±4p,±p2	NOUN
ejpam-2305	73	49	,	,	PUNCT
ejpam-2305	73	50	±2p2,±4p2	±2p2,±4p2	CCONJ
ejpam-2305	73	51	–	–	PUNCT
ejpam-2305	73	52	–	–	PUNCT
ejpam-2305	73	53	16p2	16p2	NUM
ejpam-2305	73	54	±1,±2,±4,±8,±16,±p,±2p	±1,±2,±4,±8,±16,±p,±2p	NOUN
ejpam-2305	73	55	,	,	PUNCT
ejpam-2305	73	56	±4p,±8p,±16p	±4p,±8p,±16p	X
ejpam-2305	73	57	–	–	PUNCT
ejpam-2305	73	58	–	–	PUNCT
ejpam-2305	73	59	64p2	64p2	NUM
ejpam-2305	73	60	±1,±2,±4,±8,±16,±32,±64	±1,±2,±4,±8,±16,±32,±64	PROPN
ejpam-2305	73	61	,	,	PUNCT
ejpam-2305	73	62	±p,±2p,±4p,±8p,±16p,±32p	±p,±2p,±4p,±8p,±16p,±32p	PROPN
ejpam-2305	73	63	±64p,±p2,±2p2,±4p2,±8p2	±64p,±p2,±2p2,±4p2,±8p2	PROPN
ejpam-2305	73	64	,	,	PUNCT
ejpam-2305	73	65	±16p2,±32p2,±64p2,±64p2	±16p2,±32p2,±64p2,±64p2	CCONJ
ejpam-2305	73	66	(	(	PUNCT
ejpam-2305	73	67	14	14	NUM
ejpam-2305	73	68	,	,	PUNCT
ejpam-2305	73	69	3136	3136	NUM
ejpam-2305	73	70	;	;	PUNCT
ejpam-2305	73	71	7	7	X
ejpam-2305	73	72	)	)	PUNCT
ejpam-2305	73	73	9	9	NUM
ejpam-2305	73	74	4	4	NUM
ejpam-2305	73	75	256p2	256p2	NUM
ejpam-2305	73	76	±1,±2,±4,±8,±16,±32,±64	±1,±2,±4,±8,±16,±32,±64	NOUN
ejpam-2305	73	77	,	,	PUNCT
ejpam-2305	73	78	±128,±256,±p,±2p,±4p,±8p	±128,±256,±p,±2p,±4p,±8p	NOUN
ejpam-2305	73	79	,	,	PUNCT
ejpam-2305	73	80	±16p,±32p,±64p,±128p,±256	±16p,±32p,±64p,±128p,±256	PROPN
ejpam-2305	73	81	±p2,±2p2,±4p2,±8p2,±16p2	±p2,±2p2,±4p2,±8p2,±16p2	NOUN
ejpam-2305	73	82	±32p2,±64p2,±128p2,±256p2	±32p2,±64p2,±128p2,±256p2	X
ejpam-2305	73	83	(	(	PUNCT
ejpam-2305	73	84	62	62	NUM
ejpam-2305	73	85	,	,	PUNCT
ejpam-2305	73	86	246016	246016	NUM
ejpam-2305	73	87	;	;	PUNCT
ejpam-2305	73	88	31	31	NUM
ejpam-2305	73	89	)	)	PUNCT
ejpam-2305	73	90	225	225	NUM
ejpam-2305	73	91	16	16	NUM
ejpam-2305	73	92	the	the	DET
ejpam-2305	73	93	symbol	symbol	NOUN
ejpam-2305	73	94	‘	'	PUNCT
ejpam-2305	73	95	–	–	PUNCT
ejpam-2305	73	96	’	'	PUNCT
ejpam-2305	73	97	in	in	ADP
ejpam-2305	73	98	table	table	NOUN
ejpam-2305	73	99	1	1	NUM
ejpam-2305	73	100	means	mean	VERB
ejpam-2305	73	101	that	that	SCONJ
ejpam-2305	73	102	the	the	DET
ejpam-2305	73	103	equation	equation	NOUN
ejpam-2305	73	104	y2	y2	NOUN
ejpam-2305	73	105	=	=	PUNCT
ejpam-2305	74	1	x3	x3	PROPN
ejpam-2305	75	1	+	+	CCONJ
ejpam-2305	75	2	4px	4px	NOUN
ejpam-2305	75	3	has	have	VERB
ejpam-2305	75	4	no	no	DET
ejpam-2305	75	5	integer	integer	NOUN
ejpam-2305	75	6	solution	solution	NOUN
ejpam-2305	75	7	(	(	PUNCT
ejpam-2305	75	8	x	x	X
ejpam-2305	75	9	,	,	PUNCT
ejpam-2305	75	10	y	y	PROPN
ejpam-2305	75	11	;	;	PUNCT
ejpam-2305	75	12	p	p	X
ejpam-2305	75	13	)	)	PUNCT
ejpam-2305	75	14	and	and	CCONJ
ejpam-2305	75	15	hence	hence	ADV
ejpam-2305	75	16	no	no	DET
ejpam-2305	75	17	solution	solution	NOUN
ejpam-2305	75	18	for	for	ADP
ejpam-2305	75	19	x2	x2	PROPN
ejpam-2305	75	20	.	.	PUNCT
ejpam-2305	76	1	we	we	PRON
ejpam-2305	76	2	see	see	VERB
ejpam-2305	76	3	that	that	SCONJ
ejpam-2305	76	4	x2	x2	PRON
ejpam-2305	76	5	is	be	AUX
ejpam-2305	76	6	never	never	ADV
ejpam-2305	76	7	zero	zero	NUM
ejpam-2305	76	8	and	and	CCONJ
ejpam-2305	76	9	so	so	ADV
ejpam-2305	76	10	2p	2p	NOUN
ejpam-2305	76	11	can	can	AUX
ejpam-2305	76	12	not	not	PART
ejpam-2305	76	13	be	be	AUX
ejpam-2305	76	14	of	of	ADP
ejpam-2305	76	15	finite	finite	ADJ
ejpam-2305	76	16	order	order	NOUN
ejpam-2305	76	17	.	.	PUNCT
ejpam-2305	77	1	this	this	PRON
ejpam-2305	77	2	contradicts	contradict	VERB
ejpam-2305	77	3	the	the	DET
ejpam-2305	77	4	fact	fact	NOUN
ejpam-2305	77	5	that	that	SCONJ
ejpam-2305	77	6	2p	2p	NUM
ejpam-2305	77	7	2	2	NUM
ejpam-2305	77	8	t	t	NOUN
ejpam-2305	77	9	.	.	PUNCT
ejpam-2305	78	1	3	3	X
ejpam-2305	78	2	.	.	X
ejpam-2305	78	3	a	a	DET
ejpam-2305	78	4	result	result	NOUN
ejpam-2305	78	5	on	on	ADP
ejpam-2305	78	6	selmer	selmer	PROPN
ejpam-2305	78	7	group	group	NOUN
ejpam-2305	78	8	of	of	ADP
ejpam-2305	78	9	e	e	PROPN
ejpam-2305	78	10	in	in	ADP
ejpam-2305	78	11	this	this	DET
ejpam-2305	78	12	section	section	NOUN
ejpam-2305	78	13	,	,	PUNCT
ejpam-2305	78	14	we	we	PRON
ejpam-2305	78	15	want	want	VERB
ejpam-2305	78	16	to	to	PART
ejpam-2305	78	17	evaluate	evaluate	VERB
ejpam-2305	78	18	the	the	DET
ejpam-2305	78	19	selmer	selmer	PROPN
ejpam-2305	78	20	group	group	PROPN
ejpam-2305	78	21	of	of	ADP
ejpam-2305	78	22	e.	e.	PROPN
ejpam-2305	78	23	for	for	ADP
ejpam-2305	78	24	ease	ease	NOUN
ejpam-2305	78	25	in	in	ADP
ejpam-2305	78	26	access	access	NOUN
ejpam-2305	78	27	,	,	PUNCT
ejpam-2305	78	28	we	we	PRON
ejpam-2305	78	29	recall	recall	VERB
ejpam-2305	78	30	some	some	DET
ejpam-2305	78	31	basic	basic	ADJ
ejpam-2305	78	32	facts	fact	NOUN
ejpam-2305	78	33	on	on	ADP
ejpam-2305	78	34	the	the	DET
ejpam-2305	78	35	selmer	selmer	PROPN
ejpam-2305	78	36	groups	group	NOUN
ejpam-2305	78	37	of	of	ADP
ejpam-2305	78	38	the	the	DET
ejpam-2305	78	39	elliptic	elliptic	ADJ
ejpam-2305	78	40	curves	curve	NOUN
ejpam-2305	78	41	[	[	X
ejpam-2305	78	42	4	4	NUM
ejpam-2305	78	43	,	,	PUNCT
ejpam-2305	78	44	7	7	NUM
ejpam-2305	78	45	]	]	PUNCT
ejpam-2305	78	46	.	.	PUNCT
ejpam-2305	79	1	let	let	VERB
ejpam-2305	79	2	e	e	X
ejpam-2305	79	3	,	,	PUNCT
ejpam-2305	79	4	e0	e0	PROPN
ejpam-2305	79	5	be	be	VERB
ejpam-2305	79	6	elliptic	elliptic	ADJ
ejpam-2305	79	7	curves	curve	NOUN
ejpam-2305	79	8	defined	define	VERB
ejpam-2305	79	9	over	over	ADP
ejpam-2305	79	10	q	q	PUNCT
ejpam-2305	79	11	and	and	CCONJ
ejpam-2305	79	12	assume	assume	VERB
ejpam-2305	79	13	that	that	SCONJ
ejpam-2305	79	14	there	there	PRON
ejpam-2305	79	15	exists	exist	VERB
ejpam-2305	79	16	an	an	DET
ejpam-2305	79	17	isogeny	isogeny	NOUN
ejpam-2305	79	18	'	'	PUNCT
ejpam-2305	80	1	:	:	PUNCT
ejpam-2305	80	2	e	e	PROPN
ejpam-2305	80	3	�	�	PROPN
ejpam-2305	80	4	!	!	PUNCT
ejpam-2305	80	5	e0	e0	PROPN
ejpam-2305	80	6	over	over	ADP
ejpam-2305	80	7	q	q	NOUN
ejpam-2305	80	8	with	with	ADP
ejpam-2305	80	9	'	'	NUM
ejpam-2305	80	10	0	0	NUM
ejpam-2305	80	11	:	:	PUNCT
ejpam-2305	80	12	e0	e0	PROPN
ejpam-2305	80	13	!	!	PUNCT
ejpam-2305	81	1	e	e	X
ejpam-2305	81	2	its	its	PRON
ejpam-2305	81	3	dual	dual	ADJ
ejpam-2305	81	4	.	.	PUNCT
ejpam-2305	82	1	let	let	VERB
ejpam-2305	82	2	k	k	PRON
ejpam-2305	82	3	be	be	AUX
ejpam-2305	82	4	a	a	DET
ejpam-2305	82	5	field	field	NOUN
ejpam-2305	82	6	containing	contain	VERB
ejpam-2305	82	7	q	q	NOUN
ejpam-2305	82	8	with	with	ADP
ejpam-2305	82	9	q	q	PRON
ejpam-2305	82	10	its	its	PRON
ejpam-2305	82	11	integral	integral	ADJ
ejpam-2305	82	12	closure	closure	NOUN
ejpam-2305	82	13	in	in	ADP
ejpam-2305	82	14	k.	k.	PROPN
ejpam-2305	82	15	then	then	ADV
ejpam-2305	82	16	there	there	PRON
ejpam-2305	82	17	is	be	VERB
ejpam-2305	82	18	an	an	DET
ejpam-2305	82	19	exact	exact	ADJ
ejpam-2305	82	20	sequence	sequence	NOUN
ejpam-2305	82	21	0	0	NUM
ejpam-2305	82	22	�	�	PROPN
ejpam-2305	82	23	!	!	PUNCT
ejpam-2305	83	1	e	e	X
ejpam-2305	83	2	[	[	X
ejpam-2305	83	3	'	'	X
ejpam-2305	83	4	]	]	X
ejpam-2305	83	5	�	�	PROPN
ejpam-2305	83	6	!	!	PUNCT
ejpam-2305	84	1	e	e	X
ejpam-2305	84	2	'	'	VERB
ejpam-2305	84	3	�	�	PROPN
ejpam-2305	84	4	!	!	PUNCT
ejpam-2305	84	5	e0	e0	PROPN
ejpam-2305	84	6	�	�	PROPN
ejpam-2305	84	7	!	!	PROPN
ejpam-2305	84	8	0	0	NUM
ejpam-2305	84	9	,	,	PUNCT
ejpam-2305	84	10	of	of	ADP
ejpam-2305	84	11	gal(q	gal(q	PROPN
ejpam-2305	84	12	/	/	SYM
ejpam-2305	84	13	q)-modules	q)-module	NOUN
ejpam-2305	84	14	where	where	SCONJ
ejpam-2305	84	15	e	e	X
ejpam-2305	84	16	[	[	X
ejpam-2305	84	17	'	'	X
ejpam-2305	84	18	]	]	X
ejpam-2305	84	19	=	=	SYM
ejpam-2305	84	20	ker	ker	X
ejpam-2305	84	21	(	(	PUNCT
ejpam-2305	84	22	'	'	PUNCT
ejpam-2305	84	23	)	)	PUNCT
ejpam-2305	84	24	.	.	PUNCT
ejpam-2305	85	1	taking	take	VERB
ejpam-2305	85	2	galois	galois	PROPN
ejpam-2305	85	3	cohomology	cohomology	NOUN
ejpam-2305	85	4	,	,	PUNCT
ejpam-2305	85	5	we	we	PRON
ejpam-2305	85	6	obtain	obtain	VERB
ejpam-2305	85	7	the	the	DET
ejpam-2305	85	8	exact	exact	ADJ
ejpam-2305	85	9	sequence	sequence	NOUN
ejpam-2305	85	10	0	0	NUM
ejpam-2305	85	11	�	�	PROPN
ejpam-2305	85	12	!	!	PUNCT
ejpam-2305	85	13	e0(k)/'(e(k	e0(k)/'(e(k	PROPN
ejpam-2305	85	14	)	)	PUNCT
ejpam-2305	85	15	)	)	PUNCT
ejpam-2305	85	16	�	�	PROPN
ejpam-2305	85	17	k	k	NOUN
ejpam-2305	85	18	�	�	PROPN
ejpam-2305	85	19	!	!	PUNCT
ejpam-2305	86	1	h1(k	h1(k	NOUN
ejpam-2305	86	2	,	,	PUNCT
ejpam-2305	86	3	e	e	NOUN
ejpam-2305	86	4	[	[	X
ejpam-2305	86	5	'	'	X
ejpam-2305	86	6	]	]	X
ejpam-2305	86	7	)	)	PUNCT
ejpam-2305	86	8	'	'	PUNCT
ejpam-2305	86	9	⇤	⇤	PROPN
ejpam-2305	86	10	�	�	PROPN
ejpam-2305	86	11	!	!	PUNCT
ejpam-2305	87	1	h1(k	h1(k	NOUN
ejpam-2305	87	2	,	,	PUNCT
ejpam-2305	87	3	e	e	NOUN
ejpam-2305	87	4	)	)	PUNCT
ejpam-2305	88	1	[	[	X
ejpam-2305	88	2	'	'	X
ejpam-2305	88	3	]	]	X
ejpam-2305	88	4	�	�	PROPN
ejpam-2305	88	5	!	!	PROPN
ejpam-2305	88	6	0	0	NUM
ejpam-2305	88	7	,	,	PUNCT
ejpam-2305	88	8	n.	n.	PROPN
ejpam-2305	88	9	zamani	zamani	PROPN
ejpam-2305	88	10	,	,	PUNCT
ejpam-2305	88	11	a.	a.	NOUN
ejpam-2305	88	12	shams	sham	NOUN
ejpam-2305	88	13	/	/	SYM
ejpam-2305	88	14	eur	eur	PROPN
ejpam-2305	88	15	.	.	PUNCT
ejpam-2305	89	1	j.	j.	PROPN
ejpam-2305	89	2	pure	pure	PROPN
ejpam-2305	89	3	appl	appl	PROPN
ejpam-2305	89	4	.	.	PROPN
ejpam-2305	89	5	math	math	PROPN
ejpam-2305	89	6	,	,	PUNCT
ejpam-2305	89	7	8	8	NUM
ejpam-2305	89	8	(	(	PUNCT
ejpam-2305	89	9	2015	2015	NUM
ejpam-2305	89	10	)	)	PUNCT
ejpam-2305	89	11	,	,	PUNCT
ejpam-2305	89	12	126	126	NUM
ejpam-2305	89	13	-	-	SYM
ejpam-2305	89	14	134	134	NUM
ejpam-2305	89	15	129	129	NUM
ejpam-2305	89	16	where	where	SCONJ
ejpam-2305	89	17	h1(k	h1(k	NOUN
ejpam-2305	89	18	,	,	PUNCT
ejpam-2305	89	19	e	e	NOUN
ejpam-2305	89	20	)	)	PUNCT
ejpam-2305	90	1	[	[	X
ejpam-2305	90	2	'	'	X
ejpam-2305	90	3	]	]	X
ejpam-2305	90	4	is	be	AUX
ejpam-2305	90	5	the	the	DET
ejpam-2305	90	6	kernel	kernel	NOUN
ejpam-2305	90	7	of	of	ADP
ejpam-2305	90	8	'	'	PUNCT
ejpam-2305	90	9	⇤	⇤	PROPN
ejpam-2305	90	10	and	and	CCONJ
ejpam-2305	90	11	�	�	PROPN
ejpam-2305	90	12	k	k	PROPN
ejpam-2305	90	13	is	be	AUX
ejpam-2305	90	14	the	the	DET
ejpam-2305	90	15	connecting	connect	VERB
ejpam-2305	90	16	homomorphism	homomorphism	NOUN
ejpam-2305	90	17	.	.	PUNCT
ejpam-2305	91	1	consider	consider	VERB
ejpam-2305	92	1	the	the	DET
ejpam-2305	92	2	following	follow	VERB
ejpam-2305	92	3	commutative	commutative	ADJ
ejpam-2305	92	4	diagram	diagram	NOUN
ejpam-2305	92	5	(	(	PUNCT
ejpam-2305	92	6	�	�	PROPN
ejpam-2305	92	7	q	q	NOUN
ejpam-2305	92	8	:	:	PUNCT
ejpam-2305	92	9	=	=	PUNCT
ejpam-2305	92	10	�	�	X
ejpam-2305	92	11	qq	qq	NOUN
ejpam-2305	92	12	):	):	PUNCT
ejpam-2305	92	13	0	0	NUM
ejpam-2305	92	14	�	�	PROPN
ejpam-2305	92	15	!	!	PUNCT
ejpam-2305	92	16	e0(q)/'(e(q	e0(q)/'(e(q	VERB
ejpam-2305	92	17	)	)	PUNCT
ejpam-2305	92	18	)	)	PUNCT
ejpam-2305	92	19	�	�	PROPN
ejpam-2305	92	20	q	q	PROPN
ejpam-2305	92	21	�	�	PROPN
ejpam-2305	92	22	!	!	PUNCT
ejpam-2305	93	1	h1(q	h1(q	PROPN
ejpam-2305	93	2	,	,	PUNCT
ejpam-2305	94	1	e	e	X
ejpam-2305	94	2	[	[	X
ejpam-2305	94	3	'	'	NUM
ejpam-2305	94	4	]	]	X
ejpam-2305	94	5	)	)	PUNCT
ejpam-2305	94	6	�	�	PROPN
ejpam-2305	94	7	!	!	PUNCT
ejpam-2305	95	1	h1(q	h1(q	PROPN
ejpam-2305	95	2	,	,	PUNCT
ejpam-2305	95	3	e	e	NOUN
ejpam-2305	95	4	)	)	PUNCT
ejpam-2305	96	1	[	[	X
ejpam-2305	96	2	'	'	X
ejpam-2305	96	3	]	]	X
ejpam-2305	96	4	�	�	PROPN
ejpam-2305	96	5	!	!	NOUN
ejpam-2305	96	6	0	0	NUM
ejpam-2305	97	1	#	#	NOUN
ejpam-2305	97	2	#	#	NOUN
ejpam-2305	97	3	#	#	NOUN
ejpam-2305	97	4	0	0	NUM
ejpam-2305	97	5	�	�	PROPN
ejpam-2305	97	6	!	!	PUNCT
ejpam-2305	98	1	⇧	⇧	PROPN
ejpam-2305	98	2	e0(qq)/'(e(qq	e0(qq)/'(e(qq	NOUN
ejpam-2305	98	3	)	)	PUNCT
ejpam-2305	98	4	)	)	PUNCT
ejpam-2305	99	1	⇧	⇧	PROPN
ejpam-2305	99	2	�	�	PROPN
ejpam-2305	99	3	q	q	PROPN
ejpam-2305	99	4	�	�	PROPN
ejpam-2305	99	5	!	!	PUNCT
ejpam-2305	99	6	⇧	⇧	PROPN
ejpam-2305	99	7	h1(qq	h1(qq	NOUN
ejpam-2305	99	8	,	,	PUNCT
ejpam-2305	99	9	e	e	X
ejpam-2305	99	10	[	[	X
ejpam-2305	99	11	'	'	NUM
ejpam-2305	99	12	]	]	X
ejpam-2305	99	13	)	)	PUNCT
ejpam-2305	99	14	�	�	PROPN
ejpam-2305	99	15	!	!	PUNCT
ejpam-2305	99	16	⇧	⇧	PROPN
ejpam-2305	99	17	h1(qq	h1(qq	NOUN
ejpam-2305	99	18	,	,	PUNCT
ejpam-2305	99	19	e	e	NOUN
ejpam-2305	99	20	)	)	PUNCT
ejpam-2305	100	1	[	[	X
ejpam-2305	100	2	'	'	X
ejpam-2305	100	3	]	]	X
ejpam-2305	100	4	�	�	PROPN
ejpam-2305	100	5	!	!	NOUN
ejpam-2305	100	6	0	0	NUM
ejpam-2305	100	7	where	where	SCONJ
ejpam-2305	100	8	the	the	DET
ejpam-2305	100	9	symbol	symbol	NOUN
ejpam-2305	100	10	⇧	⇧	PROPN
ejpam-2305	100	11	means	mean	VERB
ejpam-2305	100	12	the	the	DET
ejpam-2305	100	13	direct	direct	ADJ
ejpam-2305	100	14	product	product	NOUN
ejpam-2305	100	15	over	over	ADP
ejpam-2305	100	16	p1	p1	PROPN
ejpam-2305	100	17	=	=	SYM
ejpam-2305	100	18	{	{	PUNCT
ejpam-2305	100	19	primes}[{1	primes}[{1	PROPN
ejpam-2305	100	20	}	}	PUNCT
ejpam-2305	100	21	and	and	CCONJ
ejpam-2305	100	22	q	q	PROPN
ejpam-2305	100	23	2	2	NUM
ejpam-2305	100	24	p1	p1	NOUN
ejpam-2305	100	25	.	.	PUNCT
ejpam-2305	101	1	then	then	ADV
ejpam-2305	101	2	,	,	PUNCT
ejpam-2305	101	3	the	the	DET
ejpam-2305	101	4	'	'	PUNCT
ejpam-2305	101	5	-selmer	-selmer	PROPN
ejpam-2305	101	6	group	group	NOUN
ejpam-2305	101	7	s(')(e	s(')(e	PROPN
ejpam-2305	101	8	/	/	SYM
ejpam-2305	101	9	q	q	NOUN
ejpam-2305	101	10	)	)	PUNCT
ejpam-2305	101	11	and	and	CCONJ
ejpam-2305	101	12	the	the	DET
ejpam-2305	101	13	shafarevich	shafarevich	NOUN
ejpam-2305	101	14	-	-	PUNCT
ejpam-2305	101	15	tate	tate	PROPN
ejpam-2305	101	16	group	group	NOUN
ejpam-2305	101	17	qq(e	qq(e	PROPN
ejpam-2305	101	18	/	/	SYM
ejpam-2305	101	19	q	q	NOUN
ejpam-2305	101	20	)	)	PUNCT
ejpam-2305	101	21	are	be	AUX
ejpam-2305	101	22	defined	define	VERB
ejpam-2305	101	23	by	by	ADP
ejpam-2305	101	24	s(')(e	s(')(e	PROPN
ejpam-2305	101	25	/	/	SYM
ejpam-2305	101	26	q	q	NOUN
ejpam-2305	101	27	)	)	PUNCT
ejpam-2305	101	28	=	=	SYM
ejpam-2305	101	29	ker{h1(q	ker{h1(q	NOUN
ejpam-2305	101	30	,	,	PUNCT
ejpam-2305	101	31	e	e	X
ejpam-2305	101	32	[	[	X
ejpam-2305	101	33	'	'	NUM
ejpam-2305	101	34	]	]	X
ejpam-2305	101	35	)	)	PUNCT
ejpam-2305	101	36	�	�	PROPN
ejpam-2305	101	37	!	!	PUNCT
ejpam-2305	101	38	⇧	⇧	PROPN
ejpam-2305	101	39	h1(qq	h1(qq	NOUN
ejpam-2305	101	40	,	,	PUNCT
ejpam-2305	101	41	e	e	NOUN
ejpam-2305	101	42	)	)	PUNCT
ejpam-2305	102	1	[	[	X
ejpam-2305	102	2	'	'	X
ejpam-2305	102	3	]	]	X
ejpam-2305	102	4	}	}	PUNCT
ejpam-2305	102	5	and	and	CCONJ
ejpam-2305	102	6	qq(e	qq(e	PROPN
ejpam-2305	102	7	/	/	SYM
ejpam-2305	102	8	q	q	NOUN
ejpam-2305	102	9	)	)	PUNCT
ejpam-2305	102	10	=	=	SYM
ejpam-2305	102	11	ker{h1(q	ker{h1(q	NOUN
ejpam-2305	102	12	,	,	PUNCT
ejpam-2305	102	13	e	e	NOUN
ejpam-2305	102	14	)	)	PUNCT
ejpam-2305	102	15	�	�	PROPN
ejpam-2305	102	16	!	!	PUNCT
ejpam-2305	102	17	⇧	⇧	PROPN
ejpam-2305	102	18	h1(qq	h1(qq	NOUN
ejpam-2305	102	19	,	,	PUNCT
ejpam-2305	102	20	e	e	NOUN
ejpam-2305	102	21	)	)	PUNCT
ejpam-2305	102	22	}	}	PUNCT
ejpam-2305	102	23	respectively	respectively	ADV
ejpam-2305	102	24	.	.	PUNCT
ejpam-2305	103	1	we	we	PRON
ejpam-2305	103	2	note	note	VERB
ejpam-2305	103	3	that	that	SCONJ
ejpam-2305	103	4	there	there	PRON
ejpam-2305	103	5	is	be	VERB
ejpam-2305	103	6	another	another	DET
ejpam-2305	103	7	method	method	NOUN
ejpam-2305	103	8	of	of	ADP
ejpam-2305	103	9	calculating	calculate	VERB
ejpam-2305	103	10	the	the	DET
ejpam-2305	103	11	selmer	selmer	PROPN
ejpam-2305	103	12	group	group	NOUN
ejpam-2305	103	13	.	.	PUNCT
ejpam-2305	104	1	from	from	ADP
ejpam-2305	104	2	the	the	DET
ejpam-2305	104	3	above	above	ADJ
ejpam-2305	104	4	commutative	commutative	ADJ
ejpam-2305	104	5	diagram	diagram	NOUN
ejpam-2305	104	6	and	and	CCONJ
ejpam-2305	104	7	the	the	DET
ejpam-2305	104	8	definition	definition	NOUN
ejpam-2305	104	9	of	of	ADP
ejpam-2305	104	10	the	the	DET
ejpam-2305	104	11	selmer	selmer	PROPN
ejpam-2305	104	12	group	group	NOUN
ejpam-2305	104	13	,	,	PUNCT
ejpam-2305	104	14	we	we	PRON
ejpam-2305	104	15	have	have	VERB
ejpam-2305	104	16	the	the	DET
ejpam-2305	104	17	equivalent	equivalent	ADJ
ejpam-2305	104	18	definition	definition	NOUN
ejpam-2305	104	19	s(')(e	s(')(e	PROPN
ejpam-2305	104	20	/	/	SYM
ejpam-2305	104	21	q	q	NOUN
ejpam-2305	104	22	)	)	PUNCT
ejpam-2305	104	23	=	=	NOUN
ejpam-2305	104	24	{	{	PUNCT
ejpam-2305	104	25	x	x	PROPN
ejpam-2305	104	26	2	2	NUM
ejpam-2305	104	27	h1(q	h1(q	NUM
ejpam-2305	104	28	,	,	PUNCT
ejpam-2305	104	29	e	e	X
ejpam-2305	104	30	[	[	X
ejpam-2305	104	31	'	'	X
ejpam-2305	104	32	]	]	X
ejpam-2305	104	33	)	)	PUNCT
ejpam-2305	105	1	|	|	ADV
ejpam-2305	105	2	resq(x	resq(x	ADJ
ejpam-2305	105	3	)	)	PUNCT
ejpam-2305	105	4	2	2	NUM
ejpam-2305	105	5	im(	im(	NUM
ejpam-2305	105	6	�	�	NOUN
ejpam-2305	105	7	q),8q	q),8q	ADJ
ejpam-2305	105	8	2	2	NUM
ejpam-2305	105	9	p1	p1	NOUN
ejpam-2305	105	10	}	}	PUNCT
ejpam-2305	105	11	=	=	SYM
ejpam-2305	105	12	\	\	NOUN
ejpam-2305	105	13	q2p1	q2p1	PUNCT
ejpam-2305	105	14	im(	im(	X
ejpam-2305	105	15	�	�	NOUN
ejpam-2305	105	16	q	q	NOUN
ejpam-2305	105	17	)	)	PUNCT
ejpam-2305	105	18	(	(	PUNCT
ejpam-2305	105	19	1	1	X
ejpam-2305	105	20	)	)	PUNCT
ejpam-2305	105	21	where	where	SCONJ
ejpam-2305	105	22	for	for	ADP
ejpam-2305	105	23	each	each	DET
ejpam-2305	105	24	q	q	PROPN
ejpam-2305	105	25	2	2	NUM
ejpam-2305	105	26	p1	p1	NOUN
ejpam-2305	105	27	,	,	PUNCT
ejpam-2305	105	28	im(	im(	PRON
ejpam-2305	105	29	�	�	NOUN
ejpam-2305	105	30	q	q	NOUN
ejpam-2305	105	31	)	)	PUNCT
ejpam-2305	105	32	is	be	AUX
ejpam-2305	105	33	regarded	regard	VERB
ejpam-2305	105	34	as	as	ADP
ejpam-2305	105	35	the	the	DET
ejpam-2305	105	36	subgroup	subgroup	NOUN
ejpam-2305	105	37	of	of	ADP
ejpam-2305	105	38	the	the	DET
ejpam-2305	105	39	group	group	NOUN
ejpam-2305	105	40	h1(q	h1(q	NOUN
ejpam-2305	105	41	,	,	PUNCT
ejpam-2305	105	42	e	e	X
ejpam-2305	105	43	[	[	X
ejpam-2305	105	44	'	'	X
ejpam-2305	105	45	]	]	PUNCT
ejpam-2305	105	46	)	)	PUNCT
ejpam-2305	105	47	and	and	CCONJ
ejpam-2305	105	48	resq(x	resq(x	NOUN
ejpam-2305	105	49	)	)	PUNCT
ejpam-2305	105	50	is	be	AUX
ejpam-2305	105	51	the	the	DET
ejpam-2305	105	52	residue	residue	NOUN
ejpam-2305	105	53	of	of	ADP
ejpam-2305	105	54	x	x	PUNCT
ejpam-2305	105	55	at	at	ADP
ejpam-2305	105	56	q.	q.	NOUN
ejpam-2305	105	57	in	in	ADP
ejpam-2305	105	58	the	the	DET
ejpam-2305	105	59	following	following	NOUN
ejpam-2305	105	60	using	use	VERB
ejpam-2305	105	61	some	some	DET
ejpam-2305	105	62	nice	nice	ADJ
ejpam-2305	105	63	results	result	NOUN
ejpam-2305	105	64	of	of	ADP
ejpam-2305	105	65	[	[	X
ejpam-2305	105	66	4	4	NUM
ejpam-2305	105	67	]	]	PUNCT
ejpam-2305	105	68	,	,	PUNCT
ejpam-2305	105	69	we	we	PRON
ejpam-2305	105	70	are	be	AUX
ejpam-2305	105	71	able	able	ADJ
ejpam-2305	105	72	to	to	PART
ejpam-2305	105	73	calculate	calculate	VERB
ejpam-2305	105	74	the	the	DET
ejpam-2305	105	75	selmer	selmer	PROPN
ejpam-2305	105	76	group	group	PROPN
ejpam-2305	105	77	of	of	ADP
ejpam-2305	105	78	e.	e.	PROPN
ejpam-2305	105	79	theorem	theorem	PROPN
ejpam-2305	105	80	2	2	PROPN
ejpam-2305	105	81	.	.	X
ejpam-2305	105	82	assume	assume	VERB
ejpam-2305	105	83	that	that	SCONJ
ejpam-2305	105	84	q	q	PROPN
ejpam-2305	105	85	2	2	NUM
ejpam-2305	105	86	p1	p1	NOUN
ejpam-2305	105	87	and	and	CCONJ
ejpam-2305	105	88	let	let	VERB
ejpam-2305	105	89	(	(	PUNCT
ejpam-2305	105	90	,	,	PUNCT
ejpam-2305	105	91	)	)	PUNCT
ejpam-2305	105	92	q	q	PUNCT
ejpam-2305	106	1	be	be	AUX
ejpam-2305	106	2	the	the	DET
ejpam-2305	106	3	hilbert	hilbert	NOUN
ejpam-2305	106	4	symbol	symbol	NOUN
ejpam-2305	106	5	.	.	PUNCT
ejpam-2305	107	1	for	for	ADP
ejpam-2305	107	2	a	a	DET
ejpam-2305	107	3	subgroup	subgroup	NOUN
ejpam-2305	107	4	v	v	NUM
ejpam-2305	107	5	⇢	⇢	NOUN
ejpam-2305	107	6	q	q	NOUN
ejpam-2305	107	7	⇥	⇥	NUM
ejpam-2305	107	8	q	q	NOUN
ejpam-2305	107	9	/q	/q	NOUN
ejpam-2305	107	10	⇥	⇥	NUM
ejpam-2305	107	11	2	2	NUM
ejpam-2305	107	12	q	q	NOUN
ejpam-2305	107	13	we	we	PRON
ejpam-2305	107	14	define	define	VERB
ejpam-2305	107	15	v	v	ADP
ejpam-2305	107	16	?	?	PUNCT
ejpam-2305	108	1	=	=	PUNCT
ejpam-2305	108	2	¶	¶	NOUN
ejpam-2305	108	3	x	x	SYM
ejpam-2305	108	4	2	2	NUM
ejpam-2305	108	5	q	q	NOUN
ejpam-2305	108	6	⇥	⇥	NUM
ejpam-2305	108	7	q	q	NOUN
ejpam-2305	108	8	/q	/q	NOUN
ejpam-2305	108	9	⇥	⇥	NUM
ejpam-2305	108	10	2	2	NUM
ejpam-2305	108	11	q	q	NOUN
ejpam-2305	109	1	|	|	NOUN
ejpam-2305	109	2	(	(	PUNCT
ejpam-2305	109	3	x	x	NOUN
ejpam-2305	109	4	,	,	PUNCT
ejpam-2305	109	5	y)q	y)q	NOUN
ejpam-2305	109	6	=	=	SYM
ejpam-2305	109	7	1	1	NUM
ejpam-2305	109	8	,	,	PUNCT
ejpam-2305	109	9	8y	8y	NUM
ejpam-2305	109	10	2	2	NUM
ejpam-2305	109	11	v	v	NOUN
ejpam-2305	109	12	©	©	PROPN
ejpam-2305	109	13	.	.	PUNCT
ejpam-2305	110	1	then	then	ADV
ejpam-2305	110	2	we	we	PRON
ejpam-2305	110	3	have	have	VERB
ejpam-2305	110	4	(	(	PUNCT
ejpam-2305	110	5	1	1	X
ejpam-2305	110	6	)	)	PUNCT
ejpam-2305	110	7	im(	im(	PRON
ejpam-2305	110	8	�	�	NOUN
ejpam-2305	110	9	q	q	NOUN
ejpam-2305	110	10	)	)	PUNCT
ejpam-2305	110	11	=	=	SYM
ejpam-2305	110	12	im(	im(	SYM
ejpam-2305	110	13	�	�	NOUN
ejpam-2305	110	14	2	2	NUM
ejpam-2305	110	15	)	)	PUNCT
ejpam-2305	110	16	=	=	SYM
ejpam-2305	110	17	im(	im(	SYM
ejpam-2305	110	18	�	�	NOUN
ejpam-2305	110	19	02	02	NUM
ejpam-2305	110	20	)	)	PUNCT
ejpam-2305	110	21	?	?	PUNCT
ejpam-2305	111	1	=	=	PRON
ejpam-2305	111	2	(	(	PUNCT
ejpam-2305	111	3	�	�	NOUN
ejpam-2305	111	4	4q	4q	NOUN
ejpam-2305	111	5	)	)	PUNCT
ejpam-2305	111	6	(	(	PUNCT
ejpam-2305	111	7	2	2	X
ejpam-2305	111	8	)	)	PUNCT
ejpam-2305	111	9	im(	im(	PRON
ejpam-2305	111	10	�	�	NOUN
ejpam-2305	111	11	0q	0q	NOUN
ejpam-2305	111	12	)	)	PUNCT
ejpam-2305	112	1	=	=	PUNCT
ejpam-2305	112	2	(	(	PUNCT
ejpam-2305	112	3	q	q	NOUN
ejpam-2305	112	4	)	)	PUNCT
ejpam-2305	112	5	.	.	PUNCT
ejpam-2305	113	1	proof	proof	NOUN
ejpam-2305	113	2	.	.	PUNCT
ejpam-2305	114	1	it	it	PRON
ejpam-2305	114	2	follows	follow	VERB
ejpam-2305	114	3	[	[	X
ejpam-2305	114	4	4	4	NUM
ejpam-2305	114	5	,	,	PUNCT
ejpam-2305	114	6	theorem	theorem	VERB
ejpam-2305	114	7	2.1	2.1	NUM
ejpam-2305	114	8	,	,	PUNCT
ejpam-2305	114	9	propositions	proposition	NOUN
ejpam-2305	114	10	4.1	4.1	NUM
ejpam-2305	114	11	,	,	PUNCT
ejpam-2305	114	12	4.2	4.2	NUM
ejpam-2305	114	13	]	]	PUNCT
ejpam-2305	114	14	.	.	PUNCT
ejpam-2305	115	1	corollary	corollary	ADJ
ejpam-2305	115	2	1	1	NUM
ejpam-2305	115	3	.	.	PUNCT
ejpam-2305	116	1	let	let	VERB
ejpam-2305	116	2	ẽ	ẽ	PROPN
ejpam-2305	116	3	be	be	AUX
ejpam-2305	116	4	the	the	DET
ejpam-2305	116	5	simultaneous	simultaneous	ADJ
ejpam-2305	116	6	curve	curve	NOUN
ejpam-2305	116	7	of	of	ADP
ejpam-2305	116	8	e.	e.	PROPN
ejpam-2305	116	9	then	then	ADV
ejpam-2305	116	10	,	,	PUNCT
ejpam-2305	116	11	we	we	PRON
ejpam-2305	116	12	have	have	VERB
ejpam-2305	116	13	s(')(e	s(')(e	X
ejpam-2305	116	14	/	/	SYM
ejpam-2305	116	15	q	q	NOUN
ejpam-2305	116	16	)	)	PUNCT
ejpam-2305	116	17	=	=	SYM
ejpam-2305	116	18	(	(	PUNCT
ejpam-2305	116	19	�	�	NOUN
ejpam-2305	116	20	4p	4p	NUM
ejpam-2305	116	21	)	)	PUNCT
ejpam-2305	116	22	and	and	CCONJ
ejpam-2305	116	23	s('̃)(ẽ/q	s('̃)(ẽ/q	NOUN
ejpam-2305	116	24	)	)	PUNCT
ejpam-2305	117	1	=	=	SYM
ejpam-2305	117	2	(	(	PUNCT
ejpam-2305	117	3	16p	16p	NUM
ejpam-2305	117	4	)	)	PUNCT
ejpam-2305	117	5	.	.	PUNCT
ejpam-2305	118	1	n.	n.	PROPN
ejpam-2305	118	2	zamani	zamani	PROPN
ejpam-2305	118	3	,	,	PUNCT
ejpam-2305	118	4	a.	a.	NOUN
ejpam-2305	118	5	shams	sham	NOUN
ejpam-2305	118	6	/	/	SYM
ejpam-2305	118	7	eur	eur	PROPN
ejpam-2305	118	8	.	.	PUNCT
ejpam-2305	119	1	j.	j.	PROPN
ejpam-2305	119	2	pure	pure	PROPN
ejpam-2305	119	3	appl	appl	PROPN
ejpam-2305	119	4	.	.	PROPN
ejpam-2305	119	5	math	math	PROPN
ejpam-2305	119	6	,	,	PUNCT
ejpam-2305	119	7	8	8	NUM
ejpam-2305	119	8	(	(	PUNCT
ejpam-2305	119	9	2015	2015	NUM
ejpam-2305	119	10	)	)	PUNCT
ejpam-2305	119	11	,	,	PUNCT
ejpam-2305	119	12	126	126	NUM
ejpam-2305	119	13	-	-	SYM
ejpam-2305	119	14	134	134	NUM
ejpam-2305	119	15	130	130	NUM
ejpam-2305	119	16	proof	proof	NOUN
ejpam-2305	119	17	.	.	PUNCT
ejpam-2305	120	1	it	it	PRON
ejpam-2305	120	2	follows	follow	VERB
ejpam-2305	120	3	from	from	ADP
ejpam-2305	120	4	(	(	PUNCT
ejpam-2305	120	5	1	1	NUM
ejpam-2305	120	6	)	)	PUNCT
ejpam-2305	120	7	and	and	CCONJ
ejpam-2305	120	8	the	the	DET
ejpam-2305	120	9	previous	previous	ADJ
ejpam-2305	120	10	theorem	theorem	NOUN
ejpam-2305	120	11	that	that	SCONJ
ejpam-2305	120	12	s(')(e	s(')(e	PROPN
ejpam-2305	120	13	/	/	SYM
ejpam-2305	120	14	q	q	NOUN
ejpam-2305	120	15	)	)	PUNCT
ejpam-2305	120	16	=	=	SYM
ejpam-2305	120	17	im(	im(	X
ejpam-2305	120	18	�	�	PROPN
ejpam-2305	120	19	1)\	1)\	NUM
ejpam-2305	120	20	im(	im(	NUM
ejpam-2305	120	21	�	�	NOUN
ejpam-2305	120	22	2)\	2)\	NUM
ejpam-2305	120	23	im(	im(	SYM
ejpam-2305	120	24	�	�	PROPN
ejpam-2305	120	25	p	p	NOUN
ejpam-2305	120	26	)	)	PUNCT
ejpam-2305	120	27	=(	=(	NOUN
ejpam-2305	120	28	r	r	NOUN
ejpam-2305	120	29	⇥	⇥	NUM
ejpam-2305	120	30	/r	/r	NOUN
ejpam-2305	120	31	⇥	⇥	NUM
ejpam-2305	120	32	2	2	NUM
ejpam-2305	120	33	)	)	PUNCT
ejpam-2305	120	34	\	\	NOUN
ejpam-2305	120	35	(	(	PUNCT
ejpam-2305	120	36	�	�	NOUN
ejpam-2305	120	37	4p)\	4p)\	NOUN
ejpam-2305	120	38	(	(	PUNCT
ejpam-2305	120	39	�	�	NOUN
ejpam-2305	120	40	4p	4p	NUM
ejpam-2305	120	41	)	)	PUNCT
ejpam-2305	120	42	=(	=(	PROPN
ejpam-2305	120	43	�	�	PROPN
ejpam-2305	120	44	4p	4p	NUM
ejpam-2305	120	45	)	)	PUNCT
ejpam-2305	120	46	and	and	CCONJ
ejpam-2305	120	47	s	s	PROPN
ejpam-2305	120	48	(	(	PUNCT
ejpam-2305	120	49	'	'	PUNCT
ejpam-2305	120	50	0)(ẽ/q	0)(ẽ/q	NUM
ejpam-2305	120	51	)	)	PUNCT
ejpam-2305	121	1	=	=	SYM
ejpam-2305	121	2	s	s	X
ejpam-2305	121	3	(	(	PUNCT
ejpam-2305	121	4	'	'	PUNCT
ejpam-2305	121	5	0)(ẽ/q	0)(ẽ/q	NUM
ejpam-2305	121	6	)	)	PUNCT
ejpam-2305	121	7	=	=	SYM
ejpam-2305	121	8	im(	im(	X
ejpam-2305	121	9	�	�	PROPN
ejpam-2305	121	10	01)\	01)\	SYM
ejpam-2305	121	11	im(	im(	SYM
ejpam-2305	121	12	�	�	PROPN
ejpam-2305	121	13	02)\	02)\	NOUN
ejpam-2305	121	14	im(	im(	SYM
ejpam-2305	121	15	�	�	NOUN
ejpam-2305	121	16	0p	0p	NOUN
ejpam-2305	121	17	)	)	PUNCT
ejpam-2305	121	18	=	=	PRON
ejpam-2305	121	19	{	{	PUNCT
ejpam-2305	121	20	1}\	1}\	NUM
ejpam-2305	121	21	(	(	PUNCT
ejpam-2305	121	22	4p)\	4p)\	NOUN
ejpam-2305	121	23	(	(	PUNCT
ejpam-2305	121	24	16p	16p	NOUN
ejpam-2305	121	25	)	)	PUNCT
ejpam-2305	121	26	=(	=(	NOUN
ejpam-2305	121	27	16p	16p	NOUN
ejpam-2305	121	28	)	)	PUNCT
ejpam-2305	121	29	.	.	PUNCT
ejpam-2305	122	1	4	4	X
ejpam-2305	122	2	.	.	X
ejpam-2305	122	3	computation	computation	NOUN
ejpam-2305	122	4	of	of	ADP
ejpam-2305	122	5	the	the	DET
ejpam-2305	122	6	rank	rank	NOUN
ejpam-2305	122	7	of	of	ADP
ejpam-2305	122	8	e	e	PROPN
ejpam-2305	122	9	in	in	ADP
ejpam-2305	122	10	this	this	DET
ejpam-2305	122	11	section	section	NOUN
ejpam-2305	122	12	we	we	PRON
ejpam-2305	122	13	assume	assume	VERB
ejpam-2305	122	14	that	that	SCONJ
ejpam-2305	122	15	p	p	PROPN
ejpam-2305	122	16	=	=	PROPN
ejpam-2305	122	17	u4	u4	PROPN
ejpam-2305	122	18	+	+	CCONJ
ejpam-2305	122	19	v4	v4	PROPN
ejpam-2305	122	20	is	be	AUX
ejpam-2305	122	21	a	a	DET
ejpam-2305	122	22	prime	prime	ADJ
ejpam-2305	122	23	number	number	NOUN
ejpam-2305	122	24	with	with	ADP
ejpam-2305	122	25	u	u	PROPN
ejpam-2305	122	26	,	,	PUNCT
ejpam-2305	122	27	v	v	PROPN
ejpam-2305	122	28	2	2	NUM
ejpam-2305	122	29	n.	n.	NOUN
ejpam-2305	122	30	we	we	PRON
ejpam-2305	122	31	note	note	VERB
ejpam-2305	122	32	that	that	SCONJ
ejpam-2305	122	33	(	(	PUNCT
ejpam-2305	122	34	2(u4	2(u4	NUM
ejpam-2305	122	35	+	+	NUM
ejpam-2305	122	36	v4)(u+	v4)(u+	PROPN
ejpam-2305	122	37	v)2	v)2	NOUN
ejpam-2305	122	38	,	,	PUNCT
ejpam-2305	122	39	4(u2	4(u2	PROPN
ejpam-2305	123	1	+	+	CCONJ
ejpam-2305	123	2	uv	uv	NOUN
ejpam-2305	123	3	+	+	NOUN
ejpam-2305	123	4	v2)(u4	v2)(u4	X
ejpam-2305	123	5	+	+	CCONJ
ejpam-2305	123	6	v4)/(u+	v4)/(u+	PROPN
ejpam-2305	123	7	v)3	v)3	PROPN
ejpam-2305	123	8	)	)	PUNCT
ejpam-2305	123	9	is	be	AUX
ejpam-2305	123	10	a	a	DET
ejpam-2305	123	11	point	point	NOUN
ejpam-2305	123	12	of	of	ADP
ejpam-2305	123	13	e.	e.	PROPN
ejpam-2305	123	14	let	let	VERB
ejpam-2305	123	15	ẽ	ẽ	PROPN
ejpam-2305	123	16	be	be	AUX
ejpam-2305	123	17	the	the	DET
ejpam-2305	123	18	simultaneous	simultaneous	ADJ
ejpam-2305	123	19	curve	curve	NOUN
ejpam-2305	123	20	of	of	ADP
ejpam-2305	123	21	e	e	PROPN
ejpam-2305	123	22	and	and	CCONJ
ejpam-2305	123	23	�	�	PROPN
ejpam-2305	123	24	̃	̃	PROPN
ejpam-2305	123	25	be	be	VERB
ejpam-2305	123	26	its	its	PRON
ejpam-2305	123	27	corresponding	corresponding	ADJ
ejpam-2305	123	28	group	group	NOUN
ejpam-2305	123	29	.	.	PUNCT
ejpam-2305	124	1	we	we	PRON
ejpam-2305	124	2	consider	consider	VERB
ejpam-2305	124	3	↵	↵	PROPN
ejpam-2305	124	4	and	and	CCONJ
ejpam-2305	124	5	↵	↵	PROPN
ejpam-2305	124	6	̃	̃	PROPN
ejpam-2305	124	7	be	be	VERB
ejpam-2305	124	8	the	the	DET
ejpam-2305	124	9	group	group	NOUN
ejpam-2305	124	10	homomorphism	homomorphism	PROPN
ejpam-2305	124	11	↵	↵	PROPN
ejpam-2305	124	12	:	:	PUNCT
ejpam-2305	124	13	�	�	PROPN
ejpam-2305	124	14	�	�	PROPN
ejpam-2305	124	15	!	!	PUNCT
ejpam-2305	125	1	q	q	NOUN
ejpam-2305	125	2	⇥	⇥	NUM
ejpam-2305	125	3	/q	/q	NOUN
ejpam-2305	125	4	⇥	⇥	NUM
ejpam-2305	125	5	2	2	NUM
ejpam-2305	125	6	↵	↵	NUM
ejpam-2305	125	7	̃	̃	PROPN
ejpam-2305	125	8	:	:	PUNCT
ejpam-2305	125	9	�	�	PROPN
ejpam-2305	125	10	̃	̃	NOUN
ejpam-2305	125	11	�	�	PROPN
ejpam-2305	125	12	!	!	PUNCT
ejpam-2305	126	1	q	q	NOUN
ejpam-2305	126	2	⇥	⇥	NUM
ejpam-2305	126	3	/q	/q	NOUN
ejpam-2305	126	4	⇥	⇥	NUM
ejpam-2305	126	5	2	2	NUM
ejpam-2305	126	6	↵	↵	PROPN
ejpam-2305	126	7	(	(	PUNCT
ejpam-2305	126	8	p	p	NOUN
ejpam-2305	126	9	)	)	PUNCT
ejpam-2305	126	10	=	=	SYM
ejpam-2305	126	11	8	8	NUM
ejpam-2305	126	12	>	>	PUNCT
ejpam-2305	126	13	<	<	X
ejpam-2305	126	14	>	>	X
ejpam-2305	126	15	:	:	PUNCT
ejpam-2305	126	16	1	1	NUM
ejpam-2305	126	17	for	for	ADP
ejpam-2305	126	18	p	p	NOUN
ejpam-2305	126	19	=	=	PROPN
ejpam-2305	126	20	o	o	X
ejpam-2305	126	21	�	�	PROPN
ejpam-2305	126	22	(	(	PUNCT
ejpam-2305	126	23	p	p	NOUN
ejpam-2305	126	24	)	)	PUNCT
ejpam-2305	126	25	for	for	ADP
ejpam-2305	126	26	p	p	NOUN
ejpam-2305	126	27	=	=	SYM
ejpam-2305	126	28	0	0	NUM
ejpam-2305	126	29	�	�	PROPN
ejpam-2305	126	30	(	(	PUNCT
ejpam-2305	126	31	x	x	NOUN
ejpam-2305	126	32	)	)	PUNCT
ejpam-2305	126	33	for	for	ADP
ejpam-2305	126	34	x	x	SYM
ejpam-2305	126	35	6=	6=	ADP
ejpam-2305	126	36	0	0	NUM
ejpam-2305	126	37	↵	↵	NUM
ejpam-2305	126	38	̃(p	̃(p	NOUN
ejpam-2305	126	39	)	)	PUNCT
ejpam-2305	127	1	=	=	SYM
ejpam-2305	127	2	8	8	X
ejpam-2305	127	3	>	>	PUNCT
ejpam-2305	127	4	<	<	X
ejpam-2305	127	5	>	>	X
ejpam-2305	127	6	:	:	PUNCT
ejpam-2305	127	7	1	1	NUM
ejpam-2305	127	8	for	for	ADP
ejpam-2305	127	9	p	p	NOUN
ejpam-2305	127	10	=	=	PROPN
ejpam-2305	127	11	o	o	PROPN
ejpam-2305	127	12	�	�	PROPN
ejpam-2305	127	13	(	(	PUNCT
ejpam-2305	127	14	�	�	PROPN
ejpam-2305	127	15	p	p	NOUN
ejpam-2305	127	16	)	)	PUNCT
ejpam-2305	127	17	for	for	ADP
ejpam-2305	127	18	p	p	NOUN
ejpam-2305	127	19	=	=	SYM
ejpam-2305	127	20	0	0	NUM
ejpam-2305	127	21	�	�	PROPN
ejpam-2305	127	22	(	(	PUNCT
ejpam-2305	127	23	x	x	NOUN
ejpam-2305	127	24	)	)	PUNCT
ejpam-2305	127	25	for	for	ADP
ejpam-2305	127	26	x	x	SYM
ejpam-2305	127	27	6=	6=	ADP
ejpam-2305	127	28	0	0	NUM
ejpam-2305	127	29	where	where	SCONJ
ejpam-2305	127	30	p	p	NOUN
ejpam-2305	127	31	=	=	X
ejpam-2305	127	32	(	(	PUNCT
ejpam-2305	127	33	x	x	PROPN
ejpam-2305	127	34	,	,	PUNCT
ejpam-2305	127	35	y	y	PROPN
ejpam-2305	127	36	)	)	PUNCT
ejpam-2305	127	37	and	and	CCONJ
ejpam-2305	127	38	�	�	PROPN
ejpam-2305	127	39	is	be	AUX
ejpam-2305	127	40	a	a	DET
ejpam-2305	127	41	natural	natural	ADJ
ejpam-2305	127	42	group	group	NOUN
ejpam-2305	127	43	homomorphism	homomorphism	NOUN
ejpam-2305	127	44	q	q	X
ejpam-2305	127	45	⇥	⇥	NUM
ejpam-2305	127	46	7	7	NUM
ejpam-2305	127	47	�	�	NOUN
ejpam-2305	127	48	!	!	PUNCT
ejpam-2305	128	1	q	q	NOUN
ejpam-2305	128	2	⇥	⇥	NUM
ejpam-2305	128	3	/q	/q	SYM
ejpam-2305	128	4	⇥	⇥	NUM
ejpam-2305	128	5	2	2	NUM
ejpam-2305	128	6	.	.	PUNCT
ejpam-2305	128	7	to	to	PART
ejpam-2305	128	8	compute	compute	VERB
ejpam-2305	128	9	the	the	DET
ejpam-2305	128	10	rank	rank	NOUN
ejpam-2305	128	11	of	of	ADP
ejpam-2305	128	12	e	e	NOUN
ejpam-2305	128	13	we	we	PRON
ejpam-2305	128	14	use	use	VERB
ejpam-2305	128	15	the	the	DET
ejpam-2305	128	16	well	well	ADV
ejpam-2305	128	17	-	-	PUNCT
ejpam-2305	128	18	known	know	VERB
ejpam-2305	128	19	formula	formula	NOUN
ejpam-2305	128	20	(	(	PUNCT
ejpam-2305	128	21	see	see	VERB
ejpam-2305	128	22	for	for	ADP
ejpam-2305	128	23	example	example	NOUN
ejpam-2305	128	24	[	[	X
ejpam-2305	128	25	2	2	NUM
ejpam-2305	128	26	,	,	PUNCT
ejpam-2305	128	27	6	6	NUM
ejpam-2305	128	28	]	]	PUNCT
ejpam-2305	128	29	)	)	PUNCT
ejpam-2305	128	30	2r	2r	NUM
ejpam-2305	129	1	=	=	PUNCT
ejpam-2305	129	2	#	#	SYM
ejpam-2305	129	3	↵	↵	PROPN
ejpam-2305	129	4	(	(	PUNCT
ejpam-2305	129	5	�	�	PROPN
ejpam-2305	129	6	)	)	PUNCT
ejpam-2305	129	7	·	·	PUNCT
ejpam-2305	129	8	#	#	SYM
ejpam-2305	129	9	↵	↵	NUM
ejpam-2305	129	10	̃(	̃(	PROPN
ejpam-2305	129	11	�	�	PROPN
ejpam-2305	129	12	̃	̃	NOUN
ejpam-2305	129	13	)	)	PUNCT
ejpam-2305	129	14	4	4	NUM
ejpam-2305	129	15	,	,	PUNCT
ejpam-2305	129	16	r	r	NOUN
ejpam-2305	129	17	=	=	SYM
ejpam-2305	129	18	rank(e	rank(e	PROPN
ejpam-2305	129	19	)	)	PUNCT
ejpam-2305	129	20	.	.	PUNCT
ejpam-2305	130	1	(	(	PUNCT
ejpam-2305	130	2	2	2	X
ejpam-2305	130	3	)	)	PUNCT
ejpam-2305	130	4	here	here	ADV
ejpam-2305	130	5	,	,	PUNCT
ejpam-2305	130	6	↵	↵	PROPN
ejpam-2305	130	7	(	(	PUNCT
ejpam-2305	130	8	�	�	PROPN
ejpam-2305	130	9	)	)	PUNCT
ejpam-2305	130	10	and	and	CCONJ
ejpam-2305	130	11	↵	↵	PROPN
ejpam-2305	130	12	̃(	̃(	PROPN
ejpam-2305	130	13	�	�	PROPN
ejpam-2305	130	14	̃	̃	NOUN
ejpam-2305	130	15	)	)	PUNCT
ejpam-2305	130	16	are	be	AUX
ejpam-2305	130	17	given	give	VERB
ejpam-2305	130	18	as	as	ADP
ejpam-2305	130	19	1,	1,	NUM
ejpam-2305	130	20	�	�	NOUN
ejpam-2305	130	21	(p	(p	NOUN
ejpam-2305	130	22	)	)	PUNCT
ejpam-2305	130	23	2	2	NUM
ejpam-2305	130	24	↵	↵	PROPN
ejpam-2305	130	25	(	(	PUNCT
ejpam-2305	130	26	�	�	PROPN
ejpam-2305	130	27	)	)	PUNCT
ejpam-2305	130	28	=	=	PROPN
ejpam-2305	130	29	�	�	PROPN
ejpam-2305	130	30	�	�	PROPN
ejpam-2305	130	31	(	(	PUNCT
ejpam-2305	130	32	d	d	NOUN
ejpam-2305	130	33	)	)	PUNCT
ejpam-2305	130	34	:	:	PUNCT
ejpam-2305	130	35	cd	cd	PROPN
ejpam-2305	130	36	has	have	VERB
ejpam-2305	130	37	at	at	ADP
ejpam-2305	130	38	least	least	ADJ
ejpam-2305	130	39	an	an	DET
ejpam-2305	130	40	integral	integral	ADJ
ejpam-2305	130	41	solution	solution	NOUN
ejpam-2305	130	42	for	for	ADP
ejpam-2305	130	43	d|4p	d|4p	NOUN
ejpam-2305	130	44	,	,	PUNCT
ejpam-2305	130	45	1,	1,	NUM
ejpam-2305	130	46	�	�	PROPN
ejpam-2305	130	47	(	(	PUNCT
ejpam-2305	130	48	�	�	PROPN
ejpam-2305	130	49	p	p	NOUN
ejpam-2305	130	50	)	)	PUNCT
ejpam-2305	130	51	2	2	NUM
ejpam-2305	130	52	↵	↵	PROPN
ejpam-2305	130	53	̃(	̃(	PROPN
ejpam-2305	130	54	�	�	PROPN
ejpam-2305	130	55	̃	̃	NOUN
ejpam-2305	130	56	)	)	PUNCT
ejpam-2305	131	1	=	=	PROPN
ejpam-2305	131	2	�	�	PROPN
ejpam-2305	131	3	�	�	PROPN
ejpam-2305	131	4	(	(	PUNCT
ejpam-2305	131	5	d̃	d̃	PROPN
ejpam-2305	131	6	)	)	PUNCT
ejpam-2305	131	7	:	:	PUNCT
ejpam-2305	131	8	cd̃	cd̃	PROPN
ejpam-2305	131	9	has	have	VERB
ejpam-2305	131	10	at	at	ADV
ejpam-2305	131	11	least	least	ADJ
ejpam-2305	131	12	an	an	DET
ejpam-2305	131	13	integral	integral	ADJ
ejpam-2305	131	14	solution	solution	NOUN
ejpam-2305	131	15	for	for	ADP
ejpam-2305	131	16	d̃|	d̃|	PROPN
ejpam-2305	131	17	�	�	PROPN
ejpam-2305	131	18	16p	16p	PROPN
ejpam-2305	131	19	where	where	SCONJ
ejpam-2305	131	20	cd	cd	PROPN
ejpam-2305	131	21	and	and	CCONJ
ejpam-2305	131	22	cd̃	cd̃	PROPN
ejpam-2305	131	23	are	be	AUX
ejpam-2305	131	24	super	super	ADJ
ejpam-2305	131	25	-	-	ADJ
ejpam-2305	131	26	fermat	fermat	ADJ
ejpam-2305	131	27	equations	equation	NOUN
ejpam-2305	131	28	[	[	X
ejpam-2305	131	29	3	3	NUM
ejpam-2305	131	30	]	]	PUNCT
ejpam-2305	131	31	:	:	PUNCT
ejpam-2305	131	32	cd	cd	PROPN
ejpam-2305	131	33	:	:	PUNCT
ejpam-2305	131	34	d	d	PROPN
ejpam-2305	131	35	t4	t4	PROPN
ejpam-2305	131	36	+	+	PROPN
ejpam-2305	131	37	4p	4p	PROPN
ejpam-2305	131	38	d	d	NOUN
ejpam-2305	131	39	z4	z4	PROPN
ejpam-2305	131	40	=	=	SYM
ejpam-2305	131	41	w2	w2	PROPN
ejpam-2305	131	42	,	,	PUNCT
ejpam-2305	131	43	t	t	PROPN
ejpam-2305	131	44	�	�	PROPN
ejpam-2305	131	45	1	1	NUM
ejpam-2305	131	46	,	,	PUNCT
ejpam-2305	131	47	z	z	PROPN
ejpam-2305	131	48	�	�	PROPN
ejpam-2305	131	49	1	1	NUM
ejpam-2305	131	50	,	,	PUNCT
ejpam-2305	131	51	gcd	gcd	VERB
ejpam-2305	131	52	�	�	PROPN
ejpam-2305	131	53	t	t	PROPN
ejpam-2305	131	54	,	,	PUNCT
ejpam-2305	131	55	4p	4p	PROPN
ejpam-2305	131	56	/	/	SYM
ejpam-2305	131	57	d	d	X
ejpam-2305	131	58	�	�	PROPN
ejpam-2305	131	59	=	=	SYM
ejpam-2305	131	60	1	1	NUM
ejpam-2305	131	61	n.	n.	PROPN
ejpam-2305	131	62	zamani	zamani	PROPN
ejpam-2305	131	63	,	,	PUNCT
ejpam-2305	131	64	a.	a.	NOUN
ejpam-2305	131	65	shams	sham	NOUN
ejpam-2305	131	66	/	/	SYM
ejpam-2305	131	67	eur	eur	PROPN
ejpam-2305	131	68	.	.	PUNCT
ejpam-2305	132	1	j.	j.	PROPN
ejpam-2305	132	2	pure	pure	PROPN
ejpam-2305	132	3	appl	appl	PROPN
ejpam-2305	132	4	.	.	PROPN
ejpam-2305	132	5	math	math	PROPN
ejpam-2305	132	6	,	,	PUNCT
ejpam-2305	132	7	8	8	NUM
ejpam-2305	132	8	(	(	PUNCT
ejpam-2305	132	9	2015	2015	NUM
ejpam-2305	132	10	)	)	PUNCT
ejpam-2305	132	11	,	,	PUNCT
ejpam-2305	132	12	126	126	NUM
ejpam-2305	132	13	-	-	SYM
ejpam-2305	132	14	134	134	NUM
ejpam-2305	132	15	131	131	NUM
ejpam-2305	132	16	ced	ce	VERB
ejpam-2305	132	17	:	:	PUNCT
ejpam-2305	132	18	ed	ed	PROPN
ejpam-2305	132	19	t4	t4	PROPN
ejpam-2305	132	20	�	�	PROPN
ejpam-2305	132	21	16p	16p	PROPN
ejpam-2305	132	22	ed	ed	NOUN
ejpam-2305	132	23	z4	z4	PROPN
ejpam-2305	132	24	=	=	SYM
ejpam-2305	132	25	w2	w2	PROPN
ejpam-2305	132	26	,	,	PUNCT
ejpam-2305	132	27	t	t	PROPN
ejpam-2305	132	28	�	�	PROPN
ejpam-2305	132	29	1	1	NUM
ejpam-2305	132	30	,	,	PUNCT
ejpam-2305	132	31	z	z	PROPN
ejpam-2305	132	32	�	�	PROPN
ejpam-2305	132	33	1	1	NUM
ejpam-2305	132	34	,	,	PUNCT
ejpam-2305	132	35	gcd(t	gcd(t	NOUN
ejpam-2305	132	36	,	,	PUNCT
ejpam-2305	132	37	16p	16p	NUM
ejpam-2305	132	38	/	/	SYM
ejpam-2305	132	39	d̃	d̃	PROPN
ejpam-2305	132	40	)	)	PUNCT
ejpam-2305	132	41	=	=	SYM
ejpam-2305	132	42	1	1	NUM
ejpam-2305	132	43	,	,	PUNCT
ejpam-2305	132	44	with	with	ADP
ejpam-2305	132	45	integer	integer	NOUN
ejpam-2305	132	46	solutions	solution	NOUN
ejpam-2305	132	47	(	(	PUNCT
ejpam-2305	132	48	t	t	PROPN
ejpam-2305	132	49	,	,	PUNCT
ejpam-2305	132	50	z	z	PROPN
ejpam-2305	132	51	,	,	PUNCT
ejpam-2305	132	52	w	w	NOUN
ejpam-2305	132	53	)	)	PUNCT
ejpam-2305	132	54	.	.	PUNCT
ejpam-2305	133	1	hence	hence	ADV
ejpam-2305	133	2	,	,	PUNCT
ejpam-2305	133	3	d	d	PROPN
ejpam-2305	133	4	=	=	SYM
ejpam-2305	133	5	±	±	NUM
ejpam-2305	133	6	1,±2,±4,±p,±2p,±4p	1,±2,±4,±p,±2p,±4p	NUM
ejpam-2305	133	7	ed	ed	NOUN
ejpam-2305	133	8	=	=	NOUN
ejpam-2305	133	9	±	±	NUM
ejpam-2305	133	10	1,±2,±4,±8,±16,±p,±2p,±4p,±8p,±16p	1,±2,±4,±8,±16,±p,±2p,±4p,±8p,±16p	NUM
ejpam-2305	133	11	,	,	PUNCT
ejpam-2305	133	12	and	and	CCONJ
ejpam-2305	133	13	so	so	ADV
ejpam-2305	133	14	,	,	PUNCT
ejpam-2305	133	15	↵	↵	PROPN
ejpam-2305	133	16	(	(	PUNCT
ejpam-2305	133	17	�	�	PROPN
ejpam-2305	133	18	)	)	PUNCT
ejpam-2305	133	19	✓	✓	PROPN
ejpam-2305	133	20	�	�	PROPN
ejpam-2305	133	21	�	�	PROPN
ejpam-2305	133	22	(	(	PUNCT
ejpam-2305	133	23	�	�	PROPN
ejpam-2305	133	24	1),	1),	NUM
ejpam-2305	133	25	�	�	PROPN
ejpam-2305	133	26	(±2),	(±2),	PROPN
ejpam-2305	133	27	�	�	PROPN
ejpam-2305	133	28	(±p),	(±p),	PROPN
ejpam-2305	133	29	�	�	PROPN
ejpam-2305	133	30	(±2p),	(±2p),	SYM
ejpam-2305	133	31	�	�	PROPN
ejpam-2305	133	32	(	(	PUNCT
ejpam-2305	133	33	�	�	NOUN
ejpam-2305	133	34	4p	4p	NUM
ejpam-2305	133	35	)	)	PUNCT
ejpam-2305	133	36	,	,	PUNCT
ejpam-2305	133	37	↵	↵	PROPN
ejpam-2305	133	38	̃(	̃(	PROPN
ejpam-2305	133	39	�	�	PROPN
ejpam-2305	133	40	̃	̃	NOUN
ejpam-2305	133	41	)	)	PUNCT
ejpam-2305	133	42	✓	✓	PROPN
ejpam-2305	133	43	�	�	PROPN
ejpam-2305	133	44	�	�	PROPN
ejpam-2305	133	45	(	(	PUNCT
ejpam-2305	133	46	�	�	PROPN
ejpam-2305	133	47	1),	1),	NUM
ejpam-2305	133	48	�	�	PROPN
ejpam-2305	133	49	(±2),	(±2),	PROPN
ejpam-2305	133	50	�	�	PROPN
ejpam-2305	133	51	(±4),	(±4),	PROPN
ejpam-2305	133	52	�	�	PROPN
ejpam-2305	133	53	(±8),	(±8),	NOUN
ejpam-2305	133	54	�	�	PROPN
ejpam-2305	133	55	(±16),	(±16),	PROPN
ejpam-2305	133	56	�	�	PROPN
ejpam-2305	133	57	(±p),	(±p),	PROPN
ejpam-2305	133	58	�	�	PROPN
ejpam-2305	133	59	(±2p),	(±2p),	SYM
ejpam-2305	133	60	�	�	PROPN
ejpam-2305	133	61	(±4p),	(±4p),	SYM
ejpam-2305	133	62	�	�	NOUN
ejpam-2305	133	63	(16p	(16p	NUM
ejpam-2305	133	64	)	)	PUNCT
ejpam-2305	133	65	,	,	PUNCT
ejpam-2305	133	66	together	together	ADV
ejpam-2305	133	67	with	with	ADP
ejpam-2305	133	68	1,	1,	NUM
ejpam-2305	133	69	�	�	NOUN
ejpam-2305	133	70	(p	(p	NOUN
ejpam-2305	133	71	)	)	PUNCT
ejpam-2305	133	72	2	2	NUM
ejpam-2305	133	73	↵	↵	PROPN
ejpam-2305	133	74	(	(	PUNCT
ejpam-2305	133	75	�	�	PROPN
ejpam-2305	133	76	)	)	PUNCT
ejpam-2305	133	77	and	and	CCONJ
ejpam-2305	133	78	1,	1,	NUM
ejpam-2305	133	79	�	�	PROPN
ejpam-2305	133	80	(	(	PUNCT
ejpam-2305	133	81	�	�	NOUN
ejpam-2305	133	82	16p	16p	NOUN
ejpam-2305	133	83	)	)	PUNCT
ejpam-2305	133	84	2	2	NUM
ejpam-2305	133	85	↵	↵	PROPN
ejpam-2305	133	86	̃(	̃(	PROPN
ejpam-2305	133	87	�	�	PROPN
ejpam-2305	133	88	̃	̃	PROPN
ejpam-2305	133	89	)	)	PUNCT
ejpam-2305	133	90	.	.	PUNCT
ejpam-2305	134	1	now	now	ADV
ejpam-2305	134	2	,	,	PUNCT
ejpam-2305	134	3	we	we	PRON
ejpam-2305	134	4	define	define	VERB
ejpam-2305	134	5	sd	sd	ADP
ejpam-2305	134	6	=	=	SYM
ejpam-2305	134	7	�	�	PROPN
ejpam-2305	134	8	(	(	PUNCT
ejpam-2305	134	9	t	t	PROPN
ejpam-2305	134	10	,	,	PUNCT
ejpam-2305	134	11	z	z	PROPN
ejpam-2305	134	12	,	,	PUNCT
ejpam-2305	134	13	w)|cd	w)|cd	PROPN
ejpam-2305	134	14	has	have	VERB
ejpam-2305	134	15	integer	integer	NOUN
ejpam-2305	134	16	solutions	solution	NOUN
ejpam-2305	134	17	for	for	ADP
ejpam-2305	134	18	d	d	PROPN
ejpam-2305	134	19	6=	6=	PROPN
ejpam-2305	134	20	1	1	NUM
ejpam-2305	134	21	,	,	PUNCT
ejpam-2305	134	22	4p	4p	NUM
ejpam-2305	134	23	,	,	PUNCT
ejpam-2305	134	24	sed	se	VERB
ejpam-2305	134	25	=	=	SYM
ejpam-2305	134	26	�	�	PROPN
ejpam-2305	134	27	(	(	PUNCT
ejpam-2305	134	28	t	t	PROPN
ejpam-2305	134	29	,	,	PUNCT
ejpam-2305	134	30	z	z	PROPN
ejpam-2305	134	31	,	,	PUNCT
ejpam-2305	134	32	w)|ced	w)|ce	VERB
ejpam-2305	134	33	has	have	VERB
ejpam-2305	134	34	integer	integer	NOUN
ejpam-2305	134	35	solutions	solution	NOUN
ejpam-2305	134	36	for	for	ADP
ejpam-2305	134	37	d	d	PROPN
ejpam-2305	134	38	6=	6=	PROPN
ejpam-2305	134	39	1,	1,	NUM
ejpam-2305	134	40	�	�	NOUN
ejpam-2305	134	41	16p	16p	NOUN
ejpam-2305	134	42	.	.	PUNCT
ejpam-2305	135	1	according	accord	VERB
ejpam-2305	135	2	to	to	ADP
ejpam-2305	135	3	[	[	X
ejpam-2305	135	4	2	2	X
ejpam-2305	135	5	]	]	SYM
ejpam-2305	135	6	9s,9s̃	9s,9s̃	NUM
ejpam-2305	135	7	2	2	NUM
ejpam-2305	135	8	n	n	DET
ejpam-2305	135	9	such	such	ADJ
ejpam-2305	135	10	that	that	SCONJ
ejpam-2305	135	11	x	x	SYM
ejpam-2305	135	12	d|4p	d|4p	NOUN
ejpam-2305	135	13	#	#	SYM
ejpam-2305	135	14	sd	sd	NOUN
ejpam-2305	135	15	=	=	PUNCT
ejpam-2305	135	16	2s	2s	NOUN
ejpam-2305	135	17	�	�	PROPN
ejpam-2305	135	18	2	2	NUM
ejpam-2305	135	19	,	,	PUNCT
ejpam-2305	135	20	x	x	PRON
ejpam-2305	135	21	d̃|16p	d̃|16p	VERB
ejpam-2305	135	22	#	#	NOUN
ejpam-2305	135	23	sd̃	sd̃	NOUN
ejpam-2305	135	24	=	=	SYM
ejpam-2305	135	25	2s̃	2s̃	NUM
ejpam-2305	135	26	�	�	PROPN
ejpam-2305	135	27	2	2	NUM
ejpam-2305	135	28	,	,	PUNCT
ejpam-2305	135	29	where	where	SCONJ
ejpam-2305	135	30	d	d	NOUN
ejpam-2305	135	31	and	and	CCONJ
ejpam-2305	135	32	d̃	d̃	PROPN
ejpam-2305	135	33	are	be	AUX
ejpam-2305	135	34	square	square	ADV
ejpam-2305	135	35	free	free	ADJ
ejpam-2305	135	36	,	,	PUNCT
ejpam-2305	136	1	#	#	SYM
ejpam-2305	136	2	sd	sd	NOUN
ejpam-2305	136	3	=	=	SYM
ejpam-2305	136	4	0	0	PUNCT
ejpam-2305	136	5	if	if	SCONJ
ejpam-2305	136	6	sd	sd	ADV
ejpam-2305	136	7	=	=	PUNCT
ejpam-2305	136	8	;	;	PUNCT
ejpam-2305	136	9	and	and	CCONJ
ejpam-2305	136	10	#	#	SYM
ejpam-2305	136	11	sd	sd	NOUN
ejpam-2305	136	12	=	=	SYM
ejpam-2305	136	13	1	1	NUM
ejpam-2305	136	14	if	if	SCONJ
ejpam-2305	136	15	sd	sd	ADP
ejpam-2305	136	16	6=	6=	NUM
ejpam-2305	136	17	;	;	PUNCT
ejpam-2305	136	18	.	.	PUNCT
ejpam-2305	137	1	similarly	similarly	ADV
ejpam-2305	137	2	for	for	ADP
ejpam-2305	137	3	sd̃	sd̃	PUNCT
ejpam-2305	137	4	.	.	PUNCT
ejpam-2305	138	1	by	by	ADP
ejpam-2305	138	2	(	(	PUNCT
ejpam-2305	138	3	2	2	X
ejpam-2305	138	4	)	)	PUNCT
ejpam-2305	138	5	we	we	PRON
ejpam-2305	138	6	conclude	conclude	VERB
ejpam-2305	138	7	that	that	SCONJ
ejpam-2305	138	8	r	r	NOUN
ejpam-2305	138	9	=	=	PUNCT
ejpam-2305	138	10	s	s	PART
ejpam-2305	138	11	+	+	X
ejpam-2305	138	12	s̃	s̃	PROPN
ejpam-2305	138	13	�	�	PROPN
ejpam-2305	138	14	2	2	NUM
ejpam-2305	138	15	.	.	PUNCT
ejpam-2305	138	16	by	by	ADP
ejpam-2305	138	17	the	the	DET
ejpam-2305	138	18	closed	closed	ADJ
ejpam-2305	138	19	property	property	NOUN
ejpam-2305	138	20	of	of	ADP
ejpam-2305	138	21	↵	↵	PROPN
ejpam-2305	138	22	(	(	PUNCT
ejpam-2305	138	23	�	�	PROPN
ejpam-2305	138	24	)	)	PUNCT
ejpam-2305	138	25	and	and	CCONJ
ejpam-2305	138	26	having	have	VERB
ejpam-2305	138	27	a	a	DET
ejpam-2305	138	28	note	note	NOUN
ejpam-2305	138	29	to	to	ADP
ejpam-2305	138	30	the	the	DET
ejpam-2305	138	31	table	table	NOUN
ejpam-2305	138	32	2	2	NUM
ejpam-2305	138	33	,	,	PUNCT
ejpam-2305	138	34	we	we	PRON
ejpam-2305	138	35	conclude	conclude	VERB
ejpam-2305	139	1	that	that	SCONJ
ejpam-2305	139	2	↵	↵	PROPN
ejpam-2305	139	3	(	(	PUNCT
ejpam-2305	139	4	�	�	PROPN
ejpam-2305	139	5	)	)	PUNCT
ejpam-2305	139	6	=	=	PRON
ejpam-2305	139	7	{	{	PUNCT
ejpam-2305	139	8	1,	1,	NUM
ejpam-2305	139	9	�	�	PROPN
ejpam-2305	139	10	(2),	(2),	SYM
ejpam-2305	139	11	�	�	NOUN
ejpam-2305	139	12	(p),	(p),	SYM
ejpam-2305	139	13	�	�	NOUN
ejpam-2305	139	14	(2p	(2p	PUNCT
ejpam-2305	139	15	)	)	PUNCT
ejpam-2305	139	16	}	}	PUNCT
ejpam-2305	139	17	.	.	PUNCT
ejpam-2305	140	1	also	also	ADV
ejpam-2305	140	2	,	,	PUNCT
ejpam-2305	140	3	using	use	VERB
ejpam-2305	140	4	tables	table	NOUN
ejpam-2305	140	5	3	3	NUM
ejpam-2305	140	6	and	and	CCONJ
ejpam-2305	140	7	4	4	NUM
ejpam-2305	140	8	,	,	PUNCT
ejpam-2305	140	9	we	we	PRON
ejpam-2305	140	10	have	have	VERB
ejpam-2305	140	11	↵	↵	NUM
ejpam-2305	140	12	̃(	̃(	PROPN
ejpam-2305	140	13	�	�	PROPN
ejpam-2305	140	14	̃	̃	PROPN
ejpam-2305	140	15	)	)	PUNCT
ejpam-2305	140	16	=	=	PUNCT
ejpam-2305	140	17	{	{	PUNCT
ejpam-2305	140	18	1,	1,	NUM
ejpam-2305	140	19	�	�	PROPN
ejpam-2305	140	20	(	(	PUNCT
ejpam-2305	140	21	�	�	PROPN
ejpam-2305	140	22	1),	1),	NUM
ejpam-2305	140	23	�	�	PROPN
ejpam-2305	140	24	(p),	(p),	SYM
ejpam-2305	140	25	�	�	PROPN
ejpam-2305	140	26	(	(	PUNCT
ejpam-2305	140	27	�	�	PROPN
ejpam-2305	140	28	p	p	NOUN
ejpam-2305	140	29	)	)	PUNCT
ejpam-2305	140	30	}	}	PUNCT
ejpam-2305	140	31	.	.	PUNCT
ejpam-2305	141	1	now	now	ADV
ejpam-2305	141	2	,	,	PUNCT
ejpam-2305	141	3	using	use	VERB
ejpam-2305	141	4	these	these	DET
ejpam-2305	141	5	two	two	NUM
ejpam-2305	141	6	equalities	equality	NOUN
ejpam-2305	141	7	together	together	ADV
ejpam-2305	141	8	with	with	ADP
ejpam-2305	141	9	(	(	PUNCT
ejpam-2305	141	10	2	2	X
ejpam-2305	141	11	)	)	PUNCT
ejpam-2305	141	12	gives	give	VERB
ejpam-2305	141	13	that	that	DET
ejpam-2305	141	14	r	r	NOUN
ejpam-2305	141	15	=	=	SYM
ejpam-2305	141	16	2	2	NUM
ejpam-2305	141	17	.	.	NOUN
ejpam-2305	141	18	table	table	NOUN
ejpam-2305	141	19	2	2	NUM
ejpam-2305	141	20	:	:	PUNCT
ejpam-2305	141	21	elements	element	NOUN
ejpam-2305	141	22	of	of	ADP
ejpam-2305	141	23	sd	sd	NOUN
ejpam-2305	141	24	d	d	PROPN
ejpam-2305	141	25	cd	cd	PROPN
ejpam-2305	141	26	integer	integer	NOUN
ejpam-2305	141	27	solutions	solution	NOUN
ejpam-2305	141	28	2	2	NUM
ejpam-2305	141	29	2t4	2t4	NUM
ejpam-2305	141	30	+	+	CCONJ
ejpam-2305	141	31	2pz4	2pz4	NUM
ejpam-2305	141	32	=	=	NOUN
ejpam-2305	141	33	w2	w2	NOUN
ejpam-2305	141	34	(	(	PUNCT
ejpam-2305	141	35	u±	u±	PROPN
ejpam-2305	141	36	v	v	PROPN
ejpam-2305	141	37	,	,	PUNCT
ejpam-2305	141	38	1	1	NUM
ejpam-2305	141	39	,	,	PUNCT
ejpam-2305	141	40	2u2	2u2	NUM
ejpam-2305	141	41	±	±	NUM
ejpam-2305	141	42	2uv	2uv	ADJ
ejpam-2305	141	43	+	+	CCONJ
ejpam-2305	141	44	2v2	2v2	NUM
ejpam-2305	141	45	)	)	PUNCT
ejpam-2305	141	46	2p	2p	NUM
ejpam-2305	141	47	2pt4	2pt4	NUM
ejpam-2305	141	48	+	+	CCONJ
ejpam-2305	141	49	2z4	2z4	NUM
ejpam-2305	141	50	=	=	NOUN
ejpam-2305	141	51	w2	w2	NOUN
ejpam-2305	141	52	(	(	PUNCT
ejpam-2305	141	53	1	1	NUM
ejpam-2305	141	54	,	,	PUNCT
ejpam-2305	141	55	u±	u±	PROPN
ejpam-2305	141	56	v	v	NOUN
ejpam-2305	141	57	,	,	PUNCT
ejpam-2305	141	58	2u2	2u2	NUM
ejpam-2305	141	59	±	±	NUM
ejpam-2305	141	60	2uv	2uv	ADJ
ejpam-2305	141	61	+	+	CCONJ
ejpam-2305	141	62	2v2	2v2	NUM
ejpam-2305	141	63	)	)	PUNCT
ejpam-2305	141	64	table	table	NOUN
ejpam-2305	141	65	3	3	NUM
ejpam-2305	141	66	:	:	PUNCT
ejpam-2305	141	67	elements	element	NOUN
ejpam-2305	141	68	of	of	ADP
ejpam-2305	141	69	sd̃	sd̃	PUNCT
ejpam-2305	141	70	for	for	ADP
ejpam-2305	141	71	d̃	d̃	PROPN
ejpam-2305	141	72	>	>	X
ejpam-2305	141	73	0	0	PUNCT
ejpam-2305	142	1	d	d	NOUN
ejpam-2305	142	2	cd̃	cd̃	NOUN
ejpam-2305	142	3	integer	integer	NOUN
ejpam-2305	142	4	solutions	solution	NOUN
ejpam-2305	142	5	2	2	NUM
ejpam-2305	142	6	2t4	2t4	NUM
ejpam-2305	142	7	�	�	PROPN
ejpam-2305	142	8	8pz4	8pz4	NUM
ejpam-2305	142	9	=	=	NOUN
ejpam-2305	142	10	w2	w2	NOUN
ejpam-2305	142	11	–	–	PUNCT
ejpam-2305	142	12	2p	2p	NUM
ejpam-2305	142	13	2pt4	2pt4	NUM
ejpam-2305	142	14	�	�	PROPN
ejpam-2305	142	15	8z4	8z4	NUM
ejpam-2305	142	16	=	=	SYM
ejpam-2305	142	17	w2	w2	PROPN
ejpam-2305	142	18	–	–	PUNCT
ejpam-2305	142	19	n.	n.	PROPN
ejpam-2305	142	20	zamani	zamani	PROPN
ejpam-2305	142	21	,	,	PUNCT
ejpam-2305	142	22	a.	a.	NOUN
ejpam-2305	142	23	shams	sham	NOUN
ejpam-2305	142	24	/	/	SYM
ejpam-2305	142	25	eur	eur	PROPN
ejpam-2305	142	26	.	.	PUNCT
ejpam-2305	143	1	j.	j.	PROPN
ejpam-2305	143	2	pure	pure	PROPN
ejpam-2305	143	3	appl	appl	PROPN
ejpam-2305	143	4	.	.	PROPN
ejpam-2305	143	5	math	math	PROPN
ejpam-2305	143	6	,	,	PUNCT
ejpam-2305	143	7	8	8	NUM
ejpam-2305	143	8	(	(	PUNCT
ejpam-2305	143	9	2015	2015	NUM
ejpam-2305	143	10	)	)	PUNCT
ejpam-2305	143	11	,	,	PUNCT
ejpam-2305	143	12	126	126	NUM
ejpam-2305	143	13	-	-	SYM
ejpam-2305	143	14	134	134	NUM
ejpam-2305	143	15	132	132	NUM
ejpam-2305	143	16	table	table	NOUN
ejpam-2305	143	17	4	4	NUM
ejpam-2305	143	18	:	:	PUNCT
ejpam-2305	143	19	elements	element	NOUN
ejpam-2305	143	20	of	of	ADP
ejpam-2305	143	21	sd̃	sd̃	PUNCT
ejpam-2305	143	22	for	for	ADP
ejpam-2305	143	23	d̃	d̃	PROPN
ejpam-2305	143	24	<	<	X
ejpam-2305	143	25	0	0	PUNCT
ejpam-2305	143	26	d	d	NOUN
ejpam-2305	143	27	cd̃	cd̃	NOUN
ejpam-2305	143	28	integer	integer	NOUN
ejpam-2305	143	29	solutions	solution	NOUN
ejpam-2305	143	30	�	�	PROPN
ejpam-2305	143	31	1	1	NUM
ejpam-2305	143	32	�	�	PROPN
ejpam-2305	143	33	t4	t4	PROPN
ejpam-2305	143	34	+	+	CCONJ
ejpam-2305	143	35	16pz4	16pz4	ADJ
ejpam-2305	143	36	=	=	SYM
ejpam-2305	143	37	w2	w2	PROPN
ejpam-2305	143	38	–	–	PUNCT
ejpam-2305	143	39	�	�	PROPN
ejpam-2305	143	40	2	2	NUM
ejpam-2305	143	41	�	�	NOUN
ejpam-2305	143	42	2t4	2t4	NUM
ejpam-2305	143	43	+	+	SYM
ejpam-2305	143	44	8pz4	8pz4	NUM
ejpam-2305	143	45	=	=	SYM
ejpam-2305	143	46	w2	w2	PROPN
ejpam-2305	143	47	–	–	PUNCT
ejpam-2305	143	48	�	�	PROPN
ejpam-2305	143	49	2p	2p	NUM
ejpam-2305	143	50	�	�	NOUN
ejpam-2305	143	51	2pt4	2pt4	NUM
ejpam-2305	143	52	+	+	CCONJ
ejpam-2305	143	53	8z4	8z4	NUM
ejpam-2305	143	54	=	=	SYM
ejpam-2305	143	55	w2	w2	NOUN
ejpam-2305	143	56	–	–	PUNCT
ejpam-2305	143	57	in	in	ADP
ejpam-2305	143	58	tables	table	NOUN
ejpam-2305	143	59	3	3	NUM
ejpam-2305	143	60	and	and	CCONJ
ejpam-2305	143	61	4	4	NUM
ejpam-2305	143	62	,	,	PUNCT
ejpam-2305	143	63	the	the	DET
ejpam-2305	143	64	symbol	symbol	NOUN
ejpam-2305	143	65	‘	'	PUNCT
ejpam-2305	143	66	–	–	PUNCT
ejpam-2305	143	67	’	'	PUNCT
ejpam-2305	143	68	shows	show	VERB
ejpam-2305	143	69	that	that	SCONJ
ejpam-2305	143	70	the	the	DET
ejpam-2305	143	71	corresponding	correspond	VERB
ejpam-2305	143	72	equation	equation	NOUN
ejpam-2305	143	73	dose	dose	VERB
ejpam-2305	143	74	not	not	PART
ejpam-2305	143	75	have	have	VERB
ejpam-2305	143	76	any	any	DET
ejpam-2305	143	77	integer	integer	NOUN
ejpam-2305	143	78	solution	solution	NOUN
ejpam-2305	143	79	(	(	PUNCT
ejpam-2305	143	80	t	t	PROPN
ejpam-2305	143	81	,	,	PUNCT
ejpam-2305	143	82	z	z	PROPN
ejpam-2305	143	83	,	,	PUNCT
ejpam-2305	143	84	w	w	PROPN
ejpam-2305	143	85	)	)	PUNCT
ejpam-2305	143	86	.	.	PUNCT
ejpam-2305	144	1	one	one	PRON
ejpam-2305	144	2	can	can	AUX
ejpam-2305	144	3	check	check	VERB
ejpam-2305	144	4	this	this	DET
ejpam-2305	144	5	straightforward	straightforward	NOUN
ejpam-2305	144	6	.	.	PUNCT
ejpam-2305	145	1	for	for	ADP
ejpam-2305	145	2	example	example	NOUN
ejpam-2305	145	3	,	,	PUNCT
ejpam-2305	145	4	concerning	concern	VERB
ejpam-2305	145	5	c2̃	c2̃	NOUN
ejpam-2305	145	6	in	in	ADP
ejpam-2305	145	7	the	the	DET
ejpam-2305	145	8	table	table	NOUN
ejpam-2305	145	9	3	3	NUM
ejpam-2305	145	10	,	,	PUNCT
ejpam-2305	145	11	if	if	SCONJ
ejpam-2305	145	12	there	there	PRON
ejpam-2305	145	13	is	be	VERB
ejpam-2305	145	14	any	any	DET
ejpam-2305	145	15	solution	solution	NOUN
ejpam-2305	145	16	,	,	PUNCT
ejpam-2305	145	17	then	then	ADV
ejpam-2305	145	18	we	we	PRON
ejpam-2305	145	19	conclude	conclude	VERB
ejpam-2305	145	20	that	that	SCONJ
ejpam-2305	145	21	2t4	2t4	NUM
ejpam-2305	145	22	⌘	⌘	SYM
ejpam-2305	145	23	0	0	NUM
ejpam-2305	145	24	(	(	PUNCT
ejpam-2305	145	25	mod	mod	PROPN
ejpam-2305	145	26	4	4	NUM
ejpam-2305	145	27	)	)	PUNCT
ejpam-2305	145	28	,	,	PUNCT
ejpam-2305	145	29	a	a	DET
ejpam-2305	145	30	contradiction	contradiction	NOUN
ejpam-2305	145	31	with	with	ADP
ejpam-2305	145	32	gcd(t,	gcd(t,	PROPN
ejpam-2305	145	33	�	�	NOUN
ejpam-2305	145	34	8p	8p	NUM
ejpam-2305	145	35	)	)	PUNCT
ejpam-2305	145	36	=	=	SYM
ejpam-2305	146	1	1	1	X
ejpam-2305	146	2	.	.	PUNCT
ejpam-2305	146	3	also	also	ADV
ejpam-2305	146	4	,	,	PUNCT
ejpam-2305	146	5	concerning	concern	VERB
ejpam-2305	146	6	c2̃p	c2̃p	PROPN
ejpam-2305	146	7	in	in	ADP
ejpam-2305	146	8	the	the	DET
ejpam-2305	146	9	table	table	NOUN
ejpam-2305	146	10	3	3	NUM
ejpam-2305	146	11	,	,	PUNCT
ejpam-2305	146	12	if	if	SCONJ
ejpam-2305	146	13	there	there	PRON
ejpam-2305	146	14	is	be	VERB
ejpam-2305	146	15	any	any	DET
ejpam-2305	146	16	solution	solution	NOUN
ejpam-2305	146	17	(	(	PUNCT
ejpam-2305	146	18	t	t	PROPN
ejpam-2305	146	19	,	,	PUNCT
ejpam-2305	146	20	z	z	PROPN
ejpam-2305	146	21	,	,	PUNCT
ejpam-2305	146	22	w	w	PROPN
ejpam-2305	146	23	)	)	PUNCT
ejpam-2305	146	24	,	,	PUNCT
ejpam-2305	146	25	then	then	ADV
ejpam-2305	146	26	we	we	PRON
ejpam-2305	146	27	conclude	conclude	VERB
ejpam-2305	146	28	that	that	SCONJ
ejpam-2305	146	29	2|t	2|t	NUM
ejpam-2305	146	30	which	which	PRON
ejpam-2305	146	31	contradicts	contradict	VERB
ejpam-2305	146	32	gcd(t,	gcd(t,	PROPN
ejpam-2305	146	33	�	�	PROPN
ejpam-2305	146	34	8)	8)	NUM
ejpam-2305	146	35	=	=	SYM
ejpam-2305	146	36	1	1	NUM
ejpam-2305	146	37	.	.	PUNCT
ejpam-2305	146	38	similar	similar	ADJ
ejpam-2305	146	39	arguments	argument	NOUN
ejpam-2305	146	40	can	can	AUX
ejpam-2305	146	41	be	be	AUX
ejpam-2305	146	42	done	do	VERB
ejpam-2305	146	43	for	for	ADP
ejpam-2305	146	44	other	other	ADJ
ejpam-2305	146	45	cases	case	NOUN
ejpam-2305	146	46	.	.	PUNCT
ejpam-2305	147	1	the	the	DET
ejpam-2305	147	2	following	follow	VERB
ejpam-2305	147	3	theorem	theorem	NOUN
ejpam-2305	147	4	,	,	PUNCT
ejpam-2305	147	5	thus	thus	ADV
ejpam-2305	147	6	,	,	PUNCT
ejpam-2305	147	7	has	have	AUX
ejpam-2305	147	8	been	be	AUX
ejpam-2305	147	9	proved	prove	VERB
ejpam-2305	147	10	.	.	PUNCT
ejpam-2305	148	1	theorem	theorem	ADJ
ejpam-2305	148	2	3	3	NUM
ejpam-2305	148	3	.	.	X
ejpam-2305	148	4	for	for	ADP
ejpam-2305	148	5	the	the	DET
ejpam-2305	148	6	elliptic	elliptic	ADJ
ejpam-2305	148	7	curve	curve	NOUN
ejpam-2305	148	8	e	e	NOUN
ejpam-2305	148	9	:	:	PUNCT
ejpam-2305	148	10	y2	y2	NOUN
ejpam-2305	148	11	=	=	SYM
ejpam-2305	149	1	x3	x3	PROPN
ejpam-2305	149	2	+	+	CCONJ
ejpam-2305	149	3	4px	4px	NOUN
ejpam-2305	149	4	(	(	PUNCT
ejpam-2305	149	5	p	p	X
ejpam-2305	149	6	=	=	PROPN
ejpam-2305	149	7	u4	u4	PROPN
ejpam-2305	149	8	+	+	CCONJ
ejpam-2305	149	9	v4	v4	PROPN
ejpam-2305	149	10	)	)	PUNCT
ejpam-2305	149	11	,	,	PUNCT
ejpam-2305	149	12	the	the	DET
ejpam-2305	149	13	mordell	mordell	PROPN
ejpam-2305	149	14	-	-	PUNCT
ejpam-2305	149	15	weil	weil	PROPN
ejpam-2305	149	16	theorem	theorem	NOUN
ejpam-2305	149	17	holds	hold	NOUN
ejpam-2305	149	18	as	as	ADP
ejpam-2305	149	19	following	follow	VERB
ejpam-2305	149	20	:	:	PUNCT
ejpam-2305	149	21	�	�	PROPN
ejpam-2305	149	22	⇠	⇠	PROPN
ejpam-2305	149	23	=	=	PROPN
ejpam-2305	149	24	z2	z2	PROPN
ejpam-2305	149	25	�	�	PROPN
ejpam-2305	149	26	z2	z2	PROPN
ejpam-2305	149	27	.	.	PUNCT
ejpam-2305	150	1	as	as	SCONJ
ejpam-2305	150	2	other	other	ADJ
ejpam-2305	150	3	observations	observation	NOUN
ejpam-2305	150	4	about	about	ADP
ejpam-2305	150	5	the	the	DET
ejpam-2305	150	6	rank	rank	NOUN
ejpam-2305	150	7	of	of	ADP
ejpam-2305	150	8	e	e	NOUN
ejpam-2305	150	9	:	:	PUNCT
ejpam-2305	150	10	y2	y2	X
ejpam-2305	150	11	=	=	SYM
ejpam-2305	150	12	x3	x3	PROPN
ejpam-2305	150	13	+	+	CCONJ
ejpam-2305	150	14	4px	4px	NOUN
ejpam-2305	150	15	,	,	PUNCT
ejpam-2305	150	16	we	we	PRON
ejpam-2305	150	17	also	also	ADV
ejpam-2305	150	18	examined	examine	VERB
ejpam-2305	150	19	rank(e	rank(e	PROPN
ejpam-2305	150	20	)	)	PUNCT
ejpam-2305	150	21	in	in	ADP
ejpam-2305	150	22	the	the	DET
ejpam-2305	150	23	cases	case	NOUN
ejpam-2305	150	24	p	p	X
ejpam-2305	150	25	=	=	NOUN
ejpam-2305	150	26	3,5	3,5	NUM
ejpam-2305	150	27	.	.	PUNCT
ejpam-2305	151	1	the	the	DET
ejpam-2305	151	2	resulting	result	VERB
ejpam-2305	151	3	illustrations	illustration	NOUN
ejpam-2305	151	4	done	do	VERB
ejpam-2305	151	5	with	with	ADP
ejpam-2305	151	6	mwrank†	mwrank†	PROPN
ejpam-2305	151	7	have	have	AUX
ejpam-2305	151	8	been	be	AUX
ejpam-2305	151	9	collected	collect	VERB
ejpam-2305	151	10	in	in	ADP
ejpam-2305	151	11	tables	table	NOUN
ejpam-2305	151	12	5	5	NUM
ejpam-2305	151	13	-	-	SYM
ejpam-2305	151	14	7	7	NUM
ejpam-2305	151	15	.	.	PUNCT
ejpam-2305	151	16	table	table	NOUN
ejpam-2305	151	17	5	5	NUM
ejpam-2305	151	18	:	:	PUNCT
ejpam-2305	151	19	p	p	NOUN
ejpam-2305	151	20	=	=	SYM
ejpam-2305	151	21	3	3	NUM
ejpam-2305	151	22	cd	cd	NOUN
ejpam-2305	151	23	,	,	PUNCT
ejpam-2305	151	24	cd̃	cd̃	PROPN
ejpam-2305	151	25	legendre	legendre	PROPN
ejpam-2305	151	26	value	value	NOUN
ejpam-2305	151	27	integer	integer	NOUN
ejpam-2305	151	28	solutions	solution	NOUN
ejpam-2305	151	29	w2	w2	NOUN
ejpam-2305	151	30	=	=	SYM
ejpam-2305	151	31	2t4	2t4	NUM
ejpam-2305	151	32	+	+	SYM
ejpam-2305	151	33	6z4	6z4	NUM
ejpam-2305	151	34	�	�	NOUN
ejpam-2305	151	35	2	2	NUM
ejpam-2305	151	36	6	6	NUM
ejpam-2305	151	37	�	�	NOUN
ejpam-2305	151	38	=	=	SYM
ejpam-2305	151	39	�	�	PROPN
ejpam-2305	151	40	1	1	NUM
ejpam-2305	151	41	not	not	PART
ejpam-2305	151	42	w2	w2	NOUN
ejpam-2305	151	43	=	=	SYM
ejpam-2305	151	44	3t4	3t4	NUM
ejpam-2305	151	45	+	+	NUM
ejpam-2305	151	46	4z4	4z4	NUM
ejpam-2305	151	47	�	�	NOUN
ejpam-2305	151	48	3	3	NUM
ejpam-2305	151	49	4	4	NUM
ejpam-2305	151	50	�	�	NOUN
ejpam-2305	151	51	=	=	SYM
ejpam-2305	151	52	�	�	PROPN
ejpam-2305	151	53	1	1	NUM
ejpam-2305	151	54	not	not	PART
ejpam-2305	151	55	w2	w2	NOUN
ejpam-2305	151	56	=	=	SYM
ejpam-2305	151	57	6t4	6t4	NUM
ejpam-2305	151	58	+	+	CCONJ
ejpam-2305	151	59	2z4	2z4	NUM
ejpam-2305	151	60	�	�	NOUN
ejpam-2305	151	61	6	6	NUM
ejpam-2305	151	62	2	2	NUM
ejpam-2305	151	63	�	�	NOUN
ejpam-2305	151	64	=	=	SYM
ejpam-2305	151	65	�	�	PROPN
ejpam-2305	151	66	1	1	NUM
ejpam-2305	151	67	not	not	PART
ejpam-2305	151	68	w2	w2	NOUN
ejpam-2305	151	69	=	=	SYM
ejpam-2305	151	70	2t4	2t4	NUM
ejpam-2305	151	71	�	�	PROPN
ejpam-2305	151	72	24z4	24z4	NUM
ejpam-2305	151	73	�	�	PROPN
ejpam-2305	151	74	�	�	PROPN
ejpam-2305	151	75	2	2	NUM
ejpam-2305	151	76	24	24	NUM
ejpam-2305	151	77	�	�	PROPN
ejpam-2305	151	78	=	=	SYM
ejpam-2305	151	79	�	�	PROPN
ejpam-2305	151	80	1	1	NUM
ejpam-2305	151	81	not	not	PART
ejpam-2305	151	82	w2	w2	NOUN
ejpam-2305	151	83	=	=	SYM
ejpam-2305	151	84	3t4	3t4	NUM
ejpam-2305	151	85	�	�	PROPN
ejpam-2305	151	86	16z4	16z4	NUM
ejpam-2305	151	87	�	�	PROPN
ejpam-2305	151	88	�	�	PROPN
ejpam-2305	151	89	3	3	NUM
ejpam-2305	151	90	16	16	NUM
ejpam-2305	151	91	�	�	PROPN
ejpam-2305	151	92	=	=	SYM
ejpam-2305	151	93	�	�	PROPN
ejpam-2305	151	94	1	1	NUM
ejpam-2305	151	95	not	not	PART
ejpam-2305	151	96	w2	w2	NOUN
ejpam-2305	151	97	=	=	SYM
ejpam-2305	151	98	6t4	6t4	NUM
ejpam-2305	151	99	�	�	PROPN
ejpam-2305	151	100	8z4	8z4	NUM
ejpam-2305	151	101	�	�	PROPN
ejpam-2305	151	102	�	�	PROPN
ejpam-2305	151	103	6	6	NUM
ejpam-2305	151	104	8	8	NUM
ejpam-2305	151	105	�	�	PROPN
ejpam-2305	151	106	=	=	SYM
ejpam-2305	151	107	�	�	PROPN
ejpam-2305	151	108	1	1	NUM
ejpam-2305	151	109	not	not	PART
ejpam-2305	151	110	w2	w2	NOUN
ejpam-2305	151	111	=	=	SYM
ejpam-2305	151	112	�	�	PROPN
ejpam-2305	151	113	t4	t4	PROPN
ejpam-2305	151	114	+	+	PROPN
ejpam-2305	151	115	48z4	48z4	PROPN
ejpam-2305	151	116	�	�	PROPN
ejpam-2305	151	117	�	�	PROPN
ejpam-2305	151	118	1	1	NUM
ejpam-2305	151	119	48	48	NUM
ejpam-2305	151	120	�	�	PROPN
ejpam-2305	151	121	=	=	SYM
ejpam-2305	151	122	�	�	PROPN
ejpam-2305	151	123	1	1	NUM
ejpam-2305	151	124	not	not	PART
ejpam-2305	151	125	w2	w2	NOUN
ejpam-2305	151	126	=	=	SYM
ejpam-2305	151	127	�	�	PROPN
ejpam-2305	151	128	2t4	2t4	NUM
ejpam-2305	151	129	+	+	CCONJ
ejpam-2305	151	130	24z4	24z4	NUM
ejpam-2305	151	131	�	�	PROPN
ejpam-2305	151	132	�	�	PROPN
ejpam-2305	151	133	2	2	NUM
ejpam-2305	151	134	24	24	NUM
ejpam-2305	151	135	�	�	PROPN
ejpam-2305	151	136	=	=	SYM
ejpam-2305	151	137	�	�	PROPN
ejpam-2305	151	138	1	1	NUM
ejpam-2305	151	139	not	not	PART
ejpam-2305	151	140	w2	w2	NOUN
ejpam-2305	151	141	=	=	SYM
ejpam-2305	151	142	�	�	PROPN
ejpam-2305	151	143	3t4	3t4	NUM
ejpam-2305	151	144	+	+	SYM
ejpam-2305	151	145	16z4	16z4	NUM
ejpam-2305	151	146	�	�	NOUN
ejpam-2305	151	147	�	�	PROPN
ejpam-2305	151	148	3	3	NUM
ejpam-2305	151	149	16	16	NUM
ejpam-2305	151	150	�	�	PROPN
ejpam-2305	151	151	=	=	SYM
ejpam-2305	151	152	�	�	PROPN
ejpam-2305	151	153	1	1	NUM
ejpam-2305	151	154	not	not	PART
ejpam-2305	151	155	w2	w2	NOUN
ejpam-2305	151	156	=	=	SYM
ejpam-2305	151	157	�	�	PROPN
ejpam-2305	151	158	4t4	4t4	PROPN
ejpam-2305	151	159	+	+	CCONJ
ejpam-2305	151	160	12z4	12z4	NUM
ejpam-2305	151	161	�	�	PROPN
ejpam-2305	151	162	�	�	PROPN
ejpam-2305	151	163	4	4	NUM
ejpam-2305	151	164	12	12	NUM
ejpam-2305	151	165	�	�	PROPN
ejpam-2305	151	166	=	=	SYM
ejpam-2305	151	167	�	�	PROPN
ejpam-2305	151	168	1	1	NUM
ejpam-2305	151	169	not	not	PART
ejpam-2305	151	170	w2	w2	NOUN
ejpam-2305	151	171	=	=	SYM
ejpam-2305	151	172	�	�	PROPN
ejpam-2305	151	173	6t4	6t4	NUM
ejpam-2305	151	174	+	+	CCONJ
ejpam-2305	151	175	8z4	8z4	NUM
ejpam-2305	151	176	�	�	NOUN
ejpam-2305	151	177	�	�	PROPN
ejpam-2305	151	178	6	6	NUM
ejpam-2305	151	179	8	8	NUM
ejpam-2305	151	180	�	�	PROPN
ejpam-2305	151	181	=	=	SYM
ejpam-2305	151	182	�	�	PROPN
ejpam-2305	151	183	1	1	NUM
ejpam-2305	151	184	not	not	PART
ejpam-2305	151	185	†	†	PROPN
ejpam-2305	151	186	http://homepages.warwick.ac.uk/~masgaj/mwrank/	http://homepages.warwick.ac.uk/~masgaj/mwrank/	PROPN
ejpam-2305	151	187	n.	n.	PROPN
ejpam-2305	151	188	zamani	zamani	PROPN
ejpam-2305	151	189	,	,	PUNCT
ejpam-2305	151	190	a.	a.	NOUN
ejpam-2305	151	191	shams	sham	NOUN
ejpam-2305	151	192	/	/	SYM
ejpam-2305	151	193	eur	eur	PROPN
ejpam-2305	151	194	.	.	PUNCT
ejpam-2305	152	1	j.	j.	PROPN
ejpam-2305	152	2	pure	pure	PROPN
ejpam-2305	152	3	appl	appl	PROPN
ejpam-2305	152	4	.	.	PROPN
ejpam-2305	152	5	math	math	PROPN
ejpam-2305	152	6	,	,	PUNCT
ejpam-2305	152	7	8	8	NUM
ejpam-2305	152	8	(	(	PUNCT
ejpam-2305	152	9	2015	2015	NUM
ejpam-2305	152	10	)	)	PUNCT
ejpam-2305	152	11	,	,	PUNCT
ejpam-2305	152	12	126	126	NUM
ejpam-2305	152	13	-	-	SYM
ejpam-2305	152	14	134	134	NUM
ejpam-2305	152	15	133	133	NUM
ejpam-2305	152	16	table	table	NOUN
ejpam-2305	152	17	6	6	NUM
ejpam-2305	152	18	:	:	PUNCT
ejpam-2305	152	19	rank	rank	NOUN
ejpam-2305	152	20	p	p	PROPN
ejpam-2305	152	21	rank	rank	NOUN
ejpam-2305	152	22	of	of	ADP
ejpam-2305	152	23	e	e	NOUN
ejpam-2305	152	24	#	#	SYM
ejpam-2305	152	25	qq(e	qq(e	X
ejpam-2305	152	26	/	/	SYM
ejpam-2305	152	27	q)[2	q)[2	PROPN
ejpam-2305	152	28	]	]	X
ejpam-2305	152	29	2	2	NUM
ejpam-2305	152	30	1	1	NUM
ejpam-2305	152	31	1	1	NUM
ejpam-2305	152	32	3	3	NUM
ejpam-2305	152	33	0	0	NUM
ejpam-2305	152	34	1	1	NUM
ejpam-2305	152	35	5	5	NUM
ejpam-2305	152	36	1	1	NUM
ejpam-2305	152	37	1	1	NUM
ejpam-2305	152	38	17	17	NUM
ejpam-2305	152	39	p	p	NOUN
ejpam-2305	152	40			NOUN
ejpam-2305	152	41	106	106	NUM
ejpam-2305	152	42	2	2	NUM
ejpam-2305	152	43	1	1	NUM
ejpam-2305	152	44	table	table	NOUN
ejpam-2305	152	45	7	7	NUM
ejpam-2305	152	46	:	:	PUNCT
ejpam-2305	152	47	p	p	X
ejpam-2305	152	48	=	=	SYM
ejpam-2305	152	49	5	5	NUM
ejpam-2305	152	50	cd	cd	NOUN
ejpam-2305	152	51	,	,	PUNCT
ejpam-2305	152	52	cd̃	cd̃	PROPN
ejpam-2305	152	53	legendre	legendre	PROPN
ejpam-2305	152	54	value	value	NOUN
ejpam-2305	152	55	integer	integer	NOUN
ejpam-2305	152	56	solutions	solution	NOUN
ejpam-2305	152	57	w2	w2	NOUN
ejpam-2305	152	58	=	=	SYM
ejpam-2305	152	59	2t4	2t4	NUM
ejpam-2305	153	1	+	+	CCONJ
ejpam-2305	153	2	10z4	10z4	NUM
ejpam-2305	153	3	�	�	NOUN
ejpam-2305	153	4	2	2	NUM
ejpam-2305	153	5	10	10	NUM
ejpam-2305	153	6	�	�	PROPN
ejpam-2305	153	7	=	=	SYM
ejpam-2305	153	8	�	�	PROPN
ejpam-2305	153	9	1	1	NUM
ejpam-2305	153	10	not	not	PART
ejpam-2305	153	11	w2	w2	NOUN
ejpam-2305	153	12	=	=	SYM
ejpam-2305	153	13	4t4	4t4	PROPN
ejpam-2305	153	14	+	+	CCONJ
ejpam-2305	153	15	5z4	5z4	NUM
ejpam-2305	153	16	�	�	NOUN
ejpam-2305	153	17	4	4	NUM
ejpam-2305	153	18	5	5	NUM
ejpam-2305	153	19	�	�	NOUN
ejpam-2305	153	20	=	=	SYM
ejpam-2305	153	21	1	1	NUM
ejpam-2305	153	22	(	(	PUNCT
ejpam-2305	153	23	1	1	NUM
ejpam-2305	153	24	,	,	PUNCT
ejpam-2305	153	25	1,3	1,3	NUM
ejpam-2305	153	26	)	)	PUNCT
ejpam-2305	153	27	w2	w2	NOUN
ejpam-2305	153	28	=	=	NOUN
ejpam-2305	153	29	5t4	5t4	NUM
ejpam-2305	153	30	+	+	SYM
ejpam-2305	153	31	4z4	4z4	NUM
ejpam-2305	153	32	�	�	NOUN
ejpam-2305	153	33	5	5	NUM
ejpam-2305	153	34	4	4	NUM
ejpam-2305	153	35	�	�	NOUN
ejpam-2305	153	36	=	=	SYM
ejpam-2305	153	37	1	1	NUM
ejpam-2305	153	38	(	(	PUNCT
ejpam-2305	153	39	1	1	NUM
ejpam-2305	153	40	,	,	PUNCT
ejpam-2305	153	41	1,3	1,3	NUM
ejpam-2305	153	42	)	)	PUNCT
ejpam-2305	153	43	w2	w2	NOUN
ejpam-2305	153	44	=	=	PROPN
ejpam-2305	153	45	10t4	10t4	NUM
ejpam-2305	153	46	+	+	NUM
ejpam-2305	153	47	2z4	2z4	NUM
ejpam-2305	153	48	�	�	NOUN
ejpam-2305	153	49	2	2	NUM
ejpam-2305	153	50	10	10	NUM
ejpam-2305	153	51	�	�	PROPN
ejpam-2305	153	52	=	=	SYM
ejpam-2305	153	53	�	�	PROPN
ejpam-2305	153	54	1	1	NUM
ejpam-2305	153	55	not	not	PART
ejpam-2305	153	56	w2	w2	NOUN
ejpam-2305	153	57	=	=	SYM
ejpam-2305	153	58	2t4	2t4	NUM
ejpam-2305	153	59	�	�	PROPN
ejpam-2305	153	60	40z4	40z4	NUM
ejpam-2305	153	61	�	�	PROPN
ejpam-2305	153	62	�	�	PROPN
ejpam-2305	153	63	2	2	NUM
ejpam-2305	153	64	40	40	NUM
ejpam-2305	153	65	�	�	PROPN
ejpam-2305	153	66	=	=	SYM
ejpam-2305	153	67	�	�	PROPN
ejpam-2305	153	68	1	1	NUM
ejpam-2305	153	69	not	not	PART
ejpam-2305	153	70	w2	w2	NOUN
ejpam-2305	153	71	=	=	SYM
ejpam-2305	153	72	5t4	5t4	NUM
ejpam-2305	153	73	�	�	PROPN
ejpam-2305	153	74	16z4	16z4	NUM
ejpam-2305	153	75	�	�	PROPN
ejpam-2305	153	76	�	�	PROPN
ejpam-2305	153	77	5	5	NUM
ejpam-2305	153	78	16	16	NUM
ejpam-2305	153	79	�	�	PROPN
ejpam-2305	153	80	=	=	SYM
ejpam-2305	153	81	�	�	PROPN
ejpam-2305	153	82	1	1	NUM
ejpam-2305	153	83	not	not	PART
ejpam-2305	153	84	w2	w2	NOUN
ejpam-2305	153	85	=	=	SYM
ejpam-2305	153	86	10t4	10t4	NUM
ejpam-2305	153	87	�	�	PROPN
ejpam-2305	153	88	8z4	8z4	NUM
ejpam-2305	153	89	�	�	PROPN
ejpam-2305	153	90	�	�	PROPN
ejpam-2305	153	91	8	8	NUM
ejpam-2305	153	92	10	10	NUM
ejpam-2305	153	93	�	�	PROPN
ejpam-2305	153	94	=	=	SYM
ejpam-2305	153	95	�	�	PROPN
ejpam-2305	153	96	1	1	NUM
ejpam-2305	153	97	not	not	PART
ejpam-2305	153	98	w2	w2	NOUN
ejpam-2305	153	99	=	=	SYM
ejpam-2305	153	100	�	�	PROPN
ejpam-2305	153	101	t4	t4	PROPN
ejpam-2305	153	102	+	+	PROPN
ejpam-2305	153	103	80z4	80z4	NUM
ejpam-2305	153	104	�	�	PROPN
ejpam-2305	153	105	�	�	PROPN
ejpam-2305	153	106	1	1	NUM
ejpam-2305	153	107	80	80	NUM
ejpam-2305	153	108	�	�	PROPN
ejpam-2305	153	109	=	=	SYM
ejpam-2305	153	110	�	�	PROPN
ejpam-2305	153	111	1	1	NUM
ejpam-2305	153	112	not	not	PART
ejpam-2305	153	113	w2	w2	NOUN
ejpam-2305	153	114	=	=	SYM
ejpam-2305	153	115	�	�	PROPN
ejpam-2305	153	116	2t4	2t4	NUM
ejpam-2305	153	117	+	+	CCONJ
ejpam-2305	153	118	40z4	40z4	NUM
ejpam-2305	153	119	�	�	PROPN
ejpam-2305	153	120	�	�	PROPN
ejpam-2305	153	121	4	4	NUM
ejpam-2305	153	122	20	20	NUM
ejpam-2305	153	123	�	�	PROPN
ejpam-2305	153	124	=	=	SYM
ejpam-2305	153	125	�	�	PROPN
ejpam-2305	153	126	1	1	NUM
ejpam-2305	153	127	not	not	PART
ejpam-2305	153	128	w2	w2	NOUN
ejpam-2305	153	129	=	=	SYM
ejpam-2305	153	130	�	�	PROPN
ejpam-2305	153	131	4t4	4t4	PROPN
ejpam-2305	153	132	+	+	CCONJ
ejpam-2305	153	133	20z4	20z4	NUM
ejpam-2305	153	134	�	�	NOUN
ejpam-2305	153	135	�	�	PROPN
ejpam-2305	153	136	4	4	NUM
ejpam-2305	153	137	20	20	NUM
ejpam-2305	153	138	�	�	PROPN
ejpam-2305	153	139	=	=	SYM
ejpam-2305	153	140	�	�	PROPN
ejpam-2305	153	141	1	1	NUM
ejpam-2305	153	142	not	not	PART
ejpam-2305	153	143	w2	w2	NOUN
ejpam-2305	153	144	=	=	SYM
ejpam-2305	153	145	�	�	PROPN
ejpam-2305	153	146	5t4	5t4	NUM
ejpam-2305	153	147	+	+	SYM
ejpam-2305	153	148	16z4	16z4	NUM
ejpam-2305	153	149	�	�	NOUN
ejpam-2305	153	150	�	�	PROPN
ejpam-2305	153	151	5	5	NUM
ejpam-2305	153	152	16	16	NUM
ejpam-2305	153	153	�	�	PROPN
ejpam-2305	153	154	=	=	SYM
ejpam-2305	153	155	�	�	PROPN
ejpam-2305	153	156	1	1	NUM
ejpam-2305	153	157	not	not	PART
ejpam-2305	153	158	w2	w2	NOUN
ejpam-2305	153	159	=	=	SYM
ejpam-2305	153	160	�	�	PROPN
ejpam-2305	153	161	10t4	10t4	NUM
ejpam-2305	153	162	+	+	NUM
ejpam-2305	153	163	8z4	8z4	NUM
ejpam-2305	153	164	�	�	PROPN
ejpam-2305	153	165	10	10	NUM
ejpam-2305	153	166	�	�	PROPN
ejpam-2305	153	167	8	8	NUM
ejpam-2305	153	168	�	�	PROPN
ejpam-2305	153	169	=	=	SYM
ejpam-2305	153	170	�	�	PROPN
ejpam-2305	153	171	1	1	NUM
ejpam-2305	153	172	not	not	PART
ejpam-2305	153	173	references	reference	NOUN
ejpam-2305	153	174	134	134	NUM
ejpam-2305	153	175	references	reference	NOUN
ejpam-2305	153	176	[	[	X
ejpam-2305	153	177	1	1	NUM
ejpam-2305	153	178	]	]	PUNCT
ejpam-2305	153	179	a.	a.	NOUN
ejpam-2305	153	180	brumer	brumer	NOUN
ejpam-2305	153	181	and	and	CCONJ
ejpam-2305	153	182	o	o	PROPN
ejpam-2305	153	183	mc	mc	PROPN
ejpam-2305	153	184	.	.	PROPN
ejpam-2305	153	185	guinness	guinness	PROPN
ejpam-2305	153	186	.	.	PUNCT
ejpam-2305	154	1	the	the	DET
ejpam-2305	154	2	behaviour	behaviour	NOUN
ejpam-2305	154	3	of	of	ADP
ejpam-2305	154	4	the	the	DET
ejpam-2305	154	5	mordell	mordell	PROPN
ejpam-2305	154	6	-	-	PUNCT
ejpam-2305	154	7	weil	weil	PROPN
ejpam-2305	154	8	group	group	NOUN
ejpam-2305	154	9	of	of	ADP
ejpam-2305	154	10	elliptic	elliptic	ADJ
ejpam-2305	154	11	curves	curve	NOUN
ejpam-2305	154	12	,	,	PUNCT
ejpam-2305	154	13	bulletin	bulletin	NOUN
ejpam-2305	154	14	of	of	ADP
ejpam-2305	154	15	american	american	PROPN
ejpam-2305	154	16	mathematical	mathematical	PROPN
ejpam-2305	154	17	society	society	NOUN
ejpam-2305	154	18	,	,	PUNCT
ejpam-2305	154	19	23	23	NUM
ejpam-2305	154	20	,	,	PUNCT
ejpam-2305	154	21	375	375	NUM
ejpam-2305	154	22	-	-	SYM
ejpam-2305	154	23	382	382	NUM
ejpam-2305	154	24	,	,	PUNCT
ejpam-2305	154	25	1990	1990	NUM
ejpam-2305	154	26	.	.	PUNCT
ejpam-2305	155	1	[	[	X
ejpam-2305	155	2	2	2	X
ejpam-2305	155	3	]	]	PUNCT
ejpam-2305	155	4	j.	j.	PROPN
ejpam-2305	155	5	s.	s.	PROPN
ejpam-2305	155	6	chahal	chahal	PROPN
ejpam-2305	155	7	.	.	PUNCT
ejpam-2305	156	1	topics	topic	NOUN
ejpam-2305	156	2	in	in	ADP
ejpam-2305	156	3	number	number	NOUN
ejpam-2305	156	4	theory	theory	NOUN
ejpam-2305	156	5	,	,	PUNCT
ejpam-2305	156	6	kluwer	kluwer	PROPN
ejpam-2305	156	7	academic	academic	PROPN
ejpam-2305	156	8	/	/	SYM
ejpam-2305	156	9	plenum	plenum	PROPN
ejpam-2305	156	10	publisher	publisher	NOUN
ejpam-2305	156	11	,	,	PUNCT
ejpam-2305	156	12	1988	1988	NUM
ejpam-2305	156	13	.	.	PUNCT
ejpam-2305	157	1	[	[	X
ejpam-2305	157	2	3	3	X
ejpam-2305	157	3	]	]	X
ejpam-2305	157	4	h.	h.	PROPN
ejpam-2305	157	5	cohen	cohen	PROPN
ejpam-2305	157	6	.	.	PUNCT
ejpam-2305	158	1	number	number	NOUN
ejpam-2305	158	2	theory	theory	NOUN
ejpam-2305	158	3	:	:	PUNCT
ejpam-2305	158	4	tools	tool	NOUN
ejpam-2305	158	5	and	and	CCONJ
ejpam-2305	158	6	diophantine	diophantine	VERB
ejpam-2305	158	7	equations	equation	NOUN
ejpam-2305	158	8	,	,	PUNCT
ejpam-2305	158	9	springer	springer	NOUN
ejpam-2305	158	10	,	,	PUNCT
ejpam-2305	158	11	vol	vol	NOUN
ejpam-2305	158	12	.	.	PUNCT
ejpam-2305	159	1	i	i	PRON
ejpam-2305	159	2	,	,	PUNCT
ejpam-2305	159	3	2007	2007	NUM
ejpam-2305	159	4	.	.	PUNCT
ejpam-2305	160	1	[	[	X
ejpam-2305	160	2	4	4	X
ejpam-2305	160	3	]	]	PUNCT
ejpam-2305	160	4	t.	t.	NOUN
ejpam-2305	160	5	goto	goto	NOUN
ejpam-2305	160	6	.	.	PUNCT
ejpam-2305	161	1	a	a	DET
ejpam-2305	161	2	study	study	NOUN
ejpam-2305	161	3	on	on	ADP
ejpam-2305	161	4	the	the	DET
ejpam-2305	161	5	selmer	selmer	PROPN
ejpam-2305	161	6	groups	group	NOUN
ejpam-2305	161	7	of	of	ADP
ejpam-2305	161	8	elliptic	elliptic	ADJ
ejpam-2305	161	9	curves	curve	NOUN
ejpam-2305	161	10	with	with	ADP
ejpam-2305	161	11	a	a	DET
ejpam-2305	161	12	rational	rational	ADJ
ejpam-2305	161	13	2	2	NUM
ejpam-2305	161	14	-	-	PUNCT
ejpam-2305	161	15	torsion	torsion	NOUN
ejpam-2305	161	16	,	,	PUNCT
ejpam-2305	161	17	kyushu	kyushu	PROPN
ejpam-2305	161	18	university	university	PROPN
ejpam-2305	161	19	,	,	PUNCT
ejpam-2305	161	20	phd	phd	NOUN
ejpam-2305	161	21	thesis	thesis	NOUN
ejpam-2305	161	22	2002	2002	NUM
ejpam-2305	161	23	.	.	PUNCT
ejpam-2305	162	1	[	[	X
ejpam-2305	162	2	5	5	X
ejpam-2305	162	3	]	]	PUNCT
ejpam-2305	162	4	t.	t.	PROPN
ejpam-2305	162	5	kudo	kudo	PROPN
ejpam-2305	162	6	and	and	CCONJ
ejpam-2305	162	7	k.	k.	PROPN
ejpam-2305	162	8	motose	motose	PROPN
ejpam-2305	162	9	.	.	PUNCT
ejpam-2305	163	1	on	on	ADP
ejpam-2305	163	2	group	group	NOUN
ejpam-2305	163	3	structures	structure	NOUN
ejpam-2305	163	4	of	of	ADP
ejpam-2305	163	5	some	some	DET
ejpam-2305	163	6	special	special	ADJ
ejpam-2305	163	7	elliptic	elliptic	ADJ
ejpam-2305	163	8	curves	curve	NOUN
ejpam-2305	163	9	,	,	PUNCT
ejpam-2305	163	10	mathematical	mathematical	ADJ
ejpam-2305	163	11	journal	journal	NOUN
ejpam-2305	163	12	of	of	ADP
ejpam-2305	163	13	okayama	okayama	PROPN
ejpam-2305	163	14	university	university	PROPN
ejpam-2305	163	15	,	,	PUNCT
ejpam-2305	163	16	47	47	NUM
ejpam-2305	163	17	,	,	PUNCT
ejpam-2305	163	18	81	81	NUM
ejpam-2305	163	19	-	-	SYM
ejpam-2305	163	20	84	84	NUM
ejpam-2305	163	21	,	,	PUNCT
ejpam-2305	163	22	2005	2005	NUM
ejpam-2305	163	23	.	.	PUNCT
ejpam-2305	164	1	[	[	X
ejpam-2305	164	2	6	6	X
ejpam-2305	164	3	]	]	PUNCT
ejpam-2305	164	4	j.	j.	PROPN
ejpam-2305	164	5	h.	h.	PROPN
ejpam-2305	164	6	silverman	silverman	PROPN
ejpam-2305	164	7	and	and	CCONJ
ejpam-2305	164	8	j.	j.	PROPN
ejpam-2305	164	9	tate	tate	PROPN
ejpam-2305	164	10	.	.	PUNCT
ejpam-2305	165	1	rational	rational	ADJ
ejpam-2305	165	2	points	point	NOUN
ejpam-2305	165	3	on	on	ADP
ejpam-2305	165	4	elliptic	elliptic	ADJ
ejpam-2305	165	5	curves	curve	NOUN
ejpam-2305	165	6	,	,	PUNCT
ejpam-2305	165	7	springer	springer	NOUN
ejpam-2305	165	8	,	,	PUNCT
ejpam-2305	165	9	1992	1992	NUM
ejpam-2305	165	10	.	.	PUNCT
ejpam-2305	166	1	[	[	X
ejpam-2305	166	2	7	7	X
ejpam-2305	166	3	]	]	PUNCT
ejpam-2305	166	4	j.	j.	PROPN
ejpam-2305	166	5	h.	h.	PROPN
ejpam-2305	166	6	silverman	silverman	PROPN
ejpam-2305	166	7	,	,	PUNCT
ejpam-2305	166	8	the	the	DET
ejpam-2305	166	9	arithmetic	arithmetic	NOUN
ejpam-2305	166	10	of	of	ADP
ejpam-2305	166	11	elliptic	elliptic	ADJ
ejpam-2305	166	12	curves	curve	NOUN
ejpam-2305	166	13	,	,	PUNCT
ejpam-2305	166	14	springer	springer	NOUN
ejpam-2305	166	15	,	,	PUNCT
ejpam-2305	166	16	2009	2009	NUM
ejpam-2305	166	17	.	.	PUNCT
ejpam-2305	167	1	[	[	X
ejpam-2305	167	2	8	8	NUM
ejpam-2305	167	3	]	]	X
ejpam-2305	167	4	b.	b.	PROPN
ejpam-2305	167	5	k.	k.	PROPN
ejpam-2305	167	6	spearman	spearman	PROPN
ejpam-2305	167	7	.	.	PUNCT
ejpam-2305	168	1	elliptic	elliptic	ADJ
ejpam-2305	168	2	curves	curve	NOUN
ejpam-2305	168	3	y2	y2	NOUN
ejpam-2305	168	4	=	=	SYM
ejpam-2305	168	5	x3	x3	PROPN
ejpam-2305	168	6	�	�	PROPN
ejpam-2305	168	7	px	px	PROPN
ejpam-2305	168	8	of	of	ADP
ejpam-2305	168	9	rank	rank	PROPN
ejpam-2305	168	10	two	two	NUM
ejpam-2305	168	11	,	,	PUNCT
ejpam-2305	168	12	mathematical	mathematical	ADJ
ejpam-2305	168	13	journal	journal	NOUN
ejpam-2305	168	14	of	of	ADP
ejpam-2305	168	15	okayama	okayama	PROPN
ejpam-2305	168	16	university	university	PROPN
ejpam-2305	168	17	,	,	PUNCT
ejpam-2305	168	18	49	49	NUM
ejpam-2305	168	19	,	,	PUNCT
ejpam-2305	168	20	183	183	NUM
ejpam-2305	168	21	-	-	SYM
ejpam-2305	168	22	184	184	NUM
ejpam-2305	168	23	,	,	PUNCT
ejpam-2305	168	24	2007	2007	NUM
ejpam-2305	168	25	.	.	PUNCT
ejpam-2305	169	1	[	[	X
ejpam-2305	169	2	9	9	NUM
ejpam-2305	169	3	]	]	PUNCT
ejpam-2305	169	4	d.	d.	PROPN
ejpam-2305	169	5	zagier	zagier	PROPN
ejpam-2305	169	6	and	and	CCONJ
ejpam-2305	169	7	g.	g.	PROPN
ejpam-2305	169	8	kramarz	kramarz	PROPN
ejpam-2305	169	9	.	.	PUNCT
ejpam-2305	170	1	numerical	numerical	ADJ
ejpam-2305	170	2	investigations	investigation	NOUN
ejpam-2305	170	3	related	relate	VERB
ejpam-2305	170	4	to	to	ADP
ejpam-2305	170	5	the	the	DET
ejpam-2305	170	6	l	l	NOUN
ejpam-2305	170	7	-	-	NOUN
ejpam-2305	170	8	series	series	NOUN
ejpam-2305	170	9	of	of	ADP
ejpam-2305	170	10	certain	certain	ADJ
ejpam-2305	170	11	elliptic	elliptic	ADJ
ejpam-2305	170	12	curves	curve	NOUN
ejpam-2305	170	13	,	,	PUNCT
ejpam-2305	170	14	journal	journal	NOUN
ejpam-2305	170	15	of	of	ADP
ejpam-2305	170	16	indian	indian	PROPN
ejpam-2305	170	17	mathematical	mathematical	ADJ
ejpam-2305	170	18	society	society	NOUN
ejpam-2305	170	19	,	,	PUNCT
ejpam-2305	170	20	52	52	NUM
ejpam-2305	170	21	,	,	PUNCT
ejpam-2305	170	22	51	51	NUM
ejpam-2305	170	23	-	-	SYM
ejpam-2305	170	24	69	69	NUM
ejpam-2305	170	25	,	,	PUNCT
ejpam-2305	170	26	1987	1987	NUM
ejpam-2305	170	27	.	.	PUNCT