id	sid	tid	token	lemma	pos
ejpam-2421	1	1	compile	compile	NOUN
ejpam-2421	1	2	/	/	SYM
ejpam-2421	1	3	output.dvi	output.dvi	NOUN
ejpam-2421	1	4	european	european	ADJ
ejpam-2421	1	5	journal	journal	NOUN
ejpam-2421	1	6	of	of	ADP
ejpam-2421	1	7	pure	pure	ADJ
ejpam-2421	1	8	and	and	CCONJ
ejpam-2421	1	9	applied	apply	VERB
ejpam-2421	1	10	mathematics	mathematic	NOUN
ejpam-2421	1	11	vol	vol	NOUN
ejpam-2421	1	12	.	.	PROPN
ejpam-2421	1	13	8	8	NUM
ejpam-2421	1	14	,	,	PUNCT
ejpam-2421	1	15	no	no	INTJ
ejpam-2421	1	16	.	.	NOUN
ejpam-2421	1	17	3	3	NUM
ejpam-2421	1	18	,	,	PUNCT
ejpam-2421	1	19	2015	2015	NUM
ejpam-2421	1	20	,	,	PUNCT
ejpam-2421	1	21	343	343	NUM
ejpam-2421	1	22	-	-	SYM
ejpam-2421	1	23	356	356	NUM
ejpam-2421	1	24	issn	issn	PROPN
ejpam-2421	1	25	1307	1307	NUM
ejpam-2421	1	26	-	-	SYM
ejpam-2421	1	27	5543	5543	NUM
ejpam-2421	1	28	–	–	PUNCT
ejpam-2421	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2421	1	30	an	an	DET
ejpam-2421	1	31	algorithm	algorithm	NOUN
ejpam-2421	1	32	for	for	ADP
ejpam-2421	1	33	explicit	explicit	ADJ
ejpam-2421	1	34	form	form	NOUN
ejpam-2421	1	35	of	of	ADP
ejpam-2421	1	36	fundamental	fundamental	ADJ
ejpam-2421	1	37	units	unit	NOUN
ejpam-2421	1	38	of	of	ADP
ejpam-2421	1	39	certain	certain	ADJ
ejpam-2421	1	40	real	real	ADJ
ejpam-2421	1	41	quadratic	quadratic	ADJ
ejpam-2421	1	42	fields	field	NOUN
ejpam-2421	1	43	and	and	CCONJ
ejpam-2421	1	44	period	period	NOUN
ejpam-2421	1	45	eight	eight	NUM
ejpam-2421	1	46	özen	özen	NOUN
ejpam-2421	1	47	özer1,∗	özer1,∗	NOUN
ejpam-2421	1	48	,	,	PUNCT
ejpam-2421	1	49	ayten	ayten	ADJ
ejpam-2421	1	50	pekin	pekin	NOUN
ejpam-2421	1	51	2	2	NUM
ejpam-2421	1	52	1	1	NUM
ejpam-2421	1	53	kırklareli	kırklareli	NOUN
ejpam-2421	1	54	university	university	NOUN
ejpam-2421	1	55	faculty	faculty	NOUN
ejpam-2421	1	56	of	of	ADP
ejpam-2421	1	57	art	art	NOUN
ejpam-2421	1	58	and	and	CCONJ
ejpam-2421	1	59	sciences	sciences	PROPN
ejpam-2421	1	60	department	department	PROPN
ejpam-2421	1	61	of	of	ADP
ejpam-2421	1	62	mathematics	mathematics	PROPN
ejpam-2421	1	63	,	,	PUNCT
ejpam-2421	1	64	kırklareli	kırklareli	PROPN
ejpam-2421	1	65	,	,	PUNCT
ejpam-2421	1	66	turkey	turkey	PROPN
ejpam-2421	1	67	2	2	NUM
ejpam-2421	1	68	department	department	NOUN
ejpam-2421	1	69	of	of	ADP
ejpam-2421	1	70	mathematics	mathematic	NOUN
ejpam-2421	1	71	,	,	PUNCT
ejpam-2421	1	72	faculty	faculty	NOUN
ejpam-2421	1	73	of	of	ADP
ejpam-2421	1	74	sciences	sciences	PROPN
ejpam-2421	1	75	,	,	PUNCT
ejpam-2421	1	76	istanbul	istanbul	PROPN
ejpam-2421	1	77	university	university	PROPN
ejpam-2421	1	78	,	,	PUNCT
ejpam-2421	1	79	istanbul	istanbul	PROPN
ejpam-2421	1	80	,	,	PUNCT
ejpam-2421	1	81	turkey	turkey	PROPN
ejpam-2421	1	82	abstract	abstract	NOUN
ejpam-2421	1	83	.	.	PUNCT
ejpam-2421	2	1	in	in	ADP
ejpam-2421	2	2	this	this	DET
ejpam-2421	2	3	paper	paper	NOUN
ejpam-2421	2	4	,	,	PUNCT
ejpam-2421	2	5	we	we	PRON
ejpam-2421	2	6	have	have	AUX
ejpam-2421	2	7	given	give	VERB
ejpam-2421	2	8	an	an	DET
ejpam-2421	2	9	explicit	explicit	ADJ
ejpam-2421	2	10	formulation	formulation	NOUN
ejpam-2421	2	11	to	to	PART
ejpam-2421	2	12	determine	determine	VERB
ejpam-2421	2	13	the	the	DET
ejpam-2421	2	14	form	form	NOUN
ejpam-2421	2	15	of	of	ADP
ejpam-2421	2	16	the	the	DET
ejpam-2421	2	17	fundamental	fundamental	ADJ
ejpam-2421	2	18	units	unit	NOUN
ejpam-2421	2	19	of	of	ADP
ejpam-2421	2	20	certain	certain	ADJ
ejpam-2421	2	21	real	real	ADJ
ejpam-2421	2	22	quadratic	quadratic	ADJ
ejpam-2421	2	23	number	number	NOUN
ejpam-2421	2	24	fields	field	NOUN
ejpam-2421	2	25	.	.	PUNCT
ejpam-2421	3	1	this	this	DET
ejpam-2421	3	2	new	new	ADJ
ejpam-2421	3	3	algorithm	algorithm	NOUN
ejpam-2421	3	4	for	for	ADP
ejpam-2421	3	5	such	such	ADJ
ejpam-2421	3	6	quadratic	quadratic	ADJ
ejpam-2421	3	7	fields	field	NOUN
ejpam-2421	3	8	is	be	AUX
ejpam-2421	3	9	first	first	ADJ
ejpam-2421	3	10	in	in	ADP
ejpam-2421	3	11	the	the	DET
ejpam-2421	3	12	literature	literature	NOUN
ejpam-2421	3	13	and	and	CCONJ
ejpam-2421	3	14	it	it	PRON
ejpam-2421	3	15	gives	give	VERB
ejpam-2421	3	16	us	we	PRON
ejpam-2421	3	17	a	a	DET
ejpam-2421	3	18	more	more	ADV
ejpam-2421	3	19	practical	practical	ADJ
ejpam-2421	3	20	way	way	NOUN
ejpam-2421	3	21	to	to	PART
ejpam-2421	3	22	calculate	calculate	VERB
ejpam-2421	3	23	the	the	DET
ejpam-2421	3	24	fundamental	fundamental	ADJ
ejpam-2421	3	25	unit	unit	NOUN
ejpam-2421	3	26	.	.	PUNCT
ejpam-2421	4	1	where	where	SCONJ
ejpam-2421	4	2	,	,	PUNCT
ejpam-2421	4	3	the	the	DET
ejpam-2421	4	4	period	period	NOUN
ejpam-2421	4	5	in	in	ADP
ejpam-2421	4	6	the	the	DET
ejpam-2421	4	7	continued	continue	VERB
ejpam-2421	4	8	fraction	fraction	NOUN
ejpam-2421	4	9	expansion	expansion	NOUN
ejpam-2421	4	10	of	of	ADP
ejpam-2421	4	11	the	the	DET
ejpam-2421	4	12	quadratic	quadratic	ADJ
ejpam-2421	4	13	irrational	irrational	ADJ
ejpam-2421	4	14	number	number	NOUN
ejpam-2421	4	15	of	of	ADP
ejpam-2421	4	16	the	the	DET
ejpam-2421	4	17	certain	certain	ADJ
ejpam-2421	4	18	real	real	ADJ
ejpam-2421	4	19	quadratic	quadratic	ADJ
ejpam-2421	4	20	fields	field	NOUN
ejpam-2421	4	21	is	be	AUX
ejpam-2421	4	22	equal	equal	ADJ
ejpam-2421	4	23	to	to	ADP
ejpam-2421	4	24	8	8	NUM
ejpam-2421	4	25	.	.	PUNCT
ejpam-2421	5	1	2010	2010	NUM
ejpam-2421	5	2	mathematics	mathematic	NOUN
ejpam-2421	5	3	subject	subject	NOUN
ejpam-2421	5	4	classifications	classification	NOUN
ejpam-2421	5	5	:	:	PUNCT
ejpam-2421	5	6	11a55	11a55	NUM
ejpam-2421	5	7	,	,	PUNCT
ejpam-2421	5	8	11r27	11r27	NUM
ejpam-2421	5	9	key	key	ADJ
ejpam-2421	5	10	words	word	NOUN
ejpam-2421	5	11	and	and	CCONJ
ejpam-2421	5	12	phrases	phrase	NOUN
ejpam-2421	5	13	:	:	PUNCT
ejpam-2421	5	14	real	real	ADJ
ejpam-2421	5	15	quadratic	quadratic	ADJ
ejpam-2421	5	16	field	field	NOUN
ejpam-2421	5	17	,	,	PUNCT
ejpam-2421	5	18	continued	continued	ADJ
ejpam-2421	5	19	fraction	fraction	NOUN
ejpam-2421	5	20	,	,	PUNCT
ejpam-2421	5	21	fundamental	fundamental	ADJ
ejpam-2421	5	22	unit	unit	NOUN
ejpam-2421	5	23	1	1	NUM
ejpam-2421	5	24	.	.	PUNCT
ejpam-2421	6	1	introduction	introduction	NOUN
ejpam-2421	6	2	and	and	CCONJ
ejpam-2421	6	3	notation	notation	NOUN
ejpam-2421	6	4	determination	determination	NOUN
ejpam-2421	6	5	of	of	ADP
ejpam-2421	6	6	the	the	DET
ejpam-2421	6	7	fundamental	fundamental	ADJ
ejpam-2421	6	8	units	unit	NOUN
ejpam-2421	6	9	of	of	ADP
ejpam-2421	6	10	quadratic	quadratic	ADJ
ejpam-2421	6	11	fields	field	NOUN
ejpam-2421	6	12	has	have	VERB
ejpam-2421	6	13	a	a	DET
ejpam-2421	6	14	great	great	ADJ
ejpam-2421	6	15	importance	importance	NOUN
ejpam-2421	6	16	at	at	ADP
ejpam-2421	6	17	many	many	ADJ
ejpam-2421	6	18	branches	branch	NOUN
ejpam-2421	6	19	in	in	ADP
ejpam-2421	6	20	number	number	NOUN
ejpam-2421	6	21	theory	theory	NOUN
ejpam-2421	6	22	.	.	PUNCT
ejpam-2421	7	1	although	although	SCONJ
ejpam-2421	7	2	the	the	DET
ejpam-2421	7	3	fundamental	fundamental	ADJ
ejpam-2421	7	4	units	unit	NOUN
ejpam-2421	7	5	of	of	ADP
ejpam-2421	7	6	real	real	ADJ
ejpam-2421	7	7	quadratic	quadratic	ADJ
ejpam-2421	7	8	fields	field	NOUN
ejpam-2421	7	9	of	of	ADP
ejpam-2421	7	10	richautdegert	richautdegert	NOUN
ejpam-2421	7	11	type	type	NOUN
ejpam-2421	7	12	are	be	AUX
ejpam-2421	7	13	well	well	ADV
ejpam-2421	7	14	-	-	PUNCT
ejpam-2421	7	15	known	know	VERB
ejpam-2421	7	16	,	,	PUNCT
ejpam-2421	7	17	explicit	explicit	ADJ
ejpam-2421	7	18	form	form	NOUN
ejpam-2421	7	19	of	of	ADP
ejpam-2421	7	20	the	the	DET
ejpam-2421	7	21	fundamental	fundamental	ADJ
ejpam-2421	7	22	units	unit	NOUN
ejpam-2421	7	23	are	be	AUX
ejpam-2421	7	24	not	not	PART
ejpam-2421	7	25	known	know	VERB
ejpam-2421	7	26	very	very	ADV
ejpam-2421	7	27	well	well	ADV
ejpam-2421	7	28	and	and	CCONJ
ejpam-2421	7	29	these	these	DET
ejpam-2421	7	30	determinations	determination	NOUN
ejpam-2421	7	31	were	be	AUX
ejpam-2421	7	32	very	very	ADV
ejpam-2421	7	33	limited	limited	ADJ
ejpam-2421	7	34	except	except	SCONJ
ejpam-2421	7	35	for	for	ADP
ejpam-2421	7	36	these	these	DET
ejpam-2421	7	37	type	type	NOUN
ejpam-2421	7	38	an	an	DET
ejpam-2421	7	39	k.	k.	NOUN
ejpam-2421	7	40	therefore	therefore	ADV
ejpam-2421	7	41	,	,	PUNCT
ejpam-2421	7	42	tomita	tomita	PROPN
ejpam-2421	7	43	has	have	AUX
ejpam-2421	7	44	described	describe	VERB
ejpam-2421	7	45	explicitly	explicitly	ADV
ejpam-2421	7	46	the	the	DET
ejpam-2421	7	47	form	form	NOUN
ejpam-2421	7	48	of	of	ADP
ejpam-2421	7	49	the	the	DET
ejpam-2421	7	50	fundamental	fundamental	ADJ
ejpam-2421	7	51	units	unit	NOUN
ejpam-2421	7	52	of	of	ADP
ejpam-2421	7	53	the	the	DET
ejpam-2421	7	54	real	real	ADJ
ejpam-2421	7	55	quadratic	quadratic	ADJ
ejpam-2421	7	56	fields	field	NOUN
ejpam-2421	7	57	q	q	NOUN
ejpam-2421	7	58	(	(	PUNCT
ejpam-2421	7	59	p	p	NOUN
ejpam-2421	7	60	d	d	NOUN
ejpam-2421	7	61	)	)	PUNCT
ejpam-2421	7	62	such	such	ADJ
ejpam-2421	7	63	that	that	SCONJ
ejpam-2421	7	64	d	d	NOUN
ejpam-2421	7	65	is	be	AUX
ejpam-2421	7	66	a	a	DET
ejpam-2421	7	67	square	square	ADJ
ejpam-2421	7	68	-	-	PUNCT
ejpam-2421	7	69	free	free	ADJ
ejpam-2421	7	70	positive	positive	ADJ
ejpam-2421	7	71	integer	integer	NOUN
ejpam-2421	7	72	congruent	congruent	NOUN
ejpam-2421	7	73	to	to	ADP
ejpam-2421	7	74	1	1	NUM
ejpam-2421	7	75	modulo	modulo	NOUN
ejpam-2421	7	76	4	4	NUM
ejpam-2421	7	77	and	and	CCONJ
ejpam-2421	7	78	the	the	DET
ejpam-2421	7	79	period	period	NOUN
ejpam-2421	7	80	kd	kd	PROPN
ejpam-2421	7	81	in	in	ADP
ejpam-2421	7	82	the	the	DET
ejpam-2421	7	83	continued	continue	VERB
ejpam-2421	7	84	fraction	fraction	NOUN
ejpam-2421	7	85	expansion	expansion	NOUN
ejpam-2421	7	86	of	of	ADP
ejpam-2421	7	87	the	the	DET
ejpam-2421	7	88	quadratic	quadratic	ADJ
ejpam-2421	7	89	irrational	irrational	ADJ
ejpam-2421	7	90	number	number	NOUN
ejpam-2421	7	91	ωd	ωd	NOUN
ejpam-2421	8	1	=	=	SYM
ejpam-2421	8	2	(	(	PUNCT
ejpam-2421	8	3	1	1	NUM
ejpam-2421	8	4	+	+	SYM
ejpam-2421	8	5	p	p	X
ejpam-2421	8	6	d	d	PROPN
ejpam-2421	8	7	2	2	NUM
ejpam-2421	8	8	)	)	PUNCT
ejpam-2421	8	9	in	in	ADP
ejpam-2421	8	10	q	q	PROPN
ejpam-2421	8	11	(	(	PUNCT
ejpam-2421	8	12	p	p	NOUN
ejpam-2421	8	13	d	d	NOUN
ejpam-2421	8	14	)	)	PUNCT
ejpam-2421	8	15	is	be	AUX
ejpam-2421	8	16	equal	equal	ADJ
ejpam-2421	8	17	to	to	ADP
ejpam-2421	8	18	3	3	NUM
ejpam-2421	8	19	and	and	CCONJ
ejpam-2421	8	20	4	4	NUM
ejpam-2421	8	21	,	,	PUNCT
ejpam-2421	8	22	5	5	NUM
ejpam-2421	8	23	respectively	respectively	ADV
ejpam-2421	8	24	in	in	ADP
ejpam-2421	8	25	[	[	X
ejpam-2421	8	26	4	4	NUM
ejpam-2421	8	27	]	]	PUNCT
ejpam-2421	8	28	and	and	CCONJ
ejpam-2421	9	1	[	[	X
ejpam-2421	9	2	5	5	NUM
ejpam-2421	9	3	]	]	PUNCT
ejpam-2421	9	4	.	.	PUNCT
ejpam-2421	10	1	later	later	ADV
ejpam-2421	10	2	,	,	PUNCT
ejpam-2421	10	3	explicit	explicit	ADJ
ejpam-2421	10	4	form	form	NOUN
ejpam-2421	10	5	of	of	ADP
ejpam-2421	10	6	the	the	DET
ejpam-2421	10	7	fundamental	fundamental	ADJ
ejpam-2421	10	8	units	unit	NOUN
ejpam-2421	10	9	for	for	ADP
ejpam-2421	10	10	all	all	DET
ejpam-2421	10	11	real	real	ADJ
ejpam-2421	10	12	quadratic	quadratic	ADJ
ejpam-2421	10	13	fields	field	NOUN
ejpam-2421	10	14	q	q	NOUN
ejpam-2421	10	15	(	(	PUNCT
ejpam-2421	10	16	p	p	NOUN
ejpam-2421	10	17	d	d	NOUN
ejpam-2421	10	18	)	)	PUNCT
ejpam-2421	10	19	such	such	ADJ
ejpam-2421	10	20	that	that	SCONJ
ejpam-2421	10	21	the	the	DET
ejpam-2421	10	22	period	period	NOUN
ejpam-2421	10	23	kd	kd	PROPN
ejpam-2421	10	24	in	in	ADP
ejpam-2421	10	25	the	the	DET
ejpam-2421	10	26	continued	continue	VERB
ejpam-2421	10	27	fraction	fraction	NOUN
ejpam-2421	10	28	expansion	expansion	NOUN
ejpam-2421	10	29	of	of	ADP
ejpam-2421	10	30	the	the	DET
ejpam-2421	10	31	quadratic	quadratic	ADJ
ejpam-2421	10	32	irrational	irrational	ADJ
ejpam-2421	10	33	number	number	NOUN
ejpam-2421	10	34	ωd	ωd	ADP
ejpam-2421	10	35	is	be	AUX
ejpam-2421	10	36	equal	equal	ADJ
ejpam-2421	10	37	to	to	ADP
ejpam-2421	10	38	6	6	NUM
ejpam-2421	10	39	,	,	PUNCT
ejpam-2421	10	40	has	have	AUX
ejpam-2421	10	41	been	be	AUX
ejpam-2421	10	42	described	describe	VERB
ejpam-2421	10	43	in	in	ADP
ejpam-2421	10	44	[	[	X
ejpam-2421	10	45	3	3	NUM
ejpam-2421	10	46	]	]	PUNCT
ejpam-2421	10	47	.	.	PUNCT
ejpam-2421	11	1	in	in	ADP
ejpam-2421	11	2	this	this	DET
ejpam-2421	11	3	paper	paper	NOUN
ejpam-2421	11	4	,	,	PUNCT
ejpam-2421	11	5	we	we	PRON
ejpam-2421	11	6	will	will	AUX
ejpam-2421	11	7	deal	deal	VERB
ejpam-2421	11	8	with	with	ADP
ejpam-2421	11	9	all	all	DET
ejpam-2421	11	10	real	real	ADJ
ejpam-2421	11	11	quadratic	quadratic	ADJ
ejpam-2421	11	12	fields	field	NOUN
ejpam-2421	11	13	q	q	NOUN
ejpam-2421	11	14	(	(	PUNCT
ejpam-2421	11	15	p	p	NOUN
ejpam-2421	11	16	d	d	NOUN
ejpam-2421	11	17	)	)	PUNCT
ejpam-2421	11	18	such	such	ADJ
ejpam-2421	11	19	that	that	SCONJ
ejpam-2421	11	20	d	d	NOUN
ejpam-2421	11	21	is	be	AUX
ejpam-2421	11	22	a	a	DET
ejpam-2421	11	23	square	square	ADJ
ejpam-2421	11	24	free	free	ADJ
ejpam-2421	11	25	positive	positive	ADJ
ejpam-2421	11	26	integer	integer	NOUN
ejpam-2421	11	27	congruent	congruent	NOUN
ejpam-2421	11	28	to	to	ADP
ejpam-2421	11	29	1	1	NUM
ejpam-2421	11	30	modulo	modulo	NOUN
ejpam-2421	11	31	4	4	NUM
ejpam-2421	11	32	and	and	CCONJ
ejpam-2421	11	33	the	the	DET
ejpam-2421	11	34	period	period	NOUN
ejpam-2421	11	35	kd	kd	PROPN
ejpam-2421	11	36	in	in	ADP
ejpam-2421	11	37	the	the	DET
ejpam-2421	11	38	continued	continue	VERB
ejpam-2421	11	39	fraction	fraction	NOUN
ejpam-2421	11	40	expansion	expansion	NOUN
ejpam-2421	11	41	of	of	ADP
ejpam-2421	11	42	the	the	DET
ejpam-2421	11	43	quadratic	quadratic	ADJ
ejpam-2421	11	44	irrational	irrational	ADJ
ejpam-2421	11	45	number	number	NOUN
ejpam-2421	11	46	ωd	ωd	NOUN
ejpam-2421	12	1	=	=	SYM
ejpam-2421	13	1	(	(	PUNCT
ejpam-2421	13	2	1	1	NUM
ejpam-2421	13	3	+	+	SYM
ejpam-2421	13	4	p	p	X
ejpam-2421	13	5	d	d	PROPN
ejpam-2421	13	6	2	2	NUM
ejpam-2421	13	7	)	)	PUNCT
ejpam-2421	13	8	in	in	ADP
ejpam-2421	13	9	q	q	PROPN
ejpam-2421	13	10	(	(	PUNCT
ejpam-2421	13	11	p	p	NOUN
ejpam-2421	13	12	d	d	NOUN
ejpam-2421	13	13	)	)	PUNCT
ejpam-2421	13	14	is	be	AUX
ejpam-2421	13	15	equal	equal	ADJ
ejpam-2421	13	16	to	to	ADP
ejpam-2421	13	17	8	8	NUM
ejpam-2421	13	18	and	and	CCONJ
ejpam-2421	13	19	describe	describe	VERB
ejpam-2421	13	20	explicitly	explicitly	ADV
ejpam-2421	13	21	td	td	NOUN
ejpam-2421	13	22	,	,	PUNCT
ejpam-2421	13	23	ud	ud	INTJ
ejpam-2421	13	24	in	in	ADP
ejpam-2421	13	25	the	the	DET
ejpam-2421	13	26	fundamental	fundamental	ADJ
ejpam-2421	13	27	unit	unit	NOUN
ejpam-2421	13	28	ǫd	ǫd	NOUN
ejpam-2421	13	29	=	=	SYM
ejpam-2421	13	30	(	(	PUNCT
ejpam-2421	13	31	td+ud	td+ud	NOUN
ejpam-2421	14	1	p	p	X
ejpam-2421	14	2	d	d	PROPN
ejpam-2421	14	3	2	2	NUM
ejpam-2421	14	4	)	)	PUNCT
ejpam-2421	14	5	>	>	X
ejpam-2421	14	6	1	1	NUM
ejpam-2421	14	7	of	of	ADP
ejpam-2421	14	8	q	q	X
ejpam-2421	14	9	(	(	PUNCT
ejpam-2421	14	10	p	p	NOUN
ejpam-2421	14	11	d	d	NOUN
ejpam-2421	14	12	)	)	PUNCT
ejpam-2421	14	13	and	and	CCONJ
ejpam-2421	14	14	d	d	ADP
ejpam-2421	14	15	itself	itself	PRON
ejpam-2421	14	16	by	by	ADP
ejpam-2421	14	17	using	use	VERB
ejpam-2421	14	18	at	at	ADP
ejpam-2421	14	19	most	most	ADJ
ejpam-2421	14	20	five	five	NUM
ejpam-2421	14	21	parameters	parameter	NOUN
ejpam-2421	14	22	appearing	appear	VERB
ejpam-2421	14	23	in	in	ADP
ejpam-2421	14	24	the	the	DET
ejpam-2421	14	25	continued	continue	VERB
ejpam-2421	14	26	fraction	fraction	NOUN
ejpam-2421	14	27	expansion	expansion	NOUN
ejpam-2421	14	28	of	of	ADP
ejpam-2421	14	29	ωd	ωd	INTJ
ejpam-2421	14	30	.	.	PUNCT
ejpam-2421	15	1	∗corresponding	∗corresponde	VERB
ejpam-2421	15	2	author	author	NOUN
ejpam-2421	15	3	.	.	PUNCT
ejpam-2421	16	1	email	email	NOUN
ejpam-2421	16	2	addresses	address	NOUN
ejpam-2421	16	3	:	:	PUNCT
ejpam-2421	16	4	ozenozer@klu.edu.tr	ozenozer@klu.edu.tr	PROPN
ejpam-2421	16	5	(	(	PUNCT
ejpam-2421	16	6	ö.	ö.	NOUN
ejpam-2421	16	7	özer	özer	NOUN
ejpam-2421	16	8	)	)	PUNCT
ejpam-2421	16	9	,	,	PUNCT
ejpam-2421	16	10	aypekin@istanbul.edu.tr	aypekin@istanbul.edu.tr	INTJ
ejpam-2421	16	11	(	(	PUNCT
ejpam-2421	16	12	a.	a.	NOUN
ejpam-2421	16	13	pekin	pekin	PROPN
ejpam-2421	16	14	)	)	PUNCT
ejpam-2421	16	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2421	17	1	343	343	NUM
ejpam-2421	17	2	c	c	X
ejpam-2421	17	3	©	©	PROPN
ejpam-2421	17	4	2015	2015	NUM
ejpam-2421	17	5	ejpam	ejpam	VERB
ejpam-2421	17	6	all	all	DET
ejpam-2421	17	7	rights	right	NOUN
ejpam-2421	17	8	reserved	reserve	VERB
ejpam-2421	17	9	.	.	PUNCT
ejpam-2421	18	1	ö.	ö.	PROPN
ejpam-2421	18	2	özer	özer	NOUN
ejpam-2421	18	3	,	,	PUNCT
ejpam-2421	18	4	a.	a.	NOUN
ejpam-2421	18	5	pekin	pekin	PROPN
ejpam-2421	18	6	/	/	SYM
ejpam-2421	18	7	eur	eur	PROPN
ejpam-2421	18	8	.	.	PUNCT
ejpam-2421	19	1	j.	j.	PROPN
ejpam-2421	19	2	pure	pure	PROPN
ejpam-2421	19	3	appl	appl	PROPN
ejpam-2421	19	4	.	.	PROPN
ejpam-2421	19	5	math	math	PROPN
ejpam-2421	19	6	,	,	PUNCT
ejpam-2421	19	7	8	8	NUM
ejpam-2421	19	8	(	(	PUNCT
ejpam-2421	19	9	2015	2015	NUM
ejpam-2421	19	10	)	)	PUNCT
ejpam-2421	19	11	,	,	PUNCT
ejpam-2421	19	12	343	343	NUM
ejpam-2421	19	13	-	-	SYM
ejpam-2421	19	14	356	356	NUM
ejpam-2421	19	15	344	344	NUM
ejpam-2421	19	16	let	let	VERB
ejpam-2421	19	17	i(d	i(d	NOUN
ejpam-2421	19	18	)	)	PUNCT
ejpam-2421	19	19	be	be	VERB
ejpam-2421	19	20	the	the	DET
ejpam-2421	19	21	set	set	NOUN
ejpam-2421	19	22	of	of	ADP
ejpam-2421	19	23	all	all	DET
ejpam-2421	19	24	quadratic	quadratic	ADJ
ejpam-2421	19	25	irrational	irrational	ADJ
ejpam-2421	19	26	numbers	number	NOUN
ejpam-2421	19	27	in	in	ADP
ejpam-2421	19	28	q	q	PROPN
ejpam-2421	19	29	(	(	PUNCT
ejpam-2421	19	30	p	p	NOUN
ejpam-2421	19	31	d	d	NOUN
ejpam-2421	19	32	)	)	PUNCT
ejpam-2421	19	33	.	.	PUNCT
ejpam-2421	20	1	for	for	ADP
ejpam-2421	20	2	an	an	DET
ejpam-2421	20	3	element	element	NOUN
ejpam-2421	20	4	ξ	ξ	PROPN
ejpam-2421	20	5	of	of	ADP
ejpam-2421	20	6	i(d	i(d	NOUN
ejpam-2421	20	7	)	)	PUNCT
ejpam-2421	20	8	if	if	SCONJ
ejpam-2421	20	9	ξ	ξ	X
ejpam-2421	20	10	>	>	SYM
ejpam-2421	20	11	1	1	NUM
ejpam-2421	20	12	,	,	PUNCT
ejpam-2421	20	13	−1	−1	NOUN
ejpam-2421	20	14	<	<	X
ejpam-2421	20	15	ξ	ξ	X
ejpam-2421	20	16	′	′	NOUN
ejpam-2421	20	17	<	<	X
ejpam-2421	20	18	0	0	PUNCT
ejpam-2421	21	1	then	then	ADV
ejpam-2421	21	2	ξ	ξ	PROPN
ejpam-2421	21	3	is	be	AUX
ejpam-2421	21	4	called	call	VERB
ejpam-2421	21	5	reduced	reduce	VERB
ejpam-2421	21	6	,	,	PUNCT
ejpam-2421	21	7	where	where	SCONJ
ejpam-2421	21	8	ξ	ξ	X
ejpam-2421	21	9	′	′	NOUN
ejpam-2421	21	10	is	be	AUX
ejpam-2421	21	11	the	the	DET
ejpam-2421	21	12	conjugate	conjugate	NOUN
ejpam-2421	21	13	of	of	ADP
ejpam-2421	21	14	ξ	ξ	PROPN
ejpam-2421	21	15	with	with	ADP
ejpam-2421	21	16	respect	respect	NOUN
ejpam-2421	21	17	to	to	ADP
ejpam-2421	21	18	q.	q.	PROPN
ejpam-2421	21	19	more	more	ADJ
ejpam-2421	21	20	information	information	NOUN
ejpam-2421	21	21	on	on	ADP
ejpam-2421	21	22	reduced	reduced	ADJ
ejpam-2421	21	23	irrational	irrational	ADJ
ejpam-2421	21	24	numbers	number	NOUN
ejpam-2421	21	25	may	may	AUX
ejpam-2421	21	26	be	be	AUX
ejpam-2421	21	27	found	find	VERB
ejpam-2421	21	28	in	in	ADP
ejpam-2421	21	29	[	[	X
ejpam-2421	21	30	2	2	NUM
ejpam-2421	21	31	]	]	PUNCT
ejpam-2421	21	32	.	.	PUNCT
ejpam-2421	22	1	we	we	PRON
ejpam-2421	22	2	denote	denote	VERB
ejpam-2421	22	3	by	by	ADP
ejpam-2421	22	4	r(d	r(d	NOUN
ejpam-2421	22	5	)	)	PUNCT
ejpam-2421	22	6	the	the	DET
ejpam-2421	22	7	set	set	NOUN
ejpam-2421	22	8	of	of	ADP
ejpam-2421	22	9	all	all	DET
ejpam-2421	22	10	reduced	reduce	VERB
ejpam-2421	22	11	quadratic	quadratic	ADJ
ejpam-2421	22	12	irrational	irrational	ADJ
ejpam-2421	22	13	numbers	number	NOUN
ejpam-2421	22	14	in	in	ADP
ejpam-2421	22	15	i(d	i(d	NOUN
ejpam-2421	22	16	)	)	PUNCT
ejpam-2421	22	17	.	.	PUNCT
ejpam-2421	23	1	it	it	PRON
ejpam-2421	23	2	is	be	AUX
ejpam-2421	23	3	well	well	ADV
ejpam-2421	23	4	known	know	VERB
ejpam-2421	23	5	that	that	SCONJ
ejpam-2421	23	6	if	if	SCONJ
ejpam-2421	23	7	an	an	DET
ejpam-2421	23	8	element	element	NOUN
ejpam-2421	23	9	ξ	ξ	PROPN
ejpam-2421	23	10	of	of	ADP
ejpam-2421	23	11	i(d	i(d	NOUN
ejpam-2421	23	12	)	)	PUNCT
ejpam-2421	23	13	is	be	AUX
ejpam-2421	23	14	in	in	ADP
ejpam-2421	23	15	r(d	r(d	NOUN
ejpam-2421	23	16	)	)	PUNCT
ejpam-2421	23	17	then	then	ADV
ejpam-2421	23	18	the	the	DET
ejpam-2421	23	19	continued	continue	VERB
ejpam-2421	23	20	fractional	fractional	ADJ
ejpam-2421	23	21	expansion	expansion	NOUN
ejpam-2421	23	22	of	of	ADP
ejpam-2421	23	23	ξ	ξ	PROPN
ejpam-2421	23	24	is	be	AUX
ejpam-2421	23	25	purely	purely	ADV
ejpam-2421	23	26	periodic	periodic	ADJ
ejpam-2421	23	27	.	.	PUNCT
ejpam-2421	24	1	moreover	moreover	ADV
ejpam-2421	24	2	,	,	PUNCT
ejpam-2421	24	3	the	the	DET
ejpam-2421	24	4	denominator	denominator	NOUN
ejpam-2421	24	5	of	of	ADP
ejpam-2421	24	6	its	its	PRON
ejpam-2421	24	7	modular	modular	ADJ
ejpam-2421	24	8	automorphism	automorphism	NOUN
ejpam-2421	24	9	is	be	AUX
ejpam-2421	24	10	equal	equal	ADJ
ejpam-2421	24	11	to	to	ADP
ejpam-2421	24	12	fundamental	fundamental	ADJ
ejpam-2421	24	13	unit	unit	NOUN
ejpam-2421	24	14	ǫd	ǫd	NOUN
ejpam-2421	24	15	of	of	ADP
ejpam-2421	24	16	q	q	PROPN
ejpam-2421	24	17	(	(	PUNCT
ejpam-2421	24	18	p	p	NOUN
ejpam-2421	24	19	d	d	NOUN
ejpam-2421	24	20	)	)	PUNCT
ejpam-2421	24	21	and	and	CCONJ
ejpam-2421	24	22	the	the	DET
ejpam-2421	24	23	norm	norm	NOUN
ejpam-2421	24	24	of	of	ADP
ejpam-2421	24	25	ǫd	ǫd	NUM
ejpam-2421	24	26	is	be	AUX
ejpam-2421	24	27	(	(	PUNCT
ejpam-2421	24	28	−1)kd	−1)kd	PROPN
ejpam-2421	25	1	[	[	X
ejpam-2421	25	2	3	3	NUM
ejpam-2421	25	3	]	]	PUNCT
ejpam-2421	25	4	.	.	PUNCT
ejpam-2421	26	1	in	in	ADP
ejpam-2421	26	2	this	this	DET
ejpam-2421	26	3	paper	paper	NOUN
ejpam-2421	26	4	[	[	X
ejpam-2421	26	5	x	x	X
ejpam-2421	26	6	]	]	X
ejpam-2421	26	7	means	mean	VERB
ejpam-2421	26	8	the	the	DET
ejpam-2421	26	9	greatest	great	ADJ
ejpam-2421	26	10	integer	integer	NOUN
ejpam-2421	26	11	less	less	ADJ
ejpam-2421	26	12	than	than	ADP
ejpam-2421	26	13	or	or	CCONJ
ejpam-2421	26	14	equal	equal	ADJ
ejpam-2421	26	15	to	to	ADP
ejpam-2421	26	16	x	x	PUNCT
ejpam-2421	26	17	and	and	CCONJ
ejpam-2421	26	18	continued	continued	ADJ
ejpam-2421	26	19	fraction	fraction	NOUN
ejpam-2421	26	20	with	with	ADP
ejpam-2421	26	21	period	period	NOUN
ejpam-2421	26	22	k	k	PROPN
ejpam-2421	26	23	is	be	AUX
ejpam-2421	26	24	generally	generally	ADV
ejpam-2421	26	25	denoted	denote	VERB
ejpam-2421	26	26	by	by	ADP
ejpam-2421	26	27	[	[	X
ejpam-2421	26	28	a0	a0	PROPN
ejpam-2421	26	29	,	,	PUNCT
ejpam-2421	26	30	a1	a1	NOUN
ejpam-2421	26	31	,	,	PUNCT
ejpam-2421	26	32	a2	a2	PROPN
ejpam-2421	26	33	,	,	PUNCT
ejpam-2421	26	34	.	.	PUNCT
ejpam-2421	26	35	.	.	PUNCT
ejpam-2421	27	1	.	.	PUNCT
ejpam-2421	28	1	,	,	PUNCT
ejpam-2421	28	2	ak	ak	PROPN
ejpam-2421	28	3	]	]	PROPN
ejpam-2421	28	4	.	.	PUNCT
ejpam-2421	29	1	2	2	X
ejpam-2421	29	2	.	.	NUM
ejpam-2421	29	3	preliminaries	preliminary	NOUN
ejpam-2421	29	4	and	and	CCONJ
ejpam-2421	29	5	lemmas	lemma	NOUN
ejpam-2421	29	6	in	in	ADP
ejpam-2421	29	7	this	this	DET
ejpam-2421	29	8	section	section	NOUN
ejpam-2421	29	9	some	some	PRON
ejpam-2421	29	10	of	of	ADP
ejpam-2421	29	11	the	the	DET
ejpam-2421	29	12	important	important	ADJ
ejpam-2421	29	13	required	require	VERB
ejpam-2421	29	14	preliminaries	preliminary	NOUN
ejpam-2421	29	15	and	and	CCONJ
ejpam-2421	29	16	lemmas	lemma	NOUN
ejpam-2421	29	17	are	be	AUX
ejpam-2421	29	18	given	give	VERB
ejpam-2421	29	19	.	.	PUNCT
ejpam-2421	30	1	now	now	ADV
ejpam-2421	30	2	,	,	PUNCT
ejpam-2421	30	3	for	for	ADP
ejpam-2421	30	4	any	any	DET
ejpam-2421	30	5	square	square	ADJ
ejpam-2421	30	6	-	-	PUNCT
ejpam-2421	30	7	free	free	ADJ
ejpam-2421	30	8	positive	positive	ADJ
ejpam-2421	30	9	integer	integer	NOUN
ejpam-2421	30	10	d	d	NOUN
ejpam-2421	30	11	,	,	PUNCT
ejpam-2421	30	12	we	we	PRON
ejpam-2421	30	13	can	can	AUX
ejpam-2421	30	14	put	put	VERB
ejpam-2421	30	15	d	d	NOUN
ejpam-2421	30	16	=	=	PUNCT
ejpam-2421	30	17	a2+b	a2+b	NOUN
ejpam-2421	30	18	with	with	ADP
ejpam-2421	30	19	a	a	DET
ejpam-2421	30	20	,	,	PUNCT
ejpam-2421	30	21	b	b	PROPN
ejpam-2421	30	22	∈	∈	PROPN
ejpam-2421	30	23	z	z	NOUN
ejpam-2421	30	24	,	,	PUNCT
ejpam-2421	30	25	0	0	PUNCT
ejpam-2421	30	26	<	<	X
ejpam-2421	30	27	b	b	X
ejpam-2421	30	28	≤	≤	NUM
ejpam-2421	30	29	2a	2a	NUM
ejpam-2421	30	30	.	.	PUNCT
ejpam-2421	31	1	here	here	ADV
ejpam-2421	31	2	,	,	PUNCT
ejpam-2421	31	3	since	since	SCONJ
ejpam-2421	31	4	p	p	PROPN
ejpam-2421	31	5	d	d	X
ejpam-2421	31	6	−	−	PROPN
ejpam-2421	31	7	1	1	NUM
ejpam-2421	31	8	<	<	X
ejpam-2421	31	9	a	a	PRON
ejpam-2421	31	10	<	<	X
ejpam-2421	31	11	p	p	X
ejpam-2421	31	12	d	d	X
ejpam-2421	31	13	the	the	DET
ejpam-2421	31	14	integers	integer	NOUN
ejpam-2421	31	15	a	a	PRON
ejpam-2421	31	16	and	and	CCONJ
ejpam-2421	31	17	b	b	NOUN
ejpam-2421	31	18	are	be	AUX
ejpam-2421	31	19	uniquely	uniquely	ADV
ejpam-2421	31	20	determined	determine	VERB
ejpam-2421	31	21	by	by	ADP
ejpam-2421	31	22	d.	d.	PROPN
ejpam-2421	31	23	let	let	VERB
ejpam-2421	31	24	d	d	PRON
ejpam-2421	31	25	be	be	AUX
ejpam-2421	31	26	a	a	DET
ejpam-2421	31	27	square	square	ADJ
ejpam-2421	31	28	-	-	PUNCT
ejpam-2421	31	29	free	free	ADJ
ejpam-2421	31	30	positive	positive	ADJ
ejpam-2421	31	31	integer	integer	NOUN
ejpam-2421	31	32	congruent	congruent	NOUN
ejpam-2421	31	33	to	to	ADP
ejpam-2421	31	34	1	1	NUM
ejpam-2421	31	35	modulo	modulo	NOUN
ejpam-2421	31	36	4	4	NUM
ejpam-2421	31	37	,	,	PUNCT
ejpam-2421	31	38	then	then	ADV
ejpam-2421	31	39	we	we	PRON
ejpam-2421	31	40	consider	consider	VERB
ejpam-2421	31	41	the	the	DET
ejpam-2421	31	42	following	follow	VERB
ejpam-2421	31	43	two	two	NUM
ejpam-2421	31	44	cases	case	NOUN
ejpam-2421	31	45	:	:	PUNCT
ejpam-2421	31	46	case	case	NOUN
ejpam-2421	31	47	1	1	NUM
ejpam-2421	31	48	.	.	PUNCT
ejpam-2421	32	1	if	if	SCONJ
ejpam-2421	32	2	a	a	PRON
ejpam-2421	32	3	is	be	AUX
ejpam-2421	32	4	even	even	ADV
ejpam-2421	32	5	,	,	PUNCT
ejpam-2421	32	6	then	then	ADV
ejpam-2421	32	7	b	b	X
ejpam-2421	32	8	=	=	SYM
ejpam-2421	32	9	4ℓ+	4ℓ+	NUM
ejpam-2421	32	10	1	1	NUM
ejpam-2421	32	11	with	with	ADP
ejpam-2421	32	12	l	l	PROPN
ejpam-2421	32	13	∈	∈	PROPN
ejpam-2421	32	14	z	z	NOUN
ejpam-2421	32	15	,	,	PUNCT
ejpam-2421	32	16	ℓ≥	ℓ≥	PROPN
ejpam-2421	32	17	0	0	NUM
ejpam-2421	32	18	.	.	PUNCT
ejpam-2421	32	19	case	case	NOUN
ejpam-2421	32	20	2	2	NUM
ejpam-2421	32	21	.	.	PUNCT
ejpam-2421	33	1	if	if	SCONJ
ejpam-2421	33	2	a	a	PRON
ejpam-2421	33	3	is	be	AUX
ejpam-2421	33	4	odd	odd	ADJ
ejpam-2421	33	5	,	,	PUNCT
ejpam-2421	33	6	then	then	ADV
ejpam-2421	33	7	b	b	X
ejpam-2421	33	8	=	=	SYM
ejpam-2421	33	9	4ℓ	4ℓ	NOUN
ejpam-2421	33	10	with	with	ADP
ejpam-2421	33	11	l	l	PROPN
ejpam-2421	33	12	∈	∈	PROPN
ejpam-2421	33	13	z	z	NOUN
ejpam-2421	33	14	,	,	PUNCT
ejpam-2421	33	15	ℓ≥	ℓ≥	PROPN
ejpam-2421	33	16	1	1	X
ejpam-2421	33	17	.	.	PUNCT
ejpam-2421	34	1	let	let	AUX
ejpam-2421	34	2	denote	denote	VERB
ejpam-2421	34	3	by	by	ADP
ejpam-2421	34	4	d	d	PROPN
ejpam-2421	34	5	the	the	DET
ejpam-2421	34	6	set	set	NOUN
ejpam-2421	34	7	of	of	ADP
ejpam-2421	34	8	all	all	DET
ejpam-2421	34	9	positive	positive	ADJ
ejpam-2421	34	10	square	square	ADJ
ejpam-2421	34	11	-	-	PUNCT
ejpam-2421	34	12	free	free	ADJ
ejpam-2421	34	13	integers	integer	NOUN
ejpam-2421	34	14	and	and	CCONJ
ejpam-2421	34	15	by	by	ADP
ejpam-2421	34	16	dt	dt	PROPN
ejpam-2421	34	17	k	k	PROPN
ejpam-2421	34	18	the	the	DET
ejpam-2421	34	19	set	set	NOUN
ejpam-2421	34	20	of	of	ADP
ejpam-2421	34	21	all	all	DET
ejpam-2421	34	22	positive	positive	ADJ
ejpam-2421	34	23	square	square	ADJ
ejpam-2421	34	24	-	-	PUNCT
ejpam-2421	34	25	free	free	ADJ
ejpam-2421	34	26	integer	integer	NOUN
ejpam-2421	34	27	d	d	X
ejpam-2421	35	1	such	such	ADJ
ejpam-2421	35	2	that	that	SCONJ
ejpam-2421	35	3	d	d	PROPN
ejpam-2421	35	4	≡	≡	PROPN
ejpam-2421	35	5	k(8	k(8	PROPN
ejpam-2421	35	6	)	)	PUNCT
ejpam-2421	35	7	and	and	CCONJ
ejpam-2421	35	8	b	b	PROPN
ejpam-2421	35	9	≡	≡	PROPN
ejpam-2421	35	10	t(8	t(8	PROPN
ejpam-2421	35	11	)	)	PUNCT
ejpam-2421	35	12	.	.	PUNCT
ejpam-2421	36	1	hence	hence	ADV
ejpam-2421	36	2	,	,	PUNCT
ejpam-2421	36	3	we	we	PRON
ejpam-2421	36	4	have	have	VERB
ejpam-2421	36	5	dt	dt	X
ejpam-2421	37	1	k	k	X
ejpam-2421	37	2	=	=	PUNCT
ejpam-2421	37	3	{	{	PUNCT
ejpam-2421	37	4	d	d	X
ejpam-2421	37	5	∈	∈	PROPN
ejpam-2421	37	6	z	z	NOUN
ejpam-2421	37	7	|	|	NOUN
ejpam-2421	37	8	d	d	PROPN
ejpam-2421	37	9	≡	≡	PROPN
ejpam-2421	37	10	k(8	k(8	PROPN
ejpam-2421	37	11	)	)	PUNCT
ejpam-2421	37	12	,	,	PUNCT
ejpam-2421	37	13	b	b	PROPN
ejpam-2421	37	14	≡	≡	PROPN
ejpam-2421	37	15	t(8	t(8	PROPN
ejpam-2421	37	16	)	)	PUNCT
ejpam-2421	37	17	}	}	PUNCT
ejpam-2421	37	18	.	.	PUNCT
ejpam-2421	38	1	then	then	ADV
ejpam-2421	38	2	,	,	PUNCT
ejpam-2421	38	3	we	we	PRON
ejpam-2421	38	4	get	get	VERB
ejpam-2421	38	5	some	some	DET
ejpam-2421	38	6	remarks	remark	NOUN
ejpam-2421	38	7	as	as	SCONJ
ejpam-2421	38	8	follows	follow	VERB
ejpam-2421	38	9	:	:	PUNCT
ejpam-2421	38	10	remark	remark	NOUN
ejpam-2421	38	11	1	1	NUM
ejpam-2421	38	12	.	.	PUNCT
ejpam-2421	39	1	d	d	NOUN
ejpam-2421	39	2	can	can	AUX
ejpam-2421	39	3	be	be	AUX
ejpam-2421	39	4	congruent	congruent	ADJ
ejpam-2421	39	5	to	to	ADP
ejpam-2421	39	6	1	1	NUM
ejpam-2421	39	7	or	or	CCONJ
ejpam-2421	39	8	5	5	NUM
ejpam-2421	39	9	modulo	modulo	NOUN
ejpam-2421	39	10	8	8	NUM
ejpam-2421	39	11	since	since	SCONJ
ejpam-2421	39	12	d	d	PROPN
ejpam-2421	39	13	is	be	AUX
ejpam-2421	39	14	congruent	congruent	ADJ
ejpam-2421	39	15	to	to	ADP
ejpam-2421	39	16	1	1	NUM
ejpam-2421	39	17	modulo	modulo	NOUN
ejpam-2421	39	18	4	4	NUM
ejpam-2421	39	19	.	.	PUNCT
ejpam-2421	39	20	in	in	ADP
ejpam-2421	39	21	the	the	DET
ejpam-2421	39	22	case	case	NOUN
ejpam-2421	39	23	of	of	ADP
ejpam-2421	39	24	d	d	PROPN
ejpam-2421	39	25	≡	≡	PROPN
ejpam-2421	39	26	1(8	1(8	NUM
ejpam-2421	39	27	)	)	PUNCT
ejpam-2421	39	28	,	,	PUNCT
ejpam-2421	39	29	b	b	NOUN
ejpam-2421	39	30	can	can	AUX
ejpam-2421	39	31	be	be	AUX
ejpam-2421	39	32	congruent	congruent	ADJ
ejpam-2421	39	33	to	to	ADP
ejpam-2421	39	34	0	0	NUM
ejpam-2421	39	35	,	,	PUNCT
ejpam-2421	39	36	1	1	NUM
ejpam-2421	39	37	or	or	CCONJ
ejpam-2421	39	38	5	5	NUM
ejpam-2421	39	39	modulo	modulo	NOUN
ejpam-2421	39	40	8	8	NUM
ejpam-2421	39	41	.	.	PUNCT
ejpam-2421	40	1	therefore	therefore	ADV
ejpam-2421	40	2	,	,	PUNCT
ejpam-2421	40	3	the	the	DET
ejpam-2421	40	4	set	set	NOUN
ejpam-2421	40	5	of	of	ADP
ejpam-2421	40	6	all	all	DET
ejpam-2421	40	7	positive	positive	ADJ
ejpam-2421	40	8	square	square	ADJ
ejpam-2421	40	9	-	-	PUNCT
ejpam-2421	40	10	free	free	ADJ
ejpam-2421	40	11	integers	integer	NOUN
ejpam-2421	40	12	congruent	congruent	ADJ
ejpam-2421	40	13	to	to	ADP
ejpam-2421	40	14	1	1	NUM
ejpam-2421	40	15	modulo	modulo	NOUN
ejpam-2421	40	16	8	8	NUM
ejpam-2421	40	17	is	be	AUX
ejpam-2421	40	18	equal	equal	ADJ
ejpam-2421	40	19	d0	d0	NOUN
ejpam-2421	40	20	1∪d1	1∪d1	X
ejpam-2421	40	21	1∪d5	1∪d5	NOUN
ejpam-2421	40	22	1	1	NUM
ejpam-2421	40	23	.	.	PUNCT
ejpam-2421	41	1	thus	thus	ADV
ejpam-2421	41	2	the	the	DET
ejpam-2421	41	3	set	set	NOUN
ejpam-2421	41	4	of	of	ADP
ejpam-2421	41	5	all	all	DET
ejpam-2421	41	6	positive	positive	ADJ
ejpam-2421	41	7	square	square	ADJ
ejpam-2421	41	8	free	free	ADJ
ejpam-2421	41	9	integers	integer	NOUN
ejpam-2421	41	10	congruent	congruent	ADJ
ejpam-2421	41	11	to1	to1	PROPN
ejpam-2421	41	12	modulo	modulo	PROPN
ejpam-2421	41	13	8	8	NUM
ejpam-2421	41	14	is	be	AUX
ejpam-2421	41	15	the	the	DET
ejpam-2421	41	16	union	union	NOUN
ejpam-2421	41	17	of	of	ADP
ejpam-2421	41	18	d0	d0	PROPN
ejpam-2421	41	19	1	1	NUM
ejpam-2421	41	20	,	,	PUNCT
ejpam-2421	41	21	d1	d1	PROPN
ejpam-2421	41	22	1	1	NUM
ejpam-2421	41	23	,	,	PUNCT
ejpam-2421	41	24	d5	d5	NOUN
ejpam-2421	41	25	1	1	NUM
ejpam-2421	41	26	.	.	PUNCT
ejpam-2421	42	1	in	in	ADP
ejpam-2421	42	2	the	the	DET
ejpam-2421	42	3	case	case	NOUN
ejpam-2421	42	4	of	of	ADP
ejpam-2421	42	5	d	d	PROPN
ejpam-2421	42	6	≡	≡	PROPN
ejpam-2421	42	7	5(8	5(8	NUM
ejpam-2421	42	8	)	)	PUNCT
ejpam-2421	42	9	,	,	PUNCT
ejpam-2421	42	10	b	b	NOUN
ejpam-2421	42	11	can	can	AUX
ejpam-2421	42	12	be	be	AUX
ejpam-2421	42	13	congruent	congruent	ADJ
ejpam-2421	42	14	to	to	ADP
ejpam-2421	42	15	1	1	NUM
ejpam-2421	42	16	,	,	PUNCT
ejpam-2421	42	17	4	4	NUM
ejpam-2421	42	18	or	or	CCONJ
ejpam-2421	42	19	5	5	NUM
ejpam-2421	42	20	modulo	modulo	NOUN
ejpam-2421	42	21	8	8	NUM
ejpam-2421	42	22	.	.	PUNCT
ejpam-2421	43	1	so	so	ADV
ejpam-2421	43	2	the	the	DET
ejpam-2421	43	3	set	set	NOUN
ejpam-2421	43	4	of	of	ADP
ejpam-2421	43	5	all	all	DET
ejpam-2421	43	6	positive	positive	ADJ
ejpam-2421	43	7	square	square	ADJ
ejpam-2421	43	8	-	-	PUNCT
ejpam-2421	43	9	free	free	ADJ
ejpam-2421	43	10	integers	integer	NOUN
ejpam-2421	43	11	congruent	congruent	ADJ
ejpam-2421	43	12	to	to	ADP
ejpam-2421	43	13	5	5	NUM
ejpam-2421	43	14	modulo	modulo	NOUN
ejpam-2421	43	15	8	8	NUM
ejpam-2421	43	16	is	be	AUX
ejpam-2421	43	17	equal	equal	ADJ
ejpam-2421	43	18	to	to	ADP
ejpam-2421	43	19	d1	d1	PROPN
ejpam-2421	43	20	5	5	NUM
ejpam-2421	43	21	∪	∪	ADJ
ejpam-2421	43	22	d4	d4	PROPN
ejpam-2421	43	23	5	5	NUM
ejpam-2421	43	24	∪	∪	NOUN
ejpam-2421	43	25	d5	d5	NOUN
ejpam-2421	43	26	5	5	NUM
ejpam-2421	43	27	.	.	PUNCT
ejpam-2421	43	28	remark	remark	NOUN
ejpam-2421	43	29	2	2	NUM
ejpam-2421	43	30	.	.	PUNCT
ejpam-2421	44	1	let	let	VERB
ejpam-2421	44	2	d	d	PRON
ejpam-2421	44	3	be	be	AUX
ejpam-2421	44	4	a	a	DET
ejpam-2421	44	5	square	square	ADJ
ejpam-2421	44	6	-	-	PUNCT
ejpam-2421	44	7	free	free	ADJ
ejpam-2421	44	8	positive	positive	ADJ
ejpam-2421	44	9	integer	integer	NOUN
ejpam-2421	44	10	congruent	congruent	NOUN
ejpam-2421	44	11	to	to	ADP
ejpam-2421	44	12	1	1	NUM
ejpam-2421	44	13	modulo	modulo	NOUN
ejpam-2421	44	14	4	4	NUM
ejpam-2421	44	15	,	,	PUNCT
ejpam-2421	44	16	then	then	ADV
ejpam-2421	44	17	:	:	PUNCT
ejpam-2421	44	18	•	•	ADP
ejpam-2421	44	19	if	if	SCONJ
ejpam-2421	44	20	a	a	PRON
ejpam-2421	44	21	is	be	AUX
ejpam-2421	44	22	even	even	ADV
ejpam-2421	44	23	;	;	PUNCT
ejpam-2421	44	24	b	b	X
ejpam-2421	44	25	can	can	AUX
ejpam-2421	44	26	only	only	ADV
ejpam-2421	44	27	be	be	AUX
ejpam-2421	44	28	congruent	congruent	ADJ
ejpam-2421	44	29	to	to	ADP
ejpam-2421	44	30	1	1	NUM
ejpam-2421	44	31	or	or	CCONJ
ejpam-2421	44	32	5	5	NUM
ejpam-2421	44	33	modulo	modulo	NOUN
ejpam-2421	44	34	8	8	NUM
ejpam-2421	44	35	since	since	SCONJ
ejpam-2421	44	36	b	b	PROPN
ejpam-2421	44	37	≡	≡	PROPN
ejpam-2421	44	38	1(mod4	1(mod4	NUM
ejpam-2421	44	39	)	)	PUNCT
ejpam-2421	44	40	when	when	SCONJ
ejpam-2421	44	41	a	a	PRON
ejpam-2421	44	42	is	be	AUX
ejpam-2421	44	43	even	even	ADV
ejpam-2421	44	44	.	.	PUNCT
ejpam-2421	45	1	then	then	ADV
ejpam-2421	45	2	,	,	PUNCT
ejpam-2421	45	3	d	d	NOUN
ejpam-2421	45	4	belongs	belong	VERB
ejpam-2421	45	5	to	to	ADP
ejpam-2421	45	6	d1	d1	PROPN
ejpam-2421	45	7	5	5	NUM
ejpam-2421	45	8	∪	∪	NOUN
ejpam-2421	45	9	d5	d5	NOUN
ejpam-2421	45	10	5	5	NUM
ejpam-2421	45	11	∪	∪	NOUN
ejpam-2421	45	12	d5	d5	NOUN
ejpam-2421	45	13	1	1	NUM
ejpam-2421	45	14	∪	∪	ADP
ejpam-2421	45	15	d1	d1	PROPN
ejpam-2421	45	16	1	1	NUM
ejpam-2421	45	17	in	in	ADP
ejpam-2421	45	18	the	the	DET
ejpam-2421	45	19	case	case	NOUN
ejpam-2421	45	20	of	of	ADP
ejpam-2421	45	21	a	a	PRON
ejpam-2421	45	22	is	be	AUX
ejpam-2421	45	23	even	even	ADV
ejpam-2421	45	24	.	.	PUNCT
ejpam-2421	46	1	•	•	INTJ
ejpam-2421	46	2	if	if	SCONJ
ejpam-2421	46	3	a	a	PRON
ejpam-2421	46	4	is	be	AUX
ejpam-2421	46	5	odd	odd	ADJ
ejpam-2421	46	6	;	;	PUNCT
ejpam-2421	46	7	b	b	X
ejpam-2421	46	8	can	can	AUX
ejpam-2421	46	9	be	be	AUX
ejpam-2421	46	10	only	only	ADV
ejpam-2421	46	11	be	be	AUX
ejpam-2421	46	12	congruent	congruent	ADJ
ejpam-2421	46	13	to	to	ADP
ejpam-2421	46	14	0	0	NUM
ejpam-2421	46	15	or	or	CCONJ
ejpam-2421	46	16	4	4	NUM
ejpam-2421	46	17	modulo	modulo	NOUN
ejpam-2421	46	18	8	8	NUM
ejpam-2421	46	19	since	since	SCONJ
ejpam-2421	46	20	b	b	PROPN
ejpam-2421	46	21	≡	≡	PROPN
ejpam-2421	46	22	0(mod4	0(mod4	NUM
ejpam-2421	46	23	)	)	PUNCT
ejpam-2421	46	24	when	when	SCONJ
ejpam-2421	46	25	a	a	PRON
ejpam-2421	46	26	is	be	AUX
ejpam-2421	46	27	odd	odd	ADJ
ejpam-2421	46	28	.	.	PUNCT
ejpam-2421	47	1	then	then	ADV
ejpam-2421	47	2	,	,	PUNCT
ejpam-2421	47	3	d	d	NOUN
ejpam-2421	47	4	belongs	belong	VERB
ejpam-2421	47	5	to	to	ADP
ejpam-2421	47	6	d0	d0	NOUN
ejpam-2421	47	7	1	1	NUM
ejpam-2421	47	8	∪	∪	NOUN
ejpam-2421	47	9	d4	d4	PROPN
ejpam-2421	47	10	5	5	NUM
ejpam-2421	47	11	in	in	ADP
ejpam-2421	47	12	the	the	DET
ejpam-2421	47	13	case	case	NOUN
ejpam-2421	47	14	of	of	ADP
ejpam-2421	47	15	a	a	PRON
ejpam-2421	47	16	is	be	AUX
ejpam-2421	47	17	odd	odd	ADJ
ejpam-2421	47	18	.	.	PUNCT
ejpam-2421	48	1	remark	remark	PROPN
ejpam-2421	48	2	3	3	NUM
ejpam-2421	48	3	.	.	PUNCT
ejpam-2421	49	1	the	the	DET
ejpam-2421	49	2	sets	set	NOUN
ejpam-2421	49	3	d0	d0	NOUN
ejpam-2421	49	4	1	1	NUM
ejpam-2421	49	5	,	,	PUNCT
ejpam-2421	49	6	d1	d1	PROPN
ejpam-2421	49	7	1	1	NUM
ejpam-2421	49	8	,	,	PUNCT
ejpam-2421	49	9	d5	d5	NOUN
ejpam-2421	49	10	1	1	NUM
ejpam-2421	49	11	,	,	PUNCT
ejpam-2421	49	12	d1	d1	PROPN
ejpam-2421	49	13	5	5	NUM
ejpam-2421	49	14	,	,	PUNCT
ejpam-2421	49	15	d4	d4	PROPN
ejpam-2421	49	16	5	5	NUM
ejpam-2421	49	17	and	and	CCONJ
ejpam-2421	49	18	d5	d5	NOUN
ejpam-2421	49	19	5	5	NUM
ejpam-2421	49	20	are	be	AUX
ejpam-2421	49	21	represented	represent	VERB
ejpam-2421	49	22	as	as	SCONJ
ejpam-2421	49	23	follows	follow	VERB
ejpam-2421	49	24	:	:	PUNCT
ejpam-2421	49	25	d0	d0	NOUN
ejpam-2421	49	26	1	1	NUM
ejpam-2421	49	27	=	=	NOUN
ejpam-2421	49	28	{	{	PUNCT
ejpam-2421	49	29	d	d	NOUN
ejpam-2421	49	30	∈	∈	PROPN
ejpam-2421	50	1	d	d	NOUN
ejpam-2421	50	2	|	|	NOUN
ejpam-2421	50	3	d	d	PROPN
ejpam-2421	50	4	=	=	PROPN
ejpam-2421	50	5	a2	a2	PROPN
ejpam-2421	50	6	+	+	CCONJ
ejpam-2421	50	7	8	8	NUM
ejpam-2421	50	8	m	m	NOUN
ejpam-2421	50	9	,	,	PUNCT
ejpam-2421	50	10	a	a	DET
ejpam-2421	50	11	≡	≡	PROPN
ejpam-2421	50	12	1(mod2	1(mod2	NUM
ejpam-2421	50	13	)	)	PUNCT
ejpam-2421	50	14	,	,	PUNCT
ejpam-2421	50	15	0	0	PUNCT
ejpam-2421	50	16	<	<	X
ejpam-2421	50	17	4	4	NUM
ejpam-2421	50	18	m	m	NOUN
ejpam-2421	50	19	<	<	X
ejpam-2421	50	20	a	a	PRON
ejpam-2421	50	21	}	}	PUNCT
ejpam-2421	50	22	d1	d1	NOUN
ejpam-2421	50	23	1	1	NUM
ejpam-2421	50	24	=	=	NOUN
ejpam-2421	50	25	{	{	PUNCT
ejpam-2421	50	26	d	d	NOUN
ejpam-2421	50	27	∈	∈	PROPN
ejpam-2421	51	1	d	d	NOUN
ejpam-2421	51	2	|	|	NOUN
ejpam-2421	51	3	d	d	PROPN
ejpam-2421	51	4	=	=	PROPN
ejpam-2421	51	5	a2	a2	PROPN
ejpam-2421	51	6	+	+	CCONJ
ejpam-2421	51	7	8m+	8m+	NUM
ejpam-2421	51	8	1	1	NUM
ejpam-2421	51	9	,	,	PUNCT
ejpam-2421	51	10	a	a	DET
ejpam-2421	51	11	≡	≡	PROPN
ejpam-2421	51	12	0(mod4	0(mod4	NUM
ejpam-2421	51	13	)	)	PUNCT
ejpam-2421	51	14	,	,	PUNCT
ejpam-2421	51	15	0≤	0≤	NUM
ejpam-2421	51	16	4	4	NUM
ejpam-2421	51	17	m	m	NOUN
ejpam-2421	51	18	<	<	X
ejpam-2421	51	19	a	a	DET
ejpam-2421	51	20	}	}	PUNCT
ejpam-2421	51	21	d5	d5	NOUN
ejpam-2421	51	22	1	1	NUM
ejpam-2421	51	23	=	=	NOUN
ejpam-2421	51	24	{	{	PUNCT
ejpam-2421	51	25	d	d	NOUN
ejpam-2421	51	26	∈	∈	PROPN
ejpam-2421	52	1	d	d	NOUN
ejpam-2421	52	2	|	|	NOUN
ejpam-2421	52	3	d	d	PROPN
ejpam-2421	52	4	=	=	PROPN
ejpam-2421	52	5	a2	a2	PROPN
ejpam-2421	52	6	+	+	CCONJ
ejpam-2421	52	7	8m+	8m+	NUM
ejpam-2421	52	8	5	5	NUM
ejpam-2421	52	9	,	,	PUNCT
ejpam-2421	52	10	a	a	DET
ejpam-2421	52	11	≡	≡	PROPN
ejpam-2421	52	12	2(mod4	2(mod4	NUM
ejpam-2421	52	13	)	)	PUNCT
ejpam-2421	52	14	,	,	PUNCT
ejpam-2421	52	15	0≤	0≤	NUM
ejpam-2421	52	16	4	4	NUM
ejpam-2421	52	17	m	m	NOUN
ejpam-2421	52	18	<	<	X
ejpam-2421	52	19	a−	a−	PROPN
ejpam-2421	52	20	2	2	NUM
ejpam-2421	52	21	}	}	PUNCT
ejpam-2421	52	22	ö.	ö.	NOUN
ejpam-2421	52	23	özer	özer	NOUN
ejpam-2421	52	24	,	,	PUNCT
ejpam-2421	52	25	a.	a.	NOUN
ejpam-2421	52	26	pekin	pekin	PROPN
ejpam-2421	52	27	/	/	SYM
ejpam-2421	52	28	eur	eur	PROPN
ejpam-2421	52	29	.	.	PUNCT
ejpam-2421	53	1	j.	j.	PROPN
ejpam-2421	53	2	pure	pure	PROPN
ejpam-2421	53	3	appl	appl	PROPN
ejpam-2421	53	4	.	.	PROPN
ejpam-2421	53	5	math	math	PROPN
ejpam-2421	53	6	,	,	PUNCT
ejpam-2421	53	7	8	8	NUM
ejpam-2421	53	8	(	(	PUNCT
ejpam-2421	53	9	2015	2015	NUM
ejpam-2421	53	10	)	)	PUNCT
ejpam-2421	53	11	,	,	PUNCT
ejpam-2421	53	12	343	343	NUM
ejpam-2421	53	13	-	-	SYM
ejpam-2421	53	14	356	356	NUM
ejpam-2421	53	15	345	345	NUM
ejpam-2421	53	16	d1	d1	NOUN
ejpam-2421	53	17	5	5	NUM
ejpam-2421	53	18	=	=	NOUN
ejpam-2421	53	19	{	{	PUNCT
ejpam-2421	53	20	d	d	NOUN
ejpam-2421	53	21	∈	∈	PROPN
ejpam-2421	54	1	d	d	NOUN
ejpam-2421	54	2	|	|	NOUN
ejpam-2421	54	3	d	d	PROPN
ejpam-2421	54	4	=	=	PROPN
ejpam-2421	54	5	a2	a2	PROPN
ejpam-2421	54	6	+	+	CCONJ
ejpam-2421	54	7	8m+	8m+	NUM
ejpam-2421	54	8	1	1	NUM
ejpam-2421	54	9	,	,	PUNCT
ejpam-2421	54	10	a	a	DET
ejpam-2421	54	11	≡	≡	PROPN
ejpam-2421	54	12	2(mod4	2(mod4	NUM
ejpam-2421	54	13	)	)	PUNCT
ejpam-2421	54	14	,	,	PUNCT
ejpam-2421	54	15	0≤	0≤	NUM
ejpam-2421	54	16	4	4	NUM
ejpam-2421	54	17	m	m	NOUN
ejpam-2421	54	18	<	<	X
ejpam-2421	54	19	a	a	PRON
ejpam-2421	54	20	}	}	PUNCT
ejpam-2421	54	21	d4	d4	PROPN
ejpam-2421	54	22	5	5	NUM
ejpam-2421	54	23	=	=	NOUN
ejpam-2421	54	24	{	{	PUNCT
ejpam-2421	54	25	d	d	NOUN
ejpam-2421	54	26	∈	∈	PROPN
ejpam-2421	55	1	d	d	NOUN
ejpam-2421	55	2	|	|	NOUN
ejpam-2421	55	3	d	d	PROPN
ejpam-2421	55	4	=	=	PROPN
ejpam-2421	55	5	a2	a2	PROPN
ejpam-2421	55	6	+	+	CCONJ
ejpam-2421	55	7	8m+	8m+	NUM
ejpam-2421	55	8	4	4	NUM
ejpam-2421	55	9	,	,	PUNCT
ejpam-2421	55	10	a	a	DET
ejpam-2421	55	11	≡	≡	PROPN
ejpam-2421	55	12	1(mod2	1(mod2	NUM
ejpam-2421	55	13	)	)	PUNCT
ejpam-2421	55	14	,	,	PUNCT
ejpam-2421	55	15	0≤	0≤	NUM
ejpam-2421	55	16	4	4	NUM
ejpam-2421	55	17	m	m	NOUN
ejpam-2421	55	18	<	<	X
ejpam-2421	55	19	a−	a−	PROPN
ejpam-2421	55	20	2	2	NUM
ejpam-2421	55	21	}	}	PUNCT
ejpam-2421	55	22	d5	d5	NOUN
ejpam-2421	55	23	5	5	NUM
ejpam-2421	55	24	=	=	NOUN
ejpam-2421	55	25	{	{	PUNCT
ejpam-2421	55	26	d	d	NOUN
ejpam-2421	55	27	∈	∈	PROPN
ejpam-2421	56	1	d	d	NOUN
ejpam-2421	56	2	|	|	NOUN
ejpam-2421	56	3	d	d	PROPN
ejpam-2421	56	4	=	=	PROPN
ejpam-2421	56	5	a2	a2	PROPN
ejpam-2421	56	6	+	+	CCONJ
ejpam-2421	56	7	8m+	8m+	NUM
ejpam-2421	56	8	5	5	NUM
ejpam-2421	56	9	,	,	PUNCT
ejpam-2421	56	10	a	a	DET
ejpam-2421	56	11	≡	≡	PROPN
ejpam-2421	56	12	0(mod4	0(mod4	NUM
ejpam-2421	56	13	)	)	PUNCT
ejpam-2421	56	14	,	,	PUNCT
ejpam-2421	56	15	0≤	0≤	NUM
ejpam-2421	56	16	4	4	NUM
ejpam-2421	56	17	m	m	NOUN
ejpam-2421	56	18	<	<	X
ejpam-2421	56	19	a−	a−	PROPN
ejpam-2421	56	20	2	2	NUM
ejpam-2421	56	21	}	}	PUNCT
ejpam-2421	56	22	now	now	ADV
ejpam-2421	56	23	in	in	ADP
ejpam-2421	56	24	order	order	NOUN
ejpam-2421	56	25	to	to	PART
ejpam-2421	56	26	prove	prove	VERB
ejpam-2421	56	27	our	our	PRON
ejpam-2421	56	28	theorems	theorem	NOUN
ejpam-2421	56	29	we	we	PRON
ejpam-2421	56	30	need	need	VERB
ejpam-2421	56	31	the	the	DET
ejpam-2421	56	32	following	follow	VERB
ejpam-2421	56	33	lemmas	lemmas	NOUN
ejpam-2421	56	34	.	.	PUNCT
ejpam-2421	57	1	lemma	lemma	PROPN
ejpam-2421	57	2	1	1	NUM
ejpam-2421	57	3	.	.	PUNCT
ejpam-2421	58	1	for	for	ADP
ejpam-2421	58	2	a	a	DET
ejpam-2421	58	3	square	square	ADJ
ejpam-2421	58	4	-	-	PUNCT
ejpam-2421	58	5	free	free	ADJ
ejpam-2421	58	6	positive	positive	ADJ
ejpam-2421	58	7	integer	integer	NOUN
ejpam-2421	58	8	d	d	PROPN
ejpam-2421	58	9	>	>	X
ejpam-2421	58	10	5	5	NUM
ejpam-2421	58	11	congruent	congruent	ADJ
ejpam-2421	58	12	to	to	ADP
ejpam-2421	58	13	1	1	NUM
ejpam-2421	58	14	modulo	modulo	NOUN
ejpam-2421	58	15	4	4	NUM
ejpam-2421	58	16	,	,	PUNCT
ejpam-2421	58	17	we	we	PRON
ejpam-2421	58	18	putωd	putωd	VERB
ejpam-2421	58	19	=	=	PUNCT
ejpam-2421	58	20	(	(	PUNCT
ejpam-2421	58	21	1	1	NUM
ejpam-2421	58	22	+	+	SYM
ejpam-2421	58	23	p	p	X
ejpam-2421	58	24	d	d	PROPN
ejpam-2421	58	25	2	2	NUM
ejpam-2421	58	26	)	)	PUNCT
ejpam-2421	58	27	,	,	PUNCT
ejpam-2421	58	28	q0	q0	NOUN
ejpam-2421	58	29	=	=	PUNCT
ejpam-2421	59	1	[	[	X
ejpam-2421	59	2	ωd	ωd	X
ejpam-2421	59	3	]	]	X
ejpam-2421	59	4	ωr	ωr	NOUN
ejpam-2421	59	5	=	=	PUNCT
ejpam-2421	59	6	q0	q0	PROPN
ejpam-2421	59	7	−	−	PROPN
ejpam-2421	59	8	1	1	NUM
ejpam-2421	59	9	+	+	NOUN
ejpam-2421	59	10	ω	ω	NOUN
ejpam-2421	59	11	.	.	PUNCT
ejpam-2421	60	1	then	then	ADV
ejpam-2421	60	2	ωd	ωd	INTJ
ejpam-2421	60	3	/∈	/∈	PUNCT
ejpam-2421	60	4	r(d	r(d	NOUN
ejpam-2421	60	5	)	)	PUNCT
ejpam-2421	60	6	,	,	PUNCT
ejpam-2421	60	7	but	but	CCONJ
ejpam-2421	60	8	ωr	ωr	ADP
ejpam-2421	60	9	∈	∈	PROPN
ejpam-2421	60	10	r(d	r(d	NOUN
ejpam-2421	60	11	)	)	PUNCT
ejpam-2421	60	12	holds	hold	VERB
ejpam-2421	60	13	.	.	PUNCT
ejpam-2421	61	1	moreover	moreover	ADV
ejpam-2421	61	2	for	for	ADP
ejpam-2421	61	3	the	the	DET
ejpam-2421	61	4	period	period	NOUN
ejpam-2421	61	5	k	k	PROPN
ejpam-2421	61	6	of	of	ADP
ejpam-2421	61	7	ωr	ωr	PROPN
ejpam-2421	61	8	,	,	PUNCT
ejpam-2421	61	9	we	we	PRON
ejpam-2421	61	10	get	get	VERB
ejpam-2421	61	11	ωr	ωr	ADV
ejpam-2421	61	12	=	=	PUNCT
ejpam-2421	62	1	[	[	X
ejpam-2421	62	2	2q0	2q0	NUM
ejpam-2421	62	3	−	−	NOUN
ejpam-2421	62	4	1,q1	1,q1	NUM
ejpam-2421	62	5	,	,	PUNCT
ejpam-2421	62	6	.	.	PUNCT
ejpam-2421	62	7	.	.	PUNCT
ejpam-2421	62	8	.	.	PUNCT
ejpam-2421	63	1	,	,	PUNCT
ejpam-2421	63	2	qk−1	qk−1	PROPN
ejpam-2421	63	3	]	]	PUNCT
ejpam-2421	63	4	and	and	CCONJ
ejpam-2421	63	5	ωd	ωd	X
ejpam-2421	63	6	=	=	SYM
ejpam-2421	64	1	[	[	X
ejpam-2421	64	2	q0,q1	q0,q1	PROPN
ejpam-2421	64	3	,	,	PUNCT
ejpam-2421	64	4	.	.	PUNCT
ejpam-2421	64	5	.	.	PUNCT
ejpam-2421	65	1	.	.	PUNCT
ejpam-2421	66	1	,	,	PUNCT
ejpam-2421	66	2	qk−1	qk−1	PROPN
ejpam-2421	66	3	,	,	PUNCT
ejpam-2421	66	4	2q0	2q0	NUM
ejpam-2421	66	5	−	−	NOUN
ejpam-2421	66	6	1	1	NUM
ejpam-2421	66	7	]	]	PUNCT
ejpam-2421	66	8	.	.	PUNCT
ejpam-2421	67	1	furthermore	furthermore	ADV
ejpam-2421	67	2	,	,	PUNCT
ejpam-2421	67	3	let	let	VERB
ejpam-2421	67	4	ωr	ωr	VERB
ejpam-2421	67	5	=	=	PUNCT
ejpam-2421	67	6	(	(	PUNCT
ejpam-2421	67	7	pk−1ωr+pk−2	pk−1ωr+pk−2	NOUN
ejpam-2421	67	8	)	)	PUNCT
ejpam-2421	67	9	(	(	PUNCT
ejpam-2421	67	10	qk−1ωr+qk−2	qk−1ωr+qk−2	NOUN
ejpam-2421	67	11	)	)	PUNCT
ejpam-2421	67	12	=	=	PUNCT
ejpam-2421	68	1	[	[	X
ejpam-2421	68	2	2q0	2q0	NUM
ejpam-2421	68	3	−	−	NOUN
ejpam-2421	68	4	1,q1	1,q1	NUM
ejpam-2421	68	5	,	,	PUNCT
ejpam-2421	68	6	.	.	PUNCT
ejpam-2421	68	7	.	.	PUNCT
ejpam-2421	69	1	.	.	PUNCT
ejpam-2421	70	1	,	,	PUNCT
ejpam-2421	70	2	qk−1,ωr	qk−1,ωr	PROPN
ejpam-2421	70	3	]	]	PUNCT
ejpam-2421	70	4	be	be	VERB
ejpam-2421	70	5	a	a	DET
ejpam-2421	70	6	modular	modular	ADJ
ejpam-2421	70	7	automorphism	automorphism	NOUN
ejpam-2421	70	8	of	of	ADP
ejpam-2421	70	9	ωr	ωr	NOUN
ejpam-2421	70	10	,	,	PUNCT
ejpam-2421	70	11	then	then	ADV
ejpam-2421	70	12	the	the	DET
ejpam-2421	70	13	fundamental	fundamental	ADJ
ejpam-2421	70	14	unit	unit	NOUN
ejpam-2421	70	15	ǫd	ǫd	NOUN
ejpam-2421	70	16	of	of	ADP
ejpam-2421	70	17	q	q	PROPN
ejpam-2421	70	18	(	(	PUNCT
ejpam-2421	70	19	p	p	NOUN
ejpam-2421	70	20	d	d	NOUN
ejpam-2421	70	21	)	)	PUNCT
ejpam-2421	70	22	is	be	AUX
ejpam-2421	70	23	given	give	VERB
ejpam-2421	70	24	by	by	ADP
ejpam-2421	70	25	the	the	DET
ejpam-2421	70	26	following	follow	VERB
ejpam-2421	70	27	formula	formula	NOUN
ejpam-2421	70	28	:	:	PUNCT
ejpam-2421	70	29	ǫd	ǫd	NUM
ejpam-2421	70	30	=	=	SYM
ejpam-2421	70	31	(	(	PUNCT
ejpam-2421	70	32	td	td	NOUN
ejpam-2421	71	1	+	+	CCONJ
ejpam-2421	71	2	ud	ud	INTJ
ejpam-2421	71	3	p	p	X
ejpam-2421	71	4	d	d	PROPN
ejpam-2421	71	5	2	2	NUM
ejpam-2421	71	6	)	)	PUNCT
ejpam-2421	71	7	>	>	X
ejpam-2421	71	8	1	1	NUM
ejpam-2421	71	9	,	,	PUNCT
ejpam-2421	71	10	where	where	SCONJ
ejpam-2421	71	11	td	td	NOUN
ejpam-2421	71	12	=	=	PUNCT
ejpam-2421	71	13	(	(	PUNCT
ejpam-2421	71	14	2q0	2q0	NUM
ejpam-2421	71	15	−	−	PROPN
ejpam-2421	71	16	1)qk−1	1)qk−1	NUM
ejpam-2421	71	17	+	+	NUM
ejpam-2421	71	18	2qk−2	2qk−2	NUM
ejpam-2421	71	19	,	,	PUNCT
ejpam-2421	71	20	ud	ud	INTJ
ejpam-2421	71	21	=	=	PUNCT
ejpam-2421	71	22	qk−1	qk−1	PROPN
ejpam-2421	71	23	,	,	PUNCT
ejpam-2421	71	24	and	and	CCONJ
ejpam-2421	71	25	q	q	X
ejpam-2421	71	26	i	i	PRON
ejpam-2421	71	27	is	be	AUX
ejpam-2421	71	28	determined	determine	VERB
ejpam-2421	71	29	by	by	ADP
ejpam-2421	71	30	q−1	q−1	PROPN
ejpam-2421	71	31	=	=	PUNCT
ejpam-2421	71	32	0	0	PROPN
ejpam-2421	71	33	,	,	PUNCT
ejpam-2421	71	34	q0	q0	NOUN
ejpam-2421	71	35	=	=	SYM
ejpam-2421	71	36	1	1	NUM
ejpam-2421	71	37	,	,	PUNCT
ejpam-2421	71	38	q	q	NOUN
ejpam-2421	71	39	i+1	i+1	NOUN
ejpam-2421	71	40	=	=	SYM
ejpam-2421	71	41	qi+1q	qi+1q	NOUN
ejpam-2421	71	42	i	i	PRON
ejpam-2421	72	1	+	+	PROPN
ejpam-2421	72	2	q	q	PROPN
ejpam-2421	72	3	i−1	i−1	PROPN
ejpam-2421	72	4	,	,	PUNCT
ejpam-2421	72	5	(	(	PUNCT
ejpam-2421	72	6	i	i	PRON
ejpam-2421	72	7	≥	≥	VERB
ejpam-2421	72	8	0	0	NUM
ejpam-2421	72	9	)	)	PUNCT
ejpam-2421	72	10	.	.	PUNCT
ejpam-2421	73	1	proof	proof	NOUN
ejpam-2421	73	2	.	.	PUNCT
ejpam-2421	74	1	see	see	VERB
ejpam-2421	74	2	[	[	X
ejpam-2421	74	3	5	5	NUM
ejpam-2421	74	4	,	,	PUNCT
ejpam-2421	74	5	lemma	lemma	PROPN
ejpam-2421	74	6	1	1	NUM
ejpam-2421	74	7	]	]	PUNCT
ejpam-2421	74	8	.	.	PUNCT
ejpam-2421	75	1	lemma	lemma	PROPN
ejpam-2421	75	2	2	2	NUM
ejpam-2421	75	3	.	.	X
ejpam-2421	76	1	for	for	ADP
ejpam-2421	76	2	a	a	DET
ejpam-2421	76	3	square	square	ADJ
ejpam-2421	76	4	-	-	PUNCT
ejpam-2421	76	5	free	free	ADJ
ejpam-2421	76	6	positive	positive	ADJ
ejpam-2421	76	7	integer	integer	NOUN
ejpam-2421	76	8	d	d	NOUN
ejpam-2421	76	9	,	,	PUNCT
ejpam-2421	76	10	we	we	PRON
ejpam-2421	76	11	put	put	VERB
ejpam-2421	76	12	d	d	NOUN
ejpam-2421	76	13	=	=	SYM
ejpam-2421	76	14	a2	a2	PROPN
ejpam-2421	76	15	+	+	CCONJ
ejpam-2421	76	16	b	b	X
ejpam-2421	76	17	(	(	PUNCT
ejpam-2421	76	18	0	0	NUM
ejpam-2421	76	19	<	<	X
ejpam-2421	76	20	b	b	X
ejpam-2421	76	21	≤	≤	NUM
ejpam-2421	76	22	2a	2a	NUM
ejpam-2421	76	23	)	)	PUNCT
ejpam-2421	76	24	,	,	PUNCT
ejpam-2421	76	25	a	a	PRON
ejpam-2421	76	26	,	,	PUNCT
ejpam-2421	76	27	b	b	PROPN
ejpam-2421	76	28	∈	∈	PROPN
ejpam-2421	77	1	z.	z.	PROPN
ejpam-2421	78	1	moreover	moreover	ADV
ejpam-2421	78	2	let	let	VERB
ejpam-2421	78	3	ωi	ωi	PROPN
ejpam-2421	78	4	=	=	PUNCT
ejpam-2421	78	5	ℓi	ℓi	PROPN
ejpam-2421	78	6	+	+	CCONJ
ejpam-2421	78	7	1	1	NUM
ejpam-2421	78	8	ωi+1	ωi+1	NUM
ejpam-2421	78	9	(	(	PUNCT
ejpam-2421	78	10	ℓi	ℓi	NOUN
ejpam-2421	78	11	=	=	SYM
ejpam-2421	78	12	[	[	X
ejpam-2421	78	13	ωi	ωi	X
ejpam-2421	78	14	]	]	X
ejpam-2421	78	15	,	,	PUNCT
ejpam-2421	78	16	i	i	PRON
ejpam-2421	78	17	≥	≥	VERB
ejpam-2421	78	18	0	0	NUM
ejpam-2421	78	19	)	)	PUNCT
ejpam-2421	78	20	be	be	AUX
ejpam-2421	78	21	the	the	DET
ejpam-2421	78	22	continued	continue	VERB
ejpam-2421	78	23	fraction	fraction	NOUN
ejpam-2421	78	24	expansion	expansion	NOUN
ejpam-2421	78	25	of	of	ADP
ejpam-2421	78	26	ω	ω	NOUN
ejpam-2421	78	27	=	=	SYM
ejpam-2421	78	28	ω0	ω0	PROPN
ejpam-2421	78	29	in	in	ADP
ejpam-2421	78	30	r(d	r(d	NOUN
ejpam-2421	78	31	)	)	PUNCT
ejpam-2421	78	32	.	.	PUNCT
ejpam-2421	79	1	then	then	ADV
ejpam-2421	79	2	each	each	DET
ejpam-2421	79	3	ωi	ωi	PROPN
ejpam-2421	79	4	is	be	AUX
ejpam-2421	79	5	expressed	express	VERB
ejpam-2421	79	6	in	in	ADP
ejpam-2421	79	7	the	the	DET
ejpam-2421	79	8	form	form	NOUN
ejpam-2421	79	9	ωi	ωi	X
ejpam-2421	79	10	=	=	SYM
ejpam-2421	79	11	a−ri+	a−ri+	PROPN
ejpam-2421	79	12	p	p	PROPN
ejpam-2421	79	13	d	d	X
ejpam-2421	79	14	ci	ci	PROPN
ejpam-2421	79	15	(	(	PUNCT
ejpam-2421	79	16	ci	ci	PROPN
ejpam-2421	79	17	,	,	PUNCT
ejpam-2421	79	18	ri	ri	PROPN
ejpam-2421	79	19	∈	∈	PROPN
ejpam-2421	79	20	z	z	PROPN
ejpam-2421	79	21	)	)	PUNCT
ejpam-2421	79	22	,	,	PUNCT
ejpam-2421	79	23	and	and	CCONJ
ejpam-2421	79	24	ℓi	ℓi	PROPN
ejpam-2421	79	25	,	,	PUNCT
ejpam-2421	79	26	ci	ci	PROPN
ejpam-2421	79	27	,	,	PUNCT
ejpam-2421	79	28	ri	ri	PROPN
ejpam-2421	79	29	can	can	AUX
ejpam-2421	79	30	be	be	AUX
ejpam-2421	79	31	obtained	obtain	VERB
ejpam-2421	79	32	from	from	ADP
ejpam-2421	79	33	the	the	DET
ejpam-2421	79	34	following	follow	VERB
ejpam-2421	79	35	recurrence	recurrence	NOUN
ejpam-2421	79	36	formula	formula	NOUN
ejpam-2421	79	37	:	:	PUNCT
ejpam-2421	79	38	ω0	ω0	ADV
ejpam-2421	79	39	=	=	SYM
ejpam-2421	79	40	a−	a−	NOUN
ejpam-2421	79	41	r0	r0	NOUN
ejpam-2421	79	42	+	+	CCONJ
ejpam-2421	79	43	p	p	X
ejpam-2421	79	44	d	d	PROPN
ejpam-2421	79	45	c0	c0	PROPN
ejpam-2421	79	46	,	,	PUNCT
ejpam-2421	79	47	2a−	2a−	PROPN
ejpam-2421	79	48	ri	ri	PROPN
ejpam-2421	80	1	=	=	NOUN
ejpam-2421	80	2	ciℓi	ciℓi	NOUN
ejpam-2421	80	3	+	+	CCONJ
ejpam-2421	80	4	ri+1	ri+1	NOUN
ejpam-2421	80	5	,	,	PUNCT
ejpam-2421	80	6	ci+1	ci+1	PROPN
ejpam-2421	81	1	=	=	X
ejpam-2421	81	2	ci−1	ci−1	PROPN
ejpam-2421	81	3	+	+	CCONJ
ejpam-2421	81	4	(	(	PUNCT
ejpam-2421	81	5	ri+1	ri+1	PROPN
ejpam-2421	81	6	−	−	PROPN
ejpam-2421	82	1	ri)ℓi	ri)ℓi	PROPN
ejpam-2421	82	2	(	(	PUNCT
ejpam-2421	82	3	i	i	PRON
ejpam-2421	82	4	≥	≥	NOUN
ejpam-2421	82	5	0	0	NUM
ejpam-2421	82	6	)	)	PUNCT
ejpam-2421	82	7	,	,	PUNCT
ejpam-2421	82	8	where	where	SCONJ
ejpam-2421	82	9	0≤	0≤	NUM
ejpam-2421	82	10	ri+1	ri+1	PROPN
ejpam-2421	82	11	<	<	X
ejpam-2421	82	12	ci	ci	PROPN
ejpam-2421	82	13	,	,	PUNCT
ejpam-2421	82	14	c−1	c−1	PROPN
ejpam-2421	82	15	=	=	PUNCT
ejpam-2421	82	16	(	(	PUNCT
ejpam-2421	82	17	b+	b+	X
ejpam-2421	82	18	2ar0	2ar0	NUM
ejpam-2421	82	19	−	−	PROPN
ejpam-2421	82	20	r0	r0	NOUN
ejpam-2421	82	21	2	2	NUM
ejpam-2421	82	22	)	)	PUNCT
ejpam-2421	82	23	c0	c0	NOUN
ejpam-2421	82	24	.	.	PUNCT
ejpam-2421	83	1	moreover	moreover	ADV
ejpam-2421	83	2	for	for	ADP
ejpam-2421	83	3	the	the	DET
ejpam-2421	83	4	period	period	NOUN
ejpam-2421	83	5	k	k	X
ejpam-2421	83	6	≥	≥	NUM
ejpam-2421	83	7	1	1	NUM
ejpam-2421	83	8	of	of	ADP
ejpam-2421	83	9	ω0	ω0	NOUN
ejpam-2421	83	10	,	,	PUNCT
ejpam-2421	83	11	we	we	PRON
ejpam-2421	83	12	get	get	VERB
ejpam-2421	83	13	ℓi	ℓi	NOUN
ejpam-2421	83	14	=	=	PRON
ejpam-2421	83	15	ℓk−i	ℓk−i	X
ejpam-2421	83	16	(	(	PUNCT
ejpam-2421	83	17	1≤	1≤	NUM
ejpam-2421	83	18	i	i	PROPN
ejpam-2421	83	19	≤	≤	PROPN
ejpam-2421	83	20	k−	k−	PROPN
ejpam-2421	83	21	1	1	NUM
ejpam-2421	83	22	)	)	PUNCT
ejpam-2421	83	23	,	,	PUNCT
ejpam-2421	83	24	ri	ri	PROPN
ejpam-2421	83	25	=	=	NOUN
ejpam-2421	83	26	rk−i+1	rk−i+1	PROPN
ejpam-2421	83	27	,	,	PUNCT
ejpam-2421	83	28	ci	ci	NOUN
ejpam-2421	84	1	=	=	NOUN
ejpam-2421	84	2	ck−i	ck−i	NOUN
ejpam-2421	84	3	(	(	PUNCT
ejpam-2421	84	4	1≤	1≤	INTJ
ejpam-2421	84	5	i	i	X
ejpam-2421	84	6	≤	≤	PUNCT
ejpam-2421	84	7	k	k	X
ejpam-2421	84	8	)	)	PUNCT
ejpam-2421	84	9	.	.	PUNCT
ejpam-2421	85	1	proof	proof	NOUN
ejpam-2421	85	2	.	.	PUNCT
ejpam-2421	86	1	see	see	VERB
ejpam-2421	86	2	[	[	X
ejpam-2421	86	3	1	1	NUM
ejpam-2421	86	4	,	,	PUNCT
ejpam-2421	86	5	proposition	proposition	NOUN
ejpam-2421	86	6	1	1	NUM
ejpam-2421	86	7	]	]	PUNCT
ejpam-2421	86	8	.	.	PUNCT
ejpam-2421	87	1	lemma	lemma	PROPN
ejpam-2421	87	2	3	3	X
ejpam-2421	87	3	.	.	PUNCT
ejpam-2421	88	1	for	for	ADP
ejpam-2421	88	2	a	a	DET
ejpam-2421	88	3	square	square	ADJ
ejpam-2421	88	4	-	-	PUNCT
ejpam-2421	88	5	free	free	ADJ
ejpam-2421	88	6	positive	positive	ADJ
ejpam-2421	88	7	integer	integer	NOUN
ejpam-2421	89	1	d	d	X
ejpam-2421	89	2	congruent	congruent	ADJ
ejpam-2421	89	3	to	to	ADP
ejpam-2421	89	4	1	1	NUM
ejpam-2421	89	5	modulo	modulo	NOUN
ejpam-2421	89	6	4	4	NUM
ejpam-2421	89	7	,	,	PUNCT
ejpam-2421	89	8	we	we	PRON
ejpam-2421	89	9	put	put	VERB
ejpam-2421	89	10	ωd	ωd	NOUN
ejpam-2421	90	1	=	=	SYM
ejpam-2421	90	2	(	(	PUNCT
ejpam-2421	90	3	1	1	NUM
ejpam-2421	90	4	+	+	SYM
ejpam-2421	90	5	p	p	X
ejpam-2421	90	6	d	d	PROPN
ejpam-2421	90	7	2	2	NUM
ejpam-2421	90	8	)	)	PUNCT
ejpam-2421	90	9	,	,	PUNCT
ejpam-2421	90	10	q0	q0	NOUN
ejpam-2421	90	11	=	=	PUNCT
ejpam-2421	91	1	[	[	X
ejpam-2421	91	2	ωd	ωd	X
ejpam-2421	91	3	]	]	PUNCT
ejpam-2421	91	4	and	and	CCONJ
ejpam-2421	91	5	ωr	ωr	NOUN
ejpam-2421	91	6	=	=	PUNCT
ejpam-2421	91	7	q0	q0	NOUN
ejpam-2421	91	8	−	−	PROPN
ejpam-2421	92	1	1	1	NUM
ejpam-2421	93	1	+	+	CCONJ
ejpam-2421	94	1	[	[	X
ejpam-2421	94	2	ωd	ωd	X
ejpam-2421	94	3	]	]	X
ejpam-2421	94	4	.	.	PUNCT
ejpam-2421	95	1	if	if	SCONJ
ejpam-2421	95	2	we	we	PRON
ejpam-2421	95	3	put	put	VERB
ejpam-2421	95	4	ω	ω	NOUN
ejpam-2421	95	5	=	=	SYM
ejpam-2421	95	6	ωr	ωr	X
ejpam-2421	95	7	in	in	ADP
ejpam-2421	95	8	lemma	lemma	PROPN
ejpam-2421	95	9	2	2	NUM
ejpam-2421	95	10	.	.	NUM
ejpam-2421	95	11	,	,	PUNCT
ejpam-2421	95	12	then	then	ADV
ejpam-2421	95	13	we	we	PRON
ejpam-2421	95	14	have	have	VERB
ejpam-2421	95	15	the	the	DET
ejpam-2421	95	16	following	follow	VERB
ejpam-2421	95	17	recurrence	recurrence	NOUN
ejpam-2421	95	18	formula	formula	NOUN
ejpam-2421	95	19	:	:	PUNCT
ejpam-2421	95	20	r0	r0	NOUN
ejpam-2421	95	21	=	=	NOUN
ejpam-2421	95	22	r1	r1	PROPN
ejpam-2421	95	23	=	=	SYM
ejpam-2421	95	24	a−	a−	PROPN
ejpam-2421	95	25	l0	l0	NOUN
ejpam-2421	95	26	=	=	SYM
ejpam-2421	95	27	a−	a−	PROPN
ejpam-2421	95	28	2q0	2q0	NUM
ejpam-2421	96	1	+	+	CCONJ
ejpam-2421	96	2	1	1	NUM
ejpam-2421	96	3	,	,	PUNCT
ejpam-2421	96	4	c0	c0	NOUN
ejpam-2421	96	5	=	=	PROPN
ejpam-2421	96	6	2	2	NUM
ejpam-2421	96	7	,	,	PUNCT
ejpam-2421	96	8	c1	c1	NOUN
ejpam-2421	96	9	=	=	SYM
ejpam-2421	96	10	c−1	c−1	PROPN
ejpam-2421	96	11	=	=	SYM
ejpam-2421	96	12	(	(	PUNCT
ejpam-2421	96	13	b+	b+	X
ejpam-2421	96	14	2ar0	2ar0	NUM
ejpam-2421	96	15	−	−	PROPN
ejpam-2421	96	16	r0	r0	NOUN
ejpam-2421	96	17	2	2	NUM
ejpam-2421	96	18	)	)	PUNCT
ejpam-2421	96	19	c0	c0	NOUN
ejpam-2421	96	20	,	,	PUNCT
ejpam-2421	96	21	ℓ0	ℓ0	PROPN
ejpam-2421	96	22	=	=	PROPN
ejpam-2421	96	23	2q0	2q0	NUM
ejpam-2421	96	24	−	−	PROPN
ejpam-2421	96	25	1,ℓi	1,ℓi	PROPN
ejpam-2421	96	26	=	=	SYM
ejpam-2421	96	27	qi	qi	PROPN
ejpam-2421	96	28	(	(	PUNCT
ejpam-2421	96	29	1≤	1≤	NUM
ejpam-2421	96	30	i	i	PROPN
ejpam-2421	96	31	≤	≤	PROPN
ejpam-2421	96	32	k−	k−	PROPN
ejpam-2421	96	33	1	1	NUM
ejpam-2421	96	34	)	)	PUNCT
ejpam-2421	96	35	.	.	PUNCT
ejpam-2421	97	1	ö.	ö.	PROPN
ejpam-2421	97	2	özer	özer	NOUN
ejpam-2421	97	3	,	,	PUNCT
ejpam-2421	97	4	a.	a.	NOUN
ejpam-2421	97	5	pekin	pekin	PROPN
ejpam-2421	97	6	/	/	SYM
ejpam-2421	97	7	eur	eur	PROPN
ejpam-2421	97	8	.	.	PUNCT
ejpam-2421	98	1	j.	j.	PROPN
ejpam-2421	98	2	pure	pure	PROPN
ejpam-2421	98	3	appl	appl	PROPN
ejpam-2421	98	4	.	.	PROPN
ejpam-2421	98	5	math	math	PROPN
ejpam-2421	98	6	,	,	PUNCT
ejpam-2421	98	7	8	8	NUM
ejpam-2421	98	8	(	(	PUNCT
ejpam-2421	98	9	2015	2015	NUM
ejpam-2421	98	10	)	)	PUNCT
ejpam-2421	98	11	,	,	PUNCT
ejpam-2421	98	12	343	343	NUM
ejpam-2421	98	13	-	-	SYM
ejpam-2421	98	14	356	356	NUM
ejpam-2421	98	15	346	346	NUM
ejpam-2421	98	16	proof	proof	NOUN
ejpam-2421	98	17	.	.	PUNCT
ejpam-2421	99	1	it	it	PRON
ejpam-2421	99	2	can	can	AUX
ejpam-2421	99	3	be	be	AUX
ejpam-2421	99	4	easily	easily	ADV
ejpam-2421	99	5	proved	prove	VERB
ejpam-2421	99	6	by	by	ADP
ejpam-2421	99	7	using	use	VERB
ejpam-2421	99	8	lemma	lemma	PROPN
ejpam-2421	99	9	2	2	NUM
ejpam-2421	99	10	.	.	NOUN
ejpam-2421	99	11	3	3	NUM
ejpam-2421	99	12	.	.	PUNCT
ejpam-2421	99	13	theorems	theorem	NOUN
ejpam-2421	99	14	theorem	theorem	VERB
ejpam-2421	99	15	1	1	NUM
ejpam-2421	99	16	.	.	PUNCT
ejpam-2421	100	1	let	let	AUX
ejpam-2421	100	2	d	d	NOUN
ejpam-2421	100	3	=	=	SYM
ejpam-2421	100	4	a2	a2	PROPN
ejpam-2421	100	5	+	+	CCONJ
ejpam-2421	100	6	b	b	PROPN
ejpam-2421	100	7	≡	≡	PROPN
ejpam-2421	100	8	1mod(4	1mod(4	NUM
ejpam-2421	100	9	)	)	PUNCT
ejpam-2421	100	10	is	be	AUX
ejpam-2421	100	11	a	a	DET
ejpam-2421	100	12	square	square	ADJ
ejpam-2421	100	13	free	free	ADJ
ejpam-2421	100	14	integer	integer	NOUN
ejpam-2421	100	15	for	for	ADP
ejpam-2421	100	16	positive	positive	ADJ
ejpam-2421	100	17	integers	integer	NOUN
ejpam-2421	100	18	a	a	DET
ejpam-2421	100	19	and	and	CCONJ
ejpam-2421	100	20	b	b	NOUN
ejpam-2421	100	21	satisfying	satisfy	VERB
ejpam-2421	100	22	0	0	PUNCT
ejpam-2421	100	23	<	<	X
ejpam-2421	100	24	b	b	X
ejpam-2421	100	25	≤	≤	NUM
ejpam-2421	100	26	2a	2a	NUM
ejpam-2421	100	27	.	.	PUNCT
ejpam-2421	101	1	let	let	VERB
ejpam-2421	101	2	the	the	DET
ejpam-2421	101	3	period	period	NOUN
ejpam-2421	101	4	kd	kd	PROPN
ejpam-2421	101	5	of	of	ADP
ejpam-2421	101	6	the	the	DET
ejpam-2421	101	7	integral	integral	ADJ
ejpam-2421	101	8	basis	basis	NOUN
ejpam-2421	101	9	element	element	NOUN
ejpam-2421	101	10	of	of	ADP
ejpam-2421	101	11	ωd	ωd	NOUN
ejpam-2421	101	12	=	=	PUNCT
ejpam-2421	101	13	(	(	PUNCT
ejpam-2421	101	14	1	1	NUM
ejpam-2421	101	15	+	+	SYM
ejpam-2421	101	16	p	p	X
ejpam-2421	101	17	d	d	PROPN
ejpam-2421	101	18	2	2	NUM
ejpam-2421	101	19	)	)	PUNCT
ejpam-2421	101	20	in	in	ADP
ejpam-2421	101	21	q	q	PROPN
ejpam-2421	101	22	(	(	PUNCT
ejpam-2421	101	23	p	p	NOUN
ejpam-2421	101	24	d	d	NOUN
ejpam-2421	101	25	)	)	PUNCT
ejpam-2421	101	26	be	be	VERB
ejpam-2421	101	27	8	8	NUM
ejpam-2421	101	28	.	.	PUNCT
ejpam-2421	102	1	if	if	SCONJ
ejpam-2421	102	2	a	a	PRON
ejpam-2421	102	3	is	be	AUX
ejpam-2421	102	4	odd	odd	ADJ
ejpam-2421	102	5	then	then	ADV
ejpam-2421	102	6	,	,	PUNCT
ejpam-2421	102	7	wd	wd	PROPN
ejpam-2421	102	8	=	=	PUNCT
ejpam-2421	102	9	[	[	PUNCT
ejpam-2421	102	10	a+	a+	PUNCT
ejpam-2421	102	11	1	1	NUM
ejpam-2421	102	12	2	2	NUM
ejpam-2421	102	13	,	,	PUNCT
ejpam-2421	102	14	l1	l1	PROPN
ejpam-2421	102	15	,	,	PUNCT
ejpam-2421	102	16	l2	l2	NOUN
ejpam-2421	102	17	,	,	PUNCT
ejpam-2421	102	18	l3	l3	PROPN
ejpam-2421	102	19	,	,	PUNCT
ejpam-2421	102	20	s1(c	s1(c	X
ejpam-2421	102	21	+	+	SYM
ejpam-2421	102	22	l3a)−	l3a)−	VERB
ejpam-2421	102	23	2l2b	2l2b	NUM
ejpam-2421	102	24	−	−	PROPN
ejpam-2421	103	1	ra	ra	PROPN
ejpam-2421	103	2	c(r	c(r	PROPN
ejpam-2421	103	3	−	−	PROPN
ejpam-2421	103	4	s1l3	s1l3	NOUN
ejpam-2421	103	5	)	)	PUNCT
ejpam-2421	103	6	+	+	NUM
ejpam-2421	103	7	b2	b2	NOUN
ejpam-2421	103	8	,	,	PUNCT
ejpam-2421	103	9	l3	l3	NOUN
ejpam-2421	103	10	,	,	PUNCT
ejpam-2421	103	11	l2	l2	NOUN
ejpam-2421	103	12	,	,	PUNCT
ejpam-2421	103	13	l1	l1	PROPN
ejpam-2421	103	14	,	,	PUNCT
ejpam-2421	103	15	a	a	DET
ejpam-2421	103	16	]	]	X
ejpam-2421	103	17	,	,	PUNCT
ejpam-2421	103	18	where	where	SCONJ
ejpam-2421	103	19	(	(	PUNCT
ejpam-2421	103	20	i	i	NOUN
ejpam-2421	103	21	=	=	NOUN
ejpam-2421	103	22	1,2,3,4	1,2,3,4	NUM
ejpam-2421	103	23	)	)	PUNCT
ejpam-2421	103	24	,	,	PUNCT
ejpam-2421	103	25	li	li	PROPN
ejpam-2421	103	26	≥	≥	PROPN
ejpam-2421	103	27	1	1	NUM
ejpam-2421	103	28	.	.	PUNCT
ejpam-2421	104	1	then	then	ADV
ejpam-2421	104	2	the	the	DET
ejpam-2421	104	3	coefficients	coefficient	NOUN
ejpam-2421	104	4	td	td	VERB
ejpam-2421	104	5	and	and	CCONJ
ejpam-2421	104	6	ud	ud	INTJ
ejpam-2421	104	7	of	of	ADP
ejpam-2421	104	8	ǫd	ǫd	PROPN
ejpam-2421	104	9	(	(	PUNCT
ejpam-2421	104	10	td	td	NOUN
ejpam-2421	104	11	,	,	PUNCT
ejpam-2421	104	12	ud	ud	INTJ
ejpam-2421	104	13	)	)	PUNCT
ejpam-2421	104	14	=	=	SYM
ejpam-2421	105	1	(	(	PUNCT
ejpam-2421	105	2	[	[	X
ejpam-2421	105	3	(	(	PUNCT
ejpam-2421	105	4	ar	ar	NOUN
ejpam-2421	105	5	+	+	CCONJ
ejpam-2421	105	6	s1l1)(c	s1l1)(c	PROPN
ejpam-2421	105	7	2l4	2l4	NUM
ejpam-2421	105	8	+	+	CCONJ
ejpam-2421	105	9	2ac	2ac	NOUN
ejpam-2421	105	10	)	)	PUNCT
ejpam-2421	106	1	+	+	CCONJ
ejpam-2421	106	2	2(c(bl4	2(c(bl4	NUM
ejpam-2421	106	3	+	+	NUM
ejpam-2421	106	4	ℓ2	ℓ2	NOUN
ejpam-2421	106	5	)	)	PUNCT
ejpam-2421	107	1	+	+	SYM
ejpam-2421	107	2	b	b	X
ejpam-2421	107	3	)	)	PUNCT
ejpam-2421	107	4	]	]	PUNCT
ejpam-2421	107	5	,	,	PUNCT
ejpam-2421	107	6	c(cl4	c(cl4	PROPN
ejpam-2421	107	7	+	+	NUM
ejpam-2421	107	8	2a	2a	NUM
ejpam-2421	107	9	)	)	PUNCT
ejpam-2421	107	10	)	)	PUNCT
ejpam-2421	108	1	and	and	CCONJ
ejpam-2421	108	2	d	d	NOUN
ejpam-2421	108	3	=	=	SYM
ejpam-2421	108	4	(	(	PUNCT
ejpam-2421	108	5	ar	ar	PROPN
ejpam-2421	108	6	+	+	NOUN
ejpam-2421	108	7	s1l1	s1l1	NOUN
ejpam-2421	108	8	)	)	PUNCT
ejpam-2421	108	9	2	2	NUM
ejpam-2421	108	10	+	+	CCONJ
ejpam-2421	108	11	4rl2	4rl2	NUM
ejpam-2421	108	12	+	+	NUM
ejpam-2421	108	13	4s1	4s1	NUM
ejpam-2421	108	14	hold	hold	VERB
ejpam-2421	108	15	.	.	PUNCT
ejpam-2421	109	1	where	where	SCONJ
ejpam-2421	109	2	a	a	DET
ejpam-2421	109	3	,	,	PUNCT
ejpam-2421	109	4	b	b	NOUN
ejpam-2421	109	5	,	,	PUNCT
ejpam-2421	109	6	c	c	PROPN
ejpam-2421	109	7	are	be	AUX
ejpam-2421	109	8	determined	determine	VERB
ejpam-2421	109	9	by	by	ADP
ejpam-2421	109	10	a=	a=	PROPN
ejpam-2421	109	11	l1l2	l1l2	X
ejpam-2421	110	1	+	+	ADP
ejpam-2421	110	2	1	1	NUM
ejpam-2421	110	3	,	,	PUNCT
ejpam-2421	110	4	b	b	NOUN
ejpam-2421	110	5	=	=	SYM
ejpam-2421	110	6	l2l3	l2l3	NOUN
ejpam-2421	110	7	+	+	NUM
ejpam-2421	110	8	1	1	NUM
ejpam-2421	110	9	,	,	PUNCT
ejpam-2421	110	10	and	and	CCONJ
ejpam-2421	110	11	c	c	X
ejpam-2421	110	12	=	=	PROPN
ejpam-2421	110	13	l1	l1	PROPN
ejpam-2421	110	14	+	+	CCONJ
ejpam-2421	110	15	al3	al3	PROPN
ejpam-2421	110	16	,	,	PUNCT
ejpam-2421	110	17	moreover	moreover	ADV
ejpam-2421	110	18	r	r	NOUN
ejpam-2421	110	19	and	and	CCONJ
ejpam-2421	110	20	s	s	NOUN
ejpam-2421	110	21	are	be	AUX
ejpam-2421	110	22	uniquely	uniquely	ADV
ejpam-2421	110	23	determined	determined	ADJ
ejpam-2421	110	24	with	with	ADP
ejpam-2421	110	25	the	the	DET
ejpam-2421	110	26	equalities	equality	NOUN
ejpam-2421	110	27	a	a	DET
ejpam-2421	110	28	=	=	X
ejpam-2421	110	29	ar	ar	PROPN
ejpam-2421	110	30	+	+	NOUN
ejpam-2421	110	31	s1l1	s1l1	NOUN
ejpam-2421	110	32	and	and	CCONJ
ejpam-2421	110	33	b(bl4	b(bl4	PROPN
ejpam-2421	110	34	+	+	CCONJ
ejpam-2421	110	35	2l2	2l2	NUM
ejpam-2421	110	36	)	)	PUNCT
ejpam-2421	110	37	=	=	SYM
ejpam-2421	110	38	s1[c(1	s1[c(1	PROPN
ejpam-2421	110	39	+	+	X
ejpam-2421	110	40	l3l4	l3l4	NOUN
ejpam-2421	110	41	)	)	PUNCT
ejpam-2421	110	42	+	+	CCONJ
ejpam-2421	110	43	al3]−	al3]−	PROPN
ejpam-2421	110	44	r(a+	r(a+	PROPN
ejpam-2421	110	45	cl4	cl4	PROPN
ejpam-2421	110	46	)	)	PUNCT
ejpam-2421	110	47	.	.	PUNCT
ejpam-2421	111	1	proof	proof	NOUN
ejpam-2421	111	2	.	.	PUNCT
ejpam-2421	112	1	let	let	VERB
ejpam-2421	112	2	a	a	PRON
ejpam-2421	112	3	be	be	AUX
ejpam-2421	112	4	an	an	DET
ejpam-2421	112	5	odd	odd	ADJ
ejpam-2421	112	6	integer	integer	NOUN
ejpam-2421	112	7	then	then	ADV
ejpam-2421	112	8	d	d	PROPN
ejpam-2421	112	9	∈	∈	PROPN
ejpam-2421	112	10	d1	d1	PROPN
ejpam-2421	112	11	0	0	NUM
ejpam-2421	112	12	∪	∪	PROPN
ejpam-2421	112	13	d5	d5	NOUN
ejpam-2421	112	14	4	4	NUM
ejpam-2421	112	15	.	.	PUNCT
ejpam-2421	113	1	since	since	SCONJ
ejpam-2421	113	2	q0	q0	PROPN
ejpam-2421	113	3	=	=	PROPN
ejpam-2421	113	4	ωd	ωd	NOUN
ejpam-2421	113	5	=	=	SYM
ejpam-2421	113	6	a+1	a+1	PROPN
ejpam-2421	113	7	2	2	NUM
ejpam-2421	113	8	then	then	ADV
ejpam-2421	113	9	from	from	ADP
ejpam-2421	113	10	lemma	lemma	PROPN
ejpam-2421	113	11	3	3	NUM
ejpam-2421	113	12	we	we	PRON
ejpam-2421	113	13	obtain	obtain	VERB
ejpam-2421	113	14	r0	r0	NOUN
ejpam-2421	113	15	=	=	NOUN
ejpam-2421	113	16	r1	r1	NOUN
ejpam-2421	113	17	=	=	SYM
ejpam-2421	113	18	a−	a−	PROPN
ejpam-2421	113	19	2q0	2q0	NUM
ejpam-2421	114	1	+	+	CCONJ
ejpam-2421	114	2	1=	1=	X
ejpam-2421	114	3	0	0	NUM
ejpam-2421	114	4	,	,	PUNCT
ejpam-2421	114	5	c0	c0	NOUN
ejpam-2421	114	6	=	=	PROPN
ejpam-2421	114	7	2	2	NUM
ejpam-2421	114	8	,	,	PUNCT
ejpam-2421	114	9	l0	l0	PROPN
ejpam-2421	114	10	=	=	NOUN
ejpam-2421	114	11	a	a	DET
ejpam-2421	114	12	(	(	PUNCT
ejpam-2421	114	13	1	1	NUM
ejpam-2421	114	14	)	)	PUNCT
ejpam-2421	114	15	and	and	CCONJ
ejpam-2421	114	16	from	from	ADP
ejpam-2421	114	17	the	the	DET
ejpam-2421	114	18	lemma	lemma	PROPN
ejpam-2421	114	19	2	2	NUM
ejpam-2421	114	20	:	:	PUNCT
ejpam-2421	114	21	l1	l1	PROPN
ejpam-2421	114	22	=	=	SYM
ejpam-2421	114	23	7	7	NUM
ejpam-2421	114	24	,	,	PUNCT
ejpam-2421	114	25	l2	l2	NOUN
ejpam-2421	114	26	=	=	SYM
ejpam-2421	114	27	l6	l6	PROPN
ejpam-2421	114	28	,	,	PUNCT
ejpam-2421	114	29	l3	l3	PROPN
ejpam-2421	114	30	=	=	SYM
ejpam-2421	114	31	l5	l5	PROPN
ejpam-2421	114	32	,	,	PUNCT
ejpam-2421	114	33	wd	wd	PROPN
ejpam-2421	114	34	=	=	SYM
ejpam-2421	114	35	[	[	PUNCT
ejpam-2421	114	36	a+1	a+1	PROPN
ejpam-2421	114	37	2	2	NUM
ejpam-2421	114	38	,	,	PUNCT
ejpam-2421	114	39	l1	l1	PROPN
ejpam-2421	114	40	,	,	PUNCT
ejpam-2421	114	41	l2	l2	NOUN
ejpam-2421	114	42	,	,	PUNCT
ejpam-2421	114	43	l3	l3	PROPN
ejpam-2421	114	44	,	,	PUNCT
ejpam-2421	114	45	l4	l4	PROPN
ejpam-2421	114	46	,	,	PUNCT
ejpam-2421	114	47	l3	l3	PROPN
ejpam-2421	114	48	,	,	PUNCT
ejpam-2421	114	49	l2	l2	NOUN
ejpam-2421	114	50	,	,	PUNCT
ejpam-2421	114	51	l1	l1	PROPN
ejpam-2421	114	52	,	,	PUNCT
ejpam-2421	114	53	a	a	DET
ejpam-2421	114	54	]	]	X
ejpam-2421	114	55	hold	hold	NOUN
ejpam-2421	114	56	for	for	ADP
ejpam-2421	114	57	kd	kd	PROPN
ejpam-2421	114	58	=	=	PROPN
ejpam-2421	114	59	8	8	NUM
ejpam-2421	114	60	.	.	PUNCT
ejpam-2421	115	1	furthermore	furthermore	ADV
ejpam-2421	115	2	we	we	PRON
ejpam-2421	115	3	have	have	VERB
ejpam-2421	115	4	r1	r1	NOUN
ejpam-2421	115	5	=	=	SYM
ejpam-2421	115	6	r8	r8	PROPN
ejpam-2421	115	7	,	,	PUNCT
ejpam-2421	115	8	r2	r2	NOUN
ejpam-2421	115	9	=	=	SYM
ejpam-2421	115	10	r7	r7	PROPN
ejpam-2421	115	11	,	,	PUNCT
ejpam-2421	115	12	r3	r3	PROPN
ejpam-2421	115	13	=	=	SYM
ejpam-2421	115	14	r6	r6	PROPN
ejpam-2421	115	15	,	,	PUNCT
ejpam-2421	115	16	r4	r4	NOUN
ejpam-2421	115	17	=	=	SYM
ejpam-2421	115	18	r5	r5	PROPN
ejpam-2421	115	19	,	,	PUNCT
ejpam-2421	115	20	c1	c1	PROPN
ejpam-2421	115	21	=	=	PROPN
ejpam-2421	115	22	c7	c7	PROPN
ejpam-2421	115	23	,	,	PUNCT
ejpam-2421	115	24	c2	c2	PROPN
ejpam-2421	115	25	=	=	SYM
ejpam-2421	115	26	c6	c6	PROPN
ejpam-2421	115	27	,	,	PUNCT
ejpam-2421	115	28	c3	c3	PROPN
ejpam-2421	115	29	=	=	PROPN
ejpam-2421	115	30	c5	c5	PROPN
ejpam-2421	115	31	.	.	PUNCT
ejpam-2421	116	1	let	let	VERB
ejpam-2421	116	2	d	d	X
ejpam-2421	116	3	∈	∈	PROPN
ejpam-2421	116	4	d1	d1	PROPN
ejpam-2421	116	5	0	0	NUM
ejpam-2421	116	6	,	,	PUNCT
ejpam-2421	116	7	where	where	SCONJ
ejpam-2421	116	8	d1	d1	PROPN
ejpam-2421	116	9	0	0	PUNCT
ejpam-2421	117	1	=	=	NUM
ejpam-2421	117	2	{	{	PUNCT
ejpam-2421	117	3	d	d	PROPN
ejpam-2421	117	4	∈	∈	PROPN
ejpam-2421	117	5	d|d	d|d	VERB
ejpam-2421	117	6	≡	≡	PROPN
ejpam-2421	117	7	1(mod8	1(mod8	NUM
ejpam-2421	117	8	)	)	PUNCT
ejpam-2421	117	9	,	,	PUNCT
ejpam-2421	117	10	b	b	PROPN
ejpam-2421	117	11	≡	≡	PROPN
ejpam-2421	117	12	0(mod8	0(mod8	NUM
ejpam-2421	117	13	)	)	PUNCT
ejpam-2421	117	14	}	}	PUNCT
ejpam-2421	118	1	=	=	X
ejpam-2421	118	2	{	{	PUNCT
ejpam-2421	118	3	d	d	NOUN
ejpam-2421	118	4	∈	∈	PROPN
ejpam-2421	118	5	d|d	d|d	VERB
ejpam-2421	118	6	=	=	SYM
ejpam-2421	118	7	a2	a2	PROPN
ejpam-2421	118	8	+	+	CCONJ
ejpam-2421	118	9	8	8	NUM
ejpam-2421	118	10	m	m	NOUN
ejpam-2421	118	11	,	,	PUNCT
ejpam-2421	118	12	a	a	DET
ejpam-2421	118	13	≡	≡	PROPN
ejpam-2421	118	14	1(mod2	1(mod2	NUM
ejpam-2421	118	15	)	)	PUNCT
ejpam-2421	118	16	,	,	PUNCT
ejpam-2421	118	17	0	0	PUNCT
ejpam-2421	118	18	<	<	X
ejpam-2421	118	19	4	4	NUM
ejpam-2421	118	20	m	m	NOUN
ejpam-2421	118	21	<	<	X
ejpam-2421	118	22	a	a	X
ejpam-2421	118	23	}	}	PUNCT
ejpam-2421	118	24	in	in	ADP
ejpam-2421	118	25	this	this	DET
ejpam-2421	118	26	case	case	NOUN
ejpam-2421	118	27	we	we	PRON
ejpam-2421	118	28	have	have	VERB
ejpam-2421	118	29	b	b	NOUN
ejpam-2421	118	30	=	=	SYM
ejpam-2421	118	31	8	8	NUM
ejpam-2421	118	32	m	m	NOUN
ejpam-2421	118	33	∋	∋	NOUN
ejpam-2421	118	34	m	m	PROPN
ejpam-2421	118	35	>	>	X
ejpam-2421	118	36	0	0	PROPN
ejpam-2421	118	37	.	.	PUNCT
ejpam-2421	118	38	from	from	ADP
ejpam-2421	118	39	lemma	lemma	PROPN
ejpam-2421	118	40	2	2	NUM
ejpam-2421	118	41	,	,	PUNCT
ejpam-2421	118	42	it	it	PRON
ejpam-2421	118	43	can	can	AUX
ejpam-2421	118	44	easily	easily	ADV
ejpam-2421	118	45	seen	see	VERB
ejpam-2421	118	46	that	that	DET
ejpam-2421	118	47	c1	c1	NOUN
ejpam-2421	118	48	=	=	PROPN
ejpam-2421	118	49	c−1	c−1	PROPN
ejpam-2421	118	50	=	=	PUNCT
ejpam-2421	118	51	4	4	NUM
ejpam-2421	118	52	m	m	NOUN
ejpam-2421	118	53	and	and	CCONJ
ejpam-2421	118	54	2a	2a	NUM
ejpam-2421	118	55	=	=	SYM
ejpam-2421	118	56	4ml1	4ml1	PUNCT
ejpam-2421	118	57	+	+	NUM
ejpam-2421	118	58	r2	r2	PROPN
ejpam-2421	118	59	(	(	PUNCT
ejpam-2421	118	60	for	for	ADP
ejpam-2421	118	61	i	i	PRON
ejpam-2421	118	62	=	=	NOUN
ejpam-2421	118	63	1	1	NUM
ejpam-2421	118	64	)	)	PUNCT
ejpam-2421	118	65	.	.	PUNCT
ejpam-2421	119	1	since	since	SCONJ
ejpam-2421	119	2	r2	r2	PROPN
ejpam-2421	119	3	=	=	PUNCT
ejpam-2421	119	4	2a	2a	NUM
ejpam-2421	119	5	−	−	NOUN
ejpam-2421	119	6	4ml1	4ml1	NUM
ejpam-2421	119	7	is	be	AUX
ejpam-2421	119	8	even	even	ADV
ejpam-2421	119	9	then	then	ADV
ejpam-2421	119	10	there	there	PRON
ejpam-2421	119	11	exists	exist	VERB
ejpam-2421	119	12	a	a	DET
ejpam-2421	119	13	positive	positive	ADJ
ejpam-2421	119	14	integer	integer	NOUN
ejpam-2421	119	15	r	r	NOUN
ejpam-2421	120	1	such	such	ADJ
ejpam-2421	120	2	that	that	DET
ejpam-2421	120	3	r2	r2	PROPN
ejpam-2421	120	4	=	=	SYM
ejpam-2421	120	5	2r	2r	NUM
ejpam-2421	120	6	.	.	PUNCT
ejpam-2421	121	1	therefore	therefore	ADV
ejpam-2421	121	2	2r	2r	NUM
ejpam-2421	121	3	=	=	PUNCT
ejpam-2421	122	1	2a−	2a−	NUM
ejpam-2421	122	2	4ml1⇒	4ml1⇒	NUM
ejpam-2421	122	3	r	r	NOUN
ejpam-2421	122	4	=	=	SYM
ejpam-2421	122	5	a−	a−	PROPN
ejpam-2421	122	6	2ml1	2ml1	NUM
ejpam-2421	123	1	and	and	CCONJ
ejpam-2421	123	2	so	so	ADV
ejpam-2421	123	3	r	r	NOUN
ejpam-2421	123	4	is	be	AUX
ejpam-2421	123	5	an	an	DET
ejpam-2421	123	6	odd	odd	ADJ
ejpam-2421	123	7	integer	integer	NOUN
ejpam-2421	123	8	.	.	PUNCT
ejpam-2421	124	1	from	from	ADP
ejpam-2421	124	2	lemma	lemma	PROPN
ejpam-2421	124	3	2	2	NUM
ejpam-2421	124	4	,	,	PUNCT
ejpam-2421	124	5	we	we	PRON
ejpam-2421	124	6	have	have	VERB
ejpam-2421	124	7	2a	2a	NUM
ejpam-2421	124	8	=	=	SYM
ejpam-2421	124	9	c2l2	c2l2	PROPN
ejpam-2421	124	10	+	+	NUM
ejpam-2421	124	11	r2	r2	PROPN
ejpam-2421	124	12	+	+	CCONJ
ejpam-2421	124	13	r3	r3	PROPN
ejpam-2421	124	14	for	for	ADP
ejpam-2421	124	15	i	i	PRON
ejpam-2421	124	16	=	=	SYM
ejpam-2421	124	17	2	2	NUM
ejpam-2421	124	18	and	and	CCONJ
ejpam-2421	124	19	2a	2a	NUM
ejpam-2421	124	20	=	=	SYM
ejpam-2421	124	21	(	(	PUNCT
ejpam-2421	124	22	2	2	NUM
ejpam-2421	124	23	+	+	NUM
ejpam-2421	124	24	2rl1	2rl1	NUM
ejpam-2421	124	25	)	)	PUNCT
ejpam-2421	124	26	·	·	PUNCT
ejpam-2421	124	27	l2	l2	VERB
ejpam-2421	124	28	+	+	CCONJ
ejpam-2421	124	29	r2	r2	PROPN
ejpam-2421	124	30	+	+	CCONJ
ejpam-2421	124	31	r3	r3	PROPN
ejpam-2421	124	32	(	(	PUNCT
ejpam-2421	124	33	2	2	NUM
ejpam-2421	124	34	)	)	PUNCT
ejpam-2421	124	35	ö.	ö.	NOUN
ejpam-2421	124	36	özer	özer	NOUN
ejpam-2421	124	37	,	,	PUNCT
ejpam-2421	124	38	a.	a.	NOUN
ejpam-2421	124	39	pekin	pekin	PROPN
ejpam-2421	124	40	/	/	SYM
ejpam-2421	124	41	eur	eur	PROPN
ejpam-2421	124	42	.	.	PUNCT
ejpam-2421	125	1	j.	j.	PROPN
ejpam-2421	125	2	pure	pure	PROPN
ejpam-2421	125	3	appl	appl	PROPN
ejpam-2421	125	4	.	.	PROPN
ejpam-2421	125	5	math	math	PROPN
ejpam-2421	125	6	,	,	PUNCT
ejpam-2421	125	7	8	8	NUM
ejpam-2421	125	8	(	(	PUNCT
ejpam-2421	125	9	2015	2015	NUM
ejpam-2421	125	10	)	)	PUNCT
ejpam-2421	125	11	,	,	PUNCT
ejpam-2421	125	12	343	343	NUM
ejpam-2421	125	13	-	-	SYM
ejpam-2421	125	14	356	356	NUM
ejpam-2421	125	15	347	347	NUM
ejpam-2421	125	16	for	for	ADP
ejpam-2421	125	17	c2	c2	PROPN
ejpam-2421	125	18	=	=	SYM
ejpam-2421	125	19	c0	c0	PROPN
ejpam-2421	125	20	=	=	SYM
ejpam-2421	125	21	(	(	PUNCT
ejpam-2421	125	22	r2	r2	PROPN
ejpam-2421	125	23	−	−	PROPN
ejpam-2421	125	24	r1)l1	r1)l1	PROPN
ejpam-2421	125	25	,	,	PUNCT
ejpam-2421	125	26	c2	c2	PROPN
ejpam-2421	125	27	=	=	PUNCT
ejpam-2421	125	28	2	2	NUM
ejpam-2421	125	29	+	+	NUM
ejpam-2421	125	30	2rl1	2rl1	NUM
ejpam-2421	125	31	.	.	PUNCT
ejpam-2421	126	1	if	if	SCONJ
ejpam-2421	126	2	we	we	PRON
ejpam-2421	126	3	put	put	VERB
ejpam-2421	126	4	4m=	4m=	NUM
ejpam-2421	126	5	2rl2	2rl2	NUM
ejpam-2421	126	6	+	+	SYM
ejpam-2421	126	7	s	s	AUX
ejpam-2421	126	8	in	in	ADP
ejpam-2421	126	9	(	(	PUNCT
ejpam-2421	126	10	1	1	NUM
ejpam-2421	126	11	)	)	PUNCT
ejpam-2421	126	12	then	then	ADV
ejpam-2421	126	13	we	we	PRON
ejpam-2421	126	14	obtain	obtain	VERB
ejpam-2421	126	15	4ml1	4ml1	NOUN
ejpam-2421	126	16	=	=	SYM
ejpam-2421	127	1	2l2(rl2	2l2(rl2	NOUN
ejpam-2421	127	2	+	+	CCONJ
ejpam-2421	127	3	rl1	rl1	VERB
ejpam-2421	127	4	+	+	CCONJ
ejpam-2421	127	5	1	1	NUM
ejpam-2421	127	6	)	)	PUNCT
ejpam-2421	127	7	+	+	NUM
ejpam-2421	127	8	r3	r3	PROPN
ejpam-2421	127	9	.	.	PUNCT
ejpam-2421	128	1	(	(	PUNCT
ejpam-2421	128	2	3	3	X
ejpam-2421	128	3	)	)	PUNCT
ejpam-2421	128	4	where	where	SCONJ
ejpam-2421	128	5	2l2	2l2	NUM
ejpam-2421	128	6	+	+	NUM
ejpam-2421	128	7	r3	r3	PROPN
ejpam-2421	128	8	≡	≡	PROPN
ejpam-2421	128	9	0(modl1	0(modl1	PROPN
ejpam-2421	128	10	)	)	PUNCT
ejpam-2421	129	1	and	and	CCONJ
ejpam-2421	129	2	so	so	ADV
ejpam-2421	129	3	there	there	PRON
ejpam-2421	129	4	exists	exist	VERB
ejpam-2421	129	5	positive	positive	ADJ
ejpam-2421	129	6	integer	integer	NOUN
ejpam-2421	129	7	s	s	VERB
ejpam-2421	130	1	such	such	ADJ
ejpam-2421	130	2	that	that	SCONJ
ejpam-2421	130	3	2l2	2l2	NUM
ejpam-2421	130	4	+	+	NUM
ejpam-2421	130	5	r3	r3	PROPN
ejpam-2421	130	6	=	=	SYM
ejpam-2421	130	7	sl1	sl1	PROPN
ejpam-2421	130	8	then	then	ADV
ejpam-2421	130	9	we	we	PRON
ejpam-2421	130	10	can	can	AUX
ejpam-2421	130	11	obtain	obtain	VERB
ejpam-2421	130	12	r3	r3	PROPN
ejpam-2421	130	13	=	=	SYM
ejpam-2421	130	14	sl1	sl1	PROPN
ejpam-2421	130	15	−	−	PROPN
ejpam-2421	130	16	2l2	2l2	NUM
ejpam-2421	130	17	.	.	PUNCT
ejpam-2421	131	1	(	(	PUNCT
ejpam-2421	131	2	4	4	X
ejpam-2421	131	3	)	)	PUNCT
ejpam-2421	131	4	here	here	ADV
ejpam-2421	131	5	if	if	SCONJ
ejpam-2421	131	6	the	the	DET
ejpam-2421	131	7	value	value	NOUN
ejpam-2421	131	8	r3	r3	PROPN
ejpam-2421	131	9	is	be	AUX
ejpam-2421	131	10	written	write	VERB
ejpam-2421	131	11	in	in	ADP
ejpam-2421	131	12	(	(	PUNCT
ejpam-2421	131	13	3	3	NUM
ejpam-2421	131	14	)	)	PUNCT
ejpam-2421	131	15	then	then	ADV
ejpam-2421	131	16	it	it	PRON
ejpam-2421	131	17	is	be	AUX
ejpam-2421	131	18	immediately	immediately	ADV
ejpam-2421	131	19	seen	see	VERB
ejpam-2421	131	20	that	that	SCONJ
ejpam-2421	131	21	4	4	NUM
ejpam-2421	131	22	m	m	NOUN
ejpam-2421	131	23	=	=	NOUN
ejpam-2421	131	24	2rl2	2rl2	NUM
ejpam-2421	131	25	+	+	SYM
ejpam-2421	131	26	s	s	VERB
ejpam-2421	131	27	and	and	CCONJ
ejpam-2421	131	28	s	s	VERB
ejpam-2421	131	29	is	be	AUX
ejpam-2421	131	30	even	even	ADV
ejpam-2421	131	31	.	.	PUNCT
ejpam-2421	132	1	if	if	SCONJ
ejpam-2421	132	2	we	we	PRON
ejpam-2421	132	3	put	put	VERB
ejpam-2421	132	4	4m=	4m=	NUM
ejpam-2421	132	5	2rl2	2rl2	NUM
ejpam-2421	132	6	+	+	SYM
ejpam-2421	132	7	s	s	AUX
ejpam-2421	132	8	in	in	ADP
ejpam-2421	132	9	(	(	PUNCT
ejpam-2421	132	10	1	1	NUM
ejpam-2421	132	11	)	)	PUNCT
ejpam-2421	132	12	then	then	ADV
ejpam-2421	132	13	2a	2a	NUM
ejpam-2421	132	14	=(	=(	NOUN
ejpam-2421	132	15	2rl2	2rl2	NUM
ejpam-2421	132	16	+	+	CCONJ
ejpam-2421	132	17	s)l1	s)l1	ADJ
ejpam-2421	132	18	+	+	CCONJ
ejpam-2421	132	19	2r	2r	NUM
ejpam-2421	132	20	⇒	⇒	NOUN
ejpam-2421	132	21	2a	2a	NUM
ejpam-2421	132	22	=	=	SYM
ejpam-2421	133	1	2rl1l2	2rl1l2	NUM
ejpam-2421	133	2	+	+	NUM
ejpam-2421	133	3	2r	2r	NUM
ejpam-2421	133	4	+	+	CCONJ
ejpam-2421	133	5	sl1	sl1	PROPN
ejpam-2421	133	6	⇒	⇒	NOUN
ejpam-2421	133	7	2a	2a	NUM
ejpam-2421	134	1	=	=	SYM
ejpam-2421	134	2	r(2l1l2	r(2l1l2	NOUN
ejpam-2421	135	1	+	+	CCONJ
ejpam-2421	135	2	2	2	NUM
ejpam-2421	135	3	)	)	PUNCT
ejpam-2421	135	4	+	+	CCONJ
ejpam-2421	135	5	sl1	sl1	PROPN
ejpam-2421	135	6	⇒	⇒	NOUN
ejpam-2421	135	7	2a	2a	NUM
ejpam-2421	135	8	=	=	SYM
ejpam-2421	135	9	2r(l1l2	2r(l1l2	NUM
ejpam-2421	135	10	+	+	NOUN
ejpam-2421	135	11	1	1	NUM
ejpam-2421	135	12	)	)	PUNCT
ejpam-2421	136	1	+	+	CCONJ
ejpam-2421	136	2	sl1	sl1	PROPN
ejpam-2421	136	3	hold	hold	NOUN
ejpam-2421	136	4	.	.	PUNCT
ejpam-2421	137	1	if	if	SCONJ
ejpam-2421	137	2	we	we	PRON
ejpam-2421	137	3	take	take	VERB
ejpam-2421	137	4	a	a	DET
ejpam-2421	137	5	=	=	X
ejpam-2421	137	6	l1	l1	PROPN
ejpam-2421	137	7	·	·	PUNCT
ejpam-2421	137	8	l2	l2	NOUN
ejpam-2421	138	1	+	+	CCONJ
ejpam-2421	138	2	1	1	NUM
ejpam-2421	138	3	then	then	ADV
ejpam-2421	138	4	we	we	PRON
ejpam-2421	138	5	have	have	AUX
ejpam-2421	138	6	a	a	DET
ejpam-2421	138	7	=	=	X
ejpam-2421	138	8	ra+	ra+	NOUN
ejpam-2421	138	9	s1l1	s1l1	NOUN
ejpam-2421	138	10	because	because	SCONJ
ejpam-2421	138	11	of	of	ADP
ejpam-2421	138	12	s	s	PART
ejpam-2421	138	13	=	=	SYM
ejpam-2421	138	14	2s1	2s1	NUM
ejpam-2421	138	15	is	be	AUX
ejpam-2421	138	16	even	even	ADV
ejpam-2421	138	17	,	,	PUNCT
ejpam-2421	138	18	s1	s1	PROPN
ejpam-2421	138	19	>	>	X
ejpam-2421	138	20	0	0	PROPN
ejpam-2421	138	21	,	,	PUNCT
ejpam-2421	138	22	s1	s1	PROPN
ejpam-2421	138	23	∈	∈	PROPN
ejpam-2421	138	24	z	z	NOUN
ejpam-2421	138	25	.	.	PUNCT
ejpam-2421	139	1	on	on	ADP
ejpam-2421	139	2	the	the	DET
ejpam-2421	139	3	other	other	ADJ
ejpam-2421	139	4	hand	hand	NOUN
ejpam-2421	139	5	,	,	PUNCT
ejpam-2421	139	6	for	for	ADP
ejpam-2421	139	7	i	i	PRON
ejpam-2421	139	8	=	=	SYM
ejpam-2421	139	9	2	2	NUM
ejpam-2421	139	10	we	we	PRON
ejpam-2421	139	11	have	have	AUX
ejpam-2421	139	12	c3	c3	PROPN
ejpam-2421	139	13	=	=	PROPN
ejpam-2421	139	14	c1	c1	PROPN
ejpam-2421	139	15	+	+	CCONJ
ejpam-2421	139	16	(	(	PUNCT
ejpam-2421	139	17	r3	r3	PROPN
ejpam-2421	139	18	−	−	PROPN
ejpam-2421	139	19	r2)l2	r2)l2	VERB
ejpam-2421	139	20	=	=	SYM
ejpam-2421	139	21	4m+	4m+	NUM
ejpam-2421	139	22	(	(	PUNCT
ejpam-2421	139	23	r2	r2	PROPN
ejpam-2421	139	24	−	−	PROPN
ejpam-2421	139	25	r2)l2	r2)l2	VERB
ejpam-2421	139	26	c4	c4	NOUN
ejpam-2421	139	27	=	=	PROPN
ejpam-2421	139	28	c2	c2	PROPN
ejpam-2421	139	29	+	+	CCONJ
ejpam-2421	139	30	(	(	PUNCT
ejpam-2421	139	31	r4	r4	VERB
ejpam-2421	139	32	−	−	NOUN
ejpam-2421	139	33	r2)l3	r2)l3	NOUN
ejpam-2421	139	34	=	=	SYM
ejpam-2421	139	35	(	(	PUNCT
ejpam-2421	139	36	2	2	NUM
ejpam-2421	139	37	+	+	NUM
ejpam-2421	139	38	2rl1	2rl1	NUM
ejpam-2421	139	39	)	)	PUNCT
ejpam-2421	140	1	+	+	CCONJ
ejpam-2421	140	2	(	(	PUNCT
ejpam-2421	140	3	r4	r4	VERB
ejpam-2421	140	4	−	−	PROPN
ejpam-2421	140	5	r3)l3	r3)l3	PROPN
ejpam-2421	140	6	c5	c5	PROPN
ejpam-2421	140	7	=	=	PROPN
ejpam-2421	140	8	c3	c3	PROPN
ejpam-2421	140	9	+	+	CCONJ
ejpam-2421	140	10	(	(	PUNCT
ejpam-2421	140	11	r5	r5	PROPN
ejpam-2421	140	12	−	−	PROPN
ejpam-2421	140	13	r4)l4	r4)l4	NOUN
ejpam-2421	140	14	=	=	SYM
ejpam-2421	140	15	4m+	4m+	NUM
ejpam-2421	140	16	(	(	PUNCT
ejpam-2421	140	17	r3	r3	PROPN
ejpam-2421	140	18	−	−	PROPN
ejpam-2421	140	19	r2)l2	r2)l2	VERB
ejpam-2421	140	20	+	+	CCONJ
ejpam-2421	140	21	(	(	PUNCT
ejpam-2421	140	22	r5	r5	PROPN
ejpam-2421	140	23	−	−	PROPN
ejpam-2421	140	24	r4)l4	r4)l4	NOUN
ejpam-2421	140	25	)	)	PUNCT
ejpam-2421	140	26	=	=	SYM
ejpam-2421	140	27	c3	c3	PROPN
ejpam-2421	140	28	,	,	PUNCT
ejpam-2421	140	29	for	for	ADP
ejpam-2421	140	30	(	(	PUNCT
ejpam-2421	140	31	c3	c3	PROPN
ejpam-2421	140	32	=	=	PROPN
ejpam-2421	140	33	c1	c1	PROPN
ejpam-2421	140	34	+	+	CCONJ
ejpam-2421	140	35	(	(	PUNCT
ejpam-2421	140	36	r3	r3	PROPN
ejpam-2421	140	37	−	−	PROPN
ejpam-2421	140	38	r2)l2⇒	r2)l2⇒	ADP
ejpam-2421	140	39	c3	c3	PROPN
ejpam-2421	140	40	=	=	SYM
ejpam-2421	140	41	4m+	4m+	NUM
ejpam-2421	140	42	(	(	PUNCT
ejpam-2421	140	43	r3	r3	PROPN
ejpam-2421	140	44	−	−	PROPN
ejpam-2421	140	45	r2)l2	r2)l2	VERB
ejpam-2421	140	46	)	)	PUNCT
ejpam-2421	140	47	.	.	PUNCT
ejpam-2421	141	1	from	from	ADP
ejpam-2421	141	2	lemma	lemma	PROPN
ejpam-2421	141	3	2	2	NUM
ejpam-2421	141	4	:	:	PUNCT
ejpam-2421	141	5	(	(	PUNCT
ejpam-2421	141	6	i	i	NOUN
ejpam-2421	141	7	=	=	NOUN
ejpam-2421	141	8	3	3	NUM
ejpam-2421	141	9	)	)	PUNCT
ejpam-2421	141	10	,	,	PUNCT
ejpam-2421	141	11	2a	2a	NUM
ejpam-2421	141	12	=	=	SYM
ejpam-2421	141	13	c3l3	c3l3	NOUN
ejpam-2421	141	14	+	+	X
ejpam-2421	141	15	r3	r3	PROPN
ejpam-2421	141	16	+	+	CCONJ
ejpam-2421	141	17	r4	r4	PROPN
ejpam-2421	141	18	,	,	PUNCT
ejpam-2421	141	19	r3	r3	PROPN
ejpam-2421	141	20	=	=	SYM
ejpam-2421	141	21	2a−	2a−	PROPN
ejpam-2421	141	22	c3l3	c3l3	VERB
ejpam-2421	141	23	−	−	NOUN
ejpam-2421	141	24	r4⇒	r4⇒	PROPN
ejpam-2421	141	25	r3	r3	PROPN
ejpam-2421	141	26	=	=	SYM
ejpam-2421	141	27	2a−	2a−	PROPN
ejpam-2421	141	28	(	(	PUNCT
ejpam-2421	141	29	4m+	4m+	NUM
ejpam-2421	141	30	(	(	PUNCT
ejpam-2421	141	31	r3	r3	PROPN
ejpam-2421	141	32	−	−	PROPN
ejpam-2421	141	33	r2)l2)l3	r2)l2)l3	PROPN
ejpam-2421	141	34	−	−	PROPN
ejpam-2421	141	35	r4	r4	PROPN
ejpam-2421	141	36	⇒	⇒	NOUN
ejpam-2421	141	37	r4	r4	PROPN
ejpam-2421	141	38	=	=	PUNCT
ejpam-2421	141	39	2a−	2a−	PROPN
ejpam-2421	141	40	4ml3	4ml3	NUM
ejpam-2421	142	1	+	+	CCONJ
ejpam-2421	142	2	(	(	PUNCT
ejpam-2421	142	3	2r	2r	NUM
ejpam-2421	142	4	−	−	NUM
ejpam-2421	142	5	r3)l2l3	r3)l2l3	NOUN
ejpam-2421	142	6	−	−	PROPN
ejpam-2421	142	7	r3	r3	PROPN
ejpam-2421	142	8	)	)	PUNCT
ejpam-2421	142	9	for	for	ADP
ejpam-2421	142	10	i	i	PRON
ejpam-2421	142	11	=	=	NOUN
ejpam-2421	142	12	4	4	NUM
ejpam-2421	142	13	2a	2a	NUM
ejpam-2421	142	14	=	=	NOUN
ejpam-2421	142	15	c4l4	c4l4	ADJ
ejpam-2421	142	16	+	+	CCONJ
ejpam-2421	142	17	r5	r5	PROPN
ejpam-2421	142	18	+	+	CCONJ
ejpam-2421	142	19	r4	r4	NOUN
ejpam-2421	142	20	,	,	PUNCT
ejpam-2421	142	21	r4	r4	NOUN
ejpam-2421	142	22	=	=	NOUN
ejpam-2421	142	23	r5⇒	r5⇒	NOUN
ejpam-2421	142	24	2a	2a	NUM
ejpam-2421	142	25	=	=	SYM
ejpam-2421	142	26	(	(	PUNCT
ejpam-2421	142	27	2	2	NUM
ejpam-2421	142	28	+	+	NUM
ejpam-2421	142	29	2rl1)l4	2rl1)l4	NUM
ejpam-2421	142	30	+	+	CCONJ
ejpam-2421	142	31	(	(	PUNCT
ejpam-2421	142	32	r4	r4	VERB
ejpam-2421	142	33	−	−	PROPN
ejpam-2421	142	34	r3)l3l4	r3)l3l4	NOUN
ejpam-2421	142	35	+	+	CCONJ
ejpam-2421	142	36	2r4	2r4	NUM
ejpam-2421	142	37	r4	r4	NOUN
ejpam-2421	142	38	=	=	PROPN
ejpam-2421	142	39	2ra+	2ra+	PROPN
ejpam-2421	142	40	2s1l1	2s1l1	NUM
ejpam-2421	142	41	−	−	PROPN
ejpam-2421	143	1	2rl2l3	2rl2l3	NUM
ejpam-2421	143	2	−	−	PROPN
ejpam-2421	143	3	2s1l3	2s1l3	NUM
ejpam-2421	144	1	+	+	CCONJ
ejpam-2421	144	2	2rl2l3	2rl2l3	NUM
ejpam-2421	144	3	−	−	NOUN
ejpam-2421	144	4	(	(	PUNCT
ejpam-2421	144	5	sl1	sl1	PROPN
ejpam-2421	144	6	−	−	PROPN
ejpam-2421	144	7	2l2)(l2l3	2l2)(l2l3	NUM
ejpam-2421	144	8	+	+	CCONJ
ejpam-2421	144	9	1	1	X
ejpam-2421	144	10	)	)	PUNCT
ejpam-2421	144	11	⇒	⇒	VERB
ejpam-2421	144	12	r4	r4	NOUN
ejpam-2421	144	13	=	=	PUNCT
ejpam-2421	144	14	2ra+	2ra+	PROPN
ejpam-2421	144	15	2s1l1	2s1l1	NUM
ejpam-2421	144	16	−	−	PROPN
ejpam-2421	144	17	2rl2l3	2rl2l3	NUM
ejpam-2421	144	18	−	−	PROPN
ejpam-2421	144	19	2s1l3	2s1l3	NUM
ejpam-2421	144	20	+	+	CCONJ
ejpam-2421	144	21	2rl2l3	2rl2l3	NUM
ejpam-2421	144	22	−	−	PROPN
ejpam-2421	144	23	sl1l2l3	sl1l2l3	PROPN
ejpam-2421	144	24	−	−	PROPN
ejpam-2421	144	25	sl1	sl1	PROPN
ejpam-2421	144	26	+	+	CCONJ
ejpam-2421	144	27	2l2	2l2	NUM
ejpam-2421	144	28	2	2	NUM
ejpam-2421	144	29	l3	l3	NOUN
ejpam-2421	144	30	+	+	CCONJ
ejpam-2421	144	31	2l2	2l2	NUM
ejpam-2421	144	32	⇒	⇒	NOUN
ejpam-2421	144	33	r4	r4	NOUN
ejpam-2421	144	34	=	=	PUNCT
ejpam-2421	144	35	2ra−	2ra−	NUM
ejpam-2421	144	36	2rl2l3	2rl2l3	NUM
ejpam-2421	144	37	−	−	PROPN
ejpam-2421	144	38	2s1l3	2s1l3	NUM
ejpam-2421	144	39	+	+	CCONJ
ejpam-2421	144	40	2rl2l3	2rl2l3	NUM
ejpam-2421	144	41	−	−	NUM
ejpam-2421	144	42	2s1l1l2l3	2s1l1l2l3	NUM
ejpam-2421	144	43	+	+	CCONJ
ejpam-2421	144	44	2l2	2l2	NUM
ejpam-2421	144	45	2	2	NUM
ejpam-2421	144	46	l3	l3	NOUN
ejpam-2421	144	47	+	+	CCONJ
ejpam-2421	144	48	2l2	2l2	NUM
ejpam-2421	144	49	r4	r4	NOUN
ejpam-2421	144	50	=	=	NOUN
ejpam-2421	144	51	2rl1l2	2rl1l2	NUM
ejpam-2421	144	52	+	+	NUM
ejpam-2421	144	53	2r	2r	NUM
ejpam-2421	144	54	−	−	ADP
ejpam-2421	144	55	2rl2l3	2rl2l3	NUM
ejpam-2421	144	56	−	−	PROPN
ejpam-2421	144	57	2s1l3	2s1l3	NUM
ejpam-2421	144	58	+	+	CCONJ
ejpam-2421	144	59	2rl2l3	2rl2l3	NUM
ejpam-2421	145	1	+	+	CCONJ
ejpam-2421	146	1	2s1l1l2l3	2s1l1l2l3	NUM
ejpam-2421	146	2	+	+	CCONJ
ejpam-2421	146	3	2l2	2l2	NUM
ejpam-2421	146	4	2	2	NUM
ejpam-2421	146	5	l3	l3	NOUN
ejpam-2421	146	6	+	+	CCONJ
ejpam-2421	146	7	2l2	2l2	NUM
ejpam-2421	146	8	hold	hold	NOUN
ejpam-2421	146	9	.	.	PUNCT
ejpam-2421	147	1	therefore	therefore	ADV
ejpam-2421	147	2	we	we	PRON
ejpam-2421	147	3	obtain	obtain	VERB
ejpam-2421	147	4	the	the	DET
ejpam-2421	147	5	value	value	NOUN
ejpam-2421	147	6	r4	r4	NOUN
ejpam-2421	147	7	,	,	PUNCT
ejpam-2421	147	8	as	as	SCONJ
ejpam-2421	147	9	r4	r4	PROPN
ejpam-2421	147	10	=	=	SYM
ejpam-2421	147	11	2[(r	2[(r	NUM
ejpam-2421	147	12	−	−	NOUN
ejpam-2421	147	13	s1l3)a+	s1l3)a+	NOUN
ejpam-2421	147	14	l2b	l2b	X
ejpam-2421	147	15	]	]	X
ejpam-2421	147	16	=	=	SYM
ejpam-2421	147	17	(	(	PUNCT
ejpam-2421	147	18	r	r	NOUN
ejpam-2421	147	19	−	−	PROPN
ejpam-2421	147	20	s1l3)a+	s1l3)a+	NOUN
ejpam-2421	147	21	l2b	l2b	ADJ
ejpam-2421	147	22	for	for	ADP
ejpam-2421	147	23	b	b	NOUN
ejpam-2421	147	24	=	=	SYM
ejpam-2421	147	25	l2l3	l2l3	PROPN
ejpam-2421	147	26	+	+	CCONJ
ejpam-2421	147	27	1,a=	1,a=	PROPN
ejpam-2421	147	28	l1l2	l1l2	PROPN
ejpam-2421	148	1	+	+	NOUN
ejpam-2421	148	2	1	1	X
ejpam-2421	148	3	.	.	PUNCT
ejpam-2421	148	4	(	(	PUNCT
ejpam-2421	148	5	5	5	X
ejpam-2421	148	6	)	)	PUNCT
ejpam-2421	148	7	furthermore	furthermore	ADV
ejpam-2421	148	8	c4	c4	NOUN
ejpam-2421	148	9	=(	=(	NOUN
ejpam-2421	148	10	2	2	NUM
ejpam-2421	148	11	+	+	NUM
ejpam-2421	148	12	r2l1	r2l1	NOUN
ejpam-2421	148	13	)	)	PUNCT
ejpam-2421	148	14	+	+	CCONJ
ejpam-2421	148	15	(	(	PUNCT
ejpam-2421	148	16	r4	r4	VERB
ejpam-2421	148	17	−	−	PROPN
ejpam-2421	148	18	r3)l3	r3)l3	X
ejpam-2421	148	19	=	=	SYM
ejpam-2421	148	20	(	(	PUNCT
ejpam-2421	148	21	2	2	NUM
ejpam-2421	148	22	+	+	NUM
ejpam-2421	148	23	2rl1	2rl1	NUM
ejpam-2421	148	24	)	)	PUNCT
ejpam-2421	149	1	+	+	CCONJ
ejpam-2421	150	1	[	[	X
ejpam-2421	150	2	(	(	PUNCT
ejpam-2421	150	3	2r	2r	NUM
ejpam-2421	150	4	−	−	PROPN
ejpam-2421	150	5	sl3)a+	sl3)a+	NOUN
ejpam-2421	150	6	2l2b	2l2b	NOUN
ejpam-2421	150	7	−	−	PROPN
ejpam-2421	150	8	sl1	sl1	PROPN
ejpam-2421	150	9	+	+	CCONJ
ejpam-2421	150	10	2l2]l3	2l2]l3	NUM
ejpam-2421	150	11	ö.	ö.	NOUN
ejpam-2421	150	12	özer	özer	NOUN
ejpam-2421	150	13	,	,	PUNCT
ejpam-2421	150	14	a.	a.	NOUN
ejpam-2421	150	15	pekin	pekin	PROPN
ejpam-2421	150	16	/	/	SYM
ejpam-2421	150	17	eur	eur	PROPN
ejpam-2421	150	18	.	.	PUNCT
ejpam-2421	151	1	j.	j.	PROPN
ejpam-2421	151	2	pure	pure	PROPN
ejpam-2421	151	3	appl	appl	PROPN
ejpam-2421	151	4	.	.	PROPN
ejpam-2421	151	5	math	math	PROPN
ejpam-2421	151	6	,	,	PUNCT
ejpam-2421	151	7	8	8	NUM
ejpam-2421	151	8	(	(	PUNCT
ejpam-2421	151	9	2015	2015	NUM
ejpam-2421	151	10	)	)	PUNCT
ejpam-2421	151	11	,	,	PUNCT
ejpam-2421	151	12	343	343	NUM
ejpam-2421	151	13	-	-	SYM
ejpam-2421	151	14	356	356	NUM
ejpam-2421	151	15	348	348	NUM
ejpam-2421	151	16	=(	=(	NOUN
ejpam-2421	151	17	2	2	NUM
ejpam-2421	151	18	+	+	NUM
ejpam-2421	151	19	2rl1	2rl1	NUM
ejpam-2421	151	20	)	)	PUNCT
ejpam-2421	152	1	+	+	CCONJ
ejpam-2421	152	2	2ral3	2ral3	NUM
ejpam-2421	152	3	−	−	PROPN
ejpam-2421	152	4	sl3	sl3	PROPN
ejpam-2421	152	5	2a+	2a+	NUM
ejpam-2421	152	6	2l2l3b	2l2l3b	NUM
ejpam-2421	152	7	−	−	PROPN
ejpam-2421	152	8	sl1l3	sl1l3	PROPN
ejpam-2421	152	9	+	+	NUM
ejpam-2421	152	10	2l3	2l3	NUM
ejpam-2421	152	11	=	=	NOUN
ejpam-2421	152	12	2rc	2rc	NOUN
ejpam-2421	152	13	−	−	NOUN
ejpam-2421	152	14	sl3c	sl3c	PROPN
ejpam-2421	152	15	+	+	CCONJ
ejpam-2421	152	16	2(1	2(1	NUM
ejpam-2421	152	17	+	+	CCONJ
ejpam-2421	152	18	l2l3	l2l3	X
ejpam-2421	152	19	)	)	PUNCT
ejpam-2421	152	20	+	+	SYM
ejpam-2421	153	1	2l2l3b	2l2l3b	NUM
ejpam-2421	153	2	=	=	NUM
ejpam-2421	153	3	c(2r	c(2r	PROPN
ejpam-2421	153	4	−	−	PROPN
ejpam-2421	153	5	sl3	sl3	PROPN
ejpam-2421	153	6	)	)	PUNCT
ejpam-2421	153	7	+	+	NUM
ejpam-2421	153	8	2b	2b	NUM
ejpam-2421	153	9	+	+	CCONJ
ejpam-2421	153	10	2bl2l3	2bl2l3	NUM
ejpam-2421	153	11	=	=	NUM
ejpam-2421	153	12	c(2r	c(2r	PROPN
ejpam-2421	153	13	−	−	PROPN
ejpam-2421	153	14	sl3	sl3	PROPN
ejpam-2421	153	15	)	)	PUNCT
ejpam-2421	154	1	+	+	NUM
ejpam-2421	154	2	2b(1	2b(1	NUM
ejpam-2421	154	3	+	+	SYM
ejpam-2421	154	4	l2l3	l2l3	X
ejpam-2421	154	5	)	)	PUNCT
ejpam-2421	154	6	and	and	CCONJ
ejpam-2421	154	7	so	so	ADV
ejpam-2421	154	8	we	we	PRON
ejpam-2421	154	9	have	have	VERB
ejpam-2421	154	10	c4	c4	NOUN
ejpam-2421	154	11	=	=	PUNCT
ejpam-2421	154	12	c(2r	c(2r	PROPN
ejpam-2421	154	13	−	−	PROPN
ejpam-2421	154	14	sl3	sl3	PROPN
ejpam-2421	154	15	)	)	PUNCT
ejpam-2421	155	1	+	+	NUM
ejpam-2421	155	2	2b2	2b2	NUM
ejpam-2421	155	3	(	(	PUNCT
ejpam-2421	155	4	for	for	ADP
ejpam-2421	155	5	the	the	DET
ejpam-2421	155	6	values	value	NOUN
ejpam-2421	155	7	a	a	PRON
ejpam-2421	155	8	,	,	PUNCT
ejpam-2421	155	9	b	b	NOUN
ejpam-2421	155	10	and	and	CCONJ
ejpam-2421	155	11	c	c	PROPN
ejpam-2421	155	12	=	=	PROPN
ejpam-2421	155	13	l1	l1	PROPN
ejpam-2421	155	14	+	+	CCONJ
ejpam-2421	155	15	al3	al3	PROPN
ejpam-2421	155	16	)	)	PUNCT
ejpam-2421	155	17	.	.	PUNCT
ejpam-2421	156	1	(	(	PUNCT
ejpam-2421	156	2	6	6	NUM
ejpam-2421	156	3	)	)	PUNCT
ejpam-2421	156	4	if	if	SCONJ
ejpam-2421	156	5	the	the	DET
ejpam-2421	156	6	equalities	equality	NOUN
ejpam-2421	156	7	a	a	DET
ejpam-2421	156	8	=	=	X
ejpam-2421	156	9	ra+	ra+	PROPN
ejpam-2421	156	10	sl1	sl1	PROPN
ejpam-2421	156	11	,	,	PUNCT
ejpam-2421	156	12	r4	r4	NOUN
ejpam-2421	156	13	=	=	PUNCT
ejpam-2421	156	14	(	(	PUNCT
ejpam-2421	156	15	r	r	NOUN
ejpam-2421	156	16	−	−	PROPN
ejpam-2421	156	17	s1l3)a+	s1l3)a+	NOUN
ejpam-2421	156	18	l2b	l2b	ADJ
ejpam-2421	156	19	and	and	CCONJ
ejpam-2421	156	20	c4	c4	NOUN
ejpam-2421	156	21	=	=	SYM
ejpam-2421	156	22	c(2r	c(2r	PROPN
ejpam-2421	156	23	−	−	PROPN
ejpam-2421	156	24	sl3	sl3	PROPN
ejpam-2421	156	25	)	)	PUNCT
ejpam-2421	157	1	+	+	NUM
ejpam-2421	157	2	2b2	2b2	NUM
ejpam-2421	157	3	are	be	AUX
ejpam-2421	157	4	written	write	VERB
ejpam-2421	157	5	in	in	ADP
ejpam-2421	157	6	l4	l4	PROPN
ejpam-2421	157	7	then	then	ADV
ejpam-2421	157	8	l4	l4	PROPN
ejpam-2421	157	9	=	=	PROPN
ejpam-2421	157	10	2a−	2a−	PROPN
ejpam-2421	157	11	2r4	2r4	NUM
ejpam-2421	157	12	c4	c4	NOUN
ejpam-2421	157	13	=	=	PROPN
ejpam-2421	157	14	2ra+	2ra+	PROPN
ejpam-2421	157	15	sl1	sl1	PROPN
ejpam-2421	157	16	−	−	PROPN
ejpam-2421	157	17	2(2r	2(2r	NUM
ejpam-2421	157	18	−	−	ADP
ejpam-2421	157	19	sl3)a−	sl3)a−	NOUN
ejpam-2421	157	20	4l2b	4l2b	NOUN
ejpam-2421	157	21	c(2r	c(2r	PROPN
ejpam-2421	158	1	−	−	PROPN
ejpam-2421	158	2	sl3	sl3	PROPN
ejpam-2421	158	3	)	)	PUNCT
ejpam-2421	159	1	+	+	NUM
ejpam-2421	159	2	2b2	2b2	NUM
ejpam-2421	159	3	holds	hold	NOUN
ejpam-2421	159	4	.	.	PUNCT
ejpam-2421	160	1	by	by	ADP
ejpam-2421	160	2	taking	take	VERB
ejpam-2421	160	3	s	s	PART
ejpam-2421	160	4	=	=	SYM
ejpam-2421	160	5	2s1	2s1	NUM
ejpam-2421	160	6	we	we	PRON
ejpam-2421	160	7	obtain	obtain	VERB
ejpam-2421	160	8	l4	l4	PROPN
ejpam-2421	160	9	=	=	PUNCT
ejpam-2421	161	1	s1(c	s1(c	PROPN
ejpam-2421	161	2	+	+	SYM
ejpam-2421	161	3	l3a)−	l3a)−	VERB
ejpam-2421	161	4	2l2b	2l2b	NUM
ejpam-2421	161	5	−	−	PROPN
ejpam-2421	162	1	ra	ra	PROPN
ejpam-2421	162	2	c(r	c(r	PROPN
ejpam-2421	162	3	−	−	PROPN
ejpam-2421	162	4	s1l3	s1l3	NOUN
ejpam-2421	162	5	)	)	PUNCT
ejpam-2421	162	6	+	+	NUM
ejpam-2421	162	7	b2	b2	NOUN
ejpam-2421	162	8	.	.	PUNCT
ejpam-2421	163	1	(	(	PUNCT
ejpam-2421	163	2	7	7	NUM
ejpam-2421	163	3	)	)	PUNCT
ejpam-2421	163	4	from	from	ADP
ejpam-2421	163	5	this	this	DET
ejpam-2421	163	6	equation	equation	NOUN
ejpam-2421	163	7	c(r	c(r	PROPN
ejpam-2421	163	8	−	−	PROPN
ejpam-2421	163	9	s1l3)l4	s1l3)l4	VERB
ejpam-2421	163	10	+	+	CCONJ
ejpam-2421	163	11	b2l4	b2l4	X
ejpam-2421	163	12	=	=	SYM
ejpam-2421	163	13	s1(c	s1(c	X
ejpam-2421	163	14	+	+	PRON
ejpam-2421	163	15	l3a)−	l3a)−	VERB
ejpam-2421	163	16	2l2b	2l2b	NUM
ejpam-2421	163	17	−	−	PROPN
ejpam-2421	163	18	ra	ra	PROPN
ejpam-2421	163	19	⇒	⇒	NOUN
ejpam-2421	163	20	b2l4	b2l4	PUNCT
ejpam-2421	164	1	+	+	PUNCT
ejpam-2421	164	2	2l2b	2l2b	NUM
ejpam-2421	164	3	=	=	PUNCT
ejpam-2421	164	4	s1c	s1c	PROPN
ejpam-2421	164	5	+	+	NUM
ejpam-2421	165	1	s1l3a−	s1l3a−	X
ejpam-2421	166	1	ra−	ra−	PROPN
ejpam-2421	166	2	rc	rc	PROPN
ejpam-2421	166	3	l4	l4	PROPN
ejpam-2421	166	4	+	+	CCONJ
ejpam-2421	166	5	s1cl3l4	s1cl3l4	PROPN
ejpam-2421	166	6	⇒	⇒	NOUN
ejpam-2421	166	7	b2l4	b2l4	PUNCT
ejpam-2421	167	1	+	+	PUNCT
ejpam-2421	167	2	2l2b	2l2b	NUM
ejpam-2421	167	3	=	=	SYM
ejpam-2421	167	4	s1(c	s1(c	X
ejpam-2421	167	5	+	+	NUM
ejpam-2421	167	6	l3a+	l3a+	NOUN
ejpam-2421	167	7	cl3l4)−	cl3l4)−	ADP
ejpam-2421	167	8	ra+	ra+	ADJ
ejpam-2421	167	9	cl4	cl4	PROPN
ejpam-2421	167	10	⇒	⇒	NOUN
ejpam-2421	167	11	b2l4	b2l4	PUNCT
ejpam-2421	168	1	+	+	PUNCT
ejpam-2421	168	2	2l2b	2l2b	NUM
ejpam-2421	168	3	=	=	SYM
ejpam-2421	168	4	s1[c(1	s1[c(1	NOUN
ejpam-2421	168	5	+	+	X
ejpam-2421	168	6	l3l4	l3l4	NOUN
ejpam-2421	168	7	)	)	PUNCT
ejpam-2421	169	1	+	+	CCONJ
ejpam-2421	169	2	al3]−	al3]−	PROPN
ejpam-2421	169	3	r(a+	r(a+	PROPN
ejpam-2421	169	4	cl4	cl4	NOUN
ejpam-2421	169	5	)	)	PUNCT
ejpam-2421	169	6	hold	hold	VERB
ejpam-2421	169	7	and	and	CCONJ
ejpam-2421	169	8	this	this	PRON
ejpam-2421	169	9	proves	prove	VERB
ejpam-2421	169	10	that	that	SCONJ
ejpam-2421	169	11	r	r	NOUN
ejpam-2421	169	12	and	and	CCONJ
ejpam-2421	169	13	s1	s1	NOUN
ejpam-2421	169	14	are	be	AUX
ejpam-2421	169	15	uniquely	uniquely	ADV
ejpam-2421	169	16	determined	determine	VERB
ejpam-2421	169	17	by	by	ADP
ejpam-2421	169	18	a	a	DET
ejpam-2421	169	19	=	=	X
ejpam-2421	169	20	ra+	ra+	PROPN
ejpam-2421	169	21	s1l1	s1l1	NOUN
ejpam-2421	169	22	.	.	PUNCT
ejpam-2421	170	1	now	now	ADV
ejpam-2421	170	2	,	,	PUNCT
ejpam-2421	170	3	let	let	VERB
ejpam-2421	170	4	’s	’s	PRON
ejpam-2421	170	5	determine	determine	VERB
ejpam-2421	170	6	the	the	DET
ejpam-2421	170	7	coefficients	coefficient	NOUN
ejpam-2421	170	8	td	td	NOUN
ejpam-2421	171	1	and	and	CCONJ
ejpam-2421	171	2	ud	ud	INTJ
ejpam-2421	171	3	of	of	ADP
ejpam-2421	171	4	the	the	DET
ejpam-2421	171	5	fundamental	fundamental	ADJ
ejpam-2421	171	6	unit	unit	NOUN
ejpam-2421	171	7	ǫd	ǫd	NOUN
ejpam-2421	171	8	=	=	SYM
ejpam-2421	172	1	(	(	PUNCT
ejpam-2421	172	2	td+ud	td+ud	NOUN
ejpam-2421	172	3	p	p	X
ejpam-2421	172	4	d	d	PROPN
ejpam-2421	172	5	2	2	NUM
ejpam-2421	172	6	)	)	PUNCT
ejpam-2421	172	7	>	>	X
ejpam-2421	172	8	1	1	NUM
ejpam-2421	172	9	)	)	PUNCT
ejpam-2421	172	10	for	for	ADP
ejpam-2421	172	11	d	d	PROPN
ejpam-2421	172	12	≡	≡	PROPN
ejpam-2421	172	13	1(mod4	1(mod4	NUM
ejpam-2421	172	14	)	)	PUNCT
ejpam-2421	172	15	and	and	CCONJ
ejpam-2421	172	16	the	the	DET
ejpam-2421	172	17	period	period	NOUN
ejpam-2421	172	18	kd	kd	X
ejpam-2421	172	19	=	=	NOUN
ejpam-2421	172	20	8	8	NUM
ejpam-2421	172	21	.	.	PUNCT
ejpam-2421	173	1	since	since	SCONJ
ejpam-2421	173	2	q−1=0	q−1=0	PROPN
ejpam-2421	173	3	q0	q0	PROPN
ejpam-2421	173	4	=	=	NOUN
ejpam-2421	173	5	1	1	NUM
ejpam-2421	173	6	q	q	NOUN
ejpam-2421	173	7	i+1	i+1	SYM
ejpam-2421	173	8	=	=	NOUN
ejpam-2421	173	9	qi+1q	qi+1q	NOUN
ejpam-2421	173	10	i	i	PRON
ejpam-2421	173	11	+	+	ADJ
ejpam-2421	173	12	q	q	PROPN
ejpam-2421	173	13	i−1	i−1	PROPN
ejpam-2421	173	14	,	,	PUNCT
ejpam-2421	173	15	(	(	PUNCT
ejpam-2421	173	16	i	i	PRON
ejpam-2421	173	17	≥	≥	VERB
ejpam-2421	173	18	0	0	NUM
ejpam-2421	173	19	)	)	PUNCT
ejpam-2421	173	20	q1	q1	NOUN
ejpam-2421	173	21	=	=	SYM
ejpam-2421	173	22	q1q0	q1q0	PROPN
ejpam-2421	173	23	+	+	ADJ
ejpam-2421	173	24	q−1⇒q1	q−1⇒q1	NOUN
ejpam-2421	173	25	=	=	SYM
ejpam-2421	173	26	l11	l11	PROPN
ejpam-2421	173	27	+	+	PROPN
ejpam-2421	173	28	0⇒q1	0⇒q1	PROPN
ejpam-2421	173	29	=	=	SYM
ejpam-2421	173	30	l1	l1	PROPN
ejpam-2421	173	31	q2	q2	NOUN
ejpam-2421	173	32	=	=	PROPN
ejpam-2421	173	33	q2q1	q2q1	PROPN
ejpam-2421	173	34	+	+	PROPN
ejpam-2421	173	35	q0⇒q2	q0⇒q2	NOUN
ejpam-2421	173	36	=	=	SYM
ejpam-2421	173	37	l2l1	l2l1	PROPN
ejpam-2421	174	1	+	+	CCONJ
ejpam-2421	174	2	1⇒q2	1⇒q2	NUM
ejpam-2421	174	3	=	=	PUNCT
ejpam-2421	174	4	a	a	DET
ejpam-2421	174	5	q3	q3	NOUN
ejpam-2421	174	6	=	=	NOUN
ejpam-2421	174	7	q3q2	q3q2	X
ejpam-2421	174	8	+	+	NOUN
ejpam-2421	174	9	q1⇒q3	q1⇒q3	X
ejpam-2421	174	10	=	=	NOUN
ejpam-2421	174	11	l3a+	l3a+	NOUN
ejpam-2421	175	1	l1⇒q3	l1⇒q3	NOUN
ejpam-2421	175	2	=	=	PUNCT
ejpam-2421	175	3	c	c	PROPN
ejpam-2421	175	4	q4	q4	PROPN
ejpam-2421	175	5	=	=	PROPN
ejpam-2421	175	6	q4q3⇒q4	q4q3⇒q4	PROPN
ejpam-2421	175	7	=	=	SYM
ejpam-2421	175	8	l4c	l4c	NOUN
ejpam-2421	175	9	+	+	CCONJ
ejpam-2421	175	10	a	a	DET
ejpam-2421	175	11	q5	q5	PROPN
ejpam-2421	175	12	=	=	SYM
ejpam-2421	175	13	q5q4	q5q4	PROPN
ejpam-2421	175	14	+	+	NOUN
ejpam-2421	175	15	q3⇒q5	q3⇒q5	NOUN
ejpam-2421	175	16	=	=	PUNCT
ejpam-2421	176	1	l3(l4c	l3(l4c	PROPN
ejpam-2421	177	1	+	+	CCONJ
ejpam-2421	177	2	a	a	X
ejpam-2421	177	3	)	)	PUNCT
ejpam-2421	178	1	+	+	PUNCT
ejpam-2421	178	2	c	c	VERB
ejpam-2421	178	3	⇒q5	⇒q5	NOUN
ejpam-2421	178	4	=	=	PUNCT
ejpam-2421	178	5	l3l4c	l3l4c	X
ejpam-2421	179	1	+	+	NUM
ejpam-2421	179	2	c	c	X
ejpam-2421	179	3	+	+	CCONJ
ejpam-2421	179	4	l3a	l3a	X
ejpam-2421	179	5	⇒q5	⇒q5	NOUN
ejpam-2421	179	6	=	=	PUNCT
ejpam-2421	179	7	c(l3l4	c(l3l4	PROPN
ejpam-2421	179	8	+	+	CCONJ
ejpam-2421	179	9	1	1	NUM
ejpam-2421	179	10	)	)	PUNCT
ejpam-2421	179	11	+	+	CCONJ
ejpam-2421	179	12	l3a	l3a	NOUN
ejpam-2421	179	13	.	.	PUNCT
ejpam-2421	180	1	q6	q6	NOUN
ejpam-2421	180	2	=	=	NOUN
ejpam-2421	180	3	ℓ2q5	ℓ2q5	PROPN
ejpam-2421	180	4	+	+	PROPN
ejpam-2421	180	5	q4	q4	PROPN
ejpam-2421	180	6	=	=	NOUN
ejpam-2421	180	7	⇒q6	⇒q6	NOUN
ejpam-2421	180	8	=	=	PUNCT
ejpam-2421	180	9	ℓ2[c(ℓ3ℓ4	ℓ2[c(ℓ3ℓ4	X
ejpam-2421	180	10	+	+	NOUN
ejpam-2421	180	11	1	1	NUM
ejpam-2421	180	12	)	)	PUNCT
ejpam-2421	180	13	+	+	CCONJ
ejpam-2421	180	14	ℓ3a	ℓ3a	ADV
ejpam-2421	180	15	]	]	PUNCT
ejpam-2421	181	1	+	+	CCONJ
ejpam-2421	181	2	ℓ4c	ℓ4c	NOUN
ejpam-2421	181	3	+	+	CCONJ
ejpam-2421	181	4	a=	a=	ADV
ejpam-2421	181	5	cℓ4(ℓ2ℓ3	cℓ4(ℓ2ℓ3	X
ejpam-2421	182	1	+	+	CCONJ
ejpam-2421	182	2	1	1	X
ejpam-2421	182	3	)	)	PUNCT
ejpam-2421	182	4	+	+	CCONJ
ejpam-2421	182	5	cℓ2	cℓ2	NOUN
ejpam-2421	182	6	+	+	ADJ
ejpam-2421	182	7	a(1	a(1	ADJ
ejpam-2421	182	8	+	+	CCONJ
ejpam-2421	182	9	ℓ2ℓ3	ℓ2ℓ3	NOUN
ejpam-2421	182	10	)	)	PUNCT
ejpam-2421	182	11	holds	hold	NOUN
ejpam-2421	182	12	,	,	PUNCT
ejpam-2421	182	13	where	where	SCONJ
ejpam-2421	182	14	if	if	SCONJ
ejpam-2421	182	15	we	we	PRON
ejpam-2421	182	16	take	take	VERB
ejpam-2421	182	17	b	b	NOUN
ejpam-2421	182	18	=	=	SYM
ejpam-2421	182	19	(	(	PUNCT
ejpam-2421	182	20	ℓ2ℓ3	ℓ2ℓ3	SYM
ejpam-2421	182	21	+	+	NUM
ejpam-2421	182	22	1	1	X
ejpam-2421	182	23	)	)	PUNCT
ejpam-2421	182	24	q6	q6	NOUN
ejpam-2421	182	25	=	=	PROPN
ejpam-2421	182	26	cℓ4b	cℓ4b	PROPN
ejpam-2421	182	27	+	+	CCONJ
ejpam-2421	183	1	cℓ2	cℓ2	PROPN
ejpam-2421	183	2	+	+	CCONJ
ejpam-2421	183	3	ab	ab	NOUN
ejpam-2421	183	4	=	=	PUNCT
ejpam-2421	183	5	c(ℓ4b	c(ℓ4b	X
ejpam-2421	183	6	+	+	NOUN
ejpam-2421	183	7	ℓ2	ℓ2	NOUN
ejpam-2421	183	8	)	)	PUNCT
ejpam-2421	184	1	+	+	CCONJ
ejpam-2421	184	2	ab	ab	PROPN
ejpam-2421	184	3	ö.	ö.	PROPN
ejpam-2421	184	4	özer	özer	NOUN
ejpam-2421	184	5	,	,	PUNCT
ejpam-2421	184	6	a.	a.	NOUN
ejpam-2421	184	7	pekin	pekin	PROPN
ejpam-2421	184	8	/	/	SYM
ejpam-2421	184	9	eur	eur	PROPN
ejpam-2421	184	10	.	.	PUNCT
ejpam-2421	185	1	j.	j.	PROPN
ejpam-2421	185	2	pure	pure	PROPN
ejpam-2421	185	3	appl	appl	PROPN
ejpam-2421	185	4	.	.	PROPN
ejpam-2421	185	5	math	math	PROPN
ejpam-2421	185	6	,	,	PUNCT
ejpam-2421	185	7	8	8	NUM
ejpam-2421	185	8	(	(	PUNCT
ejpam-2421	185	9	2015	2015	NUM
ejpam-2421	185	10	)	)	PUNCT
ejpam-2421	185	11	,	,	PUNCT
ejpam-2421	185	12	343	343	NUM
ejpam-2421	185	13	-	-	SYM
ejpam-2421	185	14	356	356	NUM
ejpam-2421	185	15	349	349	NUM
ejpam-2421	185	16	q7	q7	PROPN
ejpam-2421	185	17	=	=	SYM
ejpam-2421	185	18	ℓ1q6	ℓ1q6	X
ejpam-2421	185	19	+	+	ADJ
ejpam-2421	185	20	q5	q5	PROPN
ejpam-2421	185	21	=	=	SYM
ejpam-2421	185	22	⇒q7	⇒q7	ADV
ejpam-2421	185	23	=	=	SYM
ejpam-2421	185	24	ℓ1[c(bℓ4	ℓ1[c(bℓ4	PROPN
ejpam-2421	185	25	+	+	SYM
ejpam-2421	185	26	ℓ2	ℓ2	NOUN
ejpam-2421	185	27	)	)	PUNCT
ejpam-2421	185	28	+	+	CCONJ
ejpam-2421	185	29	ab	ab	X
ejpam-2421	185	30	]	]	X
ejpam-2421	185	31	+	+	CCONJ
ejpam-2421	185	32	c(ℓ3ℓ4	c(ℓ3ℓ4	X
ejpam-2421	185	33	+	+	NUM
ejpam-2421	185	34	1	1	NUM
ejpam-2421	185	35	)	)	PUNCT
ejpam-2421	185	36	+	+	CCONJ
ejpam-2421	185	37	aℓ3	aℓ3	NOUN
ejpam-2421	185	38	=	=	SYM
ejpam-2421	185	39	⇒q7	⇒q7	NOUN
ejpam-2421	185	40	=	=	SYM
ejpam-2421	185	41	cbℓ4ℓ1	cbℓ4ℓ1	NOUN
ejpam-2421	185	42	+	+	CCONJ
ejpam-2421	185	43	cℓ1ℓ2	cℓ1ℓ2	PROPN
ejpam-2421	185	44	+	+	NUM
ejpam-2421	185	45	abℓ1	abℓ1	PROPN
ejpam-2421	185	46	+	+	CCONJ
ejpam-2421	185	47	cℓ3ℓ4	cℓ3ℓ4	PROPN
ejpam-2421	185	48	+	+	PUNCT
ejpam-2421	185	49	c	c	NOUN
ejpam-2421	185	50	+	+	CCONJ
ejpam-2421	185	51	ℓ3a	ℓ3a	ADV
ejpam-2421	185	52	=(	=(	ADJ
ejpam-2421	185	53	cℓ4	cℓ4	NOUN
ejpam-2421	186	1	+	+	CCONJ
ejpam-2421	186	2	a)(ℓ1ℓ2ℓ3	a)(ℓ1ℓ2ℓ3	PROPN
ejpam-2421	186	3	+	+	CCONJ
ejpam-2421	186	4	ℓ1	ℓ1	ADJ
ejpam-2421	186	5	+	+	CCONJ
ejpam-2421	186	6	ℓ3	ℓ3	NOUN
ejpam-2421	186	7	)	)	PUNCT
ejpam-2421	187	1	+	+	CCONJ
ejpam-2421	187	2	ca	can	AUX
ejpam-2421	187	3	=(	=(	PROPN
ejpam-2421	187	4	cℓ4	cℓ4	PROPN
ejpam-2421	188	1	+	+	CCONJ
ejpam-2421	188	2	a)(aℓ3	a)(aℓ3	NOUN
ejpam-2421	189	1	+	+	CCONJ
ejpam-2421	189	2	ℓ1	ℓ1	NOUN
ejpam-2421	189	3	)	)	PUNCT
ejpam-2421	190	1	+	+	CCONJ
ejpam-2421	190	2	ca	can	AUX
ejpam-2421	191	1	and	and	CCONJ
ejpam-2421	191	2	so	so	ADV
ejpam-2421	191	3	we	we	PRON
ejpam-2421	191	4	can	can	AUX
ejpam-2421	191	5	obtain	obtain	VERB
ejpam-2421	191	6	q7	q7	PROPN
ejpam-2421	191	7	=	=	SYM
ejpam-2421	191	8	c2ℓ4	c2ℓ4	PROPN
ejpam-2421	192	1	+	+	X
ejpam-2421	192	2	2ac	2ac	X
ejpam-2421	192	3	for	for	ADP
ejpam-2421	192	4	c	c	NOUN
ejpam-2421	192	5	=	=	SYM
ejpam-2421	192	6	(	(	PUNCT
ejpam-2421	192	7	aℓ3	aℓ3	NOUN
ejpam-2421	192	8	+	+	CCONJ
ejpam-2421	192	9	ℓ1	ℓ1	NOUN
ejpam-2421	192	10	)	)	PUNCT
ejpam-2421	192	11	.	.	PUNCT
ejpam-2421	193	1	therefore	therefore	ADV
ejpam-2421	193	2	we	we	PRON
ejpam-2421	193	3	can	can	AUX
ejpam-2421	193	4	determine	determine	VERB
ejpam-2421	193	5	that	that	PRON
ejpam-2421	193	6	(	(	PUNCT
ejpam-2421	193	7	td	td	NOUN
ejpam-2421	193	8	,	,	PUNCT
ejpam-2421	193	9	ud	ud	INTJ
ejpam-2421	193	10	)	)	PUNCT
ejpam-2421	193	11	=	=	SYM
ejpam-2421	194	1	(	(	PUNCT
ejpam-2421	194	2	[	[	X
ejpam-2421	194	3	(	(	PUNCT
ejpam-2421	194	4	ar	ar	NOUN
ejpam-2421	194	5	+	+	PROPN
ejpam-2421	194	6	s1ℓ1)(c	s1ℓ1)(c	PROPN
ejpam-2421	194	7	2ℓ4	2ℓ4	X
ejpam-2421	195	1	+	+	X
ejpam-2421	195	2	2ac	2ac	X
ejpam-2421	195	3	)	)	PUNCT
ejpam-2421	196	1	+	+	NUM
ejpam-2421	196	2	2(c(bℓ4	2(c(bℓ4	NUM
ejpam-2421	196	3	+	+	NUM
ejpam-2421	196	4	ℓ2	ℓ2	NOUN
ejpam-2421	196	5	)	)	PUNCT
ejpam-2421	196	6	+	+	NUM
ejpam-2421	196	7	ab	ab	PROPN
ejpam-2421	196	8	)	)	PUNCT
ejpam-2421	197	1	]	]	PUNCT
ejpam-2421	197	2	,	,	PUNCT
ejpam-2421	197	3	c(cℓ4	c(cℓ4	PROPN
ejpam-2421	197	4	+	+	NOUN
ejpam-2421	197	5	2a	2a	NUM
ejpam-2421	197	6	)	)	PUNCT
ejpam-2421	197	7	)	)	PUNCT
ejpam-2421	198	1	and	and	CCONJ
ejpam-2421	198	2	d	d	NOUN
ejpam-2421	198	3	=	=	SYM
ejpam-2421	198	4	(	(	PUNCT
ejpam-2421	198	5	ar	ar	PROPN
ejpam-2421	198	6	+	+	NOUN
ejpam-2421	198	7	s1ℓ1	s1ℓ1	NOUN
ejpam-2421	198	8	)	)	PUNCT
ejpam-2421	198	9	2	2	NUM
ejpam-2421	198	10	+	+	NUM
ejpam-2421	198	11	4rℓ2	4rℓ2	NUM
ejpam-2421	198	12	+	+	NUM
ejpam-2421	198	13	4s1	4s1	NOUN
ejpam-2421	198	14	.	.	PUNCT
ejpam-2421	199	1	now	now	ADV
ejpam-2421	199	2	let	let	VERB
ejpam-2421	199	3	d	d	X
ejpam-2421	199	4	∈	∈	PROPN
ejpam-2421	199	5	d5	d5	NOUN
ejpam-2421	199	6	4	4	NUM
ejpam-2421	199	7	where	where	SCONJ
ejpam-2421	199	8	,	,	PUNCT
ejpam-2421	199	9	d5	d5	NOUN
ejpam-2421	199	10	4	4	NUM
ejpam-2421	199	11	=	=	NOUN
ejpam-2421	199	12	{	{	PUNCT
ejpam-2421	199	13	d	d	PROPN
ejpam-2421	199	14	∈	∈	PROPN
ejpam-2421	199	15	d|d	d|d	VERB
ejpam-2421	199	16	≡	≡	PROPN
ejpam-2421	199	17	5(mod8	5(mod8	NUM
ejpam-2421	199	18	)	)	PUNCT
ejpam-2421	199	19	,	,	PUNCT
ejpam-2421	199	20	b	b	PROPN
ejpam-2421	199	21	≡	≡	PROPN
ejpam-2421	199	22	4(mod8	4(mod8	NUM
ejpam-2421	199	23	)	)	PUNCT
ejpam-2421	199	24	}	}	PUNCT
ejpam-2421	200	1	=	=	X
ejpam-2421	200	2	{	{	PUNCT
ejpam-2421	200	3	d	d	X
ejpam-2421	200	4	∈	∈	PROPN
ejpam-2421	201	1	d	d	NOUN
ejpam-2421	201	2	|	|	NOUN
ejpam-2421	201	3	d	d	PROPN
ejpam-2421	201	4	=	=	PROPN
ejpam-2421	201	5	a2	a2	PROPN
ejpam-2421	201	6	+	+	CCONJ
ejpam-2421	201	7	8m+	8m+	NUM
ejpam-2421	201	8	4	4	NUM
ejpam-2421	201	9	,	,	PUNCT
ejpam-2421	201	10	a	a	DET
ejpam-2421	201	11	≡	≡	PROPN
ejpam-2421	201	12	1(mod2	1(mod2	NUM
ejpam-2421	201	13	)	)	PUNCT
ejpam-2421	201	14	,	,	PUNCT
ejpam-2421	201	15	0≤	0≤	NUM
ejpam-2421	201	16	4	4	NUM
ejpam-2421	201	17	m	m	NOUN
ejpam-2421	201	18	<	<	X
ejpam-2421	201	19	a−	a−	PROPN
ejpam-2421	201	20	2	2	NUM
ejpam-2421	201	21	}	}	PUNCT
ejpam-2421	201	22	therefore	therefore	ADV
ejpam-2421	201	23	b	b	X
ejpam-2421	201	24	=	=	PUNCT
ejpam-2421	201	25	8m+	8m+	NUM
ejpam-2421	201	26	4	4	NUM
ejpam-2421	201	27	and	and	CCONJ
ejpam-2421	201	28	m	m	PRON
ejpam-2421	201	29	>	>	X
ejpam-2421	201	30	0	0	NUM
ejpam-2421	202	1	hold	hold	NOUN
ejpam-2421	202	2	.	.	PUNCT
ejpam-2421	203	1	besides	besides	SCONJ
ejpam-2421	203	2	we	we	PRON
ejpam-2421	203	3	have	have	VERB
ejpam-2421	203	4	the	the	DET
ejpam-2421	203	5	following	follow	VERB
ejpam-2421	203	6	equations	equation	NOUN
ejpam-2421	203	7	from	from	ADP
ejpam-2421	203	8	lemma	lemma	PROPN
ejpam-2421	203	9	2	2	NUM
ejpam-2421	203	10	:	:	PUNCT
ejpam-2421	203	11	c−1	c−1	PROPN
ejpam-2421	203	12	=	=	SYM
ejpam-2421	203	13	b	b	PROPN
ejpam-2421	203	14	2	2	NUM
ejpam-2421	203	15	=	=	SYM
ejpam-2421	203	16	4m+	4m+	NUM
ejpam-2421	203	17	2	2	NUM
ejpam-2421	203	18	c1	c1	NOUN
ejpam-2421	203	19	=	=	PROPN
ejpam-2421	203	20	c−1	c−1	PROPN
ejpam-2421	203	21	+	+	CCONJ
ejpam-2421	203	22	(	(	PUNCT
ejpam-2421	203	23	r1	r1	PROPN
ejpam-2421	203	24	−	−	PROPN
ejpam-2421	203	25	r0)ℓ0	r0)ℓ0	NOUN
ejpam-2421	203	26	=	=	NOUN
ejpam-2421	203	27	⇒	⇒	NOUN
ejpam-2421	203	28	c1	c1	NOUN
ejpam-2421	203	29	=	=	SYM
ejpam-2421	203	30	c−1	c−1	PROPN
ejpam-2421	203	31	=	=	PROPN
ejpam-2421	203	32	⇒	⇒	NOUN
ejpam-2421	203	33	c1	c1	NOUN
ejpam-2421	203	34	=	=	PUNCT
ejpam-2421	204	1	4m+	4m+	NUM
ejpam-2421	204	2	2	2	NUM
ejpam-2421	204	3	and	and	CCONJ
ejpam-2421	204	4	2a−	2a−	NUM
ejpam-2421	204	5	ri	ri	PROPN
ejpam-2421	205	1	=	=	NOUN
ejpam-2421	205	2	ciℓi	ciℓi	NOUN
ejpam-2421	205	3	+	+	CCONJ
ejpam-2421	205	4	ri+1	ri+1	NOUN
ejpam-2421	205	5	=	=	SYM
ejpam-2421	205	6	⇒	⇒	NOUN
ejpam-2421	205	7	(	(	PUNCT
ejpam-2421	205	8	i	i	NOUN
ejpam-2421	205	9	=	=	NOUN
ejpam-2421	205	10	1	1	X
ejpam-2421	205	11	)	)	PUNCT
ejpam-2421	205	12	2a−	2a−	PROPN
ejpam-2421	205	13	r1	r1	NOUN
ejpam-2421	205	14	=	=	SYM
ejpam-2421	205	15	c1ℓ1	c1ℓ1	NOUN
ejpam-2421	205	16	+	+	NUM
ejpam-2421	205	17	r2	r2	NOUN
ejpam-2421	205	18	=	=	NOUN
ejpam-2421	205	19	⇒	⇒	NOUN
ejpam-2421	205	20	2a	2a	NUM
ejpam-2421	205	21	=	=	SYM
ejpam-2421	205	22	(	(	PUNCT
ejpam-2421	205	23	4m+	4m+	NUM
ejpam-2421	205	24	2)ℓ1	2)ℓ1	NUM
ejpam-2421	205	25	+	+	NUM
ejpam-2421	205	26	r2	r2	NOUN
ejpam-2421	205	27	,	,	PUNCT
ejpam-2421	205	28	r2	r2	PROPN
ejpam-2421	205	29	=	=	PROPN
ejpam-2421	205	30	2a−	2a−	PROPN
ejpam-2421	205	31	2(m+	2(m+	NUM
ejpam-2421	205	32	1)ℓ1	1)ℓ1	NUM
ejpam-2421	205	33	=	=	NOUN
ejpam-2421	205	34	⇒	⇒	NOUN
ejpam-2421	205	35	r1	r1	NOUN
ejpam-2421	205	36	=	=	SYM
ejpam-2421	205	37	r8	r8	PROPN
ejpam-2421	205	38	,	,	PUNCT
ejpam-2421	205	39	c1	c1	PROPN
ejpam-2421	205	40	=	=	PROPN
ejpam-2421	205	41	c7	c7	PROPN
ejpam-2421	205	42	,	,	PUNCT
ejpam-2421	205	43	r2	r2	PROPN
ejpam-2421	205	44	=	=	SYM
ejpam-2421	205	45	r7	r7	PROPN
ejpam-2421	205	46	,	,	PUNCT
ejpam-2421	205	47	c2	c2	PROPN
ejpam-2421	205	48	=	=	SYM
ejpam-2421	205	49	c6	c6	PROPN
ejpam-2421	205	50	,	,	PUNCT
ejpam-2421	205	51	r3	r3	PROPN
ejpam-2421	205	52	=	=	SYM
ejpam-2421	205	53	r6	r6	PROPN
ejpam-2421	205	54	,	,	PUNCT
ejpam-2421	205	55	c3	c3	PROPN
ejpam-2421	205	56	=	=	SYM
ejpam-2421	205	57	c5	c5	PROPN
ejpam-2421	205	58	,	,	PUNCT
ejpam-2421	205	59	r4	r4	NOUN
ejpam-2421	205	60	=	=	SYM
ejpam-2421	205	61	r5	r5	PROPN
ejpam-2421	205	62	.	.	PUNCT
ejpam-2421	206	1	since	since	SCONJ
ejpam-2421	206	2	r2	r2	PROPN
ejpam-2421	206	3	is	be	AUX
ejpam-2421	206	4	even	even	ADV
ejpam-2421	206	5	number	number	NOUN
ejpam-2421	206	6	then	then	ADV
ejpam-2421	206	7	∃r	∃r	PROPN
ejpam-2421	206	8	∋	∋	NOUN
ejpam-2421	206	9	r2	r2	PROPN
ejpam-2421	206	10	=	=	SYM
ejpam-2421	206	11	2r	2r	NUM
ejpam-2421	206	12	.	.	PUNCT
ejpam-2421	207	1	and	and	CCONJ
ejpam-2421	207	2	so	so	ADV
ejpam-2421	207	3	r	r	NOUN
ejpam-2421	207	4	is	be	AUX
ejpam-2421	207	5	defined	define	VERB
ejpam-2421	207	6	as	as	SCONJ
ejpam-2421	207	7	r	r	NOUN
ejpam-2421	207	8	=	=	SYM
ejpam-2421	207	9	¨	¨	NOUN
ejpam-2421	207	10	odd	odd	ADJ
ejpam-2421	207	11	ℓ1	ℓ1	NOUN
ejpam-2421	207	12	even	even	ADV
ejpam-2421	207	13	number	number	NOUN
ejpam-2421	207	14	even	even	ADV
ejpam-2421	207	15	ℓ1	ℓ1	VERB
ejpam-2421	207	16	odd	odd	ADJ
ejpam-2421	207	17	number	number	NOUN
ejpam-2421	207	18	if	if	SCONJ
ejpam-2421	207	19	we	we	PRON
ejpam-2421	207	20	take	take	VERB
ejpam-2421	207	21	i	i	PRON
ejpam-2421	207	22	=	=	NOUN
ejpam-2421	207	23	2	2	NUM
ejpam-2421	207	24	,	,	PUNCT
ejpam-2421	207	25	then	then	ADV
ejpam-2421	207	26	from	from	ADP
ejpam-2421	207	27	lemma	lemma	PROPN
ejpam-2421	207	28	2	2	NUM
ejpam-2421	207	29	2a	2a	NUM
ejpam-2421	207	30	=	=	NUM
ejpam-2421	208	1	c2ℓ2	c2ℓ2	PROPN
ejpam-2421	208	2	+	+	NUM
ejpam-2421	208	3	r2	r2	PROPN
ejpam-2421	208	4	+	+	CCONJ
ejpam-2421	208	5	r3	r3	PROPN
ejpam-2421	208	6	=	=	SYM
ejpam-2421	208	7	⇒	⇒	VERB
ejpam-2421	208	8	2a	2a	NUM
ejpam-2421	208	9	=	=	SYM
ejpam-2421	209	1	(	(	PUNCT
ejpam-2421	209	2	2	2	NUM
ejpam-2421	209	3	+	+	NUM
ejpam-2421	209	4	2rℓ1)ℓ2	2rℓ1)ℓ2	NUM
ejpam-2421	209	5	+	+	CCONJ
ejpam-2421	209	6	r2	r2	PROPN
ejpam-2421	209	7	+	+	CCONJ
ejpam-2421	209	8	r3	r3	PROPN
ejpam-2421	209	9	c2	c2	PROPN
ejpam-2421	209	10	=	=	PROPN
ejpam-2421	209	11	c0	c0	PROPN
ejpam-2421	209	12	+	+	CCONJ
ejpam-2421	209	13	(	(	PUNCT
ejpam-2421	209	14	r2	r2	PROPN
ejpam-2421	209	15	−	−	PROPN
ejpam-2421	209	16	r1)ℓ1	r1)ℓ1	NOUN
ejpam-2421	209	17	=	=	AUX
ejpam-2421	209	18	⇒	⇒	VERB
ejpam-2421	209	19	c2	c2	PROPN
ejpam-2421	209	20	=	=	PUNCT
ejpam-2421	209	21	2	2	NUM
ejpam-2421	209	22	+	+	NUM
ejpam-2421	209	23	2rℓ1	2rℓ1	NUM
ejpam-2421	209	24	.	.	PUNCT
ejpam-2421	210	1	(	(	PUNCT
ejpam-2421	210	2	8)	8)	NUM
ejpam-2421	210	3	by	by	ADP
ejpam-2421	210	4	using	use	VERB
ejpam-2421	210	5	the	the	DET
ejpam-2421	210	6	value	value	NOUN
ejpam-2421	210	7	2a	2a	NUM
ejpam-2421	210	8	=	=	SYM
ejpam-2421	211	1	(	(	PUNCT
ejpam-2421	211	2	4m+	4m+	NUM
ejpam-2421	211	3	2)ℓ1	2)ℓ1	NUM
ejpam-2421	211	4	+	+	CCONJ
ejpam-2421	211	5	r2	r2	PROPN
ejpam-2421	211	6	and	and	CCONJ
ejpam-2421	211	7	(	(	PUNCT
ejpam-2421	211	8	8)	8)	NUM
ejpam-2421	211	9	we	we	PRON
ejpam-2421	211	10	can	can	AUX
ejpam-2421	211	11	write	write	VERB
ejpam-2421	211	12	;	;	PUNCT
ejpam-2421	211	13	(	(	PUNCT
ejpam-2421	211	14	4m+	4m+	NUM
ejpam-2421	211	15	2)ℓ1	2)ℓ1	NUM
ejpam-2421	212	1	+	+	NUM
ejpam-2421	212	2	r2	r2	PROPN
ejpam-2421	212	3	=(	=(	NOUN
ejpam-2421	212	4	2	2	NUM
ejpam-2421	212	5	+	+	NUM
ejpam-2421	212	6	2rℓ1)ℓ2	2rℓ1)ℓ2	NUM
ejpam-2421	212	7	+	+	CCONJ
ejpam-2421	212	8	r2	r2	PROPN
ejpam-2421	212	9	+	+	CCONJ
ejpam-2421	212	10	r3	r3	PROPN
ejpam-2421	212	11	=	=	SYM
ejpam-2421	212	12	⇒	⇒	NOUN
ejpam-2421	212	13	(	(	PUNCT
ejpam-2421	212	14	4m+	4m+	NUM
ejpam-2421	212	15	2)ℓ1	2)ℓ1	NUM
ejpam-2421	212	16	=	=	SYM
ejpam-2421	212	17	(	(	PUNCT
ejpam-2421	212	18	2	2	NUM
ejpam-2421	212	19	+	+	NUM
ejpam-2421	212	20	2rℓ1)ℓ2	2rℓ1)ℓ2	NUM
ejpam-2421	212	21	+	+	CCONJ
ejpam-2421	212	22	r3	r3	PROPN
ejpam-2421	212	23	ö.	ö.	NOUN
ejpam-2421	212	24	özer	özer	NOUN
ejpam-2421	212	25	,	,	PUNCT
ejpam-2421	212	26	a.	a.	NOUN
ejpam-2421	212	27	pekin	pekin	PROPN
ejpam-2421	212	28	/	/	SYM
ejpam-2421	212	29	eur	eur	PROPN
ejpam-2421	212	30	.	.	PUNCT
ejpam-2421	213	1	j.	j.	PROPN
ejpam-2421	213	2	pure	pure	PROPN
ejpam-2421	213	3	appl	appl	PROPN
ejpam-2421	213	4	.	.	PROPN
ejpam-2421	213	5	math	math	PROPN
ejpam-2421	213	6	,	,	PUNCT
ejpam-2421	213	7	8	8	NUM
ejpam-2421	213	8	(	(	PUNCT
ejpam-2421	213	9	2015	2015	NUM
ejpam-2421	213	10	)	)	PUNCT
ejpam-2421	213	11	,	,	PUNCT
ejpam-2421	213	12	343	343	NUM
ejpam-2421	213	13	-	-	SYM
ejpam-2421	213	14	356	356	NUM
ejpam-2421	213	15	350	350	NUM
ejpam-2421	213	16	=	=	NOUN
ejpam-2421	213	17	⇒	⇒	NOUN
ejpam-2421	213	18	(	(	PUNCT
ejpam-2421	213	19	4m+	4m+	NUM
ejpam-2421	213	20	2)ℓ1	2)ℓ1	NUM
ejpam-2421	213	21	=	=	SYM
ejpam-2421	213	22	2ℓ2	2ℓ2	NUM
ejpam-2421	213	23	+	+	CCONJ
ejpam-2421	213	24	2rℓ1ℓ2	2rℓ1ℓ2	PROPN
ejpam-2421	213	25	+	+	CCONJ
ejpam-2421	213	26	r3	r3	PROPN
ejpam-2421	213	27	=	=	NOUN
ejpam-2421	213	28	⇒	⇒	VERB
ejpam-2421	213	29	2ℓ2	2ℓ2	NUM
ejpam-2421	213	30	+	+	CCONJ
ejpam-2421	213	31	r3	r3	PROPN
ejpam-2421	213	32	≡	≡	PROPN
ejpam-2421	213	33	0(modℓ1	0(modℓ1	PROPN
ejpam-2421	213	34	)	)	PUNCT
ejpam-2421	214	1	=	=	SYM
ejpam-2421	214	2	⇒	⇒	VERB
ejpam-2421	214	3	∃s	∃s	PROPN
ejpam-2421	214	4	∈	∈	PROPN
ejpam-2421	214	5	z	z	NOUN
ejpam-2421	214	6	∋	∋	NOUN
ejpam-2421	214	7	2ℓ2	2ℓ2	NUM
ejpam-2421	214	8	+	+	CCONJ
ejpam-2421	214	9	r3	r3	PROPN
ejpam-2421	214	10	=	=	SYM
ejpam-2421	214	11	sℓ1	sℓ1	PRON
ejpam-2421	215	1	=	=	VERB
ejpam-2421	215	2	⇒	⇒	NOUN
ejpam-2421	215	3	r3	r3	PROPN
ejpam-2421	215	4	=	=	SYM
ejpam-2421	215	5	sℓ1	sℓ1	PROPN
ejpam-2421	215	6	−	−	PROPN
ejpam-2421	215	7	2ℓ2	2ℓ2	NUM
ejpam-2421	215	8	.	.	PUNCT
ejpam-2421	216	1	for	for	ADP
ejpam-2421	216	2	the	the	DET
ejpam-2421	216	3	value	value	NOUN
ejpam-2421	216	4	r3	r3	PROPN
ejpam-2421	216	5	=	=	SYM
ejpam-2421	216	6	sℓ1	sℓ1	PROPN
ejpam-2421	216	7	−	−	PROPN
ejpam-2421	216	8	2ℓ2	2ℓ2	NUM
ejpam-2421	216	9	we	we	PRON
ejpam-2421	216	10	obtain	obtain	VERB
ejpam-2421	216	11	4	4	NUM
ejpam-2421	216	12	m	m	NOUN
ejpam-2421	216	13	+	+	ADJ
ejpam-2421	216	14	2	2	NUM
ejpam-2421	216	15	=	=	SYM
ejpam-2421	216	16	2rℓ2	2rℓ2	NUM
ejpam-2421	216	17	+	+	SYM
ejpam-2421	216	18	s	s	VERB
ejpam-2421	216	19	where	where	SCONJ
ejpam-2421	216	20	s	s	VERB
ejpam-2421	216	21	=	=	SYM
ejpam-2421	216	22	4	4	NUM
ejpam-2421	216	23	m	m	NOUN
ejpam-2421	216	24	+	+	NUM
ejpam-2421	216	25	2	2	NUM
ejpam-2421	216	26	−	−	NOUN
ejpam-2421	216	27	2rℓ2	2rℓ2	NUM
ejpam-2421	216	28	is	be	AUX
ejpam-2421	216	29	even	even	ADV
ejpam-2421	216	30	number	number	NOUN
ejpam-2421	216	31	and	and	CCONJ
ejpam-2421	216	32	so	so	ADV
ejpam-2421	216	33	there	there	PRON
ejpam-2421	216	34	exists	exist	VERB
ejpam-2421	216	35	s1	s1	PROPN
ejpam-2421	216	36	∈	∈	PROPN
ejpam-2421	216	37	z+	z+	NUM
ejpam-2421	216	38	such	such	ADJ
ejpam-2421	216	39	that	that	DET
ejpam-2421	216	40	s	s	NOUN
ejpam-2421	216	41	=	=	NOUN
ejpam-2421	216	42	2s1	2s1	NUM
ejpam-2421	216	43	.	.	PUNCT
ejpam-2421	217	1	if	if	SCONJ
ejpam-2421	217	2	we	we	PRON
ejpam-2421	217	3	write	write	VERB
ejpam-2421	217	4	4m+2=	4m+2=	NUM
ejpam-2421	217	5	2rℓ2	2rℓ2	NUM
ejpam-2421	217	6	+	+	SYM
ejpam-2421	217	7	s	s	NOUN
ejpam-2421	217	8	instead	instead	ADV
ejpam-2421	217	9	of	of	ADP
ejpam-2421	217	10	2a	2a	NUM
ejpam-2421	217	11	=	=	SYM
ejpam-2421	217	12	(	(	PUNCT
ejpam-2421	217	13	4m+	4m+	NUM
ejpam-2421	217	14	2)ℓ1	2)ℓ1	NUM
ejpam-2421	217	15	+	+	CCONJ
ejpam-2421	217	16	r2	r2	NOUN
ejpam-2421	217	17	then	then	ADV
ejpam-2421	217	18	we	we	PRON
ejpam-2421	217	19	obtain	obtain	VERB
ejpam-2421	217	20	2a	2a	NUM
ejpam-2421	217	21	=	=	SYM
ejpam-2421	218	1	2r(ℓ1ℓ2	2r(ℓ1ℓ2	NUM
ejpam-2421	218	2	+	+	NUM
ejpam-2421	218	3	1)sℓ1	1)sℓ1	NUM
ejpam-2421	218	4	and	and	CCONJ
ejpam-2421	218	5	we	we	PRON
ejpam-2421	218	6	can	can	AUX
ejpam-2421	218	7	write	write	VERB
ejpam-2421	218	8	a	a	DET
ejpam-2421	218	9	=	=	X
ejpam-2421	218	10	ra+	ra+	PROPN
ejpam-2421	218	11	s1ℓ1	s1ℓ1	NOUN
ejpam-2421	218	12	by	by	ADP
ejpam-2421	218	13	taking	take	VERB
ejpam-2421	218	14	a=	a=	ADV
ejpam-2421	218	15	ℓ1ℓ2	ℓ1ℓ2	PROPN
ejpam-2421	219	1	+	+	NUM
ejpam-2421	219	2	1	1	X
ejpam-2421	219	3	.	.	X
ejpam-2421	219	4	in	in	ADP
ejpam-2421	219	5	the	the	DET
ejpam-2421	219	6	same	same	ADJ
ejpam-2421	219	7	way	way	NOUN
ejpam-2421	219	8	,	,	PUNCT
ejpam-2421	219	9	we	we	PRON
ejpam-2421	219	10	have	have	AUX
ejpam-2421	219	11	r4	r4	NOUN
ejpam-2421	219	12	=	=	PRON
ejpam-2421	219	13	2a−	2a−	PROPN
ejpam-2421	219	14	(	(	PUNCT
ejpam-2421	219	15	4m+	4m+	NUM
ejpam-2421	219	16	2)ℓ3	2)ℓ3	NUM
ejpam-2421	219	17	+	+	CCONJ
ejpam-2421	219	18	(	(	PUNCT
ejpam-2421	219	19	2r	2r	NUM
ejpam-2421	220	1	−	−	PROPN
ejpam-2421	220	2	r3)ℓ2ℓ3	r3)ℓ2ℓ3	NOUN
ejpam-2421	220	3	−	−	PROPN
ejpam-2421	220	4	r3	r3	PROPN
ejpam-2421	220	5	=	=	NOUN
ejpam-2421	220	6	⇒	⇒	NOUN
ejpam-2421	220	7	r4	r4	NOUN
ejpam-2421	220	8	=	=	PUNCT
ejpam-2421	220	9	2ra−	2ra−	NUM
ejpam-2421	220	10	2rℓ2ℓ3	2rℓ2ℓ3	NUM
ejpam-2421	220	11	−	−	NUM
ejpam-2421	220	12	2s1ℓ3	2s1ℓ3	NUM
ejpam-2421	221	1	+	+	CCONJ
ejpam-2421	222	1	2rℓ2ℓ3	2rℓ2ℓ3	NUM
ejpam-2421	222	2	−	−	NUM
ejpam-2421	222	3	2s1ℓ1ℓ2ℓ3	2s1ℓ1ℓ2ℓ3	NUM
ejpam-2421	222	4	+	+	SYM
ejpam-2421	222	5	2ℓ22ℓ3	2ℓ22ℓ3	NUM
ejpam-2421	222	6	+	+	SYM
ejpam-2421	222	7	2ℓ2	2ℓ2	NUM
ejpam-2421	223	1	=	=	SYM
ejpam-2421	223	2	2(r	2(r	NUM
ejpam-2421	223	3	−	−	NOUN
ejpam-2421	223	4	s1ℓ3)a+	s1ℓ3)a+	NOUN
ejpam-2421	223	5	ℓ2b	ℓ2b	NOUN
ejpam-2421	223	6	for	for	ADP
ejpam-2421	223	7	a=	a=	PROPN
ejpam-2421	223	8	ℓ1ℓ2	ℓ1ℓ2	PROPN
ejpam-2421	224	1	+	+	CCONJ
ejpam-2421	224	2	1	1	NUM
ejpam-2421	224	3	and	and	CCONJ
ejpam-2421	224	4	b	b	X
ejpam-2421	224	5	=	=	SYM
ejpam-2421	225	1	ℓ2ℓ3	ℓ2ℓ3	PROPN
ejpam-2421	225	2	+	+	NUM
ejpam-2421	225	3	1	1	X
ejpam-2421	225	4	.	.	X
ejpam-2421	225	5	furthermore	furthermore	ADV
ejpam-2421	225	6	c4	c4	VERB
ejpam-2421	225	7	=(	=(	NOUN
ejpam-2421	225	8	2	2	NUM
ejpam-2421	225	9	+	+	NUM
ejpam-2421	225	10	2rℓ1	2rℓ1	NUM
ejpam-2421	225	11	)	)	PUNCT
ejpam-2421	226	1	+	+	CCONJ
ejpam-2421	227	1	[	[	X
ejpam-2421	227	2	(	(	PUNCT
ejpam-2421	227	3	2r	2r	NUM
ejpam-2421	227	4	−	−	PROPN
ejpam-2421	227	5	sℓ3)a+	sℓ3)a+	PROPN
ejpam-2421	227	6	2ℓ2b	2ℓ2b	NOUN
ejpam-2421	228	1	−	−	PROPN
ejpam-2421	228	2	sℓ1	sℓ1	ADJ
ejpam-2421	228	3	+	+	CCONJ
ejpam-2421	228	4	2ℓ2]ℓ3	2ℓ2]ℓ3	NUM
ejpam-2421	228	5	=	=	PUNCT
ejpam-2421	228	6	⇒	⇒	NOUN
ejpam-2421	228	7	c4	c4	NOUN
ejpam-2421	228	8	=	=	SYM
ejpam-2421	228	9	c(2r	c(2r	PROPN
ejpam-2421	228	10	−	−	PROPN
ejpam-2421	228	11	2s1ℓ3	2s1ℓ3	NUM
ejpam-2421	228	12	)	)	PUNCT
ejpam-2421	228	13	+	+	CCONJ
ejpam-2421	228	14	2(1	2(1	NUM
ejpam-2421	228	15	+	+	CCONJ
ejpam-2421	228	16	ℓ2ℓ3	ℓ2ℓ3	X
ejpam-2421	228	17	)	)	PUNCT
ejpam-2421	228	18	+	+	CCONJ
ejpam-2421	228	19	2ℓ2ℓ3b	2ℓ2ℓ3b	NUM
ejpam-2421	228	20	=	=	NUM
ejpam-2421	228	21	2c(r	2c(r	NUM
ejpam-2421	228	22	−	−	PROPN
ejpam-2421	228	23	s1ℓ3	s1ℓ3	PROPN
ejpam-2421	228	24	)	)	PUNCT
ejpam-2421	228	25	+	+	NOUN
ejpam-2421	228	26	2b2	2b2	NUM
ejpam-2421	228	27	and	and	CCONJ
ejpam-2421	228	28	ℓ4	ℓ4	PROPN
ejpam-2421	228	29	=	=	SYM
ejpam-2421	228	30	2a−	2a−	PROPN
ejpam-2421	228	31	2r4	2r4	NUM
ejpam-2421	228	32	c4	c4	NOUN
ejpam-2421	228	33	=	=	SYM
ejpam-2421	228	34	s1(c	s1(c	PROPN
ejpam-2421	228	35	+	+	NUM
ejpam-2421	228	36	ℓ3a)−	ℓ3a)−	NOUN
ejpam-2421	228	37	2ℓ2b	2ℓ2b	NUM
ejpam-2421	229	1	−	−	PROPN
ejpam-2421	229	2	ra	ra	PROPN
ejpam-2421	229	3	c(r	c(r	PROPN
ejpam-2421	229	4	−	−	PROPN
ejpam-2421	229	5	s1ℓ3	s1ℓ3	PROPN
ejpam-2421	229	6	)	)	PUNCT
ejpam-2421	229	7	+	+	NUM
ejpam-2421	229	8	b2	b2	NOUN
ejpam-2421	229	9	for	for	ADP
ejpam-2421	229	10	c	c	NOUN
ejpam-2421	229	11	=	=	SYM
ejpam-2421	229	12	ℓ1	ℓ1	PROPN
ejpam-2421	229	13	+	+	CCONJ
ejpam-2421	229	14	aℓ3	aℓ3	PROPN
ejpam-2421	229	15	and	and	CCONJ
ejpam-2421	229	16	(	(	PUNCT
ejpam-2421	229	17	1	1	NUM
ejpam-2421	229	18	+	+	NUM
ejpam-2421	229	19	ℓ2ℓ3	ℓ2ℓ3	NOUN
ejpam-2421	229	20	)	)	PUNCT
ejpam-2421	229	21	=	=	SYM
ejpam-2421	229	22	b.	b.	PROPN
ejpam-2421	230	1	this	this	PRON
ejpam-2421	230	2	is	be	AUX
ejpam-2421	230	3	completed	complete	VERB
ejpam-2421	230	4	the	the	DET
ejpam-2421	230	5	proof	proof	NOUN
ejpam-2421	230	6	of	of	ADP
ejpam-2421	230	7	the	the	DET
ejpam-2421	230	8	theorem	theorem	PROPN
ejpam-2421	230	9	.	.	PROPN
ejpam-2421	230	10	example	example	NOUN
ejpam-2421	231	1	1	1	NUM
ejpam-2421	231	2	.	.	PUNCT
ejpam-2421	232	1	let	let	VERB
ejpam-2421	232	2	a	a	PRON
ejpam-2421	232	3	is	be	AUX
ejpam-2421	232	4	odd	odd	ADJ
ejpam-2421	232	5	,	,	PUNCT
ejpam-2421	232	6	d	d	PROPN
ejpam-2421	232	7	∈	∈	PROPN
ejpam-2421	232	8	d5	d5	NOUN
ejpam-2421	232	9	4	4	NUM
ejpam-2421	232	10	and	and	CCONJ
ejpam-2421	232	11	d	d	NOUN
ejpam-2421	232	12	=	=	SYM
ejpam-2421	232	13	869≡	869≡	NUM
ejpam-2421	232	14	5(mod8	5(mod8	NUM
ejpam-2421	232	15	)	)	PUNCT
ejpam-2421	232	16	.	.	PUNCT
ejpam-2421	233	1	since	since	SCONJ
ejpam-2421	233	2	a	a	DET
ejpam-2421	233	3	=	=	SYM
ejpam-2421	233	4	29	29	NUM
ejpam-2421	233	5	,	,	PUNCT
ejpam-2421	233	6	b	b	X
ejpam-2421	233	7	=	=	SYM
ejpam-2421	233	8	28	28	NUM
ejpam-2421	233	9	,	,	PUNCT
ejpam-2421	233	10	b	b	X
ejpam-2421	233	11	=	=	SYM
ejpam-2421	233	12	3	3	NUM
ejpam-2421	233	13	·	·	SYM
ejpam-2421	233	14	8	8	NUM
ejpam-2421	233	15	+	+	NUM
ejpam-2421	233	16	4	4	NUM
ejpam-2421	233	17	,	,	PUNCT
ejpam-2421	233	18	m=	m=	X
ejpam-2421	233	19	3	3	NUM
ejpam-2421	233	20	then	then	ADV
ejpam-2421	233	21	we	we	PRON
ejpam-2421	233	22	can	can	AUX
ejpam-2421	233	23	determine	determine	VERB
ejpam-2421	233	24	that	that	DET
ejpam-2421	233	25	ℓ1	ℓ1	NOUN
ejpam-2421	233	26	=	=	SYM
ejpam-2421	233	27	4	4	NUM
ejpam-2421	233	28	,	,	PUNCT
ejpam-2421	233	29	ℓ2	ℓ2	NOUN
ejpam-2421	233	30	=	=	SYM
ejpam-2421	233	31	5	5	NUM
ejpam-2421	233	32	,	,	PUNCT
ejpam-2421	233	33	ℓ3	ℓ3	NOUN
ejpam-2421	233	34	=	=	SYM
ejpam-2421	233	35	1	1	NUM
ejpam-2421	233	36	,	,	PUNCT
ejpam-2421	233	37	c1	c1	NOUN
ejpam-2421	233	38	=	=	PROPN
ejpam-2421	233	39	14	14	NUM
ejpam-2421	233	40	and	and	CCONJ
ejpam-2421	233	41	r2	r2	PROPN
ejpam-2421	233	42	=	=	SYM
ejpam-2421	234	1	2a−	2a−	NUM
ejpam-2421	234	2	(	(	PUNCT
ejpam-2421	234	3	4m+	4m+	NUM
ejpam-2421	234	4	2)ℓ1	2)ℓ1	NUM
ejpam-2421	234	5	=	=	NOUN
ejpam-2421	234	6	⇒	⇒	NOUN
ejpam-2421	234	7	r2	r2	NOUN
ejpam-2421	234	8	=	=	PUNCT
ejpam-2421	234	9	58−	58−	NUM
ejpam-2421	234	10	14	14	NUM
ejpam-2421	234	11	·	·	SYM
ejpam-2421	234	12	4=	4=	NUM
ejpam-2421	234	13	58−	58−	NOUN
ejpam-2421	235	1	56=	56=	NOUN
ejpam-2421	235	2	2=⇒	2=⇒	NUM
ejpam-2421	235	3	r	r	NOUN
ejpam-2421	235	4	=	=	SYM
ejpam-2421	235	5	1	1	NUM
ejpam-2421	235	6	,	,	PUNCT
ejpam-2421	235	7	c2	c2	PROPN
ejpam-2421	235	8	=	=	PUNCT
ejpam-2421	235	9	10	10	NUM
ejpam-2421	235	10	because	because	SCONJ
ejpam-2421	235	11	of	of	ADP
ejpam-2421	235	12	ℓ1	ℓ1	NOUN
ejpam-2421	235	13	is	be	AUX
ejpam-2421	235	14	even	even	ADV
ejpam-2421	235	15	.	.	PUNCT
ejpam-2421	236	1	(	(	PUNCT
ejpam-2421	236	2	4m+	4m+	NUM
ejpam-2421	236	3	2)ℓ1	2)ℓ1	NUM
ejpam-2421	236	4	=	=	SYM
ejpam-2421	236	5	(	(	PUNCT
ejpam-2421	236	6	2	2	NUM
ejpam-2421	236	7	+	+	NUM
ejpam-2421	236	8	2rℓ1	2rℓ1	NUM
ejpam-2421	236	9	)	)	PUNCT
ejpam-2421	236	10	·	·	PUNCT
ejpam-2421	237	1	ℓ2	ℓ2	PROPN
ejpam-2421	237	2	+	+	CCONJ
ejpam-2421	237	3	r3	r3	PROPN
ejpam-2421	237	4	=	=	SYM
ejpam-2421	237	5	⇒	⇒	PROPN
ejpam-2421	237	6	14	14	NUM
ejpam-2421	237	7	·	·	SYM
ejpam-2421	237	8	4=	4=	NUM
ejpam-2421	237	9	10	10	NUM
ejpam-2421	237	10	·	·	SYM
ejpam-2421	237	11	5	5	NUM
ejpam-2421	237	12	+	+	NUM
ejpam-2421	237	13	r3	r3	NOUN
ejpam-2421	237	14	=	=	SYM
ejpam-2421	237	15	⇒	⇒	X
ejpam-2421	237	16	r3	r3	PROPN
ejpam-2421	237	17	=	=	SYM
ejpam-2421	237	18	6	6	NUM
ejpam-2421	237	19	,	,	PUNCT
ejpam-2421	237	20	s	s	PART
ejpam-2421	237	21	=	=	SYM
ejpam-2421	237	22	2s1	2s1	NUM
ejpam-2421	237	23	=	=	SYM
ejpam-2421	237	24	4	4	X
ejpam-2421	237	25	.	.	PUNCT
ejpam-2421	238	1	therefore	therefore	ADV
ejpam-2421	238	2	we	we	PRON
ejpam-2421	238	3	obtain	obtain	VERB
ejpam-2421	238	4	a	a	DET
ejpam-2421	238	5	=	=	SYM
ejpam-2421	238	6	21	21	NUM
ejpam-2421	238	7	,	,	PUNCT
ejpam-2421	238	8	b	b	NOUN
ejpam-2421	238	9	=	=	SYM
ejpam-2421	238	10	6	6	NUM
ejpam-2421	238	11	,	,	PUNCT
ejpam-2421	238	12	c	c	NOUN
ejpam-2421	238	13	=	=	SYM
ejpam-2421	238	14	25	25	NUM
ejpam-2421	238	15	and	and	CCONJ
ejpam-2421	238	16	r4	r4	VERB
ejpam-2421	238	17	=	=	SYM
ejpam-2421	238	18	18	18	NUM
ejpam-2421	238	19	,	,	PUNCT
ejpam-2421	238	20	c4	c4	NOUN
ejpam-2421	238	21	=	=	SYM
ejpam-2421	238	22	22	22	NUM
ejpam-2421	238	23	,	,	PUNCT
ejpam-2421	238	24	ℓ4	ℓ4	NOUN
ejpam-2421	238	25	=	=	SYM
ejpam-2421	238	26	1	1	X
ejpam-2421	238	27	.	.	PUNCT
ejpam-2421	239	1	if	if	SCONJ
ejpam-2421	239	2	it	it	PRON
ejpam-2421	239	3	is	be	AUX
ejpam-2421	239	4	taken	take	VERB
ejpam-2421	239	5	above	above	ADP
ejpam-2421	239	6	values	value	NOUN
ejpam-2421	239	7	then	then	ADV
ejpam-2421	239	8	the	the	DET
ejpam-2421	239	9	coefficients	coefficient	NOUN
ejpam-2421	239	10	of	of	ADP
ejpam-2421	239	11	the	the	DET
ejpam-2421	239	12	fundamental	fundamental	ADJ
ejpam-2421	239	13	units	unit	NOUN
ejpam-2421	239	14	of	of	ADP
ejpam-2421	239	15	q	q	PROPN
ejpam-2421	239	16	(	(	PUNCT
ejpam-2421	239	17	p	p	PROPN
ejpam-2421	239	18	869	869	NUM
ejpam-2421	239	19	)	)	PUNCT
ejpam-2421	239	20	is	be	AUX
ejpam-2421	239	21	easily	easily	ADV
ejpam-2421	239	22	determined	determined	ADJ
ejpam-2421	239	23	as	as	ADP
ejpam-2421	239	24	td	td	NOUN
ejpam-2421	239	25	=	=	SYM
ejpam-2421	239	26	49377	49377	NUM
ejpam-2421	239	27	,	,	PUNCT
ejpam-2421	239	28	ud	ud	ADV
ejpam-2421	239	29	=	=	NOUN
ejpam-2421	239	30	1675	1675	NUM
ejpam-2421	239	31	and	and	CCONJ
ejpam-2421	239	32	so	so	ADV
ejpam-2421	239	33	ǫd	ǫd	ADJ
ejpam-2421	239	34	=	=	NOUN
ejpam-2421	239	35	49377	49377	NUM
ejpam-2421	239	36	+	+	NOUN
ejpam-2421	239	37	1675	1675	NUM
ejpam-2421	239	38	p	p	NOUN
ejpam-2421	239	39	869	869	NUM
ejpam-2421	239	40	2	2	NUM
ejpam-2421	239	41	>	>	SYM
ejpam-2421	239	42	1	1	NUM
ejpam-2421	239	43	holds	hold	NOUN
ejpam-2421	239	44	.	.	PUNCT
ejpam-2421	240	1	theorem	theorem	NOUN
ejpam-2421	240	2	2	2	NUM
ejpam-2421	240	3	.	.	PUNCT
ejpam-2421	241	1	let	let	AUX
ejpam-2421	241	2	d	d	NOUN
ejpam-2421	241	3	=	=	SYM
ejpam-2421	241	4	a2	a2	PROPN
ejpam-2421	241	5	+	+	CCONJ
ejpam-2421	241	6	b	b	PROPN
ejpam-2421	241	7	≡	≡	PROPN
ejpam-2421	241	8	1mod(4	1mod(4	NUM
ejpam-2421	241	9	)	)	PUNCT
ejpam-2421	241	10	is	be	AUX
ejpam-2421	241	11	a	a	DET
ejpam-2421	241	12	square	square	ADJ
ejpam-2421	241	13	free	free	ADJ
ejpam-2421	241	14	integer	integer	NOUN
ejpam-2421	241	15	for	for	ADP
ejpam-2421	241	16	positive	positive	ADJ
ejpam-2421	241	17	integers	integer	NOUN
ejpam-2421	241	18	a	a	DET
ejpam-2421	241	19	and	and	CCONJ
ejpam-2421	241	20	b	b	NOUN
ejpam-2421	241	21	satisfying	satisfy	VERB
ejpam-2421	241	22	0	0	PUNCT
ejpam-2421	241	23	<	<	X
ejpam-2421	241	24	b	b	X
ejpam-2421	241	25	≤	≤	NUM
ejpam-2421	241	26	2a	2a	NUM
ejpam-2421	241	27	.	.	PUNCT
ejpam-2421	242	1	let	let	VERB
ejpam-2421	242	2	the	the	DET
ejpam-2421	242	3	period	period	NOUN
ejpam-2421	242	4	kd	kd	PROPN
ejpam-2421	242	5	of	of	ADP
ejpam-2421	242	6	the	the	DET
ejpam-2421	242	7	integral	integral	ADJ
ejpam-2421	242	8	basis	basis	NOUN
ejpam-2421	242	9	element	element	NOUN
ejpam-2421	242	10	of	of	ADP
ejpam-2421	242	11	ωd	ωd	NOUN
ejpam-2421	242	12	=	=	PUNCT
ejpam-2421	242	13	(	(	PUNCT
ejpam-2421	242	14	1	1	NUM
ejpam-2421	242	15	+	+	SYM
ejpam-2421	242	16	p	p	X
ejpam-2421	242	17	d	d	PROPN
ejpam-2421	242	18	2	2	NUM
ejpam-2421	242	19	)	)	PUNCT
ejpam-2421	242	20	in	in	ADP
ejpam-2421	242	21	q	q	PROPN
ejpam-2421	242	22	(	(	PUNCT
ejpam-2421	242	23	p	p	NOUN
ejpam-2421	242	24	d	d	NOUN
ejpam-2421	242	25	)	)	PUNCT
ejpam-2421	242	26	be	be	VERB
ejpam-2421	242	27	8	8	NUM
ejpam-2421	242	28	.	.	PUNCT
ejpam-2421	243	1	if	if	SCONJ
ejpam-2421	243	2	a	a	PRON
ejpam-2421	243	3	is	be	AUX
ejpam-2421	243	4	even	even	ADV
ejpam-2421	243	5	then	then	ADV
ejpam-2421	243	6	,	,	PUNCT
ejpam-2421	243	7	wd	wd	PROPN
ejpam-2421	243	8	=	=	PUNCT
ejpam-2421	243	9	[	[	PUNCT
ejpam-2421	243	10	a	a	DET
ejpam-2421	243	11	2	2	NUM
ejpam-2421	243	12	;	;	PUNCT
ejpam-2421	243	13	ℓ,ℓ2,ℓ3	ℓ,ℓ2,ℓ3	NOUN
ejpam-2421	243	14	,	,	PUNCT
ejpam-2421	243	15	bc	bc	PROPN
ejpam-2421	243	16	+	+	CCONJ
ejpam-2421	243	17	ad−	ad−	PROPN
ejpam-2421	243	18	2ℓ3	2ℓ3	NUM
ejpam-2421	243	19	ℓ23	ℓ23	NOUN
ejpam-2421	243	20	−	−	PROPN
ejpam-2421	243	21	c	c	PROPN
ejpam-2421	244	1	d	d	NOUN
ejpam-2421	244	2	,	,	PUNCT
ejpam-2421	244	3	ℓ3,ℓ2,ℓ1	ℓ3,ℓ2,ℓ1	PROPN
ejpam-2421	244	4	,	,	PUNCT
ejpam-2421	244	5	a−	a−	PROPN
ejpam-2421	244	6	1	1	NUM
ejpam-2421	244	7	]	]	PUNCT
ejpam-2421	244	8	,	,	PUNCT
ejpam-2421	244	9	1≤	1≤	PROPN
ejpam-2421	244	10	ℓi	ℓi	PROPN
ejpam-2421	244	11	,	,	PUNCT
ejpam-2421	244	12	(	(	PUNCT
ejpam-2421	244	13	i	i	NOUN
ejpam-2421	244	14	=	=	NOUN
ejpam-2421	244	15	2,3	2,3	NUM
ejpam-2421	244	16	)	)	PUNCT
ejpam-2421	244	17	ö.	ö.	NOUN
ejpam-2421	244	18	özer	özer	NOUN
ejpam-2421	244	19	,	,	PUNCT
ejpam-2421	244	20	a.	a.	NOUN
ejpam-2421	244	21	pekin	pekin	PROPN
ejpam-2421	244	22	/	/	SYM
ejpam-2421	244	23	eur	eur	PROPN
ejpam-2421	244	24	.	.	PUNCT
ejpam-2421	245	1	j.	j.	PROPN
ejpam-2421	245	2	pure	pure	PROPN
ejpam-2421	245	3	appl	appl	PROPN
ejpam-2421	245	4	.	.	PROPN
ejpam-2421	245	5	math	math	PROPN
ejpam-2421	245	6	,	,	PUNCT
ejpam-2421	245	7	8	8	NUM
ejpam-2421	245	8	(	(	PUNCT
ejpam-2421	245	9	2015	2015	NUM
ejpam-2421	245	10	)	)	PUNCT
ejpam-2421	245	11	,	,	PUNCT
ejpam-2421	245	12	343	343	NUM
ejpam-2421	245	13	-	-	SYM
ejpam-2421	245	14	356	356	NUM
ejpam-2421	245	15	351	351	NUM
ejpam-2421	245	16	and	and	CCONJ
ejpam-2421	245	17	then	then	ADV
ejpam-2421	245	18	the	the	DET
ejpam-2421	245	19	coefficients	coefficient	NOUN
ejpam-2421	245	20	td	td	VERB
ejpam-2421	246	1	and	and	CCONJ
ejpam-2421	246	2	ud	ud	INTJ
ejpam-2421	246	3	of	of	ADP
ejpam-2421	246	4	ǫd	ǫd	NUM
ejpam-2421	246	5	td	td	NOUN
ejpam-2421	246	6	=[	=[	NOUN
ejpam-2421	246	7	(	(	PUNCT
ejpam-2421	246	8	a(r	a(r	PROPN
ejpam-2421	246	9	+	+	PROPN
ejpam-2421	246	10	1	1	NUM
ejpam-2421	246	11	)	)	PUNCT
ejpam-2421	247	1	+	+	NOUN
ejpam-2421	247	2	b	b	X
ejpam-2421	247	3	−	−	NOUN
ejpam-2421	247	4	2	2	NUM
ejpam-2421	247	5	)	)	PUNCT
ejpam-2421	247	6	·	·	PUNCT
ejpam-2421	248	1	c	c	X
ejpam-2421	249	1	+	+	CCONJ
ejpam-2421	249	2	2(c	2(c	NUM
ejpam-2421	249	3	−	−	NOUN
ejpam-2421	249	4	ℓ3)](cℓ4	ℓ3)](cℓ4	NOUN
ejpam-2421	249	5	+	+	NOUN
ejpam-2421	249	6	2a	2a	NUM
ejpam-2421	249	7	)	)	PUNCT
ejpam-2421	250	1	+	+	CCONJ
ejpam-2421	250	2	2cℓ2	2cℓ2	NUM
ejpam-2421	250	3	ud	ud	NOUN
ejpam-2421	250	4	=	=	NUM
ejpam-2421	250	5	c(cℓ4	c(cℓ4	NOUN
ejpam-2421	250	6	+	+	NOUN
ejpam-2421	250	7	2a	2a	NUM
ejpam-2421	250	8	)	)	PUNCT
ejpam-2421	250	9	and	and	CCONJ
ejpam-2421	250	10	d	d	NOUN
ejpam-2421	251	1	=	=	PUNCT
ejpam-2421	252	1	[	[	X
ejpam-2421	252	2	a(r	a(r	X
ejpam-2421	252	3	+	+	NOUN
ejpam-2421	252	4	1	1	NUM
ejpam-2421	252	5	)	)	PUNCT
ejpam-2421	252	6	+	+	NOUN
ejpam-2421	252	7	b	b	X
ejpam-2421	252	8	−	−	NOUN
ejpam-2421	252	9	1]2	1]2	NUM
ejpam-2421	253	1	+	+	CCONJ
ejpam-2421	253	2	2[a(r	2[a(r	NUM
ejpam-2421	253	3	+	+	CCONJ
ejpam-2421	253	4	1	1	NUM
ejpam-2421	253	5	)	)	PUNCT
ejpam-2421	253	6	+	+	NOUN
ejpam-2421	253	7	b	b	X
ejpam-2421	253	8	−	−	PROPN
ejpam-2421	253	9	2s−	2s−	NUM
ejpam-2421	253	10	2]−	2]−	NUM
ejpam-2421	253	11	1	1	NUM
ejpam-2421	253	12	hold	hold	NOUN
ejpam-2421	253	13	.	.	PUNCT
ejpam-2421	254	1	where	where	SCONJ
ejpam-2421	254	2	a=	a=	ADJ
ejpam-2421	254	3	ℓ2	ℓ2	NOUN
ejpam-2421	254	4	+	+	CCONJ
ejpam-2421	254	5	1	1	NUM
ejpam-2421	254	6	,	,	PUNCT
ejpam-2421	254	7	b	b	NOUN
ejpam-2421	254	8	=	=	SYM
ejpam-2421	254	9	2s	2s	NUM
ejpam-2421	254	10	−	−	NOUN
ejpam-2421	254	11	r	r	NOUN
ejpam-2421	254	12	,	,	PUNCT
ejpam-2421	254	13	c	c	NOUN
ejpam-2421	254	14	=	=	SYM
ejpam-2421	254	15	1	1	NUM
ejpam-2421	254	16	+	+	NUM
ejpam-2421	254	17	aℓ3	aℓ3	NOUN
ejpam-2421	254	18	=	=	SYM
ejpam-2421	254	19	1	1	NUM
ejpam-2421	254	20	+	+	NUM
ejpam-2421	254	21	ℓ3	ℓ3	PROPN
ejpam-2421	254	22	+	+	CCONJ
ejpam-2421	254	23	ℓ2ℓ3	ℓ2ℓ3	PROPN
ejpam-2421	254	24	,	,	PUNCT
ejpam-2421	254	25	d	d	PROPN
ejpam-2421	254	26	=	=	PUNCT
ejpam-2421	254	27	bℓ3	bℓ3	PROPN
ejpam-2421	255	1	−	−	NOUN
ejpam-2421	255	2	r	r	NOUN
ejpam-2421	255	3	−	−	NOUN
ejpam-2421	255	4	1	1	NUM
ejpam-2421	255	5	,	,	PUNCT
ejpam-2421	255	6	e	e	X
ejpam-2421	255	7	=	=	SYM
ejpam-2421	255	8	ℓ3	ℓ3	PROPN
ejpam-2421	255	9	+	+	CCONJ
ejpam-2421	255	10	1	1	NUM
ejpam-2421	255	11	and	and	CCONJ
ejpam-2421	255	12	r	r	NOUN
ejpam-2421	255	13	and	and	CCONJ
ejpam-2421	255	14	s	s	NOUN
ejpam-2421	255	15	are	be	AUX
ejpam-2421	255	16	uniquely	uniquely	ADV
ejpam-2421	255	17	determined	determined	ADJ
ejpam-2421	255	18	with	with	ADP
ejpam-2421	255	19	the	the	DET
ejpam-2421	255	20	equations	equation	NOUN
ejpam-2421	255	21	a	a	DET
ejpam-2421	255	22	=	=	SYM
ejpam-2421	255	23	a(r	a(r	NOUN
ejpam-2421	255	24	+	+	NOUN
ejpam-2421	255	25	1	1	NUM
ejpam-2421	255	26	)	)	PUNCT
ejpam-2421	256	1	+	+	NOUN
ejpam-2421	257	1	b	b	X
ejpam-2421	257	2	−	−	NOUN
ejpam-2421	257	3	1	1	NUM
ejpam-2421	257	4	and	and	CCONJ
ejpam-2421	257	5	ℓ3(ℓ3ℓ4	ℓ3(ℓ3ℓ4	VERB
ejpam-2421	257	6	+	+	CCONJ
ejpam-2421	257	7	2	2	NUM
ejpam-2421	257	8	)	)	PUNCT
ejpam-2421	257	9	=	=	SYM
ejpam-2421	257	10	bc	bc	PROPN
ejpam-2421	257	11	+	+	CCONJ
ejpam-2421	258	1	ad+	ad+	PROPN
ejpam-2421	258	2	2c	2c	NUM
ejpam-2421	258	3	dℓ4	dℓ4	ADJ
ejpam-2421	258	4	.	.	PUNCT
ejpam-2421	259	1	proof	proof	NOUN
ejpam-2421	259	2	.	.	PUNCT
ejpam-2421	260	1	let	let	VERB
ejpam-2421	260	2	a	a	PRON
ejpam-2421	260	3	be	be	AUX
ejpam-2421	260	4	even	even	ADV
ejpam-2421	260	5	and	and	CCONJ
ejpam-2421	260	6	kd	kd	X
ejpam-2421	260	7	=	=	NOUN
ejpam-2421	260	8	8	8	NUM
ejpam-2421	260	9	.	.	PUNCT
ejpam-2421	261	1	if	if	SCONJ
ejpam-2421	261	2	d	d	PROPN
ejpam-2421	261	3	≡	≡	PROPN
ejpam-2421	261	4	1(mod8	1(mod8	NUM
ejpam-2421	261	5	)	)	PUNCT
ejpam-2421	261	6	then	then	ADV
ejpam-2421	261	7	b	b	PROPN
ejpam-2421	261	8	≡	≡	PROPN
ejpam-2421	261	9	1(mod8	1(mod8	NUM
ejpam-2421	261	10	)	)	PUNCT
ejpam-2421	261	11	or	or	CCONJ
ejpam-2421	261	12	b	b	PROPN
ejpam-2421	261	13	≡	≡	PROPN
ejpam-2421	261	14	5(mod8	5(mod8	NUM
ejpam-2421	261	15	)	)	PUNCT
ejpam-2421	261	16	hold	hold	NOUN
ejpam-2421	261	17	.	.	PUNCT
ejpam-2421	262	1	furthermore	furthermore	ADV
ejpam-2421	262	2	in	in	ADP
ejpam-2421	262	3	the	the	DET
ejpam-2421	262	4	case	case	NOUN
ejpam-2421	262	5	when	when	SCONJ
ejpam-2421	262	6	a	a	PRON
ejpam-2421	262	7	is	be	AUX
ejpam-2421	262	8	even	even	ADV
ejpam-2421	262	9	,	,	PUNCT
ejpam-2421	262	10	d	d	PROPN
ejpam-2421	262	11	can	can	AUX
ejpam-2421	262	12	belong	belong	VERB
ejpam-2421	262	13	to	to	ADP
ejpam-2421	262	14	d5	d5	NOUN
ejpam-2421	262	15	1	1	NUM
ejpam-2421	262	16	∪	∪	NOUN
ejpam-2421	262	17	d5	d5	NOUN
ejpam-2421	262	18	5	5	NUM
ejpam-2421	262	19	∪	∪	ADP
ejpam-2421	262	20	d1	d1	NOUN
ejpam-2421	262	21	5	5	NUM
ejpam-2421	262	22	∪	∪	ADJ
ejpam-2421	262	23	d1	d1	PROPN
ejpam-2421	262	24	1	1	NUM
ejpam-2421	262	25	.	.	PUNCT
ejpam-2421	263	1	q0	q0	PROPN
ejpam-2421	263	2	=	=	PUNCT
ejpam-2421	264	1	[	[	X
ejpam-2421	264	2	wd	wd	X
ejpam-2421	264	3	]	]	X
ejpam-2421	264	4	=	=	PUNCT
ejpam-2421	264	5	a	a	DET
ejpam-2421	264	6	2	2	NUM
ejpam-2421	264	7	and	and	CCONJ
ejpam-2421	264	8	from	from	ADP
ejpam-2421	264	9	lemma	lemma	PROPN
ejpam-2421	264	10	3	3	NUM
ejpam-2421	264	11	we	we	PRON
ejpam-2421	264	12	can	can	AUX
ejpam-2421	264	13	write	write	VERB
ejpam-2421	264	14	r0	r0	NOUN
ejpam-2421	264	15	=	=	SYM
ejpam-2421	264	16	r1	r1	PROPN
ejpam-2421	264	17	=	=	PUNCT
ejpam-2421	264	18	a	a	DET
ejpam-2421	264	19	−	−	PROPN
ejpam-2421	264	20	2q0	2q0	NUM
ejpam-2421	264	21	+	+	CCONJ
ejpam-2421	264	22	1⇒	1⇒	PROPN
ejpam-2421	264	23	r0	r0	NOUN
ejpam-2421	264	24	=	=	PROPN
ejpam-2421	264	25	r1	r1	PROPN
ejpam-2421	264	26	=	=	SYM
ejpam-2421	264	27	1	1	NUM
ejpam-2421	264	28	,	,	PUNCT
ejpam-2421	264	29	c0	c0	NOUN
ejpam-2421	264	30	=	=	PUNCT
ejpam-2421	265	1	2,ℓ0	2,ℓ0	NUM
ejpam-2421	265	2	=	=	PUNCT
ejpam-2421	265	3	a	a	DET
ejpam-2421	265	4	−	−	PROPN
ejpam-2421	265	5	1	1	NUM
ejpam-2421	265	6	and	and	CCONJ
ejpam-2421	265	7	because	because	SCONJ
ejpam-2421	265	8	of	of	ADP
ejpam-2421	265	9	kd	kd	PROPN
ejpam-2421	265	10	=	=	PUNCT
ejpam-2421	265	11	8	8	NUM
ejpam-2421	265	12	and	and	CCONJ
ejpam-2421	265	13	from	from	ADP
ejpam-2421	265	14	lemma	lemma	PROPN
ejpam-2421	265	15	2	2	NUM
ejpam-2421	265	16	we	we	PRON
ejpam-2421	265	17	have	have	VERB
ejpam-2421	265	18	ℓ1	ℓ1	NOUN
ejpam-2421	265	19	=	=	SYM
ejpam-2421	265	20	ℓ7	ℓ7	PROPN
ejpam-2421	265	21	,	,	PUNCT
ejpam-2421	265	22	ℓ2	ℓ2	NOUN
ejpam-2421	265	23	=	=	SYM
ejpam-2421	265	24	ℓ6	ℓ6	PROPN
ejpam-2421	265	25	,	,	PUNCT
ejpam-2421	265	26	ℓ3	ℓ3	NOUN
ejpam-2421	265	27	=	=	SYM
ejpam-2421	265	28	ℓ5	ℓ5	NOUN
ejpam-2421	265	29	and	and	CCONJ
ejpam-2421	265	30	r1	r1	NOUN
ejpam-2421	265	31	=	=	SYM
ejpam-2421	265	32	r8	r8	PROPN
ejpam-2421	265	33	,	,	PUNCT
ejpam-2421	265	34	r2	r2	NOUN
ejpam-2421	265	35	=	=	SYM
ejpam-2421	265	36	r7	r7	PROPN
ejpam-2421	265	37	,	,	PUNCT
ejpam-2421	265	38	r3	r3	PROPN
ejpam-2421	265	39	=	=	SYM
ejpam-2421	265	40	r6	r6	PROPN
ejpam-2421	265	41	,	,	PUNCT
ejpam-2421	265	42	r4	r4	NOUN
ejpam-2421	265	43	=	=	PROPN
ejpam-2421	265	44	r5	r5	PROPN
ejpam-2421	265	45	and	and	CCONJ
ejpam-2421	265	46	c1	c1	PROPN
ejpam-2421	265	47	=	=	PROPN
ejpam-2421	265	48	c7	c7	PROPN
ejpam-2421	265	49	,	,	PUNCT
ejpam-2421	265	50	c2	c2	PROPN
ejpam-2421	265	51	=	=	SYM
ejpam-2421	265	52	c6	c6	PROPN
ejpam-2421	265	53	,	,	PUNCT
ejpam-2421	265	54	c3	c3	PROPN
ejpam-2421	265	55	=	=	PROPN
ejpam-2421	265	56	c5	c5	PROPN
ejpam-2421	265	57	.	.	PUNCT
ejpam-2421	266	1	we	we	PRON
ejpam-2421	266	2	first	first	ADV
ejpam-2421	266	3	assume	assume	VERB
ejpam-2421	266	4	that	that	SCONJ
ejpam-2421	266	5	d	d	NOUN
ejpam-2421	266	6	is	be	AUX
ejpam-2421	266	7	in	in	ADP
ejpam-2421	266	8	d1	d1	PROPN
ejpam-2421	266	9	1∪d5	1∪d5	NOUN
ejpam-2421	266	10	1	1	NUM
ejpam-2421	266	11	.	.	PUNCT
ejpam-2421	267	1	then	then	ADV
ejpam-2421	267	2	we	we	PRON
ejpam-2421	267	3	get	get	VERB
ejpam-2421	267	4	b	b	PRON
ejpam-2421	267	5	≡	≡	PROPN
ejpam-2421	267	6	1(mod8	1(mod8	NUM
ejpam-2421	267	7	)	)	PUNCT
ejpam-2421	267	8	and	and	CCONJ
ejpam-2421	267	9	so	so	ADV
ejpam-2421	267	10	∃m	∃m	PROPN
ejpam-2421	267	11	∈	∈	PROPN
ejpam-2421	267	12	z+	z+	NUM
ejpam-2421	267	13	∋	∋	NOUN
ejpam-2421	267	14	b	b	PROPN
ejpam-2421	267	15	=	=	SYM
ejpam-2421	267	16	8m+1	8m+1	PROPN
ejpam-2421	267	17	holds	hold	VERB
ejpam-2421	267	18	.	.	PUNCT
ejpam-2421	268	1	from	from	ADP
ejpam-2421	268	2	lemma	lemma	PROPN
ejpam-2421	268	3	?	?	PUNCT
ejpam-2421	268	4	?	?	PUNCT
ejpam-2421	268	5	?	?	PUNCT
ejpam-2421	269	1	c−1	c−1	PROPN
ejpam-2421	269	2	=	=	SYM
ejpam-2421	269	3	(	(	PUNCT
ejpam-2421	269	4	8m+1	8m+1	PROPN
ejpam-2421	269	5	+	+	NOUN
ejpam-2421	269	6	2a−1	2a−1	NOUN
ejpam-2421	269	7	)	)	PUNCT
ejpam-2421	269	8	2	2	NUM
ejpam-2421	269	9	⇒	⇒	NOUN
ejpam-2421	269	10	c−1	c−1	PROPN
ejpam-2421	269	11	=	=	SYM
ejpam-2421	269	12	4m+	4m+	NUM
ejpam-2421	269	13	a	a	NOUN
ejpam-2421	269	14	and	and	CCONJ
ejpam-2421	269	15	c1	c1	NOUN
ejpam-2421	269	16	=	=	PROPN
ejpam-2421	269	17	c−1	c−1	PROPN
ejpam-2421	269	18	+	+	CCONJ
ejpam-2421	269	19	(	(	PUNCT
ejpam-2421	269	20	r1	r1	PROPN
ejpam-2421	269	21	−	−	PROPN
ejpam-2421	269	22	r0)ℓ0⇒	r0)ℓ0⇒	PROPN
ejpam-2421	269	23	c1	c1	NOUN
ejpam-2421	269	24	=	=	PROPN
ejpam-2421	269	25	4m+	4m+	NUM
ejpam-2421	269	26	a	a	DET
ejpam-2421	269	27	hold	hold	NOUN
ejpam-2421	269	28	.	.	PUNCT
ejpam-2421	270	1	by	by	ADP
ejpam-2421	270	2	taking	take	VERB
ejpam-2421	270	3	equation	equation	NOUN
ejpam-2421	270	4	2a−	2a−	PROPN
ejpam-2421	270	5	ri	ri	X
ejpam-2421	270	6	=	=	PUNCT
ejpam-2421	270	7	ciℓi	ciℓi	NOUN
ejpam-2421	270	8	+	+	CCONJ
ejpam-2421	270	9	ri+1	ri+1	NOUN
ejpam-2421	270	10	in	in	ADP
ejpam-2421	270	11	lemma	lemma	PROPN
ejpam-2421	270	12	2	2	NUM
ejpam-2421	270	13	for	for	ADP
ejpam-2421	270	14	i	i	PRON
ejpam-2421	270	15	=	=	NOUN
ejpam-2421	270	16	1	1	NUM
ejpam-2421	270	17	,	,	PUNCT
ejpam-2421	270	18	we	we	PRON
ejpam-2421	270	19	obtain	obtain	VERB
ejpam-2421	270	20	2a−	2a−	NUM
ejpam-2421	270	21	r1	r1	NOUN
ejpam-2421	270	22	=	=	SYM
ejpam-2421	270	23	c1ℓ1	c1ℓ1	NOUN
ejpam-2421	270	24	+	+	X
ejpam-2421	270	25	r2⇒	r2⇒	ADJ
ejpam-2421	270	26	(	(	PUNCT
ejpam-2421	270	27	r1	r1	NOUN
ejpam-2421	270	28	=	=	SYM
ejpam-2421	270	29	1	1	NUM
ejpam-2421	270	30	and	and	CCONJ
ejpam-2421	270	31	c1	c1	NOUN
ejpam-2421	270	32	=	=	PUNCT
ejpam-2421	271	1	4m+	4m+	NUM
ejpam-2421	271	2	a	a	NOUN
ejpam-2421	271	3	)	)	PUNCT
ejpam-2421	271	4	⇒	⇒	VERB
ejpam-2421	271	5	2a−	2a−	NUM
ejpam-2421	271	6	1=	1=	X
ejpam-2421	271	7	(	(	PUNCT
ejpam-2421	271	8	4m+	4m+	NUM
ejpam-2421	271	9	a)ℓ1	a)ℓ1	PROPN
ejpam-2421	271	10	+	+	CCONJ
ejpam-2421	271	11	r2	r2	PROPN
ejpam-2421	271	12	⇒	⇒	NOUN
ejpam-2421	271	13	2a−	2a−	NUM
ejpam-2421	271	14	1=	1=	X
ejpam-2421	271	15	4mℓ1	4mℓ1	NOUN
ejpam-2421	272	1	+	+	NUM
ejpam-2421	272	2	aℓ1	aℓ1	NOUN
ejpam-2421	272	3	+	+	X
ejpam-2421	272	4	r2	r2	PROPN
ejpam-2421	272	5	⇒	⇒	NOUN
ejpam-2421	272	6	(	(	PUNCT
ejpam-2421	272	7	2−	2−	NUM
ejpam-2421	272	8	ℓ1)a	ℓ1)a	NOUN
ejpam-2421	272	9	=	=	SYM
ejpam-2421	272	10	4mℓ1	4mℓ1	ADP
ejpam-2421	272	11	+	+	NUM
ejpam-2421	272	12	r2	r2	PROPN
ejpam-2421	272	13	+	+	CCONJ
ejpam-2421	272	14	1	1	NUM
ejpam-2421	272	15	>	>	SYM
ejpam-2421	272	16	0	0	NUM
ejpam-2421	272	17	⇒	⇒	NOUN
ejpam-2421	272	18	2−	2−	NUM
ejpam-2421	272	19	ℓ1	ℓ1	NOUN
ejpam-2421	272	20	>	>	X
ejpam-2421	272	21	0	0	PUNCT
ejpam-2421	273	1	⇒	⇒	NOUN
ejpam-2421	273	2	ℓ1	ℓ1	NOUN
ejpam-2421	273	3	<	<	X
ejpam-2421	273	4	2	2	NUM
ejpam-2421	273	5	and	and	CCONJ
ejpam-2421	273	6	ℓ1	ℓ1	VERB
ejpam-2421	273	7	≥	≥	NOUN
ejpam-2421	273	8	1	1	NUM
ejpam-2421	273	9	⇒	⇒	NOUN
ejpam-2421	273	10	ℓ1	ℓ1	NOUN
ejpam-2421	273	11	=	=	SYM
ejpam-2421	273	12	1	1	NUM
ejpam-2421	274	1	and	and	CCONJ
ejpam-2421	274	2	so	so	ADV
ejpam-2421	274	3	we	we	PRON
ejpam-2421	274	4	have	have	VERB
ejpam-2421	274	5	wd	wd	NOUN
ejpam-2421	274	6	=	=	PUNCT
ejpam-2421	274	7	[	[	PUNCT
ejpam-2421	274	8	a	a	DET
ejpam-2421	274	9	2	2	NUM
ejpam-2421	274	10	;	;	PUNCT
ejpam-2421	274	11	1,ℓ2,ℓ3,ℓ4,ℓ3,ℓ2	1,ℓ2,ℓ3,ℓ4,ℓ3,ℓ2	NUM
ejpam-2421	274	12	,	,	PUNCT
ejpam-2421	274	13	1	1	NUM
ejpam-2421	274	14	,	,	PUNCT
ejpam-2421	274	15	a−	a−	PROPN
ejpam-2421	274	16	1	1	NUM
ejpam-2421	274	17	]	]	PUNCT
ejpam-2421	274	18	.	.	PUNCT
ejpam-2421	275	1	since	since	SCONJ
ejpam-2421	275	2	ℓ1	ℓ1	NOUN
ejpam-2421	275	3	=	=	NOUN
ejpam-2421	275	4	1	1	NUM
ejpam-2421	275	5	then	then	ADV
ejpam-2421	275	6	a	a	DET
ejpam-2421	275	7	=	=	SYM
ejpam-2421	275	8	4m+	4m+	NUM
ejpam-2421	275	9	1	1	NUM
ejpam-2421	275	10	+	+	NUM
ejpam-2421	275	11	r2	r2	NOUN
ejpam-2421	275	12	and	and	CCONJ
ejpam-2421	275	13	if	if	SCONJ
ejpam-2421	275	14	r2	r2	PROPN
ejpam-2421	275	15	=	=	PUNCT
ejpam-2421	275	16	a	a	DET
ejpam-2421	275	17	−	−	NOUN
ejpam-2421	275	18	4m−	4m−	PROPN
ejpam-2421	275	19	1	1	NUM
ejpam-2421	275	20	then	then	ADV
ejpam-2421	275	21	a	a	PRON
ejpam-2421	275	22	,	,	PUNCT
ejpam-2421	275	23	4	4	NUM
ejpam-2421	275	24	m	m	NOUN
ejpam-2421	275	25	are	be	AUX
ejpam-2421	275	26	even	even	ADV
ejpam-2421	275	27	and	and	CCONJ
ejpam-2421	275	28	r2	r2	PROPN
ejpam-2421	275	29	≥	≥	NUM
ejpam-2421	275	30	1	1	NUM
ejpam-2421	275	31	is	be	AUX
ejpam-2421	275	32	odd	odd	ADJ
ejpam-2421	275	33	and	and	CCONJ
ejpam-2421	275	34	so	so	ADV
ejpam-2421	275	35	there	there	PRON
ejpam-2421	275	36	exists	exist	VERB
ejpam-2421	275	37	r	r	NOUN
ejpam-2421	275	38	≥	≥	NOUN
ejpam-2421	275	39	0	0	NUM
ejpam-2421	275	40	such	such	ADJ
ejpam-2421	275	41	that	that	DET
ejpam-2421	275	42	r2	r2	NOUN
ejpam-2421	276	1	=	=	PUNCT
ejpam-2421	276	2	2r	2r	NUM
ejpam-2421	277	1	+	+	CCONJ
ejpam-2421	277	2	1	1	NUM
ejpam-2421	277	3	and	and	CCONJ
ejpam-2421	277	4	we	we	PRON
ejpam-2421	277	5	can	can	AUX
ejpam-2421	277	6	obtain	obtain	VERB
ejpam-2421	277	7	r2	r2	PROPN
ejpam-2421	277	8	<	<	X
ejpam-2421	277	9	a.	a.	NOUN
ejpam-2421	277	10	if	if	SCONJ
ejpam-2421	277	11	we	we	PRON
ejpam-2421	277	12	use	use	VERB
ejpam-2421	277	13	ci+1	ci+1	PROPN
ejpam-2421	277	14	=	=	SYM
ejpam-2421	277	15	ci−1	ci−1	PROPN
ejpam-2421	277	16	+	+	CCONJ
ejpam-2421	277	17	(	(	PUNCT
ejpam-2421	277	18	ri+1	ri+1	PROPN
ejpam-2421	277	19	−	−	PROPN
ejpam-2421	277	20	ri)ℓi	ri)ℓi	PROPN
ejpam-2421	277	21	for	for	ADP
ejpam-2421	277	22	i	i	PRON
ejpam-2421	277	23	≥	≥	NOUN
ejpam-2421	277	24	0	0	NUM
ejpam-2421	278	1	then	then	ADV
ejpam-2421	278	2	we	we	PRON
ejpam-2421	278	3	obtain	obtain	VERB
ejpam-2421	278	4	c2	c2	PROPN
ejpam-2421	278	5	=	=	SYM
ejpam-2421	278	6	c0	c0	PROPN
ejpam-2421	278	7	+	+	CCONJ
ejpam-2421	278	8	(	(	PUNCT
ejpam-2421	278	9	r2	r2	PROPN
ejpam-2421	278	10	−	−	PROPN
ejpam-2421	278	11	r1)ℓ1	r1)ℓ1	NOUN
ejpam-2421	278	12	=	=	PUNCT
ejpam-2421	278	13	2	2	NUM
ejpam-2421	278	14	+	+	CCONJ
ejpam-2421	278	15	(	(	PUNCT
ejpam-2421	278	16	r2	r2	PROPN
ejpam-2421	278	17	−	−	PROPN
ejpam-2421	278	18	1)1=	1)1=	NUM
ejpam-2421	278	19	2r	2r	NUM
ejpam-2421	279	1	+	+	CCONJ
ejpam-2421	279	2	2	2	X
ejpam-2421	279	3	.	.	X
ejpam-2421	279	4	furthermore	furthermore	ADV
ejpam-2421	279	5	we	we	PRON
ejpam-2421	279	6	have	have	AUX
ejpam-2421	279	7	obtain	obtain	VERB
ejpam-2421	279	8	the	the	DET
ejpam-2421	279	9	following	follow	VERB
ejpam-2421	279	10	equalities	equality	NOUN
ejpam-2421	279	11	from	from	ADP
ejpam-2421	279	12	lemma	lemma	PROPN
ejpam-2421	279	13	2	2	NUM
ejpam-2421	279	14	c2	c2	PROPN
ejpam-2421	279	15	=	=	PUNCT
ejpam-2421	279	16	2r	2r	NUM
ejpam-2421	280	1	+	+	CCONJ
ejpam-2421	280	2	2	2	NUM
ejpam-2421	280	3	,	,	PUNCT
ejpam-2421	280	4	2a	2a	NUM
ejpam-2421	280	5	=	=	SYM
ejpam-2421	280	6	c2ℓ2	c2ℓ2	PROPN
ejpam-2421	281	1	+	+	NUM
ejpam-2421	281	2	r2	r2	PROPN
ejpam-2421	281	3	+	+	CCONJ
ejpam-2421	281	4	r3⇒	r3⇒	PROPN
ejpam-2421	281	5	2a	2a	NUM
ejpam-2421	281	6	=	=	SYM
ejpam-2421	281	7	(	(	PUNCT
ejpam-2421	281	8	2r	2r	NUM
ejpam-2421	281	9	+	+	CCONJ
ejpam-2421	281	10	2)ℓ2	2)ℓ2	NUM
ejpam-2421	282	1	+	+	SYM
ejpam-2421	282	2	2r	2r	NUM
ejpam-2421	282	3	+	+	CCONJ
ejpam-2421	282	4	1	1	NUM
ejpam-2421	282	5	+	+	NUM
ejpam-2421	282	6	r3	r3	PROPN
ejpam-2421	282	7	and	and	CCONJ
ejpam-2421	282	8	by	by	ADP
ejpam-2421	282	9	taking	take	VERB
ejpam-2421	282	10	a	a	PRON
ejpam-2421	282	11	=	=	NOUN
ejpam-2421	282	12	4m+	4m+	NUM
ejpam-2421	282	13	1	1	NUM
ejpam-2421	282	14	+	+	NUM
ejpam-2421	282	15	r2	r2	PROPN
ejpam-2421	282	16	and	and	CCONJ
ejpam-2421	282	17	a	a	DET
ejpam-2421	282	18	=	=	SYM
ejpam-2421	282	19	4m+	4m+	NUM
ejpam-2421	282	20	2r	2r	NUM
ejpam-2421	283	1	+	+	CCONJ
ejpam-2421	283	2	2	2	NUM
ejpam-2421	283	3	we	we	PRON
ejpam-2421	283	4	have	have	VERB
ejpam-2421	283	5	8m+	8m+	NUM
ejpam-2421	283	6	4r	4r	NOUN
ejpam-2421	283	7	+	+	CCONJ
ejpam-2421	283	8	4=	4=	NUM
ejpam-2421	283	9	(	(	PUNCT
ejpam-2421	283	10	2r	2r	NUM
ejpam-2421	283	11	+	+	CCONJ
ejpam-2421	283	12	2)ℓ2	2)ℓ2	NUM
ejpam-2421	283	13	+	+	SYM
ejpam-2421	283	14	2r	2r	NUM
ejpam-2421	284	1	+	+	CCONJ
ejpam-2421	284	2	1	1	NUM
ejpam-2421	284	3	+	+	NUM
ejpam-2421	284	4	r3	r3	NOUN
ejpam-2421	284	5	=	=	SYM
ejpam-2421	284	6	(	(	PUNCT
ejpam-2421	284	7	2r	2r	NUM
ejpam-2421	284	8	+	+	CCONJ
ejpam-2421	284	9	2)ℓ2	2)ℓ2	NUM
ejpam-2421	284	10	+	+	CCONJ
ejpam-2421	284	11	r3	r3	PROPN
ejpam-2421	284	12	−	−	NOUN
ejpam-2421	284	13	2r	2r	NUM
ejpam-2421	284	14	−	−	NOUN
ejpam-2421	284	15	3	3	X
ejpam-2421	284	16	.	.	PUNCT
ejpam-2421	284	17	ö.	ö.	PROPN
ejpam-2421	284	18	özer	özer	NOUN
ejpam-2421	284	19	,	,	PUNCT
ejpam-2421	284	20	a.	a.	NOUN
ejpam-2421	284	21	pekin	pekin	PROPN
ejpam-2421	284	22	/	/	SYM
ejpam-2421	284	23	eur	eur	PROPN
ejpam-2421	284	24	.	.	PUNCT
ejpam-2421	285	1	j.	j.	PROPN
ejpam-2421	285	2	pure	pure	PROPN
ejpam-2421	285	3	appl	appl	PROPN
ejpam-2421	285	4	.	.	PROPN
ejpam-2421	285	5	math	math	PROPN
ejpam-2421	285	6	,	,	PUNCT
ejpam-2421	285	7	8	8	NUM
ejpam-2421	285	8	(	(	PUNCT
ejpam-2421	285	9	2015	2015	NUM
ejpam-2421	285	10	)	)	PUNCT
ejpam-2421	285	11	,	,	PUNCT
ejpam-2421	285	12	343	343	NUM
ejpam-2421	285	13	-	-	SYM
ejpam-2421	285	14	356	356	NUM
ejpam-2421	285	15	352	352	NUM
ejpam-2421	285	16	since	since	SCONJ
ejpam-2421	285	17	a	a	PRON
ejpam-2421	285	18	is	be	AUX
ejpam-2421	285	19	even	even	ADV
ejpam-2421	285	20	then	then	ADV
ejpam-2421	285	21	2a	2a	NUM
ejpam-2421	285	22	=(	=(	NOUN
ejpam-2421	285	23	2r	2r	NUM
ejpam-2421	286	1	+	+	CCONJ
ejpam-2421	286	2	2)ℓ2	2)ℓ2	NUM
ejpam-2421	286	3	+	+	CCONJ
ejpam-2421	286	4	(	(	PUNCT
ejpam-2421	286	5	2r	2r	NUM
ejpam-2421	286	6	+	+	CCONJ
ejpam-2421	286	7	1	1	NUM
ejpam-2421	286	8	)	)	PUNCT
ejpam-2421	286	9	+	+	CCONJ
ejpam-2421	286	10	r3	r3	PROPN
ejpam-2421	286	11	≡	≡	PROPN
ejpam-2421	286	12	0(mod4	0(mod4	NUM
ejpam-2421	286	13	)	)	PUNCT
ejpam-2421	286	14	⇒	⇒	PROPN
ejpam-2421	286	15	r3	r3	PROPN
ejpam-2421	286	16	+	+	CCONJ
ejpam-2421	286	17	2r	2r	NUM
ejpam-2421	286	18	+	+	CCONJ
ejpam-2421	286	19	1≡	1≡	NUM
ejpam-2421	286	20	0(mod4	0(mod4	NUM
ejpam-2421	286	21	)	)	PUNCT
ejpam-2421	286	22	and	and	CCONJ
ejpam-2421	286	23	ℓ2	ℓ2	PROPN
ejpam-2421	286	24	≡	≡	PROPN
ejpam-2421	286	25	0(mod2	0(mod2	PROPN
ejpam-2421	286	26	)	)	PUNCT
ejpam-2421	286	27	⇒	⇒	NOUN
ejpam-2421	286	28	∃s	∃s	PROPN
ejpam-2421	286	29	∈	∈	PROPN
ejpam-2421	286	30	z+	z+	NUM
ejpam-2421	286	31	∋	∋	NOUN
ejpam-2421	286	32	r3	r3	PROPN
ejpam-2421	286	33	+	+	CCONJ
ejpam-2421	286	34	2r	2r	NUM
ejpam-2421	287	1	+	+	CCONJ
ejpam-2421	287	2	1=	1=	NUM
ejpam-2421	287	3	4s	4s	NUM
ejpam-2421	287	4	,	,	PUNCT
ejpam-2421	287	5	r3	r3	PROPN
ejpam-2421	287	6	≥	≥	NOUN
ejpam-2421	287	7	0	0	NUM
ejpam-2421	287	8	⇒	⇒	PROPN
ejpam-2421	287	9	4s−	4s−	PROPN
ejpam-2421	287	10	2r	2r	NUM
ejpam-2421	287	11	−	−	NUM
ejpam-2421	287	12	1≥	1≥	NUM
ejpam-2421	287	13	0	0	NUM
ejpam-2421	287	14	⇒	⇒	NOUN
ejpam-2421	287	15	4s	4s	NUM
ejpam-2421	287	16	>	>	SYM
ejpam-2421	288	1	2r	2r	NUM
ejpam-2421	289	1	+	+	CCONJ
ejpam-2421	289	2	1	1	NUM
ejpam-2421	289	3	hold	hold	NOUN
ejpam-2421	289	4	,	,	PUNCT
ejpam-2421	289	5	where	where	SCONJ
ejpam-2421	289	6	r3	r3	PROPN
ejpam-2421	289	7	=	=	SYM
ejpam-2421	289	8	4s−	4s−	NUM
ejpam-2421	289	9	2r	2r	NUM
ejpam-2421	290	1	−	−	NOUN
ejpam-2421	290	2	1	1	NUM
ejpam-2421	290	3	is	be	AUX
ejpam-2421	290	4	odd	odd	ADJ
ejpam-2421	290	5	number	number	NOUN
ejpam-2421	290	6	because	because	SCONJ
ejpam-2421	290	7	of	of	ADP
ejpam-2421	290	8	4s	4s	NUM
ejpam-2421	290	9	is	be	AUX
ejpam-2421	290	10	even	even	ADV
ejpam-2421	290	11	and	and	CCONJ
ejpam-2421	290	12	2r	2r	NUM
ejpam-2421	291	1	+	+	CCONJ
ejpam-2421	291	2	1	1	NUM
ejpam-2421	291	3	is	be	AUX
ejpam-2421	291	4	odd	odd	ADJ
ejpam-2421	291	5	.	.	PUNCT
ejpam-2421	292	1	from	from	ADP
ejpam-2421	292	2	lemma	lemma	PROPN
ejpam-2421	292	3	2	2	NUM
ejpam-2421	292	4	.	.	X
ejpam-2421	293	1	we	we	PRON
ejpam-2421	293	2	have	have	VERB
ejpam-2421	293	3	c3	c3	PROPN
ejpam-2421	293	4	=	=	PROPN
ejpam-2421	293	5	c1	c1	PROPN
ejpam-2421	293	6	+	+	CCONJ
ejpam-2421	293	7	(	(	PUNCT
ejpam-2421	293	8	r3	r3	PROPN
ejpam-2421	293	9	−	−	PROPN
ejpam-2421	293	10	r2)ℓ2	r2)ℓ2	NOUN
ejpam-2421	293	11	=	=	SYM
ejpam-2421	293	12	4m+	4m+	NUM
ejpam-2421	293	13	a+	a+	PUNCT
ejpam-2421	293	14	(	(	PUNCT
ejpam-2421	293	15	4s−	4s−	NOUN
ejpam-2421	293	16	2r	2r	NUM
ejpam-2421	293	17	−	−	PROPN
ejpam-2421	293	18	1−	1−	NUM
ejpam-2421	293	19	2r	2r	NUM
ejpam-2421	293	20	−	−	PROPN
ejpam-2421	293	21	1)ℓ2	1)ℓ2	NUM
ejpam-2421	293	22	=	=	SYM
ejpam-2421	293	23	a−	a−	X
ejpam-2421	293	24	2r	2r	NUM
ejpam-2421	293	25	−	−	ADP
ejpam-2421	293	26	2	2	NUM
ejpam-2421	293	27	+	+	NUM
ejpam-2421	293	28	a+	a+	PUNCT
ejpam-2421	293	29	(	(	PUNCT
ejpam-2421	293	30	4s−	4s−	NOUN
ejpam-2421	293	31	4r	4r	NOUN
ejpam-2421	293	32	−	−	NOUN
ejpam-2421	293	33	2)ℓ2	2)ℓ2	NUM
ejpam-2421	293	34	=	=	SYM
ejpam-2421	293	35	2a−	2a−	NUM
ejpam-2421	293	36	2r	2r	NUM
ejpam-2421	293	37	−	−	NOUN
ejpam-2421	293	38	2	2	NUM
ejpam-2421	293	39	+	+	CCONJ
ejpam-2421	293	40	(	(	PUNCT
ejpam-2421	293	41	4s−	4s−	NOUN
ejpam-2421	293	42	4r	4r	NOUN
ejpam-2421	293	43	−	−	NUM
ejpam-2421	293	44	2)ℓ2	2)ℓ2	NUM
ejpam-2421	293	45	and	and	CCONJ
ejpam-2421	293	46	if	if	SCONJ
ejpam-2421	293	47	the	the	DET
ejpam-2421	293	48	value	value	NOUN
ejpam-2421	293	49	2a	2a	NUM
ejpam-2421	293	50	is	be	AUX
ejpam-2421	293	51	written	write	VERB
ejpam-2421	293	52	instead	instead	ADV
ejpam-2421	293	53	of	of	ADP
ejpam-2421	293	54	c3	c3	PROPN
ejpam-2421	293	55	then	then	ADV
ejpam-2421	293	56	c3	c3	PROPN
ejpam-2421	293	57	is	be	AUX
ejpam-2421	293	58	obtained	obtain	VERB
ejpam-2421	293	59	as	as	ADP
ejpam-2421	293	60	c3	c3	PROPN
ejpam-2421	293	61	=(	=(	NOUN
ejpam-2421	293	62	2r	2r	NUM
ejpam-2421	294	1	+	+	CCONJ
ejpam-2421	294	2	2)ℓ2	2)ℓ2	NUM
ejpam-2421	294	3	+	+	PUNCT
ejpam-2421	294	4	4s−	4s−	NUM
ejpam-2421	294	5	2r	2r	NUM
ejpam-2421	294	6	−	−	ADP
ejpam-2421	295	1	2	2	NUM
ejpam-2421	295	2	+	+	NUM
ejpam-2421	295	3	4sℓ2	4sℓ2	NUM
ejpam-2421	295	4	−	−	NOUN
ejpam-2421	295	5	4rℓ2	4rℓ2	NUM
ejpam-2421	295	6	−	−	PROPN
ejpam-2421	295	7	2ℓ2	2ℓ2	NUM
ejpam-2421	295	8	=(	=(	NOUN
ejpam-2421	295	9	4s−	4s−	NUM
ejpam-2421	295	10	2r)(ℓ2	2r)(ℓ2	NUM
ejpam-2421	295	11	+	+	CCONJ
ejpam-2421	295	12	1)−	1)−	PROPN
ejpam-2421	295	13	2	2	NUM
ejpam-2421	295	14	.	.	PUNCT
ejpam-2421	295	15	(	(	PUNCT
ejpam-2421	295	16	9	9	NUM
ejpam-2421	295	17	)	)	PUNCT
ejpam-2421	295	18	by	by	ADP
ejpam-2421	295	19	using	use	VERB
ejpam-2421	295	20	the	the	DET
ejpam-2421	295	21	values	value	NOUN
ejpam-2421	295	22	c3	c3	NOUN
ejpam-2421	295	23	,	,	PUNCT
ejpam-2421	295	24	a=	a=	ADJ
ejpam-2421	295	25	ℓ2	ℓ2	NOUN
ejpam-2421	295	26	+	+	CCONJ
ejpam-2421	295	27	1	1	NUM
ejpam-2421	295	28	and	and	CCONJ
ejpam-2421	295	29	b	b	X
ejpam-2421	295	30	=	=	SYM
ejpam-2421	295	31	2s−	2s−	NUM
ejpam-2421	295	32	r	r	NOUN
ejpam-2421	295	33	we	we	PRON
ejpam-2421	295	34	have	have	VERB
ejpam-2421	295	35	2a	2a	NUM
ejpam-2421	295	36	=(	=(	NOUN
ejpam-2421	295	37	2r	2r	NUM
ejpam-2421	296	1	+	+	CCONJ
ejpam-2421	296	2	2)ℓ2	2)ℓ2	NUM
ejpam-2421	296	3	+	+	CCONJ
ejpam-2421	296	4	r3	r3	PROPN
ejpam-2421	296	5	+	+	CCONJ
ejpam-2421	296	6	2r	2r	NUM
ejpam-2421	296	7	+	+	CCONJ
ejpam-2421	296	8	1=	1=	NUM
ejpam-2421	296	9	(	(	PUNCT
ejpam-2421	296	10	2r	2r	NUM
ejpam-2421	296	11	+	+	CCONJ
ejpam-2421	296	12	2)ℓ2	2)ℓ2	NUM
ejpam-2421	296	13	+	+	PUNCT
ejpam-2421	296	14	4s−	4s−	NUM
ejpam-2421	296	15	2r	2r	NUM
ejpam-2421	296	16	−	−	NOUN
ejpam-2421	296	17	1	1	NUM
ejpam-2421	296	18	+	+	SYM
ejpam-2421	296	19	2r	2r	NUM
ejpam-2421	296	20	+	+	CCONJ
ejpam-2421	296	21	1	1	NUM
ejpam-2421	296	22	=	=	SYM
ejpam-2421	296	23	2[(r	2[(r	NUM
ejpam-2421	296	24	+	+	NUM
ejpam-2421	296	25	1)ℓ2	1)ℓ2	NUM
ejpam-2421	296	26	+	+	CCONJ
ejpam-2421	296	27	2s	2	VERB
ejpam-2421	296	28	]	]	X
ejpam-2421	296	29	a	a	DET
ejpam-2421	296	30	=(	=(	NOUN
ejpam-2421	296	31	r	r	NOUN
ejpam-2421	296	32	+	+	NOUN
ejpam-2421	296	33	1)ℓ2	1)ℓ2	NUM
ejpam-2421	296	34	+	+	CCONJ
ejpam-2421	296	35	2s	2s	NUM
ejpam-2421	296	36	(	(	PUNCT
ejpam-2421	296	37	10	10	NUM
ejpam-2421	296	38	)	)	PUNCT
ejpam-2421	296	39	and	and	CCONJ
ejpam-2421	296	40	2a	2a	NUM
ejpam-2421	296	41	=	=	SYM
ejpam-2421	296	42	c3ℓ3	c3ℓ3	X
ejpam-2421	296	43	+	+	NUM
ejpam-2421	296	44	r3	r3	PROPN
ejpam-2421	296	45	+	+	CCONJ
ejpam-2421	296	46	r4	r4	PROPN
ejpam-2421	296	47	ise	ise	NOUN
ejpam-2421	296	48	r4	r4	NOUN
ejpam-2421	296	49	=	=	PUNCT
ejpam-2421	297	1	2a−	2a−	PROPN
ejpam-2421	297	2	c3ℓ3	c3ℓ3	NOUN
ejpam-2421	298	1	−	−	PROPN
ejpam-2421	298	2	r3	r3	PROPN
ejpam-2421	298	3	r4	r4	NOUN
ejpam-2421	298	4	=	=	PROPN
ejpam-2421	298	5	2[(r	2[(r	NUM
ejpam-2421	298	6	+	+	NUM
ejpam-2421	298	7	1)ℓ2	1)ℓ2	NUM
ejpam-2421	298	8	+	+	CCONJ
ejpam-2421	298	9	2s]−	2s]−	NUM
ejpam-2421	299	1	[	[	X
ejpam-2421	299	2	(	(	PUNCT
ejpam-2421	299	3	4s−	4s−	NOUN
ejpam-2421	299	4	2r)(ℓ2	2r)(ℓ2	NUM
ejpam-2421	299	5	+	+	CCONJ
ejpam-2421	299	6	1)−	1)−	PROPN
ejpam-2421	299	7	2]ℓ3	2]ℓ3	NUM
ejpam-2421	299	8	−	−	PROPN
ejpam-2421	299	9	(	(	PUNCT
ejpam-2421	299	10	4s−	4s−	NOUN
ejpam-2421	299	11	2r	2r	NUM
ejpam-2421	299	12	−	−	NOUN
ejpam-2421	299	13	1	1	NUM
ejpam-2421	299	14	)	)	PUNCT
ejpam-2421	299	15	=	=	NOUN
ejpam-2421	299	16	2(r	2(r	NUM
ejpam-2421	299	17	+	+	NUM
ejpam-2421	299	18	1)ℓ2	1)ℓ2	NUM
ejpam-2421	299	19	+	+	SYM
ejpam-2421	299	20	4s−	4s−	NUM
ejpam-2421	299	21	[	[	X
ejpam-2421	299	22	(	(	PUNCT
ejpam-2421	299	23	4s−	4s−	NOUN
ejpam-2421	299	24	2r)(ℓ2	2r)(ℓ2	NUM
ejpam-2421	299	25	+	+	CCONJ
ejpam-2421	300	1	1)−	1)−	NUM
ejpam-2421	300	2	2]ℓ3	2]ℓ3	NUM
ejpam-2421	301	1	−	−	PROPN
ejpam-2421	302	1	4s+	4s+	NUM
ejpam-2421	302	2	2r	2r	NUM
ejpam-2421	303	1	+	+	CCONJ
ejpam-2421	303	2	1	1	NUM
ejpam-2421	303	3	=	=	SYM
ejpam-2421	303	4	2(r	2(r	NUM
ejpam-2421	303	5	+	+	NUM
ejpam-2421	303	6	1)ℓ2	1)ℓ2	NUM
ejpam-2421	303	7	+	+	NUM
ejpam-2421	303	8	2r	2r	NUM
ejpam-2421	304	1	+	+	CCONJ
ejpam-2421	305	1	1	1	NUM
ejpam-2421	305	2	+	+	CCONJ
ejpam-2421	305	3	[	[	X
ejpam-2421	305	4	(	(	PUNCT
ejpam-2421	305	5	4s−	4s−	NOUN
ejpam-2421	305	6	2r)(ℓ2	2r)(ℓ2	NUM
ejpam-2421	305	7	+	+	CCONJ
ejpam-2421	305	8	1)−	1)−	PROPN
ejpam-2421	305	9	2]ℓ3	2]ℓ3	NUM
ejpam-2421	305	10	(	(	PUNCT
ejpam-2421	305	11	11	11	NUM
ejpam-2421	305	12	)	)	PUNCT
ejpam-2421	305	13	hold	hold	VERB
ejpam-2421	305	14	from	from	ADP
ejpam-2421	305	15	lemma	lemma	PROPN
ejpam-2421	305	16	2	2	NUM
ejpam-2421	305	17	.	.	PUNCT
ejpam-2421	306	1	moreover	moreover	ADV
ejpam-2421	306	2	we	we	PRON
ejpam-2421	306	3	have	have	VERB
ejpam-2421	306	4	a	a	DET
ejpam-2421	306	5	=	=	PUNCT
ejpam-2421	306	6	(	(	PUNCT
ejpam-2421	306	7	r	r	NOUN
ejpam-2421	306	8	+	+	NUM
ejpam-2421	306	9	1)ℓ2	1)ℓ2	NUM
ejpam-2421	306	10	+	+	CCONJ
ejpam-2421	306	11	2s	2s	NUM
ejpam-2421	306	12	=	=	NOUN
ejpam-2421	306	13	a(r	a(r	PROPN
ejpam-2421	306	14	+	+	NOUN
ejpam-2421	306	15	1	1	NUM
ejpam-2421	306	16	)	)	PUNCT
ejpam-2421	307	1	+	+	NOUN
ejpam-2421	307	2	b	b	X
ejpam-2421	307	3	−	−	NOUN
ejpam-2421	307	4	1	1	NUM
ejpam-2421	307	5	(	(	PUNCT
ejpam-2421	307	6	12	12	NUM
ejpam-2421	307	7	)	)	PUNCT
ejpam-2421	307	8	for	for	ADP
ejpam-2421	307	9	a=	a=	ADJ
ejpam-2421	307	10	ℓ2	ℓ2	NOUN
ejpam-2421	307	11	+	+	CCONJ
ejpam-2421	307	12	1	1	NUM
ejpam-2421	307	13	,	,	PUNCT
ejpam-2421	307	14	b	b	X
ejpam-2421	307	15	=	=	SYM
ejpam-2421	307	16	2s−	2s−	NUM
ejpam-2421	307	17	r	r	NOUN
ejpam-2421	307	18	and	and	CCONJ
ejpam-2421	307	19	r3	r3	NOUN
ejpam-2421	307	20	=	=	SYM
ejpam-2421	307	21	4s−	4s−	NOUN
ejpam-2421	307	22	2r	2r	NUM
ejpam-2421	307	23	−	−	PROPN
ejpam-2421	307	24	1⇒	1⇒	PROPN
ejpam-2421	307	25	r3	r3	PROPN
ejpam-2421	307	26	=	=	SYM
ejpam-2421	307	27	2b	2b	NOUN
ejpam-2421	307	28	−	−	PROPN
ejpam-2421	307	29	1	1	NUM
ejpam-2421	307	30	r4	r4	NOUN
ejpam-2421	307	31	=	=	PROPN
ejpam-2421	307	32	2a−	2a−	PROPN
ejpam-2421	307	33	c3ℓ3	c3ℓ3	X
ejpam-2421	307	34	−	−	PROPN
ejpam-2421	307	35	r3⇒	r3⇒	PROPN
ejpam-2421	307	36	r4	r4	NOUN
ejpam-2421	307	37	=	=	PUNCT
ejpam-2421	308	1	2a−	2a−	NUM
ejpam-2421	308	2	2(ba−	2(ba−	NUM
ejpam-2421	308	3	1)ℓ3	1)ℓ3	NUM
ejpam-2421	308	4	−	−	NOUN
ejpam-2421	308	5	2b	2b	NOUN
ejpam-2421	308	6	+	+	SYM
ejpam-2421	308	7	1	1	NUM
ejpam-2421	308	8	⇒	⇒	NOUN
ejpam-2421	308	9	r4	r4	NOUN
ejpam-2421	308	10	=	=	SYM
ejpam-2421	308	11	2rℓ2	2rℓ2	NUM
ejpam-2421	308	12	+	+	NUM
ejpam-2421	308	13	ℓ2	ℓ2	NOUN
ejpam-2421	308	14	−	−	PROPN
ejpam-2421	308	15	2bc	2bc	ADJ
ejpam-2421	309	1	+	+	CCONJ
ejpam-2421	309	2	2ℓ3	2ℓ3	NUM
ejpam-2421	310	1	+	+	CCONJ
ejpam-2421	310	2	4s+	4s+	NUM
ejpam-2421	310	3	a.	a.	NOUN
ejpam-2421	310	4	if	if	SCONJ
ejpam-2421	310	5	c	c	NOUN
ejpam-2421	310	6	=	=	SYM
ejpam-2421	310	7	1	1	NUM
ejpam-2421	310	8	+	+	NUM
ejpam-2421	310	9	aℓ3	aℓ3	NOUN
ejpam-2421	310	10	=	=	SYM
ejpam-2421	310	11	1	1	NUM
ejpam-2421	310	12	+	+	NUM
ejpam-2421	310	13	ℓ3	ℓ3	PROPN
ejpam-2421	310	14	+	+	CCONJ
ejpam-2421	310	15	ℓ2ℓ3	ℓ2ℓ3	PROPN
ejpam-2421	310	16	,	,	PUNCT
ejpam-2421	310	17	b	b	X
ejpam-2421	310	18	=	=	SYM
ejpam-2421	310	19	2s−	2s−	NUM
ejpam-2421	310	20	r	r	NOUN
ejpam-2421	310	21	,	,	PUNCT
ejpam-2421	310	22	4s	4s	NUM
ejpam-2421	310	23	=	=	NOUN
ejpam-2421	310	24	2b	2b	NOUN
ejpam-2421	310	25	+	+	SYM
ejpam-2421	310	26	2r	2r	NUM
ejpam-2421	310	27	⇒	⇒	NOUN
ejpam-2421	310	28	r4	r4	NOUN
ejpam-2421	310	29	=	=	SYM
ejpam-2421	310	30	2rℓ2	2rℓ2	NUM
ejpam-2421	310	31	+	+	NUM
ejpam-2421	310	32	ℓ2	ℓ2	NOUN
ejpam-2421	310	33	−	−	PROPN
ejpam-2421	310	34	2bc	2bc	ADJ
ejpam-2421	311	1	+	+	CCONJ
ejpam-2421	311	2	2ℓ3	2ℓ3	NUM
ejpam-2421	312	1	+	+	SYM
ejpam-2421	312	2	2b	2b	NUM
ejpam-2421	312	3	+	+	CCONJ
ejpam-2421	312	4	2r	2r	NUM
ejpam-2421	312	5	+	+	CCONJ
ejpam-2421	312	6	a	a	DET
ejpam-2421	312	7	ö.	ö.	NOUN
ejpam-2421	312	8	özer	özer	NOUN
ejpam-2421	312	9	,	,	PUNCT
ejpam-2421	312	10	a.	a.	NOUN
ejpam-2421	312	11	pekin	pekin	PROPN
ejpam-2421	312	12	/	/	SYM
ejpam-2421	312	13	eur	eur	PROPN
ejpam-2421	312	14	.	.	PUNCT
ejpam-2421	313	1	j.	j.	PROPN
ejpam-2421	313	2	pure	pure	PROPN
ejpam-2421	313	3	appl	appl	PROPN
ejpam-2421	313	4	.	.	PROPN
ejpam-2421	313	5	math	math	PROPN
ejpam-2421	313	6	,	,	PUNCT
ejpam-2421	313	7	8	8	NUM
ejpam-2421	313	8	(	(	PUNCT
ejpam-2421	313	9	2015	2015	NUM
ejpam-2421	313	10	)	)	PUNCT
ejpam-2421	313	11	,	,	PUNCT
ejpam-2421	313	12	343	343	NUM
ejpam-2421	313	13	-	-	SYM
ejpam-2421	313	14	356	356	NUM
ejpam-2421	313	15	353	353	NUM
ejpam-2421	313	16	⇒	⇒	NOUN
ejpam-2421	313	17	r4	r4	NOUN
ejpam-2421	313	18	=	=	PUNCT
ejpam-2421	313	19	2ra+	2ra+	PROPN
ejpam-2421	313	20	2a−	2a−	PROPN
ejpam-2421	313	21	2bc	2bc	NOUN
ejpam-2421	314	1	+	+	PUNCT
ejpam-2421	314	2	2b	2b	NUM
ejpam-2421	314	3	+	+	CCONJ
ejpam-2421	314	4	2ℓ3	2ℓ3	NUM
ejpam-2421	314	5	−	−	SYM
ejpam-2421	314	6	1	1	NUM
ejpam-2421	314	7	hold	hold	VERB
ejpam-2421	314	8	.	.	PUNCT
ejpam-2421	315	1	for	for	ADP
ejpam-2421	315	2	ℓ1	ℓ1	NOUN
ejpam-2421	315	3	=	=	SYM
ejpam-2421	315	4	1	1	NUM
ejpam-2421	315	5	,	,	PUNCT
ejpam-2421	315	6	c3	c3	NOUN
ejpam-2421	315	7	=	=	SYM
ejpam-2421	315	8	2ba−2=	2ba−2=	NUM
ejpam-2421	315	9	2(ba−1	2(ba−1	NUM
ejpam-2421	315	10	)	)	PUNCT
ejpam-2421	315	11	.	.	PUNCT
ejpam-2421	316	1	if	if	SCONJ
ejpam-2421	316	2	we	we	PRON
ejpam-2421	316	3	take	take	VERB
ejpam-2421	316	4	c4	c4	NOUN
ejpam-2421	316	5	=	=	PUNCT
ejpam-2421	316	6	(	(	PUNCT
ejpam-2421	316	7	2r+2)+(2ra+2a−2bc+2ℓ3)ℓ3	2r+2)+(2ra+2a−2bc+2ℓ3)ℓ3	NUM
ejpam-2421	316	8	then	then	ADV
ejpam-2421	316	9	c4	c4	VERB
ejpam-2421	316	10	=	=	PUNCT
ejpam-2421	316	11	2r	2r	NUM
ejpam-2421	317	1	+	+	CCONJ
ejpam-2421	317	2	2	2	NUM
ejpam-2421	317	3	+	+	NUM
ejpam-2421	317	4	2raℓ3	2raℓ3	NUM
ejpam-2421	317	5	+	+	CCONJ
ejpam-2421	317	6	2aℓ3	2aℓ3	NUM
ejpam-2421	317	7	−	−	PROPN
ejpam-2421	317	8	2bcℓ3	2bcℓ3	NUM
ejpam-2421	317	9	+	+	CCONJ
ejpam-2421	317	10	2ℓ23⇒	2ℓ23⇒	NUM
ejpam-2421	317	11	c4	c4	NOUN
ejpam-2421	317	12	=	=	PUNCT
ejpam-2421	317	13	2c[r	2c[r	NUM
ejpam-2421	317	14	+	+	CCONJ
ejpam-2421	317	15	1−	1−	NUM
ejpam-2421	317	16	bℓ3	bℓ3	NOUN
ejpam-2421	317	17	]	]	PUNCT
ejpam-2421	318	1	+	+	CCONJ
ejpam-2421	318	2	2ℓ23	2ℓ23	NUM
ejpam-2421	318	3	hold	hold	VERB
ejpam-2421	318	4	.	.	PUNCT
ejpam-2421	319	1	where	where	SCONJ
ejpam-2421	319	2	if	if	SCONJ
ejpam-2421	319	3	we	we	PRON
ejpam-2421	319	4	take	take	VERB
ejpam-2421	319	5	r	r	NOUN
ejpam-2421	319	6	+	+	CCONJ
ejpam-2421	319	7	1−	1−	NUM
ejpam-2421	319	8	bℓ3	bℓ3	PROPN
ejpam-2421	319	9	=	=	PROPN
ejpam-2421	319	10	−d	−d	PROPN
ejpam-2421	319	11	then	then	ADV
ejpam-2421	319	12	we	we	PRON
ejpam-2421	319	13	obtain	obtain	VERB
ejpam-2421	319	14	c4	c4	NOUN
ejpam-2421	319	15	=	=	SYM
ejpam-2421	319	16	2ℓ23	2ℓ23	NUM
ejpam-2421	320	1	−	−	NOUN
ejpam-2421	320	2	2c	2c	NOUN
ejpam-2421	320	3	d	d	NOUN
ejpam-2421	320	4	=	=	SYM
ejpam-2421	320	5	2(ℓ23	2(ℓ23	NUM
ejpam-2421	320	6	−	−	NOUN
ejpam-2421	320	7	c	c	NOUN
ejpam-2421	320	8	d	d	NOUN
ejpam-2421	320	9	)	)	PUNCT
ejpam-2421	320	10	and	and	CCONJ
ejpam-2421	320	11	r4	r4	VERB
ejpam-2421	320	12	=	=	SYM
ejpam-2421	320	13	2ra+2a−2bc+2b+2ℓ3−1	2ra+2a−2bc+2b+2ℓ3−1	PROPN
ejpam-2421	320	14	for	for	ADP
ejpam-2421	320	15	a=	a=	ADJ
ejpam-2421	320	16	ℓ2	ℓ2	PROPN
ejpam-2421	320	17	+	+	PROPN
ejpam-2421	320	18	1	1	NUM
ejpam-2421	320	19	,	,	PUNCT
ejpam-2421	320	20	b	b	X
ejpam-2421	320	21	=	=	SYM
ejpam-2421	320	22	2s+r	2s+r	NUM
ejpam-2421	320	23	,	,	PUNCT
ejpam-2421	320	24	c	c	X
ejpam-2421	320	25	=	=	SYM
ejpam-2421	320	26	aℓ3	aℓ3	PROPN
ejpam-2421	320	27	+	+	PROPN
ejpam-2421	320	28	1	1	NUM
ejpam-2421	320	29	.	.	PUNCT
ejpam-2421	321	1	finally	finally	ADV
ejpam-2421	321	2	r4	r4	VERB
ejpam-2421	321	3	is	be	AUX
ejpam-2421	321	4	determined	determine	VERB
ejpam-2421	321	5	as	as	ADP
ejpam-2421	321	6	r4	r4	PROPN
ejpam-2421	321	7	=	=	PROPN
ejpam-2421	321	8	2ra+	2ra+	PROPN
ejpam-2421	321	9	2a−	2a−	PROPN
ejpam-2421	321	10	2b	2b	NUM
ejpam-2421	321	11	−	−	PROPN
ejpam-2421	321	12	2abℓ3	2abℓ3	NUM
ejpam-2421	321	13	+	+	CCONJ
ejpam-2421	321	14	2b	2b	NUM
ejpam-2421	321	15	+	+	CCONJ
ejpam-2421	321	16	2ℓ3	2ℓ3	NUM
ejpam-2421	321	17	−	−	NUM
ejpam-2421	321	18	1=	1=	X
ejpam-2421	321	19	2ℓ3	2ℓ3	NUM
ejpam-2421	321	20	−	−	PROPN
ejpam-2421	321	21	2a(bℓ3	2a(bℓ3	NUM
ejpam-2421	322	1	−	−	NOUN
ejpam-2421	322	2	r	r	NOUN
ejpam-2421	322	3	−	−	PROPN
ejpam-2421	322	4	1)−	1)−	NUM
ejpam-2421	322	5	1=	1=	NUM
ejpam-2421	322	6	2e	2e	NOUN
ejpam-2421	322	7	−	−	PROPN
ejpam-2421	322	8	2ad−	2ad−	NUM
ejpam-2421	322	9	3	3	NUM
ejpam-2421	322	10	for	for	ADP
ejpam-2421	322	11	the	the	DET
ejpam-2421	322	12	values	value	NOUN
ejpam-2421	322	13	d	d	X
ejpam-2421	322	14	=	=	PUNCT
ejpam-2421	322	15	bℓ3	bℓ3	PROPN
ejpam-2421	322	16	−	−	NOUN
ejpam-2421	322	17	r	r	NOUN
ejpam-2421	322	18	−	−	NOUN
ejpam-2421	322	19	1	1	NUM
ejpam-2421	322	20	and	and	CCONJ
ejpam-2421	322	21	e	e	NOUN
ejpam-2421	322	22	=	=	PROPN
ejpam-2421	322	23	ℓ3	ℓ3	PROPN
ejpam-2421	322	24	+	+	CCONJ
ejpam-2421	322	25	1	1	X
ejpam-2421	322	26	.	.	PUNCT
ejpam-2421	323	1	on	on	ADP
ejpam-2421	323	2	the	the	DET
ejpam-2421	323	3	other	other	ADJ
ejpam-2421	323	4	hand	hand	NOUN
ejpam-2421	323	5	we	we	PRON
ejpam-2421	323	6	can	can	AUX
ejpam-2421	323	7	write	write	VERB
ejpam-2421	323	8	a−	a−	PROPN
ejpam-2421	323	9	r4	r4	VERB
ejpam-2421	323	10	=(	=(	NOUN
ejpam-2421	323	11	r	r	NOUN
ejpam-2421	323	12	+	+	NOUN
ejpam-2421	323	13	1)ℓ2	1)ℓ2	NUM
ejpam-2421	323	14	+	+	SYM
ejpam-2421	323	15	2s−	2s−	NUM
ejpam-2421	323	16	2e	2e	NOUN
ejpam-2421	323	17	+	+	CCONJ
ejpam-2421	323	18	2ad+	2ad+	NUM
ejpam-2421	323	19	3	3	NUM
ejpam-2421	323	20	=(	=(	NOUN
ejpam-2421	323	21	r	r	NOUN
ejpam-2421	323	22	+	+	NOUN
ejpam-2421	323	23	1)ℓ2	1)ℓ2	NUM
ejpam-2421	323	24	+	+	SYM
ejpam-2421	323	25	b	b	NOUN
ejpam-2421	323	26	+	+	CCONJ
ejpam-2421	323	27	r	r	NOUN
ejpam-2421	323	28	−	−	NOUN
ejpam-2421	323	29	2e	2e	NOUN
ejpam-2421	323	30	+	+	CCONJ
ejpam-2421	323	31	2ad+	2ad+	NUM
ejpam-2421	323	32	3=	3=	NUM
ejpam-2421	323	33	r(ℓ2	r(ℓ2	NOUN
ejpam-2421	323	34	+	+	CCONJ
ejpam-2421	323	35	1	1	X
ejpam-2421	323	36	)	)	PUNCT
ejpam-2421	323	37	+	+	CCONJ
ejpam-2421	323	38	ℓ2	ℓ2	NOUN
ejpam-2421	323	39	+	+	CCONJ
ejpam-2421	324	1	b	b	NOUN
ejpam-2421	324	2	−	−	NOUN
ejpam-2421	324	3	2e	2e	NOUN
ejpam-2421	324	4	+	+	CCONJ
ejpam-2421	324	5	2ad+	2ad+	NUM
ejpam-2421	324	6	3	3	NUM
ejpam-2421	324	7	=	=	SYM
ejpam-2421	324	8	b	b	NOUN
ejpam-2421	324	9	−	−	PROPN
ejpam-2421	324	10	2e	2e	NOUN
ejpam-2421	324	11	+	+	CCONJ
ejpam-2421	324	12	abℓ3	abℓ3	PROPN
ejpam-2421	324	13	+	+	CCONJ
ejpam-2421	324	14	a(bℓ3	a(bℓ3	PROPN
ejpam-2421	324	15	−	−	NOUN
ejpam-2421	324	16	r	r	NOUN
ejpam-2421	324	17	−	−	NOUN
ejpam-2421	324	18	1	1	NUM
ejpam-2421	324	19	)	)	PUNCT
ejpam-2421	324	20	+	+	CCONJ
ejpam-2421	324	21	2	2	NUM
ejpam-2421	325	1	where	where	SCONJ
ejpam-2421	325	2	d	d	NOUN
ejpam-2421	325	3	=	=	PUNCT
ejpam-2421	325	4	bℓ3	bℓ3	PROPN
ejpam-2421	325	5	−	−	NOUN
ejpam-2421	325	6	r	r	NOUN
ejpam-2421	325	7	−	−	NOUN
ejpam-2421	325	8	1	1	NUM
ejpam-2421	325	9	,	,	PUNCT
ejpam-2421	325	10	a−	a−	PROPN
ejpam-2421	325	11	r4	r4	NOUN
ejpam-2421	325	12	=	=	PROPN
ejpam-2421	325	13	b	b	NOUN
ejpam-2421	325	14	−	−	PROPN
ejpam-2421	325	15	2e	2e	NOUN
ejpam-2421	325	16	+	+	CCONJ
ejpam-2421	325	17	abℓ3	abℓ3	NOUN
ejpam-2421	325	18	+	+	CCONJ
ejpam-2421	325	19	ad+	ad+	VERB
ejpam-2421	325	20	2=	2=	PROPN
ejpam-2421	325	21	b	b	NOUN
ejpam-2421	325	22	+	+	CCONJ
ejpam-2421	325	23	abℓ3	abℓ3	NOUN
ejpam-2421	325	24	+	+	CCONJ
ejpam-2421	325	25	ad+	ad+	PROPN
ejpam-2421	325	26	2−	2−	NUM
ejpam-2421	325	27	2ℓ3	2ℓ3	NUM
ejpam-2421	325	28	−	−	NOUN
ejpam-2421	325	29	2	2	NUM
ejpam-2421	325	30	=	=	SYM
ejpam-2421	325	31	b	b	NOUN
ejpam-2421	325	32	+	+	NUM
ejpam-2421	325	33	abℓ3	abℓ3	PROPN
ejpam-2421	325	34	+	+	CCONJ
ejpam-2421	325	35	ad−	ad−	PROPN
ejpam-2421	325	36	2ℓ3	2ℓ3	NUM
ejpam-2421	325	37	=	=	X
ejpam-2421	325	38	b(1	b(1	PROPN
ejpam-2421	325	39	+	+	SYM
ejpam-2421	325	40	aℓ3	aℓ3	NOUN
ejpam-2421	325	41	)	)	PUNCT
ejpam-2421	326	1	+	+	CCONJ
ejpam-2421	326	2	ad−	ad−	NOUN
ejpam-2421	326	3	2ℓ3	2ℓ3	NUM
ejpam-2421	326	4	=	=	SYM
ejpam-2421	326	5	bc	bc	PROPN
ejpam-2421	326	6	+	+	CCONJ
ejpam-2421	326	7	ad−	ad−	PROPN
ejpam-2421	326	8	2ℓ3	2ℓ3	NUM
ejpam-2421	326	9	⇒	⇒	NOUN
ejpam-2421	326	10	a−	a−	PROPN
ejpam-2421	326	11	r4	r4	NOUN
ejpam-2421	326	12	=	=	SYM
ejpam-2421	326	13	bc	bc	PROPN
ejpam-2421	326	14	+	+	CCONJ
ejpam-2421	326	15	ad−	ad−	PROPN
ejpam-2421	326	16	2ℓ3	2ℓ3	NUM
ejpam-2421	326	17	holds	hold	VERB
ejpam-2421	326	18	and	and	CCONJ
ejpam-2421	326	19	so	so	ADV
ejpam-2421	326	20	we	we	PRON
ejpam-2421	326	21	have	have	VERB
ejpam-2421	326	22	l4	l4	PROPN
ejpam-2421	326	23	as	as	ADP
ejpam-2421	326	24	ℓ4	ℓ4	PROPN
ejpam-2421	326	25	=	=	SYM
ejpam-2421	326	26	2(a−r4	2(a−r4	NUM
ejpam-2421	326	27	)	)	PUNCT
ejpam-2421	326	28	c4	c4	NOUN
ejpam-2421	326	29	=	=	SYM
ejpam-2421	326	30	2(bc+ad−2ℓ3	2(bc+ad−2ℓ3	PROPN
ejpam-2421	326	31	)	)	PUNCT
ejpam-2421	326	32	2(ℓ23−c	2(ℓ23−c	PROPN
ejpam-2421	326	33	d	d	NOUN
ejpam-2421	326	34	)	)	PUNCT
ejpam-2421	327	1	=	=	SYM
ejpam-2421	327	2	bc+ad−2ℓ3	bc+ad−2ℓ3	PROPN
ejpam-2421	327	3	ℓ23−c	ℓ23−c	PROPN
ejpam-2421	327	4	d	d	PROPN
ejpam-2421	327	5	⇒	⇒	NOUN
ejpam-2421	327	6	ℓ4	ℓ4	NOUN
ejpam-2421	327	7	=	=	SYM
ejpam-2421	327	8	bc+ad−2ℓ3	bc+ad−2ℓ3	PROPN
ejpam-2421	327	9	ℓ23−c	ℓ23−c	PROPN
ejpam-2421	327	10	d	d	NOUN
ejpam-2421	327	11	.	.	PUNCT
ejpam-2421	328	1	besides	besides	SCONJ
ejpam-2421	328	2	s	s	PROPN
ejpam-2421	328	3	and	and	CCONJ
ejpam-2421	328	4	r	r	NOUN
ejpam-2421	328	5	are	be	AUX
ejpam-2421	328	6	uniquely	uniquely	ADV
ejpam-2421	328	7	determined	determine	VERB
ejpam-2421	328	8	by	by	ADP
ejpam-2421	328	9	ℓ23ℓ4	ℓ23ℓ4	NOUN
ejpam-2421	328	10	+	+	CCONJ
ejpam-2421	328	11	2ℓ3	2ℓ3	NUM
ejpam-2421	328	12	=	=	SYM
ejpam-2421	328	13	bc	bc	PROPN
ejpam-2421	328	14	+	+	CCONJ
ejpam-2421	328	15	ad+	ad+	PROPN
ejpam-2421	328	16	2c	2c	NOUN
ejpam-2421	328	17	dℓ4	dℓ4	ADJ
ejpam-2421	328	18	and	and	CCONJ
ejpam-2421	328	19	(	(	PUNCT
ejpam-2421	328	20	9	9	NUM
ejpam-2421	328	21	)	)	PUNCT
ejpam-2421	328	22	.	.	PUNCT
ejpam-2421	329	1	now	now	ADV
ejpam-2421	329	2	,	,	PUNCT
ejpam-2421	329	3	let	let	VERB
ejpam-2421	329	4	’s	’s	PRON
ejpam-2421	329	5	determine	determine	VERB
ejpam-2421	329	6	the	the	DET
ejpam-2421	329	7	coefficients	coefficient	NOUN
ejpam-2421	329	8	td	td	NOUN
ejpam-2421	330	1	and	and	CCONJ
ejpam-2421	330	2	ud	ud	INTJ
ejpam-2421	330	3	of	of	ADP
ejpam-2421	330	4	the	the	DET
ejpam-2421	330	5	fundamental	fundamental	ADJ
ejpam-2421	330	6	unit	unit	NOUN
ejpam-2421	330	7	ǫd	ǫd	NOUN
ejpam-2421	330	8	.	.	PUNCT
ejpam-2421	331	1	since	since	SCONJ
ejpam-2421	331	2	d	d	PROPN
ejpam-2421	331	3	≡	≡	PROPN
ejpam-2421	331	4	1(mod4	1(mod4	NUM
ejpam-2421	331	5	)	)	PUNCT
ejpam-2421	331	6	then	then	ADV
ejpam-2421	331	7	we	we	PRON
ejpam-2421	331	8	know	know	VERB
ejpam-2421	331	9	that	that	SCONJ
ejpam-2421	331	10	wd	wd	PROPN
ejpam-2421	332	1	=	=	PUNCT
ejpam-2421	333	1	[	[	X
ejpam-2421	333	2	q0;q1	q0;q1	PROPN
ejpam-2421	333	3	,	,	PUNCT
ejpam-2421	333	4	.	.	PUNCT
ejpam-2421	333	5	.	.	PUNCT
ejpam-2421	334	1	.	.	PUNCT
ejpam-2421	335	1	,	,	PUNCT
ejpam-2421	335	2	qk−1	qk−1	PROPN
ejpam-2421	335	3	,	,	PUNCT
ejpam-2421	335	4	2q0	2q0	NUM
ejpam-2421	336	1	−	−	NOUN
ejpam-2421	336	2	1	1	NUM
ejpam-2421	336	3	]	]	PUNCT
ejpam-2421	336	4	and	and	CCONJ
ejpam-2421	336	5	ǫd	ǫd	NUM
ejpam-2421	336	6	=	=	SYM
ejpam-2421	336	7	(	(	PUNCT
ejpam-2421	336	8	td+ud	td+ud	NOUN
ejpam-2421	336	9	p	p	X
ejpam-2421	336	10	d	d	PROPN
ejpam-2421	336	11	2	2	NUM
ejpam-2421	336	12	)	)	PUNCT
ejpam-2421	336	13	>	>	X
ejpam-2421	337	1	1	1	X
ejpam-2421	337	2	.	.	PUNCT
ejpam-2421	338	1	furthermore	furthermore	ADV
ejpam-2421	338	2	q−1	q−1	PROPN
ejpam-2421	338	3	=	=	NOUN
ejpam-2421	338	4	0	0	NUM
ejpam-2421	338	5	q0	q0	ADJ
ejpam-2421	338	6	=	=	NOUN
ejpam-2421	338	7	1	1	NUM
ejpam-2421	338	8	q	q	NOUN
ejpam-2421	338	9	i+1	i+1	SYM
ejpam-2421	338	10	=	=	NOUN
ejpam-2421	338	11	qi+1q	qi+1q	NOUN
ejpam-2421	338	12	i	i	PRON
ejpam-2421	338	13	+	+	ADJ
ejpam-2421	338	14	q	q	PROPN
ejpam-2421	338	15	i−1	i−1	PROPN
ejpam-2421	338	16	(	(	PUNCT
ejpam-2421	338	17	i	i	PRON
ejpam-2421	338	18	≥	≥	NOUN
ejpam-2421	338	19	0	0	NUM
ejpam-2421	338	20	)	)	PUNCT
ejpam-2421	338	21	q1	q1	NOUN
ejpam-2421	338	22	=	=	SYM
ejpam-2421	338	23	q1q0	q1q0	PROPN
ejpam-2421	338	24	+	+	ADJ
ejpam-2421	338	25	q−1⇒q1	q−1⇒q1	ADJ
ejpam-2421	338	26	=	=	SYM
ejpam-2421	338	27	ℓ1	ℓ1	NOUN
ejpam-2421	338	28	,	,	PUNCT
ejpam-2421	338	29	ℓ1	ℓ1	NOUN
ejpam-2421	338	30	=	=	SYM
ejpam-2421	338	31	1⇒q1	1⇒q1	PROPN
ejpam-2421	338	32	=	=	SYM
ejpam-2421	338	33	1	1	NUM
ejpam-2421	338	34	q2	q2	NOUN
ejpam-2421	338	35	=	=	SYM
ejpam-2421	338	36	q2q1	q2q1	PROPN
ejpam-2421	338	37	+	+	PROPN
ejpam-2421	338	38	q0⇒q2	q0⇒q2	NOUN
ejpam-2421	338	39	=	=	SYM
ejpam-2421	338	40	ℓ2	ℓ2	NOUN
ejpam-2421	338	41	·	·	PUNCT
ejpam-2421	338	42	1	1	NUM
ejpam-2421	338	43	+	+	NUM
ejpam-2421	338	44	1	1	NUM
ejpam-2421	338	45	,	,	PUNCT
ejpam-2421	338	46	(	(	PUNCT
ejpam-2421	338	47	a=	a=	ADV
ejpam-2421	338	48	ℓ2	ℓ2	NOUN
ejpam-2421	338	49	+	+	CCONJ
ejpam-2421	338	50	1)⇒q2	1)⇒q2	NUM
ejpam-2421	338	51	=	=	SYM
ejpam-2421	338	52	a	a	DET
ejpam-2421	338	53	q3	q3	NOUN
ejpam-2421	338	54	=	=	NOUN
ejpam-2421	338	55	q3q2	q3q2	X
ejpam-2421	338	56	+	+	NOUN
ejpam-2421	338	57	q1⇒q3	q1⇒q3	ADJ
ejpam-2421	338	58	=	=	SYM
ejpam-2421	338	59	ℓ3a+	ℓ3a+	NOUN
ejpam-2421	338	60	1	1	NUM
ejpam-2421	338	61	,	,	PUNCT
ejpam-2421	338	62	(	(	PUNCT
ejpam-2421	338	63	c	c	X
ejpam-2421	338	64	=	=	SYM
ejpam-2421	338	65	ℓ3a+	ℓ3a+	NOUN
ejpam-2421	338	66	1)⇒q3	1)⇒q3	NUM
ejpam-2421	338	67	=	=	SYM
ejpam-2421	338	68	c	c	X
ejpam-2421	338	69	q4	q4	PROPN
ejpam-2421	338	70	=	=	PROPN
ejpam-2421	338	71	q4q3	q4q3	X
ejpam-2421	338	72	+	+	VERB
ejpam-2421	338	73	q2⇒q4	q2⇒q4	NOUN
ejpam-2421	338	74	=	=	SYM
ejpam-2421	338	75	ℓ4c	ℓ4c	NOUN
ejpam-2421	338	76	+	+	CCONJ
ejpam-2421	338	77	a	a	DET
ejpam-2421	338	78	q5	q5	PROPN
ejpam-2421	338	79	=	=	SYM
ejpam-2421	338	80	q5q4	q5q4	PROPN
ejpam-2421	338	81	+	+	NOUN
ejpam-2421	338	82	q3⇒q5	q3⇒q5	NOUN
ejpam-2421	338	83	=	=	PUNCT
ejpam-2421	338	84	ℓ3(ℓ4c	ℓ3(ℓ4c	PROPN
ejpam-2421	338	85	+	+	CCONJ
ejpam-2421	338	86	a	a	X
ejpam-2421	338	87	)	)	PUNCT
ejpam-2421	339	1	+	+	PUNCT
ejpam-2421	339	2	c	c	VERB
ejpam-2421	339	3	⇒q5	⇒q5	NOUN
ejpam-2421	339	4	=	=	PUNCT
ejpam-2421	339	5	c(ℓ3ℓ4	c(ℓ3ℓ4	VERB
ejpam-2421	339	6	+	+	CCONJ
ejpam-2421	339	7	1	1	NUM
ejpam-2421	339	8	)	)	PUNCT
ejpam-2421	339	9	+	+	CCONJ
ejpam-2421	339	10	ℓ3a	ℓ3a	NUM
ejpam-2421	339	11	q6	q6	NOUN
ejpam-2421	339	12	=	=	NOUN
ejpam-2421	339	13	q6q5	q6q5	X
ejpam-2421	339	14	+	+	NOUN
ejpam-2421	339	15	q4	q4	NOUN
ejpam-2421	339	16	=	=	PUNCT
ejpam-2421	339	17	ℓ2[c(ℓ3ℓ4	ℓ2[c(ℓ3ℓ4	X
ejpam-2421	339	18	+	+	NOUN
ejpam-2421	339	19	1	1	NUM
ejpam-2421	339	20	)	)	PUNCT
ejpam-2421	339	21	+	+	CCONJ
ejpam-2421	339	22	ℓ3a	ℓ3a	ADV
ejpam-2421	339	23	]	]	PUNCT
ejpam-2421	340	1	+	+	CCONJ
ejpam-2421	340	2	ℓ4c	ℓ4c	NOUN
ejpam-2421	340	3	+	+	CCONJ
ejpam-2421	340	4	a=	a=	ADJ
ejpam-2421	340	5	c[ℓ4(ℓ2ℓ3	c[ℓ4(ℓ2ℓ3	PROPN
ejpam-2421	340	6	+	+	CCONJ
ejpam-2421	340	7	1	1	X
ejpam-2421	340	8	)	)	PUNCT
ejpam-2421	340	9	+	+	NUM
ejpam-2421	340	10	ℓ2	ℓ2	NOUN
ejpam-2421	340	11	]	]	PUNCT
ejpam-2421	340	12	+	+	CCONJ
ejpam-2421	340	13	a(1	a(1	ADJ
ejpam-2421	340	14	+	+	CCONJ
ejpam-2421	340	15	ℓ2ℓ3	ℓ2ℓ3	NOUN
ejpam-2421	340	16	)	)	PUNCT
ejpam-2421	340	17	=	=	NOUN
ejpam-2421	340	18	c[((a−	c[((a−	PROPN
ejpam-2421	340	19	1)(e	1)(e	NUM
ejpam-2421	340	20	−	−	NOUN
ejpam-2421	340	21	1	1	NUM
ejpam-2421	340	22	)	)	PUNCT
ejpam-2421	340	23	+	+	CCONJ
ejpam-2421	340	24	1)ℓ4	1)ℓ4	NUM
ejpam-2421	340	25	+	+	CCONJ
ejpam-2421	340	26	ℓ2	ℓ2	NOUN
ejpam-2421	340	27	]	]	PUNCT
ejpam-2421	340	28	+	+	CCONJ
ejpam-2421	340	29	a[(a−	a[(a−	PROPN
ejpam-2421	340	30	1)(e	1)(e	NUM
ejpam-2421	340	31	−	−	NOUN
ejpam-2421	340	32	1	1	NUM
ejpam-2421	340	33	)	)	PUNCT
ejpam-2421	340	34	+	+	CCONJ
ejpam-2421	340	35	1	1	X
ejpam-2421	340	36	]	]	PUNCT
ejpam-2421	340	37	for	for	ADP
ejpam-2421	340	38	(	(	PUNCT
ejpam-2421	340	39	(	(	PUNCT
ejpam-2421	340	40	1	1	NUM
ejpam-2421	340	41	+	+	NUM
ejpam-2421	340	42	ℓ2ℓ3	ℓ2ℓ3	NOUN
ejpam-2421	340	43	)	)	PUNCT
ejpam-2421	340	44	=	=	SYM
ejpam-2421	340	45	(	(	PUNCT
ejpam-2421	340	46	a−	a−	PROPN
ejpam-2421	340	47	1)(e	1)(e	NUM
ejpam-2421	340	48	−	−	NOUN
ejpam-2421	340	49	1	1	NUM
ejpam-2421	340	50	)	)	PUNCT
ejpam-2421	340	51	+	+	CCONJ
ejpam-2421	340	52	1	1	NUM
ejpam-2421	340	53	or	or	CCONJ
ejpam-2421	340	54	q6	q6	PROPN
ejpam-2421	340	55	=(	=(	PROPN
ejpam-2421	340	56	c	c	PROPN
ejpam-2421	340	57	−	−	PROPN
ejpam-2421	340	58	ℓ3)(cℓ4	ℓ3)(cℓ4	PROPN
ejpam-2421	340	59	+	+	CCONJ
ejpam-2421	340	60	a	a	X
ejpam-2421	340	61	)	)	PUNCT
ejpam-2421	340	62	+	+	CCONJ
ejpam-2421	340	63	cℓ2	cℓ2	PROPN
ejpam-2421	340	64	q7	q7	PROPN
ejpam-2421	340	65	=	=	NOUN
ejpam-2421	340	66	ℓ1q6	ℓ1q6	X
ejpam-2421	340	67	+	+	ADJ
ejpam-2421	340	68	q5	q5	X
ejpam-2421	340	69	=	=	SYM
ejpam-2421	340	70	1q6	1q6	NUM
ejpam-2421	340	71	+	+	PROPN
ejpam-2421	340	72	q5	q5	PROPN
ejpam-2421	340	73	=	=	SYM
ejpam-2421	340	74	(	(	PUNCT
ejpam-2421	340	75	c	c	X
ejpam-2421	340	76	−	−	PROPN
ejpam-2421	340	77	ℓ3)(cℓ4	ℓ3)(cℓ4	PROPN
ejpam-2421	340	78	+	+	CCONJ
ejpam-2421	340	79	a	a	X
ejpam-2421	340	80	)	)	PUNCT
ejpam-2421	340	81	+	+	CCONJ
ejpam-2421	340	82	cℓ2	cℓ2	PROPN
ejpam-2421	340	83	+	+	CCONJ
ejpam-2421	340	84	(	(	PUNCT
ejpam-2421	340	85	cℓ4	cℓ4	PROPN
ejpam-2421	340	86	+	+	X
ejpam-2421	340	87	a)ℓ3	a)ℓ3	PROPN
ejpam-2421	340	88	+	+	NUM
ejpam-2421	340	89	c	c	NOUN
ejpam-2421	340	90	=	=	PUNCT
ejpam-2421	340	91	c[cℓ4	c[cℓ4	PROPN
ejpam-2421	340	92	+	+	NUM
ejpam-2421	340	93	2a	2a	NUM
ejpam-2421	340	94	]	]	PUNCT
ejpam-2421	340	95	ö.	ö.	NOUN
ejpam-2421	340	96	özer	özer	NOUN
ejpam-2421	340	97	,	,	PUNCT
ejpam-2421	340	98	a.	a.	NOUN
ejpam-2421	340	99	pekin	pekin	PROPN
ejpam-2421	340	100	/	/	SYM
ejpam-2421	340	101	eur	eur	PROPN
ejpam-2421	340	102	.	.	PUNCT
ejpam-2421	341	1	j.	j.	PROPN
ejpam-2421	341	2	pure	pure	PROPN
ejpam-2421	341	3	appl	appl	PROPN
ejpam-2421	341	4	.	.	PROPN
ejpam-2421	341	5	math	math	PROPN
ejpam-2421	341	6	,	,	PUNCT
ejpam-2421	341	7	8	8	NUM
ejpam-2421	341	8	(	(	PUNCT
ejpam-2421	341	9	2015	2015	NUM
ejpam-2421	341	10	)	)	PUNCT
ejpam-2421	341	11	,	,	PUNCT
ejpam-2421	341	12	343	343	NUM
ejpam-2421	341	13	-	-	SYM
ejpam-2421	341	14	356	356	NUM
ejpam-2421	341	15	354	354	NUM
ejpam-2421	342	1	and	and	CCONJ
ejpam-2421	342	2	so	so	ADV
ejpam-2421	342	3	we	we	PRON
ejpam-2421	342	4	obtain	obtain	VERB
ejpam-2421	342	5	that	that	DET
ejpam-2421	342	6	td	td	NOUN
ejpam-2421	342	7	=(	=(	NOUN
ejpam-2421	342	8	a(r	a(r	PROPN
ejpam-2421	342	9	+	+	NOUN
ejpam-2421	342	10	1	1	NUM
ejpam-2421	342	11	)	)	PUNCT
ejpam-2421	343	1	+	+	NOUN
ejpam-2421	343	2	b	b	X
ejpam-2421	343	3	−	−	PROPN
ejpam-2421	343	4	2)c(cℓ4	2)c(cℓ4	NUM
ejpam-2421	343	5	+	+	NUM
ejpam-2421	343	6	2a	2a	NUM
ejpam-2421	343	7	)	)	PUNCT
ejpam-2421	344	1	+	+	CCONJ
ejpam-2421	344	2	2(c	2(c	NUM
ejpam-2421	344	3	−	−	NOUN
ejpam-2421	344	4	ℓ3)(cℓ4	ℓ3)(cℓ4	PROPN
ejpam-2421	344	5	+	+	CCONJ
ejpam-2421	344	6	a	a	X
ejpam-2421	344	7	)	)	PUNCT
ejpam-2421	344	8	+	+	NOUN
ejpam-2421	344	9	2cℓ2	2cℓ2	NUM
ejpam-2421	344	10	,	,	PUNCT
ejpam-2421	344	11	ud	ud	ADP
ejpam-2421	344	12	=	=	NUM
ejpam-2421	344	13	c(cℓ4	c(cℓ4	NOUN
ejpam-2421	344	14	+	+	NOUN
ejpam-2421	344	15	2a	2a	NUM
ejpam-2421	344	16	)	)	PUNCT
ejpam-2421	344	17	and	and	CCONJ
ejpam-2421	344	18	d	d	X
ejpam-2421	344	19	=	=	PROPN
ejpam-2421	344	20	a2	a2	PROPN
ejpam-2421	344	21	+	+	CCONJ
ejpam-2421	344	22	b	b	NOUN
ejpam-2421	344	23	=	=	PUNCT
ejpam-2421	345	1	[	[	X
ejpam-2421	345	2	a(r	a(r	X
ejpam-2421	345	3	+	+	NOUN
ejpam-2421	345	4	1	1	NUM
ejpam-2421	345	5	)	)	PUNCT
ejpam-2421	345	6	+	+	NOUN
ejpam-2421	345	7	b	b	X
ejpam-2421	345	8	−	−	NOUN
ejpam-2421	345	9	1]2	1]2	NUM
ejpam-2421	346	1	+	+	CCONJ
ejpam-2421	346	2	2a(r	2a(r	NUM
ejpam-2421	347	1	+	+	CCONJ
ejpam-2421	347	2	1	1	X
ejpam-2421	347	3	)	)	PUNCT
ejpam-2421	348	1	+	+	NOUN
ejpam-2421	348	2	2b	2b	NUM
ejpam-2421	348	3	−	−	PART
ejpam-2421	348	4	4s−	4s−	NOUN
ejpam-2421	348	5	5	5	NUM
ejpam-2421	348	6	=[	=[	NOUN
ejpam-2421	348	7	a(r	a(r	NOUN
ejpam-2421	348	8	+	+	NOUN
ejpam-2421	348	9	1	1	NUM
ejpam-2421	348	10	)	)	PUNCT
ejpam-2421	348	11	+	+	NOUN
ejpam-2421	349	1	b	b	X
ejpam-2421	349	2	−	−	NOUN
ejpam-2421	350	1	1]2	1]2	NUM
ejpam-2421	351	1	+	+	CCONJ
ejpam-2421	351	2	2[a(r	2[a(r	NUM
ejpam-2421	351	3	+	+	CCONJ
ejpam-2421	351	4	1	1	NUM
ejpam-2421	351	5	)	)	PUNCT
ejpam-2421	351	6	+	+	NOUN
ejpam-2421	352	1	b	b	X
ejpam-2421	352	2	−	−	PROPN
ejpam-2421	352	3	2s−	2s−	NUM
ejpam-2421	352	4	2]−	2]−	NUM
ejpam-2421	352	5	1	1	NUM
ejpam-2421	352	6	.	.	PUNCT
ejpam-2421	352	7	now	now	ADV
ejpam-2421	352	8	let	let	VERB
ejpam-2421	352	9	d	d	X
ejpam-2421	352	10	∈	∈	PROPN
ejpam-2421	352	11	d1	d1	PROPN
ejpam-2421	352	12	5	5	NUM
ejpam-2421	352	13	∪	∪	NOUN
ejpam-2421	352	14	d5	d5	NOUN
ejpam-2421	352	15	5	5	NUM
ejpam-2421	352	16	then	then	ADV
ejpam-2421	352	17	b	b	PROPN
ejpam-2421	352	18	≡	≡	PROPN
ejpam-2421	352	19	5(mod8	5(mod8	NUM
ejpam-2421	352	20	)	)	PUNCT
ejpam-2421	352	21	and	and	CCONJ
ejpam-2421	352	22	∃m	∃m	PROPN
ejpam-2421	352	23	∈	∈	PROPN
ejpam-2421	352	24	z+	z+	NUM
ejpam-2421	352	25	∋	∋	NOUN
ejpam-2421	352	26	b	b	X
ejpam-2421	352	27	=	=	PROPN
ejpam-2421	352	28	8m+	8m+	NUM
ejpam-2421	352	29	5	5	NUM
ejpam-2421	352	30	.	.	PUNCT
ejpam-2421	352	31	from	from	ADP
ejpam-2421	352	32	lemma	lemma	PROPN
ejpam-2421	352	33	2	2	NUM
ejpam-2421	352	34	we	we	PRON
ejpam-2421	352	35	can	can	AUX
ejpam-2421	352	36	obtain	obtain	VERB
ejpam-2421	352	37	the	the	DET
ejpam-2421	352	38	following	follow	VERB
ejpam-2421	352	39	equalities	equality	NOUN
ejpam-2421	352	40	:	:	PUNCT
ejpam-2421	352	41	c−1	c−1	PROPN
ejpam-2421	352	42	=	=	SYM
ejpam-2421	352	43	(	(	PUNCT
ejpam-2421	352	44	8m+	8m+	NUM
ejpam-2421	352	45	5	5	NUM
ejpam-2421	352	46	+	+	NUM
ejpam-2421	352	47	2a−	2a−	NUM
ejpam-2421	352	48	1	1	NUM
ejpam-2421	352	49	)	)	SYM
ejpam-2421	352	50	2	2	NUM
ejpam-2421	352	51	⇒	⇒	NOUN
ejpam-2421	352	52	c−1	c−1	PROPN
ejpam-2421	352	53	=	=	PUNCT
ejpam-2421	352	54	4m+	4m+	NUM
ejpam-2421	352	55	4	4	NUM
ejpam-2421	352	56	+	+	NUM
ejpam-2421	352	57	a	a	DET
ejpam-2421	352	58	c1	c1	NOUN
ejpam-2421	352	59	=	=	PROPN
ejpam-2421	352	60	c−1	c−1	PROPN
ejpam-2421	352	61	+	+	CCONJ
ejpam-2421	352	62	(	(	PUNCT
ejpam-2421	352	63	r1	r1	PROPN
ejpam-2421	352	64	−	−	PROPN
ejpam-2421	352	65	r0)ℓ0	r0)ℓ0	NOUN
ejpam-2421	352	66	(	(	PUNCT
ejpam-2421	352	67	r1	r1	NOUN
ejpam-2421	352	68	−	−	PROPN
ejpam-2421	352	69	r0	r0	NOUN
ejpam-2421	352	70	=	=	SYM
ejpam-2421	352	71	0)⇒	0)⇒	PROPN
ejpam-2421	352	72	c1	c1	NOUN
ejpam-2421	352	73	=	=	NOUN
ejpam-2421	352	74	4m+	4m+	NUM
ejpam-2421	352	75	4	4	NUM
ejpam-2421	352	76	+	+	NUM
ejpam-2421	352	77	a	a	DET
ejpam-2421	352	78	2a−	2a−	PROPN
ejpam-2421	352	79	r1	r1	NOUN
ejpam-2421	352	80	=	=	SYM
ejpam-2421	352	81	c1ℓ1	c1ℓ1	NOUN
ejpam-2421	352	82	+	+	X
ejpam-2421	352	83	r2⇒	r2⇒	ADJ
ejpam-2421	352	84	(	(	PUNCT
ejpam-2421	352	85	r1	r1	NOUN
ejpam-2421	352	86	=	=	SYM
ejpam-2421	352	87	1	1	NUM
ejpam-2421	352	88	,	,	PUNCT
ejpam-2421	352	89	c1	c1	NOUN
ejpam-2421	352	90	=	=	NOUN
ejpam-2421	353	1	4m+	4m+	NUM
ejpam-2421	353	2	4	4	NUM
ejpam-2421	353	3	+	+	NUM
ejpam-2421	353	4	a	a	X
ejpam-2421	353	5	)	)	PUNCT
ejpam-2421	353	6	⇒	⇒	NOUN
ejpam-2421	353	7	2a−	2a−	NUM
ejpam-2421	353	8	1=	1=	X
ejpam-2421	353	9	(	(	PUNCT
ejpam-2421	353	10	4m+	4m+	NUM
ejpam-2421	353	11	4	4	NUM
ejpam-2421	353	12	+	+	NOUN
ejpam-2421	353	13	a	a	X
ejpam-2421	353	14	)	)	PUNCT
ejpam-2421	354	1	·	·	PUNCT
ejpam-2421	354	2	ℓ1	ℓ1	NOUN
ejpam-2421	354	3	+	+	CCONJ
ejpam-2421	354	4	r2	r2	PROPN
ejpam-2421	354	5	⇒	⇒	NOUN
ejpam-2421	354	6	(	(	PUNCT
ejpam-2421	354	7	2−	2−	NUM
ejpam-2421	354	8	ℓ1)a	ℓ1)a	NOUN
ejpam-2421	354	9	=	=	SYM
ejpam-2421	354	10	4mℓ1	4mℓ1	NUM
ejpam-2421	355	1	+	+	NUM
ejpam-2421	355	2	4ℓ1	4ℓ1	NUM
ejpam-2421	355	3	+	+	CCONJ
ejpam-2421	355	4	r2	r2	PROPN
ejpam-2421	355	5	+	+	CCONJ
ejpam-2421	355	6	1	1	NUM
ejpam-2421	355	7	>	>	SYM
ejpam-2421	355	8	0	0	NUM
ejpam-2421	356	1	⇒	⇒	NOUN
ejpam-2421	356	2	2−	2−	NUM
ejpam-2421	356	3	ℓ1	ℓ1	NOUN
ejpam-2421	356	4	>	>	X
ejpam-2421	356	5	0	0	NUM
ejpam-2421	356	6	,	,	PUNCT
ejpam-2421	356	7	ℓ1	ℓ1	VERB
ejpam-2421	356	8	≥	≥	NOUN
ejpam-2421	356	9	1	1	NUM
ejpam-2421	356	10	⇒	⇒	NOUN
ejpam-2421	356	11	ℓ1	ℓ1	NOUN
ejpam-2421	356	12	=	=	SYM
ejpam-2421	356	13	1	1	NUM
ejpam-2421	357	1	and	and	CCONJ
ejpam-2421	357	2	then	then	ADV
ejpam-2421	357	3	we	we	PRON
ejpam-2421	357	4	get	get	VERB
ejpam-2421	357	5	a	a	PRON
ejpam-2421	357	6	=	=	SYM
ejpam-2421	357	7	4(m+	4(m+	NUM
ejpam-2421	357	8	1	1	NUM
ejpam-2421	357	9	)	)	PUNCT
ejpam-2421	358	1	+	+	CCONJ
ejpam-2421	358	2	r2	r2	NOUN
ejpam-2421	358	3	+	+	CCONJ
ejpam-2421	358	4	1	1	NUM
ejpam-2421	358	5	r2	r2	NOUN
ejpam-2421	358	6	=	=	SYM
ejpam-2421	358	7	a−	a−	PROPN
ejpam-2421	358	8	4(m+	4(m+	NOUN
ejpam-2421	359	1	1)−	1)−	NUM
ejpam-2421	359	2	1⇒	1⇒	PROPN
ejpam-2421	359	3	r2	r2	PROPN
ejpam-2421	359	4	is	be	AUX
ejpam-2421	359	5	an	an	DET
ejpam-2421	359	6	odd	odd	ADJ
ejpam-2421	359	7	integer	integer	NOUN
ejpam-2421	359	8	so	so	SCONJ
ejpam-2421	359	9	r2	r2	PROPN
ejpam-2421	359	10	<	<	X
ejpam-2421	359	11	a	a	DET
ejpam-2421	359	12	holds	hold	NOUN
ejpam-2421	359	13	and	and	CCONJ
ejpam-2421	359	14	∃r	∃r	PROPN
ejpam-2421	359	15	≥	≥	NUM
ejpam-2421	359	16	0	0	NUM
ejpam-2421	359	17	,	,	PUNCT
ejpam-2421	359	18	r	r	NOUN
ejpam-2421	359	19	∈	∈	PROPN
ejpam-2421	359	20	z	z	NOUN
ejpam-2421	359	21	∋	∋	NOUN
ejpam-2421	359	22	r2	r2	NOUN
ejpam-2421	359	23	=	=	PUNCT
ejpam-2421	360	1	2r	2r	NUM
ejpam-2421	361	1	+	+	CCONJ
ejpam-2421	361	2	1	1	X
ejpam-2421	361	3	.	.	X
ejpam-2421	362	1	for	for	ADP
ejpam-2421	362	2	i	i	PRON
ejpam-2421	362	3	≥	≥	VERB
ejpam-2421	362	4	0	0	NUM
ejpam-2421	363	1	we	we	PRON
ejpam-2421	363	2	have	have	VERB
ejpam-2421	363	3	c2	c2	PROPN
ejpam-2421	363	4	=	=	SYM
ejpam-2421	363	5	c0	c0	PROPN
ejpam-2421	363	6	+	+	CCONJ
ejpam-2421	363	7	(	(	PUNCT
ejpam-2421	363	8	r2	r2	PROPN
ejpam-2421	363	9	−	−	PROPN
ejpam-2421	363	10	r1)ℓ1	r1)ℓ1	NOUN
ejpam-2421	363	11	=	=	PUNCT
ejpam-2421	364	1	2	2	NUM
ejpam-2421	364	2	+	+	CCONJ
ejpam-2421	364	3	(	(	PUNCT
ejpam-2421	364	4	r2	r2	PROPN
ejpam-2421	364	5	−	−	PROPN
ejpam-2421	364	6	1)1=	1)1=	NUM
ejpam-2421	364	7	2r	2r	NUM
ejpam-2421	364	8	+	+	CCONJ
ejpam-2421	364	9	2	2	NUM
ejpam-2421	364	10	from	from	ADP
ejpam-2421	364	11	relation	relation	NOUN
ejpam-2421	364	12	ci+1	ci+1	PROPN
ejpam-2421	365	1	=	=	SYM
ejpam-2421	365	2	ci−1	ci−1	PROPN
ejpam-2421	365	3	+	+	CCONJ
ejpam-2421	365	4	(	(	PUNCT
ejpam-2421	365	5	ri+1	ri+1	PROPN
ejpam-2421	365	6	−	−	PROPN
ejpam-2421	365	7	ri)ℓi	ri)ℓi	PROPN
ejpam-2421	365	8	and	and	CCONJ
ejpam-2421	365	9	2a	2a	NUM
ejpam-2421	365	10	=	=	SYM
ejpam-2421	365	11	c2ℓ2	c2ℓ2	PROPN
ejpam-2421	366	1	+	+	NUM
ejpam-2421	366	2	r2	r2	PROPN
ejpam-2421	366	3	+	+	X
ejpam-2421	366	4	r3	r3	PROPN
ejpam-2421	366	5	.	.	PUNCT
ejpam-2421	366	6	2a	2a	NUM
ejpam-2421	366	7	=	=	SYM
ejpam-2421	366	8	(	(	PUNCT
ejpam-2421	366	9	2r	2r	NUM
ejpam-2421	366	10	+	+	CCONJ
ejpam-2421	366	11	2)ℓ2	2)ℓ2	NUM
ejpam-2421	366	12	+	+	SYM
ejpam-2421	366	13	2r	2r	NUM
ejpam-2421	367	1	+	+	CCONJ
ejpam-2421	367	2	1	1	NUM
ejpam-2421	367	3	+	+	NUM
ejpam-2421	367	4	r3	r3	PROPN
ejpam-2421	367	5	and	and	CCONJ
ejpam-2421	367	6	a	a	DET
ejpam-2421	367	7	=	=	NOUN
ejpam-2421	367	8	4(m+	4(m+	NUM
ejpam-2421	367	9	1	1	NUM
ejpam-2421	367	10	)	)	PUNCT
ejpam-2421	367	11	+	+	CCONJ
ejpam-2421	368	1	1	1	NUM
ejpam-2421	368	2	+	+	NUM
ejpam-2421	368	3	r2⇒	r2⇒	ADJ
ejpam-2421	368	4	a	a	DET
ejpam-2421	368	5	=	=	SYM
ejpam-2421	368	6	4m+	4m+	NUM
ejpam-2421	368	7	2r	2r	NUM
ejpam-2421	369	1	+	+	CCONJ
ejpam-2421	369	2	6	6	NUM
ejpam-2421	369	3	⇒	⇒	NOUN
ejpam-2421	369	4	2(4m+	2(4m+	NUM
ejpam-2421	369	5	2r	2r	NUM
ejpam-2421	369	6	+	+	CCONJ
ejpam-2421	369	7	6	6	NUM
ejpam-2421	369	8	)	)	PUNCT
ejpam-2421	369	9	=	=	SYM
ejpam-2421	369	10	(	(	PUNCT
ejpam-2421	369	11	2r	2r	NUM
ejpam-2421	370	1	+	+	CCONJ
ejpam-2421	370	2	2)ℓ2	2)ℓ2	NUM
ejpam-2421	370	3	+	+	SYM
ejpam-2421	370	4	2r	2r	NUM
ejpam-2421	371	1	+	+	CCONJ
ejpam-2421	371	2	1	1	NUM
ejpam-2421	371	3	+	+	NUM
ejpam-2421	371	4	r3	r3	PROPN
ejpam-2421	371	5	⇒	⇒	NOUN
ejpam-2421	371	6	2a	2a	NUM
ejpam-2421	371	7	=	=	SYM
ejpam-2421	371	8	(	(	PUNCT
ejpam-2421	371	9	2r	2r	NUM
ejpam-2421	372	1	+	+	CCONJ
ejpam-2421	372	2	2)ℓ2	2)ℓ2	NUM
ejpam-2421	372	3	+	+	CCONJ
ejpam-2421	372	4	r3	r3	PROPN
ejpam-2421	372	5	+	+	CCONJ
ejpam-2421	372	6	2r	2r	NUM
ejpam-2421	372	7	+	+	CCONJ
ejpam-2421	372	8	1≡	1≡	NUM
ejpam-2421	372	9	0(mod4	0(mod4	NUM
ejpam-2421	372	10	)	)	PUNCT
ejpam-2421	372	11	⇒	⇒	PROPN
ejpam-2421	372	12	r3	r3	PROPN
ejpam-2421	372	13	+	+	CCONJ
ejpam-2421	372	14	2r	2r	NUM
ejpam-2421	372	15	+	+	CCONJ
ejpam-2421	372	16	1≡	1≡	NUM
ejpam-2421	372	17	0(mod4	0(mod4	NUM
ejpam-2421	372	18	)	)	PUNCT
ejpam-2421	372	19	and	and	CCONJ
ejpam-2421	372	20	ℓ2	ℓ2	PROPN
ejpam-2421	372	21	≡	≡	PROPN
ejpam-2421	372	22	0(mod2	0(mod2	PROPN
ejpam-2421	372	23	)	)	PUNCT
ejpam-2421	372	24	⇒	⇒	NOUN
ejpam-2421	372	25	∃s	∃s	PROPN
ejpam-2421	372	26	∈	∈	PROPN
ejpam-2421	372	27	z+	z+	NUM
ejpam-2421	372	28	∋	∋	NOUN
ejpam-2421	372	29	r3	r3	PROPN
ejpam-2421	372	30	+	+	CCONJ
ejpam-2421	372	31	2r	2r	NUM
ejpam-2421	373	1	+	+	CCONJ
ejpam-2421	373	2	1=	1=	NUM
ejpam-2421	373	3	4s	4s	NUM
ejpam-2421	373	4	,	,	PUNCT
ejpam-2421	373	5	r3	r3	PROPN
ejpam-2421	373	6	≥	≥	NOUN
ejpam-2421	373	7	0	0	NUM
ejpam-2421	373	8	⇒	⇒	PROPN
ejpam-2421	373	9	4s−	4s−	PROPN
ejpam-2421	373	10	2r	2r	NUM
ejpam-2421	373	11	−	−	ADP
ejpam-2421	373	12	1≥	1≥	NUM
ejpam-2421	373	13	0	0	NUM
ejpam-2421	373	14	,	,	PUNCT
ejpam-2421	373	15	therefore	therefore	ADV
ejpam-2421	373	16	r3	r3	X
ejpam-2421	373	17	=	=	SYM
ejpam-2421	373	18	4s−	4s−	NUM
ejpam-2421	373	19	2r	2r	NUM
ejpam-2421	374	1	−	−	NOUN
ejpam-2421	374	2	1	1	NUM
ejpam-2421	374	3	is	be	AUX
ejpam-2421	374	4	odd	odd	ADJ
ejpam-2421	374	5	.	.	PUNCT
ejpam-2421	375	1	(	(	PUNCT
ejpam-2421	375	2	13	13	NUM
ejpam-2421	375	3	)	)	PUNCT
ejpam-2421	375	4	ö.	ö.	NOUN
ejpam-2421	375	5	özer	özer	NOUN
ejpam-2421	375	6	,	,	PUNCT
ejpam-2421	375	7	a.	a.	NOUN
ejpam-2421	375	8	pekin	pekin	PROPN
ejpam-2421	375	9	/	/	SYM
ejpam-2421	375	10	eur	eur	PROPN
ejpam-2421	375	11	.	.	PUNCT
ejpam-2421	376	1	j.	j.	PROPN
ejpam-2421	376	2	pure	pure	PROPN
ejpam-2421	376	3	appl	appl	PROPN
ejpam-2421	376	4	.	.	PROPN
ejpam-2421	376	5	math	math	PROPN
ejpam-2421	376	6	,	,	PUNCT
ejpam-2421	376	7	8	8	NUM
ejpam-2421	376	8	(	(	PUNCT
ejpam-2421	376	9	2015	2015	NUM
ejpam-2421	376	10	)	)	PUNCT
ejpam-2421	376	11	,	,	PUNCT
ejpam-2421	376	12	343	343	NUM
ejpam-2421	376	13	-	-	SYM
ejpam-2421	376	14	356	356	NUM
ejpam-2421	376	15	355	355	NUM
ejpam-2421	376	16	from	from	ADP
ejpam-2421	376	17	lemma	lemma	PROPN
ejpam-2421	376	18	2	2	NUM
ejpam-2421	376	19	we	we	PRON
ejpam-2421	376	20	know	know	VERB
ejpam-2421	376	21	that	that	SCONJ
ejpam-2421	376	22	c3	c3	PROPN
ejpam-2421	376	23	=	=	PUNCT
ejpam-2421	376	24	c1+(r3−	c1+(r3−	PROPN
ejpam-2421	376	25	r2)ℓ2	r2)ℓ2	NOUN
ejpam-2421	376	26	=	=	SYM
ejpam-2421	376	27	4m+4	4m+4	PROPN
ejpam-2421	376	28	+	+	CCONJ
ejpam-2421	376	29	a+(4s−2r	a+(4s−2r	NOUN
ejpam-2421	376	30	−1−2r	−1−2r	NOUN
ejpam-2421	376	31	−1)ℓ2	−1)ℓ2	ADV
ejpam-2421	376	32	then	then	ADV
ejpam-2421	376	33	we	we	PRON
ejpam-2421	376	34	obtain	obtain	VERB
ejpam-2421	376	35	c3	c3	NOUN
ejpam-2421	376	36	=	=	SYM
ejpam-2421	376	37	a−	a−	PROPN
ejpam-2421	376	38	2r	2r	NUM
ejpam-2421	376	39	−	−	ADP
ejpam-2421	377	1	2	2	NUM
ejpam-2421	377	2	+	+	NUM
ejpam-2421	377	3	a+	a+	PUNCT
ejpam-2421	377	4	(	(	PUNCT
ejpam-2421	377	5	4s−	4s−	NOUN
ejpam-2421	377	6	4r	4r	NOUN
ejpam-2421	377	7	−	−	PROPN
ejpam-2421	377	8	2)ℓ2⇒	2)ℓ2⇒	NUM
ejpam-2421	377	9	c3	c3	X
ejpam-2421	377	10	=	=	PUNCT
ejpam-2421	378	1	2a−	2a−	NUM
ejpam-2421	378	2	2r	2r	NUM
ejpam-2421	378	3	−	−	NOUN
ejpam-2421	379	1	2	2	NUM
ejpam-2421	379	2	+	+	CCONJ
ejpam-2421	379	3	(	(	PUNCT
ejpam-2421	379	4	4s−	4s−	NOUN
ejpam-2421	379	5	4r	4r	NOUN
ejpam-2421	379	6	−	−	NUM
ejpam-2421	379	7	2)ℓ2	2)ℓ2	NUM
ejpam-2421	379	8	=(	=(	NOUN
ejpam-2421	379	9	2r	2r	NUM
ejpam-2421	380	1	+	+	CCONJ
ejpam-2421	380	2	2)ℓ2	2)ℓ2	NUM
ejpam-2421	380	3	+	+	PUNCT
ejpam-2421	380	4	4s−	4s−	NUM
ejpam-2421	380	5	2r	2r	NUM
ejpam-2421	380	6	−	−	ADP
ejpam-2421	380	7	2	2	NUM
ejpam-2421	380	8	+	+	NUM
ejpam-2421	380	9	(	(	PUNCT
ejpam-2421	380	10	4sℓ2	4sℓ2	NUM
ejpam-2421	380	11	−	−	PROPN
ejpam-2421	380	12	4r	4r	NOUN
ejpam-2421	380	13	−	−	PROPN
ejpam-2421	380	14	2)ℓ2	2)ℓ2	NUM
ejpam-2421	380	15	=(	=(	NOUN
ejpam-2421	380	16	4s−	4s−	PROPN
ejpam-2421	380	17	2r)(ℓ2	2r)(ℓ2	NUM
ejpam-2421	380	18	+	+	CCONJ
ejpam-2421	381	1	1)−	1)−	PROPN
ejpam-2421	381	2	2	2	NUM
ejpam-2421	381	3	hold	hold	NOUN
ejpam-2421	381	4	for	for	ADP
ejpam-2421	381	5	a	a	DET
ejpam-2421	381	6	=	=	SYM
ejpam-2421	381	7	4m+	4m+	NUM
ejpam-2421	381	8	r2	r2	NOUN
ejpam-2421	381	9	+	+	CCONJ
ejpam-2421	381	10	5⇒	5⇒	NUM
ejpam-2421	381	11	4m+	4m+	NUM
ejpam-2421	381	12	4=	4=	NUM
ejpam-2421	381	13	a−	a−	PROPN
ejpam-2421	381	14	r2	r2	NOUN
ejpam-2421	381	15	−	−	PROPN
ejpam-2421	381	16	1=	1=	X
ejpam-2421	381	17	a−	a−	X
ejpam-2421	381	18	2r	2r	NUM
ejpam-2421	381	19	−	−	NOUN
ejpam-2421	382	1	2	2	X
ejpam-2421	382	2	.	.	PUNCT
ejpam-2421	383	1	if	if	SCONJ
ejpam-2421	383	2	we	we	PRON
ejpam-2421	383	3	take	take	VERB
ejpam-2421	383	4	the	the	DET
ejpam-2421	383	5	values	value	NOUN
ejpam-2421	383	6	a=	a=	VERB
ejpam-2421	383	7	ℓ2	ℓ2	NOUN
ejpam-2421	383	8	+	+	CCONJ
ejpam-2421	383	9	1	1	NUM
ejpam-2421	383	10	and	and	CCONJ
ejpam-2421	383	11	b	b	X
ejpam-2421	384	1	=	=	SYM
ejpam-2421	384	2	2s−	2s−	NUM
ejpam-2421	384	3	r	r	NOUN
ejpam-2421	384	4	then	then	ADV
ejpam-2421	384	5	2a	2a	NUM
ejpam-2421	384	6	=	=	SYM
ejpam-2421	384	7	(	(	PUNCT
ejpam-2421	384	8	2r	2r	NUM
ejpam-2421	384	9	+	+	CCONJ
ejpam-2421	384	10	2)ℓ2	2)ℓ2	NUM
ejpam-2421	384	11	+	+	CCONJ
ejpam-2421	384	12	r3	r3	PROPN
ejpam-2421	384	13	+	+	CCONJ
ejpam-2421	384	14	2r	2r	NUM
ejpam-2421	384	15	+	+	CCONJ
ejpam-2421	384	16	1=	1=	NUM
ejpam-2421	384	17	(	(	PUNCT
ejpam-2421	384	18	2r	2r	NUM
ejpam-2421	384	19	+	+	CCONJ
ejpam-2421	384	20	2)ℓ2	2)ℓ2	NUM
ejpam-2421	384	21	+	+	PUNCT
ejpam-2421	384	22	4s−	4s−	NUM
ejpam-2421	384	23	2r	2r	NUM
ejpam-2421	384	24	−	−	NOUN
ejpam-2421	384	25	1	1	NUM
ejpam-2421	384	26	+	+	SYM
ejpam-2421	384	27	2r	2r	NUM
ejpam-2421	384	28	+	+	CCONJ
ejpam-2421	384	29	1=	1=	NUM
ejpam-2421	384	30	2[(r	2[(r	NUM
ejpam-2421	384	31	+	+	CCONJ
ejpam-2421	384	32	1)ℓ2	1)ℓ2	NUM
ejpam-2421	384	33	+	+	CCONJ
ejpam-2421	384	34	2s	2s	NOUN
ejpam-2421	384	35	]	]	X
ejpam-2421	384	36	and	and	CCONJ
ejpam-2421	384	37	a	a	PRON
ejpam-2421	384	38	=	=	PUNCT
ejpam-2421	384	39	(	(	PUNCT
ejpam-2421	384	40	r	r	NOUN
ejpam-2421	384	41	+	+	NUM
ejpam-2421	384	42	1)ℓ2	1)ℓ2	NUM
ejpam-2421	384	43	+	+	CCONJ
ejpam-2421	384	44	2s	2	VERB
ejpam-2421	384	45	.	.	PUNCT
ejpam-2421	385	1	if	if	SCONJ
ejpam-2421	385	2	2a	2a	NUM
ejpam-2421	385	3	=	=	SYM
ejpam-2421	385	4	c3ℓ3	c3ℓ3	X
ejpam-2421	385	5	+	+	NUM
ejpam-2421	385	6	r3	r3	PROPN
ejpam-2421	385	7	+	+	CCONJ
ejpam-2421	385	8	r4	r4	NOUN
ejpam-2421	385	9	then	then	ADV
ejpam-2421	385	10	r4	r4	VERB
ejpam-2421	385	11	=	=	PRON
ejpam-2421	385	12	2a−	2a−	PROPN
ejpam-2421	385	13	c3ℓ3	c3ℓ3	NOUN
ejpam-2421	385	14	−	−	PROPN
ejpam-2421	385	15	r3	r3	PROPN
ejpam-2421	385	16	⇒	⇒	NOUN
ejpam-2421	385	17	r4	r4	NOUN
ejpam-2421	385	18	=	=	PUNCT
ejpam-2421	385	19	2[(r	2[(r	NUM
ejpam-2421	386	1	+	+	NUM
ejpam-2421	386	2	1)ℓ2	1)ℓ2	NUM
ejpam-2421	386	3	+	+	CCONJ
ejpam-2421	386	4	2s]−	2s]−	NUM
ejpam-2421	387	1	[	[	X
ejpam-2421	387	2	(	(	PUNCT
ejpam-2421	387	3	4s−	4s−	NOUN
ejpam-2421	387	4	2r)(ℓ2	2r)(ℓ2	NUM
ejpam-2421	387	5	+	+	CCONJ
ejpam-2421	387	6	1)−	1)−	PROPN
ejpam-2421	387	7	2]ℓ3	2]ℓ3	NUM
ejpam-2421	387	8	−	−	PROPN
ejpam-2421	387	9	(	(	PUNCT
ejpam-2421	387	10	4s−	4s−	NOUN
ejpam-2421	387	11	2r	2r	NUM
ejpam-2421	387	12	−	−	NOUN
ejpam-2421	387	13	1	1	X
ejpam-2421	387	14	)	)	PUNCT
ejpam-2421	387	15	r4	r4	VERB
ejpam-2421	387	16	=	=	PROPN
ejpam-2421	387	17	2(r	2(r	NUM
ejpam-2421	387	18	+	+	NUM
ejpam-2421	387	19	1)ℓ2	1)ℓ2	NUM
ejpam-2421	387	20	+	+	NUM
ejpam-2421	387	21	2r	2r	NUM
ejpam-2421	387	22	+	+	CCONJ
ejpam-2421	387	23	1	1	NUM
ejpam-2421	387	24	+	+	CCONJ
ejpam-2421	387	25	[	[	X
ejpam-2421	387	26	(	(	PUNCT
ejpam-2421	387	27	4s−	4s−	NOUN
ejpam-2421	387	28	2r)(ℓ2	2r)(ℓ2	NUM
ejpam-2421	387	29	+	+	CCONJ
ejpam-2421	388	1	1)−	1)−	PROPN
ejpam-2421	388	2	2]ℓ3	2]ℓ3	NUM
ejpam-2421	388	3	(	(	PUNCT
ejpam-2421	388	4	14	14	NUM
ejpam-2421	388	5	)	)	PUNCT
ejpam-2421	388	6	if	if	SCONJ
ejpam-2421	388	7	a	a	PRON
ejpam-2421	388	8	=	=	X
ejpam-2421	388	9	(	(	PUNCT
ejpam-2421	388	10	r	r	NOUN
ejpam-2421	388	11	+	+	NUM
ejpam-2421	388	12	1)ℓ2	1)ℓ2	NUM
ejpam-2421	388	13	+	+	CCONJ
ejpam-2421	388	14	2s	2s	NUM
ejpam-2421	388	15	,	,	PUNCT
ejpam-2421	388	16	a=	a=	ADJ
ejpam-2421	388	17	ℓ2	ℓ2	NOUN
ejpam-2421	388	18	+	+	CCONJ
ejpam-2421	388	19	1	1	NUM
ejpam-2421	388	20	,	,	PUNCT
ejpam-2421	388	21	b	b	X
ejpam-2421	388	22	=	=	SYM
ejpam-2421	388	23	2s−	2s−	NUM
ejpam-2421	388	24	r	r	NOUN
ejpam-2421	388	25	then	then	ADV
ejpam-2421	388	26	a	a	DET
ejpam-2421	388	27	=	=	NOUN
ejpam-2421	388	28	rℓ2	rℓ2	NOUN
ejpam-2421	388	29	+	+	CCONJ
ejpam-2421	388	30	ℓ2	ℓ2	NOUN
ejpam-2421	388	31	+	+	CCONJ
ejpam-2421	388	32	2s	2s	NUM
ejpam-2421	388	33	=	=	SYM
ejpam-2421	388	34	rℓ2	rℓ2	NOUN
ejpam-2421	388	35	+	+	CCONJ
ejpam-2421	388	36	ℓ2	ℓ2	NOUN
ejpam-2421	388	37	+	+	CCONJ
ejpam-2421	388	38	2s+	2s+	NUM
ejpam-2421	388	39	r	r	NOUN
ejpam-2421	388	40	−	−	NOUN
ejpam-2421	388	41	r	r	NOUN
ejpam-2421	388	42	=	=	NOUN
ejpam-2421	388	43	r(ℓ2	r(ℓ2	NOUN
ejpam-2421	388	44	+	+	CCONJ
ejpam-2421	388	45	1	1	X
ejpam-2421	388	46	)	)	PUNCT
ejpam-2421	388	47	+	+	CCONJ
ejpam-2421	388	48	ℓ2	ℓ2	NOUN
ejpam-2421	388	49	+	+	CCONJ
ejpam-2421	388	50	(	(	PUNCT
ejpam-2421	388	51	2s−	2s−	NUM
ejpam-2421	388	52	r	r	NOUN
ejpam-2421	388	53	)	)	PUNCT
ejpam-2421	388	54	=	=	SYM
ejpam-2421	388	55	ar	ar	PROPN
ejpam-2421	388	56	+	+	NOUN
ejpam-2421	388	57	a−	a−	PROPN
ejpam-2421	388	58	1	1	NUM
ejpam-2421	388	59	+	+	SYM
ejpam-2421	388	60	b	b	NOUN
ejpam-2421	388	61	and	and	CCONJ
ejpam-2421	388	62	so	so	ADV
ejpam-2421	388	63	a	a	DET
ejpam-2421	388	64	=	=	PUNCT
ejpam-2421	388	65	a(r	a(r	NOUN
ejpam-2421	388	66	+	+	NOUN
ejpam-2421	388	67	1	1	NUM
ejpam-2421	388	68	)	)	PUNCT
ejpam-2421	389	1	+	+	NOUN
ejpam-2421	389	2	b	b	X
ejpam-2421	389	3	−	−	NOUN
ejpam-2421	389	4	1	1	NUM
ejpam-2421	389	5	(	(	PUNCT
ejpam-2421	389	6	15	15	NUM
ejpam-2421	389	7	)	)	PUNCT
ejpam-2421	389	8	holds	hold	VERB
ejpam-2421	389	9	.	.	PUNCT
ejpam-2421	390	1	since	since	SCONJ
ejpam-2421	390	2	a=	a=	ADJ
ejpam-2421	390	3	ℓ2	ℓ2	NOUN
ejpam-2421	390	4	+	+	CCONJ
ejpam-2421	390	5	1	1	NUM
ejpam-2421	390	6	,	,	PUNCT
ejpam-2421	390	7	and	and	CCONJ
ejpam-2421	390	8	b	b	X
ejpam-2421	390	9	=	=	SYM
ejpam-2421	390	10	2s−	2s−	NUM
ejpam-2421	390	11	r	r	NOUN
ejpam-2421	390	12	then	then	ADV
ejpam-2421	390	13	c3	c3	X
ejpam-2421	390	14	=	=	PROPN
ejpam-2421	390	15	2ba−	2ba−	NUM
ejpam-2421	390	16	2=	2=	NUM
ejpam-2421	390	17	2(ba−	2(ba−	NUM
ejpam-2421	390	18	1	1	NUM
ejpam-2421	390	19	)	)	PUNCT
ejpam-2421	390	20	r3	r3	NOUN
ejpam-2421	390	21	=	=	SYM
ejpam-2421	390	22	4s−	4s−	NOUN
ejpam-2421	390	23	2r	2r	NUM
ejpam-2421	390	24	−	−	PROPN
ejpam-2421	390	25	1⇒	1⇒	PROPN
ejpam-2421	390	26	r3	r3	PROPN
ejpam-2421	390	27	=	=	SYM
ejpam-2421	390	28	2b	2b	NOUN
ejpam-2421	390	29	−	−	PROPN
ejpam-2421	390	30	1	1	NUM
ejpam-2421	390	31	r4	r4	NOUN
ejpam-2421	390	32	=	=	PROPN
ejpam-2421	390	33	2a−	2a−	PROPN
ejpam-2421	390	34	c3ℓ3	c3ℓ3	X
ejpam-2421	390	35	−	−	PROPN
ejpam-2421	390	36	r3⇒	r3⇒	PROPN
ejpam-2421	390	37	r4	r4	NOUN
ejpam-2421	390	38	=	=	PUNCT
ejpam-2421	391	1	2a−	2a−	NUM
ejpam-2421	391	2	2(ba−	2(ba−	NUM
ejpam-2421	391	3	1)ℓ3	1)ℓ3	NUM
ejpam-2421	391	4	−	−	NOUN
ejpam-2421	391	5	2b	2b	NOUN
ejpam-2421	391	6	+	+	SYM
ejpam-2421	391	7	1	1	NUM
ejpam-2421	391	8	⇒	⇒	NOUN
ejpam-2421	391	9	r4	r4	NOUN
ejpam-2421	391	10	=	=	SYM
ejpam-2421	391	11	2rℓ2	2rℓ2	NUM
ejpam-2421	391	12	+	+	NUM
ejpam-2421	391	13	ℓ2	ℓ2	NOUN
ejpam-2421	391	14	−	−	PROPN
ejpam-2421	391	15	2b(1	2b(1	NUM
ejpam-2421	391	16	+	+	NOUN
ejpam-2421	391	17	aℓ3	aℓ3	NOUN
ejpam-2421	391	18	)	)	PUNCT
ejpam-2421	392	1	+	+	CCONJ
ejpam-2421	392	2	2ℓ3	2ℓ3	NUM
ejpam-2421	392	3	+	+	CCONJ
ejpam-2421	392	4	4s+	4s+	NUM
ejpam-2421	392	5	a	a	PRON
ejpam-2421	393	1	and	and	CCONJ
ejpam-2421	393	2	if	if	SCONJ
ejpam-2421	393	3	we	we	PRON
ejpam-2421	393	4	take	take	VERB
ejpam-2421	393	5	c	c	NOUN
ejpam-2421	393	6	=	=	SYM
ejpam-2421	394	1	1	1	NUM
ejpam-2421	394	2	+	+	NUM
ejpam-2421	394	3	aℓ3	aℓ3	NOUN
ejpam-2421	394	4	=	=	SYM
ejpam-2421	394	5	1	1	NUM
ejpam-2421	394	6	+	+	NUM
ejpam-2421	394	7	ℓ3	ℓ3	PROPN
ejpam-2421	394	8	+	+	CCONJ
ejpam-2421	394	9	ℓ2ℓ3	ℓ2ℓ3	PROPN
ejpam-2421	394	10	,	,	PUNCT
ejpam-2421	394	11	d	d	PROPN
ejpam-2421	394	12	=	=	PUNCT
ejpam-2421	394	13	bℓ3	bℓ3	PROPN
ejpam-2421	395	1	−	−	NOUN
ejpam-2421	395	2	r	r	NOUN
ejpam-2421	395	3	−	−	NOUN
ejpam-2421	395	4	1	1	NUM
ejpam-2421	395	5	and	and	CCONJ
ejpam-2421	395	6	e	e	NOUN
ejpam-2421	395	7	=	=	PROPN
ejpam-2421	395	8	ℓ3	ℓ3	PROPN
ejpam-2421	395	9	+	+	CCONJ
ejpam-2421	395	10	1	1	NUM
ejpam-2421	395	11	then	then	ADV
ejpam-2421	395	12	we	we	PRON
ejpam-2421	395	13	obtain	obtain	VERB
ejpam-2421	395	14	r4	r4	NOUN
ejpam-2421	395	15	=	=	NOUN
ejpam-2421	395	16	2rℓ2	2rℓ2	NUM
ejpam-2421	395	17	+	+	NUM
ejpam-2421	395	18	ℓ2	ℓ2	NOUN
ejpam-2421	395	19	−	−	PROPN
ejpam-2421	395	20	2bc	2bc	ADJ
ejpam-2421	395	21	+	+	CCONJ
ejpam-2421	395	22	2ℓ3	2ℓ3	NUM
ejpam-2421	395	23	+	+	SYM
ejpam-2421	395	24	2b	2b	NUM
ejpam-2421	395	25	+	+	CCONJ
ejpam-2421	395	26	2r	2r	NUM
ejpam-2421	395	27	+	+	CCONJ
ejpam-2421	395	28	a=	a=	X
ejpam-2421	395	29	2ℓ3	2ℓ3	NUM
ejpam-2421	395	30	−	−	PROPN
ejpam-2421	395	31	2a(bℓ3	2a(bℓ3	NUM
ejpam-2421	396	1	−	−	NOUN
ejpam-2421	397	1	r	r	NOUN
ejpam-2421	397	2	−	−	PROPN
ejpam-2421	397	3	1)−	1)−	NUM
ejpam-2421	397	4	1	1	NUM
ejpam-2421	397	5	=	=	SYM
ejpam-2421	397	6	2(ℓ3	2(ℓ3	NUM
ejpam-2421	397	7	+	+	CCONJ
ejpam-2421	397	8	1)−	1)−	NUM
ejpam-2421	397	9	2ad−	2ad−	NUM
ejpam-2421	397	10	3	3	NUM
ejpam-2421	397	11	⇒	⇒	NOUN
ejpam-2421	397	12	r4	r4	NOUN
ejpam-2421	397	13	=	=	SYM
ejpam-2421	397	14	2(ℓ3	2(ℓ3	PROPN
ejpam-2421	397	15	+	+	CCONJ
ejpam-2421	398	1	1)−	1)−	NUM
ejpam-2421	398	2	2ad−	2ad−	NUM
ejpam-2421	398	3	3	3	NUM
ejpam-2421	398	4	⇒	⇒	NOUN
ejpam-2421	398	5	r4	r4	NOUN
ejpam-2421	398	6	=	=	PROPN
ejpam-2421	398	7	2e	2e	PROPN
ejpam-2421	398	8	−	−	PROPN
ejpam-2421	398	9	2ad−	2ad−	NUM
ejpam-2421	398	10	3	3	X
ejpam-2421	398	11	.	.	PUNCT
ejpam-2421	399	1	at	at	ADP
ejpam-2421	399	2	the	the	DET
ejpam-2421	399	3	same	same	ADJ
ejpam-2421	399	4	way	way	NOUN
ejpam-2421	399	5	we	we	PRON
ejpam-2421	399	6	can	can	AUX
ejpam-2421	399	7	determine	determine	VERB
ejpam-2421	399	8	c4	c4	NOUN
ejpam-2421	399	9	as	as	ADP
ejpam-2421	399	10	c4	c4	NOUN
ejpam-2421	399	11	=(	=(	NOUN
ejpam-2421	399	12	2r	2r	PROPN
ejpam-2421	400	1	+	+	CCONJ
ejpam-2421	400	2	2	2	X
ejpam-2421	400	3	)	)	PUNCT
ejpam-2421	400	4	+	+	CCONJ
ejpam-2421	400	5	(	(	PUNCT
ejpam-2421	400	6	2ra+	2ra+	PROPN
ejpam-2421	400	7	2a−	2a−	NUM
ejpam-2421	400	8	2bc	2bc	NOUN
ejpam-2421	401	1	+	+	CCONJ
ejpam-2421	401	2	2ℓ3)ℓ3	2ℓ3)ℓ3	NUM
ejpam-2421	401	3	=	=	SYM
ejpam-2421	401	4	2r(1	2r(1	NUM
ejpam-2421	401	5	+	+	NUM
ejpam-2421	401	6	aℓ3	aℓ3	NOUN
ejpam-2421	401	7	)	)	PUNCT
ejpam-2421	402	1	+	+	PUNCT
ejpam-2421	403	1	2(1	2(1	NUM
ejpam-2421	403	2	+	+	CCONJ
ejpam-2421	403	3	aℓ3)−	aℓ3)−	PROPN
ejpam-2421	403	4	2bcℓ3	2bcℓ3	NUM
ejpam-2421	403	5	+	+	NUM
ejpam-2421	403	6	2ℓ23	2ℓ23	NUM
ejpam-2421	404	1	=	=	SYM
ejpam-2421	404	2	−	−	PROPN
ejpam-2421	404	3	2c(bℓ3	2c(bℓ3	NUM
ejpam-2421	405	1	−	−	NOUN
ejpam-2421	405	2	r	r	NOUN
ejpam-2421	405	3	−	−	NOUN
ejpam-2421	405	4	1	1	NUM
ejpam-2421	405	5	)	)	PUNCT
ejpam-2421	405	6	+	+	NUM
ejpam-2421	405	7	2ℓ23	2ℓ23	X
ejpam-2421	405	8	=	=	SYM
ejpam-2421	405	9	2(ℓ23	2(ℓ23	NUM
ejpam-2421	406	1	−	−	NOUN
ejpam-2421	406	2	c	c	NOUN
ejpam-2421	406	3	d	d	NOUN
ejpam-2421	406	4	)	)	PUNCT
ejpam-2421	406	5	.	.	PUNCT
ejpam-2421	407	1	references	reference	NOUN
ejpam-2421	407	2	356	356	NUM
ejpam-2421	407	3	we	we	PRON
ejpam-2421	407	4	know	know	VERB
ejpam-2421	407	5	that	that	SCONJ
ejpam-2421	407	6	ℓ4	ℓ4	NOUN
ejpam-2421	407	7	=	=	SYM
ejpam-2421	407	8	2(a−r4	2(a−r4	NUM
ejpam-2421	407	9	)	)	PUNCT
ejpam-2421	407	10	c4	c4	NOUN
ejpam-2421	407	11	from	from	ADP
ejpam-2421	407	12	lemma	lemma	PROPN
ejpam-2421	407	13	?	?	PUNCT
ejpam-2421	407	14	?	?	PUNCT
ejpam-2421	407	15	?	?	PUNCT
ejpam-2421	408	1	then	then	ADV
ejpam-2421	408	2	we	we	PRON
ejpam-2421	408	3	can	can	AUX
ejpam-2421	408	4	determine	determine	VERB
ejpam-2421	408	5	the	the	DET
ejpam-2421	408	6	value	value	NOUN
ejpam-2421	408	7	of	of	ADP
ejpam-2421	408	8	a−	a−	PROPN
ejpam-2421	408	9	r4	r4	NOUN
ejpam-2421	408	10	in	in	ADP
ejpam-2421	408	11	the	the	DET
ejpam-2421	408	12	following	following	NOUN
ejpam-2421	408	13	:	:	PUNCT
ejpam-2421	408	14	a−	a−	PROPN
ejpam-2421	408	15	r4	r4	NOUN
ejpam-2421	408	16	=(	=(	NOUN
ejpam-2421	408	17	r	r	NOUN
ejpam-2421	408	18	+	+	NOUN
ejpam-2421	408	19	1)ℓ2	1)ℓ2	NUM
ejpam-2421	408	20	+	+	SYM
ejpam-2421	408	21	b	b	NOUN
ejpam-2421	408	22	+	+	CCONJ
ejpam-2421	408	23	r	r	NOUN
ejpam-2421	408	24	−	−	NOUN
ejpam-2421	408	25	2e	2e	NOUN
ejpam-2421	408	26	+	+	CCONJ
ejpam-2421	409	1	2ad+	2ad+	NUM
ejpam-2421	409	2	3	3	NUM
ejpam-2421	409	3	⇒	⇒	NOUN
ejpam-2421	409	4	a−	a−	PROPN
ejpam-2421	409	5	r4	r4	NOUN
ejpam-2421	409	6	=	=	SYM
ejpam-2421	409	7	b	b	PROPN
ejpam-2421	409	8	−	−	PROPN
ejpam-2421	409	9	2e	2e	NOUN
ejpam-2421	409	10	+	+	CCONJ
ejpam-2421	409	11	abℓ3	abℓ3	PROPN
ejpam-2421	409	12	+	+	CCONJ
ejpam-2421	409	13	a(bℓ3	a(bℓ3	PROPN
ejpam-2421	409	14	−	−	NOUN
ejpam-2421	409	15	r	r	NOUN
ejpam-2421	409	16	−	−	NOUN
ejpam-2421	409	17	1	1	NUM
ejpam-2421	409	18	)	)	PUNCT
ejpam-2421	409	19	+	+	CCONJ
ejpam-2421	409	20	2	2	NUM
ejpam-2421	409	21	⇒	⇒	NOUN
ejpam-2421	409	22	a−	a−	ADJ
ejpam-2421	409	23	r4	r4	NOUN
ejpam-2421	409	24	=	=	PUNCT
ejpam-2421	409	25	b(1	b(1	PROPN
ejpam-2421	409	26	+	+	SYM
ejpam-2421	409	27	aℓ3	aℓ3	NOUN
ejpam-2421	409	28	)	)	PUNCT
ejpam-2421	409	29	+	+	CCONJ
ejpam-2421	409	30	ad−	ad−	NOUN
ejpam-2421	409	31	2ℓ3	2ℓ3	NUM
ejpam-2421	409	32	⇒	⇒	NOUN
ejpam-2421	409	33	a−	a−	PROPN
ejpam-2421	409	34	r4	r4	NOUN
ejpam-2421	409	35	=	=	SYM
ejpam-2421	409	36	bc	bc	PROPN
ejpam-2421	409	37	+	+	CCONJ
ejpam-2421	409	38	ad−	ad−	PROPN
ejpam-2421	409	39	2ℓ3	2ℓ3	NUM
ejpam-2421	409	40	.	.	PUNCT
ejpam-2421	410	1	moreover	moreover	ADV
ejpam-2421	410	2	we	we	PRON
ejpam-2421	410	3	can	can	AUX
ejpam-2421	410	4	easily	easily	ADV
ejpam-2421	410	5	seen	see	VERB
ejpam-2421	410	6	that	that	SCONJ
ejpam-2421	410	7	ℓ4	ℓ4	NOUN
ejpam-2421	410	8	=	=	SYM
ejpam-2421	410	9	2(a−r4	2(a−r4	NUM
ejpam-2421	410	10	)	)	PUNCT
ejpam-2421	410	11	c4	c4	NOUN
ejpam-2421	410	12	=	=	SYM
ejpam-2421	410	13	2(bc+ad−2ℓ3	2(bc+ad−2ℓ3	PROPN
ejpam-2421	410	14	)	)	PUNCT
ejpam-2421	410	15	2(ℓ23−c	2(ℓ23−c	PROPN
ejpam-2421	410	16	d	d	NOUN
ejpam-2421	410	17	)	)	PUNCT
ejpam-2421	410	18	=	=	SYM
ejpam-2421	410	19	bc+ad−2ℓ3	bc+ad−2ℓ3	PROPN
ejpam-2421	410	20	ℓ23−c	ℓ23−c	PROPN
ejpam-2421	410	21	d	d	PROPN
ejpam-2421	410	22	=	=	SYM
ejpam-2421	410	23	bc+ad−2ℓ3	bc+ad−2ℓ3	PROPN
ejpam-2421	410	24	ℓ23−c	ℓ23−c	PROPN
ejpam-2421	410	25	d	d	PROPN
ejpam-2421	410	26	and	and	CCONJ
ejpam-2421	410	27	s	s	NOUN
ejpam-2421	410	28	and	and	CCONJ
ejpam-2421	410	29	r	r	NOUN
ejpam-2421	410	30	are	be	AUX
ejpam-2421	410	31	uniquely	uniquely	ADV
ejpam-2421	410	32	determined	determined	ADJ
ejpam-2421	410	33	from	from	ADP
ejpam-2421	410	34	the	the	DET
ejpam-2421	410	35	relations	relation	NOUN
ejpam-2421	410	36	a	a	DET
ejpam-2421	410	37	=	=	SYM
ejpam-2421	410	38	a(r	a(r	NOUN
ejpam-2421	410	39	+	+	NOUN
ejpam-2421	410	40	1	1	NUM
ejpam-2421	410	41	)	)	PUNCT
ejpam-2421	410	42	+	+	NOUN
ejpam-2421	410	43	b	b	X
ejpam-2421	410	44	−	−	NOUN
ejpam-2421	410	45	1	1	NUM
ejpam-2421	410	46	and	and	CCONJ
ejpam-2421	410	47	ℓ23ℓ4	ℓ23ℓ4	VERB
ejpam-2421	410	48	+	+	CCONJ
ejpam-2421	410	49	2ℓ3	2ℓ3	NUM
ejpam-2421	410	50	=	=	SYM
ejpam-2421	410	51	bc	bc	PROPN
ejpam-2421	410	52	+	+	CCONJ
ejpam-2421	410	53	ad+	ad+	PROPN
ejpam-2421	410	54	2c	2c	NUM
ejpam-2421	410	55	dℓ4	dℓ4	NOUN
ejpam-2421	410	56	.	.	PUNCT
ejpam-2421	410	57	example	example	NOUN
ejpam-2421	411	1	2	2	NUM
ejpam-2421	411	2	.	.	PUNCT
ejpam-2421	411	3	let	let	VERB
ejpam-2421	411	4	a	a	PRON
ejpam-2421	411	5	is	be	AUX
ejpam-2421	411	6	even	even	ADV
ejpam-2421	411	7	,	,	PUNCT
ejpam-2421	411	8	d	d	PROPN
ejpam-2421	411	9	≡	≡	PROPN
ejpam-2421	411	10	1(mod4	1(mod4	NUM
ejpam-2421	411	11	)	)	PUNCT
ejpam-2421	411	12	.	.	PUNCT
ejpam-2421	412	1	if	if	SCONJ
ejpam-2421	412	2	we	we	PRON
ejpam-2421	412	3	choose	choose	VERB
ejpam-2421	412	4	d	d	NOUN
ejpam-2421	412	5	=	=	SYM
ejpam-2421	412	6	501	501	NUM
ejpam-2421	412	7	≡	≡	PROPN
ejpam-2421	412	8	5(mod8	5(mod8	NUM
ejpam-2421	412	9	)	)	PUNCT
ejpam-2421	412	10	then	then	ADV
ejpam-2421	412	11	we	we	PRON
ejpam-2421	412	12	can	can	AUX
ejpam-2421	412	13	practically	practically	ADV
ejpam-2421	412	14	determine	determine	VERB
ejpam-2421	412	15	that	that	SCONJ
ejpam-2421	412	16	a	a	DET
ejpam-2421	412	17	=	=	SYM
ejpam-2421	412	18	22	22	NUM
ejpam-2421	412	19	,	,	PUNCT
ejpam-2421	412	20	b	b	X
ejpam-2421	412	21	=	=	SYM
ejpam-2421	412	22	17≡	17≡	NUM
ejpam-2421	412	23	1(mod8	1(mod8	NUM
ejpam-2421	412	24	)	)	PUNCT
ejpam-2421	412	25	,	,	PUNCT
ejpam-2421	412	26	17=	17=	NUM
ejpam-2421	412	27	8m+	8m+	NUM
ejpam-2421	412	28	1⇒	1⇒	PROPN
ejpam-2421	412	29	m=	m=	X
ejpam-2421	412	30	2	2	NUM
ejpam-2421	412	31	,	,	PUNCT
ejpam-2421	412	32	c1	c1	NOUN
ejpam-2421	412	33	=	=	PROPN
ejpam-2421	412	34	4m+	4m+	PROPN
ejpam-2421	412	35	a⇒	a⇒	PROPN
ejpam-2421	412	36	c1	c1	PROPN
ejpam-2421	412	37	=	=	PUNCT
ejpam-2421	412	38	8	8	NUM
ejpam-2421	412	39	+	+	SYM
ejpam-2421	412	40	22⇒	22⇒	NUM
ejpam-2421	412	41	c1	c1	NOUN
ejpam-2421	412	42	=	=	SYM
ejpam-2421	412	43	30	30	NUM
ejpam-2421	412	44	,	,	PUNCT
ejpam-2421	412	45	ℓ1	ℓ1	NOUN
ejpam-2421	412	46	=	=	SYM
ejpam-2421	412	47	1	1	NUM
ejpam-2421	412	48	,	,	PUNCT
ejpam-2421	412	49	ℓ2	ℓ2	NOUN
ejpam-2421	412	50	=	=	SYM
ejpam-2421	412	51	2	2	NUM
ejpam-2421	412	52	,	,	PUNCT
ejpam-2421	412	53	ℓ3	ℓ3	NOUN
ejpam-2421	412	54	=	=	PUNCT
ejpam-2421	412	55	4	4	NUM
ejpam-2421	412	56	,	,	PUNCT
ejpam-2421	412	57	a	a	PRON
ejpam-2421	412	58	=	=	SYM
ejpam-2421	412	59	4m+	4m+	NUM
ejpam-2421	412	60	1	1	NUM
ejpam-2421	412	61	+	+	NUM
ejpam-2421	413	1	r2⇒	r2⇒	ADJ
ejpam-2421	413	2	22	22	NUM
ejpam-2421	413	3	=	=	SYM
ejpam-2421	413	4	9	9	NUM
ejpam-2421	413	5	+	+	NUM
ejpam-2421	413	6	r2⇒	r2⇒	ADJ
ejpam-2421	413	7	r2	r2	NOUN
ejpam-2421	413	8	=	=	SYM
ejpam-2421	413	9	13	13	NUM
ejpam-2421	413	10	,	,	PUNCT
ejpam-2421	413	11	r2	r2	NOUN
ejpam-2421	413	12	=	=	PUNCT
ejpam-2421	413	13	2r	2r	NUM
ejpam-2421	414	1	+	+	CCONJ
ejpam-2421	414	2	1	1	NUM
ejpam-2421	414	3	=	=	SYM
ejpam-2421	414	4	13⇒	13⇒	NUM
ejpam-2421	414	5	r	r	NOUN
ejpam-2421	414	6	=	=	SYM
ejpam-2421	414	7	6	6	NUM
ejpam-2421	414	8	,	,	PUNCT
ejpam-2421	414	9	c2	c2	PROPN
ejpam-2421	414	10	=	=	PUNCT
ejpam-2421	414	11	2r	2r	PROPN
ejpam-2421	415	1	+	+	CCONJ
ejpam-2421	415	2	2⇒	2⇒	PROPN
ejpam-2421	415	3	c2	c2	PROPN
ejpam-2421	415	4	=	=	SYM
ejpam-2421	415	5	14	14	NUM
ejpam-2421	415	6	,	,	PUNCT
ejpam-2421	415	7	2a	2a	NUM
ejpam-2421	415	8	=	=	SYM
ejpam-2421	415	9	c2ℓ2	c2ℓ2	PROPN
ejpam-2421	415	10	+	+	NUM
ejpam-2421	415	11	r2	r2	PROPN
ejpam-2421	415	12	+	+	CCONJ
ejpam-2421	415	13	r3	r3	PROPN
ejpam-2421	415	14	⇒	⇒	NOUN
ejpam-2421	415	15	r3	r3	PROPN
ejpam-2421	415	16	=	=	SYM
ejpam-2421	416	1	44	44	NUM
ejpam-2421	416	2	−	−	NUM
ejpam-2421	416	3	28	28	NUM
ejpam-2421	416	4	−	−	NOUN
ejpam-2421	416	5	13	13	NUM
ejpam-2421	416	6	=	=	SYM
ejpam-2421	416	7	3	3	NUM
ejpam-2421	416	8	,	,	PUNCT
ejpam-2421	416	9	r3	r3	PROPN
ejpam-2421	416	10	+	+	CCONJ
ejpam-2421	416	11	2r	2r	NUM
ejpam-2421	417	1	+	+	CCONJ
ejpam-2421	417	2	1	1	NUM
ejpam-2421	417	3	=	=	SYM
ejpam-2421	417	4	4s	4s	NUM
ejpam-2421	417	5	⇒	⇒	NOUN
ejpam-2421	417	6	3	3	NUM
ejpam-2421	417	7	+	+	SYM
ejpam-2421	417	8	13	13	NUM
ejpam-2421	417	9	=	=	SYM
ejpam-2421	417	10	4s	4s	NUM
ejpam-2421	417	11	⇒	⇒	NOUN
ejpam-2421	417	12	s	s	PART
ejpam-2421	417	13	=	=	SYM
ejpam-2421	417	14	4	4	NUM
ejpam-2421	417	15	,	,	PUNCT
ejpam-2421	417	16	c3	c3	PROPN
ejpam-2421	417	17	=	=	PUNCT
ejpam-2421	417	18	(	(	PUNCT
ejpam-2421	417	19	4s	4s	NUM
ejpam-2421	417	20	−	−	PROPN
ejpam-2421	417	21	2r)(ℓ2	2r)(ℓ2	NUM
ejpam-2421	417	22	+	+	CCONJ
ejpam-2421	417	23	1	1	NUM
ejpam-2421	417	24	)	)	PUNCT
ejpam-2421	417	25	=	=	SYM
ejpam-2421	417	26	2⇒	2⇒	PROPN
ejpam-2421	417	27	c3	c3	NOUN
ejpam-2421	417	28	=	=	PUNCT
ejpam-2421	417	29	4	4	NUM
ejpam-2421	417	30	·	·	SYM
ejpam-2421	417	31	3−	3−	NUM
ejpam-2421	417	32	2	2	NUM
ejpam-2421	417	33	=	=	SYM
ejpam-2421	417	34	10	10	NUM
ejpam-2421	417	35	,	,	PUNCT
ejpam-2421	417	36	r4	r4	NOUN
ejpam-2421	417	37	=	=	SYM
ejpam-2421	417	38	2a	2a	NUM
ejpam-2421	417	39	−	−	PROPN
ejpam-2421	418	1	c3ℓ3	c3ℓ3	NOUN
ejpam-2421	418	2	−	−	PROPN
ejpam-2421	418	3	r3⇒	r3⇒	PROPN
ejpam-2421	418	4	r4	r4	PROPN
ejpam-2421	418	5	=	=	PUNCT
ejpam-2421	418	6	44−	44−	NOUN
ejpam-2421	418	7	40−	40−	NOUN
ejpam-2421	418	8	3	3	NUM
ejpam-2421	418	9	=	=	SYM
ejpam-2421	418	10	1	1	NUM
ejpam-2421	418	11	,	,	PUNCT
ejpam-2421	418	12	a=	a=	ADJ
ejpam-2421	418	13	ℓ2	ℓ2	NOUN
ejpam-2421	418	14	+	+	CCONJ
ejpam-2421	418	15	1⇒	1⇒	PROPN
ejpam-2421	418	16	a=	a=	PROPN
ejpam-2421	418	17	3	3	NUM
ejpam-2421	418	18	,	,	PUNCT
ejpam-2421	418	19	b	b	X
ejpam-2421	418	20	=	=	SYM
ejpam-2421	418	21	2s−	2s−	NUM
ejpam-2421	418	22	r	r	NOUN
ejpam-2421	418	23	⇒	⇒	NOUN
ejpam-2421	418	24	b	b	PROPN
ejpam-2421	419	1	=	=	SYM
ejpam-2421	419	2	2	2	NUM
ejpam-2421	419	3	,	,	PUNCT
ejpam-2421	419	4	c	c	NOUN
ejpam-2421	419	5	=	=	SYM
ejpam-2421	419	6	1	1	NUM
ejpam-2421	419	7	+	+	NUM
ejpam-2421	420	1	aℓ3	aℓ3	NOUN
ejpam-2421	420	2	=	=	SYM
ejpam-2421	420	3	1	1	NUM
ejpam-2421	420	4	+	+	NUM
ejpam-2421	420	5	ℓ2	ℓ2	NOUN
ejpam-2421	420	6	+	+	CCONJ
ejpam-2421	420	7	ℓ2ℓ3⇒	ℓ2ℓ3⇒	X
ejpam-2421	420	8	c	c	NOUN
ejpam-2421	420	9	=	=	SYM
ejpam-2421	420	10	13	13	NUM
ejpam-2421	420	11	,	,	PUNCT
ejpam-2421	420	12	d	d	NOUN
ejpam-2421	420	13	=	=	PUNCT
ejpam-2421	421	1	−r+bℓ3−1⇒	−r+bℓ3−1⇒	PUNCT
ejpam-2421	421	2	d	d	NOUN
ejpam-2421	421	3	=	=	SYM
ejpam-2421	421	4	1	1	NUM
ejpam-2421	421	5	,	,	PUNCT
ejpam-2421	421	6	e	e	X
ejpam-2421	421	7	=	=	SYM
ejpam-2421	421	8	ℓ3	ℓ3	PROPN
ejpam-2421	421	9	+	+	PROPN
ejpam-2421	421	10	1⇒	1⇒	NOUN
ejpam-2421	421	11	e	e	NOUN
ejpam-2421	421	12	=	=	SYM
ejpam-2421	421	13	5	5	NUM
ejpam-2421	421	14	,	,	PUNCT
ejpam-2421	421	15	r4	r4	NOUN
ejpam-2421	421	16	=	=	SYM
ejpam-2421	421	17	1	1	NUM
ejpam-2421	421	18	,	,	PUNCT
ejpam-2421	421	19	a	a	DET
ejpam-2421	421	20	=	=	SYM
ejpam-2421	421	21	22	22	NUM
ejpam-2421	421	22	,	,	PUNCT
ejpam-2421	422	1	c4	c4	NOUN
ejpam-2421	422	2	=	=	SYM
ejpam-2421	422	3	6⇒	6⇒	PROPN
ejpam-2421	422	4	ℓ4	ℓ4	NOUN
ejpam-2421	422	5	=	=	SYM
ejpam-2421	422	6	7	7	X
ejpam-2421	422	7	.	.	X
ejpam-2421	423	1	therefore	therefore	ADV
ejpam-2421	423	2	the	the	DET
ejpam-2421	423	3	fundamental	fundamental	ADJ
ejpam-2421	423	4	unit	unit	NOUN
ejpam-2421	423	5	of	of	ADP
ejpam-2421	423	6	q	q	PROPN
ejpam-2421	423	7	(	(	PUNCT
ejpam-2421	423	8	p	p	NOUN
ejpam-2421	423	9	501	501	NUM
ejpam-2421	423	10	)	)	PUNCT
ejpam-2421	423	11	is	be	AUX
ejpam-2421	423	12	obtained	obtain	VERB
ejpam-2421	423	13	as	as	ADP
ejpam-2421	423	14	ǫd	ǫd	NUM
ejpam-2421	423	15	=	=	NOUN
ejpam-2421	423	16	28225	28225	NUM
ejpam-2421	423	17	+	+	NOUN
ejpam-2421	423	18	1261	1261	NUM
ejpam-2421	423	19	p	p	NOUN
ejpam-2421	423	20	501	501	NUM
ejpam-2421	423	21	2	2	NUM
ejpam-2421	423	22	for	for	ADP
ejpam-2421	423	23	td	td	NOUN
ejpam-2421	423	24	=	=	SYM
ejpam-2421	423	25	28225	28225	NUM
ejpam-2421	423	26	,	,	PUNCT
ejpam-2421	423	27	ud	ud	ADV
ejpam-2421	423	28	=	=	NOUN
ejpam-2421	423	29	1261	1261	NUM
ejpam-2421	423	30	.	.	PUNCT
ejpam-2421	424	1	acknowledgements	acknowledgement	NOUN
ejpam-2421	424	2	this	this	DET
ejpam-2421	424	3	work	work	NOUN
ejpam-2421	424	4	was	be	AUX
ejpam-2421	424	5	supported	support	VERB
ejpam-2421	424	6	by	by	ADP
ejpam-2421	424	7	the	the	DET
ejpam-2421	424	8	research	research	NOUN
ejpam-2421	424	9	scientific	scientific	ADJ
ejpam-2421	424	10	project	project	NOUN
ejpam-2421	424	11	of	of	ADP
ejpam-2421	424	12	kırklareli	kırklareli	PROPN
ejpam-2421	424	13	university	university	PROPN
ejpam-2421	424	14	with	with	ADP
ejpam-2421	424	15	the	the	DET
ejpam-2421	424	16	number	number	NOUN
ejpam-2421	424	17	klubap-044	klubap-044	NOUN
ejpam-2421	424	18	.	.	PUNCT
ejpam-2421	425	1	references	reference	NOUN
ejpam-2421	425	2	[	[	X
ejpam-2421	425	3	1	1	X
ejpam-2421	425	4	]	]	PUNCT
ejpam-2421	425	5	t.	t.	NOUN
ejpam-2421	425	6	azuhata	azuhata	NOUN
ejpam-2421	425	7	.	.	PUNCT
ejpam-2421	426	1	on	on	ADP
ejpam-2421	426	2	the	the	DET
ejpam-2421	426	3	fundamental	fundamental	ADJ
ejpam-2421	426	4	unit	unit	NOUN
ejpam-2421	426	5	and	and	CCONJ
ejpam-2421	426	6	the	the	DET
ejpam-2421	426	7	class	class	NOUN
ejpam-2421	426	8	numbers	number	NOUN
ejpam-2421	426	9	of	of	ADP
ejpam-2421	426	10	real	real	ADJ
ejpam-2421	426	11	quadratic	quadratic	ADJ
ejpam-2421	426	12	fields	field	NOUN
ejpam-2421	426	13	,	,	PUNCT
ejpam-2421	426	14	nagoya	nagoya	PROPN
ejpam-2421	426	15	math	math	PROPN
ejpam-2421	426	16	.	.	PUNCT
ejpam-2421	427	1	j.	j.	PROPN
ejpam-2421	427	2	,	,	PUNCT
ejpam-2421	427	3	95	95	NUM
ejpam-2421	427	4	:	:	PUNCT
ejpam-2421	427	5	125	125	NUM
ejpam-2421	427	6	-	-	SYM
ejpam-2421	427	7	135	135	NUM
ejpam-2421	427	8	,	,	PUNCT
ejpam-2421	427	9	1984	1984	NUM
ejpam-2421	427	10	.	.	PUNCT
ejpam-2421	428	1	[	[	X
ejpam-2421	428	2	2	2	NUM
ejpam-2421	428	3	]	]	X
ejpam-2421	428	4	r.a	r.a	PROPN
ejpam-2421	428	5	mollin	mollin	NOUN
ejpam-2421	428	6	.	.	PUNCT
ejpam-2421	429	1	quadratics	quadratic	NOUN
ejpam-2421	429	2	,	,	PUNCT
ejpam-2421	429	3	crc	crc	PROPN
ejpam-2421	429	4	press	press	PROPN
ejpam-2421	429	5	boka	boka	PROPN
ejpam-2421	429	6	raton	raton	PROPN
ejpam-2421	429	7	fl	fl	PROPN
ejpam-2421	429	8	.	.	PROPN
ejpam-2421	429	9	,	,	PUNCT
ejpam-2421	429	10	1995	1995	NUM
ejpam-2421	429	11	.	.	PUNCT
ejpam-2421	430	1	[	[	X
ejpam-2421	430	2	3	3	NUM
ejpam-2421	430	3	]	]	PUNCT
ejpam-2421	430	4	a.	a.	NOUN
ejpam-2421	430	5	pekin	pekin	NOUN
ejpam-2421	430	6	and	and	CCONJ
ejpam-2421	430	7	h.	h.	PROPN
ejpam-2421	430	8	i̇scan	i̇scan	PROPN
ejpam-2421	430	9	.	.	PUNCT
ejpam-2421	431	1	continued	continue	VERB
ejpam-2421	431	2	fractions	fraction	NOUN
ejpam-2421	431	3	of	of	ADP
ejpam-2421	431	4	period	period	NOUN
ejpam-2421	431	5	six	six	NUM
ejpam-2421	431	6	and	and	CCONJ
ejpam-2421	431	7	explicit	explicit	ADJ
ejpam-2421	431	8	representations	representation	NOUN
ejpam-2421	431	9	of	of	ADP
ejpam-2421	431	10	fundamental	fundamental	ADJ
ejpam-2421	431	11	units	unit	NOUN
ejpam-2421	431	12	of	of	ADP
ejpam-2421	431	13	some	some	DET
ejpam-2421	431	14	real	real	ADJ
ejpam-2421	431	15	quadratic	quadratic	ADJ
ejpam-2421	431	16	fields	field	NOUN
ejpam-2421	431	17	,	,	PUNCT
ejpam-2421	431	18	journal	journal	NOUN
ejpam-2421	431	19	of	of	ADP
ejpam-2421	431	20	the	the	DET
ejpam-2421	431	21	indian	indian	PROPN
ejpam-2421	431	22	mathematical	mathematical	ADJ
ejpam-2421	431	23	society	society	NOUN
ejpam-2421	431	24	72	72	NUM
ejpam-2421	431	25	:	:	PUNCT
ejpam-2421	431	26	184	184	NUM
ejpam-2421	431	27	-	-	SYM
ejpam-2421	431	28	194	194	NUM
ejpam-2421	431	29	,	,	PUNCT
ejpam-2421	431	30	2005	2005	NUM
ejpam-2421	431	31	.	.	PUNCT
ejpam-2421	432	1	[	[	X
ejpam-2421	432	2	4	4	X
ejpam-2421	432	3	]	]	PUNCT
ejpam-2421	432	4	k.	k.	PROPN
ejpam-2421	432	5	tomita	tomita	PROPN
ejpam-2421	432	6	.	.	PUNCT
ejpam-2421	433	1	explicit	explicit	ADJ
ejpam-2421	433	2	representation	representation	NOUN
ejpam-2421	433	3	of	of	ADP
ejpam-2421	433	4	fundamental	fundamental	ADJ
ejpam-2421	433	5	units	unit	NOUN
ejpam-2421	433	6	of	of	ADP
ejpam-2421	433	7	some	some	DET
ejpam-2421	433	8	quadratic	quadratic	ADJ
ejpam-2421	433	9	fields	field	NOUN
ejpam-2421	433	10	,	,	PUNCT
ejpam-2421	433	11	i.	i.	PROPN
ejpam-2421	433	12	proc	proc	PROPN
ejpam-2421	433	13	.	.	PUNCT
ejpam-2421	434	1	japan	japan	PROPN
ejpam-2421	434	2	acad	acad	PROPN
ejpam-2421	434	3	.	.	PUNCT
ejpam-2421	435	1	ser	ser	PROPN
ejpam-2421	435	2	.	.	PUNCT
ejpam-2421	436	1	a	a	DET
ejpam-2421	436	2	math	math	NOUN
ejpam-2421	436	3	.	.	PUNCT
ejpam-2421	437	1	sci	sci	PROPN
ejpam-2421	437	2	.	.	PROPN
ejpam-2421	437	3	,	,	PUNCT
ejpam-2421	437	4	71	71	NUM
ejpam-2421	437	5	:	:	SYM
ejpam-2421	437	6	41	41	NUM
ejpam-2421	437	7	-	-	SYM
ejpam-2421	437	8	43	43	NUM
ejpam-2421	437	9	,	,	PUNCT
ejpam-2421	437	10	1995	1995	NUM
ejpam-2421	437	11	.	.	PUNCT
ejpam-2421	438	1	[	[	X
ejpam-2421	438	2	5	5	X
ejpam-2421	438	3	]	]	X
ejpam-2421	438	4	y.	y.	PROPN
ejpam-2421	438	5	yamamoto	yamamoto	PROPN
ejpam-2421	438	6	.	.	PUNCT
ejpam-2421	439	1	real	real	ADJ
ejpam-2421	439	2	quadratic	quadratic	ADJ
ejpam-2421	439	3	number	number	NOUN
ejpam-2421	439	4	fields	field	NOUN
ejpam-2421	439	5	with	with	ADP
ejpam-2421	439	6	large	large	ADJ
ejpam-2421	439	7	fundamental	fundamental	ADJ
ejpam-2421	439	8	units	unit	NOUN
ejpam-2421	439	9	.	.	PUNCT
ejpam-2421	440	1	osaka	osaka	PROPN
ejpam-2421	440	2	j.	j.	PROPN
ejpam-2421	440	3	math	math	PROPN
ejpam-2421	440	4	.	.	PUNCT
ejpam-2421	440	5	,	,	PUNCT
ejpam-2421	440	6	8	8	NUM
ejpam-2421	440	7	:	:	SYM
ejpam-2421	440	8	261	261	NUM
ejpam-2421	440	9	-	-	SYM
ejpam-2421	440	10	270	270	NUM
ejpam-2421	440	11	,	,	PUNCT
ejpam-2421	440	12	1971	1971	NUM
ejpam-2421	440	13	.	.	PUNCT