id	sid	tid	token	lemma	pos
ejpam-2029	1	1	european	european	PROPN
ejpam-2029	1	2	journal	journal	PROPN
ejpam-2029	1	3	of	of	ADP
ejpam-2029	1	4	pure	pure	ADJ
ejpam-2029	1	5	and	and	CCONJ
ejpam-2029	1	6	applied	apply	VERB
ejpam-2029	1	7	mathematics	mathematic	NOUN
ejpam-2029	1	8	vol	vol	NOUN
ejpam-2029	1	9	.	.	PUNCT
ejpam-2029	2	1	7	7	NUM
ejpam-2029	2	2	,	,	PUNCT
ejpam-2029	2	3	no	no	INTJ
ejpam-2029	2	4	.	.	NOUN
ejpam-2029	2	5	1	1	NUM
ejpam-2029	2	6	,	,	PUNCT
ejpam-2029	2	7	2014	2014	NUM
ejpam-2029	2	8	,	,	PUNCT
ejpam-2029	2	9	55	55	NUM
ejpam-2029	2	10	-	-	SYM
ejpam-2029	2	11	64	64	NUM
ejpam-2029	2	12	issn	issn	PROPN
ejpam-2029	2	13	1307	1307	NUM
ejpam-2029	2	14	-	-	SYM
ejpam-2029	2	15	5543	5543	NUM
ejpam-2029	2	16	–	–	PUNCT
ejpam-2029	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2029	2	18	explicit	explicit	ADJ
ejpam-2029	2	19	form	form	NOUN
ejpam-2029	2	20	of	of	ADP
ejpam-2029	2	21	the	the	DET
ejpam-2029	2	22	fundamental	fundamental	ADJ
ejpam-2029	2	23	units	unit	NOUN
ejpam-2029	2	24	of	of	ADP
ejpam-2029	2	25	certain	certain	ADJ
ejpam-2029	2	26	real	real	ADJ
ejpam-2029	2	27	quadratic	quadratic	ADJ
ejpam-2029	2	28	fields	field	NOUN
ejpam-2029	2	29	gül	gül	PROPN
ejpam-2029	2	30	karadeniz	karadeniz	PROPN
ejpam-2029	2	31	gözeri∗	gözeri∗	PROPN
ejpam-2029	2	32	,	,	PUNCT
ejpam-2029	2	33	ayten	ayten	ADJ
ejpam-2029	2	34	pekin	pekin	PROPN
ejpam-2029	2	35	department	department	PROPN
ejpam-2029	2	36	of	of	ADP
ejpam-2029	2	37	mathematics	mathematic	NOUN
ejpam-2029	2	38	,	,	PUNCT
ejpam-2029	2	39	faculty	faculty	NOUN
ejpam-2029	2	40	of	of	ADP
ejpam-2029	2	41	science	science	NOUN
ejpam-2029	2	42	,	,	PUNCT
ejpam-2029	2	43	istanbul	istanbul	PROPN
ejpam-2029	2	44	university	university	PROPN
ejpam-2029	2	45	,	,	PUNCT
ejpam-2029	2	46	istanbul	istanbul	PROPN
ejpam-2029	2	47	,	,	PUNCT
ejpam-2029	2	48	turkey	turkey	PROPN
ejpam-2029	2	49	abstract	abstract	NOUN
ejpam-2029	2	50	.	.	PUNCT
ejpam-2029	3	1	in	in	ADP
ejpam-2029	3	2	this	this	DET
ejpam-2029	3	3	paper	paper	NOUN
ejpam-2029	3	4	,	,	PUNCT
ejpam-2029	3	5	for	for	ADP
ejpam-2029	3	6	all	all	DET
ejpam-2029	3	7	real	real	ADJ
ejpam-2029	3	8	quadratic	quadratic	ADJ
ejpam-2029	3	9	fields	field	NOUN
ejpam-2029	3	10	k	k	X
ejpam-2029	3	11	=	=	SYM
ejpam-2029	3	12	q	q	X
ejpam-2029	3	13	(	(	PUNCT
ejpam-2029	3	14	p	p	NOUN
ejpam-2029	3	15	d	d	NOUN
ejpam-2029	3	16	)	)	PUNCT
ejpam-2029	3	17	such	such	ADJ
ejpam-2029	3	18	that	that	SCONJ
ejpam-2029	3	19	d	d	NOUN
ejpam-2029	3	20	is	be	AUX
ejpam-2029	3	21	a	a	DET
ejpam-2029	3	22	positive	positive	ADJ
ejpam-2029	3	23	square	square	ADJ
ejpam-2029	3	24	free	free	ADJ
ejpam-2029	3	25	integer	integer	NOUN
ejpam-2029	3	26	congruent	congruent	NOUN
ejpam-2029	3	27	to	to	ADP
ejpam-2029	3	28	2	2	NUM
ejpam-2029	3	29	or	or	CCONJ
ejpam-2029	3	30	3	3	NUM
ejpam-2029	3	31	modulo	modulo	NOUN
ejpam-2029	3	32	4	4	NUM
ejpam-2029	3	33	and	and	CCONJ
ejpam-2029	3	34	the	the	DET
ejpam-2029	3	35	period	period	NOUN
ejpam-2029	3	36	kd	kd	PROPN
ejpam-2029	3	37	of	of	ADP
ejpam-2029	3	38	the	the	DET
ejpam-2029	3	39	continued	continue	VERB
ejpam-2029	3	40	fraction	fraction	NOUN
ejpam-2029	3	41	expansion	expansion	NOUN
ejpam-2029	3	42	of	of	ADP
ejpam-2029	3	43	the	the	DET
ejpam-2029	3	44	quadratic	quadratic	ADJ
ejpam-2029	3	45	irrational	irrational	ADJ
ejpam-2029	3	46	number	number	NOUN
ejpam-2029	3	47	ωd	ωd	NOUN
ejpam-2029	4	1	=	=	SYM
ejpam-2029	4	2	p	p	NOUN
ejpam-2029	4	3	d	d	NOUN
ejpam-2029	4	4	is	be	AUX
ejpam-2029	4	5	equal	equal	ADJ
ejpam-2029	4	6	to	to	ADP
ejpam-2029	4	7	7	7	NUM
ejpam-2029	4	8	,	,	PUNCT
ejpam-2029	4	9	we	we	PRON
ejpam-2029	4	10	describe	describe	VERB
ejpam-2029	4	11	td	td	NOUN
ejpam-2029	4	12	,	,	PUNCT
ejpam-2029	4	13	ud	ud	INTJ
ejpam-2029	4	14	explicitly	explicitly	ADV
ejpam-2029	4	15	in	in	ADP
ejpam-2029	4	16	the	the	DET
ejpam-2029	4	17	fundamental	fundamental	ADJ
ejpam-2029	4	18	unit	unit	NOUN
ejpam-2029	4	19	εd	εd	ADP
ejpam-2029	4	20	=	=	PUNCT
ejpam-2029	4	21	(	(	PUNCT
ejpam-2029	4	22	td+ud	td+ud	NOUN
ejpam-2029	4	23	p	p	X
ejpam-2029	4	24	d	d	PROPN
ejpam-2029	4	25	2	2	NUM
ejpam-2029	4	26	)	)	PUNCT
ejpam-2029	4	27	(	(	PUNCT
ejpam-2029	4	28	>	>	X
ejpam-2029	4	29	1	1	NUM
ejpam-2029	4	30	)	)	PUNCT
ejpam-2029	4	31	of	of	ADP
ejpam-2029	4	32	q	q	X
ejpam-2029	4	33	(	(	PUNCT
ejpam-2029	4	34	p	p	NOUN
ejpam-2029	4	35	d	d	NOUN
ejpam-2029	4	36	)	)	PUNCT
ejpam-2029	4	37	and	and	CCONJ
ejpam-2029	4	38	d	d	ADP
ejpam-2029	4	39	itself	itself	PRON
ejpam-2029	4	40	by	by	ADP
ejpam-2029	4	41	using	use	VERB
ejpam-2029	4	42	five	five	NUM
ejpam-2029	4	43	parameters	parameter	NOUN
ejpam-2029	4	44	appearing	appear	VERB
ejpam-2029	4	45	in	in	ADP
ejpam-2029	4	46	the	the	DET
ejpam-2029	4	47	continued	continue	VERB
ejpam-2029	4	48	fraction	fraction	NOUN
ejpam-2029	4	49	expansion	expansion	NOUN
ejpam-2029	4	50	of	of	ADP
ejpam-2029	4	51	ωd	ωd	INTJ
ejpam-2029	4	52	.	.	PUNCT
ejpam-2029	5	1	2010	2010	NUM
ejpam-2029	5	2	mathematics	mathematic	NOUN
ejpam-2029	5	3	subject	subject	NOUN
ejpam-2029	5	4	classifications	classification	NOUN
ejpam-2029	5	5	:	:	PUNCT
ejpam-2029	5	6	11a55	11a55	NUM
ejpam-2029	5	7	,	,	PUNCT
ejpam-2029	5	8	11r11	11r11	NUM
ejpam-2029	5	9	,	,	PUNCT
ejpam-2029	5	10	11r27	11r27	NUM
ejpam-2029	5	11	key	key	ADJ
ejpam-2029	5	12	words	word	NOUN
ejpam-2029	5	13	and	and	CCONJ
ejpam-2029	5	14	phrases	phrase	NOUN
ejpam-2029	5	15	:	:	PUNCT
ejpam-2029	5	16	continued	continue	VERB
ejpam-2029	5	17	fraction	fraction	NOUN
ejpam-2029	5	18	,	,	PUNCT
ejpam-2029	5	19	quadratic	quadratic	ADJ
ejpam-2029	5	20	extensions	extension	NOUN
ejpam-2029	5	21	,	,	PUNCT
ejpam-2029	5	22	fundamental	fundamental	ADJ
ejpam-2029	5	23	unit	unit	NOUN
ejpam-2029	5	24	1	1	NUM
ejpam-2029	5	25	.	.	PUNCT
ejpam-2029	6	1	introduction	introduction	NOUN
ejpam-2029	6	2	explicit	explicit	ADJ
ejpam-2029	6	3	form	form	NOUN
ejpam-2029	6	4	of	of	ADP
ejpam-2029	6	5	the	the	DET
ejpam-2029	6	6	fundamental	fundamental	ADJ
ejpam-2029	6	7	units	unit	NOUN
ejpam-2029	6	8	of	of	ADP
ejpam-2029	6	9	real	real	ADJ
ejpam-2029	6	10	quadratic	quadratic	ADJ
ejpam-2029	6	11	fieldsq	fieldsq	NOUN
ejpam-2029	6	12	(	(	PUNCT
ejpam-2029	6	13	p	p	NOUN
ejpam-2029	6	14	d	d	NOUN
ejpam-2029	6	15	)	)	PUNCT
ejpam-2029	6	16	where	where	SCONJ
ejpam-2029	6	17	d	d	NOUN
ejpam-2029	6	18	is	be	AUX
ejpam-2029	6	19	congruent	congruent	ADJ
ejpam-2029	6	20	to	to	ADP
ejpam-2029	6	21	1	1	NUM
ejpam-2029	6	22	modulo	modulo	NOUN
ejpam-2029	6	23	4	4	NUM
ejpam-2029	6	24	and	and	CCONJ
ejpam-2029	6	25	the	the	DET
ejpam-2029	6	26	period	period	NOUN
ejpam-2029	6	27	kd	kd	PROPN
ejpam-2029	6	28	in	in	ADP
ejpam-2029	6	29	the	the	DET
ejpam-2029	6	30	continued	continue	VERB
ejpam-2029	6	31	fraction	fraction	NOUN
ejpam-2029	6	32	expansion	expansion	NOUN
ejpam-2029	6	33	of	of	ADP
ejpam-2029	6	34	the	the	DET
ejpam-2029	6	35	quadratic	quadratic	ADJ
ejpam-2029	6	36	irrational	irrational	ADJ
ejpam-2029	6	37	number	number	NOUN
ejpam-2029	6	38	ωd	ωd	NOUN
ejpam-2029	6	39	in	in	ADP
ejpam-2029	6	40	q	q	PROPN
ejpam-2029	6	41	(	(	PUNCT
ejpam-2029	6	42	p	p	NOUN
ejpam-2029	6	43	d	d	NOUN
ejpam-2029	6	44	)	)	PUNCT
ejpam-2029	6	45	is	be	AUX
ejpam-2029	6	46	equal	equal	ADJ
ejpam-2029	6	47	to	to	ADP
ejpam-2029	6	48	3	3	NUM
ejpam-2029	6	49	and	and	CCONJ
ejpam-2029	6	50	4	4	NUM
ejpam-2029	6	51	,	,	PUNCT
ejpam-2029	6	52	5	5	NUM
ejpam-2029	6	53	was	be	AUX
ejpam-2029	6	54	described	describe	VERB
ejpam-2029	6	55	in	in	ADP
ejpam-2029	6	56	[	[	X
ejpam-2029	6	57	5	5	NUM
ejpam-2029	6	58	,	,	PUNCT
ejpam-2029	6	59	6	6	NUM
ejpam-2029	6	60	]	]	PUNCT
ejpam-2029	6	61	respectively	respectively	ADV
ejpam-2029	6	62	.	.	PUNCT
ejpam-2029	7	1	later	later	ADV
ejpam-2029	7	2	in	in	ADP
ejpam-2029	7	3	[	[	X
ejpam-2029	7	4	3	3	NUM
ejpam-2029	7	5	]	]	PUNCT
ejpam-2029	7	6	,	,	PUNCT
ejpam-2029	7	7	explicit	explicit	ADJ
ejpam-2029	7	8	form	form	NOUN
ejpam-2029	7	9	of	of	ADP
ejpam-2029	7	10	the	the	DET
ejpam-2029	7	11	fundamental	fundamental	ADJ
ejpam-2029	7	12	units	unit	NOUN
ejpam-2029	7	13	of	of	ADP
ejpam-2029	7	14	all	all	DET
ejpam-2029	7	15	real	real	ADJ
ejpam-2029	7	16	quadratic	quadratic	ADJ
ejpam-2029	7	17	fields	field	NOUN
ejpam-2029	7	18	q	q	NOUN
ejpam-2029	7	19	(	(	PUNCT
ejpam-2029	7	20	p	p	NOUN
ejpam-2029	7	21	d	d	NOUN
ejpam-2029	7	22	)	)	PUNCT
ejpam-2029	7	23	such	such	ADJ
ejpam-2029	7	24	that	that	SCONJ
ejpam-2029	7	25	the	the	DET
ejpam-2029	7	26	period	period	NOUN
ejpam-2029	7	27	in	in	ADP
ejpam-2029	7	28	the	the	DET
ejpam-2029	7	29	continued	continue	VERB
ejpam-2029	7	30	fraction	fraction	NOUN
ejpam-2029	7	31	expansion	expansion	NOUN
ejpam-2029	7	32	of	of	ADP
ejpam-2029	7	33	the	the	DET
ejpam-2029	7	34	quadratic	quadratic	ADJ
ejpam-2029	7	35	irrational	irrational	ADJ
ejpam-2029	7	36	number	number	NOUN
ejpam-2029	7	37	ωd	ωd	NOUN
ejpam-2029	7	38	in	in	ADP
ejpam-2029	7	39	q	q	PROPN
ejpam-2029	7	40	(	(	PUNCT
ejpam-2029	7	41	p	p	NOUN
ejpam-2029	7	42	d	d	NOUN
ejpam-2029	7	43	)	)	PUNCT
ejpam-2029	7	44	is	be	AUX
ejpam-2029	7	45	equal	equal	ADJ
ejpam-2029	7	46	to	to	ADP
ejpam-2029	7	47	6	6	NUM
ejpam-2029	7	48	was	be	AUX
ejpam-2029	7	49	obtained	obtain	VERB
ejpam-2029	7	50	.	.	PUNCT
ejpam-2029	8	1	in	in	ADP
ejpam-2029	8	2	this	this	DET
ejpam-2029	8	3	paper	paper	NOUN
ejpam-2029	8	4	,	,	PUNCT
ejpam-2029	8	5	for	for	ADP
ejpam-2029	8	6	all	all	DET
ejpam-2029	8	7	real	real	ADJ
ejpam-2029	8	8	quadratic	quadratic	ADJ
ejpam-2029	8	9	fields	field	NOUN
ejpam-2029	8	10	q	q	NOUN
ejpam-2029	8	11	(	(	PUNCT
ejpam-2029	8	12	p	p	NOUN
ejpam-2029	8	13	d	d	NOUN
ejpam-2029	8	14	)	)	PUNCT
ejpam-2029	8	15	such	such	ADJ
ejpam-2029	8	16	that	that	SCONJ
ejpam-2029	8	17	d	d	NOUN
ejpam-2029	8	18	is	be	AUX
ejpam-2029	8	19	congruent	congruent	ADJ
ejpam-2029	8	20	to	to	ADP
ejpam-2029	8	21	1	1	NUM
ejpam-2029	8	22	modulo	modulo	NOUN
ejpam-2029	8	23	4	4	NUM
ejpam-2029	8	24	and	and	CCONJ
ejpam-2029	8	25	the	the	DET
ejpam-2029	8	26	period	period	NOUN
ejpam-2029	8	27	kd	kd	PROPN
ejpam-2029	8	28	in	in	ADP
ejpam-2029	8	29	the	the	DET
ejpam-2029	8	30	continued	continue	VERB
ejpam-2029	8	31	fraction	fraction	NOUN
ejpam-2029	8	32	expansion	expansion	NOUN
ejpam-2029	8	33	of	of	ADP
ejpam-2029	8	34	the	the	DET
ejpam-2029	8	35	quadratic	quadratic	ADJ
ejpam-2029	8	36	irrational	irrational	ADJ
ejpam-2029	8	37	number	number	NOUN
ejpam-2029	8	38	ωd	ωd	NOUN
ejpam-2029	8	39	=	=	NOUN
ejpam-2029	9	1	1	1	NUM
ejpam-2029	9	2	+	+	NUM
ejpam-2029	9	3	p	p	NOUN
ejpam-2029	9	4	d	d	PROPN
ejpam-2029	9	5	2	2	NUM
ejpam-2029	9	6	is	be	AUX
ejpam-2029	9	7	equal	equal	ADJ
ejpam-2029	9	8	to	to	ADP
ejpam-2029	9	9	7	7	NUM
ejpam-2029	9	10	,	,	PUNCT
ejpam-2029	9	11	we	we	PRON
ejpam-2029	9	12	described	describe	VERB
ejpam-2029	9	13	td	td	NOUN
ejpam-2029	9	14	,	,	PUNCT
ejpam-2029	9	15	ud	ud	INTJ
ejpam-2029	9	16	explicitly	explicitly	ADV
ejpam-2029	9	17	in	in	ADP
ejpam-2029	9	18	the	the	DET
ejpam-2029	9	19	fundamental	fundamental	ADJ
ejpam-2029	9	20	unit	unit	NOUN
ejpam-2029	9	21	εd	εd	ADP
ejpam-2029	9	22	of	of	ADP
ejpam-2029	9	23	q	q	PROPN
ejpam-2029	9	24	(	(	PUNCT
ejpam-2029	9	25	p	p	NOUN
ejpam-2029	9	26	d	d	NOUN
ejpam-2029	9	27	)	)	PUNCT
ejpam-2029	9	28	and	and	CCONJ
ejpam-2029	9	29	d	d	ADP
ejpam-2029	9	30	itself	itself	PRON
ejpam-2029	9	31	by	by	ADP
ejpam-2029	9	32	using	use	VERB
ejpam-2029	9	33	five	five	NUM
ejpam-2029	9	34	parameters	parameter	NOUN
ejpam-2029	9	35	appearing	appear	VERB
ejpam-2029	9	36	in	in	ADP
ejpam-2029	9	37	the	the	DET
ejpam-2029	9	38	continued	continue	VERB
ejpam-2029	9	39	fraction	fraction	NOUN
ejpam-2029	9	40	expansion	expansion	NOUN
ejpam-2029	9	41	of	of	ADP
ejpam-2029	9	42	ωd	ωd	INTJ
ejpam-2029	9	43	.	.	PUNCT
ejpam-2029	10	1	in	in	ADP
ejpam-2029	10	2	this	this	DET
ejpam-2029	10	3	paper	paper	NOUN
ejpam-2029	10	4	,	,	PUNCT
ejpam-2029	10	5	we	we	PRON
ejpam-2029	10	6	consider	consider	VERB
ejpam-2029	10	7	all	all	DET
ejpam-2029	10	8	real	real	ADJ
ejpam-2029	10	9	quadratic	quadratic	ADJ
ejpam-2029	10	10	fields	field	NOUN
ejpam-2029	10	11	q	q	NOUN
ejpam-2029	10	12	(	(	PUNCT
ejpam-2029	10	13	p	p	NOUN
ejpam-2029	10	14	d	d	NOUN
ejpam-2029	10	15	)	)	PUNCT
ejpam-2029	10	16	where	where	SCONJ
ejpam-2029	10	17	d	d	PROPN
ejpam-2029	10	18	≡	≡	PROPN
ejpam-2029	10	19	2,3(mod4	2,3(mod4	NUM
ejpam-2029	10	20	)	)	PUNCT
ejpam-2029	10	21	and	and	CCONJ
ejpam-2029	10	22	the	the	DET
ejpam-2029	10	23	period	period	NOUN
ejpam-2029	10	24	kd	kd	PROPN
ejpam-2029	10	25	of	of	ADP
ejpam-2029	10	26	the	the	DET
ejpam-2029	10	27	continued	continue	VERB
ejpam-2029	10	28	fraction	fraction	NOUN
ejpam-2029	10	29	expansion	expansion	NOUN
ejpam-2029	10	30	ofωd	ofωd	NOUN
ejpam-2029	10	31	=	=	PUNCT
ejpam-2029	11	1	p	p	NOUN
ejpam-2029	11	2	d	d	NOUN
ejpam-2029	11	3	is	be	AUX
ejpam-2029	11	4	equal	equal	ADJ
ejpam-2029	11	5	to	to	ADP
ejpam-2029	11	6	7	7	NUM
ejpam-2029	11	7	and	and	CCONJ
ejpam-2029	11	8	describe	describe	VERB
ejpam-2029	11	9	explicitly	explicitly	ADV
ejpam-2029	11	10	coefficients	coefficient	NOUN
ejpam-2029	11	11	td	td	NOUN
ejpam-2029	12	1	and	and	CCONJ
ejpam-2029	12	2	ud	ud	INTJ
ejpam-2029	12	3	in	in	ADP
ejpam-2029	12	4	the	the	DET
ejpam-2029	12	5	fundamental	fundamental	ADJ
ejpam-2029	12	6	unit	unit	NOUN
ejpam-2029	12	7	εd	εd	ADP
ejpam-2029	12	8	=	=	PUNCT
ejpam-2029	12	9	(	(	PUNCT
ejpam-2029	12	10	td+ud	td+ud	NOUN
ejpam-2029	12	11	p	p	X
ejpam-2029	12	12	d	d	PROPN
ejpam-2029	12	13	2	2	NUM
ejpam-2029	12	14	)	)	PUNCT
ejpam-2029	12	15	(	(	PUNCT
ejpam-2029	12	16	>	>	X
ejpam-2029	12	17	1	1	NUM
ejpam-2029	12	18	)	)	PUNCT
ejpam-2029	12	19	of	of	ADP
ejpam-2029	12	20	q	q	X
ejpam-2029	12	21	(	(	PUNCT
ejpam-2029	12	22	p	p	NOUN
ejpam-2029	12	23	d	d	NOUN
ejpam-2029	12	24	)	)	PUNCT
ejpam-2029	12	25	and	and	CCONJ
ejpam-2029	12	26	d	d	ADP
ejpam-2029	12	27	itself	itself	PRON
ejpam-2029	12	28	by	by	ADP
ejpam-2029	12	29	using	use	VERB
ejpam-2029	12	30	five	five	NUM
ejpam-2029	12	31	parameters	parameter	NOUN
ejpam-2029	12	32	appearing	appear	VERB
ejpam-2029	12	33	in	in	ADP
ejpam-2029	12	34	the	the	DET
ejpam-2029	12	35	continued	continue	VERB
ejpam-2029	12	36	fraction	fraction	NOUN
ejpam-2029	12	37	expansion	expansion	NOUN
ejpam-2029	12	38	of	of	ADP
ejpam-2029	12	39	ωd	ωd	INTJ
ejpam-2029	12	40	.	.	PUNCT
ejpam-2029	13	1	∗corresponding	∗corresponde	VERB
ejpam-2029	13	2	author	author	NOUN
ejpam-2029	13	3	.	.	PUNCT
ejpam-2029	14	1	email	email	NOUN
ejpam-2029	14	2	addresses	address	NOUN
ejpam-2029	14	3	:	:	PUNCT
ejpam-2029	14	4	gulkaradeniz@istanbul.edu.tr	gulkaradeniz@istanbul.edu.tr	PROPN
ejpam-2029	14	5	(	(	PUNCT
ejpam-2029	14	6	g.	g.	PROPN
ejpam-2029	14	7	karadeniz	karadeniz	PROPN
ejpam-2029	14	8	gözeri	gözeri	PROPN
ejpam-2029	14	9	)	)	PUNCT
ejpam-2029	14	10	,	,	PUNCT
ejpam-2029	14	11	aypekin@istanbul.edu.tr	aypekin@istanbul.edu.tr	INTJ
ejpam-2029	14	12	(	(	PUNCT
ejpam-2029	14	13	a.	a.	NOUN
ejpam-2029	14	14	pekin	pekin	PROPN
ejpam-2029	14	15	)	)	PUNCT
ejpam-2029	14	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2029	15	1	55	55	NUM
ejpam-2029	15	2	c	c	X
ejpam-2029	15	3	©	©	NOUN
ejpam-2029	15	4	2014	2014	NUM
ejpam-2029	15	5	ejpam	ejpam	NOUN
ejpam-2029	15	6	all	all	DET
ejpam-2029	15	7	rights	right	NOUN
ejpam-2029	15	8	reserved	reserve	VERB
ejpam-2029	15	9	.	.	PUNCT
ejpam-2029	16	1	g.	g.	PROPN
ejpam-2029	16	2	gözeri	gözeri	PROPN
ejpam-2029	16	3	,	,	PUNCT
ejpam-2029	16	4	a.	a.	NOUN
ejpam-2029	16	5	pekin	pekin	PROPN
ejpam-2029	16	6	/	/	SYM
ejpam-2029	16	7	eur	eur	PROPN
ejpam-2029	16	8	.	.	PUNCT
ejpam-2029	17	1	j.	j.	PROPN
ejpam-2029	17	2	pure	pure	PROPN
ejpam-2029	17	3	appl	appl	PROPN
ejpam-2029	17	4	.	.	PROPN
ejpam-2029	17	5	math	math	PROPN
ejpam-2029	17	6	,	,	PUNCT
ejpam-2029	17	7	7	7	NUM
ejpam-2029	17	8	(	(	PUNCT
ejpam-2029	17	9	2014	2014	NUM
ejpam-2029	17	10	)	)	PUNCT
ejpam-2029	17	11	,	,	PUNCT
ejpam-2029	17	12	55	55	NUM
ejpam-2029	17	13	-	-	SYM
ejpam-2029	17	14	64	64	NUM
ejpam-2029	17	15	56	56	NUM
ejpam-2029	17	16	let	let	VERB
ejpam-2029	17	17	i(d	i(d	NOUN
ejpam-2029	17	18	)	)	PUNCT
ejpam-2029	17	19	be	be	VERB
ejpam-2029	17	20	the	the	DET
ejpam-2029	17	21	set	set	NOUN
ejpam-2029	17	22	of	of	ADP
ejpam-2029	17	23	all	all	DET
ejpam-2029	17	24	quadratic	quadratic	ADJ
ejpam-2029	17	25	irrational	irrational	ADJ
ejpam-2029	17	26	numbers	number	NOUN
ejpam-2029	17	27	in	in	ADP
ejpam-2029	17	28	q	q	PROPN
ejpam-2029	17	29	(	(	PUNCT
ejpam-2029	17	30	p	p	NOUN
ejpam-2029	17	31	d	d	NOUN
ejpam-2029	17	32	)	)	PUNCT
ejpam-2029	17	33	.	.	PUNCT
ejpam-2029	18	1	for	for	ADP
ejpam-2029	18	2	an	an	DET
ejpam-2029	18	3	element	element	NOUN
ejpam-2029	18	4	ξ	ξ	PROPN
ejpam-2029	18	5	of	of	ADP
ejpam-2029	18	6	i(d	i(d	NOUN
ejpam-2029	18	7	)	)	PUNCT
ejpam-2029	18	8	if	if	SCONJ
ejpam-2029	18	9	ξ	ξ	X
ejpam-2029	18	10	>	>	SYM
ejpam-2029	18	11	1	1	NUM
ejpam-2029	18	12	,	,	PUNCT
ejpam-2029	18	13	−1	−1	NOUN
ejpam-2029	18	14	<	<	X
ejpam-2029	18	15	ξ	ξ	X
ejpam-2029	18	16	′	′	NOUN
ejpam-2029	18	17	<	<	X
ejpam-2029	18	18	0	0	PUNCT
ejpam-2029	19	1	then	then	ADV
ejpam-2029	19	2	ξ	ξ	PROPN
ejpam-2029	19	3	is	be	AUX
ejpam-2029	19	4	called	call	VERB
ejpam-2029	19	5	reduced	reduce	VERB
ejpam-2029	19	6	,	,	PUNCT
ejpam-2029	19	7	where	where	SCONJ
ejpam-2029	19	8	ξ	ξ	X
ejpam-2029	19	9	′	′	NOUN
ejpam-2029	19	10	is	be	AUX
ejpam-2029	19	11	the	the	DET
ejpam-2029	19	12	conjugate	conjugate	NOUN
ejpam-2029	19	13	of	of	ADP
ejpam-2029	19	14	ξ	ξ	PROPN
ejpam-2029	19	15	with	with	ADP
ejpam-2029	19	16	respect	respect	NOUN
ejpam-2029	19	17	to	to	ADP
ejpam-2029	19	18	q.	q.	PROPN
ejpam-2029	19	19	more	more	ADJ
ejpam-2029	19	20	information	information	NOUN
ejpam-2029	19	21	on	on	ADP
ejpam-2029	19	22	reduced	reduced	ADJ
ejpam-2029	19	23	irrational	irrational	ADJ
ejpam-2029	19	24	numbers	number	NOUN
ejpam-2029	19	25	may	may	AUX
ejpam-2029	19	26	be	be	AUX
ejpam-2029	19	27	found	find	VERB
ejpam-2029	19	28	in	in	ADP
ejpam-2029	19	29	[	[	X
ejpam-2029	19	30	2	2	NUM
ejpam-2029	19	31	,	,	PUNCT
ejpam-2029	19	32	7	7	NUM
ejpam-2029	19	33	]	]	PUNCT
ejpam-2029	19	34	.	.	PUNCT
ejpam-2029	20	1	we	we	PRON
ejpam-2029	20	2	denote	denote	VERB
ejpam-2029	20	3	by	by	ADP
ejpam-2029	20	4	r(d	r(d	NOUN
ejpam-2029	20	5	)	)	PUNCT
ejpam-2029	20	6	the	the	DET
ejpam-2029	20	7	set	set	NOUN
ejpam-2029	20	8	of	of	ADP
ejpam-2029	20	9	all	all	DET
ejpam-2029	20	10	reduced	reduce	VERB
ejpam-2029	20	11	quadratic	quadratic	ADJ
ejpam-2029	20	12	irrational	irrational	ADJ
ejpam-2029	20	13	numbers	number	NOUN
ejpam-2029	20	14	in	in	ADP
ejpam-2029	20	15	i(d	i(d	NOUN
ejpam-2029	20	16	)	)	PUNCT
ejpam-2029	20	17	.	.	PUNCT
ejpam-2029	21	1	it	it	PRON
ejpam-2029	21	2	is	be	AUX
ejpam-2029	21	3	well	well	ADV
ejpam-2029	21	4	known	know	VERB
ejpam-2029	21	5	that	that	SCONJ
ejpam-2029	21	6	if	if	SCONJ
ejpam-2029	21	7	an	an	DET
ejpam-2029	21	8	element	element	NOUN
ejpam-2029	21	9	ξ	ξ	PROPN
ejpam-2029	21	10	of	of	ADP
ejpam-2029	21	11	i(d	i(d	NOUN
ejpam-2029	21	12	)	)	PUNCT
ejpam-2029	21	13	is	be	AUX
ejpam-2029	21	14	in	in	ADP
ejpam-2029	21	15	r(d	r(d	NOUN
ejpam-2029	21	16	)	)	PUNCT
ejpam-2029	21	17	then	then	ADV
ejpam-2029	21	18	the	the	DET
ejpam-2029	21	19	continued	continue	VERB
ejpam-2029	21	20	fractional	fractional	ADJ
ejpam-2029	21	21	expansion	expansion	NOUN
ejpam-2029	21	22	of	of	ADP
ejpam-2029	21	23	ξ	ξ	PROPN
ejpam-2029	21	24	is	be	AUX
ejpam-2029	21	25	purely	purely	ADV
ejpam-2029	21	26	periodic	periodic	ADJ
ejpam-2029	21	27	.	.	PUNCT
ejpam-2029	22	1	moreover	moreover	ADV
ejpam-2029	22	2	,	,	PUNCT
ejpam-2029	22	3	the	the	DET
ejpam-2029	22	4	denominator	denominator	NOUN
ejpam-2029	22	5	of	of	ADP
ejpam-2029	22	6	its	its	PRON
ejpam-2029	22	7	modular	modular	ADJ
ejpam-2029	22	8	automorphism	automorphism	NOUN
ejpam-2029	22	9	is	be	AUX
ejpam-2029	22	10	equal	equal	ADJ
ejpam-2029	22	11	to	to	ADP
ejpam-2029	22	12	fundamental	fundamental	ADJ
ejpam-2029	22	13	unit	unit	NOUN
ejpam-2029	22	14	εd	εd	ADP
ejpam-2029	22	15	of	of	ADP
ejpam-2029	22	16	q	q	PROPN
ejpam-2029	22	17	(	(	PUNCT
ejpam-2029	22	18	p	p	NOUN
ejpam-2029	22	19	d	d	NOUN
ejpam-2029	22	20	)	)	PUNCT
ejpam-2029	22	21	and	and	CCONJ
ejpam-2029	22	22	the	the	DET
ejpam-2029	22	23	norm	norm	NOUN
ejpam-2029	22	24	of	of	ADP
ejpam-2029	22	25	εd	εd	NOUN
ejpam-2029	22	26	is	be	AUX
ejpam-2029	22	27	(	(	PUNCT
ejpam-2029	22	28	−1)kd	−1)kd	PROPN
ejpam-2029	22	29	[	[	X
ejpam-2029	22	30	4	4	NUM
ejpam-2029	22	31	]	]	PUNCT
ejpam-2029	22	32	.	.	PUNCT
ejpam-2029	23	1	in	in	ADP
ejpam-2029	23	2	this	this	DET
ejpam-2029	23	3	paper	paper	NOUN
ejpam-2029	23	4	[	[	X
ejpam-2029	23	5	x]means	x]means	ADP
ejpam-2029	23	6	the	the	DET
ejpam-2029	23	7	greatest	great	ADJ
ejpam-2029	23	8	integer	integer	NOUN
ejpam-2029	23	9	less	less	ADJ
ejpam-2029	23	10	than	than	ADP
ejpam-2029	23	11	or	or	CCONJ
ejpam-2029	23	12	equal	equal	ADJ
ejpam-2029	23	13	to	to	ADP
ejpam-2029	23	14	x	x	PUNCT
ejpam-2029	23	15	and	and	CCONJ
ejpam-2029	23	16	continued	continued	ADJ
ejpam-2029	23	17	fraction	fraction	NOUN
ejpam-2029	23	18	with	with	ADP
ejpam-2029	23	19	period	period	NOUN
ejpam-2029	23	20	k	k	PROPN
ejpam-2029	23	21	is	be	AUX
ejpam-2029	23	22	generally	generally	ADV
ejpam-2029	23	23	denoted	denote	VERB
ejpam-2029	23	24	by	by	ADP
ejpam-2029	23	25	[	[	X
ejpam-2029	23	26	a0	a0	PROPN
ejpam-2029	23	27	,	,	PUNCT
ejpam-2029	23	28	a1	a1	NOUN
ejpam-2029	23	29	,	,	PUNCT
ejpam-2029	23	30	a2	a2	PROPN
ejpam-2029	23	31	,	,	PUNCT
ejpam-2029	23	32	.	.	PUNCT
ejpam-2029	23	33	.	.	PUNCT
ejpam-2029	24	1	.	.	PUNCT
ejpam-2029	25	1	,	,	PUNCT
ejpam-2029	25	2	ak	ak	PROPN
ejpam-2029	25	3	]	]	PROPN
ejpam-2029	25	4	.	.	PUNCT
ejpam-2029	26	1	2	2	X
ejpam-2029	26	2	.	.	X
ejpam-2029	26	3	preliminaries	preliminary	NOUN
ejpam-2029	26	4	in	in	ADP
ejpam-2029	26	5	this	this	DET
ejpam-2029	26	6	section	section	NOUN
ejpam-2029	26	7	some	some	PRON
ejpam-2029	26	8	of	of	ADP
ejpam-2029	26	9	the	the	DET
ejpam-2029	26	10	important	important	ADJ
ejpam-2029	26	11	required	require	VERB
ejpam-2029	26	12	preliminaries	preliminary	NOUN
ejpam-2029	26	13	and	and	CCONJ
ejpam-2029	26	14	lemmas	lemma	NOUN
ejpam-2029	26	15	are	be	AUX
ejpam-2029	26	16	given	give	VERB
ejpam-2029	26	17	.	.	PUNCT
ejpam-2029	27	1	for	for	ADP
ejpam-2029	27	2	any	any	DET
ejpam-2029	27	3	square	square	ADJ
ejpam-2029	27	4	-	-	PUNCT
ejpam-2029	27	5	free	free	ADJ
ejpam-2029	27	6	positive	positive	ADJ
ejpam-2029	27	7	integer	integer	NOUN
ejpam-2029	27	8	d	d	NOUN
ejpam-2029	27	9	,	,	PUNCT
ejpam-2029	27	10	we	we	PRON
ejpam-2029	27	11	can	can	AUX
ejpam-2029	27	12	put	put	VERB
ejpam-2029	27	13	d	d	NOUN
ejpam-2029	27	14	=	=	SYM
ejpam-2029	27	15	a2	a2	PROPN
ejpam-2029	27	16	+	+	CCONJ
ejpam-2029	27	17	b	b	NOUN
ejpam-2029	27	18	with	with	ADP
ejpam-2029	27	19	a	a	DET
ejpam-2029	27	20	,	,	PUNCT
ejpam-2029	27	21	b	b	PROPN
ejpam-2029	27	22	∈	∈	PROPN
ejpam-2029	27	23	z	z	PROPN
ejpam-2029	27	24	,	,	PUNCT
ejpam-2029	27	25	0	0	PUNCT
ejpam-2029	27	26	<	<	X
ejpam-2029	27	27	b	b	X
ejpam-2029	27	28	≤	≤	NUM
ejpam-2029	27	29	2a	2a	NUM
ejpam-2029	27	30	.	.	PUNCT
ejpam-2029	28	1	here	here	ADV
ejpam-2029	28	2	,	,	PUNCT
ejpam-2029	28	3	since	since	SCONJ
ejpam-2029	28	4	p	p	PROPN
ejpam-2029	28	5	d	d	X
ejpam-2029	28	6	−	−	PROPN
ejpam-2029	28	7	1	1	NUM
ejpam-2029	28	8	<	<	X
ejpam-2029	28	9	a	a	PRON
ejpam-2029	28	10	<	<	X
ejpam-2029	28	11	p	p	X
ejpam-2029	28	12	d	d	X
ejpam-2029	28	13	the	the	DET
ejpam-2029	28	14	integers	integer	NOUN
ejpam-2029	28	15	a	a	PRON
ejpam-2029	28	16	and	and	CCONJ
ejpam-2029	28	17	b	b	NOUN
ejpam-2029	28	18	are	be	AUX
ejpam-2029	28	19	uniquely	uniquely	ADV
ejpam-2029	28	20	determined	determine	VERB
ejpam-2029	28	21	by	by	ADP
ejpam-2029	28	22	d.	d.	PROPN
ejpam-2029	28	23	in	in	ADP
ejpam-2029	28	24	this	this	DET
ejpam-2029	28	25	paper	paper	NOUN
ejpam-2029	28	26	we	we	PRON
ejpam-2029	28	27	will	will	AUX
ejpam-2029	28	28	concern	concern	VERB
ejpam-2029	28	29	with	with	ADP
ejpam-2029	28	30	all	all	DET
ejpam-2029	28	31	real	real	ADJ
ejpam-2029	28	32	quadratic	quadratic	ADJ
ejpam-2029	28	33	fields	field	NOUN
ejpam-2029	28	34	q	q	NOUN
ejpam-2029	28	35	(	(	PUNCT
ejpam-2029	28	36	p	p	NOUN
ejpam-2029	28	37	d	d	NOUN
ejpam-2029	28	38	)	)	PUNCT
ejpam-2029	28	39	such	such	ADJ
ejpam-2029	28	40	that	that	SCONJ
ejpam-2029	28	41	d	d	NOUN
ejpam-2029	28	42	is	be	AUX
ejpam-2029	28	43	congruent	congruent	ADJ
ejpam-2029	28	44	to	to	ADP
ejpam-2029	28	45	2	2	NUM
ejpam-2029	28	46	or	or	CCONJ
ejpam-2029	28	47	3	3	NUM
ejpam-2029	28	48	modulo	modulo	NOUN
ejpam-2029	28	49	4	4	NUM
ejpam-2029	28	50	and	and	CCONJ
ejpam-2029	28	51	the	the	DET
ejpam-2029	28	52	period	period	NOUN
ejpam-2029	28	53	kd	kd	PROPN
ejpam-2029	28	54	is	be	AUX
ejpam-2029	28	55	equal	equal	ADJ
ejpam-2029	28	56	to	to	ADP
ejpam-2029	28	57	7	7	NUM
ejpam-2029	28	58	.	.	PUNCT
ejpam-2029	29	1	let	let	VERB
ejpam-2029	29	2	d	d	NOUN
ejpam-2029	29	3	=	=	SYM
ejpam-2029	29	4	a2	a2	PROPN
ejpam-2029	29	5	+	+	CCONJ
ejpam-2029	29	6	b	b	PROPN
ejpam-2029	29	7	≡	≡	PROPN
ejpam-2029	29	8	2	2	NUM
ejpam-2029	29	9	,	,	PUNCT
ejpam-2029	29	10	3(mod4	3(mod4	NUM
ejpam-2029	29	11	)	)	PUNCT
ejpam-2029	29	12	,	,	PUNCT
ejpam-2029	29	13	then	then	ADV
ejpam-2029	29	14	we	we	PRON
ejpam-2029	29	15	consider	consider	VERB
ejpam-2029	29	16	the	the	DET
ejpam-2029	29	17	following	follow	VERB
ejpam-2029	29	18	three	three	NUM
ejpam-2029	29	19	cases	case	NOUN
ejpam-2029	29	20	:	:	PUNCT
ejpam-2029	29	21	case	case	NOUN
ejpam-2029	29	22	1	1	X
ejpam-2029	29	23	.	.	PUNCT
ejpam-2029	30	1	if	if	SCONJ
ejpam-2029	30	2	b	b	NOUN
ejpam-2029	30	3	is	be	AUX
ejpam-2029	30	4	congruent	congruent	ADJ
ejpam-2029	30	5	to	to	ADP
ejpam-2029	30	6	1	1	NUM
ejpam-2029	30	7	modulo	modulo	NOUN
ejpam-2029	30	8	4	4	NUM
ejpam-2029	30	9	,	,	PUNCT
ejpam-2029	30	10	then	then	ADV
ejpam-2029	30	11	d	d	X
ejpam-2029	30	12	can	can	AUX
ejpam-2029	30	13	only	only	ADV
ejpam-2029	30	14	be	be	AUX
ejpam-2029	30	15	congruent	congruent	ADJ
ejpam-2029	30	16	to	to	ADP
ejpam-2029	30	17	2	2	NUM
ejpam-2029	30	18	modulo	modulo	NOUN
ejpam-2029	30	19	4	4	NUM
ejpam-2029	30	20	.	.	PUNCT
ejpam-2029	31	1	and	and	CCONJ
ejpam-2029	31	2	for	for	ADP
ejpam-2029	31	3	this	this	DET
ejpam-2029	31	4	case	case	NOUN
ejpam-2029	31	5	it	it	PRON
ejpam-2029	31	6	is	be	AUX
ejpam-2029	31	7	obvious	obvious	ADJ
ejpam-2029	31	8	that	that	SCONJ
ejpam-2029	31	9	a	a	PRON
ejpam-2029	31	10	is	be	AUX
ejpam-2029	31	11	odd	odd	ADJ
ejpam-2029	31	12	.	.	PUNCT
ejpam-2029	32	1	case	case	NOUN
ejpam-2029	32	2	2	2	NUM
ejpam-2029	32	3	.	.	PUNCT
ejpam-2029	33	1	if	if	SCONJ
ejpam-2029	33	2	b	b	NOUN
ejpam-2029	33	3	is	be	AUX
ejpam-2029	33	4	congruent	congruent	ADJ
ejpam-2029	33	5	to	to	ADP
ejpam-2029	33	6	2	2	NUM
ejpam-2029	33	7	modulo	modulo	NOUN
ejpam-2029	33	8	4	4	NUM
ejpam-2029	33	9	,	,	PUNCT
ejpam-2029	33	10	then	then	ADV
ejpam-2029	33	11	d	d	X
ejpam-2029	33	12	can	can	AUX
ejpam-2029	33	13	be	be	AUX
ejpam-2029	33	14	congruent	congruent	ADJ
ejpam-2029	33	15	to	to	ADP
ejpam-2029	33	16	2	2	NUM
ejpam-2029	33	17	or	or	CCONJ
ejpam-2029	33	18	3	3	NUM
ejpam-2029	33	19	modulo	modulo	NOUN
ejpam-2029	33	20	4	4	NUM
ejpam-2029	33	21	.	.	PUNCT
ejpam-2029	34	1	in	in	ADP
ejpam-2029	34	2	this	this	DET
ejpam-2029	34	3	case	case	NOUN
ejpam-2029	34	4	,	,	PUNCT
ejpam-2029	34	5	a	a	PRON
ejpam-2029	34	6	is	be	AUX
ejpam-2029	34	7	even	even	ADV
ejpam-2029	34	8	when	when	SCONJ
ejpam-2029	34	9	d	d	NOUN
ejpam-2029	34	10	is	be	AUX
ejpam-2029	34	11	congruent	congruent	ADJ
ejpam-2029	34	12	to	to	ADP
ejpam-2029	34	13	2	2	NUM
ejpam-2029	34	14	modulo	modulo	NOUN
ejpam-2029	34	15	4	4	NUM
ejpam-2029	34	16	and	and	CCONJ
ejpam-2029	34	17	a	a	PRON
ejpam-2029	34	18	is	be	AUX
ejpam-2029	34	19	odd	odd	ADJ
ejpam-2029	34	20	when	when	SCONJ
ejpam-2029	34	21	d	d	NOUN
ejpam-2029	34	22	is	be	AUX
ejpam-2029	34	23	congruent	congruent	ADJ
ejpam-2029	34	24	to	to	ADP
ejpam-2029	34	25	3	3	NUM
ejpam-2029	34	26	modulo	modulo	NOUN
ejpam-2029	34	27	4	4	NUM
ejpam-2029	34	28	.	.	NOUN
ejpam-2029	34	29	case	case	NOUN
ejpam-2029	34	30	3	3	X
ejpam-2029	34	31	.	.	PUNCT
ejpam-2029	35	1	if	if	SCONJ
ejpam-2029	35	2	b	b	NOUN
ejpam-2029	35	3	is	be	AUX
ejpam-2029	35	4	congruent	congruent	ADJ
ejpam-2029	35	5	to	to	ADP
ejpam-2029	35	6	3	3	NUM
ejpam-2029	35	7	modulo	modulo	NOUN
ejpam-2029	35	8	4	4	NUM
ejpam-2029	35	9	,	,	PUNCT
ejpam-2029	35	10	then	then	ADV
ejpam-2029	35	11	d	d	X
ejpam-2029	35	12	can	can	AUX
ejpam-2029	35	13	only	only	ADV
ejpam-2029	35	14	be	be	AUX
ejpam-2029	35	15	congruent	congruent	ADJ
ejpam-2029	35	16	to	to	ADP
ejpam-2029	35	17	3	3	NUM
ejpam-2029	35	18	modulo	modulo	NOUN
ejpam-2029	35	19	4	4	NUM
ejpam-2029	35	20	.	.	PUNCT
ejpam-2029	36	1	and	and	CCONJ
ejpam-2029	36	2	for	for	ADP
ejpam-2029	36	3	this	this	DET
ejpam-2029	36	4	case	case	NOUN
ejpam-2029	36	5	it	it	PRON
ejpam-2029	36	6	is	be	AUX
ejpam-2029	36	7	obvious	obvious	ADJ
ejpam-2029	36	8	that	that	SCONJ
ejpam-2029	36	9	a	a	PRON
ejpam-2029	36	10	is	be	AUX
ejpam-2029	36	11	even	even	ADV
ejpam-2029	36	12	.	.	PUNCT
ejpam-2029	37	1	lemma	lemma	PROPN
ejpam-2029	37	2	1	1	NUM
ejpam-2029	37	3	.	.	PUNCT
ejpam-2029	38	1	for	for	ADP
ejpam-2029	38	2	a	a	DET
ejpam-2029	38	3	square	square	ADJ
ejpam-2029	38	4	-	-	PUNCT
ejpam-2029	38	5	free	free	ADJ
ejpam-2029	38	6	positive	positive	ADJ
ejpam-2029	38	7	integer	integer	NOUN
ejpam-2029	38	8	d	d	X
ejpam-2029	38	9	congruent	congruent	ADJ
ejpam-2029	38	10	to	to	ADP
ejpam-2029	38	11	2	2	NUM
ejpam-2029	38	12	or	or	CCONJ
ejpam-2029	38	13	3	3	NUM
ejpam-2029	38	14	modulo	modulo	NOUN
ejpam-2029	38	15	4	4	NUM
ejpam-2029	38	16	,	,	PUNCT
ejpam-2029	38	17	we	we	PRON
ejpam-2029	38	18	put	put	VERB
ejpam-2029	38	19	ωd	ωd	NOUN
ejpam-2029	39	1	=	=	SYM
ejpam-2029	39	2	p	p	PROPN
ejpam-2029	39	3	d	d	PROPN
ejpam-2029	39	4	,	,	PUNCT
ejpam-2029	39	5	q0	q0	NOUN
ejpam-2029	39	6	=	=	PUNCT
ejpam-2029	40	1	[	[	X
ejpam-2029	40	2	ωd	ωd	X
ejpam-2029	40	3	]	]	X
ejpam-2029	40	4	,	,	PUNCT
ejpam-2029	40	5	ωr	ωr	ADV
ejpam-2029	40	6	=	=	PUNCT
ejpam-2029	40	7	q0	q0	PROPN
ejpam-2029	41	1	+	+	NOUN
ejpam-2029	41	2	ωd	ωd	NOUN
ejpam-2029	41	3	.	.	PUNCT
ejpam-2029	42	1	then	then	ADV
ejpam-2029	42	2	ωd	ωd	INTJ
ejpam-2029	42	3	/∈	/∈	PUNCT
ejpam-2029	42	4	r(d	r(d	NOUN
ejpam-2029	42	5	)	)	PUNCT
ejpam-2029	42	6	,	,	PUNCT
ejpam-2029	42	7	but	but	CCONJ
ejpam-2029	42	8	ωr	ωr	ADP
ejpam-2029	42	9	∈	∈	PROPN
ejpam-2029	42	10	r(d	r(d	NOUN
ejpam-2029	42	11	)	)	PUNCT
ejpam-2029	42	12	holds	hold	VERB
ejpam-2029	42	13	.	.	PUNCT
ejpam-2029	43	1	moreover	moreover	ADV
ejpam-2029	43	2	,	,	PUNCT
ejpam-2029	43	3	for	for	ADP
ejpam-2029	43	4	the	the	DET
ejpam-2029	43	5	period	period	NOUN
ejpam-2029	43	6	k	k	PROPN
ejpam-2029	43	7	of	of	ADP
ejpam-2029	43	8	ωr	ωr	PROPN
ejpam-2029	43	9	,	,	PUNCT
ejpam-2029	43	10	we	we	PRON
ejpam-2029	43	11	get	get	VERB
ejpam-2029	43	12	ωr	ωr	ADV
ejpam-2029	43	13	=	=	PUNCT
ejpam-2029	44	1	[	[	X
ejpam-2029	44	2	2q0	2q0	NUM
ejpam-2029	44	3	,	,	PUNCT
ejpam-2029	44	4	q1	q1	PROPN
ejpam-2029	44	5	,	,	PUNCT
ejpam-2029	44	6	.	.	PUNCT
ejpam-2029	44	7	.	.	PUNCT
ejpam-2029	45	1	.	.	PUNCT
ejpam-2029	46	1	,	,	PUNCT
ejpam-2029	46	2	qk−1	qk−1	PROPN
ejpam-2029	46	3	]	]	PUNCT
ejpam-2029	46	4	and	and	CCONJ
ejpam-2029	46	5	ωd	ωd	NOUN
ejpam-2029	46	6	=	=	SYM
ejpam-2029	47	1	[	[	X
ejpam-2029	47	2	q0	q0	X
ejpam-2029	47	3	,	,	PUNCT
ejpam-2029	47	4	q1	q1	PROPN
ejpam-2029	47	5	,	,	PUNCT
ejpam-2029	47	6	.	.	PUNCT
ejpam-2029	47	7	.	.	PUNCT
ejpam-2029	48	1	.	.	PUNCT
ejpam-2029	49	1	,	,	PUNCT
ejpam-2029	49	2	qk−1	qk−1	PROPN
ejpam-2029	49	3	,	,	PUNCT
ejpam-2029	49	4	2q0	2q0	NUM
ejpam-2029	49	5	]	]	PUNCT
ejpam-2029	49	6	.	.	PUNCT
ejpam-2029	50	1	furthermore	furthermore	ADV
ejpam-2029	50	2	,	,	PUNCT
ejpam-2029	50	3	let	let	VERB
ejpam-2029	50	4	ωr	ωr	VERB
ejpam-2029	50	5	=	=	PUNCT
ejpam-2029	50	6	(	(	PUNCT
ejpam-2029	50	7	pk−1ωr+pk−2	pk−1ωr+pk−2	NOUN
ejpam-2029	50	8	)	)	PUNCT
ejpam-2029	50	9	(	(	PUNCT
ejpam-2029	50	10	qk−1ωr+qk−2	qk−1ωr+qk−2	NOUN
ejpam-2029	50	11	)	)	PUNCT
ejpam-2029	50	12	=	=	PUNCT
ejpam-2029	51	1	[	[	X
ejpam-2029	51	2	2q0	2q0	NUM
ejpam-2029	51	3	,	,	PUNCT
ejpam-2029	51	4	q1	q1	PROPN
ejpam-2029	51	5	,	,	PUNCT
ejpam-2029	51	6	.	.	PUNCT
ejpam-2029	51	7	.	.	PUNCT
ejpam-2029	52	1	.	.	PUNCT
ejpam-2029	53	1	,	,	PUNCT
ejpam-2029	53	2	qk−1,ωr	qk−1,ωr	PROPN
ejpam-2029	53	3	]	]	PUNCT
ejpam-2029	53	4	be	be	VERB
ejpam-2029	53	5	a	a	DET
ejpam-2029	53	6	modular	modular	ADJ
ejpam-2029	53	7	automorphism	automorphism	NOUN
ejpam-2029	53	8	of	of	ADP
ejpam-2029	53	9	ωr	ωr	NOUN
ejpam-2029	53	10	,	,	PUNCT
ejpam-2029	53	11	then	then	ADV
ejpam-2029	53	12	the	the	DET
ejpam-2029	53	13	fundamental	fundamental	ADJ
ejpam-2029	53	14	unit	unit	NOUN
ejpam-2029	53	15	εd	εd	ADP
ejpam-2029	53	16	of	of	ADP
ejpam-2029	53	17	q	q	PROPN
ejpam-2029	53	18	(	(	PUNCT
ejpam-2029	53	19	p	p	NOUN
ejpam-2029	53	20	d	d	NOUN
ejpam-2029	53	21	)	)	PUNCT
ejpam-2029	53	22	is	be	AUX
ejpam-2029	53	23	given	give	VERB
ejpam-2029	53	24	by	by	ADP
ejpam-2029	53	25	the	the	DET
ejpam-2029	53	26	following	follow	VERB
ejpam-2029	53	27	formula	formula	NOUN
ejpam-2029	53	28	:	:	PUNCT
ejpam-2029	53	29	εd	εd	NOUN
ejpam-2029	53	30	=	=	PUNCT
ejpam-2029	53	31	(	(	PUNCT
ejpam-2029	53	32	td	td	NOUN
ejpam-2029	54	1	+	+	CCONJ
ejpam-2029	54	2	ud	ud	INTJ
ejpam-2029	54	3	p	p	X
ejpam-2029	54	4	d	d	PROPN
ejpam-2029	54	5	2	2	NUM
ejpam-2029	54	6	)	)	PUNCT
ejpam-2029	54	7	>	>	X
ejpam-2029	55	1	1	1	NUM
ejpam-2029	55	2	,	,	PUNCT
ejpam-2029	55	3	td	td	NOUN
ejpam-2029	55	4	=	=	PUNCT
ejpam-2029	55	5	2q0qk−1	2q0qk−1	X
ejpam-2029	55	6	+	+	NOUN
ejpam-2029	55	7	2qk−2	2qk−2	NUM
ejpam-2029	55	8	,	,	PUNCT
ejpam-2029	55	9	ud	ud	ADP
ejpam-2029	55	10	=	=	NOUN
ejpam-2029	55	11	2qk−1	2qk−1	NUM
ejpam-2029	55	12	where	where	SCONJ
ejpam-2029	55	13	q	q	NOUN
ejpam-2029	55	14	i	i	PRON
ejpam-2029	55	15	is	be	AUX
ejpam-2029	55	16	determined	determine	VERB
ejpam-2029	55	17	by	by	ADP
ejpam-2029	55	18	q−1	q−1	PROPN
ejpam-2029	55	19	=	=	PUNCT
ejpam-2029	55	20	0	0	PROPN
ejpam-2029	55	21	,	,	PUNCT
ejpam-2029	55	22	q0	q0	NOUN
ejpam-2029	55	23	=	=	SYM
ejpam-2029	55	24	1	1	NUM
ejpam-2029	55	25	,	,	PUNCT
ejpam-2029	55	26	q	q	NOUN
ejpam-2029	56	1	i+1	i+1	NOUN
ejpam-2029	56	2	=	=	SYM
ejpam-2029	56	3	qi+1q	qi+1q	NOUN
ejpam-2029	56	4	i	i	PRON
ejpam-2029	56	5	+	+	PROPN
ejpam-2029	56	6	q	q	PROPN
ejpam-2029	56	7	i−1	i−1	PROPN
ejpam-2029	56	8	,	,	PUNCT
ejpam-2029	56	9	(	(	PUNCT
ejpam-2029	56	10	i	i	PRON
ejpam-2029	56	11	≥	≥	VERB
ejpam-2029	56	12	0	0	NUM
ejpam-2029	56	13	)	)	PUNCT
ejpam-2029	56	14	.	.	PUNCT
ejpam-2029	57	1	proof	proof	NOUN
ejpam-2029	57	2	.	.	PUNCT
ejpam-2029	58	1	see	see	VERB
ejpam-2029	58	2	[	[	X
ejpam-2029	58	3	5	5	NUM
ejpam-2029	58	4	,	,	PUNCT
ejpam-2029	58	5	lemma	lemma	PROPN
ejpam-2029	58	6	1	1	NUM
ejpam-2029	58	7	]	]	PUNCT
ejpam-2029	58	8	.	.	PUNCT
ejpam-2029	59	1	lemma	lemma	PROPN
ejpam-2029	59	2	2	2	NUM
ejpam-2029	59	3	.	.	X
ejpam-2029	60	1	for	for	ADP
ejpam-2029	60	2	a	a	DET
ejpam-2029	60	3	square	square	ADJ
ejpam-2029	60	4	-	-	PUNCT
ejpam-2029	60	5	free	free	ADJ
ejpam-2029	60	6	positive	positive	ADJ
ejpam-2029	60	7	integer	integer	NOUN
ejpam-2029	60	8	d	d	NOUN
ejpam-2029	60	9	,	,	PUNCT
ejpam-2029	60	10	we	we	PRON
ejpam-2029	60	11	put	put	VERB
ejpam-2029	60	12	d	d	NOUN
ejpam-2029	60	13	=	=	SYM
ejpam-2029	60	14	a2	a2	PROPN
ejpam-2029	60	15	+	+	CCONJ
ejpam-2029	60	16	b	b	X
ejpam-2029	60	17	(	(	PUNCT
ejpam-2029	60	18	0	0	NUM
ejpam-2029	60	19	<	<	X
ejpam-2029	60	20	b	b	X
ejpam-2029	60	21	≤	≤	NUM
ejpam-2029	60	22	2a	2a	NUM
ejpam-2029	60	23	)	)	PUNCT
ejpam-2029	60	24	,	,	PUNCT
ejpam-2029	60	25	a	a	PRON
ejpam-2029	60	26	,	,	PUNCT
ejpam-2029	60	27	b	b	PROPN
ejpam-2029	60	28	∈	∈	PROPN
ejpam-2029	61	1	z.	z.	PROPN
ejpam-2029	62	1	moreover	moreover	ADV
ejpam-2029	62	2	let	let	VERB
ejpam-2029	62	3	ωi	ωi	NOUN
ejpam-2029	62	4	=	=	PUNCT
ejpam-2029	62	5	`	`	PUNCT
ejpam-2029	62	6	i	i	PRON
ejpam-2029	62	7	+	+	CCONJ
ejpam-2029	62	8	1	1	NUM
ejpam-2029	62	9	ωi+1	ωi+1	NUM
ejpam-2029	62	10	(	(	PUNCT
ejpam-2029	62	11	`	`	PUNCT
ejpam-2029	62	12	i	i	PRON
ejpam-2029	62	13	=	=	PUNCT
ejpam-2029	63	1	[	[	X
ejpam-2029	63	2	ωi	ωi	X
ejpam-2029	63	3	]	]	X
ejpam-2029	63	4	,	,	PUNCT
ejpam-2029	63	5	i	i	PRON
ejpam-2029	63	6	≥	≥	VERB
ejpam-2029	63	7	0	0	NUM
ejpam-2029	63	8	)	)	PUNCT
ejpam-2029	63	9	be	be	AUX
ejpam-2029	63	10	the	the	DET
ejpam-2029	63	11	continued	continue	VERB
ejpam-2029	63	12	fraction	fraction	NOUN
ejpam-2029	63	13	expansion	expansion	NOUN
ejpam-2029	63	14	of	of	ADP
ejpam-2029	63	15	ω	ω	X
ejpam-2029	63	16	=	=	SYM
ejpam-2029	63	17	ω0	ω0	PROPN
ejpam-2029	63	18	g.	g.	PROPN
ejpam-2029	63	19	gözeri	gözeri	PROPN
ejpam-2029	63	20	,	,	PUNCT
ejpam-2029	63	21	a.	a.	NOUN
ejpam-2029	63	22	pekin	pekin	PROPN
ejpam-2029	63	23	/	/	SYM
ejpam-2029	63	24	eur	eur	PROPN
ejpam-2029	63	25	.	.	PUNCT
ejpam-2029	64	1	j.	j.	PROPN
ejpam-2029	64	2	pure	pure	PROPN
ejpam-2029	64	3	appl	appl	PROPN
ejpam-2029	64	4	.	.	PROPN
ejpam-2029	64	5	math	math	PROPN
ejpam-2029	64	6	,	,	PUNCT
ejpam-2029	64	7	7	7	NUM
ejpam-2029	64	8	(	(	PUNCT
ejpam-2029	64	9	2014	2014	NUM
ejpam-2029	64	10	)	)	PUNCT
ejpam-2029	64	11	,	,	PUNCT
ejpam-2029	64	12	55	55	NUM
ejpam-2029	64	13	-	-	SYM
ejpam-2029	64	14	64	64	NUM
ejpam-2029	64	15	57	57	NUM
ejpam-2029	64	16	in	in	ADP
ejpam-2029	64	17	r(d	r(d	NOUN
ejpam-2029	64	18	)	)	PUNCT
ejpam-2029	64	19	.	.	PUNCT
ejpam-2029	65	1	then	then	ADV
ejpam-2029	65	2	each	each	DET
ejpam-2029	65	3	ωi	ωi	PROPN
ejpam-2029	65	4	is	be	AUX
ejpam-2029	65	5	expressed	express	VERB
ejpam-2029	65	6	in	in	ADP
ejpam-2029	65	7	the	the	DET
ejpam-2029	65	8	form	form	NOUN
ejpam-2029	65	9	ωi	ωi	X
ejpam-2029	65	10	=	=	SYM
ejpam-2029	65	11	a−ri+	a−ri+	PROPN
ejpam-2029	65	12	p	p	PROPN
ejpam-2029	65	13	d	d	X
ejpam-2029	65	14	ci	ci	PROPN
ejpam-2029	65	15	(	(	PUNCT
ejpam-2029	65	16	ci	ci	PROPN
ejpam-2029	65	17	,	,	PUNCT
ejpam-2029	65	18	ri	ri	PROPN
ejpam-2029	65	19	∈	∈	PROPN
ejpam-2029	65	20	z	z	PROPN
ejpam-2029	65	21	)	)	PUNCT
ejpam-2029	65	22	,	,	PUNCT
ejpam-2029	65	23	and	and	CCONJ
ejpam-2029	65	24	`	`	PUNCT
ejpam-2029	65	25	i	i	PROPN
ejpam-2029	65	26	,	,	PUNCT
ejpam-2029	65	27	ci	ci	PROPN
ejpam-2029	65	28	,	,	PUNCT
ejpam-2029	65	29	ri	ri	PROPN
ejpam-2029	65	30	can	can	AUX
ejpam-2029	65	31	be	be	AUX
ejpam-2029	65	32	obtained	obtain	VERB
ejpam-2029	65	33	from	from	ADP
ejpam-2029	65	34	the	the	DET
ejpam-2029	65	35	following	follow	VERB
ejpam-2029	65	36	recurrence	recurrence	NOUN
ejpam-2029	65	37	formula	formula	NOUN
ejpam-2029	65	38	:	:	PUNCT
ejpam-2029	65	39	ω0	ω0	ADV
ejpam-2029	65	40	=	=	SYM
ejpam-2029	65	41	a−	a−	NOUN
ejpam-2029	65	42	r0	r0	NOUN
ejpam-2029	65	43	+	+	NOUN
ejpam-2029	65	44	p	p	PROPN
ejpam-2029	65	45	d	d	PROPN
ejpam-2029	65	46	c0	c0	NOUN
ejpam-2029	65	47	,	,	PUNCT
ejpam-2029	65	48	2a−ri	2a−ri	NUM
ejpam-2029	65	49	=	=	PUNCT
ejpam-2029	65	50	ci`i	ci`i	X
ejpam-2029	65	51	+	+	CCONJ
ejpam-2029	65	52	ri+1	ri+1	NOUN
ejpam-2029	65	53	,	,	PUNCT
ejpam-2029	65	54	ci+1	ci+1	PROPN
ejpam-2029	65	55	=	=	SYM
ejpam-2029	65	56	ci−1	ci−1	PROPN
ejpam-2029	65	57	+	+	CCONJ
ejpam-2029	65	58	(	(	PUNCT
ejpam-2029	65	59	ri+1−	ri+1−	PROPN
ejpam-2029	65	60	ri)`i	ri)`i	PROPN
ejpam-2029	65	61	(	(	PUNCT
ejpam-2029	65	62	i	i	PRON
ejpam-2029	65	63	≥	≥	NOUN
ejpam-2029	65	64	0	0	NUM
ejpam-2029	65	65	)	)	PUNCT
ejpam-2029	65	66	,	,	PUNCT
ejpam-2029	65	67	where	where	SCONJ
ejpam-2029	65	68	0≤	0≤	NUM
ejpam-2029	65	69	ri+1	ri+1	PROPN
ejpam-2029	65	70	<	<	X
ejpam-2029	65	71	ci	ci	PROPN
ejpam-2029	65	72	,	,	PUNCT
ejpam-2029	65	73	c−1	c−1	PROPN
ejpam-2029	65	74	=	=	PUNCT
ejpam-2029	65	75	(	(	PUNCT
ejpam-2029	65	76	b+	b+	NUM
ejpam-2029	65	77	2ar0−	2ar0−	NUM
ejpam-2029	65	78	r0	r0	NOUN
ejpam-2029	65	79	2	2	NUM
ejpam-2029	65	80	)	)	PUNCT
ejpam-2029	65	81	c0	c0	NOUN
ejpam-2029	65	82	.	.	PUNCT
ejpam-2029	66	1	moreover	moreover	ADV
ejpam-2029	66	2	for	for	ADP
ejpam-2029	66	3	the	the	DET
ejpam-2029	66	4	period	period	NOUN
ejpam-2029	66	5	k	k	X
ejpam-2029	66	6	≥	≥	NUM
ejpam-2029	66	7	1	1	NUM
ejpam-2029	66	8	of	of	ADP
ejpam-2029	66	9	ω0	ω0	NOUN
ejpam-2029	66	10	,	,	PUNCT
ejpam-2029	66	11	we	we	PRON
ejpam-2029	66	12	get	get	VERB
ejpam-2029	66	13	`	`	PUNCT
ejpam-2029	66	14	i	i	PRON
ejpam-2029	66	15	=	=	NOUN
ejpam-2029	66	16	`	`	PUNCT
ejpam-2029	66	17	k−i	k−i	NOUN
ejpam-2029	66	18	(	(	PUNCT
ejpam-2029	66	19	1≤	1≤	NUM
ejpam-2029	66	20	i	i	PROPN
ejpam-2029	66	21	≤	≤	PROPN
ejpam-2029	66	22	k−	k−	PROPN
ejpam-2029	66	23	1	1	NUM
ejpam-2029	66	24	)	)	PUNCT
ejpam-2029	66	25	,	,	PUNCT
ejpam-2029	66	26	ri	ri	PROPN
ejpam-2029	67	1	=	=	NOUN
ejpam-2029	67	2	rk−i+1	rk−i+1	PROPN
ejpam-2029	67	3	,	,	PUNCT
ejpam-2029	67	4	ci	ci	NOUN
ejpam-2029	67	5	=	=	NOUN
ejpam-2029	67	6	ck−i	ck−i	NOUN
ejpam-2029	67	7	(	(	PUNCT
ejpam-2029	67	8	1≤	1≤	INTJ
ejpam-2029	67	9	i	i	X
ejpam-2029	67	10	≤	≤	PUNCT
ejpam-2029	67	11	k	k	X
ejpam-2029	67	12	)	)	PUNCT
ejpam-2029	67	13	.	.	PUNCT
ejpam-2029	68	1	proof	proof	NOUN
ejpam-2029	68	2	.	.	PUNCT
ejpam-2029	69	1	see	see	VERB
ejpam-2029	69	2	[	[	X
ejpam-2029	69	3	1	1	NUM
ejpam-2029	69	4	,	,	PUNCT
ejpam-2029	69	5	proposition	proposition	NOUN
ejpam-2029	69	6	1	1	NUM
ejpam-2029	69	7	]	]	PUNCT
ejpam-2029	69	8	.	.	PUNCT
ejpam-2029	70	1	lemma	lemma	PROPN
ejpam-2029	70	2	3	3	X
ejpam-2029	70	3	.	.	PUNCT
ejpam-2029	71	1	for	for	ADP
ejpam-2029	71	2	a	a	DET
ejpam-2029	71	3	square	square	ADJ
ejpam-2029	71	4	-	-	PUNCT
ejpam-2029	71	5	free	free	ADJ
ejpam-2029	71	6	positive	positive	ADJ
ejpam-2029	71	7	integer	integer	NOUN
ejpam-2029	71	8	d	d	X
ejpam-2029	71	9	congruent	congruent	ADJ
ejpam-2029	71	10	to	to	ADP
ejpam-2029	71	11	2	2	NUM
ejpam-2029	71	12	or	or	CCONJ
ejpam-2029	71	13	3	3	NUM
ejpam-2029	71	14	modulo	modulo	NOUN
ejpam-2029	71	15	4	4	NUM
ejpam-2029	71	16	,	,	PUNCT
ejpam-2029	71	17	we	we	PRON
ejpam-2029	71	18	put	put	VERB
ejpam-2029	71	19	ωd	ωd	NOUN
ejpam-2029	72	1	=	=	SYM
ejpam-2029	72	2	p	p	PROPN
ejpam-2029	72	3	d	d	PROPN
ejpam-2029	72	4	,	,	PUNCT
ejpam-2029	72	5	q0	q0	NOUN
ejpam-2029	72	6	=	=	PUNCT
ejpam-2029	73	1	[	[	X
ejpam-2029	73	2	ωd	ωd	X
ejpam-2029	73	3	]	]	PUNCT
ejpam-2029	73	4	and	and	CCONJ
ejpam-2029	73	5	ωr	ωr	NOUN
ejpam-2029	73	6	=	=	NOUN
ejpam-2029	73	7	q0+ωd	q0+ωd	NOUN
ejpam-2029	73	8	.	.	PUNCT
ejpam-2029	74	1	if	if	SCONJ
ejpam-2029	74	2	we	we	PRON
ejpam-2029	74	3	put	put	VERB
ejpam-2029	74	4	ω	ω	NOUN
ejpam-2029	74	5	=	=	NOUN
ejpam-2029	74	6	ωr	ωr	X
ejpam-2029	74	7	in	in	ADP
ejpam-2029	74	8	lemma	lemma	PROPN
ejpam-2029	74	9	2	2	NUM
ejpam-2029	74	10	,	,	PUNCT
ejpam-2029	74	11	then	then	ADV
ejpam-2029	74	12	we	we	PRON
ejpam-2029	74	13	have	have	VERB
ejpam-2029	74	14	the	the	DET
ejpam-2029	74	15	following	follow	VERB
ejpam-2029	74	16	recurrence	recurrence	NOUN
ejpam-2029	74	17	formula	formula	NOUN
ejpam-2029	74	18	:	:	PUNCT
ejpam-2029	74	19	r0	r0	NOUN
ejpam-2029	74	20	=	=	NOUN
ejpam-2029	74	21	r1	r1	PROPN
ejpam-2029	74	22	=	=	SYM
ejpam-2029	74	23	0	0	NUM
ejpam-2029	74	24	,	,	PUNCT
ejpam-2029	74	25	c0	c0	NOUN
ejpam-2029	74	26	=	=	PROPN
ejpam-2029	74	27	1	1	NUM
ejpam-2029	74	28	,	,	PUNCT
ejpam-2029	75	1	c1	c1	NOUN
ejpam-2029	75	2	=	=	SYM
ejpam-2029	75	3	b	b	PROPN
ejpam-2029	75	4	,	,	PUNCT
ejpam-2029	75	5	`	`	PUNCT
ejpam-2029	75	6	0	0	PUNCT
ejpam-2029	76	1	=	=	NUM
ejpam-2029	76	2	2q0,`i	2q0,`i	NUM
ejpam-2029	76	3	=	=	SYM
ejpam-2029	76	4	qi	qi	PROPN
ejpam-2029	76	5	(	(	PUNCT
ejpam-2029	76	6	1≤	1≤	NUM
ejpam-2029	76	7	i	i	PROPN
ejpam-2029	76	8	≤	≤	PROPN
ejpam-2029	76	9	k−	k−	PROPN
ejpam-2029	76	10	1	1	NUM
ejpam-2029	76	11	)	)	PUNCT
ejpam-2029	76	12	.	.	PUNCT
ejpam-2029	77	1	proof	proof	NOUN
ejpam-2029	77	2	.	.	PUNCT
ejpam-2029	78	1	the	the	DET
ejpam-2029	78	2	proof	proof	NOUN
ejpam-2029	78	3	follows	follow	VERB
ejpam-2029	78	4	easily	easily	ADV
ejpam-2029	78	5	from	from	ADP
ejpam-2029	78	6	lemma	lemma	PROPN
ejpam-2029	78	7	2	2	NUM
ejpam-2029	78	8	.	.	NOUN
ejpam-2029	78	9	3	3	NUM
ejpam-2029	78	10	.	.	X
ejpam-2029	78	11	main	main	ADJ
ejpam-2029	78	12	results	result	NOUN
ejpam-2029	78	13	theorem	theorem	VERB
ejpam-2029	78	14	1	1	NUM
ejpam-2029	78	15	.	.	X
ejpam-2029	79	1	for	for	ADP
ejpam-2029	79	2	a	a	DET
ejpam-2029	79	3	positive	positive	ADJ
ejpam-2029	79	4	square	square	ADJ
ejpam-2029	79	5	-	-	PUNCT
ejpam-2029	79	6	free	free	ADJ
ejpam-2029	79	7	integer	integer	NOUN
ejpam-2029	79	8	d	d	X
ejpam-2029	79	9	congruent	congruent	ADJ
ejpam-2029	79	10	to	to	ADP
ejpam-2029	79	11	2	2	NUM
ejpam-2029	79	12	modulo	modulo	NOUN
ejpam-2029	79	13	4	4	NUM
ejpam-2029	79	14	,	,	PUNCT
ejpam-2029	79	15	we	we	PRON
ejpam-2029	79	16	assume	assume	VERB
ejpam-2029	79	17	kd	kd	PROPN
ejpam-2029	79	18	=	=	PROPN
ejpam-2029	79	19	7	7	X
ejpam-2029	79	20	.	.	PUNCT
ejpam-2029	80	1	then	then	ADV
ejpam-2029	80	2	,	,	PUNCT
ejpam-2029	80	3	if	if	SCONJ
ejpam-2029	80	4	b	b	NOUN
ejpam-2029	80	5	is	be	AUX
ejpam-2029	80	6	congruent	congruent	ADJ
ejpam-2029	80	7	to	to	ADP
ejpam-2029	80	8	1	1	NUM
ejpam-2029	80	9	modulo	modulo	NOUN
ejpam-2029	80	10	4	4	NUM
ejpam-2029	80	11	,	,	PUNCT
ejpam-2029	80	12	we	we	PRON
ejpam-2029	80	13	get	get	VERB
ejpam-2029	80	14	ωd	ωd	NOUN
ejpam-2029	81	1	=	=	SYM
ejpam-2029	82	1	[	[	X
ejpam-2029	82	2	a,`1,`2,`3,`3,`2,`1	a,`1,`2,`3,`3,`2,`1	PROPN
ejpam-2029	82	3	,	,	PUNCT
ejpam-2029	82	4	2a	2a	NUM
ejpam-2029	82	5	]	]	PUNCT
ejpam-2029	82	6	for	for	ADP
ejpam-2029	82	7	three	three	NUM
ejpam-2029	82	8	positive	positive	ADJ
ejpam-2029	82	9	integers	integer	NOUN
ejpam-2029	82	10	`	`	PUNCT
ejpam-2029	82	11	1	1	NUM
ejpam-2029	82	12	,	,	PUNCT
ejpam-2029	82	13	`	`	PUNCT
ejpam-2029	82	14	2	2	NUM
ejpam-2029	82	15	,	,	PUNCT
ejpam-2029	82	16	`	`	PUNCT
ejpam-2029	82	17	3	3	NUM
ejpam-2029	82	18	such	such	ADJ
ejpam-2029	82	19	that	that	SCONJ
ejpam-2029	82	20	`	`	PUNCT
ejpam-2029	82	21	i	i	PRON
ejpam-2029	82	22	≥	≥	VERB
ejpam-2029	82	23	1	1	NUM
ejpam-2029	82	24	(	(	PUNCT
ejpam-2029	82	25	i	i	NOUN
ejpam-2029	82	26	=	=	SYM
ejpam-2029	82	27	1,2	1,2	NUM
ejpam-2029	82	28	,	,	PUNCT
ejpam-2029	82	29	3	3	NUM
ejpam-2029	82	30	)	)	PUNCT
ejpam-2029	82	31	and	and	CCONJ
ejpam-2029	82	32	then	then	ADV
ejpam-2029	82	33	(	(	PUNCT
ejpam-2029	82	34	td	td	NOUN
ejpam-2029	82	35	,	,	PUNCT
ejpam-2029	82	36	ud	ud	INTJ
ejpam-2029	82	37	)	)	PUNCT
ejpam-2029	82	38	=	=	SYM
ejpam-2029	83	1	(	(	PUNCT
ejpam-2029	83	2	2[a(a	2[a(a	NUM
ejpam-2029	83	3	2	2	NUM
ejpam-2029	83	4	+	+	NUM
ejpam-2029	83	5	b2	b2	NOUN
ejpam-2029	83	6	)	)	PUNCT
ejpam-2029	84	1	+	+	CCONJ
ejpam-2029	84	2	bc	bc	PROPN
ejpam-2029	84	3	+	+	CCONJ
ejpam-2029	84	4	a`2	a`2	PROPN
ejpam-2029	84	5	]	]	X
ejpam-2029	84	6	,	,	PUNCT
ejpam-2029	84	7	2(a2	2(a2	NUM
ejpam-2029	84	8	+	+	NUM
ejpam-2029	84	9	b2	b2	NOUN
ejpam-2029	84	10	)	)	PUNCT
ejpam-2029	84	11	)	)	PUNCT
ejpam-2029	84	12	and	and	CCONJ
ejpam-2029	84	13	d	d	NOUN
ejpam-2029	84	14	=	=	PUNCT
ejpam-2029	84	15	a2r2	a2r2	X
ejpam-2029	84	16	+	+	NOUN
ejpam-2029	84	17	2rd+	2rd+	ADJ
ejpam-2029	84	18	e	e	NOUN
ejpam-2029	84	19	hold	hold	VERB
ejpam-2029	84	20	.	.	PUNCT
ejpam-2029	85	1	moreover	moreover	ADV
ejpam-2029	85	2	r	r	NOUN
ejpam-2029	85	3	and	and	CCONJ
ejpam-2029	85	4	s	s	NOUN
ejpam-2029	85	5	are	be	AUX
ejpam-2029	85	6	positive	positive	ADJ
ejpam-2029	85	7	integers	integer	NOUN
ejpam-2029	85	8	determined	determine	VERB
ejpam-2029	85	9	uniquely	uniquely	ADV
ejpam-2029	85	10	by	by	ADP
ejpam-2029	85	11	a	a	DET
ejpam-2029	85	12	=	=	NOUN
ejpam-2029	85	13	ar	ar	NOUN
ejpam-2029	85	14	+	+	NOUN
ejpam-2029	85	15	`	`	PUNCT
ejpam-2029	85	16	1s	1s	NUM
ejpam-2029	85	17	a2+b2−	a2+b2−	ADV
ejpam-2029	85	18	c2−	c2−	NOUN
ejpam-2029	85	19	`	`	PUNCT
ejpam-2029	85	20	2	2	NUM
ejpam-2029	85	21	2	2	NUM
ejpam-2029	85	22	=	=	SYM
ejpam-2029	85	23	2rb−	2rb−	NUM
ejpam-2029	85	24	2s(a+	2s(a+	PROPN
ejpam-2029	85	25	b`3	b`3	NOUN
ejpam-2029	85	26	)	)	PUNCT
ejpam-2029	85	27	g.	g.	PROPN
ejpam-2029	85	28	gözeri	gözeri	PROPN
ejpam-2029	85	29	,	,	PUNCT
ejpam-2029	85	30	a.	a.	NOUN
ejpam-2029	85	31	pekin	pekin	PROPN
ejpam-2029	85	32	/	/	SYM
ejpam-2029	85	33	eur	eur	PROPN
ejpam-2029	85	34	.	.	PUNCT
ejpam-2029	86	1	j.	j.	PROPN
ejpam-2029	86	2	pure	pure	PROPN
ejpam-2029	86	3	appl	appl	PROPN
ejpam-2029	86	4	.	.	PROPN
ejpam-2029	86	5	math	math	PROPN
ejpam-2029	86	6	,	,	PUNCT
ejpam-2029	86	7	7	7	NUM
ejpam-2029	86	8	(	(	PUNCT
ejpam-2029	86	9	2014	2014	NUM
ejpam-2029	86	10	)	)	PUNCT
ejpam-2029	86	11	,	,	PUNCT
ejpam-2029	86	12	55	55	NUM
ejpam-2029	86	13	-	-	SYM
ejpam-2029	86	14	64	64	NUM
ejpam-2029	86	15	58	58	NUM
ejpam-2029	86	16	where	where	SCONJ
ejpam-2029	86	17	a	a	DET
ejpam-2029	86	18	,	,	PUNCT
ejpam-2029	86	19	b	b	NOUN
ejpam-2029	86	20	,	,	PUNCT
ejpam-2029	86	21	c	c	NOUN
ejpam-2029	86	22	,	,	PUNCT
ejpam-2029	86	23	d	d	NOUN
ejpam-2029	86	24	and	and	CCONJ
ejpam-2029	86	25	e	e	NOUN
ejpam-2029	86	26	are	be	AUX
ejpam-2029	86	27	determined	determine	VERB
ejpam-2029	86	28	uniquely	uniquely	ADV
ejpam-2029	86	29	as	as	SCONJ
ejpam-2029	86	30	follows	follow	VERB
ejpam-2029	86	31	:	:	PUNCT
ejpam-2029	87	1	a=`1`2	a=`1`2	PROPN
ejpam-2029	87	2	+	+	PROPN
ejpam-2029	87	3	1	1	NUM
ejpam-2029	87	4	b	b	X
ejpam-2029	87	5	=	=	NOUN
ejpam-2029	87	6	`	`	PUNCT
ejpam-2029	87	7	1	1	NUM
ejpam-2029	87	8	+	+	NUM
ejpam-2029	87	9	a`3	a`3	NOUN
ejpam-2029	87	10	c	c	AUX
ejpam-2029	87	11	=	=	PUNCT
ejpam-2029	87	12	`	`	PUNCT
ejpam-2029	87	13	2`3	2`3	NUM
ejpam-2029	87	14	+	+	SYM
ejpam-2029	87	15	1	1	NUM
ejpam-2029	87	16	d	d	NOUN
ejpam-2029	87	17	=	=	NOUN
ejpam-2029	87	18	a`1s+	a`1s+	ADP
ejpam-2029	87	19	`	`	PUNCT
ejpam-2029	87	20	2	2	NUM
ejpam-2029	87	21	e	e	NOUN
ejpam-2029	87	22	=	=	NOUN
ejpam-2029	87	23	`	`	PUNCT
ejpam-2029	87	24	1	1	NUM
ejpam-2029	87	25	2s2	2s2	NUM
ejpam-2029	87	26	+	+	SYM
ejpam-2029	87	27	2s+	2s+	NUM
ejpam-2029	87	28	1	1	NUM
ejpam-2029	87	29	proof	proof	NOUN
ejpam-2029	87	30	.	.	PUNCT
ejpam-2029	88	1	in	in	ADP
ejpam-2029	88	2	the	the	DET
ejpam-2029	88	3	case	case	NOUN
ejpam-2029	88	4	of	of	ADP
ejpam-2029	88	5	b	b	PROPN
ejpam-2029	88	6	≡	≡	PROPN
ejpam-2029	88	7	1(mod4	1(mod4	NUM
ejpam-2029	88	8	)	)	PUNCT
ejpam-2029	88	9	,	,	PUNCT
ejpam-2029	88	10	it	it	PRON
ejpam-2029	88	11	can	can	AUX
ejpam-2029	88	12	be	be	AUX
ejpam-2029	88	13	easily	easily	ADV
ejpam-2029	88	14	seen	see	VERB
ejpam-2029	88	15	that	that	SCONJ
ejpam-2029	88	16	a	a	PRON
ejpam-2029	88	17	is	be	AUX
ejpam-2029	88	18	an	an	DET
ejpam-2029	88	19	odd	odd	ADJ
ejpam-2029	88	20	integer	integer	NOUN
ejpam-2029	88	21	since	since	SCONJ
ejpam-2029	88	22	d	d	PROPN
ejpam-2029	88	23	is	be	AUX
ejpam-2029	88	24	congruent	congruent	ADJ
ejpam-2029	88	25	to	to	ADP
ejpam-2029	88	26	2	2	NUM
ejpam-2029	88	27	modulo	modulo	NOUN
ejpam-2029	88	28	4	4	NUM
ejpam-2029	88	29	.	.	PUNCT
ejpam-2029	89	1	we	we	PRON
ejpam-2029	89	2	can	can	AUX
ejpam-2029	89	3	put	put	VERB
ejpam-2029	89	4	b	b	NOUN
ejpam-2029	89	5	=	=	SYM
ejpam-2029	89	6	4m+	4m+	NUM
ejpam-2029	89	7	1	1	NUM
ejpam-2029	89	8	for	for	ADP
ejpam-2029	89	9	a	a	DET
ejpam-2029	89	10	non	non	ADJ
ejpam-2029	89	11	-	-	ADJ
ejpam-2029	89	12	negative	negative	ADJ
ejpam-2029	89	13	integer	integer	NOUN
ejpam-2029	89	14	m	m	AUX
ejpam-2029	89	15	satisfying	satisfy	VERB
ejpam-2029	89	16	0	0	NUM
ejpam-2029	89	17	≤	≤	NUM
ejpam-2029	89	18	4	4	NUM
ejpam-2029	89	19	m	m	NOUN
ejpam-2029	89	20	<	<	X
ejpam-2029	89	21	2a	2a	NUM
ejpam-2029	89	22	.	.	PUNCT
ejpam-2029	90	1	since	since	SCONJ
ejpam-2029	90	2	q0	q0	PROPN
ejpam-2029	90	3	=	=	PUNCT
ejpam-2029	91	1	[	[	X
ejpam-2029	91	2	ωd	ωd	X
ejpam-2029	91	3	]	]	X
ejpam-2029	91	4	=	=	X
ejpam-2029	92	1	[	[	PUNCT
ejpam-2029	92	2	p	p	X
ejpam-2029	92	3	d	d	X
ejpam-2029	92	4	]	]	X
ejpam-2029	92	5	=	=	PUNCT
ejpam-2029	92	6	a	a	PROPN
ejpam-2029	92	7	and	and	CCONJ
ejpam-2029	92	8	ωr	ωr	NOUN
ejpam-2029	92	9	=	=	PUNCT
ejpam-2029	92	10	a+	a+	PUNCT
ejpam-2029	92	11	p	p	PROPN
ejpam-2029	92	12	d	d	PROPN
ejpam-2029	92	13	,	,	PUNCT
ejpam-2029	92	14	it	it	PRON
ejpam-2029	92	15	follows	follow	VERB
ejpam-2029	92	16	from	from	ADP
ejpam-2029	92	17	lemma	lemma	PROPN
ejpam-2029	92	18	3	3	NUM
ejpam-2029	92	19	that	that	DET
ejpam-2029	92	20	r0	r0	NOUN
ejpam-2029	92	21	=	=	SYM
ejpam-2029	92	22	r1	r1	PROPN
ejpam-2029	92	23	=	=	SYM
ejpam-2029	92	24	0	0	NUM
ejpam-2029	92	25	,	,	PUNCT
ejpam-2029	92	26	c0	c0	NOUN
ejpam-2029	92	27	=	=	SYM
ejpam-2029	92	28	1	1	NUM
ejpam-2029	92	29	,	,	PUNCT
ejpam-2029	92	30	c1	c1	NOUN
ejpam-2029	92	31	=	=	NOUN
ejpam-2029	92	32	4m+	4m+	NUM
ejpam-2029	92	33	1	1	NUM
ejpam-2029	92	34	and	and	CCONJ
ejpam-2029	92	35	`	`	PUNCT
ejpam-2029	92	36	0	0	NUM
ejpam-2029	92	37	=	=	SYM
ejpam-2029	92	38	2a	2a	NUM
ejpam-2029	92	39	.	.	PUNCT
ejpam-2029	93	1	since	since	SCONJ
ejpam-2029	93	2	kd	kd	PROPN
ejpam-2029	93	3	=	=	PROPN
ejpam-2029	93	4	7	7	NUM
ejpam-2029	93	5	,	,	PUNCT
ejpam-2029	93	6	we	we	PRON
ejpam-2029	93	7	get	get	VERB
ejpam-2029	93	8	`	`	PUNCT
ejpam-2029	93	9	1	1	X
ejpam-2029	93	10	=	=	SYM
ejpam-2029	93	11	`	`	PUNCT
ejpam-2029	93	12	6	6	NUM
ejpam-2029	93	13	,	,	PUNCT
ejpam-2029	93	14	`	`	PUNCT
ejpam-2029	93	15	2	2	NUM
ejpam-2029	93	16	=	=	SYM
ejpam-2029	93	17	`	`	PUNCT
ejpam-2029	93	18	5	5	NUM
ejpam-2029	93	19	and	and	CCONJ
ejpam-2029	93	20	`	`	PUNCT
ejpam-2029	93	21	3	3	X
ejpam-2029	93	22	=	=	SYM
ejpam-2029	93	23	`	`	PUNCT
ejpam-2029	93	24	4	4	NUM
ejpam-2029	93	25	from	from	ADP
ejpam-2029	93	26	lemma	lemma	PROPN
ejpam-2029	93	27	2	2	NUM
ejpam-2029	93	28	.	.	PUNCT
ejpam-2029	94	1	then	then	ADV
ejpam-2029	94	2	we	we	PRON
ejpam-2029	94	3	have	have	VERB
ejpam-2029	94	4	ωd	ωd	NOUN
ejpam-2029	94	5	=	=	SYM
ejpam-2029	95	1	[	[	X
ejpam-2029	95	2	a,`1,`2,`3,`3,`2,`1	a,`1,`2,`3,`3,`2,`1	PROPN
ejpam-2029	95	3	,	,	PUNCT
ejpam-2029	95	4	2a	2a	NUM
ejpam-2029	95	5	]	]	PUNCT
ejpam-2029	95	6	for	for	ADP
ejpam-2029	95	7	three	three	NUM
ejpam-2029	95	8	positive	positive	ADJ
ejpam-2029	95	9	integers	integer	NOUN
ejpam-2029	95	10	`	`	PUNCT
ejpam-2029	95	11	1	1	NUM
ejpam-2029	95	12	,	,	PUNCT
ejpam-2029	95	13	`	`	PUNCT
ejpam-2029	95	14	2	2	NUM
ejpam-2029	95	15	,	,	PUNCT
ejpam-2029	95	16	`	`	PUNCT
ejpam-2029	95	17	3	3	NUM
ejpam-2029	95	18	such	such	ADJ
ejpam-2029	95	19	that	that	SCONJ
ejpam-2029	95	20	`	`	PUNCT
ejpam-2029	95	21	i	i	PRON
ejpam-2029	95	22	≥	≥	VERB
ejpam-2029	95	23	1	1	NUM
ejpam-2029	95	24	(	(	PUNCT
ejpam-2029	95	25	i	i	NOUN
ejpam-2029	95	26	=	=	NOUN
ejpam-2029	95	27	1	1	NUM
ejpam-2029	95	28	,	,	PUNCT
ejpam-2029	95	29	2,3	2,3	NUM
ejpam-2029	95	30	)	)	PUNCT
ejpam-2029	95	31	.	.	PUNCT
ejpam-2029	96	1	from	from	ADP
ejpam-2029	96	2	lemma	lemma	PROPN
ejpam-2029	96	3	2	2	NUM
ejpam-2029	96	4	we	we	PRON
ejpam-2029	96	5	get	get	VERB
ejpam-2029	96	6	2a	2a	NUM
ejpam-2029	96	7	=	=	SYM
ejpam-2029	96	8	(	(	PUNCT
ejpam-2029	96	9	4m+	4m+	NUM
ejpam-2029	96	10	1)`1	1)`1	NUM
ejpam-2029	96	11	+	+	NOUN
ejpam-2029	96	12	r2	r2	PROPN
ejpam-2029	96	13	(	(	PUNCT
ejpam-2029	96	14	1	1	NUM
ejpam-2029	96	15	)	)	PUNCT
ejpam-2029	96	16	since	since	SCONJ
ejpam-2029	96	17	r1	r1	NOUN
ejpam-2029	96	18	=	=	SYM
ejpam-2029	96	19	0	0	NUM
ejpam-2029	96	20	and	and	CCONJ
ejpam-2029	96	21	c1	c1	PROPN
ejpam-2029	96	22	=	=	PUNCT
ejpam-2029	97	1	4m+	4m+	NUM
ejpam-2029	97	2	1	1	NUM
ejpam-2029	97	3	.	.	PUNCT
ejpam-2029	98	1	from	from	ADP
ejpam-2029	98	2	(	(	PUNCT
ejpam-2029	98	3	1	1	NUM
ejpam-2029	98	4	)	)	PUNCT
ejpam-2029	98	5	,	,	PUNCT
ejpam-2029	98	6	we	we	PRON
ejpam-2029	98	7	obtain	obtain	VERB
ejpam-2029	98	8	(	(	PUNCT
ejpam-2029	98	9	4m+	4m+	NUM
ejpam-2029	98	10	1)`1	1)`1	NUM
ejpam-2029	98	11	+	+	CCONJ
ejpam-2029	98	12	r2	r2	PROPN
ejpam-2029	98	13	≡	≡	PROPN
ejpam-2029	98	14	0	0	PUNCT
ejpam-2029	99	1	(	(	PUNCT
ejpam-2029	99	2	mod	mod	NOUN
ejpam-2029	99	3	2	2	NUM
ejpam-2029	99	4	)	)	PUNCT
ejpam-2029	99	5	.	.	PUNCT
ejpam-2029	100	1	so	so	ADV
ejpam-2029	100	2	there	there	PRON
ejpam-2029	100	3	exists	exist	VERB
ejpam-2029	100	4	a	a	DET
ejpam-2029	100	5	positive	positive	ADJ
ejpam-2029	100	6	integer	integer	NOUN
ejpam-2029	100	7	r	r	NOUN
ejpam-2029	100	8	such	such	ADJ
ejpam-2029	100	9	that	that	DET
ejpam-2029	100	10	r2	r2	NOUN
ejpam-2029	101	1	=	=	PUNCT
ejpam-2029	101	2	2r	2r	NUM
ejpam-2029	102	1	−	−	NOUN
ejpam-2029	102	2	`	`	PUNCT
ejpam-2029	102	3	1	1	X
ejpam-2029	102	4	.	.	PUNCT
ejpam-2029	102	5	by	by	ADP
ejpam-2029	102	6	substitution	substitution	NOUN
ejpam-2029	102	7	of	of	ADP
ejpam-2029	102	8	r2	r2	PROPN
ejpam-2029	102	9	in	in	ADP
ejpam-2029	102	10	(	(	PUNCT
ejpam-2029	102	11	1	1	X
ejpam-2029	102	12	)	)	PUNCT
ejpam-2029	102	13	we	we	PRON
ejpam-2029	102	14	get	get	VERB
ejpam-2029	102	15	a	a	DET
ejpam-2029	102	16	=	=	NOUN
ejpam-2029	102	17	2m`1	2m`1	NUM
ejpam-2029	102	18	+	+	X
ejpam-2029	102	19	r.	r.	PROPN
ejpam-2029	102	20	(	(	PUNCT
ejpam-2029	102	21	2	2	NUM
ejpam-2029	102	22	)	)	PUNCT
ejpam-2029	102	23	here	here	ADV
ejpam-2029	102	24	since	since	SCONJ
ejpam-2029	102	25	a	a	PRON
ejpam-2029	102	26	is	be	AUX
ejpam-2029	102	27	odd	odd	ADJ
ejpam-2029	102	28	,	,	PUNCT
ejpam-2029	102	29	r	r	NOUN
ejpam-2029	102	30	must	must	AUX
ejpam-2029	102	31	be	be	AUX
ejpam-2029	102	32	an	an	DET
ejpam-2029	102	33	odd	odd	ADJ
ejpam-2029	102	34	integer	integer	NOUN
ejpam-2029	102	35	,	,	PUNCT
ejpam-2029	102	36	too	too	ADV
ejpam-2029	102	37	.	.	PUNCT
ejpam-2029	103	1	it	it	PRON
ejpam-2029	103	2	follows	follow	VERB
ejpam-2029	103	3	from	from	ADP
ejpam-2029	103	4	lemma	lemma	PROPN
ejpam-2029	103	5	2	2	NUM
ejpam-2029	103	6	that	that	PRON
ejpam-2029	103	7	c2	c2	PROPN
ejpam-2029	103	8	=	=	PUNCT
ejpam-2029	103	9	1	1	NUM
ejpam-2029	103	10	+	+	NUM
ejpam-2029	103	11	r2`1	r2`1	NOUN
ejpam-2029	103	12	and	and	CCONJ
ejpam-2029	103	13	2a	2a	NUM
ejpam-2029	103	14	=	=	SYM
ejpam-2029	103	15	c2`2	c2`2	ADP
ejpam-2029	103	16	+	+	NUM
ejpam-2029	103	17	r3	r3	PROPN
ejpam-2029	103	18	+	+	CCONJ
ejpam-2029	103	19	r2	r2	NOUN
ejpam-2029	103	20	.	.	PUNCT
ejpam-2029	104	1	thus	thus	ADV
ejpam-2029	104	2	,	,	PUNCT
ejpam-2029	104	3	2a	2a	NUM
ejpam-2029	104	4	=	=	SYM
ejpam-2029	104	5	(	(	PUNCT
ejpam-2029	104	6	1	1	NUM
ejpam-2029	104	7	+	+	NUM
ejpam-2029	104	8	r2`1)`2	r2`1)`2	NOUN
ejpam-2029	104	9	+	+	SYM
ejpam-2029	104	10	r3	r3	PROPN
ejpam-2029	104	11	+	+	CCONJ
ejpam-2029	104	12	r2	r2	PROPN
ejpam-2029	104	13	(	(	PUNCT
ejpam-2029	104	14	3	3	NUM
ejpam-2029	104	15	)	)	PUNCT
ejpam-2029	104	16	is	be	AUX
ejpam-2029	104	17	obtained	obtain	VERB
ejpam-2029	104	18	.	.	PUNCT
ejpam-2029	105	1	then	then	ADV
ejpam-2029	105	2	(	(	PUNCT
ejpam-2029	105	3	4m+	4m+	NUM
ejpam-2029	105	4	1)`1	1)`1	NUM
ejpam-2029	105	5	=	=	SYM
ejpam-2029	105	6	(	(	PUNCT
ejpam-2029	105	7	1	1	NUM
ejpam-2029	105	8	+	+	NUM
ejpam-2029	105	9	r2`1)`2	r2`1)`2	NOUN
ejpam-2029	105	10	+	+	X
ejpam-2029	105	11	r3	r3	PROPN
ejpam-2029	105	12	(	(	PUNCT
ejpam-2029	105	13	4	4	NUM
ejpam-2029	105	14	)	)	PUNCT
ejpam-2029	105	15	holds	hold	VERB
ejpam-2029	105	16	from	from	ADP
ejpam-2029	105	17	(	(	PUNCT
ejpam-2029	105	18	1	1	NUM
ejpam-2029	105	19	)	)	PUNCT
ejpam-2029	105	20	and	and	CCONJ
ejpam-2029	105	21	(	(	PUNCT
ejpam-2029	105	22	3	3	NUM
ejpam-2029	105	23	)	)	PUNCT
ejpam-2029	105	24	.	.	PUNCT
ejpam-2029	106	1	thus	thus	ADV
ejpam-2029	106	2	we	we	PRON
ejpam-2029	106	3	get	get	VERB
ejpam-2029	106	4	`	`	PUNCT
ejpam-2029	106	5	2	2	NUM
ejpam-2029	106	6	+	+	CCONJ
ejpam-2029	106	7	`	`	PUNCT
ejpam-2029	106	8	3	3	NUM
ejpam-2029	106	9	≡	≡	PROPN
ejpam-2029	106	10	0	0	NUM
ejpam-2029	107	1	(	(	PUNCT
ejpam-2029	107	2	mod	mod	NOUN
ejpam-2029	107	3	`	`	PUNCT
ejpam-2029	107	4	1	1	NUM
ejpam-2029	107	5	)	)	PUNCT
ejpam-2029	107	6	.	.	PUNCT
ejpam-2029	108	1	there	there	PRON
ejpam-2029	108	2	exists	exist	VERB
ejpam-2029	108	3	a	a	DET
ejpam-2029	108	4	positive	positive	ADJ
ejpam-2029	108	5	integer	integer	NOUN
ejpam-2029	108	6	t	t	PROPN
ejpam-2029	108	7	such	such	ADJ
ejpam-2029	108	8	that	that	DET
ejpam-2029	108	9	r3	r3	PROPN
ejpam-2029	108	10	=	=	PUNCT
ejpam-2029	109	1	`	`	PUNCT
ejpam-2029	109	2	1	1	NUM
ejpam-2029	109	3	t	t	NOUN
ejpam-2029	109	4	−	−	NOUN
ejpam-2029	110	1	`	`	PUNCT
ejpam-2029	110	2	2	2	X
ejpam-2029	110	3	.	.	PUNCT
ejpam-2029	110	4	by	by	ADP
ejpam-2029	110	5	substitution	substitution	NOUN
ejpam-2029	110	6	of	of	ADP
ejpam-2029	110	7	r3	r3	PROPN
ejpam-2029	110	8	in	in	ADP
ejpam-2029	110	9	(	(	PUNCT
ejpam-2029	110	10	4	4	NUM
ejpam-2029	110	11	)	)	PUNCT
ejpam-2029	110	12	,	,	PUNCT
ejpam-2029	110	13	we	we	PRON
ejpam-2029	110	14	get	get	VERB
ejpam-2029	110	15	4m=	4m=	NUM
ejpam-2029	110	16	t	t	NOUN
ejpam-2029	110	17	+	+	CCONJ
ejpam-2029	110	18	2r`2−	2r`2−	NUM
ejpam-2029	110	19	`	`	PUNCT
ejpam-2029	110	20	1`2−	1`2−	NUM
ejpam-2029	110	21	1	1	NUM
ejpam-2029	110	22	.	.	PUNCT
ejpam-2029	111	1	thus	thus	ADV
ejpam-2029	111	2	if	if	SCONJ
ejpam-2029	111	3	we	we	PRON
ejpam-2029	111	4	put	put	VERB
ejpam-2029	111	5	a=	a=	ADJ
ejpam-2029	111	6	`	`	PUNCT
ejpam-2029	111	7	1`2	1`2	NUM
ejpam-2029	111	8	+	+	NOUN
ejpam-2029	111	9	1	1	NUM
ejpam-2029	111	10	,	,	PUNCT
ejpam-2029	111	11	then	then	ADV
ejpam-2029	111	12	we	we	PRON
ejpam-2029	111	13	get	get	VERB
ejpam-2029	111	14	t−a=	t−a=	ADP
ejpam-2029	111	15	4m−2r`2	4m−2r`2	NUM
ejpam-2029	111	16	.	.	PUNCT
ejpam-2029	112	1	since	since	SCONJ
ejpam-2029	112	2	t−a	t−a	NOUN
ejpam-2029	112	3	is	be	AUX
ejpam-2029	112	4	even	even	ADV
ejpam-2029	112	5	,	,	PUNCT
ejpam-2029	112	6	we	we	PRON
ejpam-2029	112	7	can	can	AUX
ejpam-2029	112	8	put	put	VERB
ejpam-2029	112	9	t−a=	t−a=	PRON
ejpam-2029	112	10	2s	2s	NOUN
ejpam-2029	112	11	for	for	ADP
ejpam-2029	112	12	a	a	DET
ejpam-2029	112	13	positive	positive	ADJ
ejpam-2029	112	14	integer	integer	NOUN
ejpam-2029	112	15	s.	s.	PROPN
ejpam-2029	112	16	hence	hence	ADV
ejpam-2029	112	17	,	,	PUNCT
ejpam-2029	112	18	4	4	NUM
ejpam-2029	112	19	m	m	NOUN
ejpam-2029	112	20	=	=	NOUN
ejpam-2029	113	1	2s	2	NOUN
ejpam-2029	113	2	+	+	CCONJ
ejpam-2029	113	3	2r`2	2r`2	NUM
ejpam-2029	113	4	is	be	AUX
ejpam-2029	113	5	obtained	obtain	VERB
ejpam-2029	113	6	.	.	PUNCT
ejpam-2029	114	1	therefore	therefore	ADV
ejpam-2029	114	2	we	we	PRON
ejpam-2029	114	3	get	get	VERB
ejpam-2029	114	4	a	a	DET
ejpam-2029	114	5	=	=	NOUN
ejpam-2029	114	6	ar	ar	NOUN
ejpam-2029	114	7	+	+	NOUN
ejpam-2029	114	8	`	`	PUNCT
ejpam-2029	114	9	1s	1	NOUN
ejpam-2029	114	10	from	from	ADP
ejpam-2029	114	11	(	(	PUNCT
ejpam-2029	114	12	2	2	NUM
ejpam-2029	114	13	)	)	PUNCT
ejpam-2029	114	14	.	.	PUNCT
ejpam-2029	115	1	on	on	ADP
ejpam-2029	115	2	the	the	DET
ejpam-2029	115	3	other	other	ADJ
ejpam-2029	115	4	hand	hand	NOUN
ejpam-2029	115	5	,	,	PUNCT
ejpam-2029	115	6	c3	c3	PROPN
ejpam-2029	115	7	=	=	PUNCT
ejpam-2029	115	8	4m+	4m+	NUM
ejpam-2029	115	9	1	1	NUM
ejpam-2029	115	10	+	+	CCONJ
ejpam-2029	115	11	(	(	PUNCT
ejpam-2029	115	12	r3−	r3−	PROPN
ejpam-2029	115	13	r2)`2	r2)`2	PROPN
ejpam-2029	115	14	(	(	PUNCT
ejpam-2029	115	15	5	5	X
ejpam-2029	115	16	)	)	PUNCT
ejpam-2029	115	17	is	be	AUX
ejpam-2029	115	18	obtained	obtain	VERB
ejpam-2029	115	19	from	from	ADP
ejpam-2029	115	20	lemma	lemma	PROPN
ejpam-2029	115	21	2	2	NUM
ejpam-2029	115	22	.	.	PUNCT
ejpam-2029	115	23	by	by	ADP
ejpam-2029	115	24	substitution	substitution	NOUN
ejpam-2029	115	25	of	of	ADP
ejpam-2029	115	26	r2	r2	NOUN
ejpam-2029	115	27	=	=	SYM
ejpam-2029	116	1	2r	2r	NUM
ejpam-2029	117	1	−	−	NOUN
ejpam-2029	118	1	`	`	PUNCT
ejpam-2029	118	2	1	1	NUM
ejpam-2029	118	3	and	and	CCONJ
ejpam-2029	118	4	r3	r3	PROPN
ejpam-2029	118	5	=	=	SYM
ejpam-2029	119	1	`	`	PUNCT
ejpam-2029	119	2	1	1	NUM
ejpam-2029	119	3	t	t	NOUN
ejpam-2029	119	4	−	−	NOUN
ejpam-2029	120	1	`	`	PUNCT
ejpam-2029	120	2	2	2	NUM
ejpam-2029	120	3	in	in	ADP
ejpam-2029	120	4	(	(	PUNCT
ejpam-2029	120	5	5	5	NUM
ejpam-2029	120	6	)	)	PUNCT
ejpam-2029	120	7	,	,	PUNCT
ejpam-2029	120	8	we	we	PRON
ejpam-2029	120	9	get	get	VERB
ejpam-2029	120	10	c3	c3	NOUN
ejpam-2029	120	11	=	=	PUNCT
ejpam-2029	120	12	at	at	ADP
ejpam-2029	120	13	−	−	PROPN
ejpam-2029	120	14	`	`	PUNCT
ejpam-2029	120	15	2	2	NUM
ejpam-2029	120	16	2	2	NUM
ejpam-2029	120	17	.	.	PUNCT
ejpam-2029	121	1	moreover	moreover	ADV
ejpam-2029	121	2	from	from	ADP
ejpam-2029	121	3	lemma	lemma	PROPN
ejpam-2029	121	4	2	2	NUM
ejpam-2029	121	5	,	,	PUNCT
ejpam-2029	121	6	we	we	PRON
ejpam-2029	121	7	get	get	VERB
ejpam-2029	121	8	2a	2a	NUM
ejpam-2029	121	9	=	=	PUNCT
ejpam-2029	122	1	c3`3	c3`3	X
ejpam-2029	122	2	+	+	NUM
ejpam-2029	122	3	r3	r3	NOUN
ejpam-2029	122	4	+	+	CCONJ
ejpam-2029	122	5	r4	r4	NOUN
ejpam-2029	122	6	.	.	PUNCT
ejpam-2029	123	1	thus	thus	ADV
ejpam-2029	123	2	r4	r4	VERB
ejpam-2029	123	3	=	=	SYM
ejpam-2029	123	4	(	(	PUNCT
ejpam-2029	123	5	2r	2r	NUM
ejpam-2029	124	1	−	−	ADP
ejpam-2029	124	2	`	`	PUNCT
ejpam-2029	124	3	1−	1−	NUM
ejpam-2029	124	4	t`3)a+	t`3)a+	ADP
ejpam-2029	124	5	`	`	PUNCT
ejpam-2029	124	6	2(`2`3	2(`2`3	NUM
ejpam-2029	124	7	+	+	NOUN
ejpam-2029	124	8	1	1	NUM
ejpam-2029	124	9	)	)	PUNCT
ejpam-2029	124	10	(	(	PUNCT
ejpam-2029	124	11	6	6	NUM
ejpam-2029	124	12	)	)	PUNCT
ejpam-2029	124	13	g.	g.	NOUN
ejpam-2029	124	14	gözeri	gözeri	NOUN
ejpam-2029	124	15	,	,	PUNCT
ejpam-2029	124	16	a.	a.	NOUN
ejpam-2029	124	17	pekin	pekin	PROPN
ejpam-2029	124	18	/	/	SYM
ejpam-2029	124	19	eur	eur	PROPN
ejpam-2029	124	20	.	.	PUNCT
ejpam-2029	125	1	j.	j.	PROPN
ejpam-2029	125	2	pure	pure	PROPN
ejpam-2029	125	3	appl	appl	PROPN
ejpam-2029	125	4	.	.	PROPN
ejpam-2029	125	5	math	math	PROPN
ejpam-2029	125	6	,	,	PUNCT
ejpam-2029	125	7	7	7	NUM
ejpam-2029	125	8	(	(	PUNCT
ejpam-2029	125	9	2014	2014	NUM
ejpam-2029	125	10	)	)	PUNCT
ejpam-2029	125	11	,	,	PUNCT
ejpam-2029	125	12	55	55	NUM
ejpam-2029	125	13	-	-	SYM
ejpam-2029	125	14	64	64	NUM
ejpam-2029	125	15	59	59	NUM
ejpam-2029	125	16	is	be	AUX
ejpam-2029	125	17	obtained	obtain	VERB
ejpam-2029	125	18	because	because	SCONJ
ejpam-2029	125	19	of	of	ADP
ejpam-2029	125	20	(	(	PUNCT
ejpam-2029	125	21	3	3	NUM
ejpam-2029	125	22	)	)	PUNCT
ejpam-2029	125	23	and	and	CCONJ
ejpam-2029	125	24	c3	c3	PROPN
ejpam-2029	125	25	=	=	PUNCT
ejpam-2029	125	26	at	at	ADP
ejpam-2029	125	27	−	−	PROPN
ejpam-2029	125	28	`	`	PUNCT
ejpam-2029	125	29	2	2	NUM
ejpam-2029	125	30	2	2	NUM
ejpam-2029	125	31	.	.	PUNCT
ejpam-2029	126	1	furthermore	furthermore	ADV
ejpam-2029	126	2	,	,	PUNCT
ejpam-2029	126	3	c3	c3	PROPN
ejpam-2029	126	4	=	=	PUNCT
ejpam-2029	126	5	at	at	ADP
ejpam-2029	126	6	−	−	PROPN
ejpam-2029	126	7	`	`	PUNCT
ejpam-2029	126	8	2	2	NUM
ejpam-2029	126	9	2	2	NUM
ejpam-2029	126	10	and	and	CCONJ
ejpam-2029	126	11	c4	c4	NOUN
ejpam-2029	126	12	=	=	SYM
ejpam-2029	126	13	(	(	PUNCT
ejpam-2029	126	14	1	1	NUM
ejpam-2029	126	15	+	+	NUM
ejpam-2029	126	16	r2`1	r2`1	NOUN
ejpam-2029	126	17	)	)	PUNCT
ejpam-2029	126	18	+	+	CCONJ
ejpam-2029	126	19	(	(	PUNCT
ejpam-2029	126	20	r4−	r4−	NOUN
ejpam-2029	126	21	r3)`3	r3)`3	PRON
ejpam-2029	126	22	imply	imply	VERB
ejpam-2029	126	23	at	at	ADP
ejpam-2029	126	24	−	−	PROPN
ejpam-2029	126	25	`	`	PUNCT
ejpam-2029	126	26	2	2	NUM
ejpam-2029	126	27	2	2	NUM
ejpam-2029	126	28	=	=	SYM
ejpam-2029	126	29	1	1	NUM
ejpam-2029	126	30	+	+	NUM
ejpam-2029	126	31	r2`1	r2`1	NOUN
ejpam-2029	126	32	+	+	NOUN
ejpam-2029	126	33	r4`3−	r4`3−	ADJ
ejpam-2029	126	34	r3`3	r3`3	NOUN
ejpam-2029	126	35	since	since	SCONJ
ejpam-2029	126	36	c3	c3	NOUN
ejpam-2029	126	37	=	=	PROPN
ejpam-2029	126	38	c4	c4	PROPN
ejpam-2029	126	39	.	.	PUNCT
ejpam-2029	127	1	thus	thus	ADV
ejpam-2029	127	2	,	,	PUNCT
ejpam-2029	127	3	at	at	ADP
ejpam-2029	127	4	−	−	PROPN
ejpam-2029	127	5	`	`	PUNCT
ejpam-2029	127	6	2	2	NUM
ejpam-2029	127	7	2	2	NUM
ejpam-2029	127	8	=	=	SYM
ejpam-2029	127	9	(	(	PUNCT
ejpam-2029	127	10	1	1	NUM
ejpam-2029	127	11	+	+	CCONJ
ejpam-2029	127	12	`	`	PUNCT
ejpam-2029	127	13	2`3	2`3	NUM
ejpam-2029	127	14	)	)	PUNCT
ejpam-2029	127	15	2	2	NUM
ejpam-2029	127	16	+	+	NUM
ejpam-2029	127	17	2r(`1	2r(`1	NUM
ejpam-2029	127	18	+	+	NOUN
ejpam-2029	127	19	a`3)−	a`3)−	ADP
ejpam-2029	127	20	t`3(`1	t`3(`1	NOUN
ejpam-2029	127	21	+	+	NUM
ejpam-2029	127	22	a`3)−	a`3)−	ADP
ejpam-2029	127	23	`	`	PUNCT
ejpam-2029	127	24	1(`1	1(`1	NUM
ejpam-2029	127	25	+	+	SYM
ejpam-2029	127	26	a`3	a`3	NUM
ejpam-2029	127	27	)	)	PUNCT
ejpam-2029	127	28	is	be	AUX
ejpam-2029	127	29	obtained	obtain	VERB
ejpam-2029	127	30	since	since	SCONJ
ejpam-2029	127	31	r2	r2	PROPN
ejpam-2029	127	32	=	=	SYM
ejpam-2029	127	33	2r	2r	NUM
ejpam-2029	128	1	−	−	NOUN
ejpam-2029	128	2	`	`	PUNCT
ejpam-2029	128	3	1	1	NUM
ejpam-2029	128	4	,	,	PUNCT
ejpam-2029	128	5	r3	r3	X
ejpam-2029	128	6	=	=	SYM
ejpam-2029	128	7	`	`	PUNCT
ejpam-2029	128	8	1	1	NUM
ejpam-2029	128	9	t	t	NOUN
ejpam-2029	128	10	−	−	NOUN
ejpam-2029	128	11	`	`	PUNCT
ejpam-2029	128	12	2	2	NUM
ejpam-2029	128	13	and	and	CCONJ
ejpam-2029	128	14	r4	r4	VERB
ejpam-2029	128	15	=	=	SYM
ejpam-2029	128	16	(	(	PUNCT
ejpam-2029	128	17	2r	2r	NUM
ejpam-2029	128	18	−	−	NOUN
ejpam-2029	128	19	`	`	PUNCT
ejpam-2029	128	20	1	1	NUM
ejpam-2029	128	21	−	−	NOUN
ejpam-2029	128	22	t`3)a+	t`3)a+	PUNCT
ejpam-2029	128	23	`	`	PUNCT
ejpam-2029	128	24	2(`2`3	2(`2`3	PROPN
ejpam-2029	128	25	+	+	NOUN
ejpam-2029	128	26	1	1	NUM
ejpam-2029	128	27	)	)	PUNCT
ejpam-2029	128	28	.	.	PUNCT
ejpam-2029	129	1	thus	thus	ADV
ejpam-2029	129	2	if	if	SCONJ
ejpam-2029	129	3	we	we	PRON
ejpam-2029	129	4	put	put	VERB
ejpam-2029	129	5	b	b	NOUN
ejpam-2029	129	6	=	=	PUNCT
ejpam-2029	129	7	`	`	PUNCT
ejpam-2029	129	8	1	1	NUM
ejpam-2029	130	1	+	+	CCONJ
ejpam-2029	130	2	a`3	a`3	PROPN
ejpam-2029	130	3	and	and	CCONJ
ejpam-2029	130	4	c	c	NOUN
ejpam-2029	130	5	=	=	PUNCT
ejpam-2029	131	1	`	`	PUNCT
ejpam-2029	131	2	2`3	2`3	NUM
ejpam-2029	131	3	+	+	NUM
ejpam-2029	131	4	1	1	NUM
ejpam-2029	131	5	,	,	PUNCT
ejpam-2029	131	6	we	we	PRON
ejpam-2029	131	7	get	get	VERB
ejpam-2029	131	8	a2	a2	PROPN
ejpam-2029	131	9	+	+	CCONJ
ejpam-2029	131	10	b2	b2	NOUN
ejpam-2029	131	11	−	−	PROPN
ejpam-2029	131	12	c2	c2	PROPN
ejpam-2029	131	13	−	−	PROPN
ejpam-2029	132	1	`	`	PUNCT
ejpam-2029	132	2	2	2	NUM
ejpam-2029	132	3	2	2	NUM
ejpam-2029	132	4	=	=	NOUN
ejpam-2029	132	5	2rb	2rb	NOUN
ejpam-2029	132	6	−	−	PROPN
ejpam-2029	132	7	2s(a+	2s(a+	PROPN
ejpam-2029	132	8	b`3	b`3	NOUN
ejpam-2029	132	9	)	)	PUNCT
ejpam-2029	132	10	since	since	SCONJ
ejpam-2029	132	11	t	t	PROPN
ejpam-2029	132	12	−	−	PROPN
ejpam-2029	132	13	a=	a=	ADV
ejpam-2029	132	14	2s	2s	X
ejpam-2029	132	15	.	.	PUNCT
ejpam-2029	133	1	if	if	SCONJ
ejpam-2029	133	2	we	we	PRON
ejpam-2029	133	3	assume	assume	VERB
ejpam-2029	133	4	that	that	SCONJ
ejpam-2029	133	5	the	the	DET
ejpam-2029	133	6	integers	integer	NOUN
ejpam-2029	133	7	r	r	NOUN
ejpam-2029	133	8	and	and	CCONJ
ejpam-2029	133	9	s	s	NOUN
ejpam-2029	133	10	are	be	AUX
ejpam-2029	133	11	not	not	PART
ejpam-2029	133	12	uniquely	uniquely	ADV
ejpam-2029	133	13	determined	determine	VERB
ejpam-2029	133	14	,	,	PUNCT
ejpam-2029	133	15	we	we	PRON
ejpam-2029	133	16	get	get	VERB
ejpam-2029	133	17	a2	a2	NOUN
ejpam-2029	133	18	+	+	NOUN
ejpam-2029	133	19	b2	b2	NOUN
ejpam-2029	133	20	=	=	SYM
ejpam-2029	133	21	0	0	NUM
ejpam-2029	133	22	which	which	PRON
ejpam-2029	133	23	is	be	AUX
ejpam-2029	133	24	a	a	DET
ejpam-2029	133	25	contradiction	contradiction	NOUN
ejpam-2029	133	26	.	.	PUNCT
ejpam-2029	134	1	therefore	therefore	ADV
ejpam-2029	134	2	,	,	PUNCT
ejpam-2029	134	3	the	the	DET
ejpam-2029	134	4	integers	integer	NOUN
ejpam-2029	134	5	r	r	NOUN
ejpam-2029	134	6	and	and	CCONJ
ejpam-2029	134	7	s	s	NOUN
ejpam-2029	134	8	are	be	AUX
ejpam-2029	134	9	uniquely	uniquely	ADV
ejpam-2029	134	10	determined	determine	VERB
ejpam-2029	134	11	by	by	ADP
ejpam-2029	134	12	a	a	DET
ejpam-2029	134	13	=	=	X
ejpam-2029	134	14	ar	ar	PROPN
ejpam-2029	134	15	+	+	NOUN
ejpam-2029	134	16	`	`	PUNCT
ejpam-2029	134	17	1s	1s	NUM
ejpam-2029	134	18	and	and	CCONJ
ejpam-2029	134	19	a2	a2	PROPN
ejpam-2029	134	20	+	+	CCONJ
ejpam-2029	134	21	b2−	b2−	PROPN
ejpam-2029	134	22	c2−	c2−	ADJ
ejpam-2029	134	23	`	`	PUNCT
ejpam-2029	134	24	2	2	NUM
ejpam-2029	134	25	2	2	NUM
ejpam-2029	134	26	=	=	SYM
ejpam-2029	134	27	2rb−	2rb−	NUM
ejpam-2029	134	28	2s(a+	2s(a+	PROPN
ejpam-2029	134	29	b`3	b`3	NOUN
ejpam-2029	134	30	)	)	PUNCT
ejpam-2029	134	31	.	.	PUNCT
ejpam-2029	135	1	now	now	ADV
ejpam-2029	135	2	,	,	PUNCT
ejpam-2029	135	3	since	since	SCONJ
ejpam-2029	135	4	ωd	ωd	ADP
ejpam-2029	135	5	=	=	SYM
ejpam-2029	136	1	[	[	X
ejpam-2029	136	2	a,`1,`2,`3,`3,`2,`1	a,`1,`2,`3,`3,`2,`1	PROPN
ejpam-2029	136	3	,	,	PUNCT
ejpam-2029	136	4	2a	2a	NUM
ejpam-2029	136	5	]	]	PUNCT
ejpam-2029	136	6	implies	imply	VERB
ejpam-2029	136	7	q5	q5	PROPN
ejpam-2029	136	8	=	=	SYM
ejpam-2029	136	9	bc	bc	PROPN
ejpam-2029	136	10	+	+	CCONJ
ejpam-2029	136	11	a`2	a`2	PROPN
ejpam-2029	136	12	and	and	CCONJ
ejpam-2029	136	13	q6	q6	PROPN
ejpam-2029	136	14	=	=	PROPN
ejpam-2029	136	15	a2	a2	PROPN
ejpam-2029	136	16	+	+	CCONJ
ejpam-2029	136	17	b2	b2	NOUN
ejpam-2029	136	18	by	by	ADP
ejpam-2029	136	19	lemma	lemma	PROPN
ejpam-2029	136	20	1	1	NUM
ejpam-2029	136	21	,	,	PUNCT
ejpam-2029	136	22	we	we	PRON
ejpam-2029	136	23	obtain	obtain	VERB
ejpam-2029	136	24	(	(	PUNCT
ejpam-2029	136	25	td	td	NOUN
ejpam-2029	136	26	,	,	PUNCT
ejpam-2029	136	27	ud	ud	INTJ
ejpam-2029	136	28	)	)	PUNCT
ejpam-2029	136	29	=	=	SYM
ejpam-2029	137	1	(	(	PUNCT
ejpam-2029	137	2	2[a(a	2[a(a	NUM
ejpam-2029	137	3	2	2	NUM
ejpam-2029	137	4	+	+	NUM
ejpam-2029	137	5	b2	b2	NOUN
ejpam-2029	137	6	)	)	PUNCT
ejpam-2029	138	1	+	+	CCONJ
ejpam-2029	138	2	bc	bc	PROPN
ejpam-2029	138	3	+	+	CCONJ
ejpam-2029	138	4	a`2	a`2	PROPN
ejpam-2029	138	5	]	]	X
ejpam-2029	138	6	,	,	PUNCT
ejpam-2029	138	7	2(a2	2(a2	NUM
ejpam-2029	138	8	+	+	NUM
ejpam-2029	138	9	b2	b2	NOUN
ejpam-2029	138	10	)	)	PUNCT
ejpam-2029	138	11	)	)	PUNCT
ejpam-2029	138	12	.	.	PUNCT
ejpam-2029	139	1	furthermore	furthermore	ADV
ejpam-2029	139	2	,	,	PUNCT
ejpam-2029	139	3	if	if	SCONJ
ejpam-2029	139	4	we	we	PRON
ejpam-2029	139	5	put	put	VERB
ejpam-2029	139	6	d	d	NOUN
ejpam-2029	139	7	=	=	PUNCT
ejpam-2029	139	8	a`1s+	a`1s+	NOUN
ejpam-2029	139	9	`	`	PUNCT
ejpam-2029	139	10	2	2	NUM
ejpam-2029	139	11	and	and	CCONJ
ejpam-2029	139	12	e	e	NOUN
ejpam-2029	139	13	=	=	PUNCT
ejpam-2029	139	14	`	`	PUNCT
ejpam-2029	139	15	1	1	NUM
ejpam-2029	139	16	2s2	2s2	NUM
ejpam-2029	139	17	+	+	NOUN
ejpam-2029	139	18	2s+1	2s+1	NOUN
ejpam-2029	139	19	,	,	PUNCT
ejpam-2029	139	20	then	then	ADV
ejpam-2029	139	21	we	we	PRON
ejpam-2029	139	22	get	get	VERB
ejpam-2029	139	23	d	d	NOUN
ejpam-2029	139	24	=	=	PUNCT
ejpam-2029	139	25	a2r2	a2r2	X
ejpam-2029	139	26	+	+	NOUN
ejpam-2029	139	27	2rd+	2rd+	ADJ
ejpam-2029	139	28	e	e	NOUN
ejpam-2029	139	29	because	because	SCONJ
ejpam-2029	139	30	b	b	PROPN
ejpam-2029	139	31	=	=	SYM
ejpam-2029	139	32	2s+	2s+	NUM
ejpam-2029	139	33	2r`2	2r`2	NUM
ejpam-2029	139	34	+	+	CCONJ
ejpam-2029	139	35	1	1	NUM
ejpam-2029	139	36	.	.	PUNCT
ejpam-2029	140	1	thus	thus	ADV
ejpam-2029	140	2	,	,	PUNCT
ejpam-2029	140	3	the	the	DET
ejpam-2029	140	4	theorem	theorem	NOUN
ejpam-2029	140	5	is	be	AUX
ejpam-2029	140	6	proved	prove	VERB
ejpam-2029	140	7	.	.	PUNCT
ejpam-2029	141	1	as	as	ADP
ejpam-2029	141	2	an	an	DET
ejpam-2029	141	3	application	application	NOUN
ejpam-2029	141	4	of	of	ADP
ejpam-2029	141	5	this	this	DET
ejpam-2029	141	6	theorem	theorem	NOUN
ejpam-2029	141	7	,	,	PUNCT
ejpam-2029	141	8	we	we	PRON
ejpam-2029	141	9	can	can	AUX
ejpam-2029	141	10	practically	practically	ADV
ejpam-2029	141	11	determine	determine	VERB
ejpam-2029	141	12	ωd	ωd	INTJ
ejpam-2029	142	1	where	where	SCONJ
ejpam-2029	142	2	d	d	NOUN
ejpam-2029	142	3	=	=	SYM
ejpam-2029	142	4	314	314	NUM
ejpam-2029	142	5	=	=	SYM
ejpam-2029	142	6	172	172	NUM
ejpam-2029	142	7	+	+	NUM
ejpam-2029	142	8	25	25	NUM
ejpam-2029	142	9	.	.	PUNCT
ejpam-2029	143	1	since	since	SCONJ
ejpam-2029	143	2	q0	q0	PROPN
ejpam-2029	143	3	=	=	PUNCT
ejpam-2029	143	4	a	a	PROPN
ejpam-2029	143	5	and	and	CCONJ
ejpam-2029	143	6	`	`	PUNCT
ejpam-2029	143	7	0	0	NUM
ejpam-2029	143	8	=	=	SYM
ejpam-2029	143	9	2a	2a	NUM
ejpam-2029	143	10	,	,	PUNCT
ejpam-2029	143	11	it	it	PRON
ejpam-2029	143	12	follows	follow	VERB
ejpam-2029	143	13	that	that	SCONJ
ejpam-2029	143	14	q0	q0	NOUN
ejpam-2029	143	15	=	=	PUNCT
ejpam-2029	143	16	17	17	NUM
ejpam-2029	143	17	and	and	CCONJ
ejpam-2029	143	18	`	`	PUNCT
ejpam-2029	143	19	0	0	NUM
ejpam-2029	143	20	=	=	SYM
ejpam-2029	143	21	34	34	NUM
ejpam-2029	143	22	.	.	PUNCT
ejpam-2029	144	1	on	on	ADP
ejpam-2029	144	2	the	the	DET
ejpam-2029	144	3	other	other	ADJ
ejpam-2029	144	4	hand	hand	NOUN
ejpam-2029	144	5	,	,	PUNCT
ejpam-2029	144	6	we	we	PRON
ejpam-2029	144	7	get	get	VERB
ejpam-2029	144	8	m=	m=	X
ejpam-2029	144	9	6	6	NUM
ejpam-2029	144	10	,	,	PUNCT
ejpam-2029	144	11	since	since	SCONJ
ejpam-2029	144	12	b	b	PROPN
ejpam-2029	144	13	=	=	SYM
ejpam-2029	144	14	4m+1	4m+1	PROPN
ejpam-2029	144	15	.	.	PUNCT
ejpam-2029	145	1	from	from	ADP
ejpam-2029	145	2	a	a	DET
ejpam-2029	145	3	=	=	SYM
ejpam-2029	145	4	2m`1	2m`1	NUM
ejpam-2029	145	5	+	+	CCONJ
ejpam-2029	145	6	r	r	NOUN
ejpam-2029	145	7	,	,	PUNCT
ejpam-2029	145	8	we	we	PRON
ejpam-2029	145	9	obtain	obtain	VERB
ejpam-2029	145	10	`	`	PUNCT
ejpam-2029	145	11	1	1	NUM
ejpam-2029	145	12	=	=	SYM
ejpam-2029	145	13	1	1	NUM
ejpam-2029	145	14	and	and	CCONJ
ejpam-2029	145	15	r	r	NOUN
ejpam-2029	145	16	=	=	SYM
ejpam-2029	145	17	5	5	NUM
ejpam-2029	145	18	.	.	PUNCT
ejpam-2029	146	1	thus	thus	ADV
ejpam-2029	146	2	we	we	PRON
ejpam-2029	146	3	get	get	VERB
ejpam-2029	146	4	r2	r2	NOUN
ejpam-2029	146	5	=	=	NOUN
ejpam-2029	146	6	9	9	NUM
ejpam-2029	146	7	immediately	immediately	ADV
ejpam-2029	146	8	.	.	PUNCT
ejpam-2029	147	1	since	since	SCONJ
ejpam-2029	147	2	2a	2a	NUM
ejpam-2029	147	3	=	=	SYM
ejpam-2029	147	4	(	(	PUNCT
ejpam-2029	147	5	1	1	NUM
ejpam-2029	147	6	+	+	NUM
ejpam-2029	147	7	r2`1)`2	r2`1)`2	NOUN
ejpam-2029	147	8	+	+	CCONJ
ejpam-2029	147	9	r2	r2	PROPN
ejpam-2029	147	10	+	+	X
ejpam-2029	147	11	r3	r3	PROPN
ejpam-2029	147	12	,	,	PUNCT
ejpam-2029	147	13	c3	c3	X
ejpam-2029	147	14	=	=	PUNCT
ejpam-2029	147	15	4m+	4m+	NUM
ejpam-2029	147	16	1	1	NUM
ejpam-2029	147	17	+	+	CCONJ
ejpam-2029	147	18	(	(	PUNCT
ejpam-2029	147	19	r3−	r3−	PROPN
ejpam-2029	147	20	r2)`2	r2)`2	PROPN
ejpam-2029	147	21	and	and	CCONJ
ejpam-2029	147	22	2a	2a	NUM
ejpam-2029	147	23	=	=	SYM
ejpam-2029	147	24	c3`3	c3`3	X
ejpam-2029	147	25	+	+	NUM
ejpam-2029	147	26	r3	r3	NOUN
ejpam-2029	147	27	+	+	CCONJ
ejpam-2029	147	28	r4	r4	NOUN
ejpam-2029	147	29	,	,	PUNCT
ejpam-2029	147	30	we	we	PRON
ejpam-2029	147	31	obtain	obtain	VERB
ejpam-2029	147	32	`	`	PUNCT
ejpam-2029	147	33	2	2	NUM
ejpam-2029	147	34	=	=	SYM
ejpam-2029	147	35	2	2	NUM
ejpam-2029	147	36	,	,	PUNCT
ejpam-2029	147	37	r3	r3	X
ejpam-2029	147	38	=	=	SYM
ejpam-2029	147	39	5	5	NUM
ejpam-2029	147	40	,	,	PUNCT
ejpam-2029	147	41	c3	c3	PROPN
ejpam-2029	147	42	=	=	SYM
ejpam-2029	147	43	17	17	NUM
ejpam-2029	147	44	,	,	PUNCT
ejpam-2029	147	45	`	`	PUNCT
ejpam-2029	147	46	3	3	NUM
ejpam-2029	147	47	=	=	SYM
ejpam-2029	147	48	1	1	NUM
ejpam-2029	147	49	and	and	CCONJ
ejpam-2029	147	50	r4	r4	VERB
ejpam-2029	147	51	=	=	NOUN
ejpam-2029	147	52	12	12	NUM
ejpam-2029	147	53	.	.	PUNCT
ejpam-2029	148	1	hence	hence	ADV
ejpam-2029	148	2	ωd	ωd	INTJ
ejpam-2029	148	3	can	can	AUX
ejpam-2029	148	4	be	be	AUX
ejpam-2029	148	5	determined	determine	VERB
ejpam-2029	148	6	as	as	SCONJ
ejpam-2029	148	7	follows	follow	VERB
ejpam-2029	148	8	:	:	PUNCT
ejpam-2029	148	9	ωd	ωd	X
ejpam-2029	148	10	=	=	SYM
ejpam-2029	149	1	[	[	X
ejpam-2029	149	2	17	17	NUM
ejpam-2029	149	3	,	,	PUNCT
ejpam-2029	149	4	1,2	1,2	NUM
ejpam-2029	149	5	,	,	PUNCT
ejpam-2029	149	6	1,1	1,1	NUM
ejpam-2029	149	7	,	,	PUNCT
ejpam-2029	149	8	2,1	2,1	NUM
ejpam-2029	149	9	,	,	PUNCT
ejpam-2029	149	10	34	34	NUM
ejpam-2029	149	11	]	]	PUNCT
ejpam-2029	149	12	moreover	moreover	ADV
ejpam-2029	149	13	fundamental	fundamental	ADJ
ejpam-2029	149	14	unit	unit	NOUN
ejpam-2029	149	15	of	of	ADP
ejpam-2029	149	16	q	q	PROPN
ejpam-2029	149	17	(	(	PUNCT
ejpam-2029	149	18	p	p	NOUN
ejpam-2029	149	19	314	314	NUM
ejpam-2029	149	20	)	)	PUNCT
ejpam-2029	149	21	can	can	AUX
ejpam-2029	149	22	be	be	AUX
ejpam-2029	149	23	easily	easily	ADV
ejpam-2029	149	24	determined	determine	VERB
ejpam-2029	149	25	as	as	ADP
ejpam-2029	149	26	εd	εd	NOUN
ejpam-2029	149	27	=	=	SYM
ejpam-2029	149	28	886	886	NUM
ejpam-2029	149	29	+	+	NUM
ejpam-2029	149	30	50	50	NUM
ejpam-2029	149	31	p	p	NOUN
ejpam-2029	149	32	314	314	NUM
ejpam-2029	149	33	2	2	NUM
ejpam-2029	149	34	since	since	SCONJ
ejpam-2029	149	35	a=	a=	NOUN
ejpam-2029	149	36	3	3	NUM
ejpam-2029	149	37	,	,	PUNCT
ejpam-2029	149	38	b	b	NOUN
ejpam-2029	149	39	=	=	SYM
ejpam-2029	149	40	4	4	NUM
ejpam-2029	149	41	,	,	PUNCT
ejpam-2029	150	1	c	c	NOUN
ejpam-2029	150	2	=	=	SYM
ejpam-2029	150	3	3	3	X
ejpam-2029	150	4	.	.	PUNCT
ejpam-2029	150	5	furthermore	furthermore	ADV
ejpam-2029	150	6	by	by	ADP
ejpam-2029	150	7	using	use	VERB
ejpam-2029	150	8	r3	r3	PROPN
ejpam-2029	150	9	=	=	PUNCT
ejpam-2029	150	10	`	`	PUNCT
ejpam-2029	150	11	1	1	NUM
ejpam-2029	150	12	t	t	NOUN
ejpam-2029	150	13	−	−	NOUN
ejpam-2029	151	1	`	`	PUNCT
ejpam-2029	151	2	2	2	NUM
ejpam-2029	151	3	and	and	CCONJ
ejpam-2029	151	4	t	t	PROPN
ejpam-2029	151	5	−	−	PROPN
ejpam-2029	152	1	a=	a=	ADV
ejpam-2029	152	2	2s	2s	NUM
ejpam-2029	152	3	,	,	PUNCT
ejpam-2029	152	4	we	we	PRON
ejpam-2029	152	5	get	get	VERB
ejpam-2029	152	6	t	t	NOUN
ejpam-2029	152	7	=	=	SYM
ejpam-2029	152	8	7	7	NUM
ejpam-2029	152	9	and	and	CCONJ
ejpam-2029	152	10	s	s	X
ejpam-2029	152	11	=	=	SYM
ejpam-2029	152	12	2	2	NUM
ejpam-2029	152	13	.	.	PUNCT
ejpam-2029	153	1	thus	thus	ADV
ejpam-2029	153	2	d	d	X
ejpam-2029	153	3	=	=	SYM
ejpam-2029	153	4	8	8	NUM
ejpam-2029	153	5	and	and	CCONJ
ejpam-2029	153	6	e	e	NOUN
ejpam-2029	153	7	=	=	SYM
ejpam-2029	153	8	9	9	NUM
ejpam-2029	153	9	is	be	AUX
ejpam-2029	153	10	obtained	obtain	VERB
ejpam-2029	153	11	easily	easily	ADV
ejpam-2029	153	12	.	.	PUNCT
ejpam-2029	154	1	theorem	theorem	NOUN
ejpam-2029	154	2	2	2	NUM
ejpam-2029	154	3	.	.	PUNCT
ejpam-2029	155	1	let	let	VERB
ejpam-2029	155	2	d	d	NOUN
ejpam-2029	155	3	=	=	SYM
ejpam-2029	155	4	a2+b	a2+b	PROPN
ejpam-2029	155	5	≡	≡	PROPN
ejpam-2029	155	6	2,3	2,3	NUM
ejpam-2029	155	7	(	(	PUNCT
ejpam-2029	155	8	mod	mod	PROPN
ejpam-2029	155	9	4	4	X
ejpam-2029	155	10	)	)	PUNCT
ejpam-2029	155	11	be	be	AUX
ejpam-2029	155	12	a	a	DET
ejpam-2029	155	13	positive	positive	ADJ
ejpam-2029	155	14	square	square	ADJ
ejpam-2029	155	15	-	-	PUNCT
ejpam-2029	155	16	free	free	ADJ
ejpam-2029	155	17	integer	integer	NOUN
ejpam-2029	155	18	with	with	ADP
ejpam-2029	155	19	b	b	PROPN
ejpam-2029	155	20	≡	≡	PROPN
ejpam-2029	155	21	2	2	NUM
ejpam-2029	155	22	(	(	PUNCT
ejpam-2029	155	23	mod	mod	NOUN
ejpam-2029	155	24	4	4	NUM
ejpam-2029	155	25	)	)	PUNCT
ejpam-2029	155	26	.	.	PUNCT
ejpam-2029	156	1	if	if	SCONJ
ejpam-2029	156	2	kd	kd	PROPN
ejpam-2029	156	3	=	=	PROPN
ejpam-2029	156	4	7	7	NUM
ejpam-2029	156	5	,	,	PUNCT
ejpam-2029	156	6	then	then	ADV
ejpam-2029	156	7	we	we	PRON
ejpam-2029	156	8	get	get	VERB
ejpam-2029	156	9	ωd	ωd	NOUN
ejpam-2029	156	10	=	=	SYM
ejpam-2029	157	1	[	[	X
ejpam-2029	157	2	a,`1,`2,`3,`3,`2,`1	a,`1,`2,`3,`3,`2,`1	PROPN
ejpam-2029	157	3	,	,	PUNCT
ejpam-2029	157	4	2a	2a	NUM
ejpam-2029	157	5	]	]	PUNCT
ejpam-2029	157	6	for	for	ADP
ejpam-2029	157	7	the	the	DET
ejpam-2029	157	8	three	three	NUM
ejpam-2029	157	9	positive	positive	ADJ
ejpam-2029	157	10	integers	integer	NOUN
ejpam-2029	157	11	`	`	PUNCT
ejpam-2029	157	12	1	1	NUM
ejpam-2029	157	13	,	,	PUNCT
ejpam-2029	157	14	`	`	PUNCT
ejpam-2029	157	15	2	2	NUM
ejpam-2029	157	16	,	,	PUNCT
ejpam-2029	157	17	`	`	PUNCT
ejpam-2029	157	18	3	3	NUM
ejpam-2029	157	19	such	such	ADJ
ejpam-2029	157	20	that	that	SCONJ
ejpam-2029	157	21	`	`	PUNCT
ejpam-2029	157	22	i	i	PRON
ejpam-2029	157	23	≥	≥	VERB
ejpam-2029	157	24	(	(	PUNCT
ejpam-2029	157	25	i	i	NOUN
ejpam-2029	157	26	=	=	SYM
ejpam-2029	157	27	1,2	1,2	NUM
ejpam-2029	157	28	,	,	PUNCT
ejpam-2029	157	29	3	3	NUM
ejpam-2029	157	30	)	)	PUNCT
ejpam-2029	157	31	and	and	CCONJ
ejpam-2029	157	32	then	then	ADV
ejpam-2029	157	33	(	(	PUNCT
ejpam-2029	157	34	td	td	NOUN
ejpam-2029	157	35	,	,	PUNCT
ejpam-2029	157	36	ud	ud	INTJ
ejpam-2029	157	37	)	)	PUNCT
ejpam-2029	157	38	=	=	SYM
ejpam-2029	157	39	(	(	PUNCT
ejpam-2029	157	40	2[a(a	2[a(a	NUM
ejpam-2029	157	41	2	2	NUM
ejpam-2029	157	42	+	+	NUM
ejpam-2029	157	43	b2	b2	NOUN
ejpam-2029	157	44	)	)	PUNCT
ejpam-2029	157	45	+	+	CCONJ
ejpam-2029	157	46	bc	bc	PROPN
ejpam-2029	157	47	+	+	CCONJ
ejpam-2029	157	48	a`2	a`2	PROPN
ejpam-2029	157	49	]	]	X
ejpam-2029	157	50	,	,	PUNCT
ejpam-2029	157	51	2(a2	2(a2	NUM
ejpam-2029	157	52	+	+	NUM
ejpam-2029	157	53	b2	b2	NOUN
ejpam-2029	157	54	)	)	PUNCT
ejpam-2029	157	55	)	)	PUNCT
ejpam-2029	157	56	and	and	CCONJ
ejpam-2029	157	57	d	d	NOUN
ejpam-2029	157	58	=	=	PUNCT
ejpam-2029	157	59	a2r2	a2r2	X
ejpam-2029	157	60	+	+	NOUN
ejpam-2029	157	61	2rd+	2rd+	ADJ
ejpam-2029	157	62	e	e	NOUN
ejpam-2029	157	63	hold	hold	VERB
ejpam-2029	157	64	.	.	PUNCT
ejpam-2029	158	1	moreover	moreover	ADV
ejpam-2029	158	2	,	,	PUNCT
ejpam-2029	158	3	r	r	NOUN
ejpam-2029	158	4	and	and	CCONJ
ejpam-2029	158	5	s	s	NOUN
ejpam-2029	158	6	are	be	AUX
ejpam-2029	158	7	positive	positive	ADJ
ejpam-2029	158	8	integers	integer	NOUN
ejpam-2029	158	9	determined	determine	VERB
ejpam-2029	158	10	uniquely	uniquely	ADV
ejpam-2029	158	11	by	by	ADP
ejpam-2029	158	12	a	a	DET
ejpam-2029	158	13	=	=	NOUN
ejpam-2029	158	14	ar	ar	NOUN
ejpam-2029	158	15	+	+	NOUN
ejpam-2029	158	16	`	`	PUNCT
ejpam-2029	158	17	1s	1s	PROPN
ejpam-2029	158	18	g.	g.	PROPN
ejpam-2029	158	19	gözeri	gözeri	PROPN
ejpam-2029	158	20	,	,	PUNCT
ejpam-2029	158	21	a.	a.	NOUN
ejpam-2029	158	22	pekin	pekin	PROPN
ejpam-2029	158	23	/	/	SYM
ejpam-2029	158	24	eur	eur	PROPN
ejpam-2029	158	25	.	.	PUNCT
ejpam-2029	159	1	j.	j.	PROPN
ejpam-2029	159	2	pure	pure	PROPN
ejpam-2029	159	3	appl	appl	PROPN
ejpam-2029	159	4	.	.	PROPN
ejpam-2029	159	5	math	math	PROPN
ejpam-2029	159	6	,	,	PUNCT
ejpam-2029	159	7	7	7	NUM
ejpam-2029	159	8	(	(	PUNCT
ejpam-2029	159	9	2014	2014	NUM
ejpam-2029	159	10	)	)	PUNCT
ejpam-2029	159	11	,	,	PUNCT
ejpam-2029	159	12	55	55	NUM
ejpam-2029	159	13	-	-	SYM
ejpam-2029	159	14	64	64	NUM
ejpam-2029	159	15	60	60	NUM
ejpam-2029	159	16	−`2[`2	−`2[`2	ADP
ejpam-2029	159	17	+	+	NOUN
ejpam-2029	159	18	`	`	PUNCT
ejpam-2029	159	19	3(c	3(c	NUM
ejpam-2029	159	20	+	+	CCONJ
ejpam-2029	159	21	1)]−	1)]−	NUM
ejpam-2029	159	22	1=	1=	NUM
ejpam-2029	159	23	2r(`2	2r(`2	NUM
ejpam-2029	159	24	+	+	SYM
ejpam-2029	159	25	a`3)−	a`3)−	ADP
ejpam-2029	159	26	2s(b`3	2s(b`3	NUM
ejpam-2029	159	27	+	+	PROPN
ejpam-2029	159	28	a	a	X
ejpam-2029	159	29	)	)	PUNCT
ejpam-2029	159	30	where	where	SCONJ
ejpam-2029	159	31	a	a	DET
ejpam-2029	159	32	,	,	PUNCT
ejpam-2029	159	33	b	b	NOUN
ejpam-2029	159	34	,	,	PUNCT
ejpam-2029	159	35	c	c	NOUN
ejpam-2029	159	36	,	,	PUNCT
ejpam-2029	159	37	d	d	NOUN
ejpam-2029	159	38	and	and	CCONJ
ejpam-2029	159	39	e	e	NOUN
ejpam-2029	159	40	are	be	AUX
ejpam-2029	159	41	determined	determine	VERB
ejpam-2029	159	42	uniquely	uniquely	ADV
ejpam-2029	159	43	as	as	SCONJ
ejpam-2029	159	44	follows	follow	VERB
ejpam-2029	159	45	:	:	PUNCT
ejpam-2029	159	46	a=`1`2	a=`1`2	PROPN
ejpam-2029	159	47	+	+	PROPN
ejpam-2029	159	48	1	1	NUM
ejpam-2029	159	49	b	b	X
ejpam-2029	159	50	=	=	SYM
ejpam-2029	159	51	a`3	a`3	PROPN
ejpam-2029	159	52	+	+	NOUN
ejpam-2029	159	53	`	`	PUNCT
ejpam-2029	159	54	1	1	NUM
ejpam-2029	159	55	c	c	NOUN
ejpam-2029	159	56	=	=	NOUN
ejpam-2029	159	57	`	`	PUNCT
ejpam-2029	159	58	2`3	2`3	NUM
ejpam-2029	160	1	+	+	SYM
ejpam-2029	160	2	1	1	NUM
ejpam-2029	160	3	d	d	NOUN
ejpam-2029	160	4	=	=	NOUN
ejpam-2029	160	5	a`1s+	a`1s+	ADP
ejpam-2029	160	6	`	`	PUNCT
ejpam-2029	160	7	2	2	NUM
ejpam-2029	160	8	e	e	NOUN
ejpam-2029	160	9	=	=	NOUN
ejpam-2029	160	10	`	`	PUNCT
ejpam-2029	160	11	1	1	NUM
ejpam-2029	160	12	2s2	2s2	NUM
ejpam-2029	160	13	+	+	CCONJ
ejpam-2029	160	14	2s	2	VERB
ejpam-2029	160	15	.	.	PUNCT
ejpam-2029	161	1	proof	proof	NOUN
ejpam-2029	161	2	.	.	PUNCT
ejpam-2029	162	1	in	in	ADP
ejpam-2029	162	2	the	the	DET
ejpam-2029	162	3	case	case	NOUN
ejpam-2029	162	4	of	of	ADP
ejpam-2029	162	5	b	b	PROPN
ejpam-2029	162	6	≡	≡	ADJ
ejpam-2029	162	7	2	2	NUM
ejpam-2029	162	8	(	(	PUNCT
ejpam-2029	162	9	mod	mod	NOUN
ejpam-2029	162	10	4	4	NUM
ejpam-2029	162	11	)	)	PUNCT
ejpam-2029	162	12	,	,	PUNCT
ejpam-2029	162	13	we	we	PRON
ejpam-2029	162	14	put	put	VERB
ejpam-2029	162	15	b	b	NOUN
ejpam-2029	162	16	=	=	SYM
ejpam-2029	162	17	4m+	4m+	NUM
ejpam-2029	162	18	2	2	NUM
ejpam-2029	162	19	for	for	ADP
ejpam-2029	162	20	a	a	DET
ejpam-2029	162	21	positive	positive	ADJ
ejpam-2029	162	22	integer	integer	NOUN
ejpam-2029	162	23	m	m	VERB
ejpam-2029	162	24	satisfying	satisfy	VERB
ejpam-2029	162	25	0	0	PUNCT
ejpam-2029	162	26	<	<	X
ejpam-2029	162	27	2m+	2m+	NUM
ejpam-2029	162	28	1	1	NUM
ejpam-2029	162	29	≤	≤	NOUN
ejpam-2029	162	30	a.	a.	NOUN
ejpam-2029	162	31	since	since	SCONJ
ejpam-2029	162	32	q0	q0	PROPN
ejpam-2029	162	33	=	=	PUNCT
ejpam-2029	163	1	[	[	X
ejpam-2029	163	2	ωd	ωd	X
ejpam-2029	163	3	]	]	X
ejpam-2029	163	4	=	=	X
ejpam-2029	164	1	[	[	PUNCT
ejpam-2029	164	2	p	p	X
ejpam-2029	164	3	d	d	X
ejpam-2029	164	4	]	]	X
ejpam-2029	164	5	=	=	SYM
ejpam-2029	164	6	a	a	X
ejpam-2029	164	7	,	,	PUNCT
ejpam-2029	164	8	it	it	PRON
ejpam-2029	164	9	follows	follow	VERB
ejpam-2029	164	10	from	from	ADP
ejpam-2029	164	11	lemma	lemma	PROPN
ejpam-2029	164	12	3	3	NUM
ejpam-2029	164	13	that	that	DET
ejpam-2029	164	14	r0	r0	NOUN
ejpam-2029	164	15	=	=	SYM
ejpam-2029	164	16	r1	r1	PROPN
ejpam-2029	164	17	=	=	SYM
ejpam-2029	164	18	0	0	NUM
ejpam-2029	164	19	,	,	PUNCT
ejpam-2029	164	20	c0	c0	NOUN
ejpam-2029	164	21	=	=	SYM
ejpam-2029	164	22	1	1	NUM
ejpam-2029	164	23	,	,	PUNCT
ejpam-2029	164	24	c1	c1	NOUN
ejpam-2029	164	25	=	=	PUNCT
ejpam-2029	165	1	4m+	4m+	NUM
ejpam-2029	165	2	2	2	NUM
ejpam-2029	165	3	,	,	PUNCT
ejpam-2029	165	4	`	`	PUNCT
ejpam-2029	165	5	0	0	NUM
ejpam-2029	165	6	=	=	SYM
ejpam-2029	165	7	2a	2a	NUM
ejpam-2029	165	8	.	.	PUNCT
ejpam-2029	166	1	since	since	SCONJ
ejpam-2029	166	2	kd	kd	PROPN
ejpam-2029	166	3	=	=	PROPN
ejpam-2029	166	4	7	7	NUM
ejpam-2029	166	5	,	,	PUNCT
ejpam-2029	166	6	we	we	PRON
ejpam-2029	166	7	get	get	VERB
ejpam-2029	166	8	`	`	PUNCT
ejpam-2029	166	9	1	1	X
ejpam-2029	166	10	=	=	SYM
ejpam-2029	166	11	`	`	PUNCT
ejpam-2029	166	12	6	6	NUM
ejpam-2029	166	13	,	,	PUNCT
ejpam-2029	166	14	`	`	PUNCT
ejpam-2029	166	15	2	2	NUM
ejpam-2029	166	16	=	=	SYM
ejpam-2029	166	17	`	`	PUNCT
ejpam-2029	166	18	5	5	NUM
ejpam-2029	166	19	and	and	CCONJ
ejpam-2029	166	20	`	`	PUNCT
ejpam-2029	166	21	3	3	X
ejpam-2029	166	22	=	=	SYM
ejpam-2029	166	23	`	`	PUNCT
ejpam-2029	166	24	4	4	NUM
ejpam-2029	166	25	by	by	ADP
ejpam-2029	166	26	lemma	lemma	PROPN
ejpam-2029	166	27	2	2	NUM
ejpam-2029	166	28	.	.	PUNCT
ejpam-2029	167	1	then	then	ADV
ejpam-2029	167	2	we	we	PRON
ejpam-2029	167	3	have	have	VERB
ejpam-2029	167	4	ωd	ωd	NOUN
ejpam-2029	167	5	=	=	SYM
ejpam-2029	168	1	[	[	X
ejpam-2029	168	2	a,`1,`2,`3,`3,`2,`1	a,`1,`2,`3,`3,`2,`1	PROPN
ejpam-2029	168	3	,	,	PUNCT
ejpam-2029	168	4	2a	2a	NUM
ejpam-2029	168	5	]	]	PUNCT
ejpam-2029	168	6	for	for	ADP
ejpam-2029	168	7	three	three	NUM
ejpam-2029	168	8	integers	integer	NOUN
ejpam-2029	168	9	`	`	PUNCT
ejpam-2029	168	10	1	1	NUM
ejpam-2029	168	11	,	,	PUNCT
ejpam-2029	168	12	`	`	PUNCT
ejpam-2029	168	13	2	2	NUM
ejpam-2029	168	14	,	,	PUNCT
ejpam-2029	168	15	`	`	PUNCT
ejpam-2029	168	16	3	3	NUM
ejpam-2029	168	17	such	such	ADJ
ejpam-2029	168	18	that	that	SCONJ
ejpam-2029	168	19	`	`	PUNCT
ejpam-2029	168	20	i	i	PRON
ejpam-2029	168	21	≥	≥	VERB
ejpam-2029	168	22	1	1	NUM
ejpam-2029	168	23	holds	hold	VERB
ejpam-2029	168	24	.	.	PUNCT
ejpam-2029	169	1	from	from	ADP
ejpam-2029	169	2	lemma	lemma	PROPN
ejpam-2029	169	3	2	2	NUM
ejpam-2029	169	4	we	we	PRON
ejpam-2029	169	5	get	get	VERB
ejpam-2029	169	6	2a	2a	NUM
ejpam-2029	169	7	=	=	SYM
ejpam-2029	169	8	(	(	PUNCT
ejpam-2029	169	9	4m+	4m+	NUM
ejpam-2029	169	10	2)`1	2)`1	PROPN
ejpam-2029	169	11	+	+	NUM
ejpam-2029	169	12	r2	r2	PROPN
ejpam-2029	169	13	(	(	PUNCT
ejpam-2029	169	14	7	7	NUM
ejpam-2029	169	15	)	)	PUNCT
ejpam-2029	169	16	since	since	SCONJ
ejpam-2029	169	17	r1	r1	NOUN
ejpam-2029	169	18	=	=	SYM
ejpam-2029	169	19	0	0	PROPN
ejpam-2029	169	20	,	,	PUNCT
ejpam-2029	169	21	c1	c1	NOUN
ejpam-2029	169	22	=	=	NOUN
ejpam-2029	170	1	4m+	4m+	NUM
ejpam-2029	170	2	2	2	NUM
ejpam-2029	170	3	.	.	PUNCT
ejpam-2029	170	4	from	from	ADP
ejpam-2029	170	5	(	(	PUNCT
ejpam-2029	170	6	7	7	NUM
ejpam-2029	170	7	)	)	PUNCT
ejpam-2029	170	8	,	,	PUNCT
ejpam-2029	170	9	we	we	PRON
ejpam-2029	170	10	have	have	VERB
ejpam-2029	170	11	(	(	PUNCT
ejpam-2029	170	12	4m+	4m+	NUM
ejpam-2029	170	13	2)`1	2)`1	NUM
ejpam-2029	170	14	+	+	NUM
ejpam-2029	170	15	r2	r2	PROPN
ejpam-2029	170	16	≡	≡	PROPN
ejpam-2029	170	17	0	0	PUNCT
ejpam-2029	171	1	(	(	PUNCT
ejpam-2029	171	2	mod	mod	NOUN
ejpam-2029	171	3	2	2	NUM
ejpam-2029	171	4	)	)	PUNCT
ejpam-2029	171	5	and	and	CCONJ
ejpam-2029	171	6	we	we	PRON
ejpam-2029	171	7	can	can	AUX
ejpam-2029	171	8	put	put	VERB
ejpam-2029	171	9	r2	r2	NOUN
ejpam-2029	171	10	=	=	SYM
ejpam-2029	171	11	2r	2r	NUM
ejpam-2029	171	12	for	for	ADP
ejpam-2029	171	13	an	an	DET
ejpam-2029	171	14	integer	integer	NOUN
ejpam-2029	171	15	r	r	NOUN
ejpam-2029	171	16	such	such	ADJ
ejpam-2029	171	17	that	that	SCONJ
ejpam-2029	171	18	r	r	NOUN
ejpam-2029	171	19	≥	≥	NOUN
ejpam-2029	171	20	0	0	NUM
ejpam-2029	171	21	.	.	PUNCT
ejpam-2029	172	1	hence	hence	ADV
ejpam-2029	172	2	,	,	PUNCT
ejpam-2029	172	3	it	it	PRON
ejpam-2029	172	4	follows	follow	VERB
ejpam-2029	172	5	from	from	ADP
ejpam-2029	172	6	(	(	PUNCT
ejpam-2029	172	7	7	7	NUM
ejpam-2029	172	8	)	)	PUNCT
ejpam-2029	172	9	a	a	PRON
ejpam-2029	172	10	=	=	X
ejpam-2029	172	11	(	(	PUNCT
ejpam-2029	172	12	2m+	2m+	NUM
ejpam-2029	172	13	1)`1	1)`1	NUM
ejpam-2029	172	14	+	+	X
ejpam-2029	172	15	r.	r.	PROPN
ejpam-2029	172	16	(	(	PUNCT
ejpam-2029	172	17	8)	8)	NUM
ejpam-2029	172	18	it	it	PRON
ejpam-2029	172	19	follows	follow	VERB
ejpam-2029	172	20	from	from	ADP
ejpam-2029	172	21	lemma	lemma	PROPN
ejpam-2029	172	22	2	2	NUM
ejpam-2029	173	1	that	that	PRON
ejpam-2029	173	2	c2	c2	PROPN
ejpam-2029	173	3	=	=	PUNCT
ejpam-2029	173	4	1	1	NUM
ejpam-2029	173	5	+	+	CCONJ
ejpam-2029	173	6	`	`	PUNCT
ejpam-2029	173	7	1r2	1r2	NUM
ejpam-2029	173	8	(	(	PUNCT
ejpam-2029	173	9	9	9	NUM
ejpam-2029	173	10	)	)	PUNCT
ejpam-2029	173	11	and	and	CCONJ
ejpam-2029	173	12	2a	2a	NUM
ejpam-2029	173	13	=	=	SYM
ejpam-2029	173	14	c2`2	c2`2	ADP
ejpam-2029	173	15	+	+	NUM
ejpam-2029	173	16	r2	r2	NOUN
ejpam-2029	173	17	+	+	X
ejpam-2029	173	18	r3	r3	PROPN
ejpam-2029	173	19	.	.	PUNCT
ejpam-2029	174	1	(	(	PUNCT
ejpam-2029	174	2	10	10	NUM
ejpam-2029	174	3	)	)	PUNCT
ejpam-2029	174	4	then	then	ADV
ejpam-2029	174	5	from	from	ADP
ejpam-2029	174	6	(	(	PUNCT
ejpam-2029	174	7	7	7	NUM
ejpam-2029	174	8	)	)	PUNCT
ejpam-2029	174	9	,	,	PUNCT
ejpam-2029	174	10	(	(	PUNCT
ejpam-2029	174	11	9	9	NUM
ejpam-2029	174	12	)	)	PUNCT
ejpam-2029	174	13	and	and	CCONJ
ejpam-2029	174	14	(	(	PUNCT
ejpam-2029	174	15	10	10	NUM
ejpam-2029	174	16	)	)	PUNCT
ejpam-2029	174	17	we	we	PRON
ejpam-2029	174	18	have	have	VERB
ejpam-2029	174	19	(	(	PUNCT
ejpam-2029	174	20	4m+	4m+	NUM
ejpam-2029	174	21	2)`1	2)`1	NUM
ejpam-2029	174	22	=	=	SYM
ejpam-2029	174	23	c2`2	c2`2	PROPN
ejpam-2029	174	24	+	+	NUM
ejpam-2029	174	25	r3	r3	PROPN
ejpam-2029	174	26	.	.	PUNCT
ejpam-2029	175	1	(	(	PUNCT
ejpam-2029	175	2	11	11	NUM
ejpam-2029	175	3	)	)	PUNCT
ejpam-2029	175	4	moreover	moreover	ADV
ejpam-2029	175	5	,	,	PUNCT
ejpam-2029	175	6	we	we	PRON
ejpam-2029	175	7	can	can	AUX
ejpam-2029	175	8	write	write	VERB
ejpam-2029	175	9	`	`	PUNCT
ejpam-2029	175	10	2	2	NUM
ejpam-2029	175	11	+	+	NUM
ejpam-2029	175	12	r3	r3	PROPN
ejpam-2029	175	13	≡	≡	PROPN
ejpam-2029	175	14	0	0	PUNCT
ejpam-2029	176	1	(	(	PUNCT
ejpam-2029	176	2	mod	mod	PROPN
ejpam-2029	176	3	`	`	PUNCT
ejpam-2029	176	4	1	1	NUM
ejpam-2029	176	5	)	)	PUNCT
ejpam-2029	176	6	from	from	ADP
ejpam-2029	176	7	(	(	PUNCT
ejpam-2029	176	8	9	9	NUM
ejpam-2029	176	9	)	)	PUNCT
ejpam-2029	176	10	and	and	CCONJ
ejpam-2029	176	11	(	(	PUNCT
ejpam-2029	176	12	11	11	NUM
ejpam-2029	176	13	)	)	PUNCT
ejpam-2029	176	14	.	.	PUNCT
ejpam-2029	177	1	so	so	ADV
ejpam-2029	177	2	there	there	PRON
ejpam-2029	177	3	exists	exist	VERB
ejpam-2029	177	4	a	a	DET
ejpam-2029	177	5	positive	positive	ADJ
ejpam-2029	177	6	even	even	ADV
ejpam-2029	177	7	integer	integer	PROPN
ejpam-2029	177	8	t	t	PROPN
ejpam-2029	177	9	such	such	ADJ
ejpam-2029	177	10	that	that	DET
ejpam-2029	177	11	r3	r3	PROPN
ejpam-2029	177	12	=	=	PUNCT
ejpam-2029	177	13	`	`	PUNCT
ejpam-2029	177	14	1	1	NUM
ejpam-2029	177	15	t−`2	t−`2	NOUN
ejpam-2029	177	16	.	.	PUNCT
ejpam-2029	178	1	since	since	SCONJ
ejpam-2029	178	2	t	t	PROPN
ejpam-2029	178	3	is	be	AUX
ejpam-2029	178	4	even	even	ADV
ejpam-2029	178	5	,	,	PUNCT
ejpam-2029	178	6	we	we	PRON
ejpam-2029	178	7	can	can	AUX
ejpam-2029	178	8	put	put	VERB
ejpam-2029	178	9	t	t	NOUN
ejpam-2029	178	10	=	=	PUNCT
ejpam-2029	179	1	2s	2s	PROPN
ejpam-2029	179	2	for	for	ADP
ejpam-2029	179	3	a	a	DET
ejpam-2029	179	4	positive	positive	ADJ
ejpam-2029	179	5	integer	integer	NOUN
ejpam-2029	179	6	s.	s.	PROPN
ejpam-2029	179	7	thus	thus	ADV
ejpam-2029	179	8	r3	r3	PROPN
ejpam-2029	179	9	=	=	SYM
ejpam-2029	179	10	2s`1−	2s`1−	NUM
ejpam-2029	179	11	`	`	PUNCT
ejpam-2029	179	12	2	2	NUM
ejpam-2029	179	13	is	be	AUX
ejpam-2029	179	14	obtained	obtain	VERB
ejpam-2029	179	15	.	.	PUNCT
ejpam-2029	180	1	by	by	ADP
ejpam-2029	180	2	substitution	substitution	NOUN
ejpam-2029	180	3	of	of	ADP
ejpam-2029	180	4	r3	r3	PROPN
ejpam-2029	180	5	in	in	ADP
ejpam-2029	180	6	(	(	PUNCT
ejpam-2029	180	7	11	11	NUM
ejpam-2029	180	8	)	)	PUNCT
ejpam-2029	180	9	,	,	PUNCT
ejpam-2029	180	10	we	we	PRON
ejpam-2029	180	11	get	get	VERB
ejpam-2029	180	12	4m=	4m=	NUM
ejpam-2029	180	13	2s+	2s+	NUM
ejpam-2029	180	14	2r`2−	2r`2−	NUM
ejpam-2029	180	15	2	2	NUM
ejpam-2029	180	16	.	.	PUNCT
ejpam-2029	181	1	(	(	PUNCT
ejpam-2029	181	2	12	12	NUM
ejpam-2029	181	3	)	)	PUNCT
ejpam-2029	181	4	it	it	PRON
ejpam-2029	181	5	follows	follow	VERB
ejpam-2029	181	6	from	from	ADP
ejpam-2029	181	7	(	(	PUNCT
ejpam-2029	181	8	8)	8)	NUM
ejpam-2029	181	9	and	and	CCONJ
ejpam-2029	181	10	(	(	PUNCT
ejpam-2029	181	11	12	12	NUM
ejpam-2029	181	12	)	)	PUNCT
ejpam-2029	182	1	that	that	SCONJ
ejpam-2029	182	2	a	a	DET
ejpam-2029	182	3	=	=	X
ejpam-2029	182	4	r(`1`2	r(`1`2	NOUN
ejpam-2029	182	5	+	+	NOUN
ejpam-2029	182	6	1	1	NUM
ejpam-2029	182	7	)	)	PUNCT
ejpam-2029	182	8	+	+	CCONJ
ejpam-2029	182	9	s`1	s`1	PROPN
ejpam-2029	182	10	is	be	AUX
ejpam-2029	182	11	written	write	VERB
ejpam-2029	182	12	.	.	PUNCT
ejpam-2029	183	1	thus	thus	ADV
ejpam-2029	183	2	if	if	SCONJ
ejpam-2029	183	3	we	we	PRON
ejpam-2029	183	4	put	put	VERB
ejpam-2029	183	5	a	a	DET
ejpam-2029	183	6	=	=	PUNCT
ejpam-2029	183	7	`	`	PUNCT
ejpam-2029	183	8	1`2	1`2	NUM
ejpam-2029	184	1	+	+	NUM
ejpam-2029	184	2	1	1	NUM
ejpam-2029	184	3	,	,	PUNCT
ejpam-2029	184	4	then	then	ADV
ejpam-2029	184	5	we	we	PRON
ejpam-2029	184	6	get	get	VERB
ejpam-2029	184	7	a	a	DET
ejpam-2029	184	8	=	=	NOUN
ejpam-2029	184	9	ar	ar	NOUN
ejpam-2029	184	10	+	+	PROPN
ejpam-2029	184	11	s`1	s`1	PROPN
ejpam-2029	184	12	.	.	PUNCT
ejpam-2029	185	1	on	on	ADP
ejpam-2029	185	2	the	the	DET
ejpam-2029	185	3	other	other	ADJ
ejpam-2029	185	4	hand	hand	NOUN
ejpam-2029	185	5	,	,	PUNCT
ejpam-2029	185	6	we	we	PRON
ejpam-2029	185	7	get	get	VERB
ejpam-2029	185	8	2a	2a	NUM
ejpam-2029	185	9	=	=	PUNCT
ejpam-2029	185	10	c3`3	c3`3	NUM
ejpam-2029	185	11	+	+	NUM
ejpam-2029	185	12	r3	r3	NOUN
ejpam-2029	185	13	+	+	CCONJ
ejpam-2029	185	14	r4	r4	NOUN
ejpam-2029	185	15	and	and	CCONJ
ejpam-2029	185	16	c3	c3	PROPN
ejpam-2029	185	17	=	=	PUNCT
ejpam-2029	186	1	4m+	4m+	NUM
ejpam-2029	186	2	2	2	NUM
ejpam-2029	186	3	+	+	CCONJ
ejpam-2029	186	4	(	(	PUNCT
ejpam-2029	186	5	r3	r3	PROPN
ejpam-2029	186	6	−	−	NUM
ejpam-2029	186	7	r2)`2	r2)`2	PROPN
ejpam-2029	186	8	from	from	ADP
ejpam-2029	186	9	lemma	lemma	PROPN
ejpam-2029	186	10	2	2	NUM
ejpam-2029	186	11	.	.	PUNCT
ejpam-2029	187	1	it	it	PRON
ejpam-2029	187	2	follows	follow	VERB
ejpam-2029	187	3	from	from	ADP
ejpam-2029	187	4	a	a	DET
ejpam-2029	187	5	=	=	SYM
ejpam-2029	187	6	ar	ar	PROPN
ejpam-2029	187	7	+	+	CCONJ
ejpam-2029	187	8	`	`	PUNCT
ejpam-2029	187	9	1s	1s	NUM
ejpam-2029	187	10	,	,	PUNCT
ejpam-2029	187	11	2a	2a	NUM
ejpam-2029	187	12	=	=	SYM
ejpam-2029	187	13	c3`3	c3`3	NUM
ejpam-2029	187	14	+	+	NUM
ejpam-2029	187	15	r3	r3	PROPN
ejpam-2029	187	16	+	+	CCONJ
ejpam-2029	187	17	r4	r4	PROPN
ejpam-2029	187	18	,	,	PUNCT
ejpam-2029	187	19	g.	g.	PROPN
ejpam-2029	187	20	gözeri	gözeri	PROPN
ejpam-2029	187	21	,	,	PUNCT
ejpam-2029	187	22	a.	a.	NOUN
ejpam-2029	187	23	pekin	pekin	PROPN
ejpam-2029	187	24	/	/	SYM
ejpam-2029	187	25	eur	eur	PROPN
ejpam-2029	187	26	.	.	PUNCT
ejpam-2029	188	1	j.	j.	PROPN
ejpam-2029	188	2	pure	pure	PROPN
ejpam-2029	188	3	appl	appl	PROPN
ejpam-2029	188	4	.	.	PROPN
ejpam-2029	188	5	math	math	PROPN
ejpam-2029	188	6	,	,	PUNCT
ejpam-2029	188	7	7	7	NUM
ejpam-2029	188	8	(	(	PUNCT
ejpam-2029	188	9	2014	2014	NUM
ejpam-2029	188	10	)	)	PUNCT
ejpam-2029	188	11	,	,	PUNCT
ejpam-2029	188	12	55	55	NUM
ejpam-2029	188	13	-	-	SYM
ejpam-2029	188	14	64	64	NUM
ejpam-2029	188	15	61	61	NUM
ejpam-2029	188	16	c3	c3	NOUN
ejpam-2029	188	17	=	=	PUNCT
ejpam-2029	188	18	4m+	4m+	NUM
ejpam-2029	188	19	2	2	NUM
ejpam-2029	188	20	+	+	CCONJ
ejpam-2029	188	21	(	(	PUNCT
ejpam-2029	188	22	r3	r3	PROPN
ejpam-2029	188	23	−	−	PROPN
ejpam-2029	188	24	r2)`2	r2)`2	PROPN
ejpam-2029	188	25	and	and	CCONJ
ejpam-2029	188	26	(	(	PUNCT
ejpam-2029	188	27	12	12	NUM
ejpam-2029	188	28	)	)	PUNCT
ejpam-2029	188	29	that	that	PRON
ejpam-2029	188	30	r4	r4	NOUN
ejpam-2029	188	31	=	=	PUNCT
ejpam-2029	188	32	2ar	2ar	NOUN
ejpam-2029	188	33	−	−	PROPN
ejpam-2029	189	1	2s`3a+	2s`3a+	NUM
ejpam-2029	189	2	`	`	PUNCT
ejpam-2029	189	3	2(`2`3	2(`2`3	NUM
ejpam-2029	189	4	+	+	NOUN
ejpam-2029	189	5	1	1	NUM
ejpam-2029	189	6	)	)	PUNCT
ejpam-2029	189	7	.	.	PUNCT
ejpam-2029	190	1	thus	thus	ADV
ejpam-2029	190	2	,	,	PUNCT
ejpam-2029	190	3	if	if	SCONJ
ejpam-2029	190	4	we	we	PRON
ejpam-2029	190	5	put	put	VERB
ejpam-2029	190	6	c	c	NOUN
ejpam-2029	190	7	=	=	PUNCT
ejpam-2029	190	8	`	`	PUNCT
ejpam-2029	190	9	2`3	2`3	NUM
ejpam-2029	190	10	+	+	SYM
ejpam-2029	190	11	1	1	NUM
ejpam-2029	190	12	then	then	ADV
ejpam-2029	190	13	we	we	PRON
ejpam-2029	190	14	get	get	VERB
ejpam-2029	190	15	r4	r4	NOUN
ejpam-2029	190	16	=	=	NOUN
ejpam-2029	191	1	2ar	2ar	ADJ
ejpam-2029	191	2	−	−	PROPN
ejpam-2029	191	3	2s`3a+	2s`3a+	NUM
ejpam-2029	191	4	c`2	c`2	NOUN
ejpam-2029	191	5	.	.	PUNCT
ejpam-2029	192	1	(	(	PUNCT
ejpam-2029	192	2	13	13	NUM
ejpam-2029	192	3	)	)	PUNCT
ejpam-2029	192	4	moreover	moreover	ADV
ejpam-2029	192	5	,	,	PUNCT
ejpam-2029	192	6	c3	c3	PROPN
ejpam-2029	192	7	=	=	PUNCT
ejpam-2029	193	1	4m+	4m+	NUM
ejpam-2029	193	2	2	2	NUM
ejpam-2029	193	3	+	+	CCONJ
ejpam-2029	193	4	(	(	PUNCT
ejpam-2029	193	5	r3−	r3−	PROPN
ejpam-2029	193	6	r2)`2	r2)`2	PROPN
ejpam-2029	193	7	and	and	CCONJ
ejpam-2029	193	8	c4	c4	NOUN
ejpam-2029	193	9	=	=	SYM
ejpam-2029	193	10	1	1	NUM
ejpam-2029	193	11	+	+	NUM
ejpam-2029	193	12	r2`2	r2`2	PROPN
ejpam-2029	193	13	+	+	CCONJ
ejpam-2029	193	14	(	(	PUNCT
ejpam-2029	193	15	r4−	r4−	NOUN
ejpam-2029	193	16	r3)`3	r3)`3	PRON
ejpam-2029	193	17	imply	imply	VERB
ejpam-2029	193	18	4m=	4m=	NUM
ejpam-2029	193	19	2r2`2	2r2`2	NUM
ejpam-2029	193	20	+	+	CCONJ
ejpam-2029	193	21	r4`3−	r4`3−	ADJ
ejpam-2029	193	22	r3`3−	r3`3−	ADJ
ejpam-2029	193	23	r3`2−	r3`2−	NOUN
ejpam-2029	193	24	1	1	NUM
ejpam-2029	193	25	(	(	PUNCT
ejpam-2029	193	26	14	14	NUM
ejpam-2029	193	27	)	)	PUNCT
ejpam-2029	193	28	since	since	SCONJ
ejpam-2029	193	29	c3	c3	PROPN
ejpam-2029	193	30	=	=	PROPN
ejpam-2029	193	31	c4	c4	PROPN
ejpam-2029	193	32	.	.	PUNCT
ejpam-2029	194	1	then	then	ADV
ejpam-2029	194	2	by	by	ADP
ejpam-2029	194	3	substitution	substitution	NOUN
ejpam-2029	194	4	r3	r3	NOUN
ejpam-2029	194	5	=	=	SYM
ejpam-2029	194	6	2s`1−	2s`1−	NUM
ejpam-2029	194	7	`	`	PUNCT
ejpam-2029	194	8	2	2	NUM
ejpam-2029	194	9	,	,	PUNCT
ejpam-2029	194	10	(	(	PUNCT
ejpam-2029	194	11	12	12	NUM
ejpam-2029	194	12	)	)	PUNCT
ejpam-2029	194	13	and	and	CCONJ
ejpam-2029	194	14	(	(	PUNCT
ejpam-2029	194	15	13	13	NUM
ejpam-2029	194	16	)	)	PUNCT
ejpam-2029	194	17	in	in	ADP
ejpam-2029	194	18	(	(	PUNCT
ejpam-2029	194	19	14	14	NUM
ejpam-2029	194	20	)	)	PUNCT
ejpam-2029	194	21	we	we	PRON
ejpam-2029	194	22	obtain	obtain	VERB
ejpam-2029	194	23	−`2	−`2	PROPN
ejpam-2029	194	24	2−	2−	NUM
ejpam-2029	194	25	`	`	PUNCT
ejpam-2029	194	26	2`3(c	2`3(c	NUM
ejpam-2029	194	27	+	+	PROPN
ejpam-2029	194	28	1)−	1)−	NUM
ejpam-2029	194	29	1=	1=	NUM
ejpam-2029	194	30	2r(`2	2r(`2	NUM
ejpam-2029	194	31	+	+	SYM
ejpam-2029	194	32	a`3)−	a`3)−	ADP
ejpam-2029	194	33	2s[(`1	2s[(`1	NOUN
ejpam-2029	194	34	+	+	NUM
ejpam-2029	194	35	a`3)`3	a`3)`3	X
ejpam-2029	194	36	+	+	X
ejpam-2029	194	37	a	a	PRON
ejpam-2029	194	38	]	]	X
ejpam-2029	194	39	.	.	PUNCT
ejpam-2029	195	1	then	then	ADV
ejpam-2029	195	2	if	if	SCONJ
ejpam-2029	195	3	we	we	PRON
ejpam-2029	195	4	put	put	VERB
ejpam-2029	195	5	b	b	NOUN
ejpam-2029	195	6	=	=	PUNCT
ejpam-2029	195	7	`	`	PUNCT
ejpam-2029	195	8	1	1	X
ejpam-2029	195	9	+	+	NUM
ejpam-2029	195	10	a`3	a`3	INTJ
ejpam-2029	195	11	we	we	PRON
ejpam-2029	195	12	get	get	VERB
ejpam-2029	195	13	−`2	−`2	PROPN
ejpam-2029	195	14	2−	2−	NUM
ejpam-2029	195	15	`	`	PUNCT
ejpam-2029	195	16	2`3(c	2`3(c	NUM
ejpam-2029	195	17	+	+	PROPN
ejpam-2029	195	18	1)−	1)−	NUM
ejpam-2029	195	19	1=	1=	NUM
ejpam-2029	195	20	2r(`2	2r(`2	NUM
ejpam-2029	195	21	+	+	SYM
ejpam-2029	195	22	a`3)−	a`3)−	ADP
ejpam-2029	195	23	2s(b`3	2s(b`3	NUM
ejpam-2029	195	24	+	+	PROPN
ejpam-2029	195	25	a	a	X
ejpam-2029	195	26	)	)	PUNCT
ejpam-2029	195	27	.	.	PUNCT
ejpam-2029	196	1	if	if	SCONJ
ejpam-2029	196	2	we	we	PRON
ejpam-2029	196	3	assume	assume	VERB
ejpam-2029	196	4	that	that	SCONJ
ejpam-2029	196	5	the	the	DET
ejpam-2029	196	6	integers	integer	NOUN
ejpam-2029	196	7	r	r	NOUN
ejpam-2029	196	8	and	and	CCONJ
ejpam-2029	196	9	s	s	NOUN
ejpam-2029	196	10	are	be	AUX
ejpam-2029	196	11	not	not	PART
ejpam-2029	196	12	determined	determine	VERB
ejpam-2029	196	13	uniquely	uniquely	ADV
ejpam-2029	196	14	from	from	ADP
ejpam-2029	196	15	a	a	DET
ejpam-2029	196	16	=	=	SYM
ejpam-2029	196	17	ar	ar	PROPN
ejpam-2029	196	18	+	+	NOUN
ejpam-2029	196	19	`	`	PUNCT
ejpam-2029	196	20	1s	1s	NUM
ejpam-2029	196	21	and	and	CCONJ
ejpam-2029	196	22	−`2	−`2	PROPN
ejpam-2029	196	23	2	2	NUM
ejpam-2029	196	24	−	−	PROPN
ejpam-2029	196	25	`	`	PUNCT
ejpam-2029	196	26	2`3(c	2`3(c	NUM
ejpam-2029	196	27	+	+	CCONJ
ejpam-2029	196	28	1)−	1)−	NUM
ejpam-2029	196	29	1	1	NUM
ejpam-2029	196	30	=	=	SYM
ejpam-2029	196	31	2r(`2	2r(`2	NUM
ejpam-2029	196	32	+	+	CCONJ
ejpam-2029	196	33	a`3)−	a`3)−	ADP
ejpam-2029	196	34	2s(b`3	2s(b`3	NUM
ejpam-2029	196	35	+	+	CCONJ
ejpam-2029	196	36	a	a	X
ejpam-2029	196	37	)	)	PUNCT
ejpam-2029	196	38	we	we	PRON
ejpam-2029	196	39	get	get	VERB
ejpam-2029	196	40	a(a+	a(a+	INTJ
ejpam-2029	196	41	b`3	b`3	NOUN
ejpam-2029	196	42	)	)	PUNCT
ejpam-2029	197	1	+	+	CCONJ
ejpam-2029	197	2	`	`	PUNCT
ejpam-2029	197	3	1(a`3	1(a`3	NOUN
ejpam-2029	198	1	+	+	CCONJ
ejpam-2029	198	2	`	`	PUNCT
ejpam-2029	198	3	2	2	X
ejpam-2029	198	4	)	)	PUNCT
ejpam-2029	198	5	=	=	SYM
ejpam-2029	198	6	0	0	NUM
ejpam-2029	198	7	which	which	PRON
ejpam-2029	198	8	is	be	AUX
ejpam-2029	198	9	a	a	DET
ejpam-2029	198	10	contradiction	contradiction	NOUN
ejpam-2029	198	11	.	.	PUNCT
ejpam-2029	199	1	therefore	therefore	ADV
ejpam-2029	199	2	,	,	PUNCT
ejpam-2029	199	3	the	the	DET
ejpam-2029	199	4	integers	integer	NOUN
ejpam-2029	199	5	r	r	NOUN
ejpam-2029	199	6	and	and	CCONJ
ejpam-2029	199	7	s	s	NOUN
ejpam-2029	199	8	are	be	AUX
ejpam-2029	199	9	uniquely	uniquely	ADV
ejpam-2029	199	10	determined	determine	VERB
ejpam-2029	199	11	.	.	PUNCT
ejpam-2029	200	1	now	now	ADV
ejpam-2029	200	2	,	,	PUNCT
ejpam-2029	200	3	since	since	SCONJ
ejpam-2029	200	4	ωd	ωd	ADP
ejpam-2029	200	5	=	=	SYM
ejpam-2029	201	1	[	[	X
ejpam-2029	201	2	a,`1,`2,`3,`3,`2,`1	a,`1,`2,`3,`3,`2,`1	PROPN
ejpam-2029	201	3	,	,	PUNCT
ejpam-2029	201	4	2a	2a	NUM
ejpam-2029	201	5	]	]	PUNCT
ejpam-2029	201	6	implies	imply	VERB
ejpam-2029	201	7	q5	q5	PROPN
ejpam-2029	201	8	=	=	SYM
ejpam-2029	201	9	bc	bc	PROPN
ejpam-2029	201	10	+	+	CCONJ
ejpam-2029	201	11	a`2	a`2	PROPN
ejpam-2029	201	12	and	and	CCONJ
ejpam-2029	201	13	q6	q6	PROPN
ejpam-2029	201	14	=	=	PROPN
ejpam-2029	201	15	a2	a2	PROPN
ejpam-2029	201	16	+	+	CCONJ
ejpam-2029	201	17	b2	b2	NOUN
ejpam-2029	201	18	by	by	ADP
ejpam-2029	201	19	lemma	lemma	PROPN
ejpam-2029	201	20	1	1	NUM
ejpam-2029	201	21	,	,	PUNCT
ejpam-2029	201	22	we	we	PRON
ejpam-2029	201	23	obtain	obtain	VERB
ejpam-2029	201	24	td	td	NOUN
ejpam-2029	201	25	=	=	NOUN
ejpam-2029	201	26	2[a(a2	2[a(a2	NUM
ejpam-2029	201	27	+	+	NUM
ejpam-2029	201	28	b2	b2	NOUN
ejpam-2029	201	29	)	)	PUNCT
ejpam-2029	201	30	+	+	CCONJ
ejpam-2029	201	31	bc	bc	PROPN
ejpam-2029	201	32	+	+	CCONJ
ejpam-2029	201	33	a`2	a`2	PROPN
ejpam-2029	201	34	]	]	X
ejpam-2029	201	35	and	and	CCONJ
ejpam-2029	201	36	ud	ud	INTJ
ejpam-2029	201	37	=	=	SYM
ejpam-2029	201	38	2(a2	2(a2	PROPN
ejpam-2029	201	39	+	+	NUM
ejpam-2029	201	40	b2	b2	NOUN
ejpam-2029	201	41	)	)	PUNCT
ejpam-2029	201	42	,	,	PUNCT
ejpam-2029	201	43	respectively	respectively	ADV
ejpam-2029	201	44	.	.	PUNCT
ejpam-2029	202	1	moreover	moreover	ADV
ejpam-2029	202	2	if	if	SCONJ
ejpam-2029	202	3	we	we	PRON
ejpam-2029	202	4	put	put	VERB
ejpam-2029	202	5	d	d	NOUN
ejpam-2029	202	6	=	=	PUNCT
ejpam-2029	202	7	a`1s+	a`1s+	NOUN
ejpam-2029	202	8	`	`	PUNCT
ejpam-2029	202	9	2	2	NUM
ejpam-2029	202	10	and	and	CCONJ
ejpam-2029	202	11	e	e	NOUN
ejpam-2029	202	12	=	=	PUNCT
ejpam-2029	202	13	`	`	PUNCT
ejpam-2029	202	14	1	1	NUM
ejpam-2029	202	15	2s2	2s2	NUM
ejpam-2029	202	16	+	+	CCONJ
ejpam-2029	202	17	2s	2s	NUM
ejpam-2029	202	18	,	,	PUNCT
ejpam-2029	202	19	then	then	ADV
ejpam-2029	202	20	we	we	PRON
ejpam-2029	202	21	get	get	VERB
ejpam-2029	202	22	d	d	NOUN
ejpam-2029	202	23	=	=	PUNCT
ejpam-2029	202	24	a2r2	a2r2	X
ejpam-2029	202	25	+	+	SYM
ejpam-2029	202	26	2rd+	2rd+	NUM
ejpam-2029	202	27	e	e	NOUN
ejpam-2029	202	28	since	since	SCONJ
ejpam-2029	202	29	b	b	PROPN
ejpam-2029	202	30	=	=	SYM
ejpam-2029	202	31	2s+	2s+	PROPN
ejpam-2029	202	32	r`2	r`2	NOUN
ejpam-2029	202	33	.	.	PUNCT
ejpam-2029	203	1	thus	thus	ADV
ejpam-2029	203	2	,	,	PUNCT
ejpam-2029	203	3	the	the	DET
ejpam-2029	203	4	theorem	theorem	NOUN
ejpam-2029	203	5	is	be	AUX
ejpam-2029	203	6	proved	prove	VERB
ejpam-2029	203	7	completely	completely	ADV
ejpam-2029	203	8	.	.	PUNCT
ejpam-2029	204	1	as	as	ADP
ejpam-2029	204	2	an	an	DET
ejpam-2029	204	3	application	application	NOUN
ejpam-2029	204	4	of	of	ADP
ejpam-2029	204	5	this	this	DET
ejpam-2029	204	6	theorem	theorem	NOUN
ejpam-2029	204	7	,	,	PUNCT
ejpam-2029	204	8	we	we	PRON
ejpam-2029	204	9	can	can	AUX
ejpam-2029	204	10	easily	easily	ADV
ejpam-2029	204	11	determine	determine	VERB
ejpam-2029	204	12	ωd	ωd	INTJ
ejpam-2029	205	1	where	where	SCONJ
ejpam-2029	205	2	d	d	NOUN
ejpam-2029	205	3	=	=	SYM
ejpam-2029	205	4	202	202	NUM
ejpam-2029	205	5	=	=	SYM
ejpam-2029	205	6	142	142	NUM
ejpam-2029	205	7	+	+	NUM
ejpam-2029	205	8	6	6	NUM
ejpam-2029	205	9	.	.	PUNCT
ejpam-2029	205	10	since	since	SCONJ
ejpam-2029	205	11	q0	q0	PROPN
ejpam-2029	205	12	=	=	PUNCT
ejpam-2029	205	13	a	a	PROPN
ejpam-2029	205	14	and	and	CCONJ
ejpam-2029	205	15	`	`	PUNCT
ejpam-2029	205	16	0	0	NUM
ejpam-2029	205	17	=	=	SYM
ejpam-2029	205	18	2a	2a	NUM
ejpam-2029	205	19	,	,	PUNCT
ejpam-2029	205	20	we	we	PRON
ejpam-2029	205	21	get	get	VERB
ejpam-2029	205	22	q0	q0	VERB
ejpam-2029	205	23	=	=	PUNCT
ejpam-2029	205	24	14	14	NUM
ejpam-2029	205	25	and	and	CCONJ
ejpam-2029	205	26	`	`	PUNCT
ejpam-2029	205	27	0	0	NUM
ejpam-2029	205	28	=	=	SYM
ejpam-2029	205	29	28	28	NUM
ejpam-2029	205	30	.	.	PUNCT
ejpam-2029	206	1	on	on	ADP
ejpam-2029	206	2	the	the	DET
ejpam-2029	206	3	other	other	ADJ
ejpam-2029	206	4	hand	hand	NOUN
ejpam-2029	206	5	,	,	PUNCT
ejpam-2029	206	6	we	we	PRON
ejpam-2029	206	7	get	get	VERB
ejpam-2029	206	8	m=	m=	X
ejpam-2029	206	9	1	1	NUM
ejpam-2029	206	10	since	since	SCONJ
ejpam-2029	206	11	b	b	NOUN
ejpam-2029	206	12	=	=	SYM
ejpam-2029	206	13	4m+	4m+	NUM
ejpam-2029	206	14	2	2	NUM
ejpam-2029	206	15	.	.	PUNCT
ejpam-2029	207	1	then	then	ADV
ejpam-2029	207	2	we	we	PRON
ejpam-2029	207	3	get	get	VERB
ejpam-2029	207	4	`	`	PUNCT
ejpam-2029	207	5	1	1	NUM
ejpam-2029	207	6	=	=	SYM
ejpam-2029	207	7	4	4	NUM
ejpam-2029	207	8	and	and	CCONJ
ejpam-2029	207	9	r	r	NOUN
ejpam-2029	207	10	=	=	SYM
ejpam-2029	207	11	2	2	NUM
ejpam-2029	207	12	from	from	ADP
ejpam-2029	207	13	a	a	DET
ejpam-2029	207	14	=	=	PUNCT
ejpam-2029	207	15	(	(	PUNCT
ejpam-2029	207	16	2m+	2m+	NUM
ejpam-2029	207	17	1)`1	1)`1	NUM
ejpam-2029	207	18	+	+	CCONJ
ejpam-2029	207	19	r	r	NOUN
ejpam-2029	207	20	and	and	CCONJ
ejpam-2029	207	21	r	r	NOUN
ejpam-2029	207	22	<	<	X
ejpam-2029	207	23	2m+	2m+	NUM
ejpam-2029	207	24	1	1	NUM
ejpam-2029	207	25	.	.	PUNCT
ejpam-2029	208	1	hence	hence	ADV
ejpam-2029	208	2	r2	r2	PROPN
ejpam-2029	208	3	=	=	SYM
ejpam-2029	208	4	4	4	NUM
ejpam-2029	208	5	is	be	AUX
ejpam-2029	208	6	obtained	obtain	VERB
ejpam-2029	208	7	.	.	PUNCT
ejpam-2029	209	1	it	it	PRON
ejpam-2029	209	2	follows	follow	VERB
ejpam-2029	209	3	from	from	ADP
ejpam-2029	209	4	4	4	NUM
ejpam-2029	209	5	m	m	NOUN
ejpam-2029	209	6	=	=	SYM
ejpam-2029	209	7	2s+	2s+	NUM
ejpam-2029	209	8	2r`2	2r`2	NUM
ejpam-2029	209	9	−	−	PROPN
ejpam-2029	209	10	2	2	NUM
ejpam-2029	210	1	that	that	SCONJ
ejpam-2029	210	2	`	`	PUNCT
ejpam-2029	210	3	2	2	NUM
ejpam-2029	210	4	=	=	SYM
ejpam-2029	210	5	1	1	NUM
ejpam-2029	210	6	and	and	CCONJ
ejpam-2029	210	7	s	s	NOUN
ejpam-2029	210	8	=	=	ADJ
ejpam-2029	210	9	1	1	X
ejpam-2029	210	10	.	.	PUNCT
ejpam-2029	210	11	moreover	moreover	ADV
ejpam-2029	210	12	,	,	PUNCT
ejpam-2029	210	13	we	we	PRON
ejpam-2029	210	14	get	get	VERB
ejpam-2029	210	15	r3	r3	PROPN
ejpam-2029	210	16	=	=	NOUN
ejpam-2029	210	17	7	7	NUM
ejpam-2029	210	18	since	since	SCONJ
ejpam-2029	210	19	r3	r3	PROPN
ejpam-2029	210	20	=	=	SYM
ejpam-2029	210	21	2s`1	2s`1	NUM
ejpam-2029	210	22	−	−	NOUN
ejpam-2029	210	23	`	`	PUNCT
ejpam-2029	210	24	2	2	X
ejpam-2029	210	25	.	.	PUNCT
ejpam-2029	210	26	since	since	SCONJ
ejpam-2029	210	27	c3	c3	PROPN
ejpam-2029	210	28	=	=	PUNCT
ejpam-2029	210	29	4m+	4m+	NUM
ejpam-2029	210	30	2	2	NUM
ejpam-2029	210	31	+	+	CCONJ
ejpam-2029	210	32	(	(	PUNCT
ejpam-2029	210	33	r3	r3	PROPN
ejpam-2029	210	34	−	−	NOUN
ejpam-2029	210	35	r2)`2	r2)`2	NOUN
ejpam-2029	210	36	we	we	PRON
ejpam-2029	210	37	obtain	obtain	VERB
ejpam-2029	210	38	c3	c3	NOUN
ejpam-2029	210	39	=	=	NOUN
ejpam-2029	210	40	9	9	X
ejpam-2029	210	41	.	.	PUNCT
ejpam-2029	210	42	by	by	ADP
ejpam-2029	210	43	using	use	VERB
ejpam-2029	210	44	2a	2a	NUM
ejpam-2029	210	45	=	=	SYM
ejpam-2029	210	46	c3`3	c3`3	NUM
ejpam-2029	210	47	+	+	NUM
ejpam-2029	210	48	r3	r3	NOUN
ejpam-2029	210	49	+	+	CCONJ
ejpam-2029	210	50	r4	r4	VERB
ejpam-2029	210	51	and	and	CCONJ
ejpam-2029	210	52	r4	r4	VERB
ejpam-2029	210	53	<	<	X
ejpam-2029	210	54	c3	c3	PROPN
ejpam-2029	210	55	,	,	PUNCT
ejpam-2029	210	56	we	we	PRON
ejpam-2029	210	57	get	get	VERB
ejpam-2029	210	58	`	`	PUNCT
ejpam-2029	210	59	3	3	NUM
ejpam-2029	210	60	=	=	SYM
ejpam-2029	210	61	2	2	NUM
ejpam-2029	210	62	and	and	CCONJ
ejpam-2029	210	63	r4	r4	VERB
ejpam-2029	210	64	=	=	NOUN
ejpam-2029	211	1	3	3	X
ejpam-2029	211	2	.	.	X
ejpam-2029	212	1	hence	hence	ADV
ejpam-2029	212	2	ωd	ωd	INTJ
ejpam-2029	212	3	can	can	AUX
ejpam-2029	212	4	be	be	AUX
ejpam-2029	212	5	determined	determine	VERB
ejpam-2029	212	6	as	as	SCONJ
ejpam-2029	212	7	follows	follow	VERB
ejpam-2029	212	8	:	:	PUNCT
ejpam-2029	212	9	ωd	ωd	ADP
ejpam-2029	212	10	=	=	SYM
ejpam-2029	213	1	[	[	X
ejpam-2029	213	2	14	14	NUM
ejpam-2029	213	3	,	,	PUNCT
ejpam-2029	213	4	4,1	4,1	NUM
ejpam-2029	213	5	,	,	PUNCT
ejpam-2029	213	6	2,2	2,2	NUM
ejpam-2029	213	7	,	,	PUNCT
ejpam-2029	213	8	1,4	1,4	NUM
ejpam-2029	213	9	,	,	PUNCT
ejpam-2029	213	10	28	28	NUM
ejpam-2029	213	11	]	]	PUNCT
ejpam-2029	213	12	furthermore	furthermore	ADV
ejpam-2029	213	13	the	the	DET
ejpam-2029	213	14	fundamental	fundamental	ADJ
ejpam-2029	213	15	unit	unit	NOUN
ejpam-2029	213	16	of	of	ADP
ejpam-2029	213	17	q	q	PROPN
ejpam-2029	213	18	(	(	PUNCT
ejpam-2029	213	19	p	p	NOUN
ejpam-2029	213	20	202	202	NUM
ejpam-2029	213	21	)	)	PUNCT
ejpam-2029	213	22	can	can	AUX
ejpam-2029	213	23	be	be	AUX
ejpam-2029	213	24	easily	easily	ADV
ejpam-2029	213	25	determined	determine	VERB
ejpam-2029	213	26	as	as	ADP
ejpam-2029	213	27	εd	εd	NOUN
ejpam-2029	213	28	=	=	SYM
ejpam-2029	213	29	6282	6282	NUM
ejpam-2029	213	30	+	+	NUM
ejpam-2029	214	1	442	442	NUM
ejpam-2029	214	2	p	p	NOUN
ejpam-2029	214	3	202	202	NUM
ejpam-2029	214	4	2	2	NUM
ejpam-2029	214	5	since	since	SCONJ
ejpam-2029	214	6	a=	a=	ADV
ejpam-2029	214	7	5	5	NUM
ejpam-2029	214	8	,	,	PUNCT
ejpam-2029	214	9	b	b	NOUN
ejpam-2029	214	10	=	=	SYM
ejpam-2029	214	11	14	14	NUM
ejpam-2029	214	12	,	,	PUNCT
ejpam-2029	214	13	c	c	NOUN
ejpam-2029	214	14	=	=	SYM
ejpam-2029	214	15	3	3	X
ejpam-2029	214	16	.	.	PUNCT
ejpam-2029	215	1	moreover	moreover	ADV
ejpam-2029	215	2	it	it	PRON
ejpam-2029	215	3	is	be	AUX
ejpam-2029	215	4	easily	easily	ADV
ejpam-2029	215	5	seen	see	VERB
ejpam-2029	215	6	that	that	SCONJ
ejpam-2029	215	7	d	d	NOUN
ejpam-2029	215	8	=	=	SYM
ejpam-2029	215	9	21	21	NUM
ejpam-2029	215	10	and	and	CCONJ
ejpam-2029	215	11	e	e	NOUN
ejpam-2029	215	12	=	=	SYM
ejpam-2029	215	13	18	18	NUM
ejpam-2029	215	14	.	.	PUNCT
ejpam-2029	215	15	theorem	theorem	NOUN
ejpam-2029	215	16	3	3	NUM
ejpam-2029	215	17	.	.	X
ejpam-2029	215	18	for	for	ADP
ejpam-2029	215	19	a	a	DET
ejpam-2029	215	20	positive	positive	ADJ
ejpam-2029	215	21	square	square	ADJ
ejpam-2029	215	22	-	-	PUNCT
ejpam-2029	215	23	free	free	ADJ
ejpam-2029	215	24	integer	integer	NOUN
ejpam-2029	216	1	d	d	PROPN
ejpam-2029	216	2	congruent	congruent	ADJ
ejpam-2029	216	3	to	to	ADP
ejpam-2029	216	4	3	3	NUM
ejpam-2029	216	5	modulo	modulo	NOUN
ejpam-2029	216	6	4	4	NUM
ejpam-2029	216	7	,	,	PUNCT
ejpam-2029	216	8	we	we	PRON
ejpam-2029	216	9	assume	assume	VERB
ejpam-2029	216	10	kd	kd	PROPN
ejpam-2029	216	11	=	=	PROPN
ejpam-2029	216	12	7	7	X
ejpam-2029	216	13	.	.	PUNCT
ejpam-2029	217	1	then	then	ADV
ejpam-2029	217	2	,	,	PUNCT
ejpam-2029	217	3	if	if	SCONJ
ejpam-2029	217	4	b	b	NOUN
ejpam-2029	217	5	is	be	AUX
ejpam-2029	217	6	congruent	congruent	ADJ
ejpam-2029	217	7	to	to	ADP
ejpam-2029	217	8	3	3	NUM
ejpam-2029	217	9	modulo	modulo	NOUN
ejpam-2029	217	10	4	4	NUM
ejpam-2029	217	11	,	,	PUNCT
ejpam-2029	217	12	we	we	PRON
ejpam-2029	217	13	get	get	VERB
ejpam-2029	217	14	ωd	ωd	NOUN
ejpam-2029	218	1	=	=	SYM
ejpam-2029	219	1	[	[	X
ejpam-2029	219	2	a,`1,`2,`3,`3,`2,`1	a,`1,`2,`3,`3,`2,`1	PROPN
ejpam-2029	219	3	,	,	PUNCT
ejpam-2029	219	4	2a	2a	NUM
ejpam-2029	219	5	]	]	PUNCT
ejpam-2029	219	6	for	for	ADP
ejpam-2029	219	7	three	three	NUM
ejpam-2029	219	8	positive	positive	ADJ
ejpam-2029	219	9	integers	integer	NOUN
ejpam-2029	219	10	`	`	PUNCT
ejpam-2029	219	11	1	1	NUM
ejpam-2029	219	12	,	,	PUNCT
ejpam-2029	219	13	`	`	PUNCT
ejpam-2029	219	14	2	2	NUM
ejpam-2029	219	15	,	,	PUNCT
ejpam-2029	219	16	`	`	PUNCT
ejpam-2029	219	17	3	3	NUM
ejpam-2029	219	18	such	such	ADJ
ejpam-2029	219	19	that	that	SCONJ
ejpam-2029	219	20	`	`	PUNCT
ejpam-2029	219	21	i	i	PRON
ejpam-2029	219	22	≥	≥	VERB
ejpam-2029	219	23	1	1	NUM
ejpam-2029	219	24	(	(	PUNCT
ejpam-2029	219	25	i	i	NOUN
ejpam-2029	219	26	=	=	SYM
ejpam-2029	219	27	1,2	1,2	NUM
ejpam-2029	219	28	,	,	PUNCT
ejpam-2029	219	29	3	3	NUM
ejpam-2029	219	30	)	)	PUNCT
ejpam-2029	219	31	,	,	PUNCT
ejpam-2029	219	32	and	and	CCONJ
ejpam-2029	219	33	then	then	ADV
ejpam-2029	219	34	(	(	PUNCT
ejpam-2029	219	35	td	td	NOUN
ejpam-2029	219	36	,	,	PUNCT
ejpam-2029	219	37	ud	ud	INTJ
ejpam-2029	219	38	)	)	PUNCT
ejpam-2029	219	39	=	=	SYM
ejpam-2029	220	1	(	(	PUNCT
ejpam-2029	220	2	2[a(a	2[a(a	NUM
ejpam-2029	220	3	2	2	NUM
ejpam-2029	220	4	+	+	NUM
ejpam-2029	220	5	b2	b2	NOUN
ejpam-2029	220	6	)	)	PUNCT
ejpam-2029	221	1	+	+	CCONJ
ejpam-2029	221	2	bc	bc	PROPN
ejpam-2029	221	3	+	+	CCONJ
ejpam-2029	221	4	a`2	a`2	PROPN
ejpam-2029	221	5	]	]	X
ejpam-2029	221	6	,	,	PUNCT
ejpam-2029	221	7	2(a2	2(a2	NUM
ejpam-2029	221	8	+	+	NUM
ejpam-2029	221	9	b2	b2	NOUN
ejpam-2029	221	10	)	)	PUNCT
ejpam-2029	221	11	)	)	PUNCT
ejpam-2029	221	12	and	and	CCONJ
ejpam-2029	221	13	d	d	NOUN
ejpam-2029	221	14	=	=	PUNCT
ejpam-2029	221	15	a2r2	a2r2	X
ejpam-2029	221	16	+	+	NUM
ejpam-2029	221	17	2rd+	2rd+	NUM
ejpam-2029	221	18	e	e	NOUN
ejpam-2029	221	19	g.	g.	NOUN
ejpam-2029	221	20	gözeri	gözeri	PROPN
ejpam-2029	221	21	,	,	PUNCT
ejpam-2029	221	22	a.	a.	NOUN
ejpam-2029	221	23	pekin	pekin	PROPN
ejpam-2029	221	24	/	/	SYM
ejpam-2029	221	25	eur	eur	PROPN
ejpam-2029	221	26	.	.	PUNCT
ejpam-2029	222	1	j.	j.	PROPN
ejpam-2029	222	2	pure	pure	PROPN
ejpam-2029	222	3	appl	appl	PROPN
ejpam-2029	222	4	.	.	PROPN
ejpam-2029	222	5	math	math	PROPN
ejpam-2029	222	6	,	,	PUNCT
ejpam-2029	222	7	7	7	NUM
ejpam-2029	222	8	(	(	PUNCT
ejpam-2029	222	9	2014	2014	NUM
ejpam-2029	222	10	)	)	PUNCT
ejpam-2029	222	11	,	,	PUNCT
ejpam-2029	222	12	55	55	NUM
ejpam-2029	222	13	-	-	SYM
ejpam-2029	222	14	64	64	NUM
ejpam-2029	222	15	62	62	NUM
ejpam-2029	222	16	hold	hold	NOUN
ejpam-2029	222	17	where	where	SCONJ
ejpam-2029	222	18	a	a	DET
ejpam-2029	222	19	,	,	PUNCT
ejpam-2029	222	20	b	b	NOUN
ejpam-2029	222	21	,	,	PUNCT
ejpam-2029	222	22	c	c	NOUN
ejpam-2029	222	23	,	,	PUNCT
ejpam-2029	222	24	d	d	NOUN
ejpam-2029	222	25	and	and	CCONJ
ejpam-2029	222	26	e	e	NOUN
ejpam-2029	222	27	are	be	AUX
ejpam-2029	222	28	determined	determine	VERB
ejpam-2029	222	29	uniquely	uniquely	ADV
ejpam-2029	222	30	as	as	SCONJ
ejpam-2029	222	31	follows	follow	VERB
ejpam-2029	222	32	:	:	PUNCT
ejpam-2029	222	33	a=`1`2	a=`1`2	PROPN
ejpam-2029	222	34	+	+	PROPN
ejpam-2029	222	35	1	1	NUM
ejpam-2029	222	36	b	b	X
ejpam-2029	222	37	=	=	NOUN
ejpam-2029	222	38	`	`	PUNCT
ejpam-2029	222	39	1	1	NUM
ejpam-2029	222	40	+	+	NUM
ejpam-2029	222	41	a`3	a`3	NOUN
ejpam-2029	222	42	c	c	AUX
ejpam-2029	222	43	=	=	PUNCT
ejpam-2029	222	44	`	`	PUNCT
ejpam-2029	222	45	2`3	2`3	NUM
ejpam-2029	223	1	+	+	SYM
ejpam-2029	223	2	1	1	NUM
ejpam-2029	223	3	d	d	NOUN
ejpam-2029	223	4	=	=	NOUN
ejpam-2029	223	5	a`1s+	a`1s+	ADP
ejpam-2029	223	6	`	`	PUNCT
ejpam-2029	223	7	2	2	NUM
ejpam-2029	223	8	e	e	NOUN
ejpam-2029	223	9	=	=	NOUN
ejpam-2029	223	10	`	`	PUNCT
ejpam-2029	223	11	1	1	NUM
ejpam-2029	223	12	2s2	2s2	NUM
ejpam-2029	223	13	+	+	SYM
ejpam-2029	223	14	2s+	2s+	NUM
ejpam-2029	223	15	3	3	NUM
ejpam-2029	223	16	.	.	PUNCT
ejpam-2029	224	1	moreover	moreover	ADV
ejpam-2029	224	2	,	,	PUNCT
ejpam-2029	224	3	r	r	NOUN
ejpam-2029	224	4	is	be	AUX
ejpam-2029	224	5	an	an	DET
ejpam-2029	224	6	odd	odd	ADJ
ejpam-2029	224	7	integer	integer	NOUN
ejpam-2029	224	8	and	and	CCONJ
ejpam-2029	224	9	s	s	NOUN
ejpam-2029	224	10	is	be	AUX
ejpam-2029	224	11	a	a	DET
ejpam-2029	224	12	positive	positive	ADJ
ejpam-2029	224	13	integer	integer	NOUN
ejpam-2029	224	14	determined	determine	VERB
ejpam-2029	224	15	uniquely	uniquely	ADV
ejpam-2029	224	16	by	by	ADP
ejpam-2029	224	17	a	a	DET
ejpam-2029	224	18	=	=	NOUN
ejpam-2029	224	19	ar	ar	NOUN
ejpam-2029	224	20	+	+	NOUN
ejpam-2029	224	21	`	`	PUNCT
ejpam-2029	224	22	1s	1s	NUM
ejpam-2029	224	23	3(a2	3(a2	NUM
ejpam-2029	224	24	+	+	X
ejpam-2029	224	25	b2)−	b2)−	ADJ
ejpam-2029	224	26	c2−	c2−	ADJ
ejpam-2029	224	27	`	`	PUNCT
ejpam-2029	224	28	2	2	NUM
ejpam-2029	224	29	2	2	NUM
ejpam-2029	224	30	=	=	SYM
ejpam-2029	224	31	2rb−	2rb−	NUM
ejpam-2029	224	32	2s(a+	2s(a+	PROPN
ejpam-2029	224	33	b`3	b`3	NOUN
ejpam-2029	224	34	)	)	PUNCT
ejpam-2029	224	35	.	.	PUNCT
ejpam-2029	225	1	proof	proof	NOUN
ejpam-2029	225	2	.	.	PUNCT
ejpam-2029	226	1	in	in	ADP
ejpam-2029	226	2	the	the	DET
ejpam-2029	226	3	case	case	NOUN
ejpam-2029	226	4	of	of	ADP
ejpam-2029	226	5	b	b	PROPN
ejpam-2029	226	6	≡	≡	PROPN
ejpam-2029	226	7	3	3	NUM
ejpam-2029	226	8	(	(	PUNCT
ejpam-2029	226	9	mod	mod	NOUN
ejpam-2029	226	10	4	4	NUM
ejpam-2029	226	11	)	)	PUNCT
ejpam-2029	226	12	,	,	PUNCT
ejpam-2029	226	13	it	it	PRON
ejpam-2029	226	14	can	can	AUX
ejpam-2029	226	15	be	be	AUX
ejpam-2029	226	16	easily	easily	ADV
ejpam-2029	226	17	seen	see	VERB
ejpam-2029	226	18	that	that	SCONJ
ejpam-2029	226	19	a	a	PRON
ejpam-2029	226	20	is	be	AUX
ejpam-2029	226	21	an	an	DET
ejpam-2029	226	22	even	even	ADV
ejpam-2029	226	23	integer	integer	NOUN
ejpam-2029	226	24	since	since	SCONJ
ejpam-2029	226	25	d	d	PROPN
ejpam-2029	226	26	is	be	AUX
ejpam-2029	226	27	congruent	congruent	ADJ
ejpam-2029	226	28	to	to	ADP
ejpam-2029	226	29	3	3	NUM
ejpam-2029	226	30	modulo	modulo	NOUN
ejpam-2029	226	31	4	4	NUM
ejpam-2029	226	32	.	.	PUNCT
ejpam-2029	227	1	we	we	PRON
ejpam-2029	227	2	can	can	AUX
ejpam-2029	227	3	put	put	VERB
ejpam-2029	227	4	b	b	NOUN
ejpam-2029	227	5	=	=	SYM
ejpam-2029	227	6	4m+	4m+	NUM
ejpam-2029	227	7	3	3	NUM
ejpam-2029	227	8	for	for	ADP
ejpam-2029	227	9	a	a	DET
ejpam-2029	227	10	non	non	ADJ
ejpam-2029	227	11	-	-	ADJ
ejpam-2029	227	12	negative	negative	ADJ
ejpam-2029	227	13	integer	integer	NOUN
ejpam-2029	227	14	m	m	AUX
ejpam-2029	227	15	satisfying	satisfy	VERB
ejpam-2029	227	16	0	0	NUM
ejpam-2029	227	17	≤	≤	NUM
ejpam-2029	227	18	4	4	NUM
ejpam-2029	227	19	m	m	NOUN
ejpam-2029	227	20	<	<	X
ejpam-2029	227	21	2a−	2a−	NUM
ejpam-2029	227	22	2	2	NUM
ejpam-2029	227	23	.	.	PUNCT
ejpam-2029	227	24	since	since	SCONJ
ejpam-2029	227	25	q0	q0	PROPN
ejpam-2029	227	26	=	=	PUNCT
ejpam-2029	228	1	[	[	X
ejpam-2029	228	2	ωd	ωd	X
ejpam-2029	228	3	]	]	X
ejpam-2029	228	4	=	=	X
ejpam-2029	229	1	[	[	PUNCT
ejpam-2029	229	2	p	p	X
ejpam-2029	229	3	d	d	X
ejpam-2029	229	4	]	]	X
ejpam-2029	229	5	=	=	PUNCT
ejpam-2029	229	6	a	a	PROPN
ejpam-2029	229	7	and	and	CCONJ
ejpam-2029	229	8	ωr	ωr	NOUN
ejpam-2029	229	9	=	=	PUNCT
ejpam-2029	229	10	a+	a+	PUNCT
ejpam-2029	229	11	p	p	PROPN
ejpam-2029	229	12	d	d	PROPN
ejpam-2029	229	13	,	,	PUNCT
ejpam-2029	229	14	it	it	PRON
ejpam-2029	229	15	follows	follow	VERB
ejpam-2029	229	16	from	from	ADP
ejpam-2029	229	17	lemma	lemma	PROPN
ejpam-2029	229	18	3	3	NUM
ejpam-2029	229	19	that	that	DET
ejpam-2029	229	20	r0	r0	NOUN
ejpam-2029	229	21	=	=	SYM
ejpam-2029	229	22	r1	r1	PROPN
ejpam-2029	229	23	=	=	SYM
ejpam-2029	229	24	0	0	NUM
ejpam-2029	229	25	,	,	PUNCT
ejpam-2029	229	26	c0	c0	NOUN
ejpam-2029	229	27	=	=	SYM
ejpam-2029	229	28	1	1	NUM
ejpam-2029	229	29	,	,	PUNCT
ejpam-2029	229	30	c1	c1	NOUN
ejpam-2029	229	31	=	=	PUNCT
ejpam-2029	230	1	4m+	4m+	NUM
ejpam-2029	230	2	3	3	NUM
ejpam-2029	230	3	and	and	CCONJ
ejpam-2029	230	4	`	`	PUNCT
ejpam-2029	230	5	0	0	NUM
ejpam-2029	231	1	=	=	SYM
ejpam-2029	231	2	2a	2a	NUM
ejpam-2029	231	3	.	.	PUNCT
ejpam-2029	232	1	since	since	SCONJ
ejpam-2029	232	2	kd	kd	PROPN
ejpam-2029	232	3	=	=	PROPN
ejpam-2029	232	4	7	7	NUM
ejpam-2029	232	5	,	,	PUNCT
ejpam-2029	232	6	we	we	PRON
ejpam-2029	232	7	get	get	VERB
ejpam-2029	232	8	`	`	PUNCT
ejpam-2029	232	9	1	1	X
ejpam-2029	232	10	=	=	SYM
ejpam-2029	232	11	`	`	PUNCT
ejpam-2029	232	12	6	6	NUM
ejpam-2029	232	13	,	,	PUNCT
ejpam-2029	232	14	`	`	PUNCT
ejpam-2029	232	15	2	2	NUM
ejpam-2029	232	16	=	=	SYM
ejpam-2029	232	17	`	`	PUNCT
ejpam-2029	232	18	5	5	NUM
ejpam-2029	232	19	and	and	CCONJ
ejpam-2029	232	20	`	`	PUNCT
ejpam-2029	232	21	3	3	X
ejpam-2029	232	22	=	=	SYM
ejpam-2029	232	23	`	`	PUNCT
ejpam-2029	232	24	4	4	NUM
ejpam-2029	232	25	from	from	ADP
ejpam-2029	232	26	lemma	lemma	PROPN
ejpam-2029	232	27	2	2	NUM
ejpam-2029	232	28	.	.	PUNCT
ejpam-2029	233	1	then	then	ADV
ejpam-2029	233	2	we	we	PRON
ejpam-2029	233	3	have	have	VERB
ejpam-2029	233	4	ωd	ωd	NOUN
ejpam-2029	233	5	=	=	SYM
ejpam-2029	234	1	[	[	X
ejpam-2029	234	2	a,`1,`2,`3,`3,`2,`1	a,`1,`2,`3,`3,`2,`1	PROPN
ejpam-2029	234	3	,	,	PUNCT
ejpam-2029	234	4	2a	2a	NUM
ejpam-2029	234	5	]	]	PUNCT
ejpam-2029	234	6	for	for	ADP
ejpam-2029	234	7	three	three	NUM
ejpam-2029	234	8	positive	positive	ADJ
ejpam-2029	234	9	integers	integer	NOUN
ejpam-2029	234	10	`	`	PUNCT
ejpam-2029	234	11	1	1	NUM
ejpam-2029	234	12	,	,	PUNCT
ejpam-2029	234	13	`	`	PUNCT
ejpam-2029	234	14	2	2	NUM
ejpam-2029	234	15	,	,	PUNCT
ejpam-2029	234	16	`	`	PUNCT
ejpam-2029	234	17	3	3	NUM
ejpam-2029	234	18	such	such	ADJ
ejpam-2029	234	19	that	that	SCONJ
ejpam-2029	234	20	`	`	PUNCT
ejpam-2029	234	21	i	i	PRON
ejpam-2029	234	22	≥	≥	VERB
ejpam-2029	234	23	1	1	NUM
ejpam-2029	234	24	(	(	PUNCT
ejpam-2029	234	25	i	i	NOUN
ejpam-2029	234	26	=	=	NOUN
ejpam-2029	234	27	1	1	NUM
ejpam-2029	234	28	,	,	PUNCT
ejpam-2029	234	29	2,3	2,3	NUM
ejpam-2029	234	30	)	)	PUNCT
ejpam-2029	234	31	.	.	PUNCT
ejpam-2029	235	1	from	from	ADP
ejpam-2029	235	2	lemma	lemma	PROPN
ejpam-2029	235	3	2	2	NUM
ejpam-2029	235	4	we	we	PRON
ejpam-2029	235	5	get	get	VERB
ejpam-2029	235	6	2a	2a	NUM
ejpam-2029	235	7	=	=	SYM
ejpam-2029	235	8	(	(	PUNCT
ejpam-2029	235	9	4m+	4m+	NUM
ejpam-2029	235	10	3)`1	3)`1	NUM
ejpam-2029	235	11	+	+	NUM
ejpam-2029	235	12	r2	r2	PROPN
ejpam-2029	235	13	(	(	PUNCT
ejpam-2029	235	14	15	15	NUM
ejpam-2029	235	15	)	)	PUNCT
ejpam-2029	235	16	since	since	SCONJ
ejpam-2029	235	17	r1	r1	NOUN
ejpam-2029	235	18	=	=	SYM
ejpam-2029	235	19	0	0	NUM
ejpam-2029	235	20	and	and	CCONJ
ejpam-2029	235	21	c1	c1	NOUN
ejpam-2029	235	22	=	=	PUNCT
ejpam-2029	236	1	4m+3	4m+3	PROPN
ejpam-2029	236	2	.	.	PUNCT
ejpam-2029	237	1	from	from	ADP
ejpam-2029	237	2	(	(	PUNCT
ejpam-2029	237	3	15	15	NUM
ejpam-2029	237	4	)	)	PUNCT
ejpam-2029	237	5	,	,	PUNCT
ejpam-2029	237	6	we	we	PRON
ejpam-2029	237	7	obtain	obtain	VERB
ejpam-2029	237	8	(	(	PUNCT
ejpam-2029	237	9	4m+3)`1+r2	4m+3)`1+r2	NUM
ejpam-2029	237	10	≡	≡	PROPN
ejpam-2029	237	11	0(mod2	0(mod2	PROPN
ejpam-2029	237	12	)	)	PUNCT
ejpam-2029	237	13	.	.	PUNCT
ejpam-2029	238	1	so	so	ADV
ejpam-2029	238	2	there	there	PRON
ejpam-2029	238	3	exists	exist	VERB
ejpam-2029	238	4	a	a	DET
ejpam-2029	238	5	positive	positive	ADJ
ejpam-2029	238	6	integer	integer	NOUN
ejpam-2029	238	7	r	r	NOUN
ejpam-2029	238	8	such	such	ADJ
ejpam-2029	238	9	that	that	DET
ejpam-2029	238	10	r2	r2	PROPN
ejpam-2029	238	11	=	=	PROPN
ejpam-2029	238	12	2r−3`1	2r−3`1	X
ejpam-2029	238	13	.	.	PUNCT
ejpam-2029	239	1	by	by	ADP
ejpam-2029	239	2	substitution	substitution	NOUN
ejpam-2029	239	3	of	of	ADP
ejpam-2029	239	4	r2	r2	PROPN
ejpam-2029	239	5	in	in	ADP
ejpam-2029	239	6	(	(	PUNCT
ejpam-2029	239	7	15	15	NUM
ejpam-2029	239	8	)	)	PUNCT
ejpam-2029	239	9	we	we	PRON
ejpam-2029	239	10	get	get	VERB
ejpam-2029	239	11	a	a	DET
ejpam-2029	239	12	=	=	NOUN
ejpam-2029	239	13	2m`1	2m`1	NUM
ejpam-2029	240	1	+	+	CCONJ
ejpam-2029	240	2	r.	r.	NOUN
ejpam-2029	240	3	here	here	ADV
ejpam-2029	240	4	r	r	NOUN
ejpam-2029	240	5	is	be	AUX
ejpam-2029	240	6	an	an	DET
ejpam-2029	240	7	even	even	ADV
ejpam-2029	240	8	integer	integer	NOUN
ejpam-2029	240	9	,	,	PUNCT
ejpam-2029	240	10	since	since	SCONJ
ejpam-2029	240	11	a	a	PRON
ejpam-2029	240	12	is	be	AUX
ejpam-2029	240	13	even	even	ADV
ejpam-2029	240	14	.	.	PUNCT
ejpam-2029	241	1	it	it	PRON
ejpam-2029	241	2	follows	follow	VERB
ejpam-2029	241	3	from	from	ADP
ejpam-2029	241	4	lemma	lemma	PROPN
ejpam-2029	241	5	2	2	NUM
ejpam-2029	241	6	that	that	PRON
ejpam-2029	241	7	c2	c2	PROPN
ejpam-2029	241	8	=	=	PUNCT
ejpam-2029	241	9	1	1	NUM
ejpam-2029	241	10	+	+	NUM
ejpam-2029	241	11	r2`1	r2`1	NOUN
ejpam-2029	241	12	and	and	CCONJ
ejpam-2029	241	13	2a	2a	NUM
ejpam-2029	241	14	=	=	SYM
ejpam-2029	241	15	c2`2	c2`2	ADP
ejpam-2029	241	16	+	+	NUM
ejpam-2029	241	17	r3	r3	PROPN
ejpam-2029	241	18	+	+	CCONJ
ejpam-2029	241	19	r2	r2	NOUN
ejpam-2029	241	20	.	.	PUNCT
ejpam-2029	242	1	thus	thus	ADV
ejpam-2029	242	2	,	,	PUNCT
ejpam-2029	242	3	2a	2a	NUM
ejpam-2029	242	4	=	=	SYM
ejpam-2029	242	5	(	(	PUNCT
ejpam-2029	242	6	1	1	NUM
ejpam-2029	242	7	+	+	NUM
ejpam-2029	242	8	r2`1)`2	r2`1)`2	NOUN
ejpam-2029	242	9	+	+	CCONJ
ejpam-2029	242	10	r3	r3	NOUN
ejpam-2029	242	11	+	+	CCONJ
ejpam-2029	242	12	r2	r2	NOUN
ejpam-2029	242	13	is	be	AUX
ejpam-2029	242	14	obtained	obtain	VERB
ejpam-2029	242	15	.	.	PUNCT
ejpam-2029	243	1	then	then	ADV
ejpam-2029	243	2	(	(	PUNCT
ejpam-2029	243	3	4m+	4m+	NUM
ejpam-2029	243	4	3)`1	3)`1	NUM
ejpam-2029	243	5	=	=	SYM
ejpam-2029	243	6	(	(	PUNCT
ejpam-2029	243	7	1	1	NUM
ejpam-2029	243	8	+	+	NUM
ejpam-2029	243	9	r2`1)`2	r2`1)`2	NOUN
ejpam-2029	243	10	+	+	X
ejpam-2029	243	11	r3	r3	PROPN
ejpam-2029	243	12	(	(	PUNCT
ejpam-2029	243	13	16	16	NUM
ejpam-2029	243	14	)	)	PUNCT
ejpam-2029	243	15	holds	hold	VERB
ejpam-2029	243	16	from	from	ADP
ejpam-2029	243	17	(	(	PUNCT
ejpam-2029	243	18	15	15	NUM
ejpam-2029	243	19	)	)	PUNCT
ejpam-2029	243	20	.	.	PUNCT
ejpam-2029	244	1	thus	thus	ADV
ejpam-2029	244	2	we	we	PRON
ejpam-2029	244	3	get	get	VERB
ejpam-2029	244	4	`	`	PUNCT
ejpam-2029	244	5	2	2	NUM
ejpam-2029	244	6	+	+	CCONJ
ejpam-2029	244	7	`	`	PUNCT
ejpam-2029	244	8	3	3	NUM
ejpam-2029	244	9	≡	≡	PROPN
ejpam-2029	244	10	0	0	NUM
ejpam-2029	245	1	(	(	PUNCT
ejpam-2029	245	2	mod	mod	NOUN
ejpam-2029	245	3	`	`	PUNCT
ejpam-2029	245	4	1	1	NUM
ejpam-2029	245	5	)	)	PUNCT
ejpam-2029	245	6	.	.	PUNCT
ejpam-2029	246	1	so	so	ADV
ejpam-2029	246	2	there	there	PRON
ejpam-2029	246	3	exists	exist	VERB
ejpam-2029	246	4	a	a	DET
ejpam-2029	246	5	positive	positive	ADJ
ejpam-2029	246	6	integer	integer	NOUN
ejpam-2029	246	7	t	t	PROPN
ejpam-2029	246	8	such	such	ADJ
ejpam-2029	246	9	that	that	DET
ejpam-2029	246	10	r3	r3	PROPN
ejpam-2029	246	11	=	=	PUNCT
ejpam-2029	247	1	`	`	PUNCT
ejpam-2029	247	2	1	1	NUM
ejpam-2029	247	3	t	t	NOUN
ejpam-2029	247	4	−	−	NOUN
ejpam-2029	248	1	`	`	PUNCT
ejpam-2029	248	2	2	2	X
ejpam-2029	248	3	.	.	PUNCT
ejpam-2029	248	4	by	by	ADP
ejpam-2029	248	5	substitution	substitution	NOUN
ejpam-2029	248	6	of	of	ADP
ejpam-2029	248	7	r3	r3	PROPN
ejpam-2029	248	8	in	in	ADP
ejpam-2029	248	9	(	(	PUNCT
ejpam-2029	248	10	16	16	NUM
ejpam-2029	248	11	)	)	PUNCT
ejpam-2029	248	12	,	,	PUNCT
ejpam-2029	248	13	we	we	PRON
ejpam-2029	248	14	get	get	VERB
ejpam-2029	248	15	4	4	NUM
ejpam-2029	248	16	m	m	NOUN
ejpam-2029	248	17	=	=	SYM
ejpam-2029	248	18	t	t	PROPN
ejpam-2029	248	19	+	+	CCONJ
ejpam-2029	248	20	2r`2	2r`2	NUM
ejpam-2029	248	21	−	−	PROPN
ejpam-2029	248	22	3(`1`2	3(`1`2	NUM
ejpam-2029	249	1	+	+	CCONJ
ejpam-2029	249	2	1	1	NUM
ejpam-2029	249	3	)	)	PUNCT
ejpam-2029	249	4	.	.	PUNCT
ejpam-2029	250	1	thus	thus	ADV
ejpam-2029	250	2	if	if	SCONJ
ejpam-2029	250	3	we	we	PRON
ejpam-2029	250	4	put	put	VERB
ejpam-2029	250	5	a	a	DET
ejpam-2029	250	6	=	=	PUNCT
ejpam-2029	250	7	`	`	PUNCT
ejpam-2029	250	8	1`2	1`2	NUM
ejpam-2029	251	1	+	+	NUM
ejpam-2029	251	2	1	1	NUM
ejpam-2029	251	3	,	,	PUNCT
ejpam-2029	251	4	then	then	ADV
ejpam-2029	251	5	we	we	PRON
ejpam-2029	251	6	get	get	VERB
ejpam-2029	251	7	t	t	PROPN
ejpam-2029	251	8	−	−	PROPN
ejpam-2029	251	9	3a	3a	NUM
ejpam-2029	251	10	=	=	SYM
ejpam-2029	252	1	4m−	4m−	NUM
ejpam-2029	252	2	2r`2	2r`2	NOUN
ejpam-2029	252	3	.	.	PUNCT
ejpam-2029	253	1	since	since	SCONJ
ejpam-2029	253	2	t	t	PROPN
ejpam-2029	253	3	−	−	PROPN
ejpam-2029	253	4	3a	3a	NUM
ejpam-2029	253	5	is	be	AUX
ejpam-2029	253	6	even	even	ADV
ejpam-2029	253	7	,	,	PUNCT
ejpam-2029	253	8	we	we	PRON
ejpam-2029	253	9	can	can	AUX
ejpam-2029	253	10	put	put	VERB
ejpam-2029	253	11	t	t	PROPN
ejpam-2029	253	12	−	−	PROPN
ejpam-2029	253	13	3a	3a	NUM
ejpam-2029	253	14	=	=	PUNCT
ejpam-2029	254	1	2s	2s	PROPN
ejpam-2029	254	2	for	for	ADP
ejpam-2029	254	3	a	a	DET
ejpam-2029	254	4	positive	positive	ADJ
ejpam-2029	254	5	integer	integer	NOUN
ejpam-2029	254	6	s.	s.	PROPN
ejpam-2029	254	7	hence	hence	ADV
ejpam-2029	254	8	,	,	PUNCT
ejpam-2029	254	9	4	4	NUM
ejpam-2029	254	10	m	m	NOUN
ejpam-2029	254	11	=	=	NOUN
ejpam-2029	255	1	2s	2	NOUN
ejpam-2029	255	2	+	+	CCONJ
ejpam-2029	255	3	2r`2	2r`2	NUM
ejpam-2029	255	4	is	be	AUX
ejpam-2029	255	5	obtained	obtain	VERB
ejpam-2029	255	6	.	.	PUNCT
ejpam-2029	256	1	therefore	therefore	ADV
ejpam-2029	256	2	we	we	PRON
ejpam-2029	256	3	get	get	VERB
ejpam-2029	256	4	a	a	DET
ejpam-2029	256	5	=	=	NOUN
ejpam-2029	256	6	ar	ar	NOUN
ejpam-2029	256	7	+	+	NOUN
ejpam-2029	256	8	`	`	PUNCT
ejpam-2029	256	9	1s	1	NOUN
ejpam-2029	256	10	since	since	SCONJ
ejpam-2029	256	11	a	a	DET
ejpam-2029	256	12	=	=	SYM
ejpam-2029	256	13	2m`1	2m`1	NUM
ejpam-2029	256	14	+	+	CCONJ
ejpam-2029	256	15	r.	r.	NOUN
ejpam-2029	256	16	on	on	ADP
ejpam-2029	256	17	the	the	DET
ejpam-2029	256	18	other	other	ADJ
ejpam-2029	256	19	hand	hand	NOUN
ejpam-2029	256	20	,	,	PUNCT
ejpam-2029	256	21	c3	c3	PROPN
ejpam-2029	256	22	=	=	PUNCT
ejpam-2029	256	23	4m+	4m+	NUM
ejpam-2029	256	24	3	3	NUM
ejpam-2029	256	25	+	+	CCONJ
ejpam-2029	256	26	(	(	PUNCT
ejpam-2029	256	27	r3−	r3−	PROPN
ejpam-2029	256	28	r2)`2	r2)`2	PROPN
ejpam-2029	256	29	(	(	PUNCT
ejpam-2029	256	30	17	17	NUM
ejpam-2029	256	31	)	)	PUNCT
ejpam-2029	256	32	is	be	AUX
ejpam-2029	256	33	obtained	obtain	VERB
ejpam-2029	256	34	from	from	ADP
ejpam-2029	256	35	lemma	lemma	PROPN
ejpam-2029	256	36	2	2	NUM
ejpam-2029	256	37	.	.	PUNCT
ejpam-2029	257	1	thus	thus	ADV
ejpam-2029	257	2	we	we	PRON
ejpam-2029	257	3	get	get	VERB
ejpam-2029	257	4	from	from	ADP
ejpam-2029	257	5	(	(	PUNCT
ejpam-2029	257	6	17	17	NUM
ejpam-2029	257	7	)	)	PUNCT
ejpam-2029	257	8	c3	c3	NOUN
ejpam-2029	257	9	=	=	PUNCT
ejpam-2029	257	10	at	at	ADP
ejpam-2029	257	11	−	−	PROPN
ejpam-2029	257	12	`	`	PUNCT
ejpam-2029	257	13	2	2	NUM
ejpam-2029	257	14	2	2	NUM
ejpam-2029	257	15	since	since	SCONJ
ejpam-2029	257	16	r2	r2	PROPN
ejpam-2029	258	1	=	=	SYM
ejpam-2029	258	2	2r	2r	NUM
ejpam-2029	259	1	−	−	NOUN
ejpam-2029	259	2	3`1	3`1	NUM
ejpam-2029	259	3	and	and	CCONJ
ejpam-2029	259	4	r3	r3	PROPN
ejpam-2029	259	5	=	=	SYM
ejpam-2029	259	6	`	`	PUNCT
ejpam-2029	259	7	1	1	NUM
ejpam-2029	259	8	t	t	NOUN
ejpam-2029	259	9	−	−	NOUN
ejpam-2029	259	10	`	`	PUNCT
ejpam-2029	259	11	2	2	X
ejpam-2029	259	12	.	.	PUNCT
ejpam-2029	260	1	moreover	moreover	ADV
ejpam-2029	260	2	,	,	PUNCT
ejpam-2029	260	3	from	from	ADP
ejpam-2029	260	4	lemma	lemma	PROPN
ejpam-2029	260	5	2	2	NUM
ejpam-2029	260	6	we	we	PRON
ejpam-2029	260	7	get	get	VERB
ejpam-2029	260	8	2a	2a	NUM
ejpam-2029	260	9	=	=	PUNCT
ejpam-2029	261	1	c3`3	c3`3	X
ejpam-2029	261	2	+	+	NUM
ejpam-2029	261	3	r3	r3	NOUN
ejpam-2029	261	4	+	+	CCONJ
ejpam-2029	261	5	r4	r4	NOUN
ejpam-2029	261	6	.	.	PUNCT
ejpam-2029	262	1	thus	thus	ADV
ejpam-2029	262	2	r4	r4	VERB
ejpam-2029	262	3	=	=	SYM
ejpam-2029	262	4	(	(	PUNCT
ejpam-2029	262	5	2r	2r	NUM
ejpam-2029	262	6	−	−	NOUN
ejpam-2029	262	7	3`1	3`1	NUM
ejpam-2029	262	8	−	−	NOUN
ejpam-2029	262	9	t`3)a+	t`3)a+	NUM
ejpam-2029	262	10	`	`	PUNCT
ejpam-2029	262	11	2(`2`3	2(`2`3	X
ejpam-2029	262	12	+	+	NOUN
ejpam-2029	262	13	1	1	NUM
ejpam-2029	262	14	)	)	PUNCT
ejpam-2029	262	15	is	be	AUX
ejpam-2029	262	16	obtained	obtain	VERB
ejpam-2029	262	17	because	because	SCONJ
ejpam-2029	262	18	of	of	ADP
ejpam-2029	262	19	2a	2a	NUM
ejpam-2029	262	20	=	=	SYM
ejpam-2029	262	21	(	(	PUNCT
ejpam-2029	262	22	1	1	NUM
ejpam-2029	262	23	+	+	NUM
ejpam-2029	262	24	r2`1)`2	r2`1)`2	NOUN
ejpam-2029	262	25	+	+	CCONJ
ejpam-2029	262	26	r2	r2	PROPN
ejpam-2029	262	27	+	+	CCONJ
ejpam-2029	262	28	r3	r3	PROPN
ejpam-2029	262	29	and	and	CCONJ
ejpam-2029	262	30	c3	c3	NOUN
ejpam-2029	262	31	=	=	PUNCT
ejpam-2029	262	32	at	at	ADP
ejpam-2029	262	33	−	−	PROPN
ejpam-2029	262	34	`	`	PUNCT
ejpam-2029	262	35	2	2	NUM
ejpam-2029	262	36	2	2	NUM
ejpam-2029	262	37	.	.	PUNCT
ejpam-2029	262	38	references	reference	NOUN
ejpam-2029	262	39	63	63	NUM
ejpam-2029	262	40	furthermore	furthermore	ADV
ejpam-2029	262	41	,	,	PUNCT
ejpam-2029	262	42	c3	c3	PROPN
ejpam-2029	262	43	=	=	PUNCT
ejpam-2029	262	44	at	at	ADP
ejpam-2029	262	45	−	−	PROPN
ejpam-2029	262	46	`	`	PUNCT
ejpam-2029	262	47	2	2	NUM
ejpam-2029	262	48	2	2	NUM
ejpam-2029	262	49	and	and	CCONJ
ejpam-2029	262	50	c4	c4	NOUN
ejpam-2029	262	51	=	=	SYM
ejpam-2029	262	52	(	(	PUNCT
ejpam-2029	262	53	1	1	NUM
ejpam-2029	262	54	+	+	NUM
ejpam-2029	262	55	r2`1	r2`1	NOUN
ejpam-2029	262	56	)	)	PUNCT
ejpam-2029	263	1	+	+	CCONJ
ejpam-2029	263	2	(	(	PUNCT
ejpam-2029	263	3	r4−	r4−	NOUN
ejpam-2029	263	4	r3)`3	r3)`3	PRON
ejpam-2029	263	5	imply	imply	VERB
ejpam-2029	263	6	at	at	ADP
ejpam-2029	263	7	−	−	PROPN
ejpam-2029	263	8	`	`	PUNCT
ejpam-2029	263	9	2	2	NUM
ejpam-2029	263	10	2	2	NUM
ejpam-2029	263	11	=	=	SYM
ejpam-2029	263	12	1	1	NUM
ejpam-2029	263	13	+	+	NUM
ejpam-2029	263	14	r2`1	r2`1	NOUN
ejpam-2029	263	15	+	+	NOUN
ejpam-2029	263	16	r4`3−	r4`3−	ADJ
ejpam-2029	263	17	r3`3	r3`3	NOUN
ejpam-2029	263	18	since	since	SCONJ
ejpam-2029	263	19	c3	c3	NOUN
ejpam-2029	263	20	=	=	PROPN
ejpam-2029	263	21	c4	c4	PROPN
ejpam-2029	263	22	.	.	PUNCT
ejpam-2029	264	1	thus	thus	ADV
ejpam-2029	264	2	,	,	PUNCT
ejpam-2029	264	3	at	at	ADP
ejpam-2029	264	4	−	−	PROPN
ejpam-2029	264	5	`	`	PUNCT
ejpam-2029	264	6	2	2	NUM
ejpam-2029	264	7	2	2	NUM
ejpam-2029	264	8	=	=	SYM
ejpam-2029	264	9	(	(	PUNCT
ejpam-2029	264	10	1	1	NUM
ejpam-2029	264	11	+	+	CCONJ
ejpam-2029	264	12	`	`	PUNCT
ejpam-2029	264	13	2`3	2`3	NUM
ejpam-2029	264	14	)	)	PUNCT
ejpam-2029	264	15	2	2	NUM
ejpam-2029	264	16	+	+	NUM
ejpam-2029	264	17	2r(`1	2r(`1	NUM
ejpam-2029	264	18	+	+	NOUN
ejpam-2029	264	19	a`3)−	a`3)−	ADP
ejpam-2029	264	20	t`3(`1	t`3(`1	NOUN
ejpam-2029	264	21	+	+	PROPN
ejpam-2029	264	22	a`3)−	a`3)−	ADP
ejpam-2029	264	23	3`1(`1	3`1(`1	NOUN
ejpam-2029	264	24	+	+	CCONJ
ejpam-2029	264	25	a`3	a`3	NUM
ejpam-2029	264	26	)	)	PUNCT
ejpam-2029	264	27	is	be	AUX
ejpam-2029	264	28	obtained	obtain	VERB
ejpam-2029	264	29	since	since	SCONJ
ejpam-2029	264	30	r2	r2	PROPN
ejpam-2029	264	31	=	=	SYM
ejpam-2029	264	32	2r	2r	NUM
ejpam-2029	265	1	−	−	NOUN
ejpam-2029	265	2	`	`	PUNCT
ejpam-2029	265	3	1	1	NUM
ejpam-2029	265	4	,	,	PUNCT
ejpam-2029	265	5	r3	r3	X
ejpam-2029	265	6	=	=	SYM
ejpam-2029	265	7	`	`	PUNCT
ejpam-2029	265	8	1	1	NUM
ejpam-2029	265	9	t	t	NOUN
ejpam-2029	265	10	−	−	NOUN
ejpam-2029	265	11	`	`	PUNCT
ejpam-2029	265	12	2	2	NUM
ejpam-2029	265	13	and	and	CCONJ
ejpam-2029	265	14	r4	r4	VERB
ejpam-2029	265	15	=	=	SYM
ejpam-2029	265	16	(	(	PUNCT
ejpam-2029	265	17	2r	2r	NUM
ejpam-2029	265	18	−	−	NOUN
ejpam-2029	265	19	3`1−	3`1−	NUM
ejpam-2029	265	20	t`3)a+	t`3)a+	ADP
ejpam-2029	265	21	`	`	PUNCT
ejpam-2029	265	22	2(`2`3	2(`2`3	NUM
ejpam-2029	265	23	+	+	NOUN
ejpam-2029	265	24	1	1	NUM
ejpam-2029	265	25	)	)	PUNCT
ejpam-2029	265	26	.	.	PUNCT
ejpam-2029	266	1	thus	thus	ADV
ejpam-2029	266	2	,	,	PUNCT
ejpam-2029	266	3	if	if	SCONJ
ejpam-2029	266	4	we	we	PRON
ejpam-2029	266	5	put	put	VERB
ejpam-2029	266	6	b	b	NOUN
ejpam-2029	266	7	=	=	PUNCT
ejpam-2029	266	8	`	`	PUNCT
ejpam-2029	266	9	1	1	NUM
ejpam-2029	267	1	+	+	CCONJ
ejpam-2029	267	2	a`3	a`3	PROPN
ejpam-2029	267	3	and	and	CCONJ
ejpam-2029	267	4	c	c	NOUN
ejpam-2029	267	5	=	=	PUNCT
ejpam-2029	268	1	`	`	PUNCT
ejpam-2029	268	2	2`3	2`3	NUM
ejpam-2029	268	3	+	+	NUM
ejpam-2029	268	4	1	1	NUM
ejpam-2029	268	5	,	,	PUNCT
ejpam-2029	268	6	we	we	PRON
ejpam-2029	268	7	get	get	VERB
ejpam-2029	268	8	3(a2	3(a2	NOUN
ejpam-2029	269	1	+	+	CCONJ
ejpam-2029	269	2	b2)−	b2)−	ADJ
ejpam-2029	269	3	c2	c2	PROPN
ejpam-2029	269	4	−	−	PROPN
ejpam-2029	270	1	`	`	PUNCT
ejpam-2029	270	2	2	2	NUM
ejpam-2029	270	3	2	2	NUM
ejpam-2029	270	4	=	=	NOUN
ejpam-2029	270	5	2rb	2rb	NOUN
ejpam-2029	270	6	−	−	PROPN
ejpam-2029	270	7	2s(a+	2s(a+	PROPN
ejpam-2029	270	8	b`3	b`3	NOUN
ejpam-2029	270	9	)	)	PUNCT
ejpam-2029	270	10	since	since	SCONJ
ejpam-2029	270	11	t	t	PROPN
ejpam-2029	270	12	−	−	PROPN
ejpam-2029	271	1	3a=	3a=	NUM
ejpam-2029	271	2	2s	2s	NOUN
ejpam-2029	271	3	.	.	PUNCT
ejpam-2029	272	1	if	if	SCONJ
ejpam-2029	272	2	we	we	PRON
ejpam-2029	272	3	assume	assume	VERB
ejpam-2029	272	4	that	that	SCONJ
ejpam-2029	272	5	the	the	DET
ejpam-2029	272	6	integers	integer	NOUN
ejpam-2029	272	7	r	r	NOUN
ejpam-2029	272	8	and	and	CCONJ
ejpam-2029	272	9	s	s	NOUN
ejpam-2029	272	10	are	be	AUX
ejpam-2029	272	11	not	not	PART
ejpam-2029	272	12	uniquely	uniquely	ADV
ejpam-2029	272	13	determined	determine	VERB
ejpam-2029	272	14	,	,	PUNCT
ejpam-2029	272	15	we	we	PRON
ejpam-2029	272	16	get	get	VERB
ejpam-2029	272	17	a2	a2	NOUN
ejpam-2029	272	18	+	+	NOUN
ejpam-2029	272	19	b2	b2	NOUN
ejpam-2029	272	20	=	=	SYM
ejpam-2029	272	21	0	0	NUM
ejpam-2029	272	22	which	which	PRON
ejpam-2029	272	23	is	be	AUX
ejpam-2029	272	24	a	a	DET
ejpam-2029	272	25	contradiction	contradiction	NOUN
ejpam-2029	272	26	.	.	PUNCT
ejpam-2029	273	1	therefore	therefore	ADV
ejpam-2029	273	2	,	,	PUNCT
ejpam-2029	273	3	the	the	DET
ejpam-2029	273	4	integers	integer	NOUN
ejpam-2029	273	5	r	r	NOUN
ejpam-2029	273	6	and	and	CCONJ
ejpam-2029	273	7	s	s	NOUN
ejpam-2029	273	8	are	be	AUX
ejpam-2029	273	9	uniquely	uniquely	ADV
ejpam-2029	273	10	determined	determine	VERB
ejpam-2029	273	11	by	by	ADP
ejpam-2029	273	12	a	a	DET
ejpam-2029	273	13	=	=	X
ejpam-2029	273	14	ar	ar	PROPN
ejpam-2029	273	15	+	+	NOUN
ejpam-2029	273	16	`	`	PUNCT
ejpam-2029	273	17	1s	1s	NUM
ejpam-2029	273	18	and	and	CCONJ
ejpam-2029	273	19	3(a2	3(a2	NUM
ejpam-2029	273	20	+	+	CCONJ
ejpam-2029	273	21	b2)−	b2)−	ADJ
ejpam-2029	273	22	c2−	c2−	ADJ
ejpam-2029	273	23	`	`	PUNCT
ejpam-2029	273	24	2	2	NUM
ejpam-2029	273	25	2	2	NUM
ejpam-2029	273	26	=	=	SYM
ejpam-2029	273	27	2rb−	2rb−	NUM
ejpam-2029	273	28	2s(a+	2s(a+	PROPN
ejpam-2029	273	29	b`3	b`3	NOUN
ejpam-2029	273	30	)	)	PUNCT
ejpam-2029	273	31	.	.	PUNCT
ejpam-2029	274	1	now	now	ADV
ejpam-2029	274	2	,	,	PUNCT
ejpam-2029	274	3	since	since	SCONJ
ejpam-2029	274	4	ωd	ωd	ADP
ejpam-2029	274	5	=	=	SYM
ejpam-2029	275	1	[	[	X
ejpam-2029	275	2	a,`1,`2,`3,`3,`2,`1	a,`1,`2,`3,`3,`2,`1	PROPN
ejpam-2029	275	3	,	,	PUNCT
ejpam-2029	275	4	2a	2a	NUM
ejpam-2029	275	5	]	]	PUNCT
ejpam-2029	275	6	implies	imply	VERB
ejpam-2029	275	7	q5	q5	PROPN
ejpam-2029	275	8	=	=	SYM
ejpam-2029	275	9	bc	bc	PROPN
ejpam-2029	275	10	+	+	CCONJ
ejpam-2029	275	11	a`2	a`2	PROPN
ejpam-2029	275	12	and	and	CCONJ
ejpam-2029	275	13	q6	q6	PROPN
ejpam-2029	275	14	=	=	PROPN
ejpam-2029	275	15	a2	a2	PROPN
ejpam-2029	275	16	+	+	CCONJ
ejpam-2029	275	17	b2	b2	NOUN
ejpam-2029	275	18	by	by	ADP
ejpam-2029	275	19	lemma	lemma	PROPN
ejpam-2029	275	20	1	1	NUM
ejpam-2029	275	21	,	,	PUNCT
ejpam-2029	275	22	we	we	PRON
ejpam-2029	275	23	obtain	obtain	VERB
ejpam-2029	275	24	td	td	NOUN
ejpam-2029	275	25	=	=	SYM
ejpam-2029	275	26	2[a(a2+b2)+bc+a`2	2[a(a2+b2)+bc+a`2	NOUN
ejpam-2029	275	27	]	]	PUNCT
ejpam-2029	275	28	and	and	CCONJ
ejpam-2029	275	29	ud	ud	INTJ
ejpam-2029	275	30	=	=	NOUN
ejpam-2029	275	31	2(a2+b2	2(a2+b2	NUM
ejpam-2029	275	32	)	)	PUNCT
ejpam-2029	275	33	.	.	PUNCT
ejpam-2029	276	1	moreover	moreover	ADV
ejpam-2029	276	2	,	,	PUNCT
ejpam-2029	276	3	if	if	SCONJ
ejpam-2029	276	4	we	we	PRON
ejpam-2029	276	5	put	put	VERB
ejpam-2029	276	6	d	d	NOUN
ejpam-2029	276	7	=	=	PUNCT
ejpam-2029	276	8	a`1s+`2	a`1s+`2	NOUN
ejpam-2029	276	9	and	and	CCONJ
ejpam-2029	276	10	e	e	NOUN
ejpam-2029	276	11	=	=	PUNCT
ejpam-2029	276	12	`	`	PUNCT
ejpam-2029	276	13	1	1	NUM
ejpam-2029	276	14	2s2	2s2	NUM
ejpam-2029	276	15	+	+	SYM
ejpam-2029	276	16	2s+3	2s+3	NUM
ejpam-2029	276	17	,	,	PUNCT
ejpam-2029	276	18	then	then	ADV
ejpam-2029	276	19	we	we	PRON
ejpam-2029	276	20	get	get	VERB
ejpam-2029	276	21	d	d	NOUN
ejpam-2029	276	22	=	=	PUNCT
ejpam-2029	276	23	a2r2	a2r2	X
ejpam-2029	276	24	+	+	NOUN
ejpam-2029	276	25	2rd+	2rd+	ADJ
ejpam-2029	276	26	e	e	NOUN
ejpam-2029	276	27	since	since	SCONJ
ejpam-2029	276	28	b	b	PROPN
ejpam-2029	276	29	=	=	SYM
ejpam-2029	276	30	2s+2r`2	2s+2r`2	NUM
ejpam-2029	276	31	+	+	NOUN
ejpam-2029	276	32	3	3	NUM
ejpam-2029	276	33	.	.	PUNCT
ejpam-2029	277	1	thus	thus	ADV
ejpam-2029	277	2	,	,	PUNCT
ejpam-2029	277	3	the	the	DET
ejpam-2029	277	4	proof	proof	NOUN
ejpam-2029	277	5	is	be	AUX
ejpam-2029	277	6	completed	complete	VERB
ejpam-2029	277	7	.	.	PUNCT
ejpam-2029	278	1	4	4	X
ejpam-2029	278	2	.	.	X
ejpam-2029	278	3	conclusion	conclusion	NOUN
ejpam-2029	278	4	in	in	ADP
ejpam-2029	278	5	this	this	DET
ejpam-2029	278	6	paper	paper	NOUN
ejpam-2029	278	7	,	,	PUNCT
ejpam-2029	278	8	some	some	DET
ejpam-2029	278	9	results	result	NOUN
ejpam-2029	278	10	are	be	AUX
ejpam-2029	278	11	presented	present	VERB
ejpam-2029	278	12	in	in	ADP
ejpam-2029	278	13	order	order	NOUN
ejpam-2029	278	14	to	to	PART
ejpam-2029	278	15	determine	determine	VERB
ejpam-2029	278	16	the	the	DET
ejpam-2029	278	17	fundamental	fundamental	ADJ
ejpam-2029	278	18	units	unit	NOUN
ejpam-2029	278	19	of	of	ADP
ejpam-2029	278	20	certain	certain	ADJ
ejpam-2029	278	21	quadratic	quadratic	ADJ
ejpam-2029	278	22	fields	field	NOUN
ejpam-2029	278	23	q	q	NOUN
ejpam-2029	278	24	(	(	PUNCT
ejpam-2029	278	25	p	p	NOUN
ejpam-2029	278	26	d	d	NOUN
ejpam-2029	278	27	)	)	PUNCT
ejpam-2029	278	28	with	with	ADP
ejpam-2029	278	29	the	the	DET
ejpam-2029	278	30	period	period	NOUN
ejpam-2029	278	31	kd	kd	PROPN
ejpam-2029	278	32	of	of	ADP
ejpam-2029	278	33	the	the	DET
ejpam-2029	278	34	continued	continue	VERB
ejpam-2029	278	35	fraction	fraction	NOUN
ejpam-2029	278	36	expansion	expansion	NOUN
ejpam-2029	278	37	of	of	ADP
ejpam-2029	278	38	the	the	DET
ejpam-2029	278	39	quadratic	quadratic	ADJ
ejpam-2029	278	40	irrational	irrational	ADJ
ejpam-2029	278	41	number	number	NOUN
ejpam-2029	278	42	ωd	ωd	ADP
ejpam-2029	278	43	is	be	AUX
ejpam-2029	278	44	equal	equal	ADJ
ejpam-2029	278	45	to	to	ADP
ejpam-2029	278	46	7	7	NUM
ejpam-2029	278	47	.	.	PUNCT
ejpam-2029	279	1	these	these	DET
ejpam-2029	279	2	results	result	NOUN
ejpam-2029	279	3	provide	provide	VERB
ejpam-2029	279	4	us	we	PRON
ejpam-2029	279	5	a	a	DET
ejpam-2029	279	6	practical	practical	ADJ
ejpam-2029	279	7	method	method	NOUN
ejpam-2029	279	8	in	in	ADP
ejpam-2029	279	9	order	order	NOUN
ejpam-2029	279	10	to	to	PART
ejpam-2029	279	11	determine	determine	VERB
ejpam-2029	279	12	both	both	DET
ejpam-2029	279	13	the	the	DET
ejpam-2029	279	14	continued	continue	VERB
ejpam-2029	279	15	fraction	fraction	NOUN
ejpam-2029	279	16	expansion	expansion	NOUN
ejpam-2029	279	17	of	of	ADP
ejpam-2029	279	18	the	the	DET
ejpam-2029	279	19	quadratic	quadratic	ADJ
ejpam-2029	279	20	irrational	irrational	ADJ
ejpam-2029	279	21	number	number	NOUN
ejpam-2029	279	22	ωd	ωd	NOUN
ejpam-2029	279	23	and	and	CCONJ
ejpam-2029	279	24	the	the	DET
ejpam-2029	279	25	fundamental	fundamental	ADJ
ejpam-2029	279	26	units	unit	NOUN
ejpam-2029	279	27	of	of	ADP
ejpam-2029	279	28	certain	certain	ADJ
ejpam-2029	279	29	real	real	ADJ
ejpam-2029	279	30	quadratic	quadratic	ADJ
ejpam-2029	279	31	fields	field	NOUN
ejpam-2029	279	32	.	.	PUNCT
ejpam-2029	280	1	by	by	ADP
ejpam-2029	280	2	using	use	VERB
ejpam-2029	280	3	these	these	DET
ejpam-2029	280	4	results	result	NOUN
ejpam-2029	280	5	both	both	CCONJ
ejpam-2029	280	6	the	the	DET
ejpam-2029	280	7	continued	continue	VERB
ejpam-2029	280	8	fraction	fraction	NOUN
ejpam-2029	280	9	expansion	expansion	NOUN
ejpam-2029	280	10	of	of	ADP
ejpam-2029	280	11	the	the	DET
ejpam-2029	280	12	quadratic	quadratic	ADJ
ejpam-2029	280	13	irrational	irrational	ADJ
ejpam-2029	280	14	number	number	NOUN
ejpam-2029	280	15	ωd	ωd	NOUN
ejpam-2029	280	16	and	and	CCONJ
ejpam-2029	280	17	the	the	DET
ejpam-2029	280	18	fundamental	fundamental	ADJ
ejpam-2029	280	19	units	unit	NOUN
ejpam-2029	280	20	of	of	ADP
ejpam-2029	280	21	certain	certain	ADJ
ejpam-2029	280	22	real	real	ADJ
ejpam-2029	280	23	quadratic	quadratic	ADJ
ejpam-2029	280	24	fields	field	NOUN
ejpam-2029	280	25	can	can	AUX
ejpam-2029	280	26	be	be	AUX
ejpam-2029	280	27	rapidly	rapidly	ADV
ejpam-2029	280	28	determined	determine	VERB
ejpam-2029	280	29	without	without	ADP
ejpam-2029	280	30	using	use	VERB
ejpam-2029	280	31	long	long	ADJ
ejpam-2029	280	32	algorithms	algorithm	NOUN
ejpam-2029	280	33	.	.	PUNCT
ejpam-2029	281	1	the	the	DET
ejpam-2029	281	2	similar	similar	ADJ
ejpam-2029	281	3	results	result	NOUN
ejpam-2029	281	4	can	can	AUX
ejpam-2029	281	5	be	be	AUX
ejpam-2029	281	6	proved	prove	VERB
ejpam-2029	281	7	for	for	ADP
ejpam-2029	281	8	all	all	DET
ejpam-2029	281	9	real	real	ADJ
ejpam-2029	281	10	quadratic	quadratic	ADJ
ejpam-2029	281	11	fields	field	NOUN
ejpam-2029	281	12	with	with	ADP
ejpam-2029	281	13	the	the	DET
ejpam-2029	281	14	period	period	NOUN
ejpam-2029	281	15	kd	kd	PROPN
ejpam-2029	281	16	of	of	ADP
ejpam-2029	281	17	the	the	DET
ejpam-2029	281	18	continued	continue	VERB
ejpam-2029	281	19	fraction	fraction	NOUN
ejpam-2029	281	20	expansion	expansion	NOUN
ejpam-2029	281	21	of	of	ADP
ejpam-2029	281	22	the	the	DET
ejpam-2029	281	23	quadratic	quadratic	ADJ
ejpam-2029	281	24	irrational	irrational	ADJ
ejpam-2029	281	25	number	number	NOUN
ejpam-2029	281	26	ωd	ωd	ADP
ejpam-2029	281	27	is	be	AUX
ejpam-2029	281	28	higher	high	ADJ
ejpam-2029	281	29	than	than	ADP
ejpam-2029	281	30	7	7	NUM
ejpam-2029	281	31	.	.	PUNCT
ejpam-2029	281	32	references	reference	NOUN
ejpam-2029	281	33	[	[	X
ejpam-2029	281	34	1	1	NUM
ejpam-2029	281	35	]	]	PUNCT
ejpam-2029	281	36	t	t	PROPN
ejpam-2029	281	37	azuhata	azuhata	NOUN
ejpam-2029	281	38	.	.	PUNCT
ejpam-2029	282	1	on	on	ADP
ejpam-2029	282	2	the	the	DET
ejpam-2029	282	3	fundamental	fundamental	ADJ
ejpam-2029	282	4	unit	unit	NOUN
ejpam-2029	282	5	and	and	CCONJ
ejpam-2029	282	6	the	the	DET
ejpam-2029	282	7	class	class	NOUN
ejpam-2029	282	8	numbers	number	NOUN
ejpam-2029	282	9	of	of	ADP
ejpam-2029	282	10	real	real	ADJ
ejpam-2029	282	11	quadratic	quadratic	ADJ
ejpam-2029	282	12	fields	field	NOUN
ejpam-2029	282	13	.	.	PUNCT
ejpam-2029	283	1	nagoya	nagoya	PROPN
ejpam-2029	283	2	mathematical	mathematical	PROPN
ejpam-2029	283	3	journal	journal	PROPN
ejpam-2029	283	4	95	95	NUM
ejpam-2029	283	5	:	:	PUNCT
ejpam-2029	283	6	125	125	NUM
ejpam-2029	283	7	-	-	SYM
ejpam-2029	283	8	135	135	NUM
ejpam-2029	283	9	,	,	PUNCT
ejpam-2029	283	10	1984	1984	NUM
ejpam-2029	283	11	.	.	PUNCT
ejpam-2029	284	1	[	[	X
ejpam-2029	284	2	2	2	NUM
ejpam-2029	284	3	]	]	X
ejpam-2029	284	4	r	r	NOUN
ejpam-2029	284	5	a	a	DET
ejpam-2029	284	6	mollin	mollin	NOUN
ejpam-2029	284	7	.	.	PUNCT
ejpam-2029	285	1	quadratics	quadratic	NOUN
ejpam-2029	285	2	.	.	PUNCT
ejpam-2029	286	1	crc	crc	PROPN
ejpam-2029	286	2	press	press	PROPN
ejpam-2029	286	3	boka	boka	PROPN
ejpam-2029	286	4	raton	raton	PROPN
ejpam-2029	286	5	,	,	PUNCT
ejpam-2029	286	6	1995	1995	NUM
ejpam-2029	286	7	.	.	PUNCT
ejpam-2029	287	1	[	[	X
ejpam-2029	287	2	3	3	X
ejpam-2029	287	3	]	]	PUNCT
ejpam-2029	287	4	a	a	DET
ejpam-2029	287	5	pekin	pekin	NOUN
ejpam-2029	287	6	and	and	CCONJ
ejpam-2029	287	7	h	h	NOUN
ejpam-2029	287	8	i̧̇scan	i̧̇scan	PROPN
ejpam-2029	287	9	.	.	PUNCT
ejpam-2029	288	1	continued	continue	VERB
ejpam-2029	288	2	fractions	fraction	NOUN
ejpam-2029	288	3	of	of	ADP
ejpam-2029	288	4	period	period	NOUN
ejpam-2029	288	5	six	six	NUM
ejpam-2029	288	6	and	and	CCONJ
ejpam-2029	288	7	explicit	explicit	ADJ
ejpam-2029	288	8	representations	representation	NOUN
ejpam-2029	288	9	of	of	ADP
ejpam-2029	288	10	fundamental	fundamental	ADJ
ejpam-2029	288	11	units	unit	NOUN
ejpam-2029	288	12	of	of	ADP
ejpam-2029	288	13	some	some	DET
ejpam-2029	288	14	real	real	ADJ
ejpam-2029	288	15	quadratic	quadratic	ADJ
ejpam-2029	288	16	fields	field	NOUN
ejpam-2029	288	17	.	.	PUNCT
ejpam-2029	289	1	journal	journal	NOUN
ejpam-2029	289	2	of	of	ADP
ejpam-2029	289	3	the	the	DET
ejpam-2029	289	4	indian	indian	PROPN
ejpam-2029	289	5	mathematical	mathematical	ADJ
ejpam-2029	289	6	society	society	NOUN
ejpam-2029	289	7	72	72	NUM
ejpam-2029	289	8	:	:	PUNCT
ejpam-2029	289	9	184	184	NUM
ejpam-2029	289	10	-	-	SYM
ejpam-2029	289	11	194	194	NUM
ejpam-2029	289	12	,	,	PUNCT
ejpam-2029	289	13	2005	2005	NUM
ejpam-2029	289	14	.	.	PUNCT
ejpam-2029	290	1	[	[	X
ejpam-2029	290	2	4	4	NUM
ejpam-2029	290	3	]	]	PUNCT
ejpam-2029	290	4	t	t	PROPN
ejpam-2029	290	5	takagi	takagi	NOUN
ejpam-2029	290	6	.	.	PUNCT
ejpam-2029	291	1	shotō	shotō	NOUN
ejpam-2029	291	2	seisūron	seisūron	ADP
ejpam-2029	291	3	kōgi	kōgi	PROPN
ejpam-2029	291	4	.	.	PUNCT
ejpam-2029	292	1	2nd	2nd	ADJ
ejpam-2029	292	2	ed	ed	NOUN
ejpam-2029	292	3	.	.	PROPN
ejpam-2029	292	4	,	,	PUNCT
ejpam-2029	292	5	kyōritsu	kyōritsu	PROPN
ejpam-2029	292	6	,	,	PUNCT
ejpam-2029	292	7	tokyo	tokyo	PROPN
ejpam-2029	293	1	[	[	X
ejpam-2029	293	2	in	in	ADP
ejpam-2029	293	3	japanese	japanese	PROPN
ejpam-2029	293	4	]	]	PUNCT
ejpam-2029	293	5	,	,	PUNCT
ejpam-2029	293	6	1971	1971	NUM
ejpam-2029	293	7	.	.	PUNCT
ejpam-2029	294	1	[	[	X
ejpam-2029	294	2	5	5	NUM
ejpam-2029	294	3	]	]	X
ejpam-2029	294	4	k	k	PROPN
ejpam-2029	294	5	tomita	tomita	PROPN
ejpam-2029	294	6	.	.	PUNCT
ejpam-2029	295	1	explicit	explicit	ADJ
ejpam-2029	295	2	represantation	represantation	NOUN
ejpam-2029	295	3	of	of	ADP
ejpam-2029	295	4	fundamental	fundamental	ADJ
ejpam-2029	295	5	units	unit	NOUN
ejpam-2029	295	6	of	of	ADP
ejpam-2029	295	7	some	some	DET
ejpam-2029	295	8	quadratic	quadratic	ADJ
ejpam-2029	295	9	fields	field	NOUN
ejpam-2029	295	10	,	,	PUNCT
ejpam-2029	295	11	i.	i.	NOUN
ejpam-2029	295	12	proceedings	proceeding	NOUN
ejpam-2029	295	13	of	of	ADP
ejpam-2029	295	14	the	the	DET
ejpam-2029	295	15	japan	japan	PROPN
ejpam-2029	295	16	academy	academy	PROPN
ejpam-2029	295	17	,	,	PUNCT
ejpam-2029	295	18	series	series	PROPN
ejpam-2029	295	19	a	a	PROPN
ejpam-2029	295	20	,	,	PUNCT
ejpam-2029	295	21	mathematical	mathematical	ADJ
ejpam-2029	295	22	sciences	science	NOUN
ejpam-2029	295	23	71	71	NUM
ejpam-2029	295	24	:	:	SYM
ejpam-2029	295	25	41	41	NUM
ejpam-2029	295	26	-	-	SYM
ejpam-2029	295	27	43	43	NUM
ejpam-2029	295	28	,	,	PUNCT
ejpam-2029	295	29	1995	1995	NUM
ejpam-2029	295	30	.	.	PUNCT
ejpam-2029	296	1	[	[	X
ejpam-2029	296	2	6	6	NUM
ejpam-2029	296	3	]	]	PUNCT
ejpam-2029	296	4	k	k	PROPN
ejpam-2029	296	5	tomita	tomita	PROPN
ejpam-2029	296	6	.	.	PUNCT
ejpam-2029	297	1	explicit	explicit	ADJ
ejpam-2029	297	2	represantation	represantation	NOUN
ejpam-2029	297	3	of	of	ADP
ejpam-2029	297	4	fundamental	fundamental	ADJ
ejpam-2029	297	5	units	unit	NOUN
ejpam-2029	297	6	of	of	ADP
ejpam-2029	297	7	some	some	DET
ejpam-2029	297	8	real	real	ADJ
ejpam-2029	297	9	quadratic	quadratic	ADJ
ejpam-2029	297	10	fields	field	NOUN
ejpam-2029	297	11	,	,	PUNCT
ejpam-2029	297	12	ii	ii	PROPN
ejpam-2029	297	13	.	.	PROPN
ejpam-2029	297	14	journal	journal	PROPN
ejpam-2029	297	15	of	of	ADP
ejpam-2029	297	16	number	number	NOUN
ejpam-2029	297	17	theory	theory	NOUN
ejpam-2029	297	18	63(2	63(2	NUM
ejpam-2029	297	19	):	):	PUNCT
ejpam-2029	297	20	275	275	NUM
ejpam-2029	297	21	-	-	SYM
ejpam-2029	297	22	285	285	NUM
ejpam-2029	297	23	,	,	PUNCT
ejpam-2029	297	24	1997	1997	NUM
ejpam-2029	297	25	.	.	PUNCT
ejpam-2029	298	1	references	reference	NOUN
ejpam-2029	298	2	64	64	NUM
ejpam-2029	298	3	[	[	X
ejpam-2029	298	4	7	7	NUM
ejpam-2029	298	5	]	]	X
ejpam-2029	298	6	y	y	PROPN
ejpam-2029	298	7	yamamoto	yamamoto	PROPN
ejpam-2029	298	8	.	.	PUNCT
ejpam-2029	299	1	real	real	ADJ
ejpam-2029	299	2	quadratic	quadratic	ADJ
ejpam-2029	299	3	number	number	NOUN
ejpam-2029	299	4	fields	field	NOUN
ejpam-2029	299	5	with	with	ADP
ejpam-2029	299	6	large	large	ADJ
ejpam-2029	299	7	fundamental	fundamental	ADJ
ejpam-2029	299	8	units	unit	NOUN
ejpam-2029	299	9	.	.	PUNCT
ejpam-2029	300	1	osaka	osaka	PROPN
ejpam-2029	300	2	journal	journal	PROPN
ejpam-2029	300	3	of	of	ADP
ejpam-2029	300	4	mathematics	mathematic	NOUN
ejpam-2029	300	5	8	8	NUM
ejpam-2029	300	6	:	:	PUNCT
ejpam-2029	300	7	261	261	NUM
ejpam-2029	300	8	-	-	SYM
ejpam-2029	300	9	270	270	NUM
ejpam-2029	300	10	,	,	PUNCT
ejpam-2029	300	11	1971	1971	NUM
ejpam-2029	300	12	.	.	PUNCT