id	sid	tid	token	lemma	pos
ejpam-3852	1	1	european	european	PROPN
ejpam-3852	1	2	journal	journal	PROPN
ejpam-3852	1	3	of	of	ADP
ejpam-3852	1	4	pure	pure	ADJ
ejpam-3852	1	5	and	and	CCONJ
ejpam-3852	1	6	applied	apply	VERB
ejpam-3852	1	7	mathematics	mathematic	NOUN
ejpam-3852	1	8	vol	vol	NOUN
ejpam-3852	1	9	.	.	PUNCT
ejpam-3852	2	1	14	14	NUM
ejpam-3852	2	2	,	,	PUNCT
ejpam-3852	2	3	no	no	INTJ
ejpam-3852	2	4	.	.	NOUN
ejpam-3852	2	5	1	1	NUM
ejpam-3852	2	6	,	,	PUNCT
ejpam-3852	2	7	2021	2021	NUM
ejpam-3852	2	8	,	,	PUNCT
ejpam-3852	2	9	1	1	NUM
ejpam-3852	2	10	-	-	SYM
ejpam-3852	2	11	18	18	NUM
ejpam-3852	2	12	issn	issn	PROPN
ejpam-3852	2	13	1307	1307	NUM
ejpam-3852	2	14	-	-	SYM
ejpam-3852	2	15	5543	5543	NUM
ejpam-3852	2	16	–	–	PUNCT
ejpam-3852	2	17	ejpam.com	ejpam.com	X
ejpam-3852	2	18	published	publish	VERB
ejpam-3852	2	19	by	by	ADP
ejpam-3852	2	20	new	new	PROPN
ejpam-3852	2	21	york	york	PROPN
ejpam-3852	2	22	business	business	PROPN
ejpam-3852	2	23	global	global	PROPN
ejpam-3852	2	24	a	a	DET
ejpam-3852	2	25	hybrid	hybrid	ADJ
ejpam-3852	2	26	inversive	inversive	ADJ
ejpam-3852	2	27	congruential	congruential	ADJ
ejpam-3852	2	28	pseudorandom	pseudorandom	NOUN
ejpam-3852	2	29	number	number	NOUN
ejpam-3852	2	30	generator	generator	NOUN
ejpam-3852	2	31	with	with	ADP
ejpam-3852	2	32	high	high	ADJ
ejpam-3852	2	33	period	period	NOUN
ejpam-3852	2	34	constanza	constanza	PROPN
ejpam-3852	2	35	riera1	riera1	PROPN
ejpam-3852	2	36	,	,	PUNCT
ejpam-3852	2	37	tapabrata	tapabrata	PROPN
ejpam-3852	2	38	roy2	roy2	PROPN
ejpam-3852	2	39	,	,	PUNCT
ejpam-3852	2	40	santanu	santanu	VERB
ejpam-3852	2	41	sarkar2	sarkar2	NOUN
ejpam-3852	2	42	,	,	PUNCT
ejpam-3852	2	43	pantelimon	pantelimon	PROPN
ejpam-3852	2	44	stănică3,∗	stănică3,∗	PROPN
ejpam-3852	2	45	1	1	NUM
ejpam-3852	2	46	department	department	NOUN
ejpam-3852	2	47	of	of	ADP
ejpam-3852	2	48	computer	computer	NOUN
ejpam-3852	2	49	science	science	NOUN
ejpam-3852	2	50	,	,	PUNCT
ejpam-3852	2	51	electrical	electrical	ADJ
ejpam-3852	2	52	engineering	engineering	NOUN
ejpam-3852	2	53	and	and	CCONJ
ejpam-3852	2	54	mathematical	mathematical	ADJ
ejpam-3852	2	55	sciences	science	NOUN
ejpam-3852	2	56	,	,	PUNCT
ejpam-3852	2	57	western	western	ADJ
ejpam-3852	2	58	norway	norway	PROPN
ejpam-3852	2	59	university	university	PROPN
ejpam-3852	2	60	of	of	ADP
ejpam-3852	2	61	applied	apply	VERB
ejpam-3852	2	62	sciences	science	NOUN
ejpam-3852	2	63	,	,	PUNCT
ejpam-3852	2	64	bergen	bergen	PROPN
ejpam-3852	2	65	,	,	PUNCT
ejpam-3852	2	66	norway	norway	PROPN
ejpam-3852	2	67	2	2	NUM
ejpam-3852	2	68	department	department	NOUN
ejpam-3852	2	69	of	of	ADP
ejpam-3852	2	70	mathematics	mathematics	PROPN
ejpam-3852	2	71	,	,	PUNCT
ejpam-3852	2	72	indian	indian	PROPN
ejpam-3852	2	73	institute	institute	PROPN
ejpam-3852	2	74	of	of	ADP
ejpam-3852	2	75	technology	technology	PROPN
ejpam-3852	2	76	madras	madras	PROPN
ejpam-3852	2	77	,	,	PUNCT
ejpam-3852	2	78	sardar	sardar	PROPN
ejpam-3852	2	79	patel	patel	PROPN
ejpam-3852	2	80	road	road	PROPN
ejpam-3852	2	81	,	,	PUNCT
ejpam-3852	2	82	chennai	chennai	PROPN
ejpam-3852	2	83	tn	tn	PROPN
ejpam-3852	2	84	600036	600036	NUM
ejpam-3852	2	85	,	,	PUNCT
ejpam-3852	2	86	india	india	PROPN
ejpam-3852	2	87	3	3	PROPN
ejpam-3852	2	88	department	department	NOUN
ejpam-3852	2	89	of	of	ADP
ejpam-3852	2	90	applied	apply	VERB
ejpam-3852	2	91	mathematics	mathematic	NOUN
ejpam-3852	2	92	,	,	PUNCT
ejpam-3852	2	93	naval	naval	ADJ
ejpam-3852	2	94	postgraduate	postgraduate	PROPN
ejpam-3852	2	95	school	school	PROPN
ejpam-3852	2	96	,	,	PUNCT
ejpam-3852	2	97	monterey	monterey	NOUN
ejpam-3852	2	98	,	,	PUNCT
ejpam-3852	2	99	ca	ca	PROPN
ejpam-3852	2	100	93943–5216	93943–5216	NUM
ejpam-3852	2	101	,	,	PUNCT
ejpam-3852	2	102	usa	usa	PROPN
ejpam-3852	2	103	abstract	abstract	NOUN
ejpam-3852	2	104	.	.	PUNCT
ejpam-3852	3	1	though	though	SCONJ
ejpam-3852	3	2	generating	generate	VERB
ejpam-3852	3	3	a	a	DET
ejpam-3852	3	4	sequence	sequence	NOUN
ejpam-3852	3	5	of	of	ADP
ejpam-3852	3	6	pseudorandom	pseudorandom	NOUN
ejpam-3852	3	7	numbers	number	NOUN
ejpam-3852	3	8	by	by	ADP
ejpam-3852	3	9	linear	linear	ADJ
ejpam-3852	3	10	methods	method	NOUN
ejpam-3852	3	11	(	(	PUNCT
ejpam-3852	3	12	lehmer	lehmer	NOUN
ejpam-3852	3	13	generator	generator	NOUN
ejpam-3852	3	14	)	)	PUNCT
ejpam-3852	3	15	displays	display	VERB
ejpam-3852	3	16	acceptable	acceptable	ADJ
ejpam-3852	3	17	behavior	behavior	NOUN
ejpam-3852	3	18	under	under	ADP
ejpam-3852	3	19	some	some	DET
ejpam-3852	3	20	conditions	condition	NOUN
ejpam-3852	3	21	of	of	ADP
ejpam-3852	3	22	the	the	DET
ejpam-3852	3	23	parameters	parameter	NOUN
ejpam-3852	3	24	,	,	PUNCT
ejpam-3852	3	25	it	it	PRON
ejpam-3852	3	26	also	also	ADV
ejpam-3852	3	27	has	have	VERB
ejpam-3852	3	28	undesirable	undesirable	ADJ
ejpam-3852	3	29	features	feature	NOUN
ejpam-3852	3	30	,	,	PUNCT
ejpam-3852	3	31	which	which	PRON
ejpam-3852	3	32	makes	make	VERB
ejpam-3852	3	33	the	the	DET
ejpam-3852	3	34	sequence	sequence	NOUN
ejpam-3852	3	35	unusable	unusable	ADJ
ejpam-3852	3	36	for	for	ADP
ejpam-3852	3	37	various	various	ADJ
ejpam-3852	3	38	stochastic	stochastic	ADJ
ejpam-3852	3	39	simulations	simulation	NOUN
ejpam-3852	3	40	.	.	PUNCT
ejpam-3852	4	1	an	an	DET
ejpam-3852	4	2	extension	extension	NOUN
ejpam-3852	4	3	which	which	PRON
ejpam-3852	4	4	showed	show	VERB
ejpam-3852	4	5	promise	promise	NOUN
ejpam-3852	4	6	for	for	ADP
ejpam-3852	4	7	such	such	ADJ
ejpam-3852	4	8	applications	application	NOUN
ejpam-3852	4	9	is	be	AUX
ejpam-3852	4	10	a	a	DET
ejpam-3852	4	11	generator	generator	NOUN
ejpam-3852	4	12	obtained	obtain	VERB
ejpam-3852	4	13	by	by	ADP
ejpam-3852	4	14	using	use	VERB
ejpam-3852	4	15	a	a	DET
ejpam-3852	4	16	first	first	ADJ
ejpam-3852	4	17	-	-	PUNCT
ejpam-3852	4	18	order	order	NOUN
ejpam-3852	4	19	recurrence	recurrence	NOUN
ejpam-3852	4	20	based	base	VERB
ejpam-3852	4	21	upon	upon	SCONJ
ejpam-3852	4	22	the	the	DET
ejpam-3852	4	23	inverse	inverse	NOUN
ejpam-3852	4	24	modulo	modulo	VERB
ejpam-3852	4	25	a	a	DET
ejpam-3852	4	26	prime	prime	NOUN
ejpam-3852	4	27	or	or	CCONJ
ejpam-3852	4	28	a	a	DET
ejpam-3852	4	29	prime	prime	ADJ
ejpam-3852	4	30	power	power	NOUN
ejpam-3852	4	31	,	,	PUNCT
ejpam-3852	4	32	called	call	VERB
ejpam-3852	4	33	inversive	inversive	ADJ
ejpam-3852	4	34	congruential	congruential	ADJ
ejpam-3852	4	35	generator	generator	NOUN
ejpam-3852	4	36	(	(	PUNCT
ejpam-3852	4	37	icg	icg	NOUN
ejpam-3852	4	38	)	)	PUNCT
ejpam-3852	4	39	.	.	PUNCT
ejpam-3852	5	1	a	a	DET
ejpam-3852	5	2	lot	lot	NOUN
ejpam-3852	5	3	of	of	ADP
ejpam-3852	5	4	work	work	NOUN
ejpam-3852	5	5	has	have	AUX
ejpam-3852	5	6	been	be	AUX
ejpam-3852	5	7	dedicated	dedicate	VERB
ejpam-3852	5	8	to	to	PART
ejpam-3852	5	9	investigate	investigate	VERB
ejpam-3852	5	10	the	the	DET
ejpam-3852	5	11	periods	period	NOUN
ejpam-3852	5	12	(	(	PUNCT
ejpam-3852	5	13	under	under	ADP
ejpam-3852	5	14	some	some	DET
ejpam-3852	5	15	conditions	condition	NOUN
ejpam-3852	5	16	of	of	ADP
ejpam-3852	5	17	the	the	DET
ejpam-3852	5	18	parameters	parameter	NOUN
ejpam-3852	5	19	)	)	PUNCT
ejpam-3852	5	20	,	,	PUNCT
ejpam-3852	5	21	the	the	DET
ejpam-3852	5	22	lattice	lattice	PROPN
ejpam-3852	5	23	test	test	NOUN
ejpam-3852	5	24	passing	passing	NOUN
ejpam-3852	5	25	,	,	PUNCT
ejpam-3852	5	26	discrepancy	discrepancy	NOUN
ejpam-3852	5	27	and	and	CCONJ
ejpam-3852	5	28	other	other	ADJ
ejpam-3852	5	29	statistical	statistical	ADJ
ejpam-3852	5	30	properties	property	NOUN
ejpam-3852	5	31	of	of	ADP
ejpam-3852	5	32	such	such	DET
ejpam-3852	5	33	a	a	DET
ejpam-3852	5	34	generator	generator	NOUN
ejpam-3852	5	35	.	.	PUNCT
ejpam-3852	6	1	here	here	ADV
ejpam-3852	6	2	,	,	PUNCT
ejpam-3852	6	3	we	we	PRON
ejpam-3852	6	4	propose	propose	VERB
ejpam-3852	6	5	a	a	DET
ejpam-3852	6	6	new	new	ADJ
ejpam-3852	6	7	method	method	NOUN
ejpam-3852	6	8	,	,	PUNCT
ejpam-3852	6	9	which	which	PRON
ejpam-3852	6	10	we	we	PRON
ejpam-3852	6	11	call	call	VERB
ejpam-3852	6	12	hybrid	hybrid	ADJ
ejpam-3852	6	13	inversive	inversive	ADJ
ejpam-3852	6	14	congruential	congruential	ADJ
ejpam-3852	6	15	generator	generator	NOUN
ejpam-3852	6	16	(	(	PUNCT
ejpam-3852	6	17	hicg	hicg	NOUN
ejpam-3852	6	18	)	)	PUNCT
ejpam-3852	6	19	,	,	PUNCT
ejpam-3852	6	20	based	base	VERB
ejpam-3852	6	21	upon	upon	SCONJ
ejpam-3852	6	22	a	a	DET
ejpam-3852	6	23	second	second	ADJ
ejpam-3852	6	24	order	order	NOUN
ejpam-3852	6	25	recurrence	recurrence	NOUN
ejpam-3852	6	26	using	use	VERB
ejpam-3852	6	27	the	the	DET
ejpam-3852	6	28	inverse	inverse	NOUN
ejpam-3852	6	29	modulo	modulo	NOUN
ejpam-3852	6	30	m	m	VERB
ejpam-3852	6	31	,	,	PUNCT
ejpam-3852	6	32	a	a	DET
ejpam-3852	6	33	power	power	NOUN
ejpam-3852	6	34	of	of	ADP
ejpam-3852	6	35	2	2	NUM
ejpam-3852	6	36	.	.	PUNCT
ejpam-3852	7	1	we	we	PRON
ejpam-3852	7	2	investigate	investigate	VERB
ejpam-3852	7	3	the	the	DET
ejpam-3852	7	4	period	period	NOUN
ejpam-3852	7	5	of	of	ADP
ejpam-3852	7	6	this	this	DET
ejpam-3852	7	7	pseudorandom	pseudorandom	PROPN
ejpam-3852	7	8	numbers	number	NOUN
ejpam-3852	7	9	generator	generator	PROPN
ejpam-3852	7	10	(	(	PUNCT
ejpam-3852	7	11	prng	prng	NOUN
ejpam-3852	7	12	)	)	PUNCT
ejpam-3852	7	13	and	and	CCONJ
ejpam-3852	7	14	give	give	VERB
ejpam-3852	7	15	necessary	necessary	ADJ
ejpam-3852	7	16	and	and	CCONJ
ejpam-3852	7	17	sufficient	sufficient	ADJ
ejpam-3852	7	18	conditions	condition	NOUN
ejpam-3852	7	19	for	for	SCONJ
ejpam-3852	7	20	our	our	PRON
ejpam-3852	7	21	prng	prng	NOUN
ejpam-3852	7	22	to	to	PART
ejpam-3852	7	23	have	have	VERB
ejpam-3852	7	24	periods	period	NOUN
ejpam-3852	7	25	m	m	VERB
ejpam-3852	7	26	(	(	PUNCT
ejpam-3852	7	27	thereby	thereby	ADV
ejpam-3852	7	28	doubling	double	VERB
ejpam-3852	7	29	the	the	DET
ejpam-3852	7	30	period	period	NOUN
ejpam-3852	7	31	of	of	ADP
ejpam-3852	7	32	the	the	DET
ejpam-3852	7	33	classical	classical	ADJ
ejpam-3852	7	34	icg	icg	NOUN
ejpam-3852	7	35	)	)	PUNCT
ejpam-3852	7	36	and	and	CCONJ
ejpam-3852	7	37	m/2	m/2	NUM
ejpam-3852	7	38	(	(	PUNCT
ejpam-3852	7	39	matching	match	VERB
ejpam-3852	7	40	the	the	DET
ejpam-3852	7	41	one	one	NUM
ejpam-3852	7	42	of	of	ADP
ejpam-3852	7	43	the	the	DET
ejpam-3852	7	44	icg	icg	NOUN
ejpam-3852	7	45	)	)	PUNCT
ejpam-3852	7	46	.	.	PUNCT
ejpam-3852	8	1	moreover	moreover	ADV
ejpam-3852	8	2	,	,	PUNCT
ejpam-3852	8	3	we	we	PRON
ejpam-3852	8	4	show	show	VERB
ejpam-3852	8	5	that	that	SCONJ
ejpam-3852	8	6	the	the	DET
ejpam-3852	8	7	lattice	lattice	PROPN
ejpam-3852	8	8	test	test	NOUN
ejpam-3852	8	9	complexity	complexity	NOUN
ejpam-3852	8	10	for	for	ADP
ejpam-3852	8	11	a	a	DET
ejpam-3852	8	12	binary	binary	ADJ
ejpam-3852	8	13	sequence	sequence	NOUN
ejpam-3852	8	14	associated	associate	VERB
ejpam-3852	8	15	to	to	ADP
ejpam-3852	8	16	(	(	PUNCT
ejpam-3852	8	17	a	a	DET
ejpam-3852	8	18	full	full	ADJ
ejpam-3852	8	19	period	period	NOUN
ejpam-3852	8	20	)	)	PUNCT
ejpam-3852	8	21	hicg	hicg	NOUN
ejpam-3852	8	22	is	be	AUX
ejpam-3852	8	23	precisely	precisely	ADV
ejpam-3852	8	24	m/2	m/2	NUM
ejpam-3852	8	25	.	.	NOUN
ejpam-3852	8	26	2020	2020	NUM
ejpam-3852	8	27	mathematics	mathematic	NOUN
ejpam-3852	8	28	subject	subject	NOUN
ejpam-3852	8	29	classifications	classification	NOUN
ejpam-3852	8	30	:	:	PUNCT
ejpam-3852	8	31	11b50	11b50	NUM
ejpam-3852	8	32	,	,	PUNCT
ejpam-3852	8	33	11k36	11k36	NUM
ejpam-3852	8	34	,	,	PUNCT
ejpam-3852	8	35	11k45	11k45	NUM
ejpam-3852	8	36	key	key	ADJ
ejpam-3852	8	37	words	word	NOUN
ejpam-3852	8	38	and	and	CCONJ
ejpam-3852	8	39	phrases	phrase	NOUN
ejpam-3852	8	40	:	:	PUNCT
ejpam-3852	8	41	pseudorandom	pseudorandom	NOUN
ejpam-3852	8	42	numbers	number	NOUN
ejpam-3852	8	43	,	,	PUNCT
ejpam-3852	8	44	congruences	congruence	NOUN
ejpam-3852	8	45	,	,	PUNCT
ejpam-3852	8	46	period	period	NOUN
ejpam-3852	8	47	,	,	PUNCT
ejpam-3852	8	48	lattice	lattice	PROPN
ejpam-3852	8	49	test	test	NOUN
ejpam-3852	8	50	.	.	PUNCT
ejpam-3852	9	1	1	1	X
ejpam-3852	9	2	.	.	X
ejpam-3852	9	3	introduction	introduction	NOUN
ejpam-3852	9	4	the	the	DET
ejpam-3852	9	5	linear	linear	ADJ
ejpam-3852	9	6	congruential	congruential	ADJ
ejpam-3852	9	7	method	method	NOUN
ejpam-3852	9	8	is	be	AUX
ejpam-3852	9	9	one	one	NUM
ejpam-3852	9	10	of	of	ADP
ejpam-3852	9	11	the	the	DET
ejpam-3852	9	12	standard	standard	ADJ
ejpam-3852	9	13	methods	method	NOUN
ejpam-3852	9	14	of	of	ADP
ejpam-3852	9	15	generating	generate	VERB
ejpam-3852	9	16	uniform	uniform	ADJ
ejpam-3852	9	17	pseudorandom	pseudorandom	NOUN
ejpam-3852	9	18	numbers	number	NOUN
ejpam-3852	9	19	(	(	PUNCT
ejpam-3852	9	20	prns	prn	NOUN
ejpam-3852	9	21	)	)	PUNCT
ejpam-3852	9	22	in	in	ADP
ejpam-3852	9	23	the	the	DET
ejpam-3852	9	24	interval	interval	NOUN
ejpam-3852	10	1	i	i	PRON
ejpam-3852	10	2	=	=	PUNCT
ejpam-3852	11	1	[	[	X
ejpam-3852	11	2	0	0	NUM
ejpam-3852	11	3	,	,	PUNCT
ejpam-3852	11	4	1	1	NUM
ejpam-3852	11	5	)	)	PUNCT
ejpam-3852	11	6	.	.	PUNCT
ejpam-3852	12	1	in	in	ADP
ejpam-3852	12	2	this	this	DET
ejpam-3852	12	3	method	method	NOUN
ejpam-3852	12	4	,	,	PUNCT
ejpam-3852	12	5	for	for	ADP
ejpam-3852	12	6	a	a	DET
ejpam-3852	12	7	(	(	PUNCT
ejpam-3852	12	8	large	large	ADJ
ejpam-3852	12	9	)	)	PUNCT
ejpam-3852	12	10	modulus	modulus	NOUN
ejpam-3852	12	11	m	m	PROPN
ejpam-3852	12	12	,	,	PUNCT
ejpam-3852	12	13	a	a	DET
ejpam-3852	12	14	sequence	sequence	NOUN
ejpam-3852	12	15	{	{	PUNCT
ejpam-3852	12	16	yn	yn	NOUN
ejpam-3852	12	17	}	}	PUNCT
ejpam-3852	12	18	of	of	ADP
ejpam-3852	12	19	integers	integer	NOUN
ejpam-3852	12	20	in	in	ADP
ejpam-3852	12	21	zm	zm	PROPN
ejpam-3852	12	22	=	=	SYM
ejpam-3852	12	23	{	{	PUNCT
ejpam-3852	12	24	0	0	NUM
ejpam-3852	12	25	,	,	PUNCT
ejpam-3852	12	26	1	1	NUM
ejpam-3852	12	27	,	,	PUNCT
ejpam-3852	12	28	.	.	PUNCT
ejpam-3852	12	29	.	.	PUNCT
ejpam-3852	12	30	.	.	PUNCT
ejpam-3852	13	1	,	,	PUNCT
ejpam-3852	13	2	m	m	VERB
ejpam-3852	13	3	−	−	NOUN
ejpam-3852	13	4	1	1	NUM
ejpam-3852	13	5	}	}	PUNCT
ejpam-3852	13	6	=	=	SYM
ejpam-3852	13	7	z	z	X
ejpam-3852	13	8	/	/	SYM
ejpam-3852	13	9	mz	mz	PROPN
ejpam-3852	13	10	is	be	AUX
ejpam-3852	13	11	generated	generate	VERB
ejpam-3852	13	12	by	by	ADP
ejpam-3852	13	13	the	the	DET
ejpam-3852	13	14	linear	linear	PROPN
ejpam-3852	13	15	recursion	recursion	NOUN
ejpam-3852	13	16	yn+1	yn+1	PROPN
ejpam-3852	13	17	≡	≡	PROPN
ejpam-3852	13	18	ayn	ayn	PROPN
ejpam-3852	14	1	+	+	CCONJ
ejpam-3852	14	2	b	b	PROPN
ejpam-3852	14	3	mod	mod	PROPN
ejpam-3852	14	4	m	m	PROPN
ejpam-3852	14	5	,	,	PUNCT
ejpam-3852	14	6	n	n	PROPN
ejpam-3852	14	7	=	=	SYM
ejpam-3852	14	8	0	0	NUM
ejpam-3852	14	9	,	,	PUNCT
ejpam-3852	14	10	1	1	NUM
ejpam-3852	14	11	,	,	PUNCT
ejpam-3852	14	12	.	.	PUNCT
ejpam-3852	14	13	.	.	PUNCT
ejpam-3852	14	14	.	.	PUNCT
ejpam-3852	15	1	;	;	PUNCT
ejpam-3852	15	2	a	a	DET
ejpam-3852	15	3	,	,	PUNCT
ejpam-3852	15	4	b	b	PROPN
ejpam-3852	15	5	∈	∈	PROPN
ejpam-3852	15	6	zm	zm	PROPN
ejpam-3852	15	7	.	.	PUNCT
ejpam-3852	16	1	(	(	PUNCT
ejpam-3852	16	2	1	1	X
ejpam-3852	16	3	)	)	PUNCT
ejpam-3852	16	4	∗corresponding	∗corresponde	VERB
ejpam-3852	16	5	author	author	NOUN
ejpam-3852	16	6	.	.	PUNCT
ejpam-3852	17	1	doi	doi	NOUN
ejpam-3852	17	2	:	:	PUNCT
ejpam-3852	17	3	https://doi.org/10.29020/nybg.ejpam.v14i1.3852	https://doi.org/10.29020/nybg.ejpam.v14i1.3852	PROPN
ejpam-3852	17	4	email	email	NOUN
ejpam-3852	17	5	addresses	address	NOUN
ejpam-3852	17	6	:	:	PUNCT
ejpam-3852	17	7	csr@hvl.no	csr@hvl.no	X
ejpam-3852	17	8	(	(	PUNCT
ejpam-3852	17	9	c.	c.	PROPN
ejpam-3852	17	10	riera	riera	PROPN
ejpam-3852	17	11	)	)	PUNCT
ejpam-3852	17	12	,	,	PUNCT
ejpam-3852	17	13	tapabrata.roy.048@gmail.com	tapabrata.roy.048@gmail.com	PROPN
ejpam-3852	17	14	(	(	PUNCT
ejpam-3852	17	15	t.	t.	PROPN
ejpam-3852	17	16	roy	roy	PROPN
ejpam-3852	17	17	)	)	PUNCT
ejpam-3852	17	18	,	,	PUNCT
ejpam-3852	17	19	sarkar.santanu.bir1@gmail.com	sarkar.santanu.bir1@gmail.com	X
ejpam-3852	17	20	(	(	PUNCT
ejpam-3852	17	21	s.	s.	PROPN
ejpam-3852	17	22	sarkar	sarkar	PROPN
ejpam-3852	17	23	)	)	PUNCT
ejpam-3852	17	24	,	,	PUNCT
ejpam-3852	17	25	pstanica@nps.edu	pstanica@nps.edu	VERB
ejpam-3852	17	26	(	(	PUNCT
ejpam-3852	17	27	p.	p.	NOUN
ejpam-3852	17	28	stănică	stănică	NUM
ejpam-3852	17	29	)	)	PUNCT
ejpam-3852	17	30	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3852	18	1	1	1	NUM
ejpam-3852	18	2	c	c	X
ejpam-3852	18	3	©	©	PROPN
ejpam-3852	18	4	2021	2021	NUM
ejpam-3852	18	5	ejpam	ejpam	VERB
ejpam-3852	18	6	all	all	DET
ejpam-3852	18	7	rights	right	NOUN
ejpam-3852	18	8	reserved	reserve	VERB
ejpam-3852	18	9	.	.	PUNCT
ejpam-3852	19	1	p.	p.	NOUN
ejpam-3852	19	2	stănică	stănică	NUM
ejpam-3852	19	3	et	et	PROPN
ejpam-3852	19	4	al	al	PROPN
ejpam-3852	19	5	.	.	PUNCT
ejpam-3852	19	6	/	/	SYM
ejpam-3852	19	7	eur	eur	PROPN
ejpam-3852	19	8	.	.	PUNCT
ejpam-3852	20	1	j.	j.	PROPN
ejpam-3852	20	2	pure	pure	PROPN
ejpam-3852	20	3	appl	appl	PROPN
ejpam-3852	20	4	.	.	PROPN
ejpam-3852	20	5	math	math	PROPN
ejpam-3852	20	6	,	,	PUNCT
ejpam-3852	20	7	14	14	NUM
ejpam-3852	20	8	(	(	PUNCT
ejpam-3852	20	9	1	1	NUM
ejpam-3852	20	10	)	)	PUNCT
ejpam-3852	20	11	(	(	PUNCT
ejpam-3852	20	12	2021	2021	NUM
ejpam-3852	20	13	)	)	PUNCT
ejpam-3852	20	14	,	,	PUNCT
ejpam-3852	20	15	1	1	NUM
ejpam-3852	20	16	-	-	SYM
ejpam-3852	20	17	18	18	NUM
ejpam-3852	20	18	2	2	NUM
ejpam-3852	20	19	and	and	CCONJ
ejpam-3852	20	20	then	then	ADV
ejpam-3852	20	21	the	the	DET
ejpam-3852	20	22	prns	prn	NOUN
ejpam-3852	20	23	are	be	AUX
ejpam-3852	20	24	obtained	obtain	VERB
ejpam-3852	20	25	by	by	ADP
ejpam-3852	20	26	the	the	DET
ejpam-3852	20	27	normalization	normalization	NOUN
ejpam-3852	20	28	xn	xn	PUNCT
ejpam-3852	21	1	=	=	SYM
ejpam-3852	21	2	yn	yn	PROPN
ejpam-3852	21	3	/	/	SYM
ejpam-3852	21	4	m.	m.	NOUN
ejpam-3852	21	5	(	(	PUNCT
ejpam-3852	21	6	2	2	X
ejpam-3852	21	7	)	)	PUNCT
ejpam-3852	21	8	this	this	DET
ejpam-3852	21	9	linear	linear	ADJ
ejpam-3852	21	10	method	method	NOUN
ejpam-3852	21	11	is	be	AUX
ejpam-3852	21	12	popular	popular	ADJ
ejpam-3852	21	13	and	and	CCONJ
ejpam-3852	21	14	has	have	AUX
ejpam-3852	21	15	been	be	AUX
ejpam-3852	21	16	thoroughly	thoroughly	ADV
ejpam-3852	21	17	analyzed	analyze	VERB
ejpam-3852	21	18	[	[	X
ejpam-3852	21	19	15	15	NUM
ejpam-3852	21	20	]	]	PUNCT
ejpam-3852	21	21	.	.	PUNCT
ejpam-3852	22	1	however	however	ADV
ejpam-3852	22	2	,	,	PUNCT
ejpam-3852	22	3	it	it	PRON
ejpam-3852	22	4	has	have	AUX
ejpam-3852	22	5	been	be	AUX
ejpam-3852	22	6	found	find	VERB
ejpam-3852	22	7	that	that	SCONJ
ejpam-3852	22	8	the	the	DET
ejpam-3852	22	9	linearity	linearity	NOUN
ejpam-3852	22	10	of	of	ADP
ejpam-3852	22	11	the	the	DET
ejpam-3852	22	12	recursion	recursion	NOUN
ejpam-3852	22	13	leads	lead	VERB
ejpam-3852	22	14	to	to	ADP
ejpam-3852	22	15	some	some	DET
ejpam-3852	22	16	drawbacks	drawback	NOUN
ejpam-3852	22	17	and	and	CCONJ
ejpam-3852	22	18	as	as	ADP
ejpam-3852	22	19	a	a	DET
ejpam-3852	22	20	result	result	NOUN
ejpam-3852	22	21	,	,	PUNCT
ejpam-3852	22	22	recently	recently	ADV
ejpam-3852	22	23	,	,	PUNCT
ejpam-3852	22	24	several	several	ADJ
ejpam-3852	22	25	nonlinear	nonlinear	ADJ
ejpam-3852	22	26	congruential	congruential	ADJ
ejpam-3852	22	27	generators	generator	NOUN
ejpam-3852	23	1	[	[	X
ejpam-3852	23	2	3–10	3–10	NOUN
ejpam-3852	23	3	,	,	PUNCT
ejpam-3852	23	4	12	12	NUM
ejpam-3852	23	5	,	,	PUNCT
ejpam-3852	23	6	15	15	NUM
ejpam-3852	23	7	,	,	PUNCT
ejpam-3852	23	8	19	19	NUM
ejpam-3852	23	9	]	]	PUNCT
ejpam-3852	23	10	have	have	AUX
ejpam-3852	23	11	been	be	AUX
ejpam-3852	23	12	proposed	propose	VERB
ejpam-3852	23	13	and	and	CCONJ
ejpam-3852	23	14	also	also	ADV
ejpam-3852	23	15	analyzed	analyze	VERB
ejpam-3852	24	1	[	[	X
ejpam-3852	24	2	11	11	NUM
ejpam-3852	24	3	]	]	PUNCT
ejpam-3852	24	4	.	.	PUNCT
ejpam-3852	25	1	amongst	amongst	ADP
ejpam-3852	25	2	these	these	PRON
ejpam-3852	25	3	,	,	PUNCT
ejpam-3852	25	4	the	the	DET
ejpam-3852	25	5	inversive	inversive	ADJ
ejpam-3852	25	6	congruential	congruential	ADJ
ejpam-3852	25	7	method	method	NOUN
ejpam-3852	25	8	(	(	PUNCT
ejpam-3852	25	9	icg	icg	NOUN
ejpam-3852	25	10	)	)	PUNCT
ejpam-3852	26	1	[	[	X
ejpam-3852	26	2	17–19	17–19	NUM
ejpam-3852	26	3	]	]	PUNCT
ejpam-3852	26	4	,	,	PUNCT
ejpam-3852	26	5	with	with	ADP
ejpam-3852	26	6	modulus	modulus	NOUN
ejpam-3852	26	7	m	m	PROPN
ejpam-3852	26	8	(	(	PUNCT
ejpam-3852	26	9	with	with	ADP
ejpam-3852	26	10	m	m	PRON
ejpam-3852	26	11	being	be	AUX
ejpam-3852	26	12	either	either	CCONJ
ejpam-3852	26	13	a	a	DET
ejpam-3852	26	14	prime	prime	NOUN
ejpam-3852	26	15	or	or	CCONJ
ejpam-3852	26	16	a	a	DET
ejpam-3852	26	17	large	large	ADJ
ejpam-3852	26	18	power	power	NOUN
ejpam-3852	26	19	of	of	ADP
ejpam-3852	26	20	2	2	NUM
ejpam-3852	26	21	)	)	PUNCT
ejpam-3852	26	22	,	,	PUNCT
ejpam-3852	26	23	is	be	AUX
ejpam-3852	26	24	one	one	NUM
ejpam-3852	26	25	of	of	ADP
ejpam-3852	26	26	the	the	DET
ejpam-3852	26	27	most	most	ADV
ejpam-3852	26	28	interesting	interesting	ADJ
ejpam-3852	26	29	ones	one	NOUN
ejpam-3852	26	30	.	.	PUNCT
ejpam-3852	27	1	here	here	ADV
ejpam-3852	27	2	,	,	PUNCT
ejpam-3852	27	3	we	we	PRON
ejpam-3852	27	4	consider	consider	VERB
ejpam-3852	27	5	the	the	DET
ejpam-3852	27	6	case	case	NOUN
ejpam-3852	27	7	where	where	SCONJ
ejpam-3852	27	8	m	m	VERB
ejpam-3852	27	9	=	=	NOUN
ejpam-3852	27	10	2ω	2ω	NOUN
ejpam-3852	27	11	,	,	PUNCT
ejpam-3852	27	12	for	for	ADP
ejpam-3852	27	13	some	some	DET
ejpam-3852	27	14	integer	integer	PROPN
ejpam-3852	27	15	ω	ω	PROPN
ejpam-3852	27	16	≥	≥	NUM
ejpam-3852	27	17	2	2	NUM
ejpam-3852	27	18	.	.	PUNCT
ejpam-3852	28	1	let	let	VERB
ejpam-3852	28	2	gm	gm	PROPN
ejpam-3852	28	3	=	=	PUNCT
ejpam-3852	28	4	{	{	PUNCT
ejpam-3852	28	5	1	1	NUM
ejpam-3852	28	6	,	,	PUNCT
ejpam-3852	28	7	3	3	NUM
ejpam-3852	28	8	,	,	PUNCT
ejpam-3852	28	9	.	.	PUNCT
ejpam-3852	28	10	.	.	PUNCT
ejpam-3852	28	11	.	.	PUNCT
ejpam-3852	29	1	,	,	PUNCT
ejpam-3852	29	2	m−1	m−1	PROPN
ejpam-3852	29	3	}	}	PUNCT
ejpam-3852	29	4	be	be	AUX
ejpam-3852	29	5	the	the	DET
ejpam-3852	29	6	set	set	NOUN
ejpam-3852	29	7	of	of	ADP
ejpam-3852	29	8	all	all	DET
ejpam-3852	29	9	positive	positive	ADJ
ejpam-3852	29	10	odd	odd	ADJ
ejpam-3852	29	11	integers	integer	NOUN
ejpam-3852	29	12	less	less	ADJ
ejpam-3852	29	13	than	than	ADP
ejpam-3852	29	14	m.	m.	NOUN
ejpam-3852	29	15	clearly	clearly	ADV
ejpam-3852	29	16	,	,	PUNCT
ejpam-3852	29	17	for	for	ADP
ejpam-3852	29	18	any	any	DET
ejpam-3852	29	19	u	u	PROPN
ejpam-3852	29	20	∈	∈	PROPN
ejpam-3852	29	21	gm	gm	PROPN
ejpam-3852	29	22	,	,	PUNCT
ejpam-3852	29	23	there	there	PRON
ejpam-3852	29	24	is	be	VERB
ejpam-3852	29	25	a	a	DET
ejpam-3852	29	26	unique	unique	ADJ
ejpam-3852	29	27	u−1	u−1	PROPN
ejpam-3852	29	28	∈	∈	PROPN
ejpam-3852	29	29	gm	gm	NOUN
ejpam-3852	29	30	such	such	ADJ
ejpam-3852	29	31	that	that	SCONJ
ejpam-3852	29	32	uu−1	uu−1	PROPN
ejpam-3852	29	33	≡	≡	PROPN
ejpam-3852	29	34	1	1	NUM
ejpam-3852	29	35	(	(	PUNCT
ejpam-3852	29	36	mod	mod	PROPN
ejpam-3852	29	37	m	m	PROPN
ejpam-3852	29	38	)	)	PUNCT
ejpam-3852	29	39	.	.	PUNCT
ejpam-3852	30	1	the	the	DET
ejpam-3852	30	2	first	first	ADJ
ejpam-3852	30	3	sequence	sequence	NOUN
ejpam-3852	30	4	{	{	PUNCT
ejpam-3852	30	5	yn	yn	NOUN
ejpam-3852	30	6	}	}	PUNCT
ejpam-3852	30	7	⊆	⊆	NUM
ejpam-3852	30	8	gm	gm	NOUN
ejpam-3852	30	9	based	base	VERB
ejpam-3852	30	10	upon	upon	SCONJ
ejpam-3852	30	11	the	the	DET
ejpam-3852	30	12	inverse	inverse	NOUN
ejpam-3852	30	13	modulo	modulo	NOUN
ejpam-3852	30	14	m	m	VERB
ejpam-3852	30	15	is	be	AUX
ejpam-3852	30	16	given	give	VERB
ejpam-3852	30	17	by	by	ADP
ejpam-3852	30	18	the	the	DET
ejpam-3852	30	19	recursion	recursion	NOUN
ejpam-3852	30	20	yn+1	yn+1	PROPN
ejpam-3852	30	21	≡	≡	PROPN
ejpam-3852	30	22	ay−1n	ay−1n	PROPN
ejpam-3852	31	1	+	+	CCONJ
ejpam-3852	31	2	b	b	X
ejpam-3852	31	3	(	(	PUNCT
ejpam-3852	31	4	mod	mod	PROPN
ejpam-3852	31	5	m	m	PROPN
ejpam-3852	31	6	)	)	PUNCT
ejpam-3852	31	7	,	,	PUNCT
ejpam-3852	31	8	n	n	PROPN
ejpam-3852	31	9	=	=	SYM
ejpam-3852	31	10	0	0	NUM
ejpam-3852	31	11	,	,	PUNCT
ejpam-3852	31	12	1	1	NUM
ejpam-3852	31	13	,	,	PUNCT
ejpam-3852	31	14	.	.	PUNCT
ejpam-3852	31	15	.	.	PUNCT
ejpam-3852	31	16	.	.	PUNCT
ejpam-3852	31	17	.	.	PUNCT
ejpam-3852	32	1	(	(	PUNCT
ejpam-3852	32	2	3	3	X
ejpam-3852	32	3	)	)	PUNCT
ejpam-3852	32	4	here	here	ADV
ejpam-3852	32	5	a	a	PRON
ejpam-3852	32	6	,	,	PUNCT
ejpam-3852	32	7	b	b	PROPN
ejpam-3852	32	8	∈	∈	PROPN
ejpam-3852	32	9	zm	zm	PROPN
ejpam-3852	32	10	are	be	AUX
ejpam-3852	32	11	chosen	choose	VERB
ejpam-3852	32	12	in	in	ADP
ejpam-3852	32	13	such	such	DET
ejpam-3852	32	14	a	a	DET
ejpam-3852	32	15	way	way	NOUN
ejpam-3852	32	16	that	that	PRON
ejpam-3852	32	17	yn+1	yn+1	PROPN
ejpam-3852	32	18	∈	∈	PROPN
ejpam-3852	32	19	gm	gm	PROPN
ejpam-3852	32	20	whenever	whenever	SCONJ
ejpam-3852	32	21	yn	yn	PROPN
ejpam-3852	32	22	∈	∈	PROPN
ejpam-3852	32	23	gm	gm	PROPN
ejpam-3852	32	24	.	.	PUNCT
ejpam-3852	33	1	the	the	DET
ejpam-3852	33	2	following	following	ADJ
ejpam-3852	33	3	result	result	NOUN
ejpam-3852	33	4	is	be	AUX
ejpam-3852	33	5	known	know	VERB
ejpam-3852	33	6	(	(	PUNCT
ejpam-3852	33	7	we	we	PRON
ejpam-3852	33	8	use	use	VERB
ejpam-3852	33	9	per	per	ADP
ejpam-3852	33	10	(	(	PUNCT
ejpam-3852	33	11	·	·	PUNCT
ejpam-3852	33	12	)	)	PUNCT
ejpam-3852	33	13	to	to	PART
ejpam-3852	33	14	denote	denote	VERB
ejpam-3852	33	15	the	the	DET
ejpam-3852	33	16	period	period	NOUN
ejpam-3852	33	17	of	of	ADP
ejpam-3852	33	18	the	the	DET
ejpam-3852	33	19	argument	argument	NOUN
ejpam-3852	33	20	sequence	sequence	NOUN
ejpam-3852	33	21	)	)	PUNCT
ejpam-3852	33	22	.	.	PUNCT
ejpam-3852	34	1	theorem	theorem	ADJ
ejpam-3852	34	2	1	1	NUM
ejpam-3852	34	3	(	(	PUNCT
ejpam-3852	34	4	[	[	X
ejpam-3852	34	5	19	19	NUM
ejpam-3852	34	6	,	,	PUNCT
ejpam-3852	34	7	p.188	p.188	NOUN
ejpam-3852	34	8	,	,	PUNCT
ejpam-3852	34	9	theorem	theorem	VERB
ejpam-3852	34	10	8.9	8.9	NUM
ejpam-3852	34	11	]	]	PUNCT
ejpam-3852	34	12	)	)	PUNCT
ejpam-3852	34	13	.	.	PUNCT
ejpam-3852	35	1	let	let	VERB
ejpam-3852	35	2	m	m	NOUN
ejpam-3852	35	3	=	=	NOUN
ejpam-3852	35	4	2ω	2ω	NUM
ejpam-3852	35	5	,	,	PUNCT
ejpam-3852	35	6	ω	ω	X
ejpam-3852	35	7	≥	≥	NOUN
ejpam-3852	35	8	3	3	NUM
ejpam-3852	35	9	.	.	PUNCT
ejpam-3852	36	1	then	then	ADV
ejpam-3852	36	2	the	the	DET
ejpam-3852	36	3	pseudorandom	pseudorandom	PROPN
ejpam-3852	36	4	number	number	NOUN
ejpam-3852	36	5	generator	generator	NOUN
ejpam-3852	36	6	(	(	PUNCT
ejpam-3852	36	7	prng	prng	NOUN
ejpam-3852	36	8	)	)	PUNCT
ejpam-3852	36	9	{	{	PUNCT
ejpam-3852	36	10	yn	yn	PROPN
ejpam-3852	36	11	}	}	PUNCT
ejpam-3852	36	12	corresponding	correspond	VERB
ejpam-3852	36	13	to	to	ADP
ejpam-3852	36	14	the	the	DET
ejpam-3852	36	15	inversive	inversive	ADJ
ejpam-3852	36	16	congruential	congruential	ADJ
ejpam-3852	36	17	generator	generator	NOUN
ejpam-3852	36	18	with	with	ADP
ejpam-3852	36	19	modulus	modulus	NOUN
ejpam-3852	36	20	m	m	VERB
ejpam-3852	36	21	satisfies	satisfie	NOUN
ejpam-3852	36	22	per(yn	per(yn	NOUN
ejpam-3852	36	23	)	)	PUNCT
ejpam-3852	37	1	=	=	SYM
ejpam-3852	37	2	m	m	VERB
ejpam-3852	37	3	2	2	NUM
ejpam-3852	37	4	if	if	SCONJ
ejpam-3852	37	5	and	and	CCONJ
ejpam-3852	37	6	only	only	ADV
ejpam-3852	37	7	if	if	SCONJ
ejpam-3852	37	8	a	a	DET
ejpam-3852	37	9	≡	≡	PROPN
ejpam-3852	37	10	1	1	NUM
ejpam-3852	37	11	(	(	PUNCT
ejpam-3852	37	12	mod	mod	NOUN
ejpam-3852	37	13	4	4	NUM
ejpam-3852	37	14	)	)	PUNCT
ejpam-3852	37	15	and	and	CCONJ
ejpam-3852	37	16	b	b	X
ejpam-3852	37	17	≡	≡	ADJ
ejpam-3852	37	18	2	2	NUM
ejpam-3852	37	19	(	(	PUNCT
ejpam-3852	37	20	mod	mod	NOUN
ejpam-3852	37	21	4	4	NUM
ejpam-3852	37	22	)	)	PUNCT
ejpam-3852	37	23	.	.	PUNCT
ejpam-3852	38	1	later	later	ADV
ejpam-3852	38	2	in	in	ADP
ejpam-3852	38	3	[	[	X
ejpam-3852	38	4	14	14	NUM
ejpam-3852	38	5	]	]	PUNCT
ejpam-3852	38	6	,	,	PUNCT
ejpam-3852	38	7	the	the	DET
ejpam-3852	38	8	authors	author	NOUN
ejpam-3852	38	9	modified	modify	VERB
ejpam-3852	38	10	(	(	PUNCT
ejpam-3852	38	11	3	3	NUM
ejpam-3852	38	12	)	)	PUNCT
ejpam-3852	38	13	and	and	CCONJ
ejpam-3852	38	14	proposed	propose	VERB
ejpam-3852	38	15	another	another	DET
ejpam-3852	38	16	nonlinear	nonlinear	ADJ
ejpam-3852	38	17	method	method	NOUN
ejpam-3852	38	18	,	,	PUNCT
ejpam-3852	38	19	which	which	PRON
ejpam-3852	38	20	we	we	PRON
ejpam-3852	38	21	will	will	AUX
ejpam-3852	38	22	describe	describe	VERB
ejpam-3852	38	23	below	below	ADP
ejpam-3852	38	24	.	.	PUNCT
ejpam-3852	39	1	for	for	ADP
ejpam-3852	39	2	a	a	DET
ejpam-3852	39	3	modulus	modulus	ADJ
ejpam-3852	39	4	m	m	NOUN
ejpam-3852	39	5	=	=	NOUN
ejpam-3852	39	6	2ω	2ω	NUM
ejpam-3852	39	7	and	and	CCONJ
ejpam-3852	39	8	y0	y0	PROPN
ejpam-3852	39	9	∈	∈	PROPN
ejpam-3852	39	10	gm	gm	NOUN
ejpam-3852	39	11	,	,	PUNCT
ejpam-3852	39	12	let	let	VERB
ejpam-3852	39	13	yn+1	yn+1	NUM
ejpam-3852	39	14	≡	≡	PROPN
ejpam-3852	39	15	ay−1n	ay−1n	PROPN
ejpam-3852	40	1	+	+	PUNCT
ejpam-3852	40	2	b+	b+	PROPN
ejpam-3852	40	3	cyn	cyn	PROPN
ejpam-3852	40	4	(	(	PUNCT
ejpam-3852	40	5	mod	mod	PROPN
ejpam-3852	40	6	m	m	PROPN
ejpam-3852	40	7	)	)	PUNCT
ejpam-3852	40	8	,	,	PUNCT
ejpam-3852	40	9	n	n	PROPN
ejpam-3852	40	10	=	=	SYM
ejpam-3852	40	11	0	0	NUM
ejpam-3852	40	12	,	,	PUNCT
ejpam-3852	40	13	1	1	NUM
ejpam-3852	40	14	,	,	PUNCT
ejpam-3852	40	15	.	.	PUNCT
ejpam-3852	40	16	.	.	PUNCT
ejpam-3852	41	1	.	.	PUNCT
ejpam-3852	42	1	,	,	PUNCT
ejpam-3852	42	2	(	(	PUNCT
ejpam-3852	42	3	4	4	X
ejpam-3852	42	4	)	)	PUNCT
ejpam-3852	42	5	where	where	SCONJ
ejpam-3852	42	6	a	a	DET
ejpam-3852	42	7	,	,	PUNCT
ejpam-3852	42	8	b	b	NOUN
ejpam-3852	42	9	,	,	PUNCT
ejpam-3852	42	10	c	c	PROPN
ejpam-3852	42	11	∈	∈	PROPN
ejpam-3852	42	12	zm	zm	PROPN
ejpam-3852	42	13	are	be	AUX
ejpam-3852	42	14	such	such	ADJ
ejpam-3852	42	15	that	that	SCONJ
ejpam-3852	42	16	yn+1	yn+1	PROPN
ejpam-3852	42	17	∈	∈	PROPN
ejpam-3852	42	18	gm	gm	PROPN
ejpam-3852	42	19	,	,	PUNCT
ejpam-3852	42	20	whenever	whenever	SCONJ
ejpam-3852	42	21	yn	yn	PROPN
ejpam-3852	42	22	∈	∈	PROPN
ejpam-3852	42	23	gm	gm	PROPN
ejpam-3852	42	24	.	.	PUNCT
ejpam-3852	43	1	the	the	DET
ejpam-3852	43	2	main	main	ADJ
ejpam-3852	43	3	result	result	NOUN
ejpam-3852	43	4	obtained	obtain	VERB
ejpam-3852	43	5	in	in	ADP
ejpam-3852	43	6	[	[	X
ejpam-3852	43	7	14	14	NUM
ejpam-3852	43	8	]	]	PUNCT
ejpam-3852	43	9	is	be	AUX
ejpam-3852	43	10	the	the	DET
ejpam-3852	43	11	following	follow	VERB
ejpam-3852	43	12	theorem	theorem	NOUN
ejpam-3852	43	13	.	.	PUNCT
ejpam-3852	44	1	theorem	theorem	ADJ
ejpam-3852	44	2	2	2	NUM
ejpam-3852	44	3	(	(	PUNCT
ejpam-3852	44	4	[	[	X
ejpam-3852	44	5	14	14	NUM
ejpam-3852	44	6	]	]	NUM
ejpam-3852	44	7	)	)	PUNCT
ejpam-3852	44	8	.	.	PUNCT
ejpam-3852	45	1	let	let	VERB
ejpam-3852	45	2	m	m	NOUN
ejpam-3852	45	3	=	=	NOUN
ejpam-3852	45	4	2ω	2ω	NUM
ejpam-3852	45	5	,	,	PUNCT
ejpam-3852	45	6	ω	ω	X
ejpam-3852	45	7	≥	≥	NOUN
ejpam-3852	45	8	3	3	NUM
ejpam-3852	45	9	.	.	PUNCT
ejpam-3852	46	1	then	then	ADV
ejpam-3852	46	2	the	the	DET
ejpam-3852	46	3	prng	prng	NOUN
ejpam-3852	46	4	{	{	PUNCT
ejpam-3852	46	5	yn	yn	PROPN
ejpam-3852	46	6	}	}	PUNCT
ejpam-3852	46	7	derived	derive	VERB
ejpam-3852	46	8	from	from	ADP
ejpam-3852	46	9	(	(	PUNCT
ejpam-3852	46	10	4	4	NUM
ejpam-3852	46	11	)	)	PUNCT
ejpam-3852	46	12	is	be	AUX
ejpam-3852	46	13	purely	purely	ADV
ejpam-3852	46	14	periodic	periodic	ADJ
ejpam-3852	46	15	with	with	ADP
ejpam-3852	46	16	period	period	NOUN
ejpam-3852	46	17	m	m	VERB
ejpam-3852	46	18	2	2	NUM
ejpam-3852	46	19	if	if	SCONJ
ejpam-3852	46	20	and	and	CCONJ
ejpam-3852	46	21	only	only	ADV
ejpam-3852	46	22	if	if	SCONJ
ejpam-3852	46	23	a+	a+	PRON
ejpam-3852	46	24	c	c	PROPN
ejpam-3852	46	25	≡	≡	PROPN
ejpam-3852	46	26	1	1	NUM
ejpam-3852	46	27	(	(	PUNCT
ejpam-3852	46	28	mod	mod	NOUN
ejpam-3852	46	29	4	4	NUM
ejpam-3852	46	30	)	)	PUNCT
ejpam-3852	46	31	and	and	CCONJ
ejpam-3852	46	32	b	b	X
ejpam-3852	46	33	≡	≡	ADJ
ejpam-3852	46	34	2	2	NUM
ejpam-3852	46	35	(	(	PUNCT
ejpam-3852	46	36	mod	mod	NOUN
ejpam-3852	46	37	4	4	NUM
ejpam-3852	46	38	)	)	PUNCT
ejpam-3852	46	39	.	.	PUNCT
ejpam-3852	47	1	in	in	ADP
ejpam-3852	47	2	this	this	DET
ejpam-3852	47	3	paper	paper	NOUN
ejpam-3852	47	4	,	,	PUNCT
ejpam-3852	47	5	we	we	PRON
ejpam-3852	47	6	propose	propose	VERB
ejpam-3852	47	7	a	a	DET
ejpam-3852	47	8	new	new	ADJ
ejpam-3852	47	9	nonlinear	nonlinear	ADJ
ejpam-3852	47	10	method	method	NOUN
ejpam-3852	47	11	,	,	PUNCT
ejpam-3852	47	12	which	which	PRON
ejpam-3852	47	13	we	we	PRON
ejpam-3852	47	14	will	will	AUX
ejpam-3852	47	15	call	call	VERB
ejpam-3852	47	16	hybrid	hybrid	ADJ
ejpam-3852	47	17	inversive	inversive	ADJ
ejpam-3852	47	18	congruential	congruential	ADJ
ejpam-3852	47	19	generator	generator	NOUN
ejpam-3852	47	20	(	(	PUNCT
ejpam-3852	47	21	hicg	hicg	NOUN
ejpam-3852	47	22	)	)	PUNCT
ejpam-3852	47	23	.	.	PUNCT
ejpam-3852	48	1	for	for	ADP
ejpam-3852	48	2	the	the	DET
ejpam-3852	48	3	modulus	modulus	ADJ
ejpam-3852	48	4	m	m	NOUN
ejpam-3852	48	5	=	=	SYM
ejpam-3852	48	6	2ω	2ω	NUM
ejpam-3852	48	7	and	and	CCONJ
ejpam-3852	48	8	y0	y0	NOUN
ejpam-3852	48	9	,	,	PUNCT
ejpam-3852	48	10	y1	y1	PROPN
ejpam-3852	48	11	∈	∈	PROPN
ejpam-3852	48	12	gm	gm	PROPN
ejpam-3852	48	13	,	,	PUNCT
ejpam-3852	48	14	we	we	PRON
ejpam-3852	48	15	let	let	VERB
ejpam-3852	48	16	yn+2	yn+2	NUM
ejpam-3852	48	17	≡	≡	PROPN
ejpam-3852	48	18	ay−1n+1	ay−1n+1	PUNCT
ejpam-3852	49	1	+	+	CCONJ
ejpam-3852	49	2	byn	byn	X
ejpam-3852	49	3	+	+	X
ejpam-3852	49	4	c	c	PROPN
ejpam-3852	49	5	(	(	PUNCT
ejpam-3852	49	6	mod	mod	PROPN
ejpam-3852	49	7	m	m	PROPN
ejpam-3852	49	8	)	)	PUNCT
ejpam-3852	49	9	,	,	PUNCT
ejpam-3852	49	10	n	n	PROPN
ejpam-3852	49	11	=	=	SYM
ejpam-3852	49	12	0	0	NUM
ejpam-3852	49	13	,	,	PUNCT
ejpam-3852	49	14	1	1	NUM
ejpam-3852	49	15	,	,	PUNCT
ejpam-3852	49	16	.	.	PUNCT
ejpam-3852	49	17	.	.	PUNCT
ejpam-3852	49	18	.	.	PUNCT
ejpam-3852	50	1	,	,	PUNCT
ejpam-3852	50	2	(	(	PUNCT
ejpam-3852	50	3	5	5	X
ejpam-3852	50	4	)	)	PUNCT
ejpam-3852	50	5	where	where	SCONJ
ejpam-3852	50	6	a	a	DET
ejpam-3852	50	7	,	,	PUNCT
ejpam-3852	50	8	b	b	NOUN
ejpam-3852	50	9	,	,	PUNCT
ejpam-3852	50	10	c	c	PROPN
ejpam-3852	50	11	∈	∈	PROPN
ejpam-3852	50	12	zm	zm	PROPN
ejpam-3852	50	13	are	be	AUX
ejpam-3852	50	14	such	such	ADJ
ejpam-3852	51	1	that	that	SCONJ
ejpam-3852	51	2	yn+2	yn+2	NUM
ejpam-3852	51	3	∈	∈	PROPN
ejpam-3852	51	4	gm	gm	PROPN
ejpam-3852	51	5	whenever	whenever	SCONJ
ejpam-3852	51	6	yn	yn	PROPN
ejpam-3852	51	7	,	,	PUNCT
ejpam-3852	51	8	yn+1	yn+1	PROPN
ejpam-3852	51	9	∈	∈	PROPN
ejpam-3852	51	10	gm	gm	PROPN
ejpam-3852	51	11	.	.	PUNCT
ejpam-3852	52	1	then	then	ADV
ejpam-3852	52	2	,	,	PUNCT
ejpam-3852	52	3	the	the	DET
ejpam-3852	52	4	prns	prn	NOUN
ejpam-3852	52	5	{	{	PUNCT
ejpam-3852	52	6	xn	xn	NUM
ejpam-3852	52	7	}	}	PUNCT
ejpam-3852	52	8	,	,	PUNCT
ejpam-3852	52	9	defined	define	VERB
ejpam-3852	52	10	by	by	ADP
ejpam-3852	52	11	(	(	PUNCT
ejpam-3852	52	12	2	2	NUM
ejpam-3852	52	13	)	)	PUNCT
ejpam-3852	52	14	,	,	PUNCT
ejpam-3852	52	15	belong	belong	VERB
ejpam-3852	52	16	to	to	ADP
ejpam-3852	52	17	the	the	DET
ejpam-3852	52	18	set	set	NOUN
ejpam-3852	52	19	hm	hm	INTJ
ejpam-3852	52	20	=	=	NOUN
ejpam-3852	52	21	{	{	PUNCT
ejpam-3852	52	22	1	1	NUM
ejpam-3852	52	23	m	m	NOUN
ejpam-3852	52	24	,	,	PUNCT
ejpam-3852	52	25	3	3	NUM
ejpam-3852	52	26	m	m	NOUN
ejpam-3852	52	27	,	,	PUNCT
ejpam-3852	52	28	.	.	PUNCT
ejpam-3852	52	29	.	.	PUNCT
ejpam-3852	53	1	.	.	PUNCT
ejpam-3852	54	1	,	,	PUNCT
ejpam-3852	54	2	m−1	m−1	PROPN
ejpam-3852	54	3	m	m	VERB
ejpam-3852	54	4	}	}	PUNCT
ejpam-3852	54	5	.	.	PUNCT
ejpam-3852	55	1	since	since	SCONJ
ejpam-3852	55	2	some	some	PRON
ejpam-3852	55	3	of	of	ADP
ejpam-3852	55	4	the	the	DET
ejpam-3852	55	5	constants	constant	NOUN
ejpam-3852	55	6	in	in	ADP
ejpam-3852	55	7	our	our	PRON
ejpam-3852	55	8	generator	generator	NOUN
ejpam-3852	55	9	may	may	AUX
ejpam-3852	55	10	be	be	AUX
ejpam-3852	55	11	zero	zero	NUM
ejpam-3852	55	12	,	,	PUNCT
ejpam-3852	55	13	equation	equation	NOUN
ejpam-3852	55	14	(	(	PUNCT
ejpam-3852	55	15	5	5	NUM
ejpam-3852	55	16	)	)	PUNCT
ejpam-3852	55	17	includes	include	VERB
ejpam-3852	55	18	(	(	PUNCT
ejpam-3852	55	19	1	1	NUM
ejpam-3852	55	20	)	)	PUNCT
ejpam-3852	55	21	and	and	CCONJ
ejpam-3852	55	22	(	(	PUNCT
ejpam-3852	55	23	3	3	NUM
ejpam-3852	55	24	)	)	PUNCT
ejpam-3852	55	25	.	.	PUNCT
ejpam-3852	56	1	in	in	ADP
ejpam-3852	56	2	our	our	PRON
ejpam-3852	56	3	first	first	ADJ
ejpam-3852	56	4	result	result	NOUN
ejpam-3852	56	5	,	,	PUNCT
ejpam-3852	56	6	we	we	PRON
ejpam-3852	56	7	show	show	VERB
ejpam-3852	56	8	that	that	SCONJ
ejpam-3852	56	9	the	the	DET
ejpam-3852	56	10	period	period	NOUN
ejpam-3852	56	11	of	of	ADP
ejpam-3852	56	12	the	the	DET
ejpam-3852	56	13	hicg	hicg	ADJ
ejpam-3852	56	14	sequence	sequence	NOUN
ejpam-3852	56	15	is	be	AUX
ejpam-3852	56	16	at	at	ADP
ejpam-3852	56	17	most	most	ADJ
ejpam-3852	56	18	m	m	NOUN
ejpam-3852	56	19	;	;	PUNCT
ejpam-3852	56	20	further	far	ADV
ejpam-3852	56	21	,	,	PUNCT
ejpam-3852	56	22	we	we	PRON
ejpam-3852	56	23	obtain	obtain	VERB
ejpam-3852	56	24	explicit	explicit	ADJ
ejpam-3852	56	25	conditions	condition	NOUN
ejpam-3852	56	26	on	on	ADP
ejpam-3852	56	27	the	the	DET
ejpam-3852	56	28	involved	involved	ADJ
ejpam-3852	56	29	parameters	parameter	NOUN
ejpam-3852	56	30	such	such	ADJ
ejpam-3852	56	31	that	that	SCONJ
ejpam-3852	56	32	the	the	DET
ejpam-3852	56	33	sequence	sequence	NOUN
ejpam-3852	56	34	{	{	PUNCT
ejpam-3852	56	35	yn	yn	NOUN
ejpam-3852	56	36	}	}	PUNCT
ejpam-3852	56	37	derived	derive	VERB
ejpam-3852	56	38	from	from	ADP
ejpam-3852	56	39	(	(	PUNCT
ejpam-3852	56	40	5	5	NUM
ejpam-3852	56	41	)	)	PUNCT
ejpam-3852	56	42	is	be	AUX
ejpam-3852	56	43	purely	purely	ADV
ejpam-3852	56	44	periodic	periodic	ADJ
ejpam-3852	56	45	with	with	ADP
ejpam-3852	56	46	period	period	NOUN
ejpam-3852	56	47	m	m	NOUN
ejpam-3852	56	48	;	;	PUNCT
ejpam-3852	56	49	moreover	moreover	ADV
ejpam-3852	56	50	,	,	PUNCT
ejpam-3852	56	51	we	we	PRON
ejpam-3852	56	52	give	give	VERB
ejpam-3852	56	53	explicit	explicit	ADJ
ejpam-3852	56	54	conditions	condition	NOUN
ejpam-3852	56	55	on	on	ADP
ejpam-3852	56	56	the	the	DET
ejpam-3852	56	57	parameters	parameter	NOUN
ejpam-3852	56	58	to	to	PART
ejpam-3852	56	59	obtain	obtain	VERB
ejpam-3852	56	60	an	an	DET
ejpam-3852	56	61	ultimate	ultimate	ADJ
ejpam-3852	56	62	period	period	NOUN
ejpam-3852	56	63	of	of	ADP
ejpam-3852	56	64	m/2	m/2	NUM
ejpam-3852	56	65	.	.	PUNCT
ejpam-3852	57	1	furthermore	furthermore	ADV
ejpam-3852	57	2	,	,	PUNCT
ejpam-3852	57	3	we	we	PRON
ejpam-3852	57	4	look	look	VERB
ejpam-3852	57	5	at	at	ADP
ejpam-3852	57	6	the	the	DET
ejpam-3852	57	7	lattice	lattice	PROPN
ejpam-3852	57	8	test	test	NOUN
ejpam-3852	57	9	passing	pass	VERB
ejpam-3852	57	10	for	for	ADP
ejpam-3852	57	11	a	a	DET
ejpam-3852	57	12	binary	binary	ADJ
ejpam-3852	57	13	sequence	sequence	NOUN
ejpam-3852	57	14	obtained	obtain	VERB
ejpam-3852	57	15	via	via	ADP
ejpam-3852	57	16	hicg	hicg	NOUN
ejpam-3852	57	17	and	and	CCONJ
ejpam-3852	57	18	show	show	VERB
ejpam-3852	57	19	that	that	SCONJ
ejpam-3852	57	20	it	it	PRON
ejpam-3852	57	21	has	have	VERB
ejpam-3852	57	22	a	a	DET
ejpam-3852	57	23	lattice	lattice	NOUN
ejpam-3852	57	24	test	test	NOUN
ejpam-3852	57	25	complexity	complexity	NOUN
ejpam-3852	57	26	(	(	PUNCT
ejpam-3852	57	27	defined	define	VERB
ejpam-3852	57	28	in	in	ADP
ejpam-3852	57	29	section	section	NOUN
ejpam-3852	57	30	4	4	NUM
ejpam-3852	57	31	)	)	PUNCT
ejpam-3852	57	32	equal	equal	ADJ
ejpam-3852	57	33	to	to	ADP
ejpam-3852	57	34	m/2	m/2	NUM
ejpam-3852	57	35	.	.	PUNCT
ejpam-3852	58	1	p.	p.	NOUN
ejpam-3852	58	2	stănică	stănică	NUM
ejpam-3852	58	3	et	et	PROPN
ejpam-3852	58	4	al	al	PROPN
ejpam-3852	58	5	.	.	PUNCT
ejpam-3852	58	6	/	/	SYM
ejpam-3852	58	7	eur	eur	PROPN
ejpam-3852	58	8	.	.	PUNCT
ejpam-3852	59	1	j.	j.	PROPN
ejpam-3852	59	2	pure	pure	PROPN
ejpam-3852	59	3	appl	appl	PROPN
ejpam-3852	59	4	.	.	PROPN
ejpam-3852	59	5	math	math	PROPN
ejpam-3852	59	6	,	,	PUNCT
ejpam-3852	59	7	14	14	NUM
ejpam-3852	59	8	(	(	PUNCT
ejpam-3852	59	9	1	1	NUM
ejpam-3852	59	10	)	)	PUNCT
ejpam-3852	59	11	(	(	PUNCT
ejpam-3852	59	12	2021	2021	NUM
ejpam-3852	59	13	)	)	PUNCT
ejpam-3852	59	14	,	,	PUNCT
ejpam-3852	59	15	1	1	NUM
ejpam-3852	59	16	-	-	SYM
ejpam-3852	59	17	18	18	NUM
ejpam-3852	59	18	3	3	NUM
ejpam-3852	59	19	2	2	NUM
ejpam-3852	59	20	.	.	PUNCT
ejpam-3852	60	1	the	the	DET
ejpam-3852	60	2	maximum	maximum	ADJ
ejpam-3852	60	3	period	period	NOUN
ejpam-3852	60	4	of	of	ADP
ejpam-3852	60	5	the	the	DET
ejpam-3852	60	6	hicg	hicg	NOUN
ejpam-3852	60	7	is	be	AUX
ejpam-3852	60	8	m	m	PRON
ejpam-3852	60	9	since	since	SCONJ
ejpam-3852	60	10	two	two	NUM
ejpam-3852	60	11	consecutive	consecutive	ADJ
ejpam-3852	60	12	residues	residue	NOUN
ejpam-3852	60	13	modulo	modulo	NOUN
ejpam-3852	60	14	m	m	NOUN
ejpam-3852	60	15	=	=	ADJ
ejpam-3852	60	16	2ω	2ω	PROPN
ejpam-3852	60	17	will	will	AUX
ejpam-3852	60	18	determine	determine	VERB
ejpam-3852	60	19	the	the	DET
ejpam-3852	60	20	next	next	ADJ
ejpam-3852	60	21	residue	residue	NOUN
ejpam-3852	60	22	(	(	PUNCT
ejpam-3852	60	23	observe	observe	VERB
ejpam-3852	60	24	that	that	SCONJ
ejpam-3852	60	25	our	our	PRON
ejpam-3852	60	26	sequence	sequence	NOUN
ejpam-3852	60	27	has	have	VERB
ejpam-3852	60	28	second	second	ADJ
ejpam-3852	60	29	order	order	NOUN
ejpam-3852	60	30	)	)	PUNCT
ejpam-3852	60	31	,	,	PUNCT
ejpam-3852	60	32	the	the	DET
ejpam-3852	60	33	maximum	maximum	ADJ
ejpam-3852	60	34	period	period	NOUN
ejpam-3852	60	35	can	can	AUX
ejpam-3852	60	36	be	be	AUX
ejpam-3852	60	37	at	at	ADV
ejpam-3852	60	38	most	most	ADV
ejpam-3852	60	39	twice	twice	DET
ejpam-3852	60	40	the	the	DET
ejpam-3852	60	41	number	number	NOUN
ejpam-3852	60	42	of	of	ADP
ejpam-3852	60	43	pairs	pair	NOUN
ejpam-3852	60	44	(	(	PUNCT
ejpam-3852	60	45	residue	residue	NOUN
ejpam-3852	60	46	repetitions	repetition	NOUN
ejpam-3852	60	47	allowed	allow	VERB
ejpam-3852	60	48	)	)	PUNCT
ejpam-3852	60	49	of	of	ADP
ejpam-3852	60	50	all	all	DET
ejpam-3852	60	51	odd	odd	ADJ
ejpam-3852	60	52	integers	integer	NOUN
ejpam-3852	60	53	modulo	modulo	VERB
ejpam-3852	60	54	m	m	VERB
ejpam-3852	60	55	,	,	PUNCT
ejpam-3852	60	56	that	that	PRON
ejpam-3852	60	57	is	is	ADV
ejpam-3852	60	58	m2	m2	PROPN
ejpam-3852	60	59	4	4	NUM
ejpam-3852	60	60	.	.	PUNCT
ejpam-3852	61	1	however	however	ADV
ejpam-3852	61	2	,	,	PUNCT
ejpam-3852	61	3	here	here	ADV
ejpam-3852	61	4	,	,	PUNCT
ejpam-3852	61	5	we	we	PRON
ejpam-3852	61	6	will	will	AUX
ejpam-3852	61	7	show	show	VERB
ejpam-3852	61	8	that	that	SCONJ
ejpam-3852	61	9	for	for	ADP
ejpam-3852	61	10	any	any	DET
ejpam-3852	61	11	values	value	NOUN
ejpam-3852	61	12	of	of	ADP
ejpam-3852	61	13	the	the	DET
ejpam-3852	61	14	parameters	parameter	NOUN
ejpam-3852	61	15	a	a	DET
ejpam-3852	61	16	,	,	PUNCT
ejpam-3852	61	17	b	b	NOUN
ejpam-3852	61	18	,	,	PUNCT
ejpam-3852	61	19	c	c	PROPN
ejpam-3852	61	20	and	and	CCONJ
ejpam-3852	61	21	any	any	DET
ejpam-3852	61	22	odd	odd	ADJ
ejpam-3852	61	23	initial	initial	ADJ
ejpam-3852	61	24	conditions	condition	NOUN
ejpam-3852	61	25	y0	y0	PROPN
ejpam-3852	61	26	,	,	PUNCT
ejpam-3852	61	27	y1	y1	PROPN
ejpam-3852	61	28	∈	∈	PROPN
ejpam-3852	61	29	gm	gm	PROPN
ejpam-3852	61	30	,	,	PUNCT
ejpam-3852	61	31	the	the	DET
ejpam-3852	61	32	(	(	PUNCT
ejpam-3852	61	33	ultimate	ultimate	ADJ
ejpam-3852	61	34	)	)	PUNCT
ejpam-3852	61	35	period	period	NOUN
ejpam-3852	61	36	of	of	ADP
ejpam-3852	61	37	{	{	PUNCT
ejpam-3852	61	38	yn	yn	PROPN
ejpam-3852	61	39	}	}	PUNCT
ejpam-3852	61	40	can	can	AUX
ejpam-3852	61	41	be	be	AUX
ejpam-3852	61	42	at	at	ADP
ejpam-3852	61	43	most	most	ADJ
ejpam-3852	61	44	m	m	NOUN
ejpam-3852	61	45	.	.	PUNCT
ejpam-3852	62	1	certainly	certainly	ADV
ejpam-3852	62	2	,	,	PUNCT
ejpam-3852	62	3	the	the	DET
ejpam-3852	62	4	sequence	sequence	NOUN
ejpam-3852	62	5	may	may	AUX
ejpam-3852	62	6	not	not	PART
ejpam-3852	62	7	be	be	AUX
ejpam-3852	62	8	purely	purely	ADV
ejpam-3852	62	9	periodic	periodic	ADJ
ejpam-3852	62	10	,	,	PUNCT
ejpam-3852	62	11	rather	rather	ADV
ejpam-3852	62	12	ultimately	ultimately	ADV
ejpam-3852	62	13	periodic	periodic	ADJ
ejpam-3852	62	14	,	,	PUNCT
ejpam-3852	62	15	but	but	CCONJ
ejpam-3852	62	16	for	for	ADP
ejpam-3852	62	17	simplicity	simplicity	NOUN
ejpam-3852	62	18	,	,	PUNCT
ejpam-3852	62	19	shifting	shift	VERB
ejpam-3852	62	20	the	the	DET
ejpam-3852	62	21	sequence	sequence	NOUN
ejpam-3852	62	22	to	to	ADP
ejpam-3852	62	23	that	that	DET
ejpam-3852	62	24	first	first	ADJ
ejpam-3852	62	25	position	position	NOUN
ejpam-3852	62	26	of	of	ADP
ejpam-3852	62	27	the	the	DET
ejpam-3852	62	28	period	period	NOUN
ejpam-3852	62	29	,	,	PUNCT
ejpam-3852	62	30	we	we	PRON
ejpam-3852	62	31	may	may	AUX
ejpam-3852	62	32	assume	assume	VERB
ejpam-3852	62	33	in	in	ADP
ejpam-3852	62	34	this	this	DET
ejpam-3852	62	35	section	section	NOUN
ejpam-3852	62	36	that	that	SCONJ
ejpam-3852	62	37	the	the	DET
ejpam-3852	62	38	period	period	NOUN
ejpam-3852	62	39	starts	start	VERB
ejpam-3852	62	40	from	from	ADP
ejpam-3852	62	41	y0	y0	NOUN
ejpam-3852	62	42	.	.	PUNCT
ejpam-3852	63	1	throughout	throughout	ADP
ejpam-3852	63	2	,	,	PUNCT
ejpam-3852	63	3	we	we	PRON
ejpam-3852	63	4	will	will	AUX
ejpam-3852	63	5	use	use	VERB
ejpam-3852	63	6	the	the	DET
ejpam-3852	63	7	notation	notation	NOUN
ejpam-3852	63	8	∵	∵	NOUN
ejpam-3852	63	9	as	as	ADP
ejpam-3852	63	10	a	a	DET
ejpam-3852	63	11	shorthand	shorthand	NOUN
ejpam-3852	63	12	for	for	ADP
ejpam-3852	63	13	“	"	PUNCT
ejpam-3852	63	14	because	because	SCONJ
ejpam-3852	63	15	/	/	SYM
ejpam-3852	63	16	since	since	SCONJ
ejpam-3852	63	17	”	"	PUNCT
ejpam-3852	63	18	.	.	PUNCT
ejpam-3852	64	1	theorem	theorem	NOUN
ejpam-3852	64	2	3	3	X
ejpam-3852	64	3	.	.	PUNCT
ejpam-3852	65	1	let	let	VERB
ejpam-3852	65	2	m	m	PRON
ejpam-3852	65	3	=	=	VERB
ejpam-3852	65	4	2ω	2ω	NUM
ejpam-3852	65	5	≥	≥	NUM
ejpam-3852	65	6	4	4	NUM
ejpam-3852	65	7	.	.	PUNCT
ejpam-3852	66	1	the	the	DET
ejpam-3852	66	2	hicg	hicg	ADJ
ejpam-3852	66	3	sequence	sequence	NOUN
ejpam-3852	66	4	{	{	PUNCT
ejpam-3852	66	5	yn	yn	PROPN
ejpam-3852	66	6	(	(	PUNCT
ejpam-3852	66	7	mod	mod	PROPN
ejpam-3852	66	8	m	m	PROPN
ejpam-3852	66	9	)	)	PUNCT
ejpam-3852	66	10	}	}	PUNCT
ejpam-3852	66	11	has	have	VERB
ejpam-3852	66	12	an	an	DET
ejpam-3852	66	13	ultimate	ultimate	ADJ
ejpam-3852	66	14	period	period	NOUN
ejpam-3852	66	15	less	less	ADJ
ejpam-3852	66	16	than	than	ADP
ejpam-3852	66	17	or	or	CCONJ
ejpam-3852	66	18	equal	equal	ADJ
ejpam-3852	66	19	to	to	ADP
ejpam-3852	66	20	m.	m.	NOUN
ejpam-3852	66	21	proof	proof	NOUN
ejpam-3852	66	22	.	.	PUNCT
ejpam-3852	67	1	we	we	PRON
ejpam-3852	67	2	will	will	AUX
ejpam-3852	67	3	show	show	VERB
ejpam-3852	67	4	our	our	PRON
ejpam-3852	67	5	result	result	NOUN
ejpam-3852	67	6	by	by	ADP
ejpam-3852	67	7	induction	induction	NOUN
ejpam-3852	67	8	.	.	PUNCT
ejpam-3852	68	1	we	we	PRON
ejpam-3852	68	2	first	first	ADV
ejpam-3852	68	3	note	note	VERB
ejpam-3852	68	4	that	that	SCONJ
ejpam-3852	68	5	for	for	ADP
ejpam-3852	68	6	m	m	PROPN
ejpam-3852	68	7	=	=	SYM
ejpam-3852	68	8	4	4	NUM
ejpam-3852	68	9	(	(	PUNCT
ejpam-3852	68	10	and	and	CCONJ
ejpam-3852	68	11	m	m	PROPN
ejpam-3852	68	12	=	=	ADJ
ejpam-3852	68	13	8)	8)	NUM
ejpam-3852	68	14	,	,	PUNCT
ejpam-3852	68	15	the	the	DET
ejpam-3852	68	16	period	period	NOUN
ejpam-3852	68	17	is	be	AUX
ejpam-3852	68	18	at	at	ADP
ejpam-3852	68	19	most	most	ADJ
ejpam-3852	68	20	m.	m.	NOUN
ejpam-3852	68	21	we	we	PRON
ejpam-3852	68	22	now	now	ADV
ejpam-3852	68	23	assume	assume	VERB
ejpam-3852	68	24	that	that	SCONJ
ejpam-3852	68	25	the	the	DET
ejpam-3852	68	26	result	result	NOUN
ejpam-3852	68	27	holds	hold	VERB
ejpam-3852	68	28	for	for	ADP
ejpam-3852	68	29	m	m	NOUN
ejpam-3852	68	30	,	,	PUNCT
ejpam-3852	68	31	that	that	ADV
ejpam-3852	68	32	is	is	ADV
ejpam-3852	68	33	,	,	PUNCT
ejpam-3852	68	34	{	{	PUNCT
ejpam-3852	68	35	yn	yn	X
ejpam-3852	68	36	(	(	PUNCT
ejpam-3852	68	37	mod	mod	PROPN
ejpam-3852	68	38	m	m	PROPN
ejpam-3852	68	39	)	)	PUNCT
ejpam-3852	68	40	}	}	PUNCT
ejpam-3852	68	41	has	have	VERB
ejpam-3852	68	42	period	period	NOUN
ejpam-3852	68	43	`	`	PUNCT
ejpam-3852	68	44	≤	≤	NUM
ejpam-3852	68	45	m	m	PROPN
ejpam-3852	68	46	,	,	PUNCT
ejpam-3852	68	47	and	and	CCONJ
ejpam-3852	68	48	show	show	VERB
ejpam-3852	68	49	that	that	SCONJ
ejpam-3852	68	50	{	{	PUNCT
ejpam-3852	68	51	yn	yn	X
ejpam-3852	68	52	(	(	PUNCT
ejpam-3852	68	53	mod	mod	PROPN
ejpam-3852	68	54	2	2	NUM
ejpam-3852	68	55	m	m	NOUN
ejpam-3852	68	56	)	)	PUNCT
ejpam-3852	68	57	}	}	PUNCT
ejpam-3852	68	58	has	have	VERB
ejpam-3852	68	59	period	period	NOUN
ejpam-3852	68	60	at	at	ADP
ejpam-3852	68	61	most	most	ADV
ejpam-3852	68	62	2	2	NUM
ejpam-3852	68	63	m.	m.	NOUN
ejpam-3852	68	64	the	the	DET
ejpam-3852	68	65	given	give	VERB
ejpam-3852	68	66	sequence	sequence	NOUN
ejpam-3852	68	67	is	be	AUX
ejpam-3852	68	68	yn+2	yn+2	NUM
ejpam-3852	68	69	≡	≡	PROPN
ejpam-3852	68	70	ay−1n+1+byn+c	ay−1n+1+byn+c	PROPN
ejpam-3852	68	71	(	(	PUNCT
ejpam-3852	68	72	mod	mod	PROPN
ejpam-3852	68	73	2	2	NUM
ejpam-3852	68	74	m	m	NOUN
ejpam-3852	68	75	)	)	PUNCT
ejpam-3852	68	76	.	.	PUNCT
ejpam-3852	69	1	now	now	ADV
ejpam-3852	69	2	,	,	PUNCT
ejpam-3852	69	3	note	note	VERB
ejpam-3852	69	4	that	that	SCONJ
ejpam-3852	69	5	(	(	PUNCT
ejpam-3852	69	6	yn+m)−1	yn+m)−1	NOUN
ejpam-3852	69	7	≡	≡	PROPN
ejpam-3852	69	8	y−1n	y−1n	PROPN
ejpam-3852	70	1	+	+	NOUN
ejpam-3852	70	2	m	m	PROPN
ejpam-3852	70	3	(	(	PUNCT
ejpam-3852	70	4	mod	mod	PROPN
ejpam-3852	70	5	2	2	NUM
ejpam-3852	70	6	m	m	NOUN
ejpam-3852	70	7	)	)	PUNCT
ejpam-3852	70	8	for	for	ADP
ejpam-3852	70	9	all	all	DET
ejpam-3852	70	10	n.	n.	PROPN
ejpam-3852	70	11	clearly	clearly	ADV
ejpam-3852	70	12	,	,	PUNCT
ejpam-3852	70	13	in	in	ADP
ejpam-3852	70	14	order	order	NOUN
ejpam-3852	70	15	for	for	SCONJ
ejpam-3852	70	16	the	the	DET
ejpam-3852	70	17	yn	yn	PROPN
ejpam-3852	70	18	to	to	PART
ejpam-3852	70	19	be	be	AUX
ejpam-3852	70	20	odd	odd	ADJ
ejpam-3852	70	21	,	,	PUNCT
ejpam-3852	70	22	a	a	DET
ejpam-3852	70	23	+	+	X
ejpam-3852	70	24	b	b	NOUN
ejpam-3852	70	25	+	+	CCONJ
ejpam-3852	70	26	c	c	NOUN
ejpam-3852	70	27	must	must	AUX
ejpam-3852	70	28	be	be	AUX
ejpam-3852	70	29	odd	odd	ADJ
ejpam-3852	70	30	.	.	PUNCT
ejpam-3852	71	1	and	and	CCONJ
ejpam-3852	71	2	so	so	ADV
ejpam-3852	71	3	,	,	PUNCT
ejpam-3852	71	4	among	among	ADP
ejpam-3852	71	5	a	a	DET
ejpam-3852	71	6	,	,	PUNCT
ejpam-3852	71	7	b	b	PROPN
ejpam-3852	71	8	and	and	CCONJ
ejpam-3852	71	9	c	c	NOUN
ejpam-3852	71	10	,	,	PUNCT
ejpam-3852	71	11	either	either	CCONJ
ejpam-3852	71	12	all	all	PRON
ejpam-3852	71	13	of	of	ADP
ejpam-3852	71	14	them	they	PRON
ejpam-3852	71	15	are	be	AUX
ejpam-3852	71	16	odd	odd	ADJ
ejpam-3852	71	17	or	or	CCONJ
ejpam-3852	71	18	one	one	NUM
ejpam-3852	71	19	of	of	ADP
ejpam-3852	71	20	them	they	PRON
ejpam-3852	71	21	is	be	AUX
ejpam-3852	71	22	odd	odd	ADJ
ejpam-3852	71	23	and	and	CCONJ
ejpam-3852	71	24	the	the	DET
ejpam-3852	71	25	others	other	NOUN
ejpam-3852	71	26	are	be	AUX
ejpam-3852	71	27	even	even	ADV
ejpam-3852	71	28	.	.	PUNCT
ejpam-3852	72	1	so	so	ADV
ejpam-3852	72	2	,	,	PUNCT
ejpam-3852	72	3	we	we	PRON
ejpam-3852	72	4	consider	consider	VERB
ejpam-3852	72	5	the	the	DET
ejpam-3852	72	6	following	follow	VERB
ejpam-3852	72	7	four	four	NUM
ejpam-3852	72	8	cases	case	NOUN
ejpam-3852	72	9	.	.	PUNCT
ejpam-3852	73	1	case	case	NOUN
ejpam-3852	73	2	1	1	NUM
ejpam-3852	73	3	.	.	PUNCT
ejpam-3852	74	1	a	a	DET
ejpam-3852	74	2	,	,	PUNCT
ejpam-3852	74	3	b	b	NOUN
ejpam-3852	74	4	and	and	CCONJ
ejpam-3852	74	5	c	c	PROPN
ejpam-3852	74	6	are	be	AUX
ejpam-3852	74	7	all	all	ADV
ejpam-3852	74	8	odd	odd	ADJ
ejpam-3852	74	9	:	:	PUNCT
ejpam-3852	74	10	as	as	ADP
ejpam-3852	74	11	yn+2	yn+2	NUM
ejpam-3852	74	12	≡	≡	PROPN
ejpam-3852	74	13	ay−1n+1	ay−1n+1	PROPN
ejpam-3852	75	1	+	+	CCONJ
ejpam-3852	75	2	byn	byn	X
ejpam-3852	75	3	+	+	X
ejpam-3852	75	4	c	c	PROPN
ejpam-3852	75	5	(	(	PUNCT
ejpam-3852	75	6	mod	mod	PROPN
ejpam-3852	75	7	m	m	PROPN
ejpam-3852	75	8	)	)	PUNCT
ejpam-3852	75	9	has	have	VERB
ejpam-3852	75	10	period	period	NOUN
ejpam-3852	75	11	`	`	PUNCT
ejpam-3852	75	12	,	,	PUNCT
ejpam-3852	75	13	then	then	ADV
ejpam-3852	75	14	we	we	PRON
ejpam-3852	75	15	can	can	AUX
ejpam-3852	75	16	have	have	VERB
ejpam-3852	75	17	the	the	DET
ejpam-3852	75	18	following	follow	VERB
ejpam-3852	75	19	four	four	NUM
ejpam-3852	75	20	subcases	subcase	NOUN
ejpam-3852	75	21	:	:	PUNCT
ejpam-3852	75	22	(	(	PUNCT
ejpam-3852	75	23	i	i	NOUN
ejpam-3852	75	24	)	)	PUNCT
ejpam-3852	75	25	y	y	PROPN
ejpam-3852	75	26	`	`	PUNCT
ejpam-3852	75	27	≡	≡	PROPN
ejpam-3852	75	28	y0	y0	PROPN
ejpam-3852	75	29	(	(	PUNCT
ejpam-3852	75	30	mod	mod	PROPN
ejpam-3852	75	31	2	2	NUM
ejpam-3852	75	32	m	m	NOUN
ejpam-3852	75	33	)	)	PUNCT
ejpam-3852	75	34	and	and	CCONJ
ejpam-3852	75	35	y`+1	y`+1	PROPN
ejpam-3852	75	36	≡	≡	PROPN
ejpam-3852	75	37	y1	y1	PROPN
ejpam-3852	75	38	(	(	PUNCT
ejpam-3852	75	39	mod	mod	PROPN
ejpam-3852	75	40	2	2	NUM
ejpam-3852	75	41	m	m	NOUN
ejpam-3852	75	42	)	)	PUNCT
ejpam-3852	75	43	,	,	PUNCT
ejpam-3852	75	44	(	(	PUNCT
ejpam-3852	75	45	ii	ii	NOUN
ejpam-3852	75	46	)	)	PUNCT
ejpam-3852	75	47	y	y	PROPN
ejpam-3852	75	48	`	`	PUNCT
ejpam-3852	75	49	≡	≡	PROPN
ejpam-3852	75	50	y0	y0	PROPN
ejpam-3852	76	1	+	+	PROPN
ejpam-3852	76	2	m	m	PROPN
ejpam-3852	76	3	(	(	PUNCT
ejpam-3852	76	4	mod	mod	PROPN
ejpam-3852	76	5	2	2	NUM
ejpam-3852	76	6	m	m	NOUN
ejpam-3852	76	7	)	)	PUNCT
ejpam-3852	76	8	and	and	CCONJ
ejpam-3852	76	9	y`+1	y`+1	PROPN
ejpam-3852	76	10	≡	≡	PROPN
ejpam-3852	77	1	y1	y1	PROPN
ejpam-3852	78	1	+	+	PROPN
ejpam-3852	78	2	m	m	PROPN
ejpam-3852	78	3	(	(	PUNCT
ejpam-3852	78	4	mod	mod	PROPN
ejpam-3852	78	5	2	2	NUM
ejpam-3852	78	6	m	m	NOUN
ejpam-3852	78	7	)	)	PUNCT
ejpam-3852	78	8	,	,	PUNCT
ejpam-3852	78	9	(	(	PUNCT
ejpam-3852	78	10	iii	iii	X
ejpam-3852	78	11	)	)	PUNCT
ejpam-3852	78	12	y	y	PROPN
ejpam-3852	78	13	`	`	PUNCT
ejpam-3852	78	14	≡	≡	PROPN
ejpam-3852	78	15	y0	y0	PROPN
ejpam-3852	78	16	(	(	PUNCT
ejpam-3852	78	17	mod	mod	PROPN
ejpam-3852	78	18	2	2	NUM
ejpam-3852	78	19	m	m	NOUN
ejpam-3852	78	20	)	)	PUNCT
ejpam-3852	78	21	and	and	CCONJ
ejpam-3852	78	22	y`+1	y`+1	PROPN
ejpam-3852	78	23	≡	≡	PROPN
ejpam-3852	78	24	y1	y1	PROPN
ejpam-3852	79	1	+	+	PROPN
ejpam-3852	79	2	m	m	PROPN
ejpam-3852	79	3	(	(	PUNCT
ejpam-3852	79	4	mod	mod	PROPN
ejpam-3852	79	5	2	2	NUM
ejpam-3852	79	6	m	m	NOUN
ejpam-3852	79	7	)	)	PUNCT
ejpam-3852	79	8	,	,	PUNCT
ejpam-3852	79	9	(	(	PUNCT
ejpam-3852	79	10	iv	iv	X
ejpam-3852	79	11	)	)	PUNCT
ejpam-3852	79	12	y	y	PROPN
ejpam-3852	79	13	`	`	PUNCT
ejpam-3852	79	14	≡	≡	PROPN
ejpam-3852	79	15	y0	y0	PROPN
ejpam-3852	80	1	+	+	PROPN
ejpam-3852	80	2	m	m	PROPN
ejpam-3852	80	3	(	(	PUNCT
ejpam-3852	80	4	mod	mod	PROPN
ejpam-3852	80	5	2	2	NUM
ejpam-3852	80	6	m	m	NOUN
ejpam-3852	80	7	)	)	PUNCT
ejpam-3852	80	8	and	and	CCONJ
ejpam-3852	81	1	y`+1	y`+1	PROPN
ejpam-3852	81	2	≡	≡	PROPN
ejpam-3852	81	3	y1	y1	PROPN
ejpam-3852	81	4	(	(	PUNCT
ejpam-3852	81	5	mod	mod	PROPN
ejpam-3852	81	6	2	2	NUM
ejpam-3852	81	7	m	m	NOUN
ejpam-3852	81	8	)	)	PUNCT
ejpam-3852	81	9	.	.	PUNCT
ejpam-3852	82	1	the	the	DET
ejpam-3852	82	2	first	first	ADJ
ejpam-3852	82	3	subcase	subcase	NOUN
ejpam-3852	82	4	follows	follow	VERB
ejpam-3852	82	5	immediately	immediately	ADV
ejpam-3852	82	6	,	,	PUNCT
ejpam-3852	82	7	and	and	CCONJ
ejpam-3852	82	8	the	the	DET
ejpam-3852	82	9	period	period	NOUN
ejpam-3852	82	10	modulo	modulo	VERB
ejpam-3852	82	11	2	2	NUM
ejpam-3852	82	12	m	m	NOUN
ejpam-3852	82	13	is	be	AUX
ejpam-3852	82	14	also	also	ADV
ejpam-3852	82	15	`	`	PUNCT
ejpam-3852	82	16	here	here	ADV
ejpam-3852	82	17	.	.	PUNCT
ejpam-3852	83	1	for	for	ADP
ejpam-3852	83	2	the	the	DET
ejpam-3852	83	3	second	second	ADJ
ejpam-3852	83	4	subcase	subcase	NOUN
ejpam-3852	83	5	,	,	PUNCT
ejpam-3852	83	6	we	we	PRON
ejpam-3852	83	7	have	have	VERB
ejpam-3852	83	8	,	,	PUNCT
ejpam-3852	83	9	y`+2	y`+2	ADJ
ejpam-3852	83	10	≡	≡	PROPN
ejpam-3852	83	11	a(y−11	a(y−11	X
ejpam-3852	83	12	+	+	PROPN
ejpam-3852	83	13	m	m	X
ejpam-3852	83	14	)	)	PUNCT
ejpam-3852	84	1	+	+	NUM
ejpam-3852	84	2	b(y0	b(y0	NOUN
ejpam-3852	84	3	+	+	NOUN
ejpam-3852	84	4	m	m	X
ejpam-3852	84	5	)	)	PUNCT
ejpam-3852	85	1	+	+	CCONJ
ejpam-3852	85	2	c	c	X
ejpam-3852	85	3	(	(	PUNCT
ejpam-3852	85	4	mod	mod	PROPN
ejpam-3852	85	5	2	2	NUM
ejpam-3852	85	6	m	m	NOUN
ejpam-3852	85	7	)	)	PUNCT
ejpam-3852	85	8	≡	≡	PROPN
ejpam-3852	85	9	y2	y2	PROPN
ejpam-3852	85	10	+	+	CCONJ
ejpam-3852	85	11	(	(	PUNCT
ejpam-3852	85	12	a+	a+	PUNCT
ejpam-3852	85	13	b)m	b)m	X
ejpam-3852	85	14	(	(	PUNCT
ejpam-3852	85	15	mod	mod	PROPN
ejpam-3852	85	16	2	2	NUM
ejpam-3852	85	17	m	m	NOUN
ejpam-3852	85	18	)	)	PUNCT
ejpam-3852	85	19	≡	≡	PROPN
ejpam-3852	85	20	y2	y2	PROPN
ejpam-3852	85	21	(	(	PUNCT
ejpam-3852	85	22	mod	mod	PROPN
ejpam-3852	85	23	2	2	NUM
ejpam-3852	85	24	m	m	NOUN
ejpam-3852	85	25	)	)	PUNCT
ejpam-3852	85	26	(	(	PUNCT
ejpam-3852	85	27	∵	∵	X
ejpam-3852	85	28	a+	a+	PRON
ejpam-3852	85	29	b	b	NOUN
ejpam-3852	85	30	is	be	AUX
ejpam-3852	85	31	even	even	ADV
ejpam-3852	85	32	)	)	PUNCT
ejpam-3852	85	33	,	,	PUNCT
ejpam-3852	85	34	y`+3	y`+3	NOUN
ejpam-3852	85	35	≡	≡	PROPN
ejpam-3852	85	36	ay−12	ay−12	PROPN
ejpam-3852	86	1	+	+	NUM
ejpam-3852	86	2	b(y1	b(y1	NOUN
ejpam-3852	86	3	+	+	PROPN
ejpam-3852	86	4	m	m	X
ejpam-3852	86	5	)	)	PUNCT
ejpam-3852	87	1	+	+	CCONJ
ejpam-3852	88	1	c	c	X
ejpam-3852	88	2	(	(	PUNCT
ejpam-3852	88	3	mod	mod	PROPN
ejpam-3852	88	4	2	2	NUM
ejpam-3852	88	5	m	m	NOUN
ejpam-3852	88	6	)	)	PUNCT
ejpam-3852	88	7	≡	≡	PROPN
ejpam-3852	88	8	y3	y3	NOUN
ejpam-3852	88	9	+	+	CCONJ
ejpam-3852	88	10	bm	bm	PROPN
ejpam-3852	88	11	(	(	PUNCT
ejpam-3852	88	12	mod	mod	PROPN
ejpam-3852	88	13	2	2	NUM
ejpam-3852	88	14	m	m	NOUN
ejpam-3852	88	15	)	)	PUNCT
ejpam-3852	88	16	≡	≡	PROPN
ejpam-3852	88	17	y3	y3	PROPN
ejpam-3852	89	1	+	+	PROPN
ejpam-3852	89	2	m	m	PROPN
ejpam-3852	89	3	(	(	PUNCT
ejpam-3852	89	4	mod	mod	PROPN
ejpam-3852	89	5	2	2	NUM
ejpam-3852	89	6	m	m	NOUN
ejpam-3852	89	7	)	)	PUNCT
ejpam-3852	89	8	(	(	PUNCT
ejpam-3852	89	9	∵	∵	NOUN
ejpam-3852	89	10	b	b	PROPN
ejpam-3852	89	11	is	be	AUX
ejpam-3852	89	12	odd	odd	ADJ
ejpam-3852	89	13	)	)	PUNCT
ejpam-3852	89	14	,	,	PUNCT
ejpam-3852	90	1	y`+4	y`+4	PROPN
ejpam-3852	90	2	≡	≡	PROPN
ejpam-3852	90	3	a(y−13	a(y−13	PROPN
ejpam-3852	90	4	+	+	NOUN
ejpam-3852	90	5	m	m	X
ejpam-3852	90	6	)	)	PUNCT
ejpam-3852	91	1	+	+	CCONJ
ejpam-3852	91	2	by2	by2	PROPN
ejpam-3852	91	3	+	+	NUM
ejpam-3852	91	4	c	c	PROPN
ejpam-3852	91	5	(	(	PUNCT
ejpam-3852	91	6	mod	mod	PROPN
ejpam-3852	91	7	2	2	NUM
ejpam-3852	91	8	m	m	NOUN
ejpam-3852	91	9	)	)	PUNCT
ejpam-3852	91	10	≡	≡	PROPN
ejpam-3852	91	11	y4	y4	PROPN
ejpam-3852	91	12	+	+	CCONJ
ejpam-3852	91	13	am	be	AUX
ejpam-3852	91	14	(	(	PUNCT
ejpam-3852	91	15	mod	mod	PROPN
ejpam-3852	91	16	2	2	NUM
ejpam-3852	91	17	m	m	NOUN
ejpam-3852	91	18	)	)	PUNCT
ejpam-3852	92	1	p.	p.	NOUN
ejpam-3852	92	2	stănică	stănică	NUM
ejpam-3852	92	3	et	et	PROPN
ejpam-3852	93	1	al	al	PROPN
ejpam-3852	93	2	.	.	PUNCT
ejpam-3852	93	3	/	/	SYM
ejpam-3852	93	4	eur	eur	PROPN
ejpam-3852	93	5	.	.	PUNCT
ejpam-3852	94	1	j.	j.	PROPN
ejpam-3852	94	2	pure	pure	PROPN
ejpam-3852	94	3	appl	appl	PROPN
ejpam-3852	94	4	.	.	PROPN
ejpam-3852	94	5	math	math	PROPN
ejpam-3852	94	6	,	,	PUNCT
ejpam-3852	94	7	14	14	NUM
ejpam-3852	94	8	(	(	PUNCT
ejpam-3852	94	9	1	1	NUM
ejpam-3852	94	10	)	)	PUNCT
ejpam-3852	94	11	(	(	PUNCT
ejpam-3852	94	12	2021	2021	NUM
ejpam-3852	94	13	)	)	PUNCT
ejpam-3852	94	14	,	,	PUNCT
ejpam-3852	94	15	1	1	NUM
ejpam-3852	94	16	-	-	SYM
ejpam-3852	94	17	18	18	NUM
ejpam-3852	94	18	4	4	NUM
ejpam-3852	94	19	≡	≡	PROPN
ejpam-3852	94	20	y4	y4	PROPN
ejpam-3852	95	1	+	+	PROPN
ejpam-3852	95	2	m	m	PROPN
ejpam-3852	95	3	(	(	PUNCT
ejpam-3852	95	4	mod	mod	PROPN
ejpam-3852	95	5	2	2	NUM
ejpam-3852	95	6	m	m	NOUN
ejpam-3852	95	7	)	)	PUNCT
ejpam-3852	95	8	(	(	PUNCT
ejpam-3852	95	9	∵	∵	DET
ejpam-3852	95	10	a	a	PRON
ejpam-3852	95	11	is	be	AUX
ejpam-3852	95	12	odd	odd	ADJ
ejpam-3852	95	13	)	)	PUNCT
ejpam-3852	96	1	,	,	PUNCT
ejpam-3852	96	2	y`+5	y`+5	NOUN
ejpam-3852	96	3	≡	≡	PROPN
ejpam-3852	96	4	a(y−14	a(y−14	PROPN
ejpam-3852	96	5	+	+	NOUN
ejpam-3852	96	6	m	m	X
ejpam-3852	96	7	)	)	PUNCT
ejpam-3852	97	1	+	+	CCONJ
ejpam-3852	97	2	b(y3	b(y3	VERB
ejpam-3852	97	3	+	+	NOUN
ejpam-3852	97	4	m	m	X
ejpam-3852	97	5	)	)	PUNCT
ejpam-3852	98	1	+	+	CCONJ
ejpam-3852	98	2	c	c	X
ejpam-3852	98	3	(	(	PUNCT
ejpam-3852	98	4	mod	mod	PROPN
ejpam-3852	98	5	2	2	NUM
ejpam-3852	98	6	m	m	NOUN
ejpam-3852	98	7	)	)	PUNCT
ejpam-3852	98	8	≡	≡	PROPN
ejpam-3852	98	9	y5	y5	PROPN
ejpam-3852	98	10	+	+	CCONJ
ejpam-3852	98	11	(	(	PUNCT
ejpam-3852	98	12	a+	a+	PUNCT
ejpam-3852	98	13	b)m	b)m	X
ejpam-3852	98	14	(	(	PUNCT
ejpam-3852	98	15	mod	mod	PROPN
ejpam-3852	98	16	2	2	NUM
ejpam-3852	98	17	m	m	NOUN
ejpam-3852	98	18	)	)	PUNCT
ejpam-3852	98	19	≡	≡	PROPN
ejpam-3852	98	20	y5	y5	PROPN
ejpam-3852	98	21	(	(	PUNCT
ejpam-3852	98	22	mod	mod	PROPN
ejpam-3852	98	23	2	2	NUM
ejpam-3852	98	24	m	m	NOUN
ejpam-3852	98	25	)	)	PUNCT
ejpam-3852	98	26	(	(	PUNCT
ejpam-3852	98	27	∵	∵	X
ejpam-3852	98	28	(	(	PUNCT
ejpam-3852	98	29	a+	a+	SYM
ejpam-3852	98	30	b	b	X
ejpam-3852	98	31	)	)	PUNCT
ejpam-3852	98	32	is	be	AUX
ejpam-3852	98	33	even	even	ADV
ejpam-3852	98	34	)	)	PUNCT
ejpam-3852	98	35	.	.	PUNCT
ejpam-3852	99	1	proceeding	proceed	VERB
ejpam-3852	99	2	similarly	similarly	ADV
ejpam-3852	99	3	,	,	PUNCT
ejpam-3852	99	4	we	we	PRON
ejpam-3852	99	5	have	have	VERB
ejpam-3852	99	6	,	,	PUNCT
ejpam-3852	99	7	y`+6	y`+6	NOUN
ejpam-3852	99	8	≡	≡	PROPN
ejpam-3852	99	9	y6	y6	PROPN
ejpam-3852	100	1	+	+	CCONJ
ejpam-3852	100	2	m	m	PROPN
ejpam-3852	100	3	(	(	PUNCT
ejpam-3852	100	4	mod	mod	PROPN
ejpam-3852	100	5	2	2	NUM
ejpam-3852	100	6	m	m	NOUN
ejpam-3852	100	7	)	)	PUNCT
ejpam-3852	100	8	,	,	PUNCT
ejpam-3852	100	9	y`+7	y`+7	NOUN
ejpam-3852	100	10	≡	≡	PROPN
ejpam-3852	100	11	y7	y7	PROPN
ejpam-3852	101	1	+	+	CCONJ
ejpam-3852	101	2	m	m	PRON
ejpam-3852	101	3	(	(	PUNCT
ejpam-3852	101	4	mod	mod	PROPN
ejpam-3852	101	5	2	2	NUM
ejpam-3852	101	6	m	m	NOUN
ejpam-3852	101	7	)	)	PUNCT
ejpam-3852	101	8	,	,	PUNCT
ejpam-3852	101	9	y`+8	y`+8	NOUN
ejpam-3852	101	10	≡	≡	PROPN
ejpam-3852	101	11	y8	y8	PROPN
ejpam-3852	101	12	(	(	PUNCT
ejpam-3852	101	13	mod	mod	PROPN
ejpam-3852	101	14	2	2	NUM
ejpam-3852	101	15	m	m	NOUN
ejpam-3852	101	16	)	)	PUNCT
ejpam-3852	101	17	,	,	PUNCT
ejpam-3852	101	18	and	and	CCONJ
ejpam-3852	101	19	so	so	ADV
ejpam-3852	101	20	on	on	ADV
ejpam-3852	101	21	.	.	PUNCT
ejpam-3852	102	1	now	now	ADV
ejpam-3852	102	2	,	,	PUNCT
ejpam-3852	102	3	computationally	computationally	ADV
ejpam-3852	102	4	we	we	PRON
ejpam-3852	102	5	can	can	AUX
ejpam-3852	102	6	check	check	VERB
ejpam-3852	102	7	that	that	PRON
ejpam-3852	102	8	for	for	ADP
ejpam-3852	102	9	m	m	PROPN
ejpam-3852	102	10	=	=	NOUN
ejpam-3852	102	11	16	16	NUM
ejpam-3852	102	12	,	,	PUNCT
ejpam-3852	102	13	`	`	PUNCT
ejpam-3852	102	14	can	can	AUX
ejpam-3852	102	15	be	be	AUX
ejpam-3852	102	16	1	1	NUM
ejpam-3852	102	17	,	,	PUNCT
ejpam-3852	102	18	3	3	NUM
ejpam-3852	102	19	,	,	PUNCT
ejpam-3852	102	20	6	6	NUM
ejpam-3852	102	21	,	,	PUNCT
ejpam-3852	102	22	12	12	NUM
ejpam-3852	102	23	.	.	PUNCT
ejpam-3852	103	1	inductively	inductively	ADV
ejpam-3852	103	2	,	,	PUNCT
ejpam-3852	103	3	it	it	PRON
ejpam-3852	103	4	follows	follow	VERB
ejpam-3852	103	5	that	that	SCONJ
ejpam-3852	103	6	if	if	SCONJ
ejpam-3852	103	7	{	{	PUNCT
ejpam-3852	103	8	yn	yn	PROPN
ejpam-3852	103	9	(	(	PUNCT
ejpam-3852	103	10	mod	mod	PROPN
ejpam-3852	103	11	m	m	PROPN
ejpam-3852	103	12	)	)	PUNCT
ejpam-3852	103	13	}	}	PUNCT
ejpam-3852	103	14	has	have	VERB
ejpam-3852	103	15	period	period	NOUN
ejpam-3852	103	16	1	1	NUM
ejpam-3852	103	17	then	then	ADV
ejpam-3852	103	18	{	{	PUNCT
ejpam-3852	103	19	yn	yn	PROPN
ejpam-3852	103	20	(	(	PUNCT
ejpam-3852	103	21	mod	mod	PROPN
ejpam-3852	103	22	2	2	NUM
ejpam-3852	103	23	m	m	NOUN
ejpam-3852	103	24	)	)	PUNCT
ejpam-3852	103	25	}	}	PUNCT
ejpam-3852	103	26	has	have	VERB
ejpam-3852	103	27	period	period	NOUN
ejpam-3852	103	28	3	3	NUM
ejpam-3852	103	29	and	and	CCONJ
ejpam-3852	103	30	if	if	SCONJ
ejpam-3852	103	31	{	{	PUNCT
ejpam-3852	103	32	yn	yn	PROPN
ejpam-3852	103	33	(	(	PUNCT
ejpam-3852	103	34	mod	mod	PROPN
ejpam-3852	103	35	m	m	PROPN
ejpam-3852	103	36	)	)	PUNCT
ejpam-3852	103	37	}	}	PUNCT
ejpam-3852	103	38	has	have	VERB
ejpam-3852	103	39	a	a	DET
ejpam-3852	103	40	period	period	NOUN
ejpam-3852	103	41	that	that	PRON
ejpam-3852	103	42	is	be	AUX
ejpam-3852	103	43	a	a	DET
ejpam-3852	103	44	multiple	multiple	NOUN
ejpam-3852	103	45	of	of	ADP
ejpam-3852	103	46	3	3	NUM
ejpam-3852	103	47	then	then	ADV
ejpam-3852	103	48	,	,	PUNCT
ejpam-3852	103	49	{	{	PUNCT
ejpam-3852	103	50	yn	yn	X
ejpam-3852	103	51	(	(	PUNCT
ejpam-3852	103	52	mod	mod	PROPN
ejpam-3852	103	53	2	2	NUM
ejpam-3852	103	54	m	m	NOUN
ejpam-3852	103	55	)	)	PUNCT
ejpam-3852	103	56	}	}	PUNCT
ejpam-3852	103	57	can	can	AUX
ejpam-3852	103	58	have	have	VERB
ejpam-3852	103	59	at	at	ADP
ejpam-3852	103	60	most	most	ADV
ejpam-3852	103	61	a	a	DET
ejpam-3852	103	62	double	double	ADJ
ejpam-3852	103	63	period	period	NOUN
ejpam-3852	103	64	.	.	PUNCT
ejpam-3852	104	1	thus	thus	ADV
ejpam-3852	104	2	,	,	PUNCT
ejpam-3852	104	3	in	in	ADP
ejpam-3852	104	4	this	this	DET
ejpam-3852	104	5	case	case	NOUN
ejpam-3852	104	6	,	,	PUNCT
ejpam-3852	104	7	{	{	PUNCT
ejpam-3852	104	8	yn	yn	X
ejpam-3852	104	9	(	(	PUNCT
ejpam-3852	104	10	mod	mod	PROPN
ejpam-3852	104	11	2	2	NUM
ejpam-3852	104	12	m	m	NOUN
ejpam-3852	104	13	)	)	PUNCT
ejpam-3852	104	14	}	}	PUNCT
ejpam-3852	104	15	can	can	AUX
ejpam-3852	104	16	have	have	VERB
ejpam-3852	104	17	the	the	DET
ejpam-3852	104	18	period	period	NOUN
ejpam-3852	104	19	at	at	ADP
ejpam-3852	104	20	most	most	ADJ
ejpam-3852	104	21	3	3	NUM
ejpam-3852	104	22	m	m	NOUN
ejpam-3852	104	23	2	2	NUM
ejpam-3852	104	24	<	<	SYM
ejpam-3852	104	25	2	2	NUM
ejpam-3852	104	26	m.	m.	NOUN
ejpam-3852	104	27	the	the	DET
ejpam-3852	104	28	other	other	ADJ
ejpam-3852	104	29	two	two	NUM
ejpam-3852	104	30	subcases	subcase	NOUN
ejpam-3852	104	31	follow	follow	VERB
ejpam-3852	104	32	similarly	similarly	ADV
ejpam-3852	104	33	and	and	CCONJ
ejpam-3852	104	34	it	it	PRON
ejpam-3852	104	35	can	can	AUX
ejpam-3852	104	36	be	be	AUX
ejpam-3852	104	37	shown	show	VERB
ejpam-3852	104	38	that	that	SCONJ
ejpam-3852	104	39	even	even	ADV
ejpam-3852	104	40	in	in	ADP
ejpam-3852	104	41	these	these	DET
ejpam-3852	104	42	subcases	subcase	NOUN
ejpam-3852	104	43	{	{	PUNCT
ejpam-3852	104	44	yn	yn	X
ejpam-3852	104	45	(	(	PUNCT
ejpam-3852	104	46	mod	mod	PROPN
ejpam-3852	104	47	2	2	NUM
ejpam-3852	104	48	m	m	NOUN
ejpam-3852	104	49	)	)	PUNCT
ejpam-3852	104	50	}	}	PUNCT
ejpam-3852	104	51	can	can	AUX
ejpam-3852	104	52	have	have	VERB
ejpam-3852	104	53	period	period	NOUN
ejpam-3852	104	54	at	at	ADP
ejpam-3852	104	55	most	most	ADJ
ejpam-3852	104	56	3	3	NUM
ejpam-3852	104	57	m	m	NOUN
ejpam-3852	104	58	2	2	NUM
ejpam-3852	104	59	<	<	SYM
ejpam-3852	104	60	2	2	NUM
ejpam-3852	104	61	m.	m.	NOUN
ejpam-3852	104	62	note	note	NOUN
ejpam-3852	104	63	that	that	SCONJ
ejpam-3852	104	64	,	,	PUNCT
ejpam-3852	104	65	in	in	ADP
ejpam-3852	104	66	this	this	DET
ejpam-3852	104	67	case	case	NOUN
ejpam-3852	104	68	,	,	PUNCT
ejpam-3852	104	69	the	the	DET
ejpam-3852	104	70	proof	proof	NOUN
ejpam-3852	104	71	implies	imply	VERB
ejpam-3852	104	72	that	that	SCONJ
ejpam-3852	104	73	{	{	PUNCT
ejpam-3852	104	74	yn	yn	PROPN
ejpam-3852	104	75	(	(	PUNCT
ejpam-3852	104	76	mod	mod	PROPN
ejpam-3852	104	77	m	m	PROPN
ejpam-3852	104	78	)	)	PUNCT
ejpam-3852	104	79	}	}	PUNCT
ejpam-3852	104	80	can	can	AUX
ejpam-3852	104	81	have	have	VERB
ejpam-3852	104	82	period	period	NOUN
ejpam-3852	104	83	at	at	ADP
ejpam-3852	104	84	most	most	ADJ
ejpam-3852	104	85	3	3	NUM
ejpam-3852	104	86	m	m	NOUN
ejpam-3852	104	87	4	4	NUM
ejpam-3852	104	88	,	,	PUNCT
ejpam-3852	104	89	for	for	ADP
ejpam-3852	104	90	all	all	DET
ejpam-3852	104	91	m	m	PROPN
ejpam-3852	104	92	≥	≥	NOUN
ejpam-3852	104	93	16	16	NUM
ejpam-3852	104	94	.	.	PUNCT
ejpam-3852	105	1	case	case	NOUN
ejpam-3852	105	2	2	2	NUM
ejpam-3852	105	3	.	.	X
ejpam-3852	106	1	a	a	PRON
ejpam-3852	106	2	is	be	AUX
ejpam-3852	106	3	odd	odd	ADJ
ejpam-3852	106	4	and	and	CCONJ
ejpam-3852	106	5	b	b	NOUN
ejpam-3852	106	6	and	and	CCONJ
ejpam-3852	106	7	c	c	PROPN
ejpam-3852	106	8	are	be	AUX
ejpam-3852	106	9	even	even	ADV
ejpam-3852	106	10	:	:	PUNCT
ejpam-3852	106	11	here	here	ADV
ejpam-3852	106	12	we	we	PRON
ejpam-3852	106	13	break	break	VERB
ejpam-3852	106	14	the	the	DET
ejpam-3852	106	15	case	case	NOUN
ejpam-3852	106	16	into	into	ADP
ejpam-3852	106	17	the	the	DET
ejpam-3852	106	18	same	same	ADJ
ejpam-3852	106	19	possible	possible	ADJ
ejpam-3852	106	20	subcases	subcase	NOUN
ejpam-3852	106	21	as	as	ADP
ejpam-3852	106	22	above	above	ADV
ejpam-3852	106	23	.	.	PUNCT
ejpam-3852	107	1	the	the	DET
ejpam-3852	107	2	first	first	ADJ
ejpam-3852	107	3	subcase	subcase	NOUN
ejpam-3852	107	4	is	be	AUX
ejpam-3852	107	5	immediate	immediate	ADJ
ejpam-3852	107	6	.	.	PUNCT
ejpam-3852	108	1	for	for	ADP
ejpam-3852	108	2	,	,	PUNCT
ejpam-3852	108	3	the	the	DET
ejpam-3852	108	4	second	second	ADJ
ejpam-3852	108	5	subcase	subcase	NOUN
ejpam-3852	108	6	,	,	PUNCT
ejpam-3852	108	7	following	follow	VERB
ejpam-3852	108	8	exactly	exactly	ADV
ejpam-3852	108	9	the	the	DET
ejpam-3852	108	10	same	same	ADJ
ejpam-3852	108	11	procedure	procedure	NOUN
ejpam-3852	108	12	as	as	ADP
ejpam-3852	108	13	above	above	ADV
ejpam-3852	108	14	,	,	PUNCT
ejpam-3852	108	15	we	we	PRON
ejpam-3852	108	16	obtain	obtain	VERB
ejpam-3852	108	17	y`+2	y`+2	NOUN
ejpam-3852	109	1	≡	≡	PROPN
ejpam-3852	109	2	y2	y2	PROPN
ejpam-3852	110	1	+	+	NOUN
ejpam-3852	110	2	m	m	PROPN
ejpam-3852	110	3	(	(	PUNCT
ejpam-3852	110	4	mod	mod	PROPN
ejpam-3852	110	5	2	2	NUM
ejpam-3852	110	6	m	m	NOUN
ejpam-3852	110	7	)	)	PUNCT
ejpam-3852	110	8	,	,	PUNCT
ejpam-3852	110	9	y`+3	y`+3	NOUN
ejpam-3852	110	10	≡	≡	PROPN
ejpam-3852	110	11	y3	y3	PROPN
ejpam-3852	111	1	+	+	PROPN
ejpam-3852	111	2	m	m	PROPN
ejpam-3852	111	3	(	(	PUNCT
ejpam-3852	111	4	mod	mod	PROPN
ejpam-3852	111	5	2	2	NUM
ejpam-3852	111	6	m	m	NOUN
ejpam-3852	111	7	)	)	PUNCT
ejpam-3852	111	8	,	,	PUNCT
ejpam-3852	111	9	y`+4	y`+4	PROPN
ejpam-3852	111	10	≡	≡	PROPN
ejpam-3852	111	11	y4	y4	PROPN
ejpam-3852	112	1	+	+	PROPN
ejpam-3852	112	2	m	m	PROPN
ejpam-3852	112	3	(	(	PUNCT
ejpam-3852	112	4	mod	mod	PROPN
ejpam-3852	112	5	2	2	NUM
ejpam-3852	112	6	m	m	NOUN
ejpam-3852	112	7	)	)	PUNCT
ejpam-3852	112	8	,	,	PUNCT
ejpam-3852	112	9	and	and	CCONJ
ejpam-3852	112	10	so	so	ADV
ejpam-3852	112	11	on	on	ADV
ejpam-3852	112	12	.	.	PUNCT
ejpam-3852	113	1	now	now	ADV
ejpam-3852	113	2	,	,	PUNCT
ejpam-3852	113	3	it	it	PRON
ejpam-3852	113	4	can	can	AUX
ejpam-3852	113	5	be	be	AUX
ejpam-3852	113	6	checked	check	VERB
ejpam-3852	113	7	that	that	PRON
ejpam-3852	113	8	for	for	ADP
ejpam-3852	113	9	m	m	PROPN
ejpam-3852	113	10	=	=	NOUN
ejpam-3852	113	11	16	16	NUM
ejpam-3852	113	12	the	the	DET
ejpam-3852	113	13	possible	possible	ADJ
ejpam-3852	113	14	periods	period	NOUN
ejpam-3852	113	15	are	be	AUX
ejpam-3852	113	16	1	1	NUM
ejpam-3852	113	17	,	,	PUNCT
ejpam-3852	113	18	2	2	NUM
ejpam-3852	113	19	,	,	PUNCT
ejpam-3852	113	20	4	4	NUM
ejpam-3852	113	21	and	and	CCONJ
ejpam-3852	113	22	8	8	NUM
ejpam-3852	113	23	.	.	PUNCT
ejpam-3852	114	1	so	so	ADV
ejpam-3852	114	2	,	,	PUNCT
ejpam-3852	114	3	inductively	inductively	ADV
ejpam-3852	114	4	,	,	PUNCT
ejpam-3852	114	5	it	it	PRON
ejpam-3852	114	6	follows	follow	VERB
ejpam-3852	114	7	that	that	SCONJ
ejpam-3852	114	8	,	,	PUNCT
ejpam-3852	114	9	the	the	DET
ejpam-3852	114	10	period	period	NOUN
ejpam-3852	114	11	of	of	ADP
ejpam-3852	114	12	{	{	PUNCT
ejpam-3852	114	13	yn	yn	PROPN
ejpam-3852	114	14	(	(	PUNCT
ejpam-3852	114	15	mod	mod	PROPN
ejpam-3852	114	16	2	2	NUM
ejpam-3852	114	17	m	m	NOUN
ejpam-3852	114	18	)	)	PUNCT
ejpam-3852	114	19	}	}	PUNCT
ejpam-3852	114	20	can	can	AUX
ejpam-3852	114	21	be	be	AUX
ejpam-3852	114	22	at	at	ADP
ejpam-3852	114	23	most	most	ADJ
ejpam-3852	114	24	m.	m.	NOUN
ejpam-3852	114	25	the	the	DET
ejpam-3852	114	26	other	other	ADJ
ejpam-3852	114	27	cases	case	NOUN
ejpam-3852	114	28	can	can	AUX
ejpam-3852	114	29	be	be	AUX
ejpam-3852	114	30	similarly	similarly	ADV
ejpam-3852	114	31	dealt	deal	VERB
ejpam-3852	114	32	with	with	ADP
ejpam-3852	114	33	.	.	PUNCT
ejpam-3852	115	1	note	note	VERB
ejpam-3852	115	2	that	that	SCONJ
ejpam-3852	115	3	,	,	PUNCT
ejpam-3852	115	4	in	in	ADP
ejpam-3852	115	5	this	this	DET
ejpam-3852	115	6	case	case	NOUN
ejpam-3852	115	7	,	,	PUNCT
ejpam-3852	115	8	the	the	DET
ejpam-3852	115	9	proof	proof	NOUN
ejpam-3852	115	10	implies	imply	VERB
ejpam-3852	115	11	that	that	SCONJ
ejpam-3852	115	12	{	{	PUNCT
ejpam-3852	115	13	yn	yn	PROPN
ejpam-3852	115	14	(	(	PUNCT
ejpam-3852	115	15	mod	mod	PROPN
ejpam-3852	115	16	m	m	PROPN
ejpam-3852	115	17	)	)	PUNCT
ejpam-3852	115	18	}	}	PUNCT
ejpam-3852	115	19	can	can	AUX
ejpam-3852	115	20	have	have	VERB
ejpam-3852	115	21	period	period	NOUN
ejpam-3852	115	22	at	at	ADP
ejpam-3852	115	23	most	most	ADJ
ejpam-3852	115	24	m	m	VERB
ejpam-3852	115	25	2	2	NUM
ejpam-3852	115	26	,	,	PUNCT
ejpam-3852	115	27	for	for	ADP
ejpam-3852	115	28	all	all	DET
ejpam-3852	115	29	m	m	PROPN
ejpam-3852	115	30	≥	≥	NOUN
ejpam-3852	115	31	16	16	NUM
ejpam-3852	115	32	.	.	PUNCT
ejpam-3852	116	1	case	case	NOUN
ejpam-3852	116	2	3	3	NUM
ejpam-3852	116	3	.	.	X
ejpam-3852	116	4	b	b	NOUN
ejpam-3852	116	5	is	be	AUX
ejpam-3852	116	6	odd	odd	ADJ
ejpam-3852	116	7	and	and	CCONJ
ejpam-3852	116	8	a	a	PRON
ejpam-3852	116	9	and	and	CCONJ
ejpam-3852	116	10	c	c	NOUN
ejpam-3852	116	11	are	be	AUX
ejpam-3852	116	12	even	even	ADV
ejpam-3852	116	13	:	:	PUNCT
ejpam-3852	116	14	this	this	DET
ejpam-3852	116	15	case	case	NOUN
ejpam-3852	116	16	follows	follow	VERB
ejpam-3852	116	17	along	along	ADP
ejpam-3852	116	18	the	the	DET
ejpam-3852	116	19	same	same	ADJ
ejpam-3852	116	20	lines	line	NOUN
ejpam-3852	116	21	as	as	ADP
ejpam-3852	116	22	the	the	DET
ejpam-3852	116	23	previous	previous	ADJ
ejpam-3852	116	24	case	case	NOUN
ejpam-3852	116	25	.	.	PUNCT
ejpam-3852	117	1	in	in	ADP
ejpam-3852	117	2	this	this	DET
ejpam-3852	117	3	case	case	NOUN
ejpam-3852	117	4	,	,	PUNCT
ejpam-3852	117	5	one	one	PRON
ejpam-3852	117	6	can	can	AUX
ejpam-3852	117	7	computationally	computationally	ADV
ejpam-3852	117	8	check	check	VERB
ejpam-3852	117	9	that	that	SCONJ
ejpam-3852	117	10	,	,	PUNCT
ejpam-3852	117	11	for	for	ADP
ejpam-3852	117	12	m	m	PROPN
ejpam-3852	117	13	=	=	SYM
ejpam-3852	117	14	16	16	NUM
ejpam-3852	117	15	,	,	PUNCT
ejpam-3852	117	16	the	the	DET
ejpam-3852	117	17	possible	possible	ADJ
ejpam-3852	117	18	periods	period	NOUN
ejpam-3852	117	19	are	be	AUX
ejpam-3852	117	20	1	1	NUM
ejpam-3852	117	21	,	,	PUNCT
ejpam-3852	117	22	2	2	NUM
ejpam-3852	117	23	,	,	PUNCT
ejpam-3852	117	24	4	4	NUM
ejpam-3852	117	25	,	,	PUNCT
ejpam-3852	117	26	8	8	NUM
ejpam-3852	117	27	and	and	CCONJ
ejpam-3852	117	28	16	16	NUM
ejpam-3852	117	29	.	.	PUNCT
ejpam-3852	118	1	so	so	ADV
ejpam-3852	118	2	,	,	PUNCT
ejpam-3852	118	3	the	the	DET
ejpam-3852	118	4	period	period	NOUN
ejpam-3852	118	5	of	of	ADP
ejpam-3852	118	6	{	{	PUNCT
ejpam-3852	118	7	yn	yn	PROPN
ejpam-3852	118	8	(	(	PUNCT
ejpam-3852	118	9	mod	mod	PROPN
ejpam-3852	118	10	2	2	NUM
ejpam-3852	118	11	m	m	NOUN
ejpam-3852	118	12	)	)	PUNCT
ejpam-3852	118	13	}	}	PUNCT
ejpam-3852	118	14	can	can	AUX
ejpam-3852	118	15	be	be	AUX
ejpam-3852	118	16	at	at	ADP
ejpam-3852	118	17	most	most	ADV
ejpam-3852	118	18	2	2	NUM
ejpam-3852	118	19	m.	m.	NOUN
ejpam-3852	118	20	therefore	therefore	ADV
ejpam-3852	118	21	,	,	PUNCT
ejpam-3852	118	22	in	in	ADP
ejpam-3852	118	23	this	this	DET
ejpam-3852	118	24	case	case	NOUN
ejpam-3852	118	25	,	,	PUNCT
ejpam-3852	118	26	the	the	DET
ejpam-3852	118	27	proof	proof	NOUN
ejpam-3852	118	28	implies	imply	VERB
ejpam-3852	118	29	that	that	SCONJ
ejpam-3852	118	30	{	{	PUNCT
ejpam-3852	118	31	yn	yn	PROPN
ejpam-3852	118	32	(	(	PUNCT
ejpam-3852	118	33	mod	mod	PROPN
ejpam-3852	118	34	m	m	PROPN
ejpam-3852	118	35	)	)	PUNCT
ejpam-3852	118	36	}	}	PUNCT
ejpam-3852	118	37	can	can	AUX
ejpam-3852	118	38	have	have	VERB
ejpam-3852	118	39	period	period	NOUN
ejpam-3852	118	40	at	at	ADP
ejpam-3852	118	41	most	most	ADJ
ejpam-3852	118	42	m	m	ADP
ejpam-3852	118	43	,	,	PUNCT
ejpam-3852	118	44	for	for	ADP
ejpam-3852	118	45	all	all	DET
ejpam-3852	118	46	m	m	PROPN
ejpam-3852	118	47	≥	≥	NOUN
ejpam-3852	118	48	16	16	NUM
ejpam-3852	118	49	.	.	PUNCT
ejpam-3852	119	1	case	case	NOUN
ejpam-3852	119	2	4	4	NUM
ejpam-3852	119	3	.	.	X
ejpam-3852	120	1	c	c	PROPN
ejpam-3852	120	2	is	be	AUX
ejpam-3852	120	3	odd	odd	ADJ
ejpam-3852	120	4	and	and	CCONJ
ejpam-3852	120	5	a	a	PRON
ejpam-3852	120	6	and	and	CCONJ
ejpam-3852	120	7	b	b	NOUN
ejpam-3852	120	8	are	be	AUX
ejpam-3852	120	9	even	even	ADV
ejpam-3852	120	10	:	:	PUNCT
ejpam-3852	120	11	here	here	ADV
ejpam-3852	120	12	we	we	PRON
ejpam-3852	120	13	break	break	VERB
ejpam-3852	120	14	the	the	DET
ejpam-3852	120	15	case	case	NOUN
ejpam-3852	120	16	into	into	ADP
ejpam-3852	120	17	the	the	DET
ejpam-3852	120	18	same	same	ADJ
ejpam-3852	120	19	possible	possible	ADJ
ejpam-3852	120	20	subcases	subcase	NOUN
ejpam-3852	120	21	as	as	ADP
ejpam-3852	120	22	in	in	ADP
ejpam-3852	120	23	case	case	NOUN
ejpam-3852	120	24	1	1	NUM
ejpam-3852	120	25	.	.	PUNCT
ejpam-3852	121	1	the	the	DET
ejpam-3852	121	2	first	first	ADJ
ejpam-3852	121	3	subcase	subcase	NOUN
ejpam-3852	121	4	follows	follow	VERB
ejpam-3852	121	5	immediately	immediately	ADV
ejpam-3852	121	6	.	.	PUNCT
ejpam-3852	122	1	for	for	ADP
ejpam-3852	122	2	,	,	PUNCT
ejpam-3852	122	3	the	the	DET
ejpam-3852	122	4	other	other	ADJ
ejpam-3852	122	5	subcases	subcase	NOUN
ejpam-3852	122	6	we	we	PRON
ejpam-3852	122	7	can	can	AUX
ejpam-3852	122	8	easily	easily	ADV
ejpam-3852	122	9	check	check	VERB
ejpam-3852	123	1	that	that	DET
ejpam-3852	123	2	y`+2	y`+2	ADJ
ejpam-3852	123	3	≡	≡	PROPN
ejpam-3852	123	4	y2	y2	PROPN
ejpam-3852	123	5	(	(	PUNCT
ejpam-3852	123	6	mod	mod	PROPN
ejpam-3852	123	7	2	2	NUM
ejpam-3852	123	8	m	m	NOUN
ejpam-3852	123	9	)	)	PUNCT
ejpam-3852	123	10	,	,	PUNCT
ejpam-3852	123	11	y`+3	y`+3	NOUN
ejpam-3852	123	12	≡	≡	PROPN
ejpam-3852	123	13	y3	y3	PROPN
ejpam-3852	123	14	(	(	PUNCT
ejpam-3852	123	15	mod	mod	PROPN
ejpam-3852	123	16	2	2	NUM
ejpam-3852	123	17	m	m	NOUN
ejpam-3852	123	18	)	)	PUNCT
ejpam-3852	123	19	,	,	PUNCT
ejpam-3852	123	20	y`+4	y`+4	PROPN
ejpam-3852	123	21	≡	≡	PROPN
ejpam-3852	123	22	y4	y4	PROPN
ejpam-3852	123	23	(	(	PUNCT
ejpam-3852	123	24	mod	mod	PROPN
ejpam-3852	123	25	2	2	NUM
ejpam-3852	123	26	m	m	NOUN
ejpam-3852	123	27	)	)	PUNCT
ejpam-3852	123	28	,	,	PUNCT
ejpam-3852	123	29	and	and	CCONJ
ejpam-3852	123	30	so	so	ADV
ejpam-3852	123	31	on	on	ADV
ejpam-3852	123	32	.	.	PUNCT
ejpam-3852	124	1	now	now	ADV
ejpam-3852	124	2	,	,	PUNCT
ejpam-3852	124	3	in	in	ADP
ejpam-3852	124	4	this	this	DET
ejpam-3852	124	5	case	case	NOUN
ejpam-3852	124	6	,	,	PUNCT
ejpam-3852	124	7	one	one	PRON
ejpam-3852	124	8	can	can	AUX
ejpam-3852	124	9	observe	observe	VERB
ejpam-3852	124	10	that	that	PRON
ejpam-3852	124	11	for	for	ADP
ejpam-3852	124	12	m	m	PROPN
ejpam-3852	124	13	=	=	NOUN
ejpam-3852	124	14	16	16	NUM
ejpam-3852	124	15	the	the	DET
ejpam-3852	124	16	period	period	NOUN
ejpam-3852	124	17	is	be	AUX
ejpam-3852	124	18	(	(	PUNCT
ejpam-3852	124	19	ultimately	ultimately	ADV
ejpam-3852	124	20	)	)	PUNCT
ejpam-3852	124	21	1	1	X
ejpam-3852	124	22	.	.	PUNCT
ejpam-3852	125	1	so	so	ADV
ejpam-3852	125	2	,	,	PUNCT
ejpam-3852	125	3	in	in	ADP
ejpam-3852	125	4	this	this	DET
ejpam-3852	125	5	case	case	NOUN
ejpam-3852	125	6	,	,	PUNCT
ejpam-3852	125	7	the	the	DET
ejpam-3852	125	8	(	(	PUNCT
ejpam-3852	125	9	ultimate	ultimate	ADJ
ejpam-3852	125	10	)	)	PUNCT
ejpam-3852	125	11	period	period	NOUN
ejpam-3852	125	12	of	of	ADP
ejpam-3852	125	13	{	{	PUNCT
ejpam-3852	125	14	yn	yn	PROPN
ejpam-3852	125	15	(	(	PUNCT
ejpam-3852	125	16	mod	mod	PROPN
ejpam-3852	125	17	2	2	NUM
ejpam-3852	125	18	m	m	NOUN
ejpam-3852	125	19	)	)	PUNCT
ejpam-3852	125	20	}	}	PUNCT
ejpam-3852	125	21	is	be	AUX
ejpam-3852	125	22	again	again	ADV
ejpam-3852	125	23	1	1	NUM
ejpam-3852	125	24	≤	≤	NUM
ejpam-3852	125	25	2	2	NUM
ejpam-3852	125	26	m.	m.	NOUN
ejpam-3852	125	27	note	note	NOUN
ejpam-3852	125	28	that	that	SCONJ
ejpam-3852	125	29	,	,	PUNCT
ejpam-3852	125	30	in	in	ADP
ejpam-3852	125	31	this	this	DET
ejpam-3852	125	32	case	case	NOUN
ejpam-3852	125	33	,	,	PUNCT
ejpam-3852	125	34	the	the	DET
ejpam-3852	125	35	proof	proof	NOUN
ejpam-3852	125	36	implies	imply	VERB
ejpam-3852	125	37	that	that	SCONJ
ejpam-3852	125	38	{	{	PUNCT
ejpam-3852	125	39	yn	yn	PROPN
ejpam-3852	125	40	(	(	PUNCT
ejpam-3852	125	41	mod	mod	PROPN
ejpam-3852	125	42	m	m	PROPN
ejpam-3852	125	43	)	)	PUNCT
ejpam-3852	125	44	}	}	PUNCT
ejpam-3852	125	45	has	have	VERB
ejpam-3852	125	46	period	period	NOUN
ejpam-3852	125	47	1	1	NUM
ejpam-3852	125	48	,	,	PUNCT
ejpam-3852	125	49	for	for	ADP
ejpam-3852	125	50	all	all	DET
ejpam-3852	125	51	m	m	PROPN
ejpam-3852	125	52	≥	≥	NOUN
ejpam-3852	125	53	16	16	NUM
ejpam-3852	125	54	.	.	PUNCT
ejpam-3852	125	55	example	example	NOUN
ejpam-3852	126	1	1	1	NUM
ejpam-3852	126	2	.	.	X
ejpam-3852	126	3	consider	consider	VERB
ejpam-3852	126	4	the	the	DET
ejpam-3852	126	5	first	first	ADJ
ejpam-3852	126	6	case	case	NOUN
ejpam-3852	126	7	,	,	PUNCT
ejpam-3852	126	8	i.e.	i.e.	X
ejpam-3852	126	9	,	,	PUNCT
ejpam-3852	126	10	a	a	DET
ejpam-3852	126	11	,	,	PUNCT
ejpam-3852	126	12	b	b	NOUN
ejpam-3852	126	13	and	and	CCONJ
ejpam-3852	126	14	c	c	PROPN
ejpam-3852	126	15	are	be	AUX
ejpam-3852	126	16	all	all	PRON
ejpam-3852	126	17	odd	odd	ADJ
ejpam-3852	126	18	.	.	PUNCT
ejpam-3852	127	1	let	let	VERB
ejpam-3852	127	2	m	m	VERB
ejpam-3852	127	3	=	=	NOUN
ejpam-3852	127	4	16	16	NUM
ejpam-3852	127	5	,	,	PUNCT
ejpam-3852	127	6	and	and	CCONJ
ejpam-3852	127	7	let	let	VERB
ejpam-3852	127	8	the	the	DET
ejpam-3852	127	9	period	period	NOUN
ejpam-3852	127	10	of	of	ADP
ejpam-3852	127	11	the	the	DET
ejpam-3852	127	12	sequence	sequence	NOUN
ejpam-3852	127	13	be	be	AUX
ejpam-3852	127	14	6	6	NUM
ejpam-3852	127	15	.	.	PUNCT
ejpam-3852	128	1	then	then	ADV
ejpam-3852	128	2	{	{	PUNCT
ejpam-3852	128	3	y0	y0	NOUN
ejpam-3852	128	4	,	,	PUNCT
ejpam-3852	128	5	y1	y1	NOUN
ejpam-3852	128	6	,	,	PUNCT
ejpam-3852	128	7	y2	y2	PROPN
ejpam-3852	128	8	,	,	PUNCT
ejpam-3852	128	9	y3	y3	PROPN
ejpam-3852	128	10	,	,	PUNCT
ejpam-3852	128	11	y4	y4	PROPN
ejpam-3852	128	12	,	,	PUNCT
ejpam-3852	128	13	y5	y5	PROPN
ejpam-3852	128	14	}	}	PUNCT
ejpam-3852	128	15	is	be	AUX
ejpam-3852	128	16	the	the	DET
ejpam-3852	128	17	core	core	NOUN
ejpam-3852	128	18	of	of	ADP
ejpam-3852	128	19	the	the	DET
ejpam-3852	128	20	sequence	sequence	NOUN
ejpam-3852	128	21	modulo	modulo	VERB
ejpam-3852	128	22	16	16	NUM
ejpam-3852	128	23	.	.	PUNCT
ejpam-3852	129	1	consider	consider	VERB
ejpam-3852	129	2	now	now	ADV
ejpam-3852	129	3	the	the	DET
ejpam-3852	129	4	same	same	ADJ
ejpam-3852	129	5	sequence	sequence	NOUN
ejpam-3852	129	6	modulo	modulo	VERB
ejpam-3852	129	7	32	32	NUM
ejpam-3852	129	8	.	.	PUNCT
ejpam-3852	130	1	we	we	PRON
ejpam-3852	130	2	show	show	VERB
ejpam-3852	130	3	that	that	SCONJ
ejpam-3852	130	4	the	the	DET
ejpam-3852	130	5	period	period	NOUN
ejpam-3852	130	6	can	can	AUX
ejpam-3852	130	7	be	be	AUX
ejpam-3852	130	8	at	at	ADP
ejpam-3852	130	9	most	most	ADV
ejpam-3852	130	10	12	12	NUM
ejpam-3852	130	11	modulo	modulo	NOUN
ejpam-3852	130	12	32	32	NUM
ejpam-3852	130	13	.	.	PUNCT
ejpam-3852	131	1	the	the	DET
ejpam-3852	131	2	first	first	ADJ
ejpam-3852	131	3	subcase	subcase	NOUN
ejpam-3852	131	4	would	would	AUX
ejpam-3852	131	5	give	give	VERB
ejpam-3852	131	6	a	a	DET
ejpam-3852	131	7	period	period	NOUN
ejpam-3852	131	8	of	of	ADP
ejpam-3852	131	9	6	6	NUM
ejpam-3852	131	10	.	.	PUNCT
ejpam-3852	132	1	for	for	ADP
ejpam-3852	132	2	the	the	DET
ejpam-3852	132	3	second	second	ADJ
ejpam-3852	132	4	subcase	subcase	NOUN
ejpam-3852	132	5	,	,	PUNCT
ejpam-3852	132	6	i.e.	i.e.	X
ejpam-3852	132	7	,	,	PUNCT
ejpam-3852	132	8	y6	y6	ADJ
ejpam-3852	132	9	≡	≡	PROPN
ejpam-3852	132	10	y0	y0	PROPN
ejpam-3852	132	11	+	+	CCONJ
ejpam-3852	132	12	16	16	NUM
ejpam-3852	132	13	and	and	CCONJ
ejpam-3852	132	14	y7	y7	ADJ
ejpam-3852	132	15	≡	≡	PROPN
ejpam-3852	132	16	y1	y1	PROPN
ejpam-3852	133	1	+	+	CCONJ
ejpam-3852	133	2	16	16	NUM
ejpam-3852	133	3	(	(	PUNCT
ejpam-3852	133	4	all	all	DET
ejpam-3852	133	5	congruences	congruence	NOUN
ejpam-3852	133	6	are	be	AUX
ejpam-3852	133	7	modulo	modulo	ADJ
ejpam-3852	133	8	32	32	NUM
ejpam-3852	133	9	in	in	ADP
ejpam-3852	133	10	this	this	DET
ejpam-3852	133	11	example	example	NOUN
ejpam-3852	133	12	)	)	PUNCT
ejpam-3852	133	13	,	,	PUNCT
ejpam-3852	133	14	we	we	PRON
ejpam-3852	133	15	can	can	AUX
ejpam-3852	133	16	p.	p.	VERB
ejpam-3852	133	17	stănică	stănică	PROPN
ejpam-3852	133	18	et	et	PROPN
ejpam-3852	133	19	al	al	PROPN
ejpam-3852	133	20	.	.	PUNCT
ejpam-3852	133	21	/	/	SYM
ejpam-3852	133	22	eur	eur	PROPN
ejpam-3852	133	23	.	.	PUNCT
ejpam-3852	134	1	j.	j.	PROPN
ejpam-3852	134	2	pure	pure	PROPN
ejpam-3852	134	3	appl	appl	PROPN
ejpam-3852	134	4	.	.	PROPN
ejpam-3852	134	5	math	math	PROPN
ejpam-3852	134	6	,	,	PUNCT
ejpam-3852	134	7	14	14	NUM
ejpam-3852	134	8	(	(	PUNCT
ejpam-3852	134	9	1	1	NUM
ejpam-3852	134	10	)	)	PUNCT
ejpam-3852	134	11	(	(	PUNCT
ejpam-3852	134	12	2021	2021	NUM
ejpam-3852	134	13	)	)	PUNCT
ejpam-3852	134	14	,	,	PUNCT
ejpam-3852	134	15	1	1	NUM
ejpam-3852	134	16	-	-	SYM
ejpam-3852	134	17	18	18	NUM
ejpam-3852	134	18	5	5	NUM
ejpam-3852	134	19	easily	easily	ADV
ejpam-3852	134	20	calculate	calculate	VERB
ejpam-3852	134	21	that	that	SCONJ
ejpam-3852	134	22	y8	y8	PROPN
ejpam-3852	134	23	≡	≡	PROPN
ejpam-3852	134	24	y2	y2	PROPN
ejpam-3852	134	25	,	,	PUNCT
ejpam-3852	134	26	y9	y9	PROPN
ejpam-3852	134	27	≡	≡	PROPN
ejpam-3852	134	28	y3	y3	NOUN
ejpam-3852	134	29	+	+	CCONJ
ejpam-3852	134	30	16	16	NUM
ejpam-3852	134	31	,	,	PUNCT
ejpam-3852	134	32	y10	y10	NOUN
ejpam-3852	134	33	≡	≡	PROPN
ejpam-3852	134	34	y4	y4	PROPN
ejpam-3852	135	1	+	+	CCONJ
ejpam-3852	135	2	16	16	NUM
ejpam-3852	135	3	,	,	PUNCT
ejpam-3852	135	4	y11	y11	NUM
ejpam-3852	135	5	≡	≡	PROPN
ejpam-3852	135	6	y5	y5	PROPN
ejpam-3852	135	7	,	,	PUNCT
ejpam-3852	135	8	y12	y12	PROPN
ejpam-3852	135	9	≡	≡	PROPN
ejpam-3852	135	10	y6	y6	PROPN
ejpam-3852	136	1	+	+	CCONJ
ejpam-3852	136	2	16	16	NUM
ejpam-3852	136	3	≡	≡	PROPN
ejpam-3852	136	4	y0	y0	PROPN
ejpam-3852	136	5	and	and	CCONJ
ejpam-3852	136	6	y13	y13	PROPN
ejpam-3852	136	7	≡	≡	PROPN
ejpam-3852	136	8	y7	y7	PROPN
ejpam-3852	137	1	+	+	CCONJ
ejpam-3852	137	2	16	16	NUM
ejpam-3852	137	3	≡	≡	PROPN
ejpam-3852	137	4	y1	y1	PROPN
ejpam-3852	137	5	.	.	PUNCT
ejpam-3852	138	1	and	and	CCONJ
ejpam-3852	138	2	so	so	ADV
ejpam-3852	138	3	,	,	PUNCT
ejpam-3852	138	4	{	{	PUNCT
ejpam-3852	138	5	y0	y0	NOUN
ejpam-3852	138	6	,	,	PUNCT
ejpam-3852	138	7	y1	y1	NOUN
ejpam-3852	138	8	,	,	PUNCT
ejpam-3852	138	9	.	.	PUNCT
ejpam-3852	138	10	.	.	PUNCT
ejpam-3852	138	11	.	.	PUNCT
ejpam-3852	139	1	,	,	PUNCT
ejpam-3852	139	2	y11	y11	NOUN
ejpam-3852	139	3	}	}	PUNCT
ejpam-3852	139	4	is	be	AUX
ejpam-3852	139	5	the	the	DET
ejpam-3852	139	6	core	core	NOUN
ejpam-3852	139	7	of	of	ADP
ejpam-3852	139	8	the	the	DET
ejpam-3852	139	9	sequence	sequence	NOUN
ejpam-3852	139	10	and	and	CCONJ
ejpam-3852	139	11	the	the	DET
ejpam-3852	139	12	period	period	NOUN
ejpam-3852	139	13	is	be	AUX
ejpam-3852	139	14	12	12	NUM
ejpam-3852	139	15	.	.	PUNCT
ejpam-3852	140	1	the	the	DET
ejpam-3852	140	2	other	other	ADJ
ejpam-3852	140	3	two	two	NUM
ejpam-3852	140	4	subcases	subcase	NOUN
ejpam-3852	140	5	are	be	AUX
ejpam-3852	140	6	similar	similar	ADJ
ejpam-3852	140	7	.	.	PUNCT
ejpam-3852	141	1	remark	remark	PROPN
ejpam-3852	141	2	1	1	NUM
ejpam-3852	141	3	.	.	PUNCT
ejpam-3852	141	4	note	note	VERB
ejpam-3852	141	5	that	that	SCONJ
ejpam-3852	141	6	,	,	PUNCT
ejpam-3852	141	7	from	from	ADP
ejpam-3852	141	8	the	the	DET
ejpam-3852	141	9	proof	proof	NOUN
ejpam-3852	141	10	,	,	PUNCT
ejpam-3852	141	11	one	one	PRON
ejpam-3852	141	12	can	can	AUX
ejpam-3852	141	13	actually	actually	ADV
ejpam-3852	141	14	infer	infer	VERB
ejpam-3852	141	15	,	,	PUNCT
ejpam-3852	141	16	for	for	ADP
ejpam-3852	141	17	m	m	PROPN
ejpam-3852	141	18	≥	≥	NOUN
ejpam-3852	141	19	16	16	NUM
ejpam-3852	141	20	,	,	PUNCT
ejpam-3852	141	21	that	that	SCONJ
ejpam-3852	141	22	the	the	DET
ejpam-3852	141	23	hicg	hicg	ADJ
ejpam-3852	141	24	sequence	sequence	NOUN
ejpam-3852	141	25	{	{	PUNCT
ejpam-3852	141	26	yn	yn	PROPN
ejpam-3852	141	27	(	(	PUNCT
ejpam-3852	141	28	mod	mod	PROPN
ejpam-3852	141	29	m	m	PROPN
ejpam-3852	141	30	)	)	PUNCT
ejpam-3852	141	31	}	}	PUNCT
ejpam-3852	141	32	has	have	VERB
ejpam-3852	141	33	an	an	DET
ejpam-3852	141	34	(	(	PUNCT
ejpam-3852	141	35	ultimate	ultimate	ADJ
ejpam-3852	141	36	)	)	PUNCT
ejpam-3852	141	37	period	period	NOUN
ejpam-3852	141	38	less	less	ADJ
ejpam-3852	141	39	than	than	ADP
ejpam-3852	141	40	or	or	CCONJ
ejpam-3852	141	41	equal	equal	ADJ
ejpam-3852	141	42	to	to	ADP
ejpam-3852	141	43	3	3	NUM
ejpam-3852	141	44	m	m	NOUN
ejpam-3852	141	45	4	4	NUM
ejpam-3852	141	46	,	,	PUNCT
ejpam-3852	141	47	if	if	SCONJ
ejpam-3852	141	48	a	a	PRON
ejpam-3852	141	49	,	,	PUNCT
ejpam-3852	141	50	b	b	NOUN
ejpam-3852	141	51	and	and	CCONJ
ejpam-3852	141	52	c	c	PROPN
ejpam-3852	141	53	are	be	AUX
ejpam-3852	141	54	odd	odd	ADJ
ejpam-3852	141	55	;	;	PUNCT
ejpam-3852	141	56	less	less	ADJ
ejpam-3852	141	57	than	than	ADP
ejpam-3852	141	58	or	or	CCONJ
ejpam-3852	141	59	equal	equal	ADJ
ejpam-3852	141	60	to	to	ADP
ejpam-3852	141	61	m	m	PROPN
ejpam-3852	141	62	2	2	NUM
ejpam-3852	141	63	,	,	PUNCT
ejpam-3852	141	64	if	if	SCONJ
ejpam-3852	141	65	a	a	PRON
ejpam-3852	141	66	is	be	AUX
ejpam-3852	141	67	odd	odd	ADJ
ejpam-3852	141	68	and	and	CCONJ
ejpam-3852	141	69	b	b	NOUN
ejpam-3852	141	70	and	and	CCONJ
ejpam-3852	141	71	c	c	PROPN
ejpam-3852	141	72	are	be	AUX
ejpam-3852	141	73	even	even	ADV
ejpam-3852	141	74	;	;	PUNCT
ejpam-3852	141	75	less	less	ADJ
ejpam-3852	141	76	than	than	ADP
ejpam-3852	141	77	or	or	CCONJ
ejpam-3852	141	78	equal	equal	ADJ
ejpam-3852	141	79	to	to	ADP
ejpam-3852	141	80	m	m	PRON
ejpam-3852	141	81	,	,	PUNCT
ejpam-3852	141	82	if	if	SCONJ
ejpam-3852	141	83	b	b	NOUN
ejpam-3852	141	84	is	be	AUX
ejpam-3852	141	85	odd	odd	ADJ
ejpam-3852	141	86	and	and	CCONJ
ejpam-3852	141	87	a	a	PRON
ejpam-3852	141	88	and	and	CCONJ
ejpam-3852	141	89	c	c	NOUN
ejpam-3852	141	90	are	be	AUX
ejpam-3852	141	91	even	even	ADV
ejpam-3852	141	92	;	;	PUNCT
ejpam-3852	141	93	and	and	CCONJ
ejpam-3852	141	94	,	,	PUNCT
ejpam-3852	141	95	finally	finally	ADV
ejpam-3852	141	96	,	,	PUNCT
ejpam-3852	141	97	the	the	DET
ejpam-3852	141	98	period	period	NOUN
ejpam-3852	141	99	is	be	AUX
ejpam-3852	141	100	always	always	ADV
ejpam-3852	141	101	1	1	NUM
ejpam-3852	141	102	,	,	PUNCT
ejpam-3852	141	103	if	if	SCONJ
ejpam-3852	141	104	c	c	PROPN
ejpam-3852	141	105	is	be	AUX
ejpam-3852	141	106	odd	odd	ADJ
ejpam-3852	141	107	and	and	CCONJ
ejpam-3852	141	108	a	a	PRON
ejpam-3852	141	109	and	and	CCONJ
ejpam-3852	141	110	b	b	NOUN
ejpam-3852	141	111	are	be	AUX
ejpam-3852	141	112	even	even	ADV
ejpam-3852	141	113	.	.	PUNCT
ejpam-3852	142	1	3	3	X
ejpam-3852	142	2	.	.	X
ejpam-3852	142	3	general	general	ADJ
ejpam-3852	142	4	periodicity	periodicity	NOUN
ejpam-3852	142	5	analysis	analysis	NOUN
ejpam-3852	142	6	of	of	ADP
ejpam-3852	142	7	the	the	DET
ejpam-3852	142	8	sequence	sequence	NOUN
ejpam-3852	142	9	let	let	VERB
ejpam-3852	142	10	m	m	NOUN
ejpam-3852	142	11	=	=	NOUN
ejpam-3852	142	12	2ω	2ω	NOUN
ejpam-3852	142	13	;	;	PUNCT
ejpam-3852	142	14	ω	ω	NUM
ejpam-3852	142	15	≥	≥	NOUN
ejpam-3852	142	16	3	3	NUM
ejpam-3852	142	17	,	,	PUNCT
ejpam-3852	142	18	y0	y0	NOUN
ejpam-3852	142	19	and	and	CCONJ
ejpam-3852	142	20	y1	y1	NOUN
ejpam-3852	142	21	are	be	AUX
ejpam-3852	142	22	chosen	choose	VERB
ejpam-3852	142	23	at	at	ADP
ejpam-3852	142	24	random	random	ADJ
ejpam-3852	142	25	from	from	ADP
ejpam-3852	142	26	gm	gm	PROPN
ejpam-3852	142	27	.	.	PUNCT
ejpam-3852	143	1	3.1	3.1	NUM
ejpam-3852	143	2	.	.	PUNCT
ejpam-3852	143	3	conditions	condition	NOUN
ejpam-3852	143	4	when	when	SCONJ
ejpam-3852	143	5	the	the	DET
ejpam-3852	143	6	period	period	NOUN
ejpam-3852	143	7	of	of	ADP
ejpam-3852	143	8	the	the	DET
ejpam-3852	143	9	sequence	sequence	NOUN
ejpam-3852	143	10	is	be	AUX
ejpam-3852	143	11	m	m	AUX
ejpam-3852	143	12	theorem	theorem	VERB
ejpam-3852	143	13	4	4	NUM
ejpam-3852	143	14	.	.	PUNCT
ejpam-3852	144	1	the	the	DET
ejpam-3852	144	2	prng	prng	PROPN
ejpam-3852	144	3	{	{	PUNCT
ejpam-3852	144	4	yn	yn	PROPN
ejpam-3852	144	5	}	}	PUNCT
ejpam-3852	144	6	derived	derive	VERB
ejpam-3852	144	7	from	from	ADP
ejpam-3852	144	8	(	(	PUNCT
ejpam-3852	144	9	5	5	NUM
ejpam-3852	144	10	)	)	PUNCT
ejpam-3852	144	11	(	(	PUNCT
ejpam-3852	144	12	regardless	regardless	ADV
ejpam-3852	144	13	of	of	ADP
ejpam-3852	144	14	the	the	DET
ejpam-3852	144	15	odd	odd	ADJ
ejpam-3852	144	16	initial	initial	ADJ
ejpam-3852	144	17	conditions	condition	NOUN
ejpam-3852	144	18	y0	y0	NOUN
ejpam-3852	144	19	,	,	PUNCT
ejpam-3852	144	20	y1	y1	NOUN
ejpam-3852	144	21	)	)	PUNCT
ejpam-3852	144	22	is	be	AUX
ejpam-3852	144	23	purely	purely	ADV
ejpam-3852	144	24	periodic	periodic	ADJ
ejpam-3852	144	25	with	with	ADP
ejpam-3852	144	26	period	period	NOUN
ejpam-3852	144	27	m	m	PROPN
ejpam-3852	144	28	and	and	CCONJ
ejpam-3852	144	29	the	the	DET
ejpam-3852	144	30	set	set	NOUN
ejpam-3852	144	31	{	{	PUNCT
ejpam-3852	144	32	y0	y0	NOUN
ejpam-3852	144	33	,	,	PUNCT
ejpam-3852	144	34	y1	y1	NOUN
ejpam-3852	144	35	,	,	PUNCT
ejpam-3852	144	36	.	.	PUNCT
ejpam-3852	144	37	.	.	PUNCT
ejpam-3852	145	1	.	.	PUNCT
ejpam-3852	146	1	,	,	PUNCT
ejpam-3852	146	2	ym−1	ym−1	PROPN
ejpam-3852	146	3	}	}	PUNCT
ejpam-3852	146	4	gives	give	VERB
ejpam-3852	146	5	the	the	DET
ejpam-3852	146	6	set	set	NOUN
ejpam-3852	146	7	gm	gm	PROPN
ejpam-3852	146	8	,	,	PUNCT
ejpam-3852	146	9	uniformly	uniformly	ADV
ejpam-3852	146	10	distributed	distribute	VERB
ejpam-3852	146	11	(	(	PUNCT
ejpam-3852	146	12	that	that	ADV
ejpam-3852	146	13	is	is	ADV
ejpam-3852	146	14	,	,	PUNCT
ejpam-3852	146	15	every	every	DET
ejpam-3852	146	16	element	element	NOUN
ejpam-3852	146	17	will	will	AUX
ejpam-3852	146	18	occur	occur	VERB
ejpam-3852	146	19	exactly	exactly	ADV
ejpam-3852	146	20	twice	twice	ADV
ejpam-3852	146	21	)	)	PUNCT
ejpam-3852	146	22	,	,	PUNCT
ejpam-3852	146	23	if	if	SCONJ
ejpam-3852	146	24	and	and	CCONJ
ejpam-3852	146	25	only	only	ADV
ejpam-3852	146	26	if	if	SCONJ
ejpam-3852	146	27	a	a	DET
ejpam-3852	146	28	≡	≡	PROPN
ejpam-3852	146	29	0	0	PUNCT
ejpam-3852	146	30	(	(	PUNCT
ejpam-3852	146	31	mod	mod	NOUN
ejpam-3852	146	32	2	2	NUM
ejpam-3852	146	33	)	)	PUNCT
ejpam-3852	146	34	,	,	PUNCT
ejpam-3852	146	35	a+	a+	PUNCT
ejpam-3852	146	36	b	b	X
ejpam-3852	146	37	≡	≡	PROPN
ejpam-3852	146	38	1	1	NUM
ejpam-3852	146	39	(	(	PUNCT
ejpam-3852	146	40	mod	mod	NOUN
ejpam-3852	146	41	4	4	NUM
ejpam-3852	146	42	)	)	PUNCT
ejpam-3852	146	43	and	and	CCONJ
ejpam-3852	146	44	c	c	PROPN
ejpam-3852	146	45	≡	≡	PROPN
ejpam-3852	146	46	2	2	NUM
ejpam-3852	146	47	(	(	PUNCT
ejpam-3852	146	48	mod	mod	NOUN
ejpam-3852	146	49	4	4	NUM
ejpam-3852	146	50	)	)	PUNCT
ejpam-3852	146	51	.	.	PUNCT
ejpam-3852	147	1	proof	proof	NOUN
ejpam-3852	147	2	.	.	PUNCT
ejpam-3852	148	1	we	we	PRON
ejpam-3852	148	2	show	show	VERB
ejpam-3852	148	3	this	this	PRON
ejpam-3852	148	4	in	in	ADP
ejpam-3852	148	5	two	two	NUM
ejpam-3852	148	6	steps	step	NOUN
ejpam-3852	148	7	.	.	PUNCT
ejpam-3852	149	1	necessity	necessity	NOUN
ejpam-3852	149	2	:	:	PUNCT
ejpam-3852	149	3	let	let	VERB
ejpam-3852	149	4	us	we	PRON
ejpam-3852	149	5	assume	assume	VERB
ejpam-3852	149	6	that	that	SCONJ
ejpam-3852	149	7	for	for	ADP
ejpam-3852	149	8	the	the	DET
ejpam-3852	149	9	sequence	sequence	NOUN
ejpam-3852	149	10	(	(	PUNCT
ejpam-3852	149	11	5	5	NUM
ejpam-3852	149	12	)	)	PUNCT
ejpam-3852	149	13	and	and	CCONJ
ejpam-3852	149	14	for	for	ADP
ejpam-3852	149	15	any	any	DET
ejpam-3852	149	16	y0	y0	NOUN
ejpam-3852	149	17	,	,	PUNCT
ejpam-3852	149	18	y1	y1	PROPN
ejpam-3852	149	19	∈	∈	PROPN
ejpam-3852	149	20	gm	gm	PROPN
ejpam-3852	149	21	,	,	PUNCT
ejpam-3852	149	22	the	the	DET
ejpam-3852	149	23	period	period	NOUN
ejpam-3852	149	24	of	of	ADP
ejpam-3852	149	25	yn	yn	PROPN
ejpam-3852	149	26	is	be	AUX
ejpam-3852	149	27	m	m	ADJ
ejpam-3852	149	28	and	and	CCONJ
ejpam-3852	149	29	{	{	PUNCT
ejpam-3852	149	30	y0	y0	NOUN
ejpam-3852	149	31	,	,	PUNCT
ejpam-3852	149	32	y1	y1	NOUN
ejpam-3852	149	33	,	,	PUNCT
ejpam-3852	149	34	.	.	PUNCT
ejpam-3852	149	35	.	.	PUNCT
ejpam-3852	150	1	.	.	PUNCT
ejpam-3852	151	1	,	,	PUNCT
ejpam-3852	151	2	ym−1	ym−1	PROPN
ejpam-3852	151	3	}	}	PUNCT
ejpam-3852	151	4	gives	give	VERB
ejpam-3852	151	5	the	the	DET
ejpam-3852	151	6	set	set	NOUN
ejpam-3852	151	7	gm	gm	PROPN
ejpam-3852	151	8	with	with	ADP
ejpam-3852	151	9	every	every	DET
ejpam-3852	151	10	element	element	NOUN
ejpam-3852	151	11	occurring	occur	VERB
ejpam-3852	151	12	exactly	exactly	ADV
ejpam-3852	151	13	twice	twice	ADV
ejpam-3852	151	14	.	.	PUNCT
ejpam-3852	152	1	we	we	PRON
ejpam-3852	152	2	will	will	AUX
ejpam-3852	152	3	prove	prove	VERB
ejpam-3852	152	4	that	that	SCONJ
ejpam-3852	152	5	a	a	PRON
ejpam-3852	152	6	is	be	AUX
ejpam-3852	152	7	even	even	ADV
ejpam-3852	152	8	,	,	PUNCT
ejpam-3852	152	9	a+	a+	PRON
ejpam-3852	152	10	b	b	PROPN
ejpam-3852	152	11	≡	≡	PROPN
ejpam-3852	152	12	1	1	NUM
ejpam-3852	152	13	(	(	PUNCT
ejpam-3852	152	14	mod	mod	NOUN
ejpam-3852	152	15	4	4	NUM
ejpam-3852	152	16	)	)	PUNCT
ejpam-3852	152	17	and	and	CCONJ
ejpam-3852	152	18	c	c	PROPN
ejpam-3852	152	19	≡	≡	PROPN
ejpam-3852	152	20	2	2	NUM
ejpam-3852	152	21	(	(	PUNCT
ejpam-3852	152	22	mod	mod	NOUN
ejpam-3852	152	23	4	4	NUM
ejpam-3852	152	24	)	)	PUNCT
ejpam-3852	152	25	.	.	PUNCT
ejpam-3852	153	1	without	without	ADP
ejpam-3852	153	2	loss	loss	NOUN
ejpam-3852	153	3	of	of	ADP
ejpam-3852	153	4	generality	generality	NOUN
ejpam-3852	153	5	we	we	PRON
ejpam-3852	153	6	may	may	AUX
ejpam-3852	153	7	take	take	VERB
ejpam-3852	153	8	y0	y0	NOUN
ejpam-3852	153	9	=	=	SYM
ejpam-3852	153	10	y1	y1	NOUN
ejpam-3852	153	11	=	=	SYM
ejpam-3852	153	12	1	1	X
ejpam-3852	153	13	.	.	PUNCT
ejpam-3852	154	1	now	now	ADV
ejpam-3852	154	2	,	,	PUNCT
ejpam-3852	154	3	it	it	PRON
ejpam-3852	154	4	is	be	AUX
ejpam-3852	154	5	easy	easy	ADJ
ejpam-3852	154	6	to	to	PART
ejpam-3852	154	7	check	check	VERB
ejpam-3852	154	8	that	that	SCONJ
ejpam-3852	154	9	under	under	ADP
ejpam-3852	154	10	the	the	DET
ejpam-3852	154	11	above	above	ADJ
ejpam-3852	154	12	assumption	assumption	NOUN
ejpam-3852	154	13	on	on	ADP
ejpam-3852	154	14	the	the	DET
ejpam-3852	154	15	parameters	parameter	NOUN
ejpam-3852	154	16	a	a	DET
ejpam-3852	154	17	,	,	PUNCT
ejpam-3852	154	18	b	b	PROPN
ejpam-3852	154	19	,	,	PUNCT
ejpam-3852	154	20	c	c	AUX
ejpam-3852	154	21	,	,	PUNCT
ejpam-3852	154	22	if	if	SCONJ
ejpam-3852	154	23	we	we	PRON
ejpam-3852	154	24	reduce	reduce	VERB
ejpam-3852	154	25	every	every	DET
ejpam-3852	154	26	element	element	NOUN
ejpam-3852	154	27	modulo	modulo	NOUN
ejpam-3852	154	28	4	4	NUM
ejpam-3852	154	29	(	(	PUNCT
ejpam-3852	154	30	respectively	respectively	ADV
ejpam-3852	154	31	,	,	PUNCT
ejpam-3852	154	32	8)	8)	NUM
ejpam-3852	154	33	,	,	PUNCT
ejpam-3852	154	34	the	the	DET
ejpam-3852	154	35	period	period	NOUN
ejpam-3852	154	36	of	of	ADP
ejpam-3852	154	37	{	{	PUNCT
ejpam-3852	154	38	yn	yn	PROPN
ejpam-3852	154	39	(	(	PUNCT
ejpam-3852	154	40	mod	mod	PROPN
ejpam-3852	154	41	4	4	NUM
ejpam-3852	154	42	)	)	PUNCT
ejpam-3852	154	43	}	}	PUNCT
ejpam-3852	154	44	(	(	PUNCT
ejpam-3852	154	45	respectively	respectively	ADV
ejpam-3852	154	46	,	,	PUNCT
ejpam-3852	154	47	{	{	PUNCT
ejpam-3852	154	48	yn	yn	X
ejpam-3852	154	49	(	(	PUNCT
ejpam-3852	154	50	mod	mod	PROPN
ejpam-3852	154	51	8)	8)	NUM
ejpam-3852	154	52	}	}	PUNCT
ejpam-3852	154	53	)	)	PUNCT
ejpam-3852	154	54	is	be	AUX
ejpam-3852	154	55	4	4	NUM
ejpam-3852	154	56	(	(	PUNCT
ejpam-3852	154	57	respectively	respectively	ADV
ejpam-3852	154	58	,	,	PUNCT
ejpam-3852	154	59	8)	8)	NUM
ejpam-3852	154	60	and	and	CCONJ
ejpam-3852	154	61	{	{	PUNCT
ejpam-3852	154	62	y0	y0	NOUN
ejpam-3852	154	63	,	,	PUNCT
ejpam-3852	154	64	y1	y1	NOUN
ejpam-3852	154	65	,	,	PUNCT
ejpam-3852	154	66	y2	y2	PROPN
ejpam-3852	154	67	,	,	PUNCT
ejpam-3852	154	68	y3	y3	NOUN
ejpam-3852	154	69	}	}	PUNCT
ejpam-3852	154	70	(	(	PUNCT
ejpam-3852	154	71	respectively	respectively	ADV
ejpam-3852	154	72	,	,	PUNCT
ejpam-3852	154	73	{	{	PUNCT
ejpam-3852	154	74	y0	y0	NOUN
ejpam-3852	154	75	,	,	PUNCT
ejpam-3852	154	76	y1	y1	NOUN
ejpam-3852	154	77	,	,	PUNCT
ejpam-3852	154	78	.	.	PUNCT
ejpam-3852	154	79	.	.	PUNCT
ejpam-3852	155	1	.	.	PUNCT
ejpam-3852	156	1	,	,	PUNCT
ejpam-3852	156	2	y7	y7	PROPN
ejpam-3852	156	3	}	}	PUNCT
ejpam-3852	156	4	)	)	PUNCT
ejpam-3852	156	5	gives	give	VERB
ejpam-3852	156	6	the	the	DET
ejpam-3852	156	7	set	set	ADJ
ejpam-3852	156	8	g4	g4	NOUN
ejpam-3852	156	9	=	=	SYM
ejpam-3852	156	10	{	{	PUNCT
ejpam-3852	156	11	1	1	NUM
ejpam-3852	156	12	,	,	PUNCT
ejpam-3852	156	13	3	3	NUM
ejpam-3852	156	14	}	}	PUNCT
ejpam-3852	156	15	(	(	PUNCT
ejpam-3852	156	16	respectively	respectively	ADV
ejpam-3852	156	17	,	,	PUNCT
ejpam-3852	156	18	g8	g8	PROPN
ejpam-3852	156	19	=	=	SYM
ejpam-3852	156	20	{	{	PUNCT
ejpam-3852	156	21	1	1	NUM
ejpam-3852	156	22	,	,	PUNCT
ejpam-3852	156	23	3	3	NUM
ejpam-3852	156	24	,	,	PUNCT
ejpam-3852	156	25	5	5	NUM
ejpam-3852	156	26	,	,	PUNCT
ejpam-3852	156	27	7	7	NUM
ejpam-3852	156	28	}	}	PUNCT
ejpam-3852	156	29	)	)	PUNCT
ejpam-3852	156	30	with	with	ADP
ejpam-3852	156	31	every	every	DET
ejpam-3852	156	32	element	element	NOUN
ejpam-3852	156	33	occurring	occur	VERB
ejpam-3852	156	34	exactly	exactly	ADV
ejpam-3852	156	35	twice	twice	ADV
ejpam-3852	156	36	.	.	PUNCT
ejpam-3852	157	1	now	now	ADV
ejpam-3852	157	2	,	,	PUNCT
ejpam-3852	157	3	for	for	ADP
ejpam-3852	157	4	our	our	PRON
ejpam-3852	157	5	convenience	convenience	NOUN
ejpam-3852	157	6	,	,	PUNCT
ejpam-3852	157	7	for	for	ADP
ejpam-3852	157	8	the	the	DET
ejpam-3852	157	9	rest	rest	NOUN
ejpam-3852	157	10	of	of	ADP
ejpam-3852	157	11	the	the	DET
ejpam-3852	157	12	necessary	necessary	ADJ
ejpam-3852	157	13	part	part	NOUN
ejpam-3852	157	14	we	we	PRON
ejpam-3852	157	15	consider	consider	VERB
ejpam-3852	157	16	every	every	DET
ejpam-3852	157	17	equality	equality	NOUN
ejpam-3852	157	18	as	as	ADP
ejpam-3852	157	19	a	a	DET
ejpam-3852	157	20	modulo	modulo	NOUN
ejpam-3852	157	21	8	8	NUM
ejpam-3852	157	22	operation	operation	NOUN
ejpam-3852	157	23	and	and	CCONJ
ejpam-3852	157	24	hence	hence	ADV
ejpam-3852	157	25	(	(	PUNCT
ejpam-3852	157	26	5	5	X
ejpam-3852	157	27	)	)	PUNCT
ejpam-3852	157	28	reduces	reduce	VERB
ejpam-3852	157	29	to	to	ADP
ejpam-3852	157	30	yn+2	yn+2	NUM
ejpam-3852	157	31	=	=	SYM
ejpam-3852	157	32	ayn+1	ayn+1	PROPN
ejpam-3852	158	1	+	+	CCONJ
ejpam-3852	159	1	byn	byn	NOUN
ejpam-3852	160	1	+	+	CCONJ
ejpam-3852	161	1	c	c	X
ejpam-3852	161	2	,	,	PUNCT
ejpam-3852	161	3	since	since	SCONJ
ejpam-3852	161	4	t	t	PROPN
ejpam-3852	161	5	≡	≡	PROPN
ejpam-3852	161	6	t−1	t−1	PROPN
ejpam-3852	161	7	(	(	PUNCT
ejpam-3852	161	8	mod	mod	PROPN
ejpam-3852	161	9	8)	8)	NUM
ejpam-3852	161	10	,	,	PUNCT
ejpam-3852	161	11	for	for	ADP
ejpam-3852	161	12	every	every	DET
ejpam-3852	161	13	odd	odd	ADJ
ejpam-3852	161	14	integer	integer	NOUN
ejpam-3852	161	15	t.	t.	PROPN
ejpam-3852	161	16	also	also	ADV
ejpam-3852	161	17	,	,	PUNCT
ejpam-3852	161	18	we	we	PRON
ejpam-3852	161	19	recall	recall	VERB
ejpam-3852	161	20	that	that	SCONJ
ejpam-3852	161	21	we	we	PRON
ejpam-3852	161	22	have	have	VERB
ejpam-3852	161	23	y0	y0	NOUN
ejpam-3852	161	24	=	=	SYM
ejpam-3852	161	25	y1	y1	NOUN
ejpam-3852	161	26	=	=	SYM
ejpam-3852	161	27	1	1	X
ejpam-3852	161	28	.	.	PUNCT
ejpam-3852	162	1	by	by	ADP
ejpam-3852	162	2	absurd	absurd	ADJ
ejpam-3852	162	3	,	,	PUNCT
ejpam-3852	162	4	we	we	PRON
ejpam-3852	162	5	now	now	ADV
ejpam-3852	162	6	assume	assume	VERB
ejpam-3852	162	7	that	that	SCONJ
ejpam-3852	162	8	a	a	DET
ejpam-3852	162	9	+	+	NOUN
ejpam-3852	162	10	b	b	NOUN
ejpam-3852	162	11	is	be	AUX
ejpam-3852	162	12	even	even	ADV
ejpam-3852	162	13	.	.	PUNCT
ejpam-3852	163	1	then	then	ADV
ejpam-3852	163	2	,	,	PUNCT
ejpam-3852	163	3	y2	y2	PROPN
ejpam-3852	163	4	=	=	PUNCT
ejpam-3852	163	5	a	a	DET
ejpam-3852	163	6	+	+	NOUN
ejpam-3852	163	7	b	b	NOUN
ejpam-3852	163	8	+	+	CCONJ
ejpam-3852	163	9	c	c	NOUN
ejpam-3852	163	10	≡	≡	PROPN
ejpam-3852	163	11	3	3	NUM
ejpam-3852	163	12	(	(	PUNCT
ejpam-3852	163	13	mod	mod	NOUN
ejpam-3852	163	14	4	4	NUM
ejpam-3852	163	15	)	)	PUNCT
ejpam-3852	163	16	implies	imply	VERB
ejpam-3852	163	17	that	that	SCONJ
ejpam-3852	163	18	c	c	PROPN
ejpam-3852	163	19	is	be	AUX
ejpam-3852	163	20	odd	odd	ADJ
ejpam-3852	163	21	.	.	PUNCT
ejpam-3852	164	1	so	so	ADV
ejpam-3852	164	2	,	,	PUNCT
ejpam-3852	164	3	let	let	VERB
ejpam-3852	164	4	a	a	DET
ejpam-3852	164	5	+	+	NOUN
ejpam-3852	164	6	b	b	NOUN
ejpam-3852	164	7	=	=	SYM
ejpam-3852	164	8	2d	2d	PROPN
ejpam-3852	164	9	and	and	CCONJ
ejpam-3852	164	10	c	c	NOUN
ejpam-3852	164	11	=	=	SYM
ejpam-3852	164	12	1	1	NUM
ejpam-3852	164	13	+	+	NUM
ejpam-3852	164	14	2e	2e	NOUN
ejpam-3852	164	15	for	for	ADP
ejpam-3852	164	16	some	some	DET
ejpam-3852	164	17	integers	integer	NOUN
ejpam-3852	164	18	d	d	NOUN
ejpam-3852	164	19	and	and	CCONJ
ejpam-3852	164	20	e.	e.	PROPN
ejpam-3852	164	21	we	we	PRON
ejpam-3852	164	22	have	have	VERB
ejpam-3852	164	23	,	,	PUNCT
ejpam-3852	164	24	y2	y2	PROPN
ejpam-3852	164	25	=	=	SYM
ejpam-3852	164	26	1	1	NUM
ejpam-3852	165	1	+	+	NUM
ejpam-3852	165	2	2(d+	2(d+	NUM
ejpam-3852	165	3	e	e	NOUN
ejpam-3852	165	4	)	)	PUNCT
ejpam-3852	165	5	where	where	SCONJ
ejpam-3852	165	6	d+	d+	PRON
ejpam-3852	165	7	e	e	X
ejpam-3852	165	8	=	=	SYM
ejpam-3852	165	9	1	1	NUM
ejpam-3852	165	10	+	+	NUM
ejpam-3852	165	11	2f	2f	NUM
ejpam-3852	165	12	,	,	PUNCT
ejpam-3852	165	13	f	f	PROPN
ejpam-3852	165	14	∈	∈	PROPN
ejpam-3852	165	15	z	z	PROPN
ejpam-3852	165	16	is	be	AUX
ejpam-3852	165	17	odd	odd	ADJ
ejpam-3852	165	18	(	(	PUNCT
ejpam-3852	165	19	since	since	SCONJ
ejpam-3852	165	20	y2	y2	PROPN
ejpam-3852	165	21	≡	≡	PROPN
ejpam-3852	165	22	3	3	NUM
ejpam-3852	165	23	(	(	PUNCT
ejpam-3852	165	24	mod	mod	NOUN
ejpam-3852	165	25	4	4	NUM
ejpam-3852	165	26	)	)	PUNCT
ejpam-3852	165	27	)	)	PUNCT
ejpam-3852	165	28	.	.	PUNCT
ejpam-3852	166	1	then	then	ADV
ejpam-3852	166	2	,	,	PUNCT
ejpam-3852	166	3	from	from	ADP
ejpam-3852	166	4	y3	y3	PROPN
ejpam-3852	166	5	≡	≡	PROPN
ejpam-3852	166	6	3a+	3a+	NUM
ejpam-3852	166	7	b+	b+	X
ejpam-3852	166	8	c	c	PROPN
ejpam-3852	166	9	≡	≡	PROPN
ejpam-3852	166	10	3	3	NUM
ejpam-3852	166	11	(	(	PUNCT
ejpam-3852	166	12	mod	mod	NOUN
ejpam-3852	166	13	4	4	X
ejpam-3852	166	14	)	)	PUNCT
ejpam-3852	166	15	we	we	PRON
ejpam-3852	166	16	have	have	VERB
ejpam-3852	166	17	3	3	NUM
ejpam-3852	166	18	+	+	NUM
ejpam-3852	166	19	2a	2a	NUM
ejpam-3852	166	20	≡	≡	PROPN
ejpam-3852	166	21	3	3	NUM
ejpam-3852	166	22	(	(	PUNCT
ejpam-3852	166	23	mod	mod	NOUN
ejpam-3852	166	24	4	4	NUM
ejpam-3852	166	25	)	)	PUNCT
ejpam-3852	166	26	and	and	CCONJ
ejpam-3852	166	27	thus	thus	ADV
ejpam-3852	166	28	a	a	PRON
ejpam-3852	166	29	is	be	AUX
ejpam-3852	166	30	even	even	ADV
ejpam-3852	166	31	.	.	PUNCT
ejpam-3852	167	1	we	we	PRON
ejpam-3852	167	2	let	let	VERB
ejpam-3852	167	3	a	a	DET
ejpam-3852	167	4	=	=	ADJ
ejpam-3852	167	5	2	2	NUM
ejpam-3852	167	6	g	g	NOUN
ejpam-3852	167	7	,	,	PUNCT
ejpam-3852	167	8	g	g	PROPN
ejpam-3852	167	9	∈	∈	PROPN
ejpam-3852	167	10	z.	z.	PROPN
ejpam-3852	168	1	thus	thus	ADV
ejpam-3852	168	2	,	,	PUNCT
ejpam-3852	168	3	y4	y4	PROPN
ejpam-3852	168	4	≡	≡	PROPN
ejpam-3852	168	5	3a+	3a+	NUM
ejpam-3852	169	1	3b+	3b+	NUM
ejpam-3852	169	2	c	c	NOUN
ejpam-3852	169	3	≡	≡	PROPN
ejpam-3852	169	4	1	1	NUM
ejpam-3852	169	5	(	(	PUNCT
ejpam-3852	169	6	mod	mod	NOUN
ejpam-3852	169	7	4	4	NUM
ejpam-3852	169	8	)	)	PUNCT
ejpam-3852	169	9	yields	yield	NOUN
ejpam-3852	169	10	3(2d	3(2d	NUM
ejpam-3852	169	11	)	)	PUNCT
ejpam-3852	170	1	+	+	CCONJ
ejpam-3852	170	2	1	1	NUM
ejpam-3852	170	3	+	+	NUM
ejpam-3852	170	4	2e	2e	NOUN
ejpam-3852	170	5	=	=	SYM
ejpam-3852	170	6	1	1	NUM
ejpam-3852	170	7	+	+	NUM
ejpam-3852	170	8	2(d+	2(d+	NUM
ejpam-3852	170	9	e	e	NOUN
ejpam-3852	170	10	)	)	PUNCT
ejpam-3852	170	11	=	=	SYM
ejpam-3852	170	12	3	3	NUM
ejpam-3852	170	13	+	+	NUM
ejpam-3852	170	14	4f	4f	NUM
ejpam-3852	170	15	≡	≡	PROPN
ejpam-3852	170	16	3	3	NUM
ejpam-3852	170	17	(	(	PUNCT
ejpam-3852	170	18	mod	mod	NOUN
ejpam-3852	170	19	4	4	NUM
ejpam-3852	170	20	)	)	PUNCT
ejpam-3852	170	21	,	,	PUNCT
ejpam-3852	170	22	which	which	PRON
ejpam-3852	170	23	is	be	AUX
ejpam-3852	170	24	a	a	DET
ejpam-3852	170	25	contradiction	contradiction	NOUN
ejpam-3852	170	26	.	.	PUNCT
ejpam-3852	171	1	hence	hence	ADV
ejpam-3852	171	2	,	,	PUNCT
ejpam-3852	171	3	a+	a+	PRON
ejpam-3852	171	4	b	b	NOUN
ejpam-3852	171	5	is	be	AUX
ejpam-3852	171	6	odd	odd	ADJ
ejpam-3852	171	7	.	.	PUNCT
ejpam-3852	172	1	p.	p.	NOUN
ejpam-3852	172	2	stănică	stănică	NUM
ejpam-3852	172	3	et	et	PROPN
ejpam-3852	172	4	al	al	PROPN
ejpam-3852	172	5	.	.	PUNCT
ejpam-3852	172	6	/	/	SYM
ejpam-3852	172	7	eur	eur	PROPN
ejpam-3852	172	8	.	.	PUNCT
ejpam-3852	173	1	j.	j.	PROPN
ejpam-3852	173	2	pure	pure	PROPN
ejpam-3852	173	3	appl	appl	PROPN
ejpam-3852	173	4	.	.	PROPN
ejpam-3852	173	5	math	math	PROPN
ejpam-3852	173	6	,	,	PUNCT
ejpam-3852	173	7	14	14	NUM
ejpam-3852	173	8	(	(	PUNCT
ejpam-3852	173	9	1	1	NUM
ejpam-3852	173	10	)	)	PUNCT
ejpam-3852	173	11	(	(	PUNCT
ejpam-3852	173	12	2021	2021	NUM
ejpam-3852	173	13	)	)	PUNCT
ejpam-3852	173	14	,	,	PUNCT
ejpam-3852	173	15	1	1	NUM
ejpam-3852	173	16	-	-	SYM
ejpam-3852	173	17	18	18	NUM
ejpam-3852	173	18	6	6	NUM
ejpam-3852	173	19	suppose	suppose	VERB
ejpam-3852	173	20	now	now	ADV
ejpam-3852	173	21	that	that	SCONJ
ejpam-3852	173	22	a+b	a+b	NUM
ejpam-3852	173	23	≡	≡	PROPN
ejpam-3852	173	24	3	3	NUM
ejpam-3852	173	25	(	(	PUNCT
ejpam-3852	173	26	mod	mod	NOUN
ejpam-3852	173	27	4	4	NUM
ejpam-3852	173	28	)	)	PUNCT
ejpam-3852	173	29	,	,	PUNCT
ejpam-3852	173	30	and	and	CCONJ
ejpam-3852	173	31	so	so	ADV
ejpam-3852	173	32	a+b	a+b	ADV
ejpam-3852	173	33	=	=	SYM
ejpam-3852	173	34	3	3	NUM
ejpam-3852	173	35	+	+	NOUN
ejpam-3852	173	36	4h	4h	NOUN
ejpam-3852	173	37	,	,	PUNCT
ejpam-3852	173	38	h	h	PROPN
ejpam-3852	173	39	∈	∈	PROPN
ejpam-3852	173	40	z.	z.	PROPN
ejpam-3852	173	41	from	from	ADP
ejpam-3852	173	42	y2	y2	PROPN
ejpam-3852	173	43	=	=	PUNCT
ejpam-3852	173	44	a+b+c	a+b+c	ADV
ejpam-3852	173	45	≡	≡	PROPN
ejpam-3852	173	46	3	3	NUM
ejpam-3852	173	47	(	(	PUNCT
ejpam-3852	173	48	mod	mod	NOUN
ejpam-3852	173	49	4	4	NUM
ejpam-3852	173	50	)	)	PUNCT
ejpam-3852	173	51	,	,	PUNCT
ejpam-3852	173	52	we	we	PRON
ejpam-3852	173	53	have	have	VERB
ejpam-3852	173	54	,	,	PUNCT
ejpam-3852	173	55	c	c	NOUN
ejpam-3852	173	56	=	=	SYM
ejpam-3852	173	57	4l	4l	NOUN
ejpam-3852	173	58	,	,	PUNCT
ejpam-3852	174	1	l	l	PROPN
ejpam-3852	174	2	∈	∈	PROPN
ejpam-3852	174	3	z.	z.	PROPN
ejpam-3852	174	4	then	then	ADV
ejpam-3852	174	5	,	,	PUNCT
ejpam-3852	174	6	y3	y3	NOUN
ejpam-3852	174	7	=	=	PUNCT
ejpam-3852	174	8	ay2	ay2	NOUN
ejpam-3852	174	9	+	+	NOUN
ejpam-3852	174	10	b	b	NOUN
ejpam-3852	174	11	+	+	X
ejpam-3852	174	12	c	c	NOUN
ejpam-3852	174	13	=	=	PUNCT
ejpam-3852	174	14	a(3	a(3	PROPN
ejpam-3852	174	15	+	+	CCONJ
ejpam-3852	175	1	4(h	4(h	NUM
ejpam-3852	176	1	+	+	NUM
ejpam-3852	176	2	l	l	NOUN
ejpam-3852	176	3	)	)	PUNCT
ejpam-3852	176	4	)	)	PUNCT
ejpam-3852	177	1	+	+	PUNCT
ejpam-3852	178	1	b	b	X
ejpam-3852	178	2	+	+	CCONJ
ejpam-3852	178	3	c	c	NOUN
ejpam-3852	178	4	=	=	SYM
ejpam-3852	178	5	3	3	NUM
ejpam-3852	178	6	+	+	NUM
ejpam-3852	178	7	2a+	2a+	NUM
ejpam-3852	178	8	4(h+	4(h+	ADJ
ejpam-3852	178	9	l)(a+	l)(a+	ADJ
ejpam-3852	178	10	1	1	NUM
ejpam-3852	178	11	)	)	PUNCT
ejpam-3852	178	12	≡	≡	PROPN
ejpam-3852	178	13	3	3	NUM
ejpam-3852	178	14	(	(	PUNCT
ejpam-3852	178	15	mod	mod	NOUN
ejpam-3852	178	16	4	4	NUM
ejpam-3852	178	17	)	)	PUNCT
ejpam-3852	178	18	gives	give	VERB
ejpam-3852	178	19	a	a	DET
ejpam-3852	178	20	=	=	SYM
ejpam-3852	178	21	2r	2r	NUM
ejpam-3852	178	22	,	,	PUNCT
ejpam-3852	178	23	r	r	NOUN
ejpam-3852	178	24	∈	∈	PROPN
ejpam-3852	178	25	z	z	NOUN
ejpam-3852	178	26	and	and	CCONJ
ejpam-3852	178	27	so	so	ADV
ejpam-3852	178	28	,	,	PUNCT
ejpam-3852	178	29	from	from	ADP
ejpam-3852	178	30	a+	a+	PRON
ejpam-3852	178	31	b	b	X
ejpam-3852	178	32	=	=	SYM
ejpam-3852	178	33	3	3	NUM
ejpam-3852	178	34	+	+	NUM
ejpam-3852	178	35	4h	4h	NUM
ejpam-3852	178	36	,	,	PUNCT
ejpam-3852	178	37	b	b	PROPN
ejpam-3852	178	38	is	be	AUX
ejpam-3852	178	39	odd	odd	ADJ
ejpam-3852	178	40	.	.	PUNCT
ejpam-3852	179	1	thus	thus	ADV
ejpam-3852	179	2	,	,	PUNCT
ejpam-3852	179	3	y3	y3	NOUN
ejpam-3852	179	4	=	=	SYM
ejpam-3852	179	5	ay2+b+c	ay2+b+c	PROPN
ejpam-3852	179	6	=	=	SYM
ejpam-3852	179	7	3	3	NUM
ejpam-3852	179	8	+	+	NOUN
ejpam-3852	179	9	4(h+`+r	4(h+`+r	NUM
ejpam-3852	179	10	)	)	PUNCT
ejpam-3852	179	11	.	.	PUNCT
ejpam-3852	180	1	thus	thus	ADV
ejpam-3852	180	2	,	,	PUNCT
ejpam-3852	180	3	y4	y4	PROPN
ejpam-3852	180	4	=	=	PUNCT
ejpam-3852	180	5	ay3+by2+c	ay3+by2+c	PROPN
ejpam-3852	180	6	=	=	PUNCT
ejpam-3852	180	7	1	1	NUM
ejpam-3852	180	8	+	+	NOUN
ejpam-3852	180	9	4(h+l)(b+1	4(h+l)(b+1	NUM
ejpam-3852	180	10	)	)	PUNCT
ejpam-3852	180	11	≡	≡	PROPN
ejpam-3852	180	12	1	1	NUM
ejpam-3852	180	13	(	(	PUNCT
ejpam-3852	180	14	mod	mod	PROPN
ejpam-3852	180	15	8)	8)	NUM
ejpam-3852	180	16	(	(	PUNCT
ejpam-3852	180	17	as	as	ADP
ejpam-3852	180	18	b	b	NOUN
ejpam-3852	180	19	is	be	AUX
ejpam-3852	180	20	odd	odd	ADJ
ejpam-3852	180	21	)	)	PUNCT
ejpam-3852	180	22	.	.	PUNCT
ejpam-3852	181	1	however	however	ADV
ejpam-3852	181	2	,	,	PUNCT
ejpam-3852	181	3	the	the	DET
ejpam-3852	181	4	periodicity	periodicity	NOUN
ejpam-3852	181	5	modulo	modulo	VERB
ejpam-3852	181	6	4	4	NUM
ejpam-3852	181	7	implies	imply	VERB
ejpam-3852	181	8	that	that	SCONJ
ejpam-3852	181	9	y4	y4	PROPN
ejpam-3852	181	10	≡	≡	PROPN
ejpam-3852	181	11	1	1	NUM
ejpam-3852	181	12	(	(	PUNCT
ejpam-3852	181	13	mod	mod	NOUN
ejpam-3852	181	14	4	4	NUM
ejpam-3852	181	15	)	)	PUNCT
ejpam-3852	181	16	,	,	PUNCT
ejpam-3852	181	17	and	and	CCONJ
ejpam-3852	181	18	therefore	therefore	ADV
ejpam-3852	181	19	,	,	PUNCT
ejpam-3852	181	20	y4	y4	PROPN
ejpam-3852	181	21	≡	≡	PROPN
ejpam-3852	181	22	1	1	NUM
ejpam-3852	181	23	or	or	CCONJ
ejpam-3852	181	24	5	5	NUM
ejpam-3852	181	25	(	(	PUNCT
ejpam-3852	181	26	mod	mod	NOUN
ejpam-3852	181	27	8)	8)	NUM
ejpam-3852	181	28	.	.	PUNCT
ejpam-3852	182	1	but	but	CCONJ
ejpam-3852	182	2	,	,	PUNCT
ejpam-3852	182	3	1	1	NUM
ejpam-3852	182	4	has	have	AUX
ejpam-3852	182	5	already	already	ADV
ejpam-3852	182	6	occurred	occur	VERB
ejpam-3852	182	7	twice	twice	ADV
ejpam-3852	182	8	.	.	PUNCT
ejpam-3852	183	1	so	so	ADV
ejpam-3852	183	2	,	,	PUNCT
ejpam-3852	183	3	y4	y4	PROPN
ejpam-3852	183	4	≡	≡	PROPN
ejpam-3852	183	5	5	5	NUM
ejpam-3852	183	6	(	(	PUNCT
ejpam-3852	183	7	mod	mod	NOUN
ejpam-3852	183	8	8)	8)	NUM
ejpam-3852	183	9	,	,	PUNCT
ejpam-3852	183	10	which	which	PRON
ejpam-3852	183	11	contradicts	contradict	VERB
ejpam-3852	183	12	y4	y4	PROPN
ejpam-3852	183	13	≡	≡	PROPN
ejpam-3852	183	14	1	1	NUM
ejpam-3852	183	15	(	(	PUNCT
ejpam-3852	183	16	mod	mod	PROPN
ejpam-3852	183	17	8)	8)	NUM
ejpam-3852	183	18	.	.	PUNCT
ejpam-3852	184	1	hence	hence	ADV
ejpam-3852	184	2	,	,	PUNCT
ejpam-3852	184	3	a+	a+	PRON
ejpam-3852	184	4	b	b	PROPN
ejpam-3852	184	5	≡	≡	PROPN
ejpam-3852	184	6	1	1	NUM
ejpam-3852	184	7	(	(	PUNCT
ejpam-3852	184	8	mod	mod	NOUN
ejpam-3852	184	9	4	4	NUM
ejpam-3852	184	10	)	)	PUNCT
ejpam-3852	184	11	which	which	PRON
ejpam-3852	184	12	implies	imply	VERB
ejpam-3852	184	13	c	c	PROPN
ejpam-3852	184	14	≡	≡	PROPN
ejpam-3852	184	15	2	2	NUM
ejpam-3852	184	16	(	(	PUNCT
ejpam-3852	184	17	mod	mod	NOUN
ejpam-3852	184	18	4	4	NUM
ejpam-3852	184	19	)	)	PUNCT
ejpam-3852	184	20	and	and	CCONJ
ejpam-3852	184	21	a	a	PRON
ejpam-3852	184	22	is	be	AUX
ejpam-3852	184	23	even	even	ADV
ejpam-3852	184	24	(	(	PUNCT
ejpam-3852	184	25	the	the	DET
ejpam-3852	184	26	parity	parity	NOUN
ejpam-3852	184	27	of	of	ADP
ejpam-3852	184	28	a	a	PRON
ejpam-3852	184	29	can	can	AUX
ejpam-3852	184	30	be	be	AUX
ejpam-3852	184	31	deduced	deduce	VERB
ejpam-3852	184	32	,	,	PUNCT
ejpam-3852	184	33	for	for	ADP
ejpam-3852	184	34	instance	instance	NOUN
ejpam-3852	184	35	,	,	PUNCT
ejpam-3852	184	36	from	from	ADP
ejpam-3852	184	37	y2	y2	PROPN
ejpam-3852	184	38	≡	≡	PROPN
ejpam-3852	185	1	a	a	DET
ejpam-3852	185	2	+	+	NOUN
ejpam-3852	185	3	b	b	NOUN
ejpam-3852	185	4	+	+	CCONJ
ejpam-3852	185	5	c	c	NOUN
ejpam-3852	185	6	≡	≡	PROPN
ejpam-3852	185	7	3	3	NUM
ejpam-3852	185	8	(	(	PUNCT
ejpam-3852	185	9	mod	mod	NOUN
ejpam-3852	185	10	4	4	NUM
ejpam-3852	185	11	)	)	PUNCT
ejpam-3852	185	12	and	and	CCONJ
ejpam-3852	185	13	y3	y3	PROPN
ejpam-3852	185	14	≡	≡	PROPN
ejpam-3852	185	15	3a	3a	PROPN
ejpam-3852	185	16	+	+	SYM
ejpam-3852	185	17	b	b	PROPN
ejpam-3852	186	1	+	+	CCONJ
ejpam-3852	186	2	c	c	NOUN
ejpam-3852	186	3	≡	≡	PROPN
ejpam-3852	186	4	3	3	NUM
ejpam-3852	186	5	(	(	PUNCT
ejpam-3852	186	6	mod	mod	NOUN
ejpam-3852	186	7	4	4	NUM
ejpam-3852	186	8	)	)	PUNCT
ejpam-3852	186	9	;	;	PUNCT
ejpam-3852	186	10	then	then	ADV
ejpam-3852	186	11	,	,	PUNCT
ejpam-3852	186	12	2a	2a	NUM
ejpam-3852	186	13	≡	≡	PROPN
ejpam-3852	186	14	0	0	PUNCT
ejpam-3852	186	15	(	(	PUNCT
ejpam-3852	186	16	mod	mod	PROPN
ejpam-3852	186	17	4	4	NUM
ejpam-3852	186	18	)	)	PUNCT
ejpam-3852	186	19	)	)	PUNCT
ejpam-3852	186	20	.	.	PUNCT
ejpam-3852	187	1	sufficiency	sufficiency	NOUN
ejpam-3852	187	2	:	:	PUNCT
ejpam-3852	187	3	let	let	VERB
ejpam-3852	187	4	now	now	ADV
ejpam-3852	187	5	a	a	DET
ejpam-3852	187	6	be	be	AUX
ejpam-3852	187	7	even	even	ADV
ejpam-3852	187	8	,	,	PUNCT
ejpam-3852	187	9	a+	a+	PRON
ejpam-3852	187	10	b	b	PROPN
ejpam-3852	187	11	≡	≡	PROPN
ejpam-3852	187	12	1	1	NUM
ejpam-3852	187	13	(	(	PUNCT
ejpam-3852	187	14	mod	mod	NOUN
ejpam-3852	187	15	4	4	NUM
ejpam-3852	187	16	)	)	PUNCT
ejpam-3852	187	17	and	and	CCONJ
ejpam-3852	187	18	c	c	PROPN
ejpam-3852	187	19	≡	≡	PROPN
ejpam-3852	187	20	2	2	NUM
ejpam-3852	187	21	(	(	PUNCT
ejpam-3852	187	22	mod	mod	NOUN
ejpam-3852	187	23	4	4	NUM
ejpam-3852	187	24	)	)	PUNCT
ejpam-3852	187	25	,	,	PUNCT
ejpam-3852	187	26	and	and	CCONJ
ejpam-3852	187	27	y0	y0	NOUN
ejpam-3852	187	28	,	,	PUNCT
ejpam-3852	187	29	y1	y1	PROPN
ejpam-3852	187	30	∈	∈	PROPN
ejpam-3852	187	31	gm	gm	PROPN
ejpam-3852	187	32	.	.	PUNCT
ejpam-3852	188	1	first	first	ADV
ejpam-3852	188	2	,	,	PUNCT
ejpam-3852	188	3	we	we	PRON
ejpam-3852	188	4	will	will	AUX
ejpam-3852	188	5	prove	prove	VERB
ejpam-3852	188	6	that	that	SCONJ
ejpam-3852	188	7	yn	yn	PROPN
ejpam-3852	188	8	∈	∈	PROPN
ejpam-3852	188	9	gm	gm	PROPN
ejpam-3852	188	10	for	for	ADP
ejpam-3852	188	11	all	all	DET
ejpam-3852	188	12	n	n	PRON
ejpam-3852	188	13	≥	≥	NOUN
ejpam-3852	188	14	0	0	NUM
ejpam-3852	188	15	,	,	PUNCT
ejpam-3852	188	16	that	that	ADV
ejpam-3852	188	17	is	is	ADV
ejpam-3852	188	18	,	,	PUNCT
ejpam-3852	188	19	yn	yn	PROPN
ejpam-3852	188	20	is	be	AUX
ejpam-3852	188	21	odd	odd	ADJ
ejpam-3852	188	22	under	under	ADP
ejpam-3852	188	23	these	these	DET
ejpam-3852	188	24	assumptions	assumption	NOUN
ejpam-3852	188	25	.	.	PUNCT
ejpam-3852	189	1	now	now	ADV
ejpam-3852	189	2	,	,	PUNCT
ejpam-3852	189	3	y0	y0	PROPN
ejpam-3852	189	4	and	and	CCONJ
ejpam-3852	189	5	y1	y1	NOUN
ejpam-3852	189	6	are	be	AUX
ejpam-3852	189	7	odd	odd	ADJ
ejpam-3852	189	8	.	.	PUNCT
ejpam-3852	190	1	suppose	suppose	VERB
ejpam-3852	190	2	that	that	SCONJ
ejpam-3852	190	3	yn	yn	PROPN
ejpam-3852	190	4	is	be	AUX
ejpam-3852	190	5	odd	odd	ADJ
ejpam-3852	190	6	.	.	PUNCT
ejpam-3852	191	1	then	then	ADV
ejpam-3852	191	2	,	,	PUNCT
ejpam-3852	191	3	yn+2	yn+2	PROPN
ejpam-3852	191	4	=	=	PUNCT
ejpam-3852	191	5	ay−1n+1	ay−1n+1	PROPN
ejpam-3852	192	1	+	+	CCONJ
ejpam-3852	192	2	byn	byn	PROPN
ejpam-3852	192	3	+	+	CCONJ
ejpam-3852	192	4	c	c	PROPN
ejpam-3852	192	5	≡	≡	PROPN
ejpam-3852	192	6	yn	yn	PROPN
ejpam-3852	192	7	≡	≡	PROPN
ejpam-3852	192	8	1	1	NUM
ejpam-3852	192	9	(	(	PUNCT
ejpam-3852	192	10	mod	mod	NOUN
ejpam-3852	192	11	2	2	NUM
ejpam-3852	192	12	)	)	PUNCT
ejpam-3852	192	13	.	.	PUNCT
ejpam-3852	193	1	we	we	PRON
ejpam-3852	193	2	will	will	AUX
ejpam-3852	193	3	now	now	ADV
ejpam-3852	193	4	prove	prove	VERB
ejpam-3852	193	5	that	that	SCONJ
ejpam-3852	193	6	the	the	DET
ejpam-3852	193	7	period	period	NOUN
ejpam-3852	193	8	is	be	AUX
ejpam-3852	193	9	m	m	PRON
ejpam-3852	193	10	.	.	PUNCT
ejpam-3852	194	1	we	we	PRON
ejpam-3852	194	2	first	first	ADV
ejpam-3852	194	3	rewrite	rewrite	VERB
ejpam-3852	194	4	the	the	DET
ejpam-3852	194	5	sequence	sequence	NOUN
ejpam-3852	194	6	(	(	PUNCT
ejpam-3852	194	7	5	5	NUM
ejpam-3852	194	8	)	)	PUNCT
ejpam-3852	194	9	as	as	ADP
ejpam-3852	194	10	yn+2	yn+2	PROPN
ejpam-3852	194	11	≡	≡	PROPN
ejpam-3852	194	12	(	(	PUNCT
ejpam-3852	194	13	a+	a+	PUNCT
ejpam-3852	194	14	b)yn	b)yn	PROPN
ejpam-3852	194	15	+	+	NUM
ejpam-3852	194	16	cyn+1	cyn+1	PROPN
ejpam-3852	194	17	+	+	CCONJ
ejpam-3852	194	18	αn	αn	NOUN
ejpam-3852	194	19	(	(	PUNCT
ejpam-3852	194	20	mod	mod	PROPN
ejpam-3852	194	21	m	m	PROPN
ejpam-3852	194	22	)	)	PUNCT
ejpam-3852	194	23	where	where	SCONJ
ejpam-3852	194	24	αn	αn	NOUN
ejpam-3852	194	25	=	=	SYM
ejpam-3852	194	26	a(y−1n+1	a(y−1n+1	PROPN
ejpam-3852	194	27	−	−	PROPN
ejpam-3852	194	28	yn	yn	SYM
ejpam-3852	194	29	)	)	PUNCT
ejpam-3852	194	30	+	+	NUM
ejpam-3852	194	31	c(1−	c(1−	NOUN
ejpam-3852	194	32	yn+1	yn+1	NUM
ejpam-3852	194	33	)	)	PUNCT
ejpam-3852	194	34	.	.	PUNCT
ejpam-3852	195	1	so	so	ADV
ejpam-3852	195	2	,	,	PUNCT
ejpam-3852	195	3	(	(	PUNCT
ejpam-3852	195	4	yn	yn	X
ejpam-3852	195	5	yn+1	yn+1	PROPN
ejpam-3852	195	6	)	)	PUNCT
ejpam-3852	195	7	≡	≡	PROPN
ejpam-3852	195	8	a	a	DET
ejpam-3852	195	9	(	(	PUNCT
ejpam-3852	195	10	yn−1	yn−1	PROPN
ejpam-3852	195	11	yn	yn	PROPN
ejpam-3852	195	12	)	)	PUNCT
ejpam-3852	196	1	+	+	CCONJ
ejpam-3852	196	2	(	(	PUNCT
ejpam-3852	196	3	0	0	NUM
ejpam-3852	196	4	αn−1	αn−1	ADJ
ejpam-3852	196	5	)	)	PUNCT
ejpam-3852	196	6	(	(	PUNCT
ejpam-3852	196	7	mod	mod	PROPN
ejpam-3852	196	8	m	m	PROPN
ejpam-3852	196	9	)	)	PUNCT
ejpam-3852	196	10	where	where	SCONJ
ejpam-3852	196	11	a	a	PRON
ejpam-3852	196	12	=	=	X
ejpam-3852	196	13	(	(	PUNCT
ejpam-3852	196	14	0	0	NUM
ejpam-3852	196	15	1	1	NUM
ejpam-3852	196	16	a+	a+	PRON
ejpam-3852	196	17	b	b	PROPN
ejpam-3852	196	18	c	c	PROPN
ejpam-3852	196	19	)	)	PUNCT
ejpam-3852	196	20	.	.	PUNCT
ejpam-3852	197	1	thus	thus	ADV
ejpam-3852	197	2	,	,	PUNCT
ejpam-3852	197	3	we	we	PRON
ejpam-3852	197	4	have	have	VERB
ejpam-3852	197	5	,	,	PUNCT
ejpam-3852	197	6	(	(	PUNCT
ejpam-3852	197	7	yn	yn	X
ejpam-3852	197	8	yn+1	yn+1	PROPN
ejpam-3852	197	9	)	)	PUNCT
ejpam-3852	197	10	≡	≡	PROPN
ejpam-3852	197	11	an	an	DET
ejpam-3852	197	12	(	(	PUNCT
ejpam-3852	197	13	y0	y0	PROPN
ejpam-3852	197	14	y1	y1	NOUN
ejpam-3852	197	15	)	)	PUNCT
ejpam-3852	198	1	+	+	PROPN
ejpam-3852	198	2	rn	rn	PROPN
ejpam-3852	198	3	(	(	PUNCT
ejpam-3852	198	4	mod	mod	PROPN
ejpam-3852	198	5	m	m	PROPN
ejpam-3852	198	6	)	)	PUNCT
ejpam-3852	198	7	(	(	PUNCT
ejpam-3852	198	8	6	6	NUM
ejpam-3852	198	9	)	)	PUNCT
ejpam-3852	198	10	where	where	SCONJ
ejpam-3852	198	11	rn	rn	PROPN
ejpam-3852	198	12	=	=	PROPN
ejpam-3852	198	13	n−1∑	n−1∑	PROPN
ejpam-3852	198	14	i=0	i=0	PROPN
ejpam-3852	198	15	ai	ai	VERB
ejpam-3852	198	16	(	(	PUNCT
ejpam-3852	198	17	0	0	NUM
ejpam-3852	198	18	αn−1−i	αn−1−i	NOUN
ejpam-3852	198	19	)	)	PUNCT
ejpam-3852	198	20	.	.	PUNCT
ejpam-3852	199	1	taking	take	VERB
ejpam-3852	199	2	into	into	ADP
ejpam-3852	199	3	account	account	NOUN
ejpam-3852	199	4	the	the	DET
ejpam-3852	199	5	fact	fact	NOUN
ejpam-3852	199	6	that	that	SCONJ
ejpam-3852	199	7	a+	a+	PRON
ejpam-3852	199	8	b	b	X
ejpam-3852	199	9	≡	≡	PROPN
ejpam-3852	199	10	1	1	NUM
ejpam-3852	199	11	(	(	PUNCT
ejpam-3852	199	12	mod	mod	NOUN
ejpam-3852	199	13	4	4	NUM
ejpam-3852	199	14	)	)	PUNCT
ejpam-3852	199	15	and	and	CCONJ
ejpam-3852	199	16	c	c	PROPN
ejpam-3852	199	17	≡	≡	PROPN
ejpam-3852	199	18	2	2	NUM
ejpam-3852	199	19	(	(	PUNCT
ejpam-3852	199	20	mod	mod	NOUN
ejpam-3852	199	21	4	4	NUM
ejpam-3852	199	22	)	)	PUNCT
ejpam-3852	199	23	,	,	PUNCT
ejpam-3852	199	24	from	from	ADP
ejpam-3852	199	25	[	[	X
ejpam-3852	199	26	16	16	NUM
ejpam-3852	199	27	]	]	PUNCT
ejpam-3852	199	28	or	or	CCONJ
ejpam-3852	199	29	[	[	X
ejpam-3852	199	30	19	19	NUM
ejpam-3852	199	31	,	,	PUNCT
ejpam-3852	199	32	p.188	p.188	X
ejpam-3852	199	33	]	]	X
ejpam-3852	199	34	we	we	PRON
ejpam-3852	199	35	have	have	AUX
ejpam-3852	199	36	for	for	ADP
ejpam-3852	199	37	m	m	PROPN
ejpam-3852	199	38	=	=	NOUN
ejpam-3852	199	39	2h	2h	NUM
ejpam-3852	199	40	,	,	PUNCT
ejpam-3852	199	41	h	h	NOUN
ejpam-3852	199	42	≥	≥	NOUN
ejpam-3852	199	43	2	2	NUM
ejpam-3852	199	44	,	,	PUNCT
ejpam-3852	199	45	am	be	AUX
ejpam-3852	199	46	≡	≡	PROPN
ejpam-3852	199	47	(	(	PUNCT
ejpam-3852	199	48	2mp+m+	2mp+m+	X
ejpam-3852	199	49	1	1	NUM
ejpam-3852	199	50	2mq	2mq	NOUN
ejpam-3852	199	51	+	+	CCONJ
ejpam-3852	199	52	3	3	NUM
ejpam-3852	199	53	m	m	NOUN
ejpam-3852	199	54	2mq	2mq	NOUN
ejpam-3852	200	1	+	+	CCONJ
ejpam-3852	200	2	3	3	NUM
ejpam-3852	200	3	m	m	NOUN
ejpam-3852	200	4	2mp+	2mp+	NUM
ejpam-3852	200	5	3m+	3m+	NUM
ejpam-3852	200	6	1	1	NUM
ejpam-3852	200	7	)	)	PUNCT
ejpam-3852	200	8	(	(	PUNCT
ejpam-3852	200	9	mod	mod	PROPN
ejpam-3852	200	10	4	4	NUM
ejpam-3852	200	11	m	m	NOUN
ejpam-3852	200	12	)	)	PUNCT
ejpam-3852	200	13	(	(	PUNCT
ejpam-3852	200	14	7	7	X
ejpam-3852	200	15	)	)	PUNCT
ejpam-3852	200	16	for	for	ADP
ejpam-3852	200	17	some	some	DET
ejpam-3852	200	18	integers	integer	NOUN
ejpam-3852	200	19	p	p	NOUN
ejpam-3852	200	20	and	and	CCONJ
ejpam-3852	200	21	q.	q.	PROPN
ejpam-3852	200	22	first	first	ADV
ejpam-3852	200	23	,	,	PUNCT
ejpam-3852	200	24	we	we	PRON
ejpam-3852	200	25	will	will	AUX
ejpam-3852	200	26	show	show	VERB
ejpam-3852	200	27	that	that	SCONJ
ejpam-3852	200	28	for	for	ADP
ejpam-3852	200	29	m	m	PROPN
ejpam-3852	200	30	=	=	NOUN
ejpam-3852	200	31	2h	2h	NUM
ejpam-3852	200	32	,	,	PUNCT
ejpam-3852	200	33	2	2	NUM
ejpam-3852	200	34	≤	≤	NUM
ejpam-3852	200	35	h	h	NOUN
ejpam-3852	200	36	≤	≤	NOUN
ejpam-3852	200	37	ω	ω	NUM
ejpam-3852	200	38	−	−	PROPN
ejpam-3852	200	39	1	1	NUM
ejpam-3852	200	40	,	,	PUNCT
ejpam-3852	200	41	rm	rm	PROPN
ejpam-3852	200	42	≡	≡	PROPN
ejpam-3852	200	43	(	(	PUNCT
ejpam-3852	200	44	m	m	VERB
ejpam-3852	200	45	m	m	VERB
ejpam-3852	200	46	)	)	PUNCT
ejpam-3852	200	47	(	(	PUNCT
ejpam-3852	200	48	mod	mod	PROPN
ejpam-3852	200	49	2	2	NUM
ejpam-3852	200	50	m	m	NOUN
ejpam-3852	200	51	)	)	PUNCT
ejpam-3852	200	52	.	.	PUNCT
ejpam-3852	201	1	(	(	PUNCT
ejpam-3852	201	2	8)	8)	NUM
ejpam-3852	201	3	p.	p.	NOUN
ejpam-3852	201	4	stănică	stănică	NUM
ejpam-3852	201	5	et	et	NOUN
ejpam-3852	201	6	al	al	PROPN
ejpam-3852	201	7	.	.	PUNCT
ejpam-3852	201	8	/	/	SYM
ejpam-3852	201	9	eur	eur	PROPN
ejpam-3852	201	10	.	.	PUNCT
ejpam-3852	202	1	j.	j.	PROPN
ejpam-3852	202	2	pure	pure	PROPN
ejpam-3852	202	3	appl	appl	PROPN
ejpam-3852	202	4	.	.	PROPN
ejpam-3852	202	5	math	math	PROPN
ejpam-3852	202	6	,	,	PUNCT
ejpam-3852	202	7	14	14	NUM
ejpam-3852	202	8	(	(	PUNCT
ejpam-3852	202	9	1	1	NUM
ejpam-3852	202	10	)	)	PUNCT
ejpam-3852	202	11	(	(	PUNCT
ejpam-3852	202	12	2021	2021	NUM
ejpam-3852	202	13	)	)	PUNCT
ejpam-3852	202	14	,	,	PUNCT
ejpam-3852	202	15	1	1	NUM
ejpam-3852	202	16	-	-	SYM
ejpam-3852	202	17	18	18	NUM
ejpam-3852	202	18	7	7	NUM
ejpam-3852	202	19	it	it	PRON
ejpam-3852	202	20	can	can	AUX
ejpam-3852	202	21	be	be	AUX
ejpam-3852	202	22	checked	check	VERB
ejpam-3852	202	23	(	(	PUNCT
ejpam-3852	202	24	tediously	tediously	ADV
ejpam-3852	202	25	by	by	ADP
ejpam-3852	202	26	hand	hand	NOUN
ejpam-3852	202	27	,	,	PUNCT
ejpam-3852	202	28	but	but	CCONJ
ejpam-3852	202	29	computationally	computationally	ADV
ejpam-3852	202	30	easily	easily	ADV
ejpam-3852	202	31	)	)	PUNCT
ejpam-3852	202	32	that	that	SCONJ
ejpam-3852	202	33	(	(	PUNCT
ejpam-3852	202	34	8)	8)	NUM
ejpam-3852	202	35	holds	hold	VERB
ejpam-3852	202	36	for	for	ADP
ejpam-3852	202	37	m	m	NOUN
ejpam-3852	202	38	=	=	SYM
ejpam-3852	202	39	4	4	NUM
ejpam-3852	202	40	(	(	PUNCT
ejpam-3852	202	41	i.e.	i.e.	X
ejpam-3852	202	42	,	,	PUNCT
ejpam-3852	202	43	h	h	NOUN
ejpam-3852	202	44	=	=	NOUN
ejpam-3852	202	45	2	2	NUM
ejpam-3852	202	46	)	)	PUNCT
ejpam-3852	202	47	.	.	PUNCT
ejpam-3852	203	1	now	now	ADV
ejpam-3852	203	2	,	,	PUNCT
ejpam-3852	203	3	let	let	VERB
ejpam-3852	203	4	us	we	PRON
ejpam-3852	203	5	assume	assume	VERB
ejpam-3852	203	6	that	that	SCONJ
ejpam-3852	203	7	it	it	PRON
ejpam-3852	203	8	holds	hold	VERB
ejpam-3852	203	9	for	for	ADP
ejpam-3852	203	10	m	m	PROPN
ejpam-3852	203	11	=	=	NOUN
ejpam-3852	203	12	2h	2h	NUM
ejpam-3852	203	13	.	.	PUNCT
ejpam-3852	204	1	then	then	ADV
ejpam-3852	204	2	,	,	PUNCT
ejpam-3852	204	3	from	from	ADP
ejpam-3852	204	4	this	this	DET
ejpam-3852	204	5	hypothesis	hypothesis	NOUN
ejpam-3852	204	6	,	,	PUNCT
ejpam-3852	204	7	(	(	PUNCT
ejpam-3852	204	8	6	6	NUM
ejpam-3852	204	9	)	)	PUNCT
ejpam-3852	204	10	and	and	CCONJ
ejpam-3852	204	11	(	(	PUNCT
ejpam-3852	204	12	7	7	NUM
ejpam-3852	204	13	)	)	PUNCT
ejpam-3852	204	14	,	,	PUNCT
ejpam-3852	204	15	and	and	CCONJ
ejpam-3852	204	16	using	use	VERB
ejpam-3852	204	17	the	the	DET
ejpam-3852	204	18	fact	fact	NOUN
ejpam-3852	204	19	that	that	SCONJ
ejpam-3852	204	20	yi	yi	PROPN
ejpam-3852	204	21	’s	’s	PART
ejpam-3852	204	22	are	be	AUX
ejpam-3852	204	23	odd	odd	ADJ
ejpam-3852	204	24	,	,	PUNCT
ejpam-3852	204	25	we	we	PRON
ejpam-3852	204	26	have	have	VERB
ejpam-3852	204	27	,	,	PUNCT
ejpam-3852	204	28	ym	ym	PROPN
ejpam-3852	204	29	≡	≡	PROPN
ejpam-3852	204	30	y0	y0	PROPN
ejpam-3852	204	31	+	+	CCONJ
ejpam-3852	204	32	2m(py0	2m(py0	NUM
ejpam-3852	204	33	+	+	CCONJ
ejpam-3852	204	34	qy1	qy1	PROPN
ejpam-3852	204	35	)	)	PUNCT
ejpam-3852	205	1	+	+	ADP
ejpam-3852	205	2	m(y0	m(y0	NOUN
ejpam-3852	205	3	+	+	X
ejpam-3852	205	4	3y1	3y1	NUM
ejpam-3852	205	5	)	)	PUNCT
ejpam-3852	205	6	+	+	CCONJ
ejpam-3852	206	1	4mt0	4mt0	NUM
ejpam-3852	207	1	+	+	ADJ
ejpam-3852	207	2	m+	m+	NOUN
ejpam-3852	207	3	2ms0	2ms0	NUM
ejpam-3852	207	4	=	=	PUNCT
ejpam-3852	208	1	y0	y0	NOUN
ejpam-3852	208	2	+	+	NOUN
ejpam-3852	208	3	m+	m+	NOUN
ejpam-3852	208	4	2mu0	2mu0	NUM
ejpam-3852	208	5	(	(	PUNCT
ejpam-3852	208	6	mod	mod	PROPN
ejpam-3852	208	7	m	m	PROPN
ejpam-3852	208	8	)	)	PUNCT
ejpam-3852	208	9	,	,	PUNCT
ejpam-3852	208	10	ym+1	ym+1	PROPN
ejpam-3852	208	11	≡	≡	PROPN
ejpam-3852	208	12	y1	y1	PROPN
ejpam-3852	208	13	+	+	NUM
ejpam-3852	208	14	2m(qy0	2m(qy0	NUM
ejpam-3852	208	15	+	+	NUM
ejpam-3852	208	16	py1	py1	NOUN
ejpam-3852	208	17	)	)	PUNCT
ejpam-3852	209	1	+	+	CCONJ
ejpam-3852	210	1	3m(y0	3m(y0	NUM
ejpam-3852	210	2	+	+	CCONJ
ejpam-3852	210	3	y1	y1	NOUN
ejpam-3852	210	4	)	)	PUNCT
ejpam-3852	210	5	+	+	CCONJ
ejpam-3852	210	6	4mt1	4mt1	NUM
ejpam-3852	210	7	+	+	ADJ
ejpam-3852	210	8	m+	m+	NOUN
ejpam-3852	210	9	2ms1	2ms1	NUM
ejpam-3852	210	10	=	=	NOUN
ejpam-3852	210	11	y1	y1	INTJ
ejpam-3852	210	12	+	+	NOUN
ejpam-3852	210	13	m+	m+	NOUN
ejpam-3852	210	14	2mu1	2mu1	NUM
ejpam-3852	210	15	(	(	PUNCT
ejpam-3852	210	16	mod	mod	PROPN
ejpam-3852	210	17	m	m	PROPN
ejpam-3852	210	18	)	)	PUNCT
ejpam-3852	210	19	,	,	PUNCT
ejpam-3852	210	20	for	for	ADP
ejpam-3852	210	21	some	some	DET
ejpam-3852	210	22	integers	integer	NOUN
ejpam-3852	210	23	t0	t0	NOUN
ejpam-3852	210	24	,	,	PUNCT
ejpam-3852	210	25	t1	t1	NOUN
ejpam-3852	210	26	,	,	PUNCT
ejpam-3852	210	27	s0	s0	PROPN
ejpam-3852	210	28	,	,	PUNCT
ejpam-3852	210	29	s1	s1	NOUN
ejpam-3852	210	30	,	,	PUNCT
ejpam-3852	210	31	u0	u0	ADJ
ejpam-3852	210	32	and	and	CCONJ
ejpam-3852	210	33	u1	u1	NOUN
ejpam-3852	210	34	.	.	PUNCT
ejpam-3852	211	1	now	now	ADV
ejpam-3852	211	2	,	,	PUNCT
ejpam-3852	211	3	it	it	PRON
ejpam-3852	211	4	follows	follow	VERB
ejpam-3852	211	5	clearly	clearly	ADV
ejpam-3852	211	6	from	from	ADP
ejpam-3852	211	7	above	above	ADP
ejpam-3852	211	8	that	that	PRON
ejpam-3852	212	1	y−1	y−1	PROPN
ejpam-3852	212	2	m	m	PROPN
ejpam-3852	212	3	≡	≡	PROPN
ejpam-3852	212	4	y−10	y−10	PROPN
ejpam-3852	213	1	+	+	NOUN
ejpam-3852	213	2	m+	m+	NOUN
ejpam-3852	213	3	2mv0	2mv0	NUM
ejpam-3852	213	4	and	and	CCONJ
ejpam-3852	213	5	y−1m+1	y−1m+1	PROPN
ejpam-3852	213	6	=	=	SYM
ejpam-3852	213	7	y−11	y−11	X
ejpam-3852	213	8	+	+	NOUN
ejpam-3852	213	9	m+	m+	NUM
ejpam-3852	213	10	2mv1	2mv1	NUM
ejpam-3852	213	11	(	(	PUNCT
ejpam-3852	213	12	mod	mod	PROPN
ejpam-3852	213	13	m	m	PROPN
ejpam-3852	213	14	)	)	PUNCT
ejpam-3852	213	15	,	,	PUNCT
ejpam-3852	214	1	for	for	ADP
ejpam-3852	214	2	some	some	DET
ejpam-3852	214	3	integers	integer	NOUN
ejpam-3852	214	4	v0	v0	NOUN
ejpam-3852	214	5	and	and	CCONJ
ejpam-3852	214	6	v1	v1	PROPN
ejpam-3852	214	7	(	(	PUNCT
ejpam-3852	214	8	inverses	inverse	NOUN
ejpam-3852	214	9	are	be	AUX
ejpam-3852	214	10	considered	consider	VERB
ejpam-3852	214	11	in	in	ADP
ejpam-3852	214	12	zm	zm	PROPN
ejpam-3852	214	13	)	)	PUNCT
ejpam-3852	214	14	.	.	PUNCT
ejpam-3852	215	1	then	then	ADV
ejpam-3852	215	2	,	,	PUNCT
ejpam-3852	215	3	as	as	SCONJ
ejpam-3852	215	4	a	a	PRON
ejpam-3852	215	5	is	be	AUX
ejpam-3852	215	6	even	even	ADV
ejpam-3852	215	7	and	and	CCONJ
ejpam-3852	215	8	c	c	PROPN
ejpam-3852	215	9	≡	≡	PROPN
ejpam-3852	215	10	2	2	NUM
ejpam-3852	215	11	(	(	PUNCT
ejpam-3852	215	12	mod	mod	NOUN
ejpam-3852	215	13	4	4	NUM
ejpam-3852	215	14	)	)	PUNCT
ejpam-3852	215	15	,	,	PUNCT
ejpam-3852	215	16	we	we	PRON
ejpam-3852	215	17	get	get	VERB
ejpam-3852	215	18	from	from	ADP
ejpam-3852	215	19	above	above	ADP
ejpam-3852	215	20	that	that	DET
ejpam-3852	215	21	αm	αm	NOUN
ejpam-3852	216	1	=	=	PUNCT
ejpam-3852	216	2	a(y−1m+1	a(y−1m+1	PROPN
ejpam-3852	216	3	−	−	PROPN
ejpam-3852	216	4	ym	ym	PROPN
ejpam-3852	216	5	)	)	PUNCT
ejpam-3852	216	6	+	+	NUM
ejpam-3852	216	7	c(1−	c(1−	NOUN
ejpam-3852	216	8	ym+1	ym+1	X
ejpam-3852	216	9	)	)	PUNCT
ejpam-3852	216	10	≡	≡	PROPN
ejpam-3852	216	11	a(y−11	a(y−11	X
ejpam-3852	217	1	+	+	NOUN
ejpam-3852	217	2	m+	m+	NOUN
ejpam-3852	217	3	2mv1	2mv1	NUM
ejpam-3852	217	4	−	−	NOUN
ejpam-3852	217	5	y0	y0	NOUN
ejpam-3852	217	6	−m−	−m−	NOUN
ejpam-3852	217	7	2mu0	2mu0	NUM
ejpam-3852	217	8	)	)	PUNCT
ejpam-3852	218	1	+	+	NUM
ejpam-3852	218	2	c(1−	c(1−	NOUN
ejpam-3852	218	3	y1	y1	NOUN
ejpam-3852	218	4	−m−	−m−	NOUN
ejpam-3852	218	5	2mu1	2mu1	NUM
ejpam-3852	218	6	)	)	PUNCT
ejpam-3852	218	7	≡	≡	PROPN
ejpam-3852	218	8	a(y−11	a(y−11	PART
ejpam-3852	218	9	−	−	PROPN
ejpam-3852	218	10	y0	y0	NUM
ejpam-3852	218	11	)	)	PUNCT
ejpam-3852	218	12	+	+	NUM
ejpam-3852	218	13	c(1−	c(1−	NOUN
ejpam-3852	218	14	y1	y1	NOUN
ejpam-3852	218	15	)	)	PUNCT
ejpam-3852	218	16	+	+	CCONJ
ejpam-3852	218	17	2am(v1	2am(v1	NUM
ejpam-3852	218	18	−	−	NOUN
ejpam-3852	218	19	u0)−mc−	u0)−mc−	PRON
ejpam-3852	218	20	2mcu1	2mcu1	NUM
ejpam-3852	218	21	≡	≡	PROPN
ejpam-3852	218	22	α0	α0	ADJ
ejpam-3852	218	23	+	+	CCONJ
ejpam-3852	218	24	2m+	2m+	NUM
ejpam-3852	218	25	4mw0	4mw0	NUM
ejpam-3852	218	26	(	(	PUNCT
ejpam-3852	218	27	mod	mod	PROPN
ejpam-3852	218	28	m	m	PROPN
ejpam-3852	218	29	)	)	PUNCT
ejpam-3852	218	30	,	,	PUNCT
ejpam-3852	218	31	for	for	ADP
ejpam-3852	218	32	some	some	DET
ejpam-3852	218	33	integer	integer	NOUN
ejpam-3852	218	34	w0	w0	PROPN
ejpam-3852	218	35	.	.	PUNCT
ejpam-3852	219	1	so	so	ADV
ejpam-3852	219	2	,	,	PUNCT
ejpam-3852	219	3	as	as	ADP
ejpam-3852	219	4	a+	a+	PRON
ejpam-3852	219	5	b	b	PROPN
ejpam-3852	219	6	≡	≡	PROPN
ejpam-3852	219	7	1	1	NUM
ejpam-3852	219	8	(	(	PUNCT
ejpam-3852	219	9	mod	mod	NOUN
ejpam-3852	219	10	4	4	NUM
ejpam-3852	219	11	)	)	PUNCT
ejpam-3852	219	12	and	and	CCONJ
ejpam-3852	219	13	c	c	PROPN
ejpam-3852	219	14	≡	≡	PROPN
ejpam-3852	219	15	2	2	NUM
ejpam-3852	219	16	(	(	PUNCT
ejpam-3852	219	17	mod	mod	NOUN
ejpam-3852	219	18	4	4	X
ejpam-3852	219	19	)	)	PUNCT
ejpam-3852	219	20	we	we	PRON
ejpam-3852	219	21	have	have	VERB
ejpam-3852	219	22	,	,	PUNCT
ejpam-3852	219	23	ym+2	ym+2	PROPN
ejpam-3852	219	24	≡	≡	PROPN
ejpam-3852	219	25	(	(	PUNCT
ejpam-3852	219	26	a+	a+	PUNCT
ejpam-3852	219	27	b)ym	b)ym	PROPN
ejpam-3852	219	28	+	+	NUM
ejpam-3852	219	29	cym+1	cym+1	PROPN
ejpam-3852	219	30	+	+	CCONJ
ejpam-3852	219	31	αm	αm	ADJ
ejpam-3852	219	32	≡	≡	PROPN
ejpam-3852	219	33	(	(	PUNCT
ejpam-3852	219	34	a+	a+	PROPN
ejpam-3852	219	35	b)y0	b)y0	PROPN
ejpam-3852	219	36	+	+	NUM
ejpam-3852	219	37	cy1	cy1	NOUN
ejpam-3852	219	38	+	+	CCONJ
ejpam-3852	219	39	α0	α0	ADJ
ejpam-3852	219	40	+	+	CCONJ
ejpam-3852	219	41	(	(	PUNCT
ejpam-3852	219	42	a+	a+	X
ejpam-3852	219	43	b)(m+	b)(m+	NOUN
ejpam-3852	219	44	2mu0	2mu0	NUM
ejpam-3852	219	45	)	)	PUNCT
ejpam-3852	220	1	+	+	CCONJ
ejpam-3852	220	2	c(m+	c(m+	NOUN
ejpam-3852	220	3	2mu1	2mu1	NUM
ejpam-3852	220	4	)	)	PUNCT
ejpam-3852	220	5	+	+	CCONJ
ejpam-3852	220	6	2m+	2m+	NUM
ejpam-3852	220	7	4mw0	4mw0	NUM
ejpam-3852	220	8	≡	≡	PROPN
ejpam-3852	220	9	y2	y2	PROPN
ejpam-3852	221	1	+	+	PROPN
ejpam-3852	221	2	m+	m+	NOUN
ejpam-3852	221	3	2mu2	2mu2	NUM
ejpam-3852	221	4	(	(	PUNCT
ejpam-3852	221	5	mod	mod	PROPN
ejpam-3852	221	6	m	m	PROPN
ejpam-3852	221	7	)	)	PUNCT
ejpam-3852	221	8	,	,	PUNCT
ejpam-3852	221	9	for	for	ADP
ejpam-3852	221	10	some	some	DET
ejpam-3852	221	11	integer	integer	NOUN
ejpam-3852	221	12	u2	u2	NOUN
ejpam-3852	221	13	.	.	PUNCT
ejpam-3852	221	14	proceeding	proceeding	NOUN
ejpam-3852	221	15	similarly	similarly	ADV
ejpam-3852	221	16	as	as	ADP
ejpam-3852	221	17	above	above	ADV
ejpam-3852	221	18	,	,	PUNCT
ejpam-3852	221	19	for	for	ADP
ejpam-3852	221	20	all	all	PRON
ejpam-3852	221	21	0	0	NUM
ejpam-3852	221	22	≤	≤	NUM
ejpam-3852	221	23	k	k	NOUN
ejpam-3852	221	24	≤	≤	ADJ
ejpam-3852	221	25	m−	m−	PROPN
ejpam-3852	221	26	1	1	NUM
ejpam-3852	221	27	,	,	PUNCT
ejpam-3852	221	28	we	we	PRON
ejpam-3852	221	29	have	have	VERB
ejpam-3852	221	30	ym+k	ym+k	PROPN
ejpam-3852	221	31	≡	≡	PROPN
ejpam-3852	221	32	yk	yk	PROPN
ejpam-3852	222	1	+	+	PROPN
ejpam-3852	222	2	m+	m+	PROPN
ejpam-3852	222	3	2muk	2muk	NUM
ejpam-3852	222	4	(	(	PUNCT
ejpam-3852	222	5	mod	mod	PROPN
ejpam-3852	222	6	m	m	PROPN
ejpam-3852	222	7	)	)	PUNCT
ejpam-3852	222	8	y−1m+k	y−1m+k	PROPN
ejpam-3852	223	1	≡	≡	PROPN
ejpam-3852	223	2	y	y	PROPN
ejpam-3852	223	3	−1	−1	PROPN
ejpam-3852	223	4	k	k	PROPN
ejpam-3852	224	1	+	+	PROPN
ejpam-3852	224	2	m+	m+	NOUN
ejpam-3852	224	3	2mvk	2mvk	PROPN
ejpam-3852	224	4	(	(	PUNCT
ejpam-3852	224	5	mod	mod	PROPN
ejpam-3852	224	6	m	m	PROPN
ejpam-3852	224	7	)	)	PUNCT
ejpam-3852	224	8	αm+k	αm+k	NUM
ejpam-3852	224	9	≡	≡	ADJ
ejpam-3852	224	10	αk	αk	CCONJ
ejpam-3852	224	11	+	+	NOUN
ejpam-3852	224	12	2m+	2m+	NUM
ejpam-3852	224	13	4mwk	4mwk	NUM
ejpam-3852	224	14	(	(	PUNCT
ejpam-3852	224	15	mod	mod	PROPN
ejpam-3852	224	16	m	m	PROPN
ejpam-3852	224	17	)	)	PUNCT
ejpam-3852	224	18	,	,	PUNCT
ejpam-3852	224	19	for	for	ADP
ejpam-3852	224	20	integers	integer	NOUN
ejpam-3852	224	21	uk	uk	PROPN
ejpam-3852	224	22	,	,	PUNCT
ejpam-3852	224	23	vk	vk	NOUN
ejpam-3852	224	24	and	and	CCONJ
ejpam-3852	224	25	wk	wk	INTJ
ejpam-3852	224	26	.	.	PUNCT
ejpam-3852	225	1	now	now	ADV
ejpam-3852	225	2	,	,	PUNCT
ejpam-3852	225	3	using	use	VERB
ejpam-3852	225	4	the	the	DET
ejpam-3852	225	5	above	above	ADJ
ejpam-3852	225	6	analysis	analysis	NOUN
ejpam-3852	225	7	,	,	PUNCT
ejpam-3852	225	8	we	we	PRON
ejpam-3852	225	9	get	get	VERB
ejpam-3852	225	10	(	(	PUNCT
ejpam-3852	225	11	we	we	PRON
ejpam-3852	225	12	let	let	VERB
ejpam-3852	225	13	i	i	PRON
ejpam-3852	225	14	be	be	AUX
ejpam-3852	225	15	the	the	DET
ejpam-3852	225	16	identity	identity	NOUN
ejpam-3852	225	17	matrix	matrix	NOUN
ejpam-3852	225	18	of	of	ADP
ejpam-3852	225	19	the	the	DET
ejpam-3852	225	20	appropriate	appropriate	ADJ
ejpam-3852	225	21	dimension	dimension	NOUN
ejpam-3852	225	22	)	)	PUNCT
ejpam-3852	225	23	,	,	PUNCT
ejpam-3852	225	24	r2	r2	PROPN
ejpam-3852	225	25	m	m	PROPN
ejpam-3852	225	26	≡	≡	PROPN
ejpam-3852	225	27	2m−1∑	2m−1∑	PROPN
ejpam-3852	226	1	i=0	i=0	PROPN
ejpam-3852	226	2	ai	ai	NOUN
ejpam-3852	226	3	(	(	PUNCT
ejpam-3852	226	4	0	0	NUM
ejpam-3852	226	5	α2m−1−i	α2m−1−i	NUM
ejpam-3852	226	6	)	)	PUNCT
ejpam-3852	226	7	(	(	PUNCT
ejpam-3852	226	8	mod	mod	PROPN
ejpam-3852	226	9	4	4	NUM
ejpam-3852	226	10	m	m	NOUN
ejpam-3852	226	11	)	)	PUNCT
ejpam-3852	226	12	≡	≡	PROPN
ejpam-3852	226	13	m−1∑	m−1∑	PROPN
ejpam-3852	226	14	i=0	i=0	PROPN
ejpam-3852	226	15	ai	ai	VERB
ejpam-3852	226	16	(	(	PUNCT
ejpam-3852	226	17	0	0	NUM
ejpam-3852	226	18	α2m−1−i	α2m−1−i	NUM
ejpam-3852	226	19	)	)	PUNCT
ejpam-3852	227	1	+	+	CCONJ
ejpam-3852	228	1	2m−1∑	2m−1∑	NUM
ejpam-3852	228	2	i	i	PRON
ejpam-3852	228	3	=	=	VERB
ejpam-3852	228	4	m	m	VERB
ejpam-3852	228	5	ai	ai	VERB
ejpam-3852	228	6	(	(	PUNCT
ejpam-3852	228	7	0	0	NUM
ejpam-3852	228	8	α2m−1−i	α2m−1−i	NUM
ejpam-3852	228	9	)	)	PUNCT
ejpam-3852	229	1	(	(	PUNCT
ejpam-3852	229	2	mod	mod	PROPN
ejpam-3852	229	3	4	4	NUM
ejpam-3852	229	4	m	m	NOUN
ejpam-3852	229	5	)	)	PUNCT
ejpam-3852	230	1	p.	p.	NOUN
ejpam-3852	230	2	stănică	stănică	NUM
ejpam-3852	230	3	et	et	PROPN
ejpam-3852	231	1	al	al	PROPN
ejpam-3852	231	2	.	.	PUNCT
ejpam-3852	231	3	/	/	SYM
ejpam-3852	231	4	eur	eur	PROPN
ejpam-3852	231	5	.	.	PUNCT
ejpam-3852	232	1	j.	j.	PROPN
ejpam-3852	232	2	pure	pure	PROPN
ejpam-3852	232	3	appl	appl	PROPN
ejpam-3852	232	4	.	.	PROPN
ejpam-3852	232	5	math	math	PROPN
ejpam-3852	232	6	,	,	PUNCT
ejpam-3852	232	7	14	14	NUM
ejpam-3852	232	8	(	(	PUNCT
ejpam-3852	232	9	1	1	NUM
ejpam-3852	232	10	)	)	PUNCT
ejpam-3852	232	11	(	(	PUNCT
ejpam-3852	232	12	2021	2021	NUM
ejpam-3852	232	13	)	)	PUNCT
ejpam-3852	232	14	,	,	PUNCT
ejpam-3852	232	15	1	1	NUM
ejpam-3852	232	16	-	-	SYM
ejpam-3852	232	17	18	18	NUM
ejpam-3852	232	18	8	8	NUM
ejpam-3852	232	19	≡	≡	PROPN
ejpam-3852	232	20	m−1∑	m−1∑	PROPN
ejpam-3852	232	21	i=0	i=0	PROPN
ejpam-3852	232	22	[	[	PUNCT
ejpam-3852	232	23	ai	ai	INTJ
ejpam-3852	232	24	(	(	PUNCT
ejpam-3852	232	25	0	0	NUM
ejpam-3852	232	26	αm−1−i	αm−1−i	NUM
ejpam-3852	232	27	)	)	PUNCT
ejpam-3852	233	1	+	+	X
ejpam-3852	233	2	ai	ai	INTJ
ejpam-3852	233	3	(	(	PUNCT
ejpam-3852	233	4	0	0	NUM
ejpam-3852	233	5	2	2	NUM
ejpam-3852	233	6	m	m	NOUN
ejpam-3852	233	7	)	)	PUNCT
ejpam-3852	233	8	]	]	PUNCT
ejpam-3852	234	1	+	+	PUNCT
ejpam-3852	234	2	am	be	AUX
ejpam-3852	234	3	m−1∑	m−1∑	PRON
ejpam-3852	234	4	i=0	i=0	PROPN
ejpam-3852	234	5	ai	ai	NOUN
ejpam-3852	234	6	(	(	PUNCT
ejpam-3852	234	7	0	0	NUM
ejpam-3852	234	8	αm−1−i	αm−1−i	NOUN
ejpam-3852	234	9	)	)	PUNCT
ejpam-3852	234	10	(	(	PUNCT
ejpam-3852	234	11	mod	mod	PROPN
ejpam-3852	234	12	4	4	NUM
ejpam-3852	234	13	m	m	NOUN
ejpam-3852	234	14	)	)	PUNCT
ejpam-3852	234	15	≡	≡	PROPN
ejpam-3852	234	16	(	(	PUNCT
ejpam-3852	234	17	i	i	PRON
ejpam-3852	234	18	+	+	NOUN
ejpam-3852	234	19	am)rm	am)rm	ADJ
ejpam-3852	234	20	+	+	NUM
ejpam-3852	234	21	2	2	NUM
ejpam-3852	234	22	m	m	NOUN
ejpam-3852	234	23	m−1∑	m−1∑	PROPN
ejpam-3852	234	24	i=0	i=0	PROPN
ejpam-3852	234	25	ai	ai	NOUN
ejpam-3852	234	26	(	(	PUNCT
ejpam-3852	234	27	0	0	NUM
ejpam-3852	234	28	1	1	NUM
ejpam-3852	234	29	)	)	PUNCT
ejpam-3852	234	30	(	(	PUNCT
ejpam-3852	234	31	mod	mod	PROPN
ejpam-3852	234	32	4	4	NUM
ejpam-3852	234	33	m	m	NOUN
ejpam-3852	234	34	)	)	PUNCT
ejpam-3852	234	35	≡	≡	PROPN
ejpam-3852	235	1	(	(	PUNCT
ejpam-3852	235	2	i	i	PRON
ejpam-3852	235	3	+	+	VERB
ejpam-3852	235	4	am	be	AUX
ejpam-3852	235	5	2	2	NUM
ejpam-3852	235	6	)	)	PUNCT
ejpam-3852	235	7	2rm	2rm	NOUN
ejpam-3852	236	1	+	+	PUNCT
ejpam-3852	236	2	2	2	NUM
ejpam-3852	236	3	m	m	NOUN
ejpam-3852	236	4	m−1∑	m−1∑	PROPN
ejpam-3852	236	5	i=0	i=0	PROPN
ejpam-3852	236	6	ai	ai	NOUN
ejpam-3852	236	7	(	(	PUNCT
ejpam-3852	236	8	0	0	NUM
ejpam-3852	236	9	1	1	NUM
ejpam-3852	236	10	)	)	PUNCT
ejpam-3852	236	11	(	(	PUNCT
ejpam-3852	236	12	mod	mod	PROPN
ejpam-3852	236	13	4	4	NUM
ejpam-3852	236	14	m	m	NOUN
ejpam-3852	236	15	)	)	PUNCT
ejpam-3852	236	16	≡	≡	PROPN
ejpam-3852	236	17	(	(	PUNCT
ejpam-3852	236	18	i	i	PRON
ejpam-3852	236	19	+	+	VERB
ejpam-3852	236	20	am	be	AUX
ejpam-3852	236	21	2	2	NUM
ejpam-3852	236	22	)	)	PUNCT
ejpam-3852	236	23	(	(	PUNCT
ejpam-3852	236	24	2	2	NUM
ejpam-3852	236	25	m	m	NOUN
ejpam-3852	236	26	2	2	NUM
ejpam-3852	236	27	m	m	NOUN
ejpam-3852	236	28	)	)	PUNCT
ejpam-3852	237	1	+	+	CCONJ
ejpam-3852	237	2	2	2	NUM
ejpam-3852	237	3	m	m	NOUN
ejpam-3852	237	4	m−1∑	m−1∑	PROPN
ejpam-3852	237	5	i=0	i=0	PROPN
ejpam-3852	237	6	ai	ai	NOUN
ejpam-3852	237	7	(	(	PUNCT
ejpam-3852	237	8	0	0	NUM
ejpam-3852	237	9	1	1	NUM
ejpam-3852	237	10	)	)	PUNCT
ejpam-3852	237	11	(	(	PUNCT
ejpam-3852	237	12	mod	mod	PROPN
ejpam-3852	237	13	4	4	NUM
ejpam-3852	237	14	m	m	NOUN
ejpam-3852	237	15	)	)	PUNCT
ejpam-3852	237	16	≡	≡	PROPN
ejpam-3852	237	17	(	(	PUNCT
ejpam-3852	237	18	2	2	NUM
ejpam-3852	237	19	m	m	NOUN
ejpam-3852	237	20	2	2	NUM
ejpam-3852	237	21	m	m	NOUN
ejpam-3852	237	22	)	)	PUNCT
ejpam-3852	238	1	+	+	CCONJ
ejpam-3852	238	2	2	2	NUM
ejpam-3852	238	3	m	m	NOUN
ejpam-3852	238	4	m−1∑	m−1∑	PROPN
ejpam-3852	238	5	i=0	i=0	PROPN
ejpam-3852	238	6	ai	ai	NOUN
ejpam-3852	238	7	(	(	PUNCT
ejpam-3852	238	8	0	0	NUM
ejpam-3852	238	9	1	1	NUM
ejpam-3852	238	10	)	)	PUNCT
ejpam-3852	238	11	(	(	PUNCT
ejpam-3852	238	12	mod	mod	PROPN
ejpam-3852	238	13	4	4	NUM
ejpam-3852	238	14	m	m	NOUN
ejpam-3852	238	15	)	)	PUNCT
ejpam-3852	238	16	≡	≡	PROPN
ejpam-3852	238	17	(	(	PUNCT
ejpam-3852	238	18	2	2	NUM
ejpam-3852	238	19	m	m	NOUN
ejpam-3852	238	20	2	2	NUM
ejpam-3852	238	21	m	m	NOUN
ejpam-3852	238	22	)	)	PUNCT
ejpam-3852	239	1	(	(	PUNCT
ejpam-3852	239	2	mod	mod	PROPN
ejpam-3852	239	3	4	4	NUM
ejpam-3852	239	4	m	m	NOUN
ejpam-3852	239	5	)	)	PUNCT
ejpam-3852	240	1	[	[	PUNCT
ejpam-3852	240	2	∵	∵	INTJ
ejpam-3852	240	3	m−1∑	m−1∑	PROPN
ejpam-3852	240	4	i=0	i=0	PROPN
ejpam-3852	240	5	ai	ai	NOUN
ejpam-3852	240	6	(	(	PUNCT
ejpam-3852	240	7	0	0	NUM
ejpam-3852	240	8	1	1	NUM
ejpam-3852	240	9	)	)	PUNCT
ejpam-3852	240	10	≡	≡	PROPN
ejpam-3852	240	11	0	0	PUNCT
ejpam-3852	241	1	(	(	PUNCT
ejpam-3852	241	2	mod	mod	NOUN
ejpam-3852	241	3	2	2	NUM
ejpam-3852	241	4	)	)	PUNCT
ejpam-3852	241	5	,	,	PUNCT
ejpam-3852	241	6	i.e.	i.e.	X
ejpam-3852	241	7	,	,	PUNCT
ejpam-3852	241	8	m−1∑	m−1∑	PROPN
ejpam-3852	241	9	i=0	i=0	PROPN
ejpam-3852	241	10	ai	ai	NOUN
ejpam-3852	241	11	(	(	PUNCT
ejpam-3852	241	12	0	0	NUM
ejpam-3852	241	13	1	1	NUM
ejpam-3852	241	14	)	)	PUNCT
ejpam-3852	241	15	is	be	AUX
ejpam-3852	241	16	even	even	ADV
ejpam-3852	241	17	]	]	PUNCT
ejpam-3852	241	18	.	.	PUNCT
ejpam-3852	242	1	therefore	therefore	ADV
ejpam-3852	242	2	,	,	PUNCT
ejpam-3852	242	3	(	(	PUNCT
ejpam-3852	242	4	8)	8)	NUM
ejpam-3852	242	5	follows	follow	VERB
ejpam-3852	242	6	by	by	ADP
ejpam-3852	242	7	induction	induction	NOUN
ejpam-3852	242	8	.	.	PUNCT
ejpam-3852	243	1	so	so	ADV
ejpam-3852	243	2	,	,	PUNCT
ejpam-3852	243	3	by	by	ADP
ejpam-3852	243	4	the	the	DET
ejpam-3852	243	5	previous	previous	ADJ
ejpam-3852	243	6	arguments	argument	NOUN
ejpam-3852	243	7	,	,	PUNCT
ejpam-3852	243	8	we	we	PRON
ejpam-3852	243	9	conclude	conclude	VERB
ejpam-3852	243	10	that	that	PRON
ejpam-3852	243	11	for	for	ADP
ejpam-3852	243	12	m	m	PROPN
ejpam-3852	243	13	=	=	SYM
ejpam-3852	243	14	2h	2h	NUM
ejpam-3852	243	15	,	,	PUNCT
ejpam-3852	243	16	h	h	PROPN
ejpam-3852	243	17	≥	≥	NOUN
ejpam-3852	243	18	2	2	NUM
ejpam-3852	243	19	and	and	CCONJ
ejpam-3852	243	20	0	0	NUM
ejpam-3852	243	21	≤	≤	NUM
ejpam-3852	243	22	k	k	X
ejpam-3852	243	23	≤	≤	PROPN
ejpam-3852	243	24	m−	m−	PROPN
ejpam-3852	243	25	1	1	NUM
ejpam-3852	243	26	,	,	PUNCT
ejpam-3852	243	27	ym+k	ym+k	PROPN
ejpam-3852	243	28	≡	≡	PROPN
ejpam-3852	243	29	yk	yk	PROPN
ejpam-3852	244	1	+	+	PROPN
ejpam-3852	244	2	m	m	PROPN
ejpam-3852	244	3	(	(	PUNCT
ejpam-3852	244	4	mod	mod	PROPN
ejpam-3852	244	5	2	2	NUM
ejpam-3852	244	6	m	m	NOUN
ejpam-3852	244	7	)	)	PUNCT
ejpam-3852	244	8	y−1m+k	y−1m+k	PUNCT
ejpam-3852	245	1	≡	≡	PROPN
ejpam-3852	245	2	y−1k	y−1k	VERB
ejpam-3852	246	1	+	+	ADJ
ejpam-3852	246	2	m	m	PROPN
ejpam-3852	246	3	(	(	PUNCT
ejpam-3852	246	4	mod	mod	PROPN
ejpam-3852	246	5	2	2	NUM
ejpam-3852	246	6	m	m	NOUN
ejpam-3852	246	7	)	)	PUNCT
ejpam-3852	247	1	αm+k	αm+k	NUM
ejpam-3852	247	2	≡	≡	ADJ
ejpam-3852	247	3	αk	αk	CCONJ
ejpam-3852	248	1	+	+	NOUN
ejpam-3852	248	2	2	2	NUM
ejpam-3852	248	3	m	m	NOUN
ejpam-3852	248	4	(	(	PUNCT
ejpam-3852	248	5	mod	mod	PROPN
ejpam-3852	248	6	4	4	NUM
ejpam-3852	248	7	m	m	NOUN
ejpam-3852	248	8	)	)	PUNCT
ejpam-3852	248	9	.	.	PUNCT
ejpam-3852	248	10	then	then	ADV
ejpam-3852	248	11	in	in	ADP
ejpam-3852	248	12	particular	particular	ADJ
ejpam-3852	248	13	for	for	ADP
ejpam-3852	248	14	m	m	PROPN
ejpam-3852	248	15	=	=	NOUN
ejpam-3852	248	16	m	m	VERB
ejpam-3852	248	17	we	we	PRON
ejpam-3852	248	18	see	see	VERB
ejpam-3852	248	19	that	that	SCONJ
ejpam-3852	248	20	ym+k	ym+k	PROPN
ejpam-3852	248	21	≡	≡	PROPN
ejpam-3852	248	22	yk	yk	PROPN
ejpam-3852	248	23	(	(	PUNCT
ejpam-3852	248	24	mod	mod	PROPN
ejpam-3852	248	25	m	m	PROPN
ejpam-3852	248	26	)	)	PUNCT
ejpam-3852	248	27	,	,	PUNCT
ejpam-3852	248	28	and	and	CCONJ
ejpam-3852	248	29	for	for	ADP
ejpam-3852	248	30	m	m	PROPN
ejpam-3852	248	31	=	=	NOUN
ejpam-3852	248	32	m	m	VERB
ejpam-3852	248	33	2	2	NUM
ejpam-3852	249	1	that	that	PRON
ejpam-3852	249	2	ym	ym	PROPN
ejpam-3852	249	3	2	2	NUM
ejpam-3852	250	1	+	+	NOUN
ejpam-3852	250	2	k	k	PROPN
ejpam-3852	250	3	≡	≡	PROPN
ejpam-3852	250	4	yk	yk	PROPN
ejpam-3852	251	1	+	+	CCONJ
ejpam-3852	251	2	m	m	VERB
ejpam-3852	251	3	2	2	NUM
ejpam-3852	251	4	(	(	PUNCT
ejpam-3852	251	5	mod	mod	PROPN
ejpam-3852	251	6	m	m	PROPN
ejpam-3852	251	7	)	)	PUNCT
ejpam-3852	251	8	,	,	PUNCT
ejpam-3852	251	9	so	so	CCONJ
ejpam-3852	251	10	the	the	DET
ejpam-3852	251	11	period	period	NOUN
ejpam-3852	251	12	is	be	AUX
ejpam-3852	251	13	m	m	PRON
ejpam-3852	251	14	.	.	PUNCT
ejpam-3852	252	1	now	now	ADV
ejpam-3852	252	2	,	,	PUNCT
ejpam-3852	252	3	for	for	ADP
ejpam-3852	252	4	m	m	PROPN
ejpam-3852	252	5	=	=	SYM
ejpam-3852	252	6	8	8	NUM
ejpam-3852	252	7	one	one	NOUN
ejpam-3852	252	8	can	can	AUX
ejpam-3852	252	9	check	check	VERB
ejpam-3852	252	10	that	that	SCONJ
ejpam-3852	252	11	under	under	ADP
ejpam-3852	252	12	the	the	DET
ejpam-3852	252	13	given	give	VERB
ejpam-3852	252	14	conditions	condition	NOUN
ejpam-3852	252	15	(	(	PUNCT
ejpam-3852	252	16	i.e.	i.e.	X
ejpam-3852	252	17	,	,	PUNCT
ejpam-3852	252	18	a	a	PRON
ejpam-3852	252	19	is	be	AUX
ejpam-3852	252	20	even	even	ADV
ejpam-3852	252	21	,	,	PUNCT
ejpam-3852	252	22	a+b	a+b	NUM
ejpam-3852	252	23	≡	≡	PROPN
ejpam-3852	252	24	1	1	NUM
ejpam-3852	252	25	(	(	PUNCT
ejpam-3852	252	26	mod	mod	NOUN
ejpam-3852	252	27	4	4	NUM
ejpam-3852	252	28	)	)	PUNCT
ejpam-3852	252	29	and	and	CCONJ
ejpam-3852	252	30	c	c	PROPN
ejpam-3852	252	31	≡	≡	PROPN
ejpam-3852	252	32	2	2	NUM
ejpam-3852	252	33	(	(	PUNCT
ejpam-3852	252	34	mod	mod	NOUN
ejpam-3852	252	35	4	4	NUM
ejpam-3852	252	36	)	)	PUNCT
ejpam-3852	252	37	)	)	PUNCT
ejpam-3852	252	38	,	,	PUNCT
ejpam-3852	252	39	the	the	DET
ejpam-3852	252	40	period	period	NOUN
ejpam-3852	252	41	of	of	ADP
ejpam-3852	252	42	{	{	PUNCT
ejpam-3852	252	43	yn	yn	NOUN
ejpam-3852	252	44	}	}	PUNCT
ejpam-3852	252	45	is	be	AUX
ejpam-3852	252	46	exactly	exactly	ADV
ejpam-3852	252	47	eight	eight	NUM
ejpam-3852	252	48	and	and	CCONJ
ejpam-3852	252	49	every	every	DET
ejpam-3852	252	50	element	element	NOUN
ejpam-3852	252	51	of	of	ADP
ejpam-3852	252	52	g8	g8	PROPN
ejpam-3852	252	53	=	=	SYM
ejpam-3852	252	54	{	{	PUNCT
ejpam-3852	252	55	1	1	NUM
ejpam-3852	252	56	,	,	PUNCT
ejpam-3852	252	57	3	3	NUM
ejpam-3852	252	58	,	,	PUNCT
ejpam-3852	252	59	5	5	NUM
ejpam-3852	252	60	,	,	PUNCT
ejpam-3852	252	61	7	7	NUM
ejpam-3852	252	62	}	}	PUNCT
ejpam-3852	252	63	occurs	occur	VERB
ejpam-3852	252	64	exactly	exactly	ADV
ejpam-3852	252	65	twice	twice	ADV
ejpam-3852	252	66	in	in	ADP
ejpam-3852	252	67	{	{	PUNCT
ejpam-3852	252	68	y0	y0	NOUN
ejpam-3852	252	69	,	,	PUNCT
ejpam-3852	252	70	y1	y1	NOUN
ejpam-3852	252	71	,	,	PUNCT
ejpam-3852	252	72	.	.	PUNCT
ejpam-3852	252	73	.	.	PUNCT
ejpam-3852	252	74	.	.	PUNCT
ejpam-3852	253	1	,	,	PUNCT
ejpam-3852	253	2	y7	y7	ADJ
ejpam-3852	253	3	}	}	PUNCT
ejpam-3852	253	4	.	.	PUNCT
ejpam-3852	254	1	moreover	moreover	ADV
ejpam-3852	254	2	,	,	PUNCT
ejpam-3852	254	3	it	it	PRON
ejpam-3852	254	4	is	be	AUX
ejpam-3852	254	5	easy	easy	ADJ
ejpam-3852	254	6	to	to	PART
ejpam-3852	254	7	verify	verify	VERB
ejpam-3852	254	8	that	that	SCONJ
ejpam-3852	254	9	for	for	ADP
ejpam-3852	254	10	any	any	DET
ejpam-3852	254	11	m	m	NOUN
ejpam-3852	254	12	=	=	NOUN
ejpam-3852	254	13	2h	2h	NUM
ejpam-3852	254	14	,	,	PUNCT
ejpam-3852	254	15	h	h	NOUN
ejpam-3852	254	16	≥	≥	NOUN
ejpam-3852	254	17	3	3	NUM
ejpam-3852	254	18	,	,	PUNCT
ejpam-3852	254	19	if	if	SCONJ
ejpam-3852	254	20	the	the	DET
ejpam-3852	254	21	period	period	NOUN
ejpam-3852	254	22	of	of	ADP
ejpam-3852	254	23	{	{	PUNCT
ejpam-3852	254	24	yn	yn	PROPN
ejpam-3852	254	25	(	(	PUNCT
ejpam-3852	254	26	mod	mod	PROPN
ejpam-3852	254	27	m	m	PROPN
ejpam-3852	254	28	)	)	PUNCT
ejpam-3852	254	29	}	}	PUNCT
ejpam-3852	254	30	is	be	AUX
ejpam-3852	254	31	exactly	exactly	ADV
ejpam-3852	254	32	m	m	ADJ
ejpam-3852	254	33	and	and	CCONJ
ejpam-3852	254	34	every	every	DET
ejpam-3852	254	35	element	element	NOUN
ejpam-3852	254	36	of	of	ADP
ejpam-3852	254	37	gm	gm	PROPN
ejpam-3852	254	38	occurs	occur	VERB
ejpam-3852	254	39	exactly	exactly	ADV
ejpam-3852	254	40	twice	twice	ADV
ejpam-3852	254	41	in	in	ADP
ejpam-3852	254	42	{	{	PUNCT
ejpam-3852	254	43	y0	y0	NOUN
ejpam-3852	254	44	,	,	PUNCT
ejpam-3852	254	45	y1	y1	NOUN
ejpam-3852	254	46	,	,	PUNCT
ejpam-3852	254	47	.	.	PUNCT
ejpam-3852	254	48	.	.	PUNCT
ejpam-3852	255	1	.	.	PUNCT
ejpam-3852	256	1	,	,	PUNCT
ejpam-3852	256	2	ym−1	ym−1	PROPN
ejpam-3852	256	3	}	}	PUNCT
ejpam-3852	256	4	then	then	ADV
ejpam-3852	256	5	the	the	DET
ejpam-3852	256	6	period	period	NOUN
ejpam-3852	256	7	of	of	ADP
ejpam-3852	256	8	{	{	PUNCT
ejpam-3852	256	9	yn	yn	PROPN
ejpam-3852	256	10	(	(	PUNCT
ejpam-3852	256	11	mod	mod	PROPN
ejpam-3852	256	12	2	2	NUM
ejpam-3852	256	13	m	m	NOUN
ejpam-3852	256	14	)	)	PUNCT
ejpam-3852	256	15	}	}	PUNCT
ejpam-3852	256	16	is	be	AUX
ejpam-3852	256	17	exactly	exactly	ADV
ejpam-3852	256	18	2	2	NUM
ejpam-3852	256	19	m	m	NOUN
ejpam-3852	256	20	and	and	CCONJ
ejpam-3852	256	21	every	every	DET
ejpam-3852	256	22	element	element	NOUN
ejpam-3852	256	23	of	of	ADP
ejpam-3852	256	24	g2	g2	PROPN
ejpam-3852	256	25	m	m	VERB
ejpam-3852	256	26	occurs	occur	VERB
ejpam-3852	256	27	exactly	exactly	ADV
ejpam-3852	256	28	twice	twice	ADV
ejpam-3852	256	29	in	in	ADP
ejpam-3852	256	30	{	{	PUNCT
ejpam-3852	256	31	y0	y0	NOUN
ejpam-3852	256	32	,	,	PUNCT
ejpam-3852	256	33	y1	y1	NOUN
ejpam-3852	256	34	,	,	PUNCT
ejpam-3852	256	35	.	.	PUNCT
ejpam-3852	256	36	.	.	PUNCT
ejpam-3852	257	1	.	.	PUNCT
ejpam-3852	258	1	,	,	PUNCT
ejpam-3852	258	2	y2m−1	y2m−1	PROPN
ejpam-3852	258	3	}	}	PUNCT
ejpam-3852	258	4	.	.	PUNCT
ejpam-3852	259	1	hence	hence	ADV
ejpam-3852	259	2	,	,	PUNCT
ejpam-3852	259	3	the	the	DET
ejpam-3852	259	4	period	period	NOUN
ejpam-3852	259	5	of	of	ADP
ejpam-3852	259	6	yn	yn	PROPN
ejpam-3852	259	7	is	be	AUX
ejpam-3852	259	8	m	m	ADJ
ejpam-3852	259	9	and	and	CCONJ
ejpam-3852	259	10	{	{	PUNCT
ejpam-3852	259	11	y0	y0	NOUN
ejpam-3852	259	12	,	,	PUNCT
ejpam-3852	259	13	y1	y1	NOUN
ejpam-3852	259	14	,	,	PUNCT
ejpam-3852	259	15	.	.	PUNCT
ejpam-3852	259	16	.	.	PUNCT
ejpam-3852	259	17	.	.	PUNCT
ejpam-3852	260	1	,	,	PUNCT
ejpam-3852	260	2	ym−1	ym−1	PROPN
ejpam-3852	260	3	}	}	PUNCT
ejpam-3852	260	4	represents	represent	VERB
ejpam-3852	260	5	gm	gm	PROPN
ejpam-3852	260	6	,	,	PUNCT
ejpam-3852	260	7	with	with	ADP
ejpam-3852	260	8	every	every	DET
ejpam-3852	260	9	element	element	NOUN
ejpam-3852	260	10	occurring	occur	VERB
ejpam-3852	260	11	exactly	exactly	ADV
ejpam-3852	260	12	twice	twice	ADV
ejpam-3852	260	13	.	.	PUNCT
ejpam-3852	261	1	remark	remark	NOUN
ejpam-3852	261	2	2	2	NUM
ejpam-3852	261	3	.	.	PUNCT
ejpam-3852	261	4	computationally	computationally	ADV
ejpam-3852	261	5	,	,	PUNCT
ejpam-3852	261	6	and	and	CCONJ
ejpam-3852	261	7	using	use	VERB
ejpam-3852	261	8	the	the	DET
ejpam-3852	261	9	proof	proof	NOUN
ejpam-3852	261	10	of	of	ADP
ejpam-3852	261	11	theorem	theorem	ADJ
ejpam-3852	261	12	3	3	NUM
ejpam-3852	261	13	,	,	PUNCT
ejpam-3852	261	14	taking	take	VERB
ejpam-3852	261	15	a	a	DET
ejpam-3852	261	16	random	random	ADJ
ejpam-3852	261	17	set	set	NOUN
ejpam-3852	261	18	of	of	ADP
ejpam-3852	261	19	initial	initial	ADJ
ejpam-3852	261	20	conditions	condition	NOUN
ejpam-3852	261	21	,	,	PUNCT
ejpam-3852	261	22	we	we	PRON
ejpam-3852	261	23	obtain	obtain	VERB
ejpam-3852	261	24	that	that	SCONJ
ejpam-3852	261	25	these	these	PRON
ejpam-3852	261	26	are	be	AUX
ejpam-3852	261	27	the	the	DET
ejpam-3852	261	28	only	only	ADJ
ejpam-3852	261	29	conditions	condition	NOUN
ejpam-3852	261	30	for	for	ADP
ejpam-3852	261	31	a	a	DET
ejpam-3852	261	32	,	,	PUNCT
ejpam-3852	261	33	b	b	NOUN
ejpam-3852	261	34	,	,	PUNCT
ejpam-3852	261	35	c	c	NOUN
ejpam-3852	261	36	under	under	ADP
ejpam-3852	261	37	which	which	PRON
ejpam-3852	261	38	we	we	PRON
ejpam-3852	261	39	obtain	obtain	VERB
ejpam-3852	261	40	period	period	NOUN
ejpam-3852	261	41	16	16	NUM
ejpam-3852	261	42	(	(	PUNCT
ejpam-3852	261	43	modulo	modulo	PROPN
ejpam-3852	261	44	16	16	NUM
ejpam-3852	261	45	)	)	PUNCT
ejpam-3852	261	46	.	.	PUNCT
ejpam-3852	262	1	from	from	ADP
ejpam-3852	262	2	the	the	DET
ejpam-3852	262	3	proof	proof	NOUN
ejpam-3852	262	4	of	of	ADP
ejpam-3852	262	5	theorem	theorem	NOUN
ejpam-3852	262	6	3	3	NUM
ejpam-3852	262	7	,	,	PUNCT
ejpam-3852	262	8	this	this	PRON
ejpam-3852	262	9	would	would	AUX
ejpam-3852	262	10	imply	imply	VERB
ejpam-3852	262	11	that	that	SCONJ
ejpam-3852	262	12	,	,	PUNCT
ejpam-3852	262	13	regardless	regardless	ADV
ejpam-3852	262	14	of	of	ADP
ejpam-3852	262	15	frequency	frequency	NOUN
ejpam-3852	262	16	,	,	PUNCT
ejpam-3852	262	17	we	we	PRON
ejpam-3852	262	18	can	can	AUX
ejpam-3852	262	19	only	only	ADV
ejpam-3852	262	20	attain	attain	VERB
ejpam-3852	262	21	the	the	DET
ejpam-3852	262	22	maximal	maximal	ADJ
ejpam-3852	262	23	period	period	NOUN
ejpam-3852	262	24	m	m	VERB
ejpam-3852	262	25	for	for	ADP
ejpam-3852	262	26	any	any	DET
ejpam-3852	262	27	initial	initial	ADJ
ejpam-3852	262	28	conditions	condition	NOUN
ejpam-3852	262	29	if	if	SCONJ
ejpam-3852	262	30	a	a	DET
ejpam-3852	262	31	≡	≡	PROPN
ejpam-3852	262	32	0	0	PUNCT
ejpam-3852	262	33	(	(	PUNCT
ejpam-3852	262	34	mod	mod	NOUN
ejpam-3852	262	35	2	2	NUM
ejpam-3852	262	36	)	)	PUNCT
ejpam-3852	262	37	,	,	PUNCT
ejpam-3852	262	38	a+	a+	PUNCT
ejpam-3852	262	39	b	b	X
ejpam-3852	262	40	≡	≡	PROPN
ejpam-3852	262	41	1	1	NUM
ejpam-3852	262	42	(	(	PUNCT
ejpam-3852	262	43	mod	mod	NOUN
ejpam-3852	262	44	4	4	NUM
ejpam-3852	262	45	)	)	PUNCT
ejpam-3852	262	46	and	and	CCONJ
ejpam-3852	262	47	c	c	PROPN
ejpam-3852	262	48	≡	≡	PROPN
ejpam-3852	262	49	2	2	NUM
ejpam-3852	262	50	(	(	PUNCT
ejpam-3852	262	51	mod	mod	NOUN
ejpam-3852	262	52	4	4	NUM
ejpam-3852	262	53	)	)	PUNCT
ejpam-3852	262	54	.	.	PUNCT
ejpam-3852	263	1	p.	p.	NOUN
ejpam-3852	263	2	stănică	stănică	NUM
ejpam-3852	263	3	et	et	PROPN
ejpam-3852	264	1	al	al	PROPN
ejpam-3852	264	2	.	.	PUNCT
ejpam-3852	264	3	/	/	SYM
ejpam-3852	264	4	eur	eur	PROPN
ejpam-3852	264	5	.	.	PUNCT
ejpam-3852	265	1	j.	j.	PROPN
ejpam-3852	265	2	pure	pure	PROPN
ejpam-3852	265	3	appl	appl	PROPN
ejpam-3852	265	4	.	.	PROPN
ejpam-3852	265	5	math	math	PROPN
ejpam-3852	265	6	,	,	PUNCT
ejpam-3852	265	7	14	14	NUM
ejpam-3852	265	8	(	(	PUNCT
ejpam-3852	265	9	1	1	NUM
ejpam-3852	265	10	)	)	PUNCT
ejpam-3852	265	11	(	(	PUNCT
ejpam-3852	265	12	2021	2021	NUM
ejpam-3852	265	13	)	)	PUNCT
ejpam-3852	265	14	,	,	PUNCT
ejpam-3852	265	15	1	1	NUM
ejpam-3852	265	16	-	-	SYM
ejpam-3852	265	17	18	18	NUM
ejpam-3852	265	18	9	9	NUM
ejpam-3852	265	19	3.2	3.2	NUM
ejpam-3852	265	20	.	.	PUNCT
ejpam-3852	266	1	conditions	condition	NOUN
ejpam-3852	266	2	when	when	SCONJ
ejpam-3852	266	3	the	the	DET
ejpam-3852	266	4	period	period	NOUN
ejpam-3852	266	5	of	of	ADP
ejpam-3852	266	6	the	the	DET
ejpam-3852	266	7	sequence	sequence	NOUN
ejpam-3852	266	8	is	be	AUX
ejpam-3852	266	9	m/2	m/2	NUM
ejpam-3852	266	10	theorem	theorem	NOUN
ejpam-3852	266	11	5	5	NUM
ejpam-3852	266	12	.	.	PUNCT
ejpam-3852	267	1	the	the	DET
ejpam-3852	267	2	prng	prng	PROPN
ejpam-3852	267	3	{	{	PUNCT
ejpam-3852	267	4	yn	yn	PROPN
ejpam-3852	267	5	}	}	PUNCT
ejpam-3852	267	6	derived	derive	VERB
ejpam-3852	267	7	from	from	ADP
ejpam-3852	267	8	(	(	PUNCT
ejpam-3852	267	9	5	5	NUM
ejpam-3852	267	10	)	)	PUNCT
ejpam-3852	267	11	is	be	AUX
ejpam-3852	267	12	purely	purely	ADV
ejpam-3852	267	13	periodic	periodic	ADJ
ejpam-3852	267	14	with	with	ADP
ejpam-3852	267	15	period	period	NOUN
ejpam-3852	267	16	m/2	m/2	NUM
ejpam-3852	267	17	,	,	PUNCT
ejpam-3852	267	18	regardless	regardless	ADV
ejpam-3852	267	19	of	of	ADP
ejpam-3852	267	20	the	the	DET
ejpam-3852	267	21	odd	odd	ADJ
ejpam-3852	267	22	initial	initial	ADJ
ejpam-3852	267	23	conditions	condition	NOUN
ejpam-3852	267	24	y0	y0	PROPN
ejpam-3852	267	25	,	,	PUNCT
ejpam-3852	267	26	y1	y1	NOUN
ejpam-3852	267	27	,	,	PUNCT
ejpam-3852	267	28	and	and	CCONJ
ejpam-3852	267	29	the	the	DET
ejpam-3852	267	30	set	set	NOUN
ejpam-3852	267	31	{	{	PUNCT
ejpam-3852	267	32	y1	y1	NOUN
ejpam-3852	267	33	,	,	PUNCT
ejpam-3852	267	34	y2	y2	PROPN
ejpam-3852	267	35	,	,	PUNCT
ejpam-3852	267	36	.	.	PUNCT
ejpam-3852	267	37	.	.	PUNCT
ejpam-3852	268	1	.	.	PUNCT
ejpam-3852	269	1	,	,	PUNCT
ejpam-3852	269	2	ym	ym	NOUN
ejpam-3852	269	3	2	2	X
ejpam-3852	269	4	}	}	PUNCT
ejpam-3852	269	5	=	=	SYM
ejpam-3852	269	6	gm	gm	PROPN
ejpam-3852	269	7	if	if	SCONJ
ejpam-3852	269	8	and	and	CCONJ
ejpam-3852	269	9	only	only	ADV
ejpam-3852	269	10	if	if	SCONJ
ejpam-3852	269	11	a	a	DET
ejpam-3852	269	12	≡	≡	PROPN
ejpam-3852	269	13	1	1	NUM
ejpam-3852	269	14	(	(	PUNCT
ejpam-3852	269	15	mod	mod	NOUN
ejpam-3852	269	16	4	4	NUM
ejpam-3852	269	17	)	)	PUNCT
ejpam-3852	269	18	,	,	PUNCT
ejpam-3852	269	19	b	b	PROPN
ejpam-3852	269	20	≡	≡	PROPN
ejpam-3852	269	21	0	0	PUNCT
ejpam-3852	270	1	(	(	PUNCT
ejpam-3852	270	2	mod	mod	PROPN
ejpam-3852	270	3	m	m	PROPN
ejpam-3852	270	4	2	2	NUM
ejpam-3852	270	5	)	)	PUNCT
ejpam-3852	270	6	and	and	CCONJ
ejpam-3852	270	7	c	c	PROPN
ejpam-3852	270	8	≡	≡	PROPN
ejpam-3852	270	9	2	2	NUM
ejpam-3852	270	10	(	(	PUNCT
ejpam-3852	270	11	mod	mod	NOUN
ejpam-3852	270	12	4	4	NUM
ejpam-3852	270	13	)	)	PUNCT
ejpam-3852	270	14	.	.	PUNCT
ejpam-3852	271	1	proof	proof	NOUN
ejpam-3852	271	2	.	.	PUNCT
ejpam-3852	272	1	we	we	PRON
ejpam-3852	272	2	show	show	VERB
ejpam-3852	272	3	this	this	PRON
ejpam-3852	272	4	in	in	ADP
ejpam-3852	272	5	two	two	NUM
ejpam-3852	272	6	parts	part	NOUN
ejpam-3852	272	7	.	.	PUNCT
ejpam-3852	273	1	necessity	necessity	NOUN
ejpam-3852	273	2	:	:	PUNCT
ejpam-3852	273	3	let	let	VERB
ejpam-3852	273	4	us	we	PRON
ejpam-3852	273	5	assume	assume	VERB
ejpam-3852	273	6	that	that	SCONJ
ejpam-3852	273	7	for	for	ADP
ejpam-3852	273	8	the	the	DET
ejpam-3852	273	9	sequence	sequence	NOUN
ejpam-3852	273	10	(	(	PUNCT
ejpam-3852	273	11	5	5	NUM
ejpam-3852	273	12	)	)	PUNCT
ejpam-3852	273	13	and	and	CCONJ
ejpam-3852	273	14	for	for	ADP
ejpam-3852	273	15	any	any	DET
ejpam-3852	273	16	y0	y0	NOUN
ejpam-3852	273	17	,	,	PUNCT
ejpam-3852	273	18	y1	y1	PROPN
ejpam-3852	273	19	∈	∈	PROPN
ejpam-3852	273	20	gm	gm	PROPN
ejpam-3852	273	21	,	,	PUNCT
ejpam-3852	273	22	the	the	DET
ejpam-3852	273	23	period	period	NOUN
ejpam-3852	273	24	of	of	ADP
ejpam-3852	273	25	yn	yn	PROPN
ejpam-3852	273	26	is	be	AUX
ejpam-3852	273	27	m	m	PROPN
ejpam-3852	273	28	2	2	NUM
ejpam-3852	273	29	and	and	CCONJ
ejpam-3852	273	30	{	{	PUNCT
ejpam-3852	273	31	y1	y1	NOUN
ejpam-3852	273	32	,	,	PUNCT
ejpam-3852	273	33	y2	y2	PROPN
ejpam-3852	273	34	,	,	PUNCT
ejpam-3852	273	35	.	.	PUNCT
ejpam-3852	273	36	.	.	PUNCT
ejpam-3852	274	1	.	.	PUNCT
ejpam-3852	275	1	,	,	PUNCT
ejpam-3852	275	2	ym	ym	NOUN
ejpam-3852	275	3	2	2	X
ejpam-3852	275	4	}	}	PUNCT
ejpam-3852	275	5	=	=	SYM
ejpam-3852	275	6	gm	gm	PROPN
ejpam-3852	275	7	.	.	PUNCT
ejpam-3852	276	1	we	we	PRON
ejpam-3852	276	2	will	will	AUX
ejpam-3852	276	3	prove	prove	VERB
ejpam-3852	276	4	that	that	SCONJ
ejpam-3852	276	5	a	a	DET
ejpam-3852	276	6	≡	≡	PROPN
ejpam-3852	276	7	1	1	NUM
ejpam-3852	276	8	(	(	PUNCT
ejpam-3852	276	9	mod	mod	NOUN
ejpam-3852	276	10	4	4	NUM
ejpam-3852	276	11	)	)	PUNCT
ejpam-3852	276	12	,	,	PUNCT
ejpam-3852	276	13	b	b	PROPN
ejpam-3852	276	14	≡	≡	PROPN
ejpam-3852	276	15	0	0	PUNCT
ejpam-3852	277	1	(	(	PUNCT
ejpam-3852	277	2	mod	mod	PROPN
ejpam-3852	277	3	m	m	PROPN
ejpam-3852	277	4	2	2	NUM
ejpam-3852	277	5	)	)	PUNCT
ejpam-3852	277	6	and	and	CCONJ
ejpam-3852	277	7	c	c	PROPN
ejpam-3852	277	8	≡	≡	PROPN
ejpam-3852	277	9	2	2	NUM
ejpam-3852	277	10	(	(	PUNCT
ejpam-3852	277	11	mod	mod	NOUN
ejpam-3852	277	12	4	4	NUM
ejpam-3852	277	13	)	)	PUNCT
ejpam-3852	277	14	.	.	PUNCT
ejpam-3852	278	1	we	we	PRON
ejpam-3852	278	2	consider	consider	VERB
ejpam-3852	278	3	y0	y0	NOUN
ejpam-3852	278	4	=	=	SYM
ejpam-3852	278	5	y1	y1	NOUN
ejpam-3852	278	6	=	=	SYM
ejpam-3852	278	7	1	1	NUM
ejpam-3852	278	8	(	(	PUNCT
ejpam-3852	278	9	there	there	PRON
ejpam-3852	278	10	is	be	VERB
ejpam-3852	278	11	no	no	DET
ejpam-3852	278	12	contradiction	contradiction	NOUN
ejpam-3852	278	13	here	here	ADV
ejpam-3852	278	14	with	with	ADP
ejpam-3852	278	15	the	the	DET
ejpam-3852	278	16	inferred	infer	VERB
ejpam-3852	278	17	assumption	assumption	NOUN
ejpam-3852	278	18	that	that	SCONJ
ejpam-3852	278	19	every	every	DET
ejpam-3852	278	20	residue	residue	NOUN
ejpam-3852	278	21	occurs	occur	VERB
ejpam-3852	278	22	once	once	ADV
ejpam-3852	278	23	only	only	ADV
ejpam-3852	278	24	,	,	PUNCT
ejpam-3852	278	25	since	since	SCONJ
ejpam-3852	278	26	we	we	PRON
ejpam-3852	278	27	consider	consider	VERB
ejpam-3852	278	28	the	the	DET
ejpam-3852	278	29	uniformity	uniformity	NOUN
ejpam-3852	278	30	of	of	ADP
ejpam-3852	278	31	the	the	DET
ejpam-3852	278	32	sequence	sequence	NOUN
ejpam-3852	278	33	starting	start	VERB
ejpam-3852	278	34	with	with	ADP
ejpam-3852	278	35	index	index	NOUN
ejpam-3852	278	36	1	1	NUM
ejpam-3852	278	37	;	;	PUNCT
ejpam-3852	278	38	certainly	certainly	ADV
ejpam-3852	278	39	,	,	PUNCT
ejpam-3852	278	40	we	we	PRON
ejpam-3852	278	41	could	could	AUX
ejpam-3852	278	42	have	have	AUX
ejpam-3852	278	43	taken	take	VERB
ejpam-3852	278	44	y0	y0	NOUN
ejpam-3852	278	45	=	=	SYM
ejpam-3852	278	46	1	1	NUM
ejpam-3852	278	47	,	,	PUNCT
ejpam-3852	278	48	y1	y1	NOUN
ejpam-3852	278	49	=	=	SYM
ejpam-3852	278	50	3	3	NUM
ejpam-3852	278	51	,	,	PUNCT
ejpam-3852	278	52	but	but	CCONJ
ejpam-3852	278	53	we	we	PRON
ejpam-3852	278	54	preferred	prefer	VERB
ejpam-3852	278	55	to	to	PART
ejpam-3852	278	56	start	start	VERB
ejpam-3852	278	57	“	"	PUNCT
ejpam-3852	278	58	at	at	ADP
ejpam-3852	278	59	a	a	DET
ejpam-3852	278	60	zero	zero	NUM
ejpam-3852	278	61	time	time	NOUN
ejpam-3852	278	62	”	"	PUNCT
ejpam-3852	278	63	and	and	CCONJ
ejpam-3852	278	64	start	start	VERB
ejpam-3852	278	65	counting	count	VERB
ejpam-3852	278	66	the	the	DET
ejpam-3852	278	67	distribution	distribution	NOUN
ejpam-3852	278	68	of	of	ADP
ejpam-3852	278	69	our	our	PRON
ejpam-3852	278	70	sequence	sequence	NOUN
ejpam-3852	278	71	at	at	ADP
ejpam-3852	278	72	index	index	NOUN
ejpam-3852	278	73	1	1	NUM
ejpam-3852	278	74	)	)	PUNCT
ejpam-3852	278	75	.	.	PUNCT
ejpam-3852	279	1	now	now	ADV
ejpam-3852	279	2	,	,	PUNCT
ejpam-3852	279	3	it	it	PRON
ejpam-3852	279	4	is	be	AUX
ejpam-3852	279	5	easy	easy	ADJ
ejpam-3852	279	6	to	to	PART
ejpam-3852	279	7	check	check	VERB
ejpam-3852	279	8	that	that	SCONJ
ejpam-3852	279	9	under	under	ADP
ejpam-3852	279	10	the	the	DET
ejpam-3852	279	11	above	above	ADJ
ejpam-3852	279	12	assumption	assumption	NOUN
ejpam-3852	279	13	if	if	SCONJ
ejpam-3852	279	14	we	we	PRON
ejpam-3852	279	15	reduce	reduce	VERB
ejpam-3852	279	16	every	every	DET
ejpam-3852	279	17	element	element	NOUN
ejpam-3852	279	18	modulo	modulo	NOUN
ejpam-3852	279	19	4	4	NUM
ejpam-3852	279	20	(	(	PUNCT
ejpam-3852	279	21	respectively	respectively	ADV
ejpam-3852	279	22	,	,	PUNCT
ejpam-3852	279	23	8)	8)	NUM
ejpam-3852	279	24	,	,	PUNCT
ejpam-3852	279	25	the	the	DET
ejpam-3852	279	26	period	period	NOUN
ejpam-3852	279	27	of	of	ADP
ejpam-3852	279	28	{	{	PUNCT
ejpam-3852	279	29	yn	yn	PROPN
ejpam-3852	279	30	(	(	PUNCT
ejpam-3852	279	31	mod	mod	PROPN
ejpam-3852	279	32	4	4	NUM
ejpam-3852	279	33	)	)	PUNCT
ejpam-3852	279	34	}	}	PUNCT
ejpam-3852	279	35	(	(	PUNCT
ejpam-3852	279	36	respectively	respectively	ADV
ejpam-3852	279	37	,	,	PUNCT
ejpam-3852	279	38	{	{	PUNCT
ejpam-3852	279	39	yn	yn	X
ejpam-3852	279	40	(	(	PUNCT
ejpam-3852	279	41	mod	mod	PROPN
ejpam-3852	279	42	8)	8)	NUM
ejpam-3852	279	43	}	}	PUNCT
ejpam-3852	279	44	)	)	PUNCT
ejpam-3852	279	45	is	be	AUX
ejpam-3852	279	46	2	2	NUM
ejpam-3852	279	47	(	(	PUNCT
ejpam-3852	279	48	respectively	respectively	ADV
ejpam-3852	279	49	,	,	PUNCT
ejpam-3852	279	50	4	4	NUM
ejpam-3852	279	51	)	)	PUNCT
ejpam-3852	279	52	and	and	CCONJ
ejpam-3852	279	53	{	{	PUNCT
ejpam-3852	279	54	y1	y1	NOUN
ejpam-3852	279	55	,	,	PUNCT
ejpam-3852	279	56	y2	y2	NOUN
ejpam-3852	279	57	}	}	PUNCT
ejpam-3852	279	58	=	=	NOUN
ejpam-3852	279	59	g4	g4	NOUN
ejpam-3852	279	60	=	=	SYM
ejpam-3852	279	61	{	{	PUNCT
ejpam-3852	279	62	1	1	NUM
ejpam-3852	279	63	,	,	PUNCT
ejpam-3852	279	64	3	3	NUM
ejpam-3852	279	65	}	}	PUNCT
ejpam-3852	279	66	(	(	PUNCT
ejpam-3852	279	67	respectively	respectively	ADV
ejpam-3852	279	68	,	,	PUNCT
ejpam-3852	279	69	{	{	PUNCT
ejpam-3852	279	70	y1	y1	NOUN
ejpam-3852	279	71	,	,	PUNCT
ejpam-3852	279	72	y2	y2	PROPN
ejpam-3852	279	73	,	,	PUNCT
ejpam-3852	279	74	y3	y3	PROPN
ejpam-3852	279	75	,	,	PUNCT
ejpam-3852	279	76	y4	y4	ADJ
ejpam-3852	279	77	}	}	PUNCT
ejpam-3852	279	78	=	=	SYM
ejpam-3852	279	79	g8	g8	PROPN
ejpam-3852	279	80	=	=	SYM
ejpam-3852	279	81	{	{	PUNCT
ejpam-3852	279	82	1	1	NUM
ejpam-3852	279	83	,	,	PUNCT
ejpam-3852	279	84	3	3	NUM
ejpam-3852	279	85	,	,	PUNCT
ejpam-3852	279	86	5	5	NUM
ejpam-3852	279	87	,	,	PUNCT
ejpam-3852	279	88	7	7	NUM
ejpam-3852	279	89	}	}	PUNCT
ejpam-3852	279	90	)	)	PUNCT
ejpam-3852	279	91	.	.	PUNCT
ejpam-3852	280	1	we	we	PRON
ejpam-3852	280	2	have	have	VERB
ejpam-3852	280	3	,	,	PUNCT
ejpam-3852	280	4	yn+2	yn+2	NUM
ejpam-3852	280	5	≡	≡	PROPN
ejpam-3852	280	6	ayn+1	ayn+1	PROPN
ejpam-3852	281	1	+	+	CCONJ
ejpam-3852	281	2	byn	byn	NOUN
ejpam-3852	281	3	+	+	X
ejpam-3852	281	4	c	c	PROPN
ejpam-3852	281	5	(	(	PUNCT
ejpam-3852	281	6	mod	mod	PROPN
ejpam-3852	281	7	4	4	NUM
ejpam-3852	281	8	)	)	PUNCT
ejpam-3852	281	9	,	,	PUNCT
ejpam-3852	281	10	and	and	CCONJ
ejpam-3852	281	11	yn+2	yn+2	NUM
ejpam-3852	281	12	≡	≡	PROPN
ejpam-3852	281	13	ayn+1	ayn+1	PROPN
ejpam-3852	281	14	+	+	CCONJ
ejpam-3852	281	15	byn	byn	NOUN
ejpam-3852	281	16	+	+	X
ejpam-3852	281	17	c	c	PROPN
ejpam-3852	281	18	(	(	PUNCT
ejpam-3852	281	19	mod	mod	PROPN
ejpam-3852	281	20	8)	8)	NUM
ejpam-3852	281	21	.	.	PUNCT
ejpam-3852	282	1	as	as	ADP
ejpam-3852	282	2	y0	y0	PROPN
ejpam-3852	282	3	=	=	SYM
ejpam-3852	282	4	y1	y1	NOUN
ejpam-3852	282	5	=	=	SYM
ejpam-3852	282	6	1	1	NUM
ejpam-3852	282	7	,	,	PUNCT
ejpam-3852	282	8	we	we	PRON
ejpam-3852	282	9	have	have	VERB
ejpam-3852	282	10	,	,	PUNCT
ejpam-3852	282	11	y2	y2	PROPN
ejpam-3852	282	12	≡	≡	PROPN
ejpam-3852	282	13	3	3	NUM
ejpam-3852	282	14	(	(	PUNCT
ejpam-3852	282	15	mod	mod	NOUN
ejpam-3852	282	16	4	4	NUM
ejpam-3852	282	17	)	)	PUNCT
ejpam-3852	282	18	,	,	PUNCT
ejpam-3852	282	19	y3	y3	PROPN
ejpam-3852	282	20	≡	≡	PROPN
ejpam-3852	282	21	1	1	NUM
ejpam-3852	282	22	(	(	PUNCT
ejpam-3852	282	23	mod	mod	NOUN
ejpam-3852	282	24	4	4	NUM
ejpam-3852	282	25	)	)	PUNCT
ejpam-3852	282	26	,	,	PUNCT
ejpam-3852	282	27	y4	y4	PROPN
ejpam-3852	282	28	≡	≡	PROPN
ejpam-3852	282	29	3	3	NUM
ejpam-3852	282	30	(	(	PUNCT
ejpam-3852	282	31	mod	mod	NOUN
ejpam-3852	282	32	4	4	NUM
ejpam-3852	282	33	)	)	PUNCT
ejpam-3852	282	34	and	and	CCONJ
ejpam-3852	282	35	y3	y3	PROPN
ejpam-3852	282	36	≡	≡	PROPN
ejpam-3852	282	37	5	5	NUM
ejpam-3852	282	38	(	(	PUNCT
ejpam-3852	282	39	mod	mod	NOUN
ejpam-3852	282	40	8)	8)	NUM
ejpam-3852	282	41	,	,	PUNCT
ejpam-3852	282	42	y5	y5	PROPN
ejpam-3852	282	43	≡	≡	PROPN
ejpam-3852	282	44	1	1	NUM
ejpam-3852	282	45	(	(	PUNCT
ejpam-3852	282	46	mod	mod	PROPN
ejpam-3852	282	47	8)	8)	NUM
ejpam-3852	282	48	.	.	PUNCT
ejpam-3852	283	1	by	by	ADP
ejpam-3852	283	2	absurd	absurd	ADJ
ejpam-3852	283	3	,	,	PUNCT
ejpam-3852	283	4	we	we	PRON
ejpam-3852	283	5	assume	assume	VERB
ejpam-3852	283	6	that	that	SCONJ
ejpam-3852	283	7	a	a	PRON
ejpam-3852	283	8	is	be	AUX
ejpam-3852	283	9	even	even	ADV
ejpam-3852	283	10	.	.	PUNCT
ejpam-3852	284	1	then	then	ADV
ejpam-3852	284	2	,	,	PUNCT
ejpam-3852	284	3	y2	y2	PROPN
ejpam-3852	284	4	≡	≡	PROPN
ejpam-3852	285	1	a	a	DET
ejpam-3852	285	2	+	+	NOUN
ejpam-3852	285	3	b	b	NOUN
ejpam-3852	285	4	+	+	CCONJ
ejpam-3852	285	5	c	c	NOUN
ejpam-3852	285	6	≡	≡	PROPN
ejpam-3852	285	7	3	3	NUM
ejpam-3852	285	8	(	(	PUNCT
ejpam-3852	285	9	mod	mod	NOUN
ejpam-3852	285	10	4	4	NUM
ejpam-3852	285	11	)	)	PUNCT
ejpam-3852	285	12	gives	give	VERB
ejpam-3852	285	13	b	b	PROPN
ejpam-3852	286	1	+	+	CCONJ
ejpam-3852	286	2	c	c	NOUN
ejpam-3852	286	3	is	be	AUX
ejpam-3852	286	4	odd	odd	ADJ
ejpam-3852	286	5	.	.	PUNCT
ejpam-3852	287	1	so	so	ADV
ejpam-3852	287	2	,	,	PUNCT
ejpam-3852	287	3	let	let	VERB
ejpam-3852	287	4	a	a	DET
ejpam-3852	287	5	=	=	SYM
ejpam-3852	287	6	2d′	2d′	NUM
ejpam-3852	287	7	and	and	CCONJ
ejpam-3852	287	8	b	b	NOUN
ejpam-3852	287	9	+	+	NUM
ejpam-3852	287	10	c	c	NOUN
ejpam-3852	287	11	=	=	SYM
ejpam-3852	287	12	1	1	NUM
ejpam-3852	287	13	+	+	NUM
ejpam-3852	287	14	2e′	2e′	NUM
ejpam-3852	287	15	for	for	ADP
ejpam-3852	287	16	some	some	DET
ejpam-3852	287	17	integers	integer	NOUN
ejpam-3852	287	18	d′	d′	PRON
ejpam-3852	287	19	and	and	CCONJ
ejpam-3852	287	20	e′.	e′.	PRON
ejpam-3852	287	21	we	we	PRON
ejpam-3852	287	22	have	have	VERB
ejpam-3852	287	23	,	,	PUNCT
ejpam-3852	287	24	y2	y2	PROPN
ejpam-3852	287	25	=	=	SYM
ejpam-3852	287	26	1	1	NUM
ejpam-3852	288	1	+	+	NUM
ejpam-3852	288	2	2(d′	2(d′	NUM
ejpam-3852	288	3	+	+	CCONJ
ejpam-3852	288	4	e′	e′	NOUN
ejpam-3852	288	5	)	)	PUNCT
ejpam-3852	289	1	where	where	SCONJ
ejpam-3852	289	2	d′	d′	PRON
ejpam-3852	289	3	+	+	CCONJ
ejpam-3852	289	4	e′	e′	X
ejpam-3852	289	5	=	=	SYM
ejpam-3852	289	6	1	1	NUM
ejpam-3852	289	7	+	+	NUM
ejpam-3852	289	8	2f	2f	NUM
ejpam-3852	289	9	′	′	NOUN
ejpam-3852	289	10	,	,	PUNCT
ejpam-3852	289	11	is	be	AUX
ejpam-3852	289	12	odd	odd	ADJ
ejpam-3852	289	13	for	for	ADP
ejpam-3852	289	14	some	some	PRON
ejpam-3852	290	1	f	f	NOUN
ejpam-3852	290	2	′	′	NUM
ejpam-3852	291	1	∈	∈	PROPN
ejpam-3852	291	2	z	z	NOUN
ejpam-3852	291	3	(	(	PUNCT
ejpam-3852	291	4	since	since	SCONJ
ejpam-3852	291	5	y2	y2	PROPN
ejpam-3852	291	6	≡	≡	PROPN
ejpam-3852	291	7	3	3	NUM
ejpam-3852	291	8	(	(	PUNCT
ejpam-3852	291	9	mod	mod	NOUN
ejpam-3852	291	10	4	4	NUM
ejpam-3852	291	11	)	)	PUNCT
ejpam-3852	291	12	)	)	PUNCT
ejpam-3852	291	13	.	.	PUNCT
ejpam-3852	292	1	then	then	ADV
ejpam-3852	292	2	,	,	PUNCT
ejpam-3852	292	3	y3	y3	PROPN
ejpam-3852	292	4	≡	≡	PROPN
ejpam-3852	292	5	3a+	3a+	NUM
ejpam-3852	292	6	b+	b+	X
ejpam-3852	292	7	c	c	PROPN
ejpam-3852	292	8	≡	≡	PROPN
ejpam-3852	292	9	3	3	NUM
ejpam-3852	292	10	+	+	CCONJ
ejpam-3852	292	11	2a	2a	NUM
ejpam-3852	292	12	≡	≡	PROPN
ejpam-3852	292	13	3	3	NUM
ejpam-3852	292	14	(	(	PUNCT
ejpam-3852	292	15	mod	mod	NOUN
ejpam-3852	292	16	4	4	NUM
ejpam-3852	292	17	)	)	PUNCT
ejpam-3852	292	18	.	.	PUNCT
ejpam-3852	293	1	which	which	PRON
ejpam-3852	293	2	is	be	AUX
ejpam-3852	293	3	a	a	DET
ejpam-3852	293	4	contradiction	contradiction	NOUN
ejpam-3852	293	5	.	.	PUNCT
ejpam-3852	294	1	so	so	ADV
ejpam-3852	294	2	a	a	PRON
ejpam-3852	294	3	is	be	AUX
ejpam-3852	294	4	odd	odd	ADJ
ejpam-3852	294	5	.	.	PUNCT
ejpam-3852	295	1	now	now	ADV
ejpam-3852	295	2	,	,	PUNCT
ejpam-3852	295	3	let	let	VERB
ejpam-3852	295	4	a	a	DET
ejpam-3852	295	5	=	=	SYM
ejpam-3852	295	6	3	3	NUM
ejpam-3852	295	7	+	+	NUM
ejpam-3852	295	8	4g′	4g′	NUM
ejpam-3852	295	9	,	,	PUNCT
ejpam-3852	295	10	g′	g′	NOUN
ejpam-3852	295	11	∈	∈	PROPN
ejpam-3852	295	12	z	z	PROPN
ejpam-3852	295	13	and	and	CCONJ
ejpam-3852	295	14	from	from	ADP
ejpam-3852	295	15	y2	y2	PROPN
ejpam-3852	295	16	≡	≡	PROPN
ejpam-3852	296	1	a	a	DET
ejpam-3852	296	2	+	+	NOUN
ejpam-3852	296	3	b	b	NOUN
ejpam-3852	296	4	+	+	CCONJ
ejpam-3852	296	5	c	c	NOUN
ejpam-3852	296	6	≡	≡	PROPN
ejpam-3852	296	7	3	3	NUM
ejpam-3852	296	8	(	(	PUNCT
ejpam-3852	296	9	mod	mod	NOUN
ejpam-3852	296	10	4	4	X
ejpam-3852	296	11	)	)	PUNCT
ejpam-3852	296	12	we	we	PRON
ejpam-3852	296	13	have	have	VERB
ejpam-3852	296	14	b	b	NOUN
ejpam-3852	296	15	+	+	NOUN
ejpam-3852	296	16	c	c	NOUN
ejpam-3852	296	17	=	=	SYM
ejpam-3852	296	18	4h′	4h′	NUM
ejpam-3852	296	19	,	,	PUNCT
ejpam-3852	296	20	h′	h′	PROPN
ejpam-3852	296	21	∈	∈	PROPN
ejpam-3852	296	22	z.	z.	PROPN
ejpam-3852	297	1	then	then	ADV
ejpam-3852	297	2	,	,	PUNCT
ejpam-3852	297	3	y3	y3	PROPN
ejpam-3852	297	4	≡	≡	PROPN
ejpam-3852	297	5	ay2	ay2	PROPN
ejpam-3852	297	6	+	+	CCONJ
ejpam-3852	297	7	b+	b+	X
ejpam-3852	297	8	c	c	PROPN
ejpam-3852	297	9	≡	≡	PROPN
ejpam-3852	297	10	a(3	a(3	PROPN
ejpam-3852	297	11	+	+	CCONJ
ejpam-3852	297	12	4(g′	4(g′	PROPN
ejpam-3852	297	13	+	+	CCONJ
ejpam-3852	297	14	h′	h′	PROPN
ejpam-3852	297	15	)	)	PUNCT
ejpam-3852	297	16	)	)	PUNCT
ejpam-3852	298	1	+	+	CCONJ
ejpam-3852	298	2	b+	b+	X
ejpam-3852	298	3	c	c	PROPN
ejpam-3852	298	4	≡	≡	PROPN
ejpam-3852	298	5	3a+	3a+	NUM
ejpam-3852	298	6	4(g′	4(g′	PROPN
ejpam-3852	298	7	+	+	CCONJ
ejpam-3852	298	8	h′	h′	PROPN
ejpam-3852	298	9	)	)	PUNCT
ejpam-3852	298	10	+	+	CCONJ
ejpam-3852	298	11	b+	b+	X
ejpam-3852	298	12	c	c	PROPN
ejpam-3852	298	13	≡	≡	PROPN
ejpam-3852	298	14	1	1	NUM
ejpam-3852	298	15	(	(	PUNCT
ejpam-3852	298	16	mod	mod	PROPN
ejpam-3852	298	17	8)	8)	NUM
ejpam-3852	298	18	.	.	PUNCT
ejpam-3852	298	19	which	which	PRON
ejpam-3852	298	20	contradicts	contradict	VERB
ejpam-3852	298	21	y3	y3	PROPN
ejpam-3852	298	22	≡	≡	PROPN
ejpam-3852	298	23	5	5	NUM
ejpam-3852	298	24	(	(	PUNCT
ejpam-3852	298	25	mod	mod	NOUN
ejpam-3852	298	26	8)	8)	NUM
ejpam-3852	298	27	.	.	PUNCT
ejpam-3852	299	1	so	so	ADV
ejpam-3852	299	2	,	,	PUNCT
ejpam-3852	299	3	a	a	DET
ejpam-3852	299	4	≡	≡	PROPN
ejpam-3852	299	5	1	1	NUM
ejpam-3852	299	6	(	(	PUNCT
ejpam-3852	299	7	mod	mod	NOUN
ejpam-3852	299	8	4	4	NUM
ejpam-3852	299	9	)	)	PUNCT
ejpam-3852	299	10	.	.	PUNCT
ejpam-3852	300	1	let	let	VERB
ejpam-3852	300	2	a	a	DET
ejpam-3852	300	3	=	=	SYM
ejpam-3852	300	4	1	1	NUM
ejpam-3852	300	5	+	+	NUM
ejpam-3852	300	6	4l′	4l′	NUM
ejpam-3852	300	7	,	,	PUNCT
ejpam-3852	300	8	l′	l′	PUNCT
ejpam-3852	300	9	∈	∈	PROPN
ejpam-3852	300	10	z.	z.	PROPN
ejpam-3852	301	1	so	so	ADV
ejpam-3852	301	2	,	,	PUNCT
ejpam-3852	301	3	b	b	PROPN
ejpam-3852	301	4	+	+	CCONJ
ejpam-3852	301	5	c	c	NOUN
ejpam-3852	301	6	=	=	SYM
ejpam-3852	301	7	2	2	NUM
ejpam-3852	301	8	+	+	NUM
ejpam-3852	301	9	4r′	4r′	NUM
ejpam-3852	301	10	for	for	ADP
ejpam-3852	301	11	some	some	DET
ejpam-3852	301	12	integer	integer	NOUN
ejpam-3852	301	13	r′	r′	PROPN
ejpam-3852	301	14	(	(	PUNCT
ejpam-3852	301	15	∵	∵	ADJ
ejpam-3852	301	16	y2	y2	PROPN
ejpam-3852	301	17	≡	≡	PROPN
ejpam-3852	302	1	a	a	DET
ejpam-3852	302	2	+	+	NOUN
ejpam-3852	302	3	b	b	NOUN
ejpam-3852	302	4	+	+	CCONJ
ejpam-3852	302	5	c	c	NOUN
ejpam-3852	302	6	≡	≡	PROPN
ejpam-3852	302	7	3	3	NUM
ejpam-3852	302	8	(	(	PUNCT
ejpam-3852	302	9	mod	mod	NOUN
ejpam-3852	302	10	4	4	NUM
ejpam-3852	302	11	)	)	PUNCT
ejpam-3852	302	12	)	)	PUNCT
ejpam-3852	302	13	.	.	PUNCT
ejpam-3852	303	1	now	now	ADV
ejpam-3852	303	2	,	,	PUNCT
ejpam-3852	303	3	y4	y4	PROPN
ejpam-3852	303	4	≡	≡	PROPN
ejpam-3852	303	5	ay3	ay3	VERB
ejpam-3852	303	6	+	+	CCONJ
ejpam-3852	304	1	by2	by2	PROPN
ejpam-3852	304	2	+	+	CCONJ
ejpam-3852	304	3	c	c	PROPN
ejpam-3852	304	4	≡	≡	PROPN
ejpam-3852	304	5	5a	5a	NUM
ejpam-3852	305	1	+	+	X
ejpam-3852	305	2	(	(	PUNCT
ejpam-3852	305	3	3	3	NUM
ejpam-3852	305	4	+	+	SYM
ejpam-3852	305	5	4(l′	4(l′	NUM
ejpam-3852	305	6	+	+	CCONJ
ejpam-3852	305	7	r′))b	r′))b	NOUN
ejpam-3852	305	8	+	+	CCONJ
ejpam-3852	305	9	c	c	NOUN
ejpam-3852	305	10	≡	≡	PROPN
ejpam-3852	305	11	7	7	NUM
ejpam-3852	306	1	+	+	NUM
ejpam-3852	306	2	2b	2b	NUM
ejpam-3852	306	3	+	+	CCONJ
ejpam-3852	306	4	4(l′	4(l′	NUM
ejpam-3852	306	5	+	+	NUM
ejpam-3852	306	6	r′	r′	NUM
ejpam-3852	306	7	)	)	PUNCT
ejpam-3852	307	1	+	+	NUM
ejpam-3852	307	2	4b(l′	4b(l′	NUM
ejpam-3852	307	3	+	+	NUM
ejpam-3852	307	4	r′	r′	NUM
ejpam-3852	307	5	)	)	PUNCT
ejpam-3852	307	6	(	(	PUNCT
ejpam-3852	307	7	mod	mod	PROPN
ejpam-3852	307	8	8)	8)	NUM
ejpam-3852	307	9	.	.	PUNCT
ejpam-3852	308	1	hence	hence	ADV
ejpam-3852	308	2	,	,	PUNCT
ejpam-3852	308	3	y4	y4	PROPN
ejpam-3852	308	4	≡	≡	PROPN
ejpam-3852	308	5	3	3	NUM
ejpam-3852	308	6	+	+	NUM
ejpam-3852	308	7	2b	2b	NUM
ejpam-3852	308	8	(	(	PUNCT
ejpam-3852	308	9	mod	mod	NOUN
ejpam-3852	308	10	4	4	NUM
ejpam-3852	308	11	)	)	PUNCT
ejpam-3852	308	12	and	and	CCONJ
ejpam-3852	308	13	so	so	ADV
ejpam-3852	308	14	from	from	ADP
ejpam-3852	308	15	y4	y4	PROPN
ejpam-3852	308	16	≡	≡	PROPN
ejpam-3852	308	17	3	3	NUM
ejpam-3852	308	18	(	(	PUNCT
ejpam-3852	308	19	mod	mod	NOUN
ejpam-3852	308	20	4	4	X
ejpam-3852	308	21	)	)	PUNCT
ejpam-3852	308	22	we	we	PRON
ejpam-3852	308	23	have	have	VERB
ejpam-3852	308	24	,	,	PUNCT
ejpam-3852	308	25	b	b	PRON
ejpam-3852	308	26	is	be	AUX
ejpam-3852	308	27	even	even	ADV
ejpam-3852	308	28	.	.	PUNCT
ejpam-3852	309	1	next	next	ADV
ejpam-3852	309	2	,	,	PUNCT
ejpam-3852	309	3	let	let	VERB
ejpam-3852	309	4	b	b	NOUN
ejpam-3852	309	5	=	=	SYM
ejpam-3852	309	6	2	2	NUM
ejpam-3852	309	7	+	+	NUM
ejpam-3852	309	8	4s′.	4s′.	NOUN
ejpam-3852	309	9	then	then	ADV
ejpam-3852	309	10	,	,	PUNCT
ejpam-3852	309	11	from	from	ADP
ejpam-3852	309	12	above	above	ADV
ejpam-3852	309	13	,	,	PUNCT
ejpam-3852	309	14	we	we	PRON
ejpam-3852	309	15	have	have	VERB
ejpam-3852	309	16	,	,	PUNCT
ejpam-3852	309	17	y4	y4	PROPN
ejpam-3852	309	18	≡	≡	PROPN
ejpam-3852	309	19	3	3	NUM
ejpam-3852	310	1	+	+	CCONJ
ejpam-3852	310	2	4(l′+	4(l′+	PROPN
ejpam-3852	310	3	r′	r′	PROPN
ejpam-3852	310	4	)	)	PUNCT
ejpam-3852	310	5	(	(	PUNCT
ejpam-3852	310	6	mod	mod	PROPN
ejpam-3852	310	7	8)	8)	NUM
ejpam-3852	310	8	.	.	PUNCT
ejpam-3852	311	1	so	so	ADV
ejpam-3852	311	2	,	,	PUNCT
ejpam-3852	311	3	y5	y5	PROPN
ejpam-3852	311	4	≡	≡	PROPN
ejpam-3852	311	5	ay4+by3+c	ay4+by3+c	PROPN
ejpam-3852	311	6	≡	≡	PROPN
ejpam-3852	311	7	3a+4a(l′+r′)+5b+c	3a+4a(l′+r′)+5b+c	NUM
ejpam-3852	311	8	≡	≡	PROPN
ejpam-3852	311	9	3a+b+c+4(l′+r′	3a+b+c+4(l′+r′	NUM
ejpam-3852	311	10	)	)	PUNCT
ejpam-3852	311	11	≡	≡	PROPN
ejpam-3852	311	12	5	5	NUM
ejpam-3852	311	13	(	(	PUNCT
ejpam-3852	311	14	mod	mod	NOUN
ejpam-3852	311	15	8)	8)	NUM
ejpam-3852	311	16	contradicting	contradict	VERB
ejpam-3852	311	17	the	the	DET
ejpam-3852	311	18	fact	fact	NOUN
ejpam-3852	311	19	y5	y5	NOUN
ejpam-3852	311	20	≡	≡	PROPN
ejpam-3852	311	21	1	1	NUM
ejpam-3852	311	22	(	(	PUNCT
ejpam-3852	311	23	mod	mod	PROPN
ejpam-3852	311	24	8)	8)	NUM
ejpam-3852	311	25	.	.	PUNCT
ejpam-3852	312	1	thus	thus	ADV
ejpam-3852	312	2	,	,	PUNCT
ejpam-3852	312	3	b	b	PROPN
ejpam-3852	312	4	≡	≡	PROPN
ejpam-3852	312	5	0	0	PUNCT
ejpam-3852	313	1	(	(	PUNCT
ejpam-3852	313	2	mod	mod	NOUN
ejpam-3852	313	3	4	4	NUM
ejpam-3852	313	4	)	)	PUNCT
ejpam-3852	313	5	and	and	CCONJ
ejpam-3852	313	6	hence	hence	ADV
ejpam-3852	313	7	,	,	PUNCT
ejpam-3852	313	8	c	c	PROPN
ejpam-3852	313	9	≡	≡	PROPN
ejpam-3852	313	10	2	2	NUM
ejpam-3852	313	11	(	(	PUNCT
ejpam-3852	313	12	mod	mod	NOUN
ejpam-3852	313	13	4	4	NUM
ejpam-3852	313	14	)	)	PUNCT
ejpam-3852	313	15	.	.	PUNCT
ejpam-3852	314	1	we	we	PRON
ejpam-3852	314	2	will	will	AUX
ejpam-3852	314	3	next	next	ADV
ejpam-3852	314	4	show	show	VERB
ejpam-3852	314	5	that	that	SCONJ
ejpam-3852	314	6	b	b	X
ejpam-3852	314	7	≡	≡	PROPN
ejpam-3852	314	8	0	0	PUNCT
ejpam-3852	315	1	(	(	PUNCT
ejpam-3852	315	2	mod	mod	PROPN
ejpam-3852	315	3	m	m	PROPN
ejpam-3852	315	4	2	2	NUM
ejpam-3852	315	5	)	)	PUNCT
ejpam-3852	315	6	.	.	PUNCT
ejpam-3852	316	1	by	by	ADP
ejpam-3852	316	2	our	our	PRON
ejpam-3852	316	3	assumption	assumption	NOUN
ejpam-3852	316	4	,	,	PUNCT
ejpam-3852	316	5	the	the	DET
ejpam-3852	316	6	period	period	NOUN
ejpam-3852	316	7	is	be	AUX
ejpam-3852	316	8	m	m	PROPN
ejpam-3852	316	9	2	2	NUM
ejpam-3852	316	10	and	and	CCONJ
ejpam-3852	316	11	{	{	PUNCT
ejpam-3852	316	12	y1	y1	NOUN
ejpam-3852	316	13	,	,	PUNCT
ejpam-3852	316	14	y2	y2	PROPN
ejpam-3852	316	15	,	,	PUNCT
ejpam-3852	316	16	.	.	PUNCT
ejpam-3852	316	17	.	.	PUNCT
ejpam-3852	317	1	.	.	PUNCT
ejpam-3852	318	1	,	,	PUNCT
ejpam-3852	318	2	ym	ym	NOUN
ejpam-3852	318	3	2	2	X
ejpam-3852	318	4	}	}	PUNCT
ejpam-3852	318	5	=	=	SYM
ejpam-3852	318	6	gm	gm	PROPN
ejpam-3852	318	7	.	.	PUNCT
ejpam-3852	319	1	now	now	ADV
ejpam-3852	319	2	,	,	PUNCT
ejpam-3852	319	3	clearly	clearly	ADV
ejpam-3852	319	4	every	every	DET
ejpam-3852	319	5	element	element	NOUN
ejpam-3852	319	6	in	in	ADP
ejpam-3852	319	7	gm	gm	PROPN
ejpam-3852	319	8	has	have	VERB
ejpam-3852	319	9	a	a	DET
ejpam-3852	319	10	unique	unique	ADJ
ejpam-3852	319	11	inverse	inverse	NOUN
ejpam-3852	319	12	in	in	ADP
ejpam-3852	319	13	gm	gm	PROPN
ejpam-3852	319	14	and	and	CCONJ
ejpam-3852	319	15	so	so	ADV
ejpam-3852	319	16	,	,	PUNCT
ejpam-3852	319	17	m	m	VERB
ejpam-3852	319	18	2∑	2∑	NUM
ejpam-3852	319	19	i=1	i=1	X
ejpam-3852	319	20	yi	yi	NOUN
ejpam-3852	320	1	=	=	PUNCT
ejpam-3852	320	2	m	m	VERB
ejpam-3852	320	3	2∑	2∑	NUM
ejpam-3852	320	4	i=1	i=1	X
ejpam-3852	321	1	y−1i	y−1i	NOUN
ejpam-3852	322	1	=	=	NOUN
ejpam-3852	322	2	m	m	VERB
ejpam-3852	322	3	2	2	NUM
ejpam-3852	322	4	−1∑	−1∑	PROPN
ejpam-3852	322	5	i=0	i=0	PROPN
ejpam-3852	322	6	(	(	PUNCT
ejpam-3852	322	7	2i+	2i+	NUM
ejpam-3852	322	8	1	1	NUM
ejpam-3852	322	9	)	)	PUNCT
ejpam-3852	322	10	=	=	SYM
ejpam-3852	322	11	m2	m2	PROPN
ejpam-3852	322	12	4	4	NUM
ejpam-3852	322	13	.	.	PUNCT
ejpam-3852	323	1	p.	p.	NOUN
ejpam-3852	323	2	stănică	stănică	NUM
ejpam-3852	323	3	et	et	PROPN
ejpam-3852	323	4	al	al	PROPN
ejpam-3852	323	5	.	.	PUNCT
ejpam-3852	323	6	/	/	SYM
ejpam-3852	323	7	eur	eur	PROPN
ejpam-3852	323	8	.	.	PUNCT
ejpam-3852	324	1	j.	j.	PROPN
ejpam-3852	324	2	pure	pure	PROPN
ejpam-3852	324	3	appl	appl	PROPN
ejpam-3852	324	4	.	.	PROPN
ejpam-3852	324	5	math	math	PROPN
ejpam-3852	324	6	,	,	PUNCT
ejpam-3852	324	7	14	14	NUM
ejpam-3852	324	8	(	(	PUNCT
ejpam-3852	324	9	1	1	NUM
ejpam-3852	324	10	)	)	PUNCT
ejpam-3852	324	11	(	(	PUNCT
ejpam-3852	324	12	2021	2021	NUM
ejpam-3852	324	13	)	)	PUNCT
ejpam-3852	324	14	,	,	PUNCT
ejpam-3852	324	15	1	1	NUM
ejpam-3852	324	16	-	-	SYM
ejpam-3852	324	17	18	18	NUM
ejpam-3852	324	18	10	10	NUM
ejpam-3852	324	19	again	again	ADV
ejpam-3852	324	20	,	,	PUNCT
ejpam-3852	324	21	as	as	SCONJ
ejpam-3852	324	22	ym	ym	PROPN
ejpam-3852	324	23	2	2	NUM
ejpam-3852	324	24	+1	+1	PROPN
ejpam-3852	324	25	≡	≡	PROPN
ejpam-3852	324	26	y1	y1	PROPN
ejpam-3852	324	27	(	(	PUNCT
ejpam-3852	324	28	mod	mod	PROPN
ejpam-3852	324	29	m	m	PROPN
ejpam-3852	324	30	)	)	PUNCT
ejpam-3852	324	31	,	,	PUNCT
ejpam-3852	324	32	we	we	PRON
ejpam-3852	324	33	have	have	VERB
ejpam-3852	324	34	the	the	DET
ejpam-3852	324	35	sequence	sequence	NOUN
ejpam-3852	324	36	of	of	ADP
ejpam-3852	324	37	equivalent	equivalent	ADJ
ejpam-3852	324	38	congruences	congruence	NOUN
ejpam-3852	324	39	m	m	VERB
ejpam-3852	324	40	2	2	NUM
ejpam-3852	324	41	−1∑	−1∑	PROPN
ejpam-3852	324	42	i=0	i=0	PROPN
ejpam-3852	325	1	yi+2	yi+2	NUM
ejpam-3852	325	2	≡	≡	PROPN
ejpam-3852	325	3	m	m	VERB
ejpam-3852	325	4	2	2	NUM
ejpam-3852	325	5	−1∑	−1∑	PROPN
ejpam-3852	325	6	i=0	i=0	PROPN
ejpam-3852	325	7	(	(	PUNCT
ejpam-3852	325	8	ay−1i+1	ay−1i+1	PROPN
ejpam-3852	325	9	+	+	NUM
ejpam-3852	325	10	byi	byi	ADJ
ejpam-3852	325	11	+	+	CCONJ
ejpam-3852	325	12	c	c	X
ejpam-3852	325	13	)	)	PUNCT
ejpam-3852	325	14	(	(	PUNCT
ejpam-3852	325	15	mod	mod	PROPN
ejpam-3852	325	16	m	m	PROPN
ejpam-3852	325	17	)	)	PUNCT
ejpam-3852	325	18	,	,	PUNCT
ejpam-3852	325	19	m	m	VERB
ejpam-3852	325	20	2∑	2∑	NUM
ejpam-3852	325	21	i=1	i=1	X
ejpam-3852	325	22	yi	yi	PROPN
ejpam-3852	325	23	≡	≡	PROPN
ejpam-3852	325	24	a	a	DET
ejpam-3852	325	25	m	m	ADJ
ejpam-3852	325	26	2	2	NUM
ejpam-3852	326	1	−1∑	−1∑	PROPN
ejpam-3852	326	2	i=0	i=0	PROPN
ejpam-3852	326	3	y−1i+1	y−1i+1	PROPN
ejpam-3852	326	4	+	+	PROPN
ejpam-3852	326	5	b	b	PROPN
ejpam-3852	326	6	m	m	VERB
ejpam-3852	326	7	2	2	NUM
ejpam-3852	326	8	−1∑	−1∑	PROPN
ejpam-3852	326	9	i=0	i=0	PROPN
ejpam-3852	326	10	yi	yi	PROPN
ejpam-3852	327	1	+	+	CCONJ
ejpam-3852	327	2	c	c	NOUN
ejpam-3852	327	3	m	m	VERB
ejpam-3852	327	4	2	2	NUM
ejpam-3852	327	5	−1∑	−1∑	PROPN
ejpam-3852	327	6	i=0	i=0	PROPN
ejpam-3852	327	7	1	1	NUM
ejpam-3852	327	8	(	(	PUNCT
ejpam-3852	327	9	mod	mod	PROPN
ejpam-3852	327	10	m	m	PROPN
ejpam-3852	327	11	)	)	PUNCT
ejpam-3852	327	12	,	,	PUNCT
ejpam-3852	327	13	m	m	VERB
ejpam-3852	327	14	2∑	2∑	NUM
ejpam-3852	327	15	i=1	i=1	X
ejpam-3852	327	16	yi	yi	PROPN
ejpam-3852	327	17	≡	≡	PROPN
ejpam-3852	327	18	a	a	DET
ejpam-3852	327	19	m	m	ADJ
ejpam-3852	328	1	2∑	2∑	NUM
ejpam-3852	328	2	i=1	i=1	X
ejpam-3852	329	1	y−1i	y−1i	PROPN
ejpam-3852	330	1	+	+	CCONJ
ejpam-3852	330	2	b	b	X
ejpam-3852	330	3	(	(	PUNCT
ejpam-3852	330	4	y0	y0	NOUN
ejpam-3852	330	5	+	+	NOUN
ejpam-3852	330	6	m	m	VERB
ejpam-3852	330	7	2∑	2∑	NUM
ejpam-3852	330	8	i=1	i=1	X
ejpam-3852	330	9	yi	yi	PROPN
ejpam-3852	331	1	−	−	NOUN
ejpam-3852	331	2	ym	ym	NOUN
ejpam-3852	331	3	2	2	NUM
ejpam-3852	331	4	)	)	PUNCT
ejpam-3852	332	1	+	+	CCONJ
ejpam-3852	333	1	c	c	X
ejpam-3852	333	2	m	m	VERB
ejpam-3852	333	3	2	2	NUM
ejpam-3852	333	4	(	(	PUNCT
ejpam-3852	333	5	mod	mod	PROPN
ejpam-3852	333	6	m	m	PROPN
ejpam-3852	333	7	)	)	PUNCT
ejpam-3852	333	8	,	,	PUNCT
ejpam-3852	333	9	m2	m2	PROPN
ejpam-3852	333	10	4	4	NUM
ejpam-3852	333	11	≡	≡	PROPN
ejpam-3852	333	12	am	be	AUX
ejpam-3852	333	13	2	2	NUM
ejpam-3852	333	14	4	4	NUM
ejpam-3852	333	15	+	+	SYM
ejpam-3852	333	16	b	b	X
ejpam-3852	333	17	(	(	PUNCT
ejpam-3852	333	18	y0	y0	PROPN
ejpam-3852	333	19	+	+	PROPN
ejpam-3852	333	20	m2	m2	PROPN
ejpam-3852	333	21	4	4	NUM
ejpam-3852	333	22	−	−	NOUN
ejpam-3852	333	23	ym	ym	NOUN
ejpam-3852	333	24	2	2	NUM
ejpam-3852	333	25	)	)	PUNCT
ejpam-3852	334	1	+	+	CCONJ
ejpam-3852	334	2	c	c	X
ejpam-3852	334	3	m	m	VERB
ejpam-3852	334	4	2	2	NUM
ejpam-3852	334	5	(	(	PUNCT
ejpam-3852	334	6	mod	mod	PROPN
ejpam-3852	334	7	m	m	PROPN
ejpam-3852	334	8	)	)	PUNCT
ejpam-3852	334	9	,	,	PUNCT
ejpam-3852	334	10	0	0	NUM
ejpam-3852	334	11	≡	≡	PROPN
ejpam-3852	334	12	b	b	PROPN
ejpam-3852	334	13	(	(	PUNCT
ejpam-3852	334	14	y0	y0	PROPN
ejpam-3852	334	15	−	−	NOUN
ejpam-3852	334	16	ym	ym	NOUN
ejpam-3852	334	17	2	2	NUM
ejpam-3852	334	18	)	)	PUNCT
ejpam-3852	334	19	(	(	PUNCT
ejpam-3852	334	20	mod	mod	PROPN
ejpam-3852	334	21	m	m	PROPN
ejpam-3852	334	22	)	)	PUNCT
ejpam-3852	334	23	(	(	PUNCT
ejpam-3852	334	24	∵	∵	NOUN
ejpam-3852	334	25	c	c	NOUN
ejpam-3852	334	26	is	be	AUX
ejpam-3852	334	27	even	even	ADV
ejpam-3852	334	28	and	and	CCONJ
ejpam-3852	334	29	ω	ω	NUM
ejpam-3852	334	30	≥	≥	NOUN
ejpam-3852	334	31	3	3	NUM
ejpam-3852	334	32	)	)	PUNCT
ejpam-3852	334	33	.	.	PUNCT
ejpam-3852	335	1	now	now	ADV
ejpam-3852	335	2	,	,	PUNCT
ejpam-3852	335	3	in	in	ADP
ejpam-3852	335	4	our	our	PRON
ejpam-3852	335	5	case	case	NOUN
ejpam-3852	335	6	,	,	PUNCT
ejpam-3852	335	7	we	we	PRON
ejpam-3852	335	8	have	have	VERB
ejpam-3852	335	9	,	,	PUNCT
ejpam-3852	335	10	y0	y0	NOUN
ejpam-3852	335	11	=	=	SYM
ejpam-3852	335	12	y1	y1	NOUN
ejpam-3852	335	13	=	=	SYM
ejpam-3852	335	14	1	1	X
ejpam-3852	335	15	.	.	PUNCT
ejpam-3852	336	1	and	and	CCONJ
ejpam-3852	336	2	so	so	ADV
ejpam-3852	336	3	,	,	PUNCT
ejpam-3852	336	4	from	from	ADP
ejpam-3852	336	5	above	above	ADV
ejpam-3852	336	6	,	,	PUNCT
ejpam-3852	336	7	we	we	PRON
ejpam-3852	336	8	have	have	VERB
ejpam-3852	336	9	,	,	PUNCT
ejpam-3852	336	10	b	b	X
ejpam-3852	336	11	(	(	PUNCT
ejpam-3852	336	12	y1	y1	INTJ
ejpam-3852	336	13	−	−	PROPN
ejpam-3852	336	14	ym	ym	NOUN
ejpam-3852	336	15	2	2	NUM
ejpam-3852	336	16	)	)	PUNCT
ejpam-3852	336	17	≡	≡	PROPN
ejpam-3852	336	18	0	0	PUNCT
ejpam-3852	337	1	(	(	PUNCT
ejpam-3852	337	2	mod	mod	PROPN
ejpam-3852	337	3	m	m	PROPN
ejpam-3852	337	4	)	)	PUNCT
ejpam-3852	337	5	.	.	PUNCT
ejpam-3852	338	1	next	next	ADV
ejpam-3852	338	2	,	,	PUNCT
ejpam-3852	338	3	note	note	VERB
ejpam-3852	338	4	that	that	SCONJ
ejpam-3852	338	5	,	,	PUNCT
ejpam-3852	338	6	in	in	ADP
ejpam-3852	338	7	our	our	PRON
ejpam-3852	338	8	case	case	NOUN
ejpam-3852	338	9	ym	ym	NOUN
ejpam-3852	338	10	2	2	NUM
ejpam-3852	338	11	−	−	NOUN
ejpam-3852	338	12	y1	y1	PROPN
ejpam-3852	338	13	≡	≡	PROPN
ejpam-3852	338	14	2	2	NUM
ejpam-3852	338	15	(	(	PUNCT
ejpam-3852	338	16	mod	mod	NOUN
ejpam-3852	338	17	4	4	NUM
ejpam-3852	338	18	)	)	PUNCT
ejpam-3852	338	19	and	and	CCONJ
ejpam-3852	338	20	so	so	ADV
ejpam-3852	338	21	,	,	PUNCT
ejpam-3852	338	22	b	b	PROPN
ejpam-3852	338	23	≡	≡	PROPN
ejpam-3852	338	24	0	0	PUNCT
ejpam-3852	339	1	(	(	PUNCT
ejpam-3852	339	2	mod	mod	PROPN
ejpam-3852	339	3	m	m	PROPN
ejpam-3852	339	4	2	2	NUM
ejpam-3852	339	5	)	)	PUNCT
ejpam-3852	339	6	.	.	PUNCT
ejpam-3852	340	1	sufficiency	sufficiency	NOUN
ejpam-3852	340	2	:	:	PUNCT
ejpam-3852	340	3	as	as	ADP
ejpam-3852	340	4	b	b	PROPN
ejpam-3852	340	5	≡	≡	PROPN
ejpam-3852	340	6	0	0	PUNCT
ejpam-3852	341	1	(	(	PUNCT
ejpam-3852	341	2	mod	mod	PROPN
ejpam-3852	341	3	m	m	PROPN
ejpam-3852	341	4	2	2	NUM
ejpam-3852	341	5	)	)	PUNCT
ejpam-3852	341	6	so	so	ADV
ejpam-3852	341	7	,	,	PUNCT
ejpam-3852	341	8	byn	byn	PROPN
ejpam-3852	341	9	≡	≡	PROPN
ejpam-3852	341	10	b	b	PROPN
ejpam-3852	341	11	(	(	PUNCT
ejpam-3852	341	12	mod	mod	PROPN
ejpam-3852	341	13	m	m	PROPN
ejpam-3852	341	14	)	)	PUNCT
ejpam-3852	341	15	and	and	CCONJ
ejpam-3852	341	16	so	so	ADV
ejpam-3852	341	17	(	(	PUNCT
ejpam-3852	341	18	5	5	X
ejpam-3852	341	19	)	)	PUNCT
ejpam-3852	341	20	reduces	reduce	VERB
ejpam-3852	341	21	to	to	ADP
ejpam-3852	341	22	yn+2	yn+2	NUM
ejpam-3852	341	23	≡	≡	PROPN
ejpam-3852	341	24	ay−1n+1	ay−1n+1	PROPN
ejpam-3852	342	1	+	+	CCONJ
ejpam-3852	342	2	(	(	PUNCT
ejpam-3852	342	3	b+	b+	X
ejpam-3852	342	4	c	c	X
ejpam-3852	342	5	)	)	PUNCT
ejpam-3852	342	6	(	(	PUNCT
ejpam-3852	342	7	mod	mod	PROPN
ejpam-3852	342	8	m	m	PROPN
ejpam-3852	342	9	)	)	PUNCT
ejpam-3852	342	10	,	,	PUNCT
ejpam-3852	342	11	where	where	SCONJ
ejpam-3852	342	12	a	a	DET
ejpam-3852	342	13	≡	≡	PROPN
ejpam-3852	342	14	1	1	NUM
ejpam-3852	342	15	(	(	PUNCT
ejpam-3852	342	16	mod	mod	NOUN
ejpam-3852	342	17	4	4	NUM
ejpam-3852	342	18	)	)	PUNCT
ejpam-3852	342	19	and	and	CCONJ
ejpam-3852	342	20	(	(	PUNCT
ejpam-3852	342	21	b	b	X
ejpam-3852	342	22	+	+	CCONJ
ejpam-3852	342	23	c	c	X
ejpam-3852	342	24	)	)	PUNCT
ejpam-3852	342	25	≡	≡	PROPN
ejpam-3852	342	26	2	2	NUM
ejpam-3852	342	27	(	(	PUNCT
ejpam-3852	342	28	mod	mod	NOUN
ejpam-3852	342	29	4	4	NUM
ejpam-3852	342	30	)	)	PUNCT
ejpam-3852	342	31	.	.	PUNCT
ejpam-3852	343	1	so	so	ADV
ejpam-3852	343	2	,	,	PUNCT
ejpam-3852	343	3	by	by	ADP
ejpam-3852	343	4	(	(	PUNCT
ejpam-3852	343	5	1	1	NUM
ejpam-3852	343	6	)	)	PUNCT
ejpam-3852	343	7	,	,	PUNCT
ejpam-3852	343	8	the	the	DET
ejpam-3852	343	9	period	period	NOUN
ejpam-3852	343	10	of	of	ADP
ejpam-3852	343	11	{	{	PUNCT
ejpam-3852	343	12	yn	yn	NOUN
ejpam-3852	343	13	}	}	PUNCT
ejpam-3852	343	14	is	be	AUX
ejpam-3852	343	15	m	m	PROPN
ejpam-3852	343	16	2	2	NUM
ejpam-3852	343	17	and	and	CCONJ
ejpam-3852	343	18	{	{	PUNCT
ejpam-3852	343	19	y1	y1	NOUN
ejpam-3852	343	20	,	,	PUNCT
ejpam-3852	343	21	y2	y2	PROPN
ejpam-3852	343	22	,	,	PUNCT
ejpam-3852	343	23	.	.	PUNCT
ejpam-3852	343	24	.	.	PUNCT
ejpam-3852	343	25	.	.	PUNCT
ejpam-3852	344	1	,	,	PUNCT
ejpam-3852	344	2	ym	ym	NOUN
ejpam-3852	344	3	2	2	X
ejpam-3852	344	4	}	}	PUNCT
ejpam-3852	344	5	=	=	SYM
ejpam-3852	344	6	gm	gm	PROPN
ejpam-3852	344	7	.	.	PUNCT
ejpam-3852	345	1	remark	remark	PROPN
ejpam-3852	345	2	3	3	NUM
ejpam-3852	345	3	.	.	PUNCT
ejpam-3852	345	4	note	note	VERB
ejpam-3852	345	5	that	that	SCONJ
ejpam-3852	345	6	,	,	PUNCT
ejpam-3852	345	7	for	for	ADP
ejpam-3852	345	8	some	some	DET
ejpam-3852	345	9	initial	initial	ADJ
ejpam-3852	345	10	conditions	condition	NOUN
ejpam-3852	345	11	,	,	PUNCT
ejpam-3852	345	12	we	we	PRON
ejpam-3852	345	13	can	can	AUX
ejpam-3852	345	14	obtain	obtain	VERB
ejpam-3852	345	15	period	period	NOUN
ejpam-3852	345	16	equal	equal	ADJ
ejpam-3852	345	17	to	to	ADP
ejpam-3852	345	18	8	8	NUM
ejpam-3852	345	19	(	(	PUNCT
ejpam-3852	345	20	mod	mod	PROPN
ejpam-3852	345	21	16	16	NUM
ejpam-3852	345	22	)	)	PUNCT
ejpam-3852	345	23	for	for	ADP
ejpam-3852	345	24	other	other	ADJ
ejpam-3852	345	25	values	value	NOUN
ejpam-3852	345	26	of	of	ADP
ejpam-3852	345	27	a	a	DET
ejpam-3852	345	28	,	,	PUNCT
ejpam-3852	345	29	b	b	PROPN
ejpam-3852	345	30	and	and	CCONJ
ejpam-3852	345	31	c	c	X
ejpam-3852	345	32	where	where	SCONJ
ejpam-3852	345	33	a	a	PRON
ejpam-3852	345	34	is	be	AUX
ejpam-3852	345	35	odd	odd	ADJ
ejpam-3852	345	36	and	and	CCONJ
ejpam-3852	345	37	b	b	NOUN
ejpam-3852	345	38	and	and	CCONJ
ejpam-3852	345	39	c	c	PROPN
ejpam-3852	345	40	are	be	AUX
ejpam-3852	345	41	even	even	ADV
ejpam-3852	345	42	,	,	PUNCT
ejpam-3852	345	43	or	or	CCONJ
ejpam-3852	345	44	where	where	SCONJ
ejpam-3852	345	45	b	b	NOUN
ejpam-3852	345	46	is	be	AUX
ejpam-3852	345	47	odd	odd	ADJ
ejpam-3852	345	48	and	and	CCONJ
ejpam-3852	345	49	a	a	PRON
ejpam-3852	345	50	and	and	CCONJ
ejpam-3852	345	51	c	c	NOUN
ejpam-3852	345	52	are	be	AUX
ejpam-3852	345	53	even	even	ADV
ejpam-3852	345	54	.	.	PUNCT
ejpam-3852	346	1	thus	thus	ADV
ejpam-3852	346	2	,	,	PUNCT
ejpam-3852	346	3	the	the	DET
ejpam-3852	346	4	conditions	condition	NOUN
ejpam-3852	346	5	of	of	ADP
ejpam-3852	346	6	theorem	theorem	NOUN
ejpam-3852	346	7	5	5	NUM
ejpam-3852	346	8	are	be	AUX
ejpam-3852	346	9	only	only	ADV
ejpam-3852	346	10	necessary	necessary	ADJ
ejpam-3852	346	11	if	if	SCONJ
ejpam-3852	346	12	the	the	DET
ejpam-3852	346	13	period	period	NOUN
ejpam-3852	346	14	is	be	AUX
ejpam-3852	346	15	m	m	PROPN
ejpam-3852	346	16	2	2	NUM
ejpam-3852	346	17	,	,	PUNCT
ejpam-3852	346	18	regardless	regardless	ADV
ejpam-3852	346	19	of	of	ADP
ejpam-3852	346	20	initial	initial	ADJ
ejpam-3852	346	21	conditions	condition	NOUN
ejpam-3852	346	22	.	.	PUNCT
ejpam-3852	347	1	4	4	X
ejpam-3852	347	2	.	.	X
ejpam-3852	347	3	lattice	lattice	NOUN
ejpam-3852	347	4	testing	testing	NOUN
ejpam-3852	347	5	for	for	ADP
ejpam-3852	347	6	a	a	DET
ejpam-3852	347	7	binary	binary	ADJ
ejpam-3852	347	8	sequence	sequence	NOUN
ejpam-3852	347	9	associated	associate	VERB
ejpam-3852	347	10	to	to	PART
ejpam-3852	347	11	hicg	hicg	NOUN
ejpam-3852	347	12	let	let	VERB
ejpam-3852	347	13	{	{	PUNCT
ejpam-3852	347	14	yn	yn	NOUN
ejpam-3852	347	15	}	}	PUNCT
ejpam-3852	347	16	be	be	VERB
ejpam-3852	347	17	our	our	PRON
ejpam-3852	347	18	hicg	hicg	ADJ
ejpam-3852	347	19	sequence	sequence	NOUN
ejpam-3852	347	20	with	with	ADP
ejpam-3852	347	21	some	some	DET
ejpam-3852	347	22	initial	initial	ADJ
ejpam-3852	347	23	conditions	condition	NOUN
ejpam-3852	347	24	.	.	PUNCT
ejpam-3852	348	1	in	in	ADP
ejpam-3852	348	2	the	the	DET
ejpam-3852	348	3	spirit	spirit	NOUN
ejpam-3852	348	4	of	of	ADP
ejpam-3852	348	5	the	the	DET
ejpam-3852	348	6	known	know	VERB
ejpam-3852	348	7	blum	blum	PROPN
ejpam-3852	348	8	-	-	PUNCT
ejpam-3852	348	9	micali	micali	ADJ
ejpam-3852	348	10	prn	prn	NOUN
ejpam-3852	348	11	[	[	X
ejpam-3852	348	12	1	1	NUM
ejpam-3852	348	13	]	]	PUNCT
ejpam-3852	348	14	,	,	PUNCT
ejpam-3852	348	15	we	we	PRON
ejpam-3852	348	16	define	define	VERB
ejpam-3852	348	17	a	a	DET
ejpam-3852	348	18	pseudorandom	pseudorandom	ADJ
ejpam-3852	348	19	binary	binary	ADJ
ejpam-3852	348	20	sequence	sequence	NOUN
ejpam-3852	348	21	{	{	PUNCT
ejpam-3852	348	22	zn	zn	NOUN
ejpam-3852	348	23	}	}	PUNCT
ejpam-3852	348	24	by	by	ADP
ejpam-3852	348	25	zn	zn	PROPN
ejpam-3852	348	26	=	=	SYM
ejpam-3852	348	27	f(yn	f(yn	PROPN
ejpam-3852	348	28	)	)	PUNCT
ejpam-3852	348	29	,	,	PUNCT
ejpam-3852	348	30	where	where	SCONJ
ejpam-3852	348	31	f	f	X
ejpam-3852	348	32	:	:	PUNCT
ejpam-3852	348	33	gm	gm	PROPN
ejpam-3852	348	34	→	→	PUNCT
ejpam-3852	348	35	{	{	PUNCT
ejpam-3852	348	36	0	0	NUM
ejpam-3852	348	37	,	,	PUNCT
ejpam-3852	348	38	1	1	NUM
ejpam-3852	348	39	}	}	PUNCT
ejpam-3852	348	40	is	be	AUX
ejpam-3852	348	41	given	give	VERB
ejpam-3852	348	42	by	by	ADP
ejpam-3852	348	43	f(x	f(x	PROPN
ejpam-3852	348	44	)	)	PUNCT
ejpam-3852	349	1	=	=	PRON
ejpam-3852	349	2	{	{	PUNCT
ejpam-3852	349	3	0	0	NUM
ejpam-3852	349	4	if	if	SCONJ
ejpam-3852	349	5	x	x	X
ejpam-3852	349	6	<	<	X
ejpam-3852	349	7	m	m	VERB
ejpam-3852	349	8	2	2	NUM
ejpam-3852	349	9	1	1	NUM
ejpam-3852	349	10	if	if	SCONJ
ejpam-3852	349	11	x	x	PROPN
ejpam-3852	349	12	>	>	X
ejpam-3852	349	13	m	m	PROPN
ejpam-3852	349	14	2	2	NUM
ejpam-3852	349	15	.	.	PUNCT
ejpam-3852	350	1	a	a	DET
ejpam-3852	350	2	sagemath	sagemath	NOUN
ejpam-3852	350	3	code	code	NOUN
ejpam-3852	350	4	with	with	ADP
ejpam-3852	350	5	the	the	DET
ejpam-3852	350	6	parameters	parameter	NOUN
ejpam-3852	350	7	ω	ω	NOUN
ejpam-3852	350	8	=	=	SYM
ejpam-3852	350	9	64	64	NUM
ejpam-3852	350	10	,	,	PUNCT
ejpam-3852	350	11	a	a	PRON
ejpam-3852	350	12	=	=	SYM
ejpam-3852	350	13	1886906	1886906	NUM
ejpam-3852	350	14	,	,	PUNCT
ejpam-3852	350	15	b	b	X
ejpam-3852	350	16	=	=	SYM
ejpam-3852	350	17	706715	706715	NUM
ejpam-3852	350	18	,	,	PUNCT
ejpam-3852	350	19	c	c	NOUN
ejpam-3852	350	20	=	=	SYM
ejpam-3852	350	21	807782	807782	NUM
ejpam-3852	350	22	,	,	PUNCT
ejpam-3852	350	23	y0	y0	PROPN
ejpam-3852	350	24	=	=	SYM
ejpam-3852	350	25	430227	430227	NUM
ejpam-3852	350	26	and	and	CCONJ
ejpam-3852	350	27	y1	y1	NOUN
ejpam-3852	350	28	=	=	SYM
ejpam-3852	350	29	1725239	1725239	NUM
ejpam-3852	350	30	has	have	AUX
ejpam-3852	350	31	been	be	AUX
ejpam-3852	350	32	provided	provide	VERB
ejpam-3852	350	33	in	in	ADP
ejpam-3852	350	34	the	the	DET
ejpam-3852	350	35	appendix	appendix	NOUN
ejpam-3852	350	36	which	which	PRON
ejpam-3852	350	37	will	will	AUX
ejpam-3852	350	38	generate	generate	VERB
ejpam-3852	350	39	108	108	NUM
ejpam-3852	350	40	p.	p.	NOUN
ejpam-3852	350	41	stănică	stănică	NUM
ejpam-3852	350	42	et	et	NOUN
ejpam-3852	350	43	al	al	PROPN
ejpam-3852	350	44	.	.	PUNCT
ejpam-3852	350	45	/	/	SYM
ejpam-3852	350	46	eur	eur	PROPN
ejpam-3852	350	47	.	.	PUNCT
ejpam-3852	351	1	j.	j.	PROPN
ejpam-3852	351	2	pure	pure	PROPN
ejpam-3852	351	3	appl	appl	PROPN
ejpam-3852	351	4	.	.	PROPN
ejpam-3852	351	5	math	math	PROPN
ejpam-3852	351	6	,	,	PUNCT
ejpam-3852	351	7	14	14	NUM
ejpam-3852	351	8	(	(	PUNCT
ejpam-3852	351	9	1	1	NUM
ejpam-3852	351	10	)	)	PUNCT
ejpam-3852	351	11	(	(	PUNCT
ejpam-3852	351	12	2021	2021	NUM
ejpam-3852	351	13	)	)	PUNCT
ejpam-3852	351	14	,	,	PUNCT
ejpam-3852	351	15	1	1	NUM
ejpam-3852	351	16	-	-	SYM
ejpam-3852	351	17	18	18	NUM
ejpam-3852	351	18	11	11	NUM
ejpam-3852	351	19	prns	prn	NOUN
ejpam-3852	351	20	.	.	PUNCT
ejpam-3852	352	1	as	as	ADP
ejpam-3852	352	2	for	for	ADP
ejpam-3852	352	3	the	the	DET
ejpam-3852	352	4	linear	linear	ADJ
ejpam-3852	352	5	and	and	CCONJ
ejpam-3852	352	6	inversive	inversive	ADJ
ejpam-3852	352	7	congruential	congruential	ADJ
ejpam-3852	352	8	generator	generator	NOUN
ejpam-3852	352	9	,	,	PUNCT
ejpam-3852	352	10	one	one	PRON
ejpam-3852	352	11	can	can	AUX
ejpam-3852	352	12	define	define	VERB
ejpam-3852	352	13	an	an	DET
ejpam-3852	352	14	sdimensional	sdimensional	ADJ
ejpam-3852	352	15	lattice	lattice	NOUN
ejpam-3852	352	16	test	test	NOUN
ejpam-3852	352	17	for	for	ADP
ejpam-3852	352	18	our	our	PRON
ejpam-3852	352	19	hybrid	hybrid	ADJ
ejpam-3852	352	20	sequence	sequence	NOUN
ejpam-3852	352	21	(	(	PUNCT
ejpam-3852	352	22	of	of	ADP
ejpam-3852	352	23	period	period	NOUN
ejpam-3852	352	24	,	,	PUNCT
ejpam-3852	352	25	say	say	VERB
ejpam-3852	352	26	t	t	PROPN
ejpam-3852	352	27	)	)	PUNCT
ejpam-3852	352	28	for	for	ADP
ejpam-3852	352	29	the	the	DET
ejpam-3852	352	30	characteristics	characteristic	NOUN
ejpam-3852	352	31	2	2	NUM
ejpam-3852	352	32	(	(	PUNCT
ejpam-3852	352	33	hence	hence	ADV
ejpam-3852	352	34	of	of	ADP
ejpam-3852	352	35	2ω	2ω	NUM
ejpam-3852	352	36	modulus	modulus	NOUN
ejpam-3852	352	37	)	)	PUNCT
ejpam-3852	352	38	.	.	PUNCT
ejpam-3852	353	1	for	for	ADP
ejpam-3852	353	2	the	the	DET
ejpam-3852	353	3	binary	binary	ADJ
ejpam-3852	353	4	sequence	sequence	NOUN
ejpam-3852	353	5	(	(	PUNCT
ejpam-3852	353	6	defined	define	VERB
ejpam-3852	353	7	above	above	ADV
ejpam-3852	353	8	)	)	PUNCT
ejpam-3852	353	9	{	{	PUNCT
ejpam-3852	353	10	zn	zn	X
ejpam-3852	353	11	}	}	PUNCT
ejpam-3852	353	12	passes	pass	VERB
ejpam-3852	353	13	the	the	DET
ejpam-3852	353	14	l	l	ADJ
ejpam-3852	353	15	-	-	ADJ
ejpam-3852	353	16	dimensional	dimensional	ADJ
ejpam-3852	353	17	lattice	lattice	NOUN
ejpam-3852	353	18	test	test	NOUN
ejpam-3852	353	19	if	if	SCONJ
ejpam-3852	353	20	the	the	DET
ejpam-3852	353	21	vectors	vector	NOUN
ejpam-3852	353	22	{	{	PUNCT
ejpam-3852	353	23	zn	zn	PROPN
ejpam-3852	353	24	:	:	PUNCT
ejpam-3852	353	25	zn	zn	PROPN
ejpam-3852	353	26	=	=	SYM
ejpam-3852	353	27	(	(	PUNCT
ejpam-3852	353	28	zn	zn	PROPN
ejpam-3852	353	29	,	,	PUNCT
ejpam-3852	353	30	zn+1	zn+1	PROPN
ejpam-3852	353	31	,	,	PUNCT
ejpam-3852	353	32	.	.	PUNCT
ejpam-3852	353	33	.	.	PUNCT
ejpam-3852	353	34	.	.	PUNCT
ejpam-3852	354	1	,	,	PUNCT
ejpam-3852	354	2	zn+l−1	zn+l−1	PROPN
ejpam-3852	354	3	)	)	PUNCT
ejpam-3852	354	4	,	,	PUNCT
ejpam-3852	354	5	for	for	ADP
ejpam-3852	354	6	0	0	NUM
ejpam-3852	354	7	≤	≤	NUM
ejpam-3852	354	8	n	n	CCONJ
ejpam-3852	354	9	<	<	X
ejpam-3852	354	10	t	t	PROPN
ejpam-3852	354	11	}	}	PUNCT
ejpam-3852	354	12	,	,	PUNCT
ejpam-3852	354	13	span	span	VERB
ejpam-3852	354	14	fl2	fl2	PROPN
ejpam-3852	354	15	(	(	PUNCT
ejpam-3852	354	16	we	we	PRON
ejpam-3852	354	17	will	will	AUX
ejpam-3852	354	18	write	write	VERB
ejpam-3852	354	19	below	below	ADP
ejpam-3852	354	20	span	span	NOUN
ejpam-3852	354	21	(	(	PUNCT
ejpam-3852	354	22	·	·	PUNCT
ejpam-3852	354	23	)	)	PUNCT
ejpam-3852	354	24	for	for	ADP
ejpam-3852	354	25	the	the	DET
ejpam-3852	354	26	span	span	NOUN
ejpam-3852	354	27	of	of	ADP
ejpam-3852	354	28	a	a	DET
ejpam-3852	354	29	set	set	NOUN
ejpam-3852	354	30	of	of	ADP
ejpam-3852	354	31	vectors	vector	NOUN
ejpam-3852	354	32	)	)	PUNCT
ejpam-3852	354	33	.	.	PUNCT
ejpam-3852	355	1	we	we	PRON
ejpam-3852	355	2	call	call	VERB
ejpam-3852	355	3	the	the	DET
ejpam-3852	355	4	smallest	small	ADJ
ejpam-3852	355	5	dimension	dimension	NOUN
ejpam-3852	355	6	,	,	PUNCT
ejpam-3852	355	7	with	with	ADP
ejpam-3852	355	8	notation	notation	NOUN
ejpam-3852	355	9	`	`	PUNCT
ejpam-3852	355	10	(	(	PUNCT
ejpam-3852	355	11	z	z	NOUN
ejpam-3852	355	12	)	)	PUNCT
ejpam-3852	355	13	,	,	PUNCT
ejpam-3852	355	14	such	such	ADJ
ejpam-3852	355	15	that	that	SCONJ
ejpam-3852	355	16	{	{	PUNCT
ejpam-3852	355	17	zn	zn	X
ejpam-3852	355	18	}	}	PUNCT
ejpam-3852	355	19	passes	pass	VERB
ejpam-3852	355	20	the	the	DET
ejpam-3852	355	21	`	`	PUNCT
ejpam-3852	355	22	(	(	PUNCT
ejpam-3852	355	23	z)-dimensional	z)-dimensional	ADJ
ejpam-3852	355	24	lattice	lattice	PROPN
ejpam-3852	355	25	test	test	NOUN
ejpam-3852	355	26	,	,	PUNCT
ejpam-3852	355	27	but	but	CCONJ
ejpam-3852	355	28	not	not	PART
ejpam-3852	355	29	the	the	DET
ejpam-3852	355	30	(	(	PUNCT
ejpam-3852	355	31	`	`	PUNCT
ejpam-3852	355	32	(	(	PUNCT
ejpam-3852	355	33	z	z	NOUN
ejpam-3852	355	34	)	)	PUNCT
ejpam-3852	355	35	+	+	CCONJ
ejpam-3852	355	36	1)-dimensional	1)-dimensional	NUM
ejpam-3852	355	37	lattice	lattice	PROPN
ejpam-3852	355	38	test	test	NOUN
ejpam-3852	355	39	,	,	PUNCT
ejpam-3852	355	40	the	the	DET
ejpam-3852	355	41	lattice	lattice	PROPN
ejpam-3852	355	42	test	test	NOUN
ejpam-3852	355	43	complexity	complexity	NOUN
ejpam-3852	355	44	.	.	PUNCT
ejpam-3852	356	1	the	the	DET
ejpam-3852	356	2	lattice	lattice	PROPN
ejpam-3852	356	3	test	test	NOUN
ejpam-3852	356	4	complexity	complexity	NOUN
ejpam-3852	356	5	is	be	AUX
ejpam-3852	356	6	known	know	VERB
ejpam-3852	356	7	for	for	ADP
ejpam-3852	356	8	the	the	DET
ejpam-3852	356	9	inversive	inversive	ADJ
ejpam-3852	356	10	congruential	congruential	ADJ
ejpam-3852	356	11	generator	generator	NOUN
ejpam-3852	356	12	(	(	PUNCT
ejpam-3852	356	13	see	see	VERB
ejpam-3852	356	14	[	[	X
ejpam-3852	356	15	6	6	NUM
ejpam-3852	356	16	,	,	PUNCT
ejpam-3852	356	17	19	19	NUM
ejpam-3852	356	18	]	]	PUNCT
ejpam-3852	356	19	,	,	PUNCT
ejpam-3852	356	20	for	for	ADP
ejpam-3852	356	21	more	more	ADJ
ejpam-3852	356	22	on	on	ADP
ejpam-3852	356	23	this	this	DET
ejpam-3852	356	24	generator	generator	NOUN
ejpam-3852	356	25	)	)	PUNCT
ejpam-3852	356	26	.	.	PUNCT
ejpam-3852	357	1	it	it	PRON
ejpam-3852	357	2	is	be	AUX
ejpam-3852	357	3	known	know	VERB
ejpam-3852	357	4	that	that	SCONJ
ejpam-3852	357	5	for	for	ADP
ejpam-3852	357	6	a	a	DET
ejpam-3852	357	7	prime	prime	ADJ
ejpam-3852	357	8	characteristic	characteristic	NOUN
ejpam-3852	357	9	p	p	X
ejpam-3852	357	10	,	,	PUNCT
ejpam-3852	357	11	the	the	DET
ejpam-3852	357	12	inversive	inversive	ADJ
ejpam-3852	357	13	congruential	congruential	ADJ
ejpam-3852	357	14	generator	generator	NOUN
ejpam-3852	357	15	over	over	ADP
ejpam-3852	357	16	fp	fp	PROPN
ejpam-3852	357	17	will	will	AUX
ejpam-3852	357	18	pass	pass	VERB
ejpam-3852	357	19	the	the	DET
ejpam-3852	357	20	s	s	NOUN
ejpam-3852	357	21	-	-	ADJ
ejpam-3852	357	22	dimensional	dimensional	ADJ
ejpam-3852	357	23	lattice	lattice	NOUN
ejpam-3852	357	24	test	test	NOUN
ejpam-3852	357	25	in	in	ADP
ejpam-3852	357	26	fp	fp	NOUN
ejpam-3852	357	27	if	if	SCONJ
ejpam-3852	358	1	and	and	CCONJ
ejpam-3852	358	2	only	only	ADV
ejpam-3852	358	3	if	if	SCONJ
ejpam-3852	358	4	s	s	VERB
ejpam-3852	358	5	≤	≤	NUM
ejpam-3852	358	6	d	d	NOUN
ejpam-3852	358	7	,	,	PUNCT
ejpam-3852	358	8	where	where	SCONJ
ejpam-3852	358	9	d	d	NOUN
ejpam-3852	358	10	is	be	AUX
ejpam-3852	358	11	the	the	DET
ejpam-3852	358	12	degree	degree	NOUN
ejpam-3852	358	13	of	of	ADP
ejpam-3852	358	14	the	the	DET
ejpam-3852	358	15	polynomial	polynomial	ADJ
ejpam-3852	358	16	g	g	NOUN
ejpam-3852	358	17	representing	represent	VERB
ejpam-3852	358	18	the	the	DET
ejpam-3852	358	19	sequence	sequence	NOUN
ejpam-3852	358	20	zn	zn	PROPN
ejpam-3852	358	21	modulo	modulo	VERB
ejpam-3852	358	22	p	p	X
ejpam-3852	358	23	,	,	PUNCT
ejpam-3852	358	24	that	that	ADV
ejpam-3852	358	25	is	is	ADV
ejpam-3852	358	26	,	,	PUNCT
ejpam-3852	358	27	g(n	g(n	PROPN
ejpam-3852	358	28	)	)	PUNCT
ejpam-3852	358	29	=	=	SYM
ejpam-3852	359	1	zn	zn	PROPN
ejpam-3852	359	2	in	in	ADP
ejpam-3852	359	3	fp	fp	X
ejpam-3852	359	4	(	(	PUNCT
ejpam-3852	359	5	see	see	VERB
ejpam-3852	359	6	[	[	X
ejpam-3852	359	7	2	2	NUM
ejpam-3852	359	8	]	]	PUNCT
ejpam-3852	359	9	,	,	PUNCT
ejpam-3852	359	10	for	for	ADP
ejpam-3852	359	11	more	more	ADJ
ejpam-3852	359	12	on	on	ADP
ejpam-3852	359	13	the	the	DET
ejpam-3852	359	14	connection	connection	NOUN
ejpam-3852	359	15	between	between	ADP
ejpam-3852	359	16	linear	linear	PROPN
ejpam-3852	359	17	complexity	complexity	NOUN
ejpam-3852	359	18	and	and	CCONJ
ejpam-3852	359	19	lattice	lattice	NOUN
ejpam-3852	359	20	tests	test	NOUN
ejpam-3852	359	21	)	)	PUNCT
ejpam-3852	359	22	.	.	PUNCT
ejpam-3852	360	1	to	to	PART
ejpam-3852	360	2	show	show	VERB
ejpam-3852	360	3	our	our	PRON
ejpam-3852	360	4	result	result	NOUN
ejpam-3852	360	5	,	,	PUNCT
ejpam-3852	360	6	we	we	PRON
ejpam-3852	360	7	shall	shall	AUX
ejpam-3852	360	8	be	be	AUX
ejpam-3852	360	9	using	use	VERB
ejpam-3852	360	10	below	below	ADP
ejpam-3852	360	11	the	the	DET
ejpam-3852	360	12	following	following	ADJ
ejpam-3852	360	13	known	know	VERB
ejpam-3852	360	14	result	result	NOUN
ejpam-3852	360	15	[	[	X
ejpam-3852	360	16	13	13	NUM
ejpam-3852	360	17	]	]	PUNCT
ejpam-3852	360	18	.	.	PUNCT
ejpam-3852	361	1	proposition	proposition	NOUN
ejpam-3852	361	2	1	1	NUM
ejpam-3852	361	3	.	.	PUNCT
ejpam-3852	362	1	the	the	DET
ejpam-3852	362	2	rank	rank	NOUN
ejpam-3852	362	3	of	of	ADP
ejpam-3852	362	4	a	a	DET
ejpam-3852	362	5	circulant	circulant	ADJ
ejpam-3852	362	6	matrix	matrix	NOUN
ejpam-3852	362	7	c	c	NOUN
ejpam-3852	362	8	of	of	ADP
ejpam-3852	362	9	order	order	NOUN
ejpam-3852	362	10	n	n	X
ejpam-3852	362	11	is	be	AUX
ejpam-3852	362	12	n	n	PRON
ejpam-3852	362	13	−	−	PROPN
ejpam-3852	362	14	d	d	NOUN
ejpam-3852	362	15	,	,	PUNCT
ejpam-3852	362	16	where	where	SCONJ
ejpam-3852	362	17	d	d	NOUN
ejpam-3852	362	18	is	be	AUX
ejpam-3852	362	19	the	the	DET
ejpam-3852	362	20	degree	degree	NOUN
ejpam-3852	362	21	of	of	ADP
ejpam-3852	362	22	the	the	DET
ejpam-3852	362	23	greatest	great	ADJ
ejpam-3852	362	24	common	common	ADJ
ejpam-3852	362	25	divisors	divisor	NOUN
ejpam-3852	362	26	of	of	ADP
ejpam-3852	362	27	1−	1−	NUM
ejpam-3852	362	28	xn	xn	PROPN
ejpam-3852	362	29	and	and	CCONJ
ejpam-3852	362	30	the	the	DET
ejpam-3852	362	31	associated	associated	ADJ
ejpam-3852	362	32	polynomial	polynomial	NOUN
ejpam-3852	362	33	of	of	ADP
ejpam-3852	362	34	c.	c.	PROPN
ejpam-3852	362	35	theorem	theorem	VERB
ejpam-3852	362	36	6	6	NUM
ejpam-3852	362	37	.	.	PUNCT
ejpam-3852	363	1	let	let	VERB
ejpam-3852	363	2	{	{	PUNCT
ejpam-3852	363	3	yn	yn	NOUN
ejpam-3852	363	4	}	}	PUNCT
ejpam-3852	363	5	be	be	VERB
ejpam-3852	363	6	the	the	DET
ejpam-3852	363	7	hicg	hicg	ADJ
ejpam-3852	363	8	sequence	sequence	NOUN
ejpam-3852	363	9	modulo	modulo	VERB
ejpam-3852	363	10	m	m	NOUN
ejpam-3852	363	11	=	=	ADJ
ejpam-3852	363	12	2ω	2ω	NOUN
ejpam-3852	363	13	,	,	PUNCT
ejpam-3852	363	14	ω	ω	X
ejpam-3852	363	15	≥	≥	NOUN
ejpam-3852	363	16	2	2	NUM
ejpam-3852	363	17	,	,	PUNCT
ejpam-3852	363	18	with	with	ADP
ejpam-3852	363	19	some	some	DET
ejpam-3852	363	20	initial	initial	ADJ
ejpam-3852	363	21	conditions	condition	NOUN
ejpam-3852	363	22	,	,	PUNCT
ejpam-3852	363	23	of	of	ADP
ejpam-3852	363	24	full	full	ADJ
ejpam-3852	363	25	period	period	NOUN
ejpam-3852	363	26	m	m	VERB
ejpam-3852	363	27	(	(	PUNCT
ejpam-3852	363	28	see	see	VERB
ejpam-3852	363	29	theorem	theorem	NOUN
ejpam-3852	363	30	4	4	NUM
ejpam-3852	363	31	for	for	ADP
ejpam-3852	363	32	conditions	condition	NOUN
ejpam-3852	363	33	on	on	ADP
ejpam-3852	363	34	the	the	DET
ejpam-3852	363	35	parameters	parameter	NOUN
ejpam-3852	363	36	)	)	PUNCT
ejpam-3852	363	37	.	.	PUNCT
ejpam-3852	364	1	the	the	DET
ejpam-3852	364	2	lattice	lattice	PROPN
ejpam-3852	364	3	test	test	NOUN
ejpam-3852	364	4	complexity	complexity	NOUN
ejpam-3852	364	5	of	of	ADP
ejpam-3852	364	6	the	the	DET
ejpam-3852	364	7	associated	associated	ADJ
ejpam-3852	364	8	binary	binary	NOUN
ejpam-3852	364	9	sequence	sequence	NOUN
ejpam-3852	364	10	{	{	PUNCT
ejpam-3852	364	11	zn	zn	NOUN
ejpam-3852	364	12	}	}	PUNCT
ejpam-3852	364	13	is	be	AUX
ejpam-3852	364	14	`	`	PUNCT
ejpam-3852	364	15	(	(	PUNCT
ejpam-3852	364	16	z	z	NOUN
ejpam-3852	364	17	)	)	PUNCT
ejpam-3852	364	18	=	=	PUNCT
ejpam-3852	364	19	m	m	VERB
ejpam-3852	364	20	2	2	NUM
ejpam-3852	364	21	.	.	PUNCT
ejpam-3852	365	1	proof	proof	NOUN
ejpam-3852	365	2	.	.	PUNCT
ejpam-3852	366	1	let	let	VERB
ejpam-3852	366	2	zn	zn	PROPN
ejpam-3852	366	3	=	=	SYM
ejpam-3852	366	4	(	(	PUNCT
ejpam-3852	366	5	zn	zn	PROPN
ejpam-3852	366	6	,	,	PUNCT
ejpam-3852	366	7	zn+1	zn+1	PROPN
ejpam-3852	366	8	,	,	PUNCT
ejpam-3852	366	9	.	.	PUNCT
ejpam-3852	366	10	.	.	PUNCT
ejpam-3852	367	1	.	.	PUNCT
ejpam-3852	368	1	,	,	PUNCT
ejpam-3852	368	2	zn+m	zn+m	NUM
ejpam-3852	368	3	2	2	NUM
ejpam-3852	368	4	−1	−1	NOUN
ejpam-3852	368	5	)	)	PUNCT
ejpam-3852	368	6	.	.	PUNCT
ejpam-3852	369	1	computationally	computationally	ADV
ejpam-3852	369	2	,	,	PUNCT
ejpam-3852	369	3	one	one	PRON
ejpam-3852	369	4	can	can	AUX
ejpam-3852	369	5	check	check	VERB
ejpam-3852	369	6	that	that	PRON
ejpam-3852	369	7	for	for	ADP
ejpam-3852	369	8	m	m	PROPN
ejpam-3852	369	9	=	=	SYM
ejpam-3852	369	10	4	4	NUM
ejpam-3852	369	11	,	,	PUNCT
ejpam-3852	369	12	the	the	DET
ejpam-3852	369	13	vectors	vector	NOUN
ejpam-3852	369	14	{	{	PUNCT
ejpam-3852	369	15	zn	zn	NOUN
ejpam-3852	369	16	}	}	PUNCT
ejpam-3852	369	17	will	will	AUX
ejpam-3852	369	18	not	not	PART
ejpam-3852	369	19	span	span	VERB
ejpam-3852	369	20	fl2	fl2	PROPN
ejpam-3852	369	21	if	if	SCONJ
ejpam-3852	369	22	l	l	NOUN
ejpam-3852	369	23	=	=	SYM
ejpam-3852	369	24	3	3	NUM
ejpam-3852	369	25	,	,	PUNCT
ejpam-3852	369	26	rather	rather	ADV
ejpam-3852	369	27	they	they	PRON
ejpam-3852	369	28	will	will	AUX
ejpam-3852	369	29	span	span	VERB
ejpam-3852	369	30	fl2	fl2	PROPN
ejpam-3852	369	31	if	if	SCONJ
ejpam-3852	369	32	l	l	NOUN
ejpam-3852	369	33	=	=	NOUN
ejpam-3852	369	34	2	2	X
ejpam-3852	369	35	.	.	NUM
ejpam-3852	369	36	from	from	ADP
ejpam-3852	369	37	the	the	DET
ejpam-3852	369	38	construction	construction	NOUN
ejpam-3852	369	39	of	of	ADP
ejpam-3852	369	40	the	the	DET
ejpam-3852	369	41	vectors	vector	NOUN
ejpam-3852	369	42	zn	zn	NUM
ejpam-3852	369	43	,	,	PUNCT
ejpam-3852	369	44	we	we	PRON
ejpam-3852	369	45	see	see	VERB
ejpam-3852	369	46	that	that	SCONJ
ejpam-3852	369	47	if	if	SCONJ
ejpam-3852	369	48	we	we	PRON
ejpam-3852	369	49	can	can	AUX
ejpam-3852	369	50	show	show	VERB
ejpam-3852	369	51	that	that	SCONJ
ejpam-3852	369	52	the	the	DET
ejpam-3852	369	53	vectors	vector	NOUN
ejpam-3852	369	54	{	{	PUNCT
ejpam-3852	369	55	zn	zn	X
ejpam-3852	369	56	}	}	PUNCT
ejpam-3852	369	57	for	for	ADP
ejpam-3852	369	58	l	l	NOUN
ejpam-3852	369	59	=	=	PUNCT
ejpam-3852	369	60	m	m	VERB
ejpam-3852	369	61	2	2	NUM
ejpam-3852	369	62	span	span	NOUN
ejpam-3852	369	63	fl2	fl2	PROPN
ejpam-3852	369	64	,	,	PUNCT
ejpam-3852	369	65	then	then	ADV
ejpam-3852	369	66	the	the	DET
ejpam-3852	369	67	corresponding	corresponding	ADJ
ejpam-3852	369	68	vectors	vector	NOUN
ejpam-3852	369	69	will	will	AUX
ejpam-3852	369	70	also	also	ADV
ejpam-3852	369	71	span	span	VERB
ejpam-3852	369	72	fl2	fl2	PROPN
ejpam-3852	369	73	,	,	PUNCT
ejpam-3852	369	74	for	for	ADP
ejpam-3852	369	75	all	all	DET
ejpam-3852	369	76	l	l	NOUN
ejpam-3852	369	77	≤	≤	NUM
ejpam-3852	369	78	m	m	VERB
ejpam-3852	369	79	2	2	NUM
ejpam-3852	369	80	.	.	PUNCT
ejpam-3852	370	1	therefore	therefore	ADV
ejpam-3852	370	2	,	,	PUNCT
ejpam-3852	370	3	it	it	PRON
ejpam-3852	370	4	suffices	suffice	VERB
ejpam-3852	370	5	to	to	PART
ejpam-3852	370	6	show	show	VERB
ejpam-3852	370	7	that	that	SCONJ
ejpam-3852	370	8	{	{	PUNCT
ejpam-3852	370	9	z0	z0	PROPN
ejpam-3852	370	10	,	,	PUNCT
ejpam-3852	370	11	z1	z1	NOUN
ejpam-3852	370	12	,	,	PUNCT
ejpam-3852	370	13	.	.	PUNCT
ejpam-3852	370	14	.	.	PUNCT
ejpam-3852	371	1	.	.	PUNCT
ejpam-3852	372	1	,	,	PUNCT
ejpam-3852	372	2	zm−1	zm−1	NOUN
ejpam-3852	372	3	}	}	PUNCT
ejpam-3852	372	4	span	span	VERB
ejpam-3852	372	5	f	f	PROPN
ejpam-3852	372	6	m	m	VERB
ejpam-3852	372	7	2	2	NUM
ejpam-3852	372	8	2	2	NUM
ejpam-3852	372	9	.	.	PUNCT
ejpam-3852	373	1	we	we	PRON
ejpam-3852	373	2	know	know	VERB
ejpam-3852	373	3	that	that	SCONJ
ejpam-3852	373	4	,	,	PUNCT
ejpam-3852	373	5	ym	ym	PROPN
ejpam-3852	373	6	2	2	NUM
ejpam-3852	374	1	+	+	ADP
ejpam-3852	374	2	k	k	PROPN
ejpam-3852	374	3	≡	≡	PROPN
ejpam-3852	374	4	yk	yk	PROPN
ejpam-3852	375	1	+	+	CCONJ
ejpam-3852	375	2	m	m	VERB
ejpam-3852	375	3	2	2	NUM
ejpam-3852	375	4	(	(	PUNCT
ejpam-3852	375	5	mod	mod	NOUN
ejpam-3852	375	6	m	m	PROPN
ejpam-3852	375	7	)	)	PUNCT
ejpam-3852	375	8	and	and	CCONJ
ejpam-3852	375	9	so	so	ADV
ejpam-3852	375	10	zm	zm	PROPN
ejpam-3852	375	11	2	2	NUM
ejpam-3852	375	12	+	+	NOUN
ejpam-3852	375	13	k	k	X
ejpam-3852	375	14	=	=	PUNCT
ejpam-3852	375	15	zk	zk	PROPN
ejpam-3852	375	16	where	where	SCONJ
ejpam-3852	375	17	0	0	NUM
ejpam-3852	375	18	=	=	SYM
ejpam-3852	375	19	1	1	NUM
ejpam-3852	375	20	and	and	CCONJ
ejpam-3852	375	21	1	1	NUM
ejpam-3852	375	22	=	=	SYM
ejpam-3852	375	23	0	0	NUM
ejpam-3852	375	24	.	.	PUNCT
ejpam-3852	375	25	to	to	PART
ejpam-3852	375	26	show	show	VERB
ejpam-3852	375	27	our	our	PRON
ejpam-3852	375	28	claim	claim	NOUN
ejpam-3852	375	29	,	,	PUNCT
ejpam-3852	375	30	p.	p.	NOUN
ejpam-3852	375	31	stănică	stănică	NUM
ejpam-3852	375	32	et	et	NOUN
ejpam-3852	375	33	al	al	PROPN
ejpam-3852	375	34	.	.	PUNCT
ejpam-3852	375	35	/	/	SYM
ejpam-3852	375	36	eur	eur	PROPN
ejpam-3852	375	37	.	.	PUNCT
ejpam-3852	376	1	j.	j.	PROPN
ejpam-3852	376	2	pure	pure	PROPN
ejpam-3852	376	3	appl	appl	PROPN
ejpam-3852	376	4	.	.	PROPN
ejpam-3852	376	5	math	math	PROPN
ejpam-3852	376	6	,	,	PUNCT
ejpam-3852	376	7	14	14	NUM
ejpam-3852	376	8	(	(	PUNCT
ejpam-3852	376	9	1	1	NUM
ejpam-3852	376	10	)	)	PUNCT
ejpam-3852	376	11	(	(	PUNCT
ejpam-3852	376	12	2021	2021	NUM
ejpam-3852	376	13	)	)	PUNCT
ejpam-3852	376	14	,	,	PUNCT
ejpam-3852	376	15	1	1	NUM
ejpam-3852	376	16	-	-	SYM
ejpam-3852	376	17	18	18	NUM
ejpam-3852	376	18	12	12	NUM
ejpam-3852	376	19	we	we	PRON
ejpam-3852	376	20	need	need	VERB
ejpam-3852	376	21	to	to	PART
ejpam-3852	376	22	prove	prove	VERB
ejpam-3852	376	23	that	that	SCONJ
ejpam-3852	376	24	the	the	DET
ejpam-3852	376	25	matrix	matrix	NOUN
ejpam-3852	376	26	z	z	NOUN
ejpam-3852	376	27	=	=	SYM
ejpam-3852	376	28			NOUN
ejpam-3852	376	29	z0	z0	PROPN
ejpam-3852	376	30	z1	z1	PROPN
ejpam-3852	376	31	z2	z2	PROPN
ejpam-3852	376	32	...	...	PUNCT
ejpam-3852	377	1	zm	zm	PROPN
ejpam-3852	377	2	2	2	NUM
ejpam-3852	377	3	−2	−2	NOUN
ejpam-3852	377	4	zm	zm	PROPN
ejpam-3852	377	5	2	2	NUM
ejpam-3852	377	6	−1	−1	NOUN
ejpam-3852	377	7	zm	zm	PROPN
ejpam-3852	377	8	2	2	NUM
ejpam-3852	377	9	zm	zm	PROPN
ejpam-3852	377	10	2	2	NUM
ejpam-3852	377	11	+1	+1	NOUN
ejpam-3852	377	12	zm	zm	PROPN
ejpam-3852	377	13	2	2	NUM
ejpam-3852	377	14	+2	+2	PRON
ejpam-3852	377	15	...	...	PUNCT
ejpam-3852	378	1	zm−2	zm−2	PROPN
ejpam-3852	378	2	zm−1	zm−1	NOUN
ejpam-3852	378	3			PUNCT
ejpam-3852	378	4	=	=	SYM
ejpam-3852	378	5			PROPN
ejpam-3852	378	6	z0	z0	PROPN
ejpam-3852	378	7	z1	z1	PROPN
ejpam-3852	378	8	z2	z2	PROPN
ejpam-3852	378	9	.	.	PUNCT
ejpam-3852	378	10	.	.	PUNCT
ejpam-3852	378	11	.	.	PUNCT
ejpam-3852	379	1	zm	zm	PROPN
ejpam-3852	379	2	2	2	NUM
ejpam-3852	379	3	−2	−2	NOUN
ejpam-3852	379	4	zm	zm	PROPN
ejpam-3852	379	5	2	2	NUM
ejpam-3852	379	6	−1	−1	NOUN
ejpam-3852	379	7	z1	z1	PROPN
ejpam-3852	379	8	z2	z2	PROPN
ejpam-3852	379	9	z3	z3	PROPN
ejpam-3852	379	10	.	.	PUNCT
ejpam-3852	379	11	.	.	PUNCT
ejpam-3852	379	12	.	.	PUNCT
ejpam-3852	380	1	zm	zm	PROPN
ejpam-3852	380	2	2	2	NUM
ejpam-3852	380	3	−1	−1	NOUN
ejpam-3852	380	4	z0	z0	PROPN
ejpam-3852	380	5	z2	z2	PROPN
ejpam-3852	380	6	z3	z3	PROPN
ejpam-3852	380	7	z4	z4	PROPN
ejpam-3852	380	8	.	.	PUNCT
ejpam-3852	380	9	.	.	PUNCT
ejpam-3852	380	10	.	.	PUNCT
ejpam-3852	381	1	z0	z0	PROPN
ejpam-3852	381	2	z1	z1	PROPN
ejpam-3852	381	3	...	...	PUNCT
ejpam-3852	382	1	zm	zm	PROPN
ejpam-3852	382	2	2	2	NUM
ejpam-3852	382	3	−2	−2	NOUN
ejpam-3852	382	4	zm	zm	PROPN
ejpam-3852	382	5	2	2	NUM
ejpam-3852	382	6	−1	−1	NOUN
ejpam-3852	382	7	z0	z0	PROPN
ejpam-3852	382	8	.	.	PUNCT
ejpam-3852	382	9	.	.	PUNCT
ejpam-3852	382	10	.	.	PUNCT
ejpam-3852	383	1	zm	zm	PROPN
ejpam-3852	383	2	2	2	NUM
ejpam-3852	383	3	−4	−4	NOUN
ejpam-3852	383	4	zm	zm	PROPN
ejpam-3852	383	5	2	2	NUM
ejpam-3852	383	6	−3	−3	PROPN
ejpam-3852	383	7	zm	zm	PROPN
ejpam-3852	383	8	2	2	NUM
ejpam-3852	383	9	−1	−1	NOUN
ejpam-3852	383	10	z0	z0	PROPN
ejpam-3852	383	11	z1	z1	PROPN
ejpam-3852	383	12	.	.	PUNCT
ejpam-3852	383	13	.	.	PUNCT
ejpam-3852	383	14	.	.	PUNCT
ejpam-3852	384	1	zm	zm	PROPN
ejpam-3852	384	2	2	2	NUM
ejpam-3852	384	3	−3	−3	PROPN
ejpam-3852	384	4	zm	zm	PROPN
ejpam-3852	384	5	2	2	NUM
ejpam-3852	384	6	−2	−2	NOUN
ejpam-3852	384	7	z0	z0	NOUN
ejpam-3852	384	8	z1	z1	NOUN
ejpam-3852	384	9	z3	z3	PROPN
ejpam-3852	384	10	.	.	PUNCT
ejpam-3852	384	11	.	.	PUNCT
ejpam-3852	384	12	.	.	PUNCT
ejpam-3852	385	1	zm	zm	PROPN
ejpam-3852	385	2	2	2	NUM
ejpam-3852	385	3	−2	−2	NOUN
ejpam-3852	385	4	zm	zm	PROPN
ejpam-3852	385	5	2	2	NUM
ejpam-3852	385	6	−1	−1	NOUN
ejpam-3852	385	7	z1	z1	PROPN
ejpam-3852	385	8	z2	z2	PROPN
ejpam-3852	385	9	z3	z3	PROPN
ejpam-3852	385	10	.	.	PUNCT
ejpam-3852	385	11	.	.	PUNCT
ejpam-3852	385	12	.	.	PUNCT
ejpam-3852	386	1	zm	zm	PROPN
ejpam-3852	386	2	2	2	NUM
ejpam-3852	386	3	−1	−1	NOUN
ejpam-3852	386	4	z0	z0	PROPN
ejpam-3852	386	5	z2	z2	PROPN
ejpam-3852	386	6	z3	z3	PROPN
ejpam-3852	386	7	z4	z4	PROPN
ejpam-3852	386	8	.	.	PUNCT
ejpam-3852	386	9	.	.	PUNCT
ejpam-3852	386	10	.	.	PUNCT
ejpam-3852	387	1	z0	z0	PROPN
ejpam-3852	387	2	z1	z1	PROPN
ejpam-3852	387	3	...	...	PUNCT
ejpam-3852	388	1	zm	zm	PROPN
ejpam-3852	388	2	2	2	NUM
ejpam-3852	388	3	−2	−2	NOUN
ejpam-3852	388	4	zm	zm	PROPN
ejpam-3852	388	5	2	2	NUM
ejpam-3852	388	6	−1	−1	NOUN
ejpam-3852	388	7	z0	z0	PROPN
ejpam-3852	388	8	.	.	PUNCT
ejpam-3852	388	9	.	.	PUNCT
ejpam-3852	388	10	.	.	PUNCT
ejpam-3852	389	1	zm	zm	PROPN
ejpam-3852	389	2	2	2	NUM
ejpam-3852	389	3	−4	−4	NOUN
ejpam-3852	389	4	zm	zm	PROPN
ejpam-3852	389	5	2	2	NUM
ejpam-3852	389	6	−3	−3	PROPN
ejpam-3852	389	7	zm	zm	PROPN
ejpam-3852	389	8	2	2	NUM
ejpam-3852	389	9	−1	−1	NOUN
ejpam-3852	389	10	z0	z0	PROPN
ejpam-3852	389	11	z1	z1	PROPN
ejpam-3852	389	12	.	.	PUNCT
ejpam-3852	389	13	.	.	PUNCT
ejpam-3852	389	14	.	.	PUNCT
ejpam-3852	390	1	zm	zm	PROPN
ejpam-3852	390	2	2	2	NUM
ejpam-3852	390	3	−3	−3	PROPN
ejpam-3852	390	4	zm	zm	PROPN
ejpam-3852	390	5	2	2	NUM
ejpam-3852	390	6	−2	−2	NOUN
ejpam-3852	390	7			PRON
ejpam-3852	390	8	has	have	AUX
ejpam-3852	390	9	rank	rank	VERB
ejpam-3852	390	10	at	at	ADP
ejpam-3852	390	11	least	least	ADJ
ejpam-3852	390	12	m	m	VERB
ejpam-3852	390	13	2	2	NUM
ejpam-3852	390	14	,	,	PUNCT
ejpam-3852	390	15	which	which	PRON
ejpam-3852	390	16	is	be	AUX
ejpam-3852	390	17	equivalent	equivalent	ADJ
ejpam-3852	390	18	to	to	ADP
ejpam-3852	390	19	the	the	DET
ejpam-3852	390	20	fact	fact	NOUN
ejpam-3852	390	21	that	that	SCONJ
ejpam-3852	390	22	zt	zt	PROPN
ejpam-3852	390	23	has	have	AUX
ejpam-3852	390	24	rank	rank	NOUN
ejpam-3852	390	25	at	at	ADP
ejpam-3852	390	26	least	least	ADJ
ejpam-3852	390	27	m	m	VERB
ejpam-3852	390	28	2	2	NUM
ejpam-3852	390	29	.	.	PUNCT
ejpam-3852	391	1	to	to	PART
ejpam-3852	391	2	achieve	achieve	VERB
ejpam-3852	391	3	that	that	DET
ejpam-3852	391	4	goal	goal	NOUN
ejpam-3852	391	5	,	,	PUNCT
ejpam-3852	391	6	we	we	PRON
ejpam-3852	391	7	define	define	VERB
ejpam-3852	391	8	a	a	DET
ejpam-3852	391	9	circulant	circulant	ADJ
ejpam-3852	391	10	matrix	matrix	NOUN
ejpam-3852	391	11	c	c	NOUN
ejpam-3852	391	12	of	of	ADP
ejpam-3852	391	13	order	order	NOUN
ejpam-3852	391	14	m	m	VERB
ejpam-3852	391	15	,	,	PUNCT
ejpam-3852	391	16	whose	whose	DET
ejpam-3852	391	17	first	first	ADJ
ejpam-3852	391	18	m	m	VERB
ejpam-3852	391	19	2	2	NUM
ejpam-3852	391	20	rows	row	NOUN
ejpam-3852	391	21	form	form	NOUN
ejpam-3852	391	22	zt	zt	PROPN
ejpam-3852	391	23	(	(	PUNCT
ejpam-3852	391	24	we	we	PRON
ejpam-3852	391	25	just	just	ADV
ejpam-3852	391	26	add	add	VERB
ejpam-3852	391	27	m	m	NUM
ejpam-3852	391	28	2	2	NUM
ejpam-3852	391	29	rows	row	NOUN
ejpam-3852	391	30	to	to	ADP
ejpam-3852	391	31	zt	zt	PROPN
ejpam-3852	391	32	accordingly	accordingly	ADV
ejpam-3852	391	33	to	to	PART
ejpam-3852	391	34	make	make	VERB
ejpam-3852	391	35	it	it	PRON
ejpam-3852	391	36	of	of	ADP
ejpam-3852	391	37	order	order	NOUN
ejpam-3852	391	38	m	m	NOUN
ejpam-3852	391	39	)	)	PUNCT
ejpam-3852	391	40	.	.	PUNCT
ejpam-3852	392	1	now	now	ADV
ejpam-3852	392	2	the	the	DET
ejpam-3852	392	3	associated	associated	ADJ
ejpam-3852	392	4	polynomial	polynomial	NOUN
ejpam-3852	392	5	of	of	ADP
ejpam-3852	392	6	c	c	PROPN
ejpam-3852	392	7	is	be	AUX
ejpam-3852	392	8	g(x	g(x	NOUN
ejpam-3852	392	9	)	)	PUNCT
ejpam-3852	393	1	=	=	PUNCT
ejpam-3852	393	2	m	m	VERB
ejpam-3852	393	3	2	2	NUM
ejpam-3852	393	4	−1∑	−1∑	PROPN
ejpam-3852	393	5	i=0	i=0	PROPN
ejpam-3852	393	6	zix	zix	X
ejpam-3852	393	7	i	i	PRON
ejpam-3852	393	8	+	+	CCONJ
ejpam-3852	393	9	m−1∑	m−1∑	NUM
ejpam-3852	393	10	i	i	NOUN
ejpam-3852	393	11	=	=	NOUN
ejpam-3852	393	12	m	m	VERB
ejpam-3852	393	13	2	2	NUM
ejpam-3852	393	14	zi−m	zi−m	ADJ
ejpam-3852	393	15	2	2	NUM
ejpam-3852	393	16	xi	xi	ADP
ejpam-3852	393	17	=	=	NOUN
ejpam-3852	393	18	m	m	PROPN
ejpam-3852	393	19	2	2	NUM
ejpam-3852	393	20	−1∑	−1∑	PROPN
ejpam-3852	393	21	i=0	i=0	PROPN
ejpam-3852	393	22	zix	zix	X
ejpam-3852	393	23	i	i	PRON
ejpam-3852	393	24	+	+	CCONJ
ejpam-3852	393	25	x	x	SYM
ejpam-3852	393	26	m	m	VERB
ejpam-3852	393	27	2	2	NUM
ejpam-3852	393	28	m	m	NUM
ejpam-3852	393	29	2	2	NUM
ejpam-3852	393	30	−1∑	−1∑	PROPN
ejpam-3852	393	31	i=0	i=0	PROPN
ejpam-3852	393	32	(	(	PUNCT
ejpam-3852	393	33	zi	zi	NOUN
ejpam-3852	393	34	+	+	CCONJ
ejpam-3852	393	35	1)xi	1)xi	NUM
ejpam-3852	393	36	=	=	SYM
ejpam-3852	393	37	(	(	PUNCT
ejpam-3852	393	38	1	1	NUM
ejpam-3852	393	39	+	+	CCONJ
ejpam-3852	393	40	x	x	NOUN
ejpam-3852	393	41	m	m	VERB
ejpam-3852	393	42	2	2	NUM
ejpam-3852	393	43	)	)	PUNCT
ejpam-3852	393	44	m	m	VERB
ejpam-3852	393	45	2	2	NUM
ejpam-3852	393	46	−1∑	−1∑	PROPN
ejpam-3852	393	47	i=0	i=0	PROPN
ejpam-3852	393	48	zix	zix	X
ejpam-3852	393	49	i	i	PRON
ejpam-3852	393	50	+	+	CCONJ
ejpam-3852	393	51	x	x	SYM
ejpam-3852	393	52	m	m	VERB
ejpam-3852	393	53	2	2	NUM
ejpam-3852	393	54	m	m	NUM
ejpam-3852	393	55	2	2	NUM
ejpam-3852	393	56	−1∑	−1∑	PROPN
ejpam-3852	393	57	i=0	i=0	PROPN
ejpam-3852	393	58	xi	xi	PROPN
ejpam-3852	393	59	=	=	PUNCT
ejpam-3852	393	60	(	(	PUNCT
ejpam-3852	393	61	1	1	NUM
ejpam-3852	393	62	+	+	NUM
ejpam-3852	393	63	x	x	X
ejpam-3852	393	64	)	)	PUNCT
ejpam-3852	393	65	m	m	VERB
ejpam-3852	393	66	2	2	NUM
ejpam-3852	393	67	m	m	NUM
ejpam-3852	393	68	2	2	NUM
ejpam-3852	393	69	−1∑	−1∑	PROPN
ejpam-3852	393	70	i=0	i=0	PROPN
ejpam-3852	393	71	zix	zix	X
ejpam-3852	393	72	i	i	PRON
ejpam-3852	393	73	+	+	CCONJ
ejpam-3852	393	74	x	x	SYM
ejpam-3852	393	75	m	m	VERB
ejpam-3852	393	76	2	2	NUM
ejpam-3852	393	77	(	(	PUNCT
ejpam-3852	393	78	1	1	NUM
ejpam-3852	393	79	+	+	NUM
ejpam-3852	393	80	x	x	X
ejpam-3852	393	81	)	)	PUNCT
ejpam-3852	393	82	m	m	VERB
ejpam-3852	393	83	2	2	NUM
ejpam-3852	393	84	−1	−1	NOUN
ejpam-3852	393	85	=	=	PUNCT
ejpam-3852	393	86	(	(	PUNCT
ejpam-3852	393	87	1	1	NUM
ejpam-3852	393	88	+	+	NUM
ejpam-3852	393	89	x	x	X
ejpam-3852	393	90	)	)	PUNCT
ejpam-3852	393	91	m	m	VERB
ejpam-3852	393	92	2	2	NUM
ejpam-3852	393	93	−1((1	−1((1	PUNCT
ejpam-3852	393	94	+	+	CCONJ
ejpam-3852	393	95	x	x	X
ejpam-3852	393	96	)	)	PUNCT
ejpam-3852	393	97	m	m	VERB
ejpam-3852	393	98	2	2	NUM
ejpam-3852	393	99	−1∑	−1∑	PROPN
ejpam-3852	393	100	i=0	i=0	PROPN
ejpam-3852	393	101	zix	zix	X
ejpam-3852	393	102	i	i	PRON
ejpam-3852	393	103	+	+	CCONJ
ejpam-3852	393	104	x	x	NOUN
ejpam-3852	393	105	m	m	VERB
ejpam-3852	393	106	2	2	NUM
ejpam-3852	393	107	)	)	PUNCT
ejpam-3852	393	108	(	(	PUNCT
ejpam-3852	393	109	all	all	DET
ejpam-3852	393	110	operations	operation	NOUN
ejpam-3852	393	111	are	be	AUX
ejpam-3852	393	112	considered	consider	VERB
ejpam-3852	393	113	modulo	modulo	ADJ
ejpam-3852	393	114	2	2	NUM
ejpam-3852	393	115	here	here	ADV
ejpam-3852	393	116	)	)	PUNCT
ejpam-3852	393	117	.	.	PUNCT
ejpam-3852	394	1	thus	thus	ADV
ejpam-3852	394	2	,	,	PUNCT
ejpam-3852	394	3	gcd	gcd	X
ejpam-3852	394	4	(	(	PUNCT
ejpam-3852	394	5	g(x	g(x	NOUN
ejpam-3852	394	6	)	)	PUNCT
ejpam-3852	394	7	,	,	PUNCT
ejpam-3852	394	8	1−	1−	NUM
ejpam-3852	394	9	xm	xm	NUM
ejpam-3852	394	10	)	)	PUNCT
ejpam-3852	394	11	=	=	PRON
ejpam-3852	394	12	gcd	gcd	INTJ
ejpam-3852	394	13	(	(	PUNCT
ejpam-3852	394	14	g(x	g(x	NOUN
ejpam-3852	394	15	)	)	PUNCT
ejpam-3852	394	16	,	,	PUNCT
ejpam-3852	394	17	(	(	PUNCT
ejpam-3852	394	18	1	1	NUM
ejpam-3852	394	19	+	+	CCONJ
ejpam-3852	394	20	x)m	x)m	PUNCT
ejpam-3852	394	21	)	)	PUNCT
ejpam-3852	395	1	=	=	PUNCT
ejpam-3852	395	2	(	(	PUNCT
ejpam-3852	395	3	1	1	NUM
ejpam-3852	395	4	+	+	NUM
ejpam-3852	395	5	x	x	X
ejpam-3852	395	6	)	)	PUNCT
ejpam-3852	395	7	m	m	VERB
ejpam-3852	395	8	2	2	NUM
ejpam-3852	395	9	−1	−1	NOUN
ejpam-3852	395	10	.	.	PUNCT
ejpam-3852	396	1	hence	hence	ADV
ejpam-3852	396	2	,	,	PUNCT
ejpam-3852	396	3	by	by	ADP
ejpam-3852	396	4	proposition	proposition	NOUN
ejpam-3852	396	5	1	1	NUM
ejpam-3852	396	6	,	,	PUNCT
ejpam-3852	396	7	the	the	DET
ejpam-3852	396	8	rank	rank	NOUN
ejpam-3852	396	9	of	of	ADP
ejpam-3852	396	10	c	c	PROPN
ejpam-3852	396	11	is	be	AUX
ejpam-3852	396	12	m	m	PRON
ejpam-3852	396	13	−	−	PROPN
ejpam-3852	396	14	(	(	PUNCT
ejpam-3852	396	15	m	m	PROPN
ejpam-3852	396	16	2	2	NUM
ejpam-3852	396	17	−	−	NOUN
ejpam-3852	396	18	1	1	NUM
ejpam-3852	396	19	)	)	PUNCT
ejpam-3852	396	20	=	=	PUNCT
ejpam-3852	397	1	m	m	VERB
ejpam-3852	397	2	2	2	NUM
ejpam-3852	397	3	+	+	NUM
ejpam-3852	397	4	1	1	NUM
ejpam-3852	397	5	.	.	PUNCT
ejpam-3852	398	1	now	now	ADV
ejpam-3852	398	2	,	,	PUNCT
ejpam-3852	398	3	it	it	PRON
ejpam-3852	398	4	is	be	AUX
ejpam-3852	398	5	easy	easy	ADJ
ejpam-3852	398	6	to	to	PART
ejpam-3852	398	7	check	check	VERB
ejpam-3852	398	8	that	that	PRON
ejpam-3852	398	9	k	k	NOUN
ejpam-3852	398	10	-	-	PUNCT
ejpam-3852	398	11	th	th	X
ejpam-3852	398	12	and	and	CCONJ
ejpam-3852	398	13	the	the	DET
ejpam-3852	398	14	(	(	PUNCT
ejpam-3852	398	15	m2	m2	PROPN
ejpam-3852	398	16	+	+	CCONJ
ejpam-3852	398	17	k)-th	k)-th	PROPN
ejpam-3852	398	18	row	row	NOUN
ejpam-3852	398	19	of	of	ADP
ejpam-3852	398	20	c	c	NOUN
ejpam-3852	398	21	add	add	VERB
ejpam-3852	398	22	up	up	ADP
ejpam-3852	398	23	to	to	ADP
ejpam-3852	398	24	the	the	DET
ejpam-3852	398	25	row	row	NOUN
ejpam-3852	398	26	with	with	ADP
ejpam-3852	398	27	all	all	DET
ejpam-3852	398	28	1	1	NUM
ejpam-3852	398	29	’s	’s	PART
ejpam-3852	398	30	;	;	PUNCT
ejpam-3852	398	31	k	k	PROPN
ejpam-3852	398	32	=	=	SYM
ejpam-3852	398	33	1	1	NUM
ejpam-3852	398	34	,	,	PUNCT
ejpam-3852	398	35	2	2	NUM
ejpam-3852	398	36	,	,	PUNCT
ejpam-3852	398	37	.	.	PUNCT
ejpam-3852	398	38	.	.	PUNCT
ejpam-3852	399	1	.	.	PUNCT
ejpam-3852	400	1	,	,	PUNCT
ejpam-3852	400	2	m2	m2	PROPN
ejpam-3852	400	3	.	.	PUNCT
ejpam-3852	401	1	so	so	ADV
ejpam-3852	401	2	,	,	PUNCT
ejpam-3852	401	3	it	it	PRON
ejpam-3852	401	4	is	be	AUX
ejpam-3852	401	5	clear	clear	ADJ
ejpam-3852	401	6	that	that	SCONJ
ejpam-3852	401	7	p.	p.	PROPN
ejpam-3852	401	8	stănică	stănică	NOUN
ejpam-3852	401	9	et	et	NOUN
ejpam-3852	401	10	al	al	PROPN
ejpam-3852	401	11	.	.	PUNCT
ejpam-3852	401	12	/	/	SYM
ejpam-3852	401	13	eur	eur	PROPN
ejpam-3852	401	14	.	.	PUNCT
ejpam-3852	402	1	j.	j.	PROPN
ejpam-3852	402	2	pure	pure	PROPN
ejpam-3852	402	3	appl	appl	PROPN
ejpam-3852	402	4	.	.	PROPN
ejpam-3852	402	5	math	math	PROPN
ejpam-3852	402	6	,	,	PUNCT
ejpam-3852	402	7	14	14	NUM
ejpam-3852	402	8	(	(	PUNCT
ejpam-3852	402	9	1	1	NUM
ejpam-3852	402	10	)	)	PUNCT
ejpam-3852	402	11	(	(	PUNCT
ejpam-3852	402	12	2021	2021	NUM
ejpam-3852	402	13	)	)	PUNCT
ejpam-3852	402	14	,	,	PUNCT
ejpam-3852	402	15	1	1	NUM
ejpam-3852	402	16	-	-	SYM
ejpam-3852	402	17	18	18	NUM
ejpam-3852	402	18	13	13	NUM
ejpam-3852	402	19	the	the	DET
ejpam-3852	402	20	rank	rank	NOUN
ejpam-3852	402	21	of	of	ADP
ejpam-3852	402	22	the	the	DET
ejpam-3852	402	23	(	(	PUNCT
ejpam-3852	402	24	m2	m2	PROPN
ejpam-3852	402	25	+	+	CCONJ
ejpam-3852	402	26	1)×m	1)×m	NUM
ejpam-3852	402	27	matrix	matrix	NOUN
ejpam-3852	402	28	,	,	PUNCT
ejpam-3852	402	29	c	c	NOUN
ejpam-3852	402	30	,	,	PUNCT
ejpam-3852	402	31	formed	form	VERB
ejpam-3852	402	32	by	by	ADP
ejpam-3852	402	33	the	the	DET
ejpam-3852	402	34	first	first	ADJ
ejpam-3852	402	35	m	m	PROPN
ejpam-3852	402	36	2	2	NUM
ejpam-3852	402	37	+	+	SYM
ejpam-3852	402	38	1	1	NUM
ejpam-3852	402	39	rows	row	NOUN
ejpam-3852	402	40	is	be	AUX
ejpam-3852	402	41	of	of	ADP
ejpam-3852	402	42	rank	rank	NOUN
ejpam-3852	402	43	m	m	VERB
ejpam-3852	402	44	2	2	NUM
ejpam-3852	402	45	+	+	CCONJ
ejpam-3852	402	46	1	1	NUM
ejpam-3852	402	47	.	.	PUNCT
ejpam-3852	403	1	again	again	ADV
ejpam-3852	403	2	,	,	PUNCT
ejpam-3852	403	3	zt	zt	PROPN
ejpam-3852	403	4	is	be	AUX
ejpam-3852	403	5	simply	simply	ADV
ejpam-3852	403	6	obtained	obtain	VERB
ejpam-3852	403	7	by	by	ADP
ejpam-3852	403	8	deleting	delete	VERB
ejpam-3852	403	9	the	the	DET
ejpam-3852	403	10	last	last	ADJ
ejpam-3852	403	11	row	row	NOUN
ejpam-3852	403	12	of	of	ADP
ejpam-3852	403	13	c	c	NOUN
ejpam-3852	403	14	,	,	PUNCT
ejpam-3852	403	15	and	and	CCONJ
ejpam-3852	403	16	so	so	ADV
ejpam-3852	403	17	,	,	PUNCT
ejpam-3852	403	18	it	it	PRON
ejpam-3852	403	19	has	have	AUX
ejpam-3852	403	20	rank	rank	NOUN
ejpam-3852	403	21	at	at	ADP
ejpam-3852	403	22	least	least	ADJ
ejpam-3852	403	23	m	m	VERB
ejpam-3852	403	24	2	2	NUM
ejpam-3852	403	25	.	.	PUNCT
ejpam-3852	404	1	it	it	PRON
ejpam-3852	404	2	is	be	AUX
ejpam-3852	404	3	perhaps	perhaps	ADV
ejpam-3852	404	4	customary	customary	ADJ
ejpam-3852	404	5	to	to	PART
ejpam-3852	404	6	define	define	VERB
ejpam-3852	404	7	the	the	DET
ejpam-3852	404	8	lattice	lattice	NOUN
ejpam-3852	404	9	passing	pass	VERB
ejpam-3852	404	10	testing	testing	NOUN
ejpam-3852	404	11	using	use	VERB
ejpam-3852	404	12	the	the	DET
ejpam-3852	404	13	set	set	NOUN
ejpam-3852	404	14	{	{	PUNCT
ejpam-3852	404	15	z0	z0	PROPN
ejpam-3852	404	16	+	+	PROPN
ejpam-3852	404	17	zn	zn	NUM
ejpam-3852	404	18	}	}	PUNCT
ejpam-3852	404	19	.	.	PUNCT
ejpam-3852	405	1	we	we	PRON
ejpam-3852	405	2	preferred	prefer	VERB
ejpam-3852	405	3	for	for	ADP
ejpam-3852	405	4	simplicity	simplicity	NOUN
ejpam-3852	405	5	to	to	PART
ejpam-3852	405	6	use	use	VERB
ejpam-3852	405	7	zn	zn	NUM
ejpam-3852	405	8	,	,	PUNCT
ejpam-3852	405	9	but	but	CCONJ
ejpam-3852	405	10	a	a	DET
ejpam-3852	405	11	similar	similar	ADJ
ejpam-3852	405	12	result	result	NOUN
ejpam-3852	405	13	holds	hold	VERB
ejpam-3852	405	14	for	for	ADP
ejpam-3852	405	15	this	this	DET
ejpam-3852	405	16	set	set	NOUN
ejpam-3852	405	17	,	,	PUNCT
ejpam-3852	405	18	as	as	ADV
ejpam-3852	405	19	well	well	ADV
ejpam-3852	405	20	.	.	PUNCT
ejpam-3852	406	1	we	we	PRON
ejpam-3852	406	2	need	need	VERB
ejpam-3852	406	3	the	the	DET
ejpam-3852	406	4	following	follow	VERB
ejpam-3852	406	5	lemma	lemma	PROPN
ejpam-3852	406	6	,	,	PUNCT
ejpam-3852	406	7	which	which	PRON
ejpam-3852	406	8	will	will	AUX
ejpam-3852	406	9	certainly	certainly	ADV
ejpam-3852	406	10	follow	follow	VERB
ejpam-3852	406	11	from	from	ADP
ejpam-3852	406	12	general	general	ADJ
ejpam-3852	406	13	results	result	NOUN
ejpam-3852	406	14	(	(	PUNCT
ejpam-3852	406	15	see	see	VERB
ejpam-3852	406	16	[	[	X
ejpam-3852	406	17	21	21	NUM
ejpam-3852	406	18	]	]	PUNCT
ejpam-3852	406	19	)	)	PUNCT
ejpam-3852	406	20	,	,	PUNCT
ejpam-3852	406	21	but	but	CCONJ
ejpam-3852	406	22	we	we	PRON
ejpam-3852	406	23	provide	provide	VERB
ejpam-3852	406	24	here	here	ADV
ejpam-3852	406	25	a	a	DET
ejpam-3852	406	26	simple	simple	ADJ
ejpam-3852	406	27	proof	proof	NOUN
ejpam-3852	406	28	for	for	ADP
ejpam-3852	406	29	completeness	completeness	NOUN
ejpam-3852	406	30	.	.	PUNCT
ejpam-3852	407	1	lemma	lemma	PROPN
ejpam-3852	407	2	1	1	X
ejpam-3852	407	3	.	.	PUNCT
ejpam-3852	408	1	let	let	VERB
ejpam-3852	408	2	m	m	NOUN
ejpam-3852	408	3	=	=	NOUN
ejpam-3852	408	4	2ω	2ω	NUM
ejpam-3852	408	5	,	,	PUNCT
ejpam-3852	408	6	ω	ω	X
ejpam-3852	408	7	≥	≥	NOUN
ejpam-3852	408	8	2	2	NUM
ejpam-3852	408	9	and	and	CCONJ
ejpam-3852	408	10	c	c	PROPN
ejpam-3852	408	11	be	be	AUX
ejpam-3852	408	12	an	an	DET
ejpam-3852	408	13	m	m	PROPN
ejpam-3852	408	14	×m	×m	NOUN
ejpam-3852	408	15	binary	binary	ADJ
ejpam-3852	408	16	circulant	circulant	NOUN
ejpam-3852	408	17	matrix	matrix	NOUN
ejpam-3852	408	18	.	.	PUNCT
ejpam-3852	409	1	then	then	ADV
ejpam-3852	409	2	c	c	PROPN
ejpam-3852	409	3	is	be	AUX
ejpam-3852	409	4	nonsingular	nonsingular	ADJ
ejpam-3852	409	5	if	if	SCONJ
ejpam-3852	409	6	and	and	CCONJ
ejpam-3852	409	7	only	only	ADV
ejpam-3852	409	8	if	if	SCONJ
ejpam-3852	409	9	there	there	PRON
ejpam-3852	409	10	is	be	VERB
ejpam-3852	409	11	an	an	DET
ejpam-3852	409	12	odd	odd	ADJ
ejpam-3852	409	13	number	number	NOUN
ejpam-3852	409	14	of	of	ADP
ejpam-3852	409	15	1	1	NUM
ejpam-3852	409	16	’s	’s	NOUN
ejpam-3852	409	17	in	in	ADP
ejpam-3852	409	18	each	each	DET
ejpam-3852	409	19	row	row	NOUN
ejpam-3852	409	20	of	of	ADP
ejpam-3852	409	21	c.	c.	NOUN
ejpam-3852	409	22	proof	proof	NOUN
ejpam-3852	409	23	.	.	PUNCT
ejpam-3852	410	1	first	first	ADV
ejpam-3852	410	2	note	note	VERB
ejpam-3852	410	3	that	that	SCONJ
ejpam-3852	410	4	as	as	SCONJ
ejpam-3852	410	5	c	c	PROPN
ejpam-3852	410	6	is	be	AUX
ejpam-3852	410	7	circulant	circulant	ADJ
ejpam-3852	410	8	so	so	ADV
ejpam-3852	410	9	every	every	DET
ejpam-3852	410	10	row	row	NOUN
ejpam-3852	410	11	has	have	AUX
ejpam-3852	410	12	same	same	ADJ
ejpam-3852	410	13	number	number	NOUN
ejpam-3852	410	14	of	of	ADP
ejpam-3852	410	15	1	1	NUM
ejpam-3852	410	16	’s	’s	NOUN
ejpam-3852	410	17	as	as	ADP
ejpam-3852	410	18	any	any	DET
ejpam-3852	410	19	row	row	NOUN
ejpam-3852	410	20	is	be	AUX
ejpam-3852	410	21	some	some	DET
ejpam-3852	410	22	permutation	permutation	NOUN
ejpam-3852	410	23	of	of	ADP
ejpam-3852	410	24	the	the	DET
ejpam-3852	410	25	first	first	ADJ
ejpam-3852	410	26	row	row	NOUN
ejpam-3852	410	27	.	.	PUNCT
ejpam-3852	411	1	so	so	ADV
ejpam-3852	411	2	,	,	PUNCT
ejpam-3852	411	3	it	it	PRON
ejpam-3852	411	4	is	be	AUX
ejpam-3852	411	5	enough	enough	ADJ
ejpam-3852	411	6	to	to	PART
ejpam-3852	411	7	look	look	VERB
ejpam-3852	411	8	at	at	ADP
ejpam-3852	411	9	the	the	DET
ejpam-3852	411	10	first	first	ADJ
ejpam-3852	411	11	row	row	NOUN
ejpam-3852	411	12	of	of	ADP
ejpam-3852	411	13	c	c	NOUN
ejpam-3852	411	14	,	,	PUNCT
ejpam-3852	411	15	say	say	INTJ
ejpam-3852	411	16	(	(	PUNCT
ejpam-3852	411	17	a0	a0	NOUN
ejpam-3852	411	18	,	,	PUNCT
ejpam-3852	411	19	a1	a1	NOUN
ejpam-3852	411	20	,	,	PUNCT
ejpam-3852	411	21	.	.	PUNCT
ejpam-3852	411	22	.	.	PUNCT
ejpam-3852	412	1	.	.	PUNCT
ejpam-3852	413	1	,	,	PUNCT
ejpam-3852	413	2	am−1	am−1	PROPN
ejpam-3852	413	3	)	)	PUNCT
ejpam-3852	413	4	.	.	PUNCT
ejpam-3852	414	1	let	let	VERB
ejpam-3852	414	2	a(x	a(x	NOUN
ejpam-3852	414	3	)	)	PUNCT
ejpam-3852	414	4	=	=	PUNCT
ejpam-3852	414	5	m−1∑	m−1∑	PROPN
ejpam-3852	414	6	i=0	i=0	PROPN
ejpam-3852	414	7	aix	aix	NOUN
ejpam-3852	414	8	i	i	PRON
ejpam-3852	414	9	be	be	VERB
ejpam-3852	414	10	the	the	DET
ejpam-3852	414	11	associated	associated	ADJ
ejpam-3852	414	12	polynomial	polynomial	NOUN
ejpam-3852	414	13	of	of	ADP
ejpam-3852	414	14	c.	c.	PROPN
ejpam-3852	414	15	now	now	ADV
ejpam-3852	414	16	,	,	PUNCT
ejpam-3852	414	17	c	c	PROPN
ejpam-3852	414	18	is	be	AUX
ejpam-3852	414	19	nonsingular	nonsingular	ADJ
ejpam-3852	414	20	if	if	SCONJ
ejpam-3852	414	21	and	and	CCONJ
ejpam-3852	414	22	only	only	ADV
ejpam-3852	414	23	if	if	SCONJ
ejpam-3852	414	24	the	the	DET
ejpam-3852	414	25	rank	rank	NOUN
ejpam-3852	414	26	of	of	ADP
ejpam-3852	414	27	c	c	PROPN
ejpam-3852	414	28	is	be	AUX
ejpam-3852	414	29	m	m	PRON
ejpam-3852	414	30	,	,	PUNCT
ejpam-3852	414	31	if	if	SCONJ
ejpam-3852	414	32	and	and	CCONJ
ejpam-3852	414	33	only	only	ADV
ejpam-3852	414	34	if	if	SCONJ
ejpam-3852	414	35	gcd	gcd	X
ejpam-3852	414	36	(	(	PUNCT
ejpam-3852	414	37	a(x	a(x	PROPN
ejpam-3852	414	38	)	)	PUNCT
ejpam-3852	414	39	,	,	PUNCT
ejpam-3852	414	40	(	(	PUNCT
ejpam-3852	414	41	1	1	NUM
ejpam-3852	414	42	+	+	CCONJ
ejpam-3852	414	43	x)m	x)m	PUNCT
ejpam-3852	414	44	)	)	PUNCT
ejpam-3852	415	1	=	=	SYM
ejpam-3852	415	2	1	1	NUM
ejpam-3852	415	3	(	(	PUNCT
ejpam-3852	415	4	using	use	VERB
ejpam-3852	415	5	proposition	proposition	NOUN
ejpam-3852	415	6	1	1	NUM
ejpam-3852	415	7	and	and	CCONJ
ejpam-3852	415	8	the	the	DET
ejpam-3852	415	9	fact	fact	NOUN
ejpam-3852	415	10	that	that	SCONJ
ejpam-3852	415	11	m	m	NOUN
ejpam-3852	415	12	is	be	AUX
ejpam-3852	415	13	a	a	DET
ejpam-3852	415	14	power	power	NOUN
ejpam-3852	415	15	of	of	ADP
ejpam-3852	415	16	2	2	NUM
ejpam-3852	415	17	)	)	PUNCT
ejpam-3852	415	18	.	.	PUNCT
ejpam-3852	416	1	clearly	clearly	ADV
ejpam-3852	416	2	,	,	PUNCT
ejpam-3852	416	3	gcd	gcd	X
ejpam-3852	416	4	(	(	PUNCT
ejpam-3852	416	5	a(x	a(x	PROPN
ejpam-3852	416	6	)	)	PUNCT
ejpam-3852	416	7	,	,	PUNCT
ejpam-3852	416	8	(	(	PUNCT
ejpam-3852	416	9	1	1	NUM
ejpam-3852	416	10	+	+	CCONJ
ejpam-3852	416	11	x)m	x)m	PUNCT
ejpam-3852	416	12	)	)	PUNCT
ejpam-3852	416	13	can	can	AUX
ejpam-3852	416	14	either	either	CCONJ
ejpam-3852	416	15	be	be	AUX
ejpam-3852	416	16	1	1	NUM
ejpam-3852	416	17	or	or	CCONJ
ejpam-3852	416	18	some	some	DET
ejpam-3852	416	19	power	power	NOUN
ejpam-3852	416	20	of	of	ADP
ejpam-3852	416	21	(	(	PUNCT
ejpam-3852	416	22	1	1	NUM
ejpam-3852	416	23	+	+	CCONJ
ejpam-3852	416	24	x	x	NOUN
ejpam-3852	416	25	)	)	PUNCT
ejpam-3852	416	26	.	.	PUNCT
ejpam-3852	417	1	again	again	ADV
ejpam-3852	417	2	,	,	PUNCT
ejpam-3852	417	3	(	(	PUNCT
ejpam-3852	417	4	1	1	NUM
ejpam-3852	417	5	+	+	NUM
ejpam-3852	417	6	x	x	X
ejpam-3852	417	7	)	)	PUNCT
ejpam-3852	417	8	|	|	ADV
ejpam-3852	417	9	a(x	a(x	NOUN
ejpam-3852	417	10	)	)	PUNCT
ejpam-3852	417	11	,	,	PUNCT
ejpam-3852	417	12	if	if	SCONJ
ejpam-3852	417	13	and	and	CCONJ
ejpam-3852	417	14	only	only	ADV
ejpam-3852	417	15	if	if	SCONJ
ejpam-3852	417	16	a(1	a(1	ADJ
ejpam-3852	417	17	)	)	PUNCT
ejpam-3852	417	18	=	=	SYM
ejpam-3852	418	1	0	0	NUM
ejpam-3852	418	2	,	,	PUNCT
ejpam-3852	418	3	if	if	SCONJ
ejpam-3852	418	4	and	and	CCONJ
ejpam-3852	418	5	only	only	ADV
ejpam-3852	418	6	if	if	SCONJ
ejpam-3852	418	7	there	there	PRON
ejpam-3852	418	8	are	be	VERB
ejpam-3852	418	9	an	an	DET
ejpam-3852	418	10	even	even	ADJ
ejpam-3852	418	11	number	number	NOUN
ejpam-3852	418	12	of	of	ADP
ejpam-3852	418	13	ai	ai	NOUN
ejpam-3852	418	14	’s	’s	ADJ
ejpam-3852	418	15	that	that	PRON
ejpam-3852	418	16	are	be	AUX
ejpam-3852	418	17	1	1	NUM
ejpam-3852	418	18	.	.	PUNCT
ejpam-3852	418	19	or	or	CCONJ
ejpam-3852	418	20	,	,	PUNCT
ejpam-3852	418	21	in	in	ADP
ejpam-3852	418	22	other	other	ADJ
ejpam-3852	418	23	words	word	NOUN
ejpam-3852	418	24	gcd	gcd	VERB
ejpam-3852	418	25	(	(	PUNCT
ejpam-3852	418	26	a(x	a(x	PROPN
ejpam-3852	418	27	)	)	PUNCT
ejpam-3852	418	28	,	,	PUNCT
ejpam-3852	418	29	(	(	PUNCT
ejpam-3852	418	30	1	1	NUM
ejpam-3852	418	31	+	+	CCONJ
ejpam-3852	418	32	x)n	x)n	PUNCT
ejpam-3852	418	33	)	)	PUNCT
ejpam-3852	419	1	=	=	PUNCT
ejpam-3852	419	2	1	1	NUM
ejpam-3852	419	3	if	if	SCONJ
ejpam-3852	419	4	and	and	CCONJ
ejpam-3852	419	5	only	only	ADV
ejpam-3852	419	6	if	if	SCONJ
ejpam-3852	419	7	there	there	PRON
ejpam-3852	419	8	are	be	VERB
ejpam-3852	419	9	an	an	DET
ejpam-3852	419	10	odd	odd	ADJ
ejpam-3852	419	11	number	number	NOUN
ejpam-3852	419	12	of	of	ADP
ejpam-3852	419	13	ai	ai	NOUN
ejpam-3852	419	14	’s	’s	ADJ
ejpam-3852	419	15	that	that	PRON
ejpam-3852	419	16	are	be	AUX
ejpam-3852	419	17	1	1	NUM
ejpam-3852	419	18	,	,	PUNCT
ejpam-3852	419	19	that	that	ADV
ejpam-3852	419	20	is	is	ADV
ejpam-3852	419	21	,	,	PUNCT
ejpam-3852	419	22	each	each	DET
ejpam-3852	419	23	row	row	NOUN
ejpam-3852	419	24	contains	contain	VERB
ejpam-3852	419	25	an	an	DET
ejpam-3852	419	26	odd	odd	ADJ
ejpam-3852	419	27	number	number	NOUN
ejpam-3852	419	28	of	of	ADP
ejpam-3852	419	29	1	1	NUM
ejpam-3852	419	30	’s	’s	PART
ejpam-3852	419	31	.	.	PUNCT
ejpam-3852	420	1	theorem	theorem	VERB
ejpam-3852	420	2	7	7	NUM
ejpam-3852	420	3	.	.	PUNCT
ejpam-3852	421	1	under	under	ADP
ejpam-3852	421	2	the	the	DET
ejpam-3852	421	3	conditions	condition	NOUN
ejpam-3852	421	4	of	of	ADP
ejpam-3852	421	5	theorem	theorem	NOUN
ejpam-3852	421	6	6	6	NUM
ejpam-3852	421	7	,	,	PUNCT
ejpam-3852	421	8	the	the	DET
ejpam-3852	421	9	set	set	NOUN
ejpam-3852	421	10	{	{	PUNCT
ejpam-3852	421	11	z	z	NOUN
ejpam-3852	421	12	′n	′n	PROPN
ejpam-3852	421	13	=	=	PUNCT
ejpam-3852	421	14	zn	zn	PROPN
ejpam-3852	421	15	+	+	CCONJ
ejpam-3852	421	16	z0;n	z0;n	PROPN
ejpam-3852	421	17	=	=	SYM
ejpam-3852	421	18	1	1	NUM
ejpam-3852	421	19	,	,	PUNCT
ejpam-3852	421	20	2	2	NUM
ejpam-3852	421	21	,	,	PUNCT
ejpam-3852	421	22	.	.	PUNCT
ejpam-3852	421	23	.	.	PUNCT
ejpam-3852	421	24	.	.	PUNCT
ejpam-3852	422	1	}	}	PUNCT
ejpam-3852	422	2	spans	span	VERB
ejpam-3852	422	3	f	f	PROPN
ejpam-3852	422	4	m	m	VERB
ejpam-3852	422	5	2	2	NUM
ejpam-3852	422	6	2	2	NUM
ejpam-3852	422	7	.	.	PUNCT
ejpam-3852	423	1	proof	proof	NOUN
ejpam-3852	423	2	.	.	PUNCT
ejpam-3852	424	1	let	let	VERB
ejpam-3852	424	2	s	s	PRON
ejpam-3852	424	3	=	=	VERB
ejpam-3852	424	4	span{z	span{z	PRON
ejpam-3852	424	5	′n;n	′n;n	NOUN
ejpam-3852	424	6	=	=	SYM
ejpam-3852	424	7	1	1	NUM
ejpam-3852	424	8	,	,	PUNCT
ejpam-3852	424	9	2	2	NUM
ejpam-3852	424	10	,	,	PUNCT
ejpam-3852	424	11	.	.	PUNCT
ejpam-3852	424	12	.	.	PUNCT
ejpam-3852	424	13	.	.	PUNCT
ejpam-3852	424	14	}	}	PUNCT
ejpam-3852	424	15	.	.	PUNCT
ejpam-3852	425	1	then	then	ADV
ejpam-3852	425	2	,	,	PUNCT
ejpam-3852	425	3	clearly	clearly	ADV
ejpam-3852	425	4	,	,	PUNCT
ejpam-3852	425	5	the	the	DET
ejpam-3852	425	6	vectors	vector	NOUN
ejpam-3852	425	7	,	,	PUNCT
ejpam-3852	425	8	z	z	NOUN
ejpam-3852	425	9	′n	′n	NOUN
ejpam-3852	425	10	+	+	CCONJ
ejpam-3852	425	11	z	z	NOUN
ejpam-3852	425	12	′n+1	′n+1	NOUN
ejpam-3852	425	13	=	=	SYM
ejpam-3852	426	1	zn	zn	PROPN
ejpam-3852	426	2	+	+	CCONJ
ejpam-3852	426	3	zn+1	zn+1	PROPN
ejpam-3852	426	4	∈	∈	NOUN
ejpam-3852	426	5	s	s	NOUN
ejpam-3852	426	6	for	for	ADP
ejpam-3852	426	7	all	all	PRON
ejpam-3852	426	8	n	n	NOUN
ejpam-3852	426	9	=	=	SYM
ejpam-3852	426	10	1	1	NUM
ejpam-3852	426	11	,	,	PUNCT
ejpam-3852	426	12	2	2	NUM
ejpam-3852	426	13	,	,	PUNCT
ejpam-3852	426	14	.	.	PUNCT
ejpam-3852	426	15	.	.	PUNCT
ejpam-3852	426	16	.	.	PUNCT
ejpam-3852	427	1	,	,	PUNCT
ejpam-3852	428	1	m2	m2	PROPN
ejpam-3852	428	2	.	.	PUNCT
ejpam-3852	429	1	then	then	ADV
ejpam-3852	429	2	,	,	PUNCT
ejpam-3852	429	3	it	it	PRON
ejpam-3852	429	4	is	be	AUX
ejpam-3852	429	5	sufficient	sufficient	ADJ
ejpam-3852	429	6	to	to	PART
ejpam-3852	429	7	show	show	VERB
ejpam-3852	429	8	that	that	SCONJ
ejpam-3852	429	9	the	the	DET
ejpam-3852	429	10	m	m	PROPN
ejpam-3852	429	11	2	2	NUM
ejpam-3852	429	12	×	×	NOUN
ejpam-3852	429	13	m	m	NOUN
ejpam-3852	429	14	2	2	NUM
ejpam-3852	429	15	matrix	matrix	NOUN
ejpam-3852	429	16	z	z	NOUN
ejpam-3852	429	17	′	′	NOUN
ejpam-3852	429	18	=	=	PUNCT
ejpam-3852	429	19			NOUN
ejpam-3852	429	20	z	z	NOUN
ejpam-3852	429	21	′1	′1	ADP
ejpam-3852	429	22	+	+	PUNCT
ejpam-3852	429	23	z	z	NOUN
ejpam-3852	429	24	′2	′2	NOUN
ejpam-3852	429	25	z	z	NOUN
ejpam-3852	429	26	′2	′2	NOUN
ejpam-3852	429	27	+	+	CCONJ
ejpam-3852	429	28	z	z	NOUN
ejpam-3852	430	1	′3	′3	NOUN
ejpam-3852	430	2	z	z	NOUN
ejpam-3852	430	3	′3	′3	NOUN
ejpam-3852	430	4	+	+	CCONJ
ejpam-3852	430	5	z	z	NOUN
ejpam-3852	430	6	′4	′4	NOUN
ejpam-3852	431	1	...	...	PUNCT
ejpam-3852	431	2	z	z	X
ejpam-3852	431	3	′m	′m	PROPN
ejpam-3852	431	4	2	2	NUM
ejpam-3852	431	5	+	+	CCONJ
ejpam-3852	431	6	z	z	NOUN
ejpam-3852	431	7	′m	′m	PROPN
ejpam-3852	431	8	2	2	NUM
ejpam-3852	431	9	+1	+1	NOUN
ejpam-3852	431	10			PUNCT
ejpam-3852	431	11	=	=	SYM
ejpam-3852	431	12			ADJ
ejpam-3852	431	13	z1	z1	VERB
ejpam-3852	431	14	+	+	CCONJ
ejpam-3852	431	15	z2	z2	PROPN
ejpam-3852	431	16	z2	z2	PROPN
ejpam-3852	431	17	+	+	CCONJ
ejpam-3852	431	18	z3	z3	PROPN
ejpam-3852	431	19	z3	z3	PROPN
ejpam-3852	431	20	+	+	CCONJ
ejpam-3852	431	21	z4	z4	PROPN
ejpam-3852	431	22	...	...	PUNCT
ejpam-3852	431	23	zm	zm	PROPN
ejpam-3852	431	24	2	2	NUM
ejpam-3852	432	1	+	+	CCONJ
ejpam-3852	432	2	zm	zm	PROPN
ejpam-3852	432	3	2	2	NUM
ejpam-3852	432	4	+1	+1	PROPN
ejpam-3852	432	5			PROPN
ejpam-3852	432	6	has	have	AUX
ejpam-3852	432	7	rank	rank	VERB
ejpam-3852	432	8	m	m	PROPN
ejpam-3852	432	9	2	2	NUM
ejpam-3852	432	10	.	.	PUNCT
ejpam-3852	433	1	now	now	ADV
ejpam-3852	433	2	,	,	PUNCT
ejpam-3852	433	3	it	it	PRON
ejpam-3852	433	4	is	be	AUX
ejpam-3852	433	5	easy	easy	ADJ
ejpam-3852	433	6	to	to	PART
ejpam-3852	433	7	check	check	VERB
ejpam-3852	433	8	that	that	PRON
ejpam-3852	434	1	z	z	NOUN
ejpam-3852	434	2	′	′	NUM
ejpam-3852	434	3	is	be	AUX
ejpam-3852	434	4	a	a	DET
ejpam-3852	434	5	left	left	ADJ
ejpam-3852	434	6	circulant	circulant	ADJ
ejpam-3852	434	7	binary	binary	ADJ
ejpam-3852	434	8	matrix	matrix	NOUN
ejpam-3852	434	9	of	of	ADP
ejpam-3852	434	10	order	order	NOUN
ejpam-3852	434	11	m	m	VERB
ejpam-3852	434	12	2	2	NUM
ejpam-3852	434	13	×	×	NOUN
ejpam-3852	434	14	m	m	NOUN
ejpam-3852	434	15	2	2	NUM
ejpam-3852	434	16	.	.	PUNCT
ejpam-3852	435	1	again	again	ADV
ejpam-3852	435	2	,	,	PUNCT
ejpam-3852	435	3	z1	z1	PROPN
ejpam-3852	435	4	+	+	NOUN
ejpam-3852	435	5	z2	z2	NOUN
ejpam-3852	435	6	=	=	SYM
ejpam-3852	435	7	(	(	PUNCT
ejpam-3852	435	8	z1	z1	PROPN
ejpam-3852	435	9	+	+	CCONJ
ejpam-3852	435	10	z2	z2	PROPN
ejpam-3852	435	11	,	,	PUNCT
ejpam-3852	435	12	z2	z2	PROPN
ejpam-3852	435	13	+	+	CCONJ
ejpam-3852	435	14	z3	z3	PROPN
ejpam-3852	435	15	,	,	PUNCT
ejpam-3852	435	16	z3	z3	PROPN
ejpam-3852	435	17	+	+	CCONJ
ejpam-3852	435	18	z4	z4	NOUN
ejpam-3852	435	19	,	,	PUNCT
ejpam-3852	435	20	.	.	PUNCT
ejpam-3852	435	21	.	.	PUNCT
ejpam-3852	436	1	.	.	PUNCT
ejpam-3852	437	1	,	,	PUNCT
ejpam-3852	437	2	zm	zm	PROPN
ejpam-3852	437	3	2	2	NUM
ejpam-3852	437	4	−1	−1	NOUN
ejpam-3852	437	5	+	+	CCONJ
ejpam-3852	437	6	z0	z0	PROPN
ejpam-3852	437	7	,	,	PUNCT
ejpam-3852	437	8	z0	z0	PROPN
ejpam-3852	437	9	+	+	CCONJ
ejpam-3852	437	10	z1	z1	PROPN
ejpam-3852	437	11	)	)	PUNCT
ejpam-3852	437	12	=	=	PUNCT
ejpam-3852	437	13	(	(	PUNCT
ejpam-3852	437	14	z1	z1	X
ejpam-3852	437	15	+	+	CCONJ
ejpam-3852	437	16	z2	z2	PROPN
ejpam-3852	437	17	,	,	PUNCT
ejpam-3852	437	18	z2	z2	PROPN
ejpam-3852	437	19	+	+	CCONJ
ejpam-3852	437	20	z3	z3	PROPN
ejpam-3852	437	21	,	,	PUNCT
ejpam-3852	437	22	z3	z3	PROPN
ejpam-3852	437	23	+	+	CCONJ
ejpam-3852	437	24	z4	z4	NOUN
ejpam-3852	437	25	,	,	PUNCT
ejpam-3852	437	26	.	.	PUNCT
ejpam-3852	437	27	.	.	PUNCT
ejpam-3852	438	1	.	.	PUNCT
ejpam-3852	439	1	,	,	PUNCT
ejpam-3852	439	2	zm	zm	PROPN
ejpam-3852	439	3	2	2	NUM
ejpam-3852	439	4	−1	−1	NOUN
ejpam-3852	439	5	+	+	CCONJ
ejpam-3852	439	6	z0	z0	NOUN
ejpam-3852	439	7	+	+	CCONJ
ejpam-3852	439	8	1	1	NUM
ejpam-3852	439	9	,	,	PUNCT
ejpam-3852	439	10	z0	z0	PROPN
ejpam-3852	439	11	+	+	CCONJ
ejpam-3852	439	12	z1	z1	PROPN
ejpam-3852	439	13	)	)	PUNCT
ejpam-3852	439	14	.	.	PUNCT
ejpam-3852	440	1	every	every	DET
ejpam-3852	440	2	element	element	NOUN
ejpam-3852	440	3	among	among	ADP
ejpam-3852	440	4	z0	z0	PROPN
ejpam-3852	440	5	,	,	PUNCT
ejpam-3852	440	6	z1	z1	NOUN
ejpam-3852	440	7	,	,	PUNCT
ejpam-3852	440	8	.	.	PUNCT
ejpam-3852	440	9	.	.	PUNCT
ejpam-3852	440	10	.	.	PUNCT
ejpam-3852	441	1	,	,	PUNCT
ejpam-3852	441	2	zm	zm	PROPN
ejpam-3852	441	3	2	2	NUM
ejpam-3852	441	4	−1	−1	NOUN
ejpam-3852	441	5	occurs	occur	VERB
ejpam-3852	441	6	exactly	exactly	ADV
ejpam-3852	441	7	twice	twice	ADV
ejpam-3852	441	8	in	in	ADP
ejpam-3852	441	9	z1	z1	ADJ
ejpam-3852	441	10	+	+	CCONJ
ejpam-3852	441	11	z2	z2	PROPN
ejpam-3852	441	12	and	and	CCONJ
ejpam-3852	441	13	an	an	DET
ejpam-3852	441	14	extra	extra	ADJ
ejpam-3852	441	15	1	1	NUM
ejpam-3852	441	16	occurs	occur	VERB
ejpam-3852	441	17	in	in	ADP
ejpam-3852	441	18	the	the	DET
ejpam-3852	441	19	second	second	NOUN
ejpam-3852	441	20	of	of	ADP
ejpam-3852	441	21	the	the	DET
ejpam-3852	441	22	last	last	ADJ
ejpam-3852	441	23	term	term	NOUN
ejpam-3852	441	24	.	.	PUNCT
ejpam-3852	442	1	therefore	therefore	ADV
ejpam-3852	442	2	,	,	PUNCT
ejpam-3852	442	3	there	there	PRON
ejpam-3852	442	4	are	be	VERB
ejpam-3852	442	5	odd	odd	ADJ
ejpam-3852	442	6	number	number	NOUN
ejpam-3852	442	7	of	of	ADP
ejpam-3852	442	8	1	1	NUM
ejpam-3852	442	9	’s	’s	NOUN
ejpam-3852	442	10	in	in	ADP
ejpam-3852	442	11	each	each	DET
ejpam-3852	442	12	row	row	NOUN
ejpam-3852	442	13	of	of	ADP
ejpam-3852	442	14	z	z	NOUN
ejpam-3852	442	15	′.	′.	NOUN
ejpam-3852	442	16	hence	hence	ADV
ejpam-3852	442	17	,	,	PUNCT
ejpam-3852	442	18	by	by	ADP
ejpam-3852	442	19	lemma	lemma	PROPN
ejpam-3852	442	20	1	1	NUM
ejpam-3852	442	21	,	,	PUNCT
ejpam-3852	442	22	we	we	PRON
ejpam-3852	442	23	infer	infer	VERB
ejpam-3852	442	24	that	that	SCONJ
ejpam-3852	442	25	z	z	NOUN
ejpam-3852	442	26	′	′	NUM
ejpam-3852	442	27	has	have	AUX
ejpam-3852	442	28	rank	rank	PROPN
ejpam-3852	442	29	m	m	PROPN
ejpam-3852	442	30	2	2	NUM
ejpam-3852	442	31	.	.	PUNCT
ejpam-3852	443	1	p.	p.	NOUN
ejpam-3852	443	2	stănică	stănică	NUM
ejpam-3852	443	3	et	et	PROPN
ejpam-3852	443	4	al	al	PROPN
ejpam-3852	443	5	.	.	PUNCT
ejpam-3852	443	6	/	/	SYM
ejpam-3852	443	7	eur	eur	PROPN
ejpam-3852	443	8	.	.	PUNCT
ejpam-3852	444	1	j.	j.	PROPN
ejpam-3852	444	2	pure	pure	PROPN
ejpam-3852	444	3	appl	appl	PROPN
ejpam-3852	444	4	.	.	PROPN
ejpam-3852	444	5	math	math	PROPN
ejpam-3852	444	6	,	,	PUNCT
ejpam-3852	444	7	14	14	NUM
ejpam-3852	444	8	(	(	PUNCT
ejpam-3852	444	9	1	1	NUM
ejpam-3852	444	10	)	)	PUNCT
ejpam-3852	444	11	(	(	PUNCT
ejpam-3852	444	12	2021	2021	NUM
ejpam-3852	444	13	)	)	PUNCT
ejpam-3852	444	14	,	,	PUNCT
ejpam-3852	444	15	1	1	NUM
ejpam-3852	444	16	-	-	SYM
ejpam-3852	444	17	18	18	NUM
ejpam-3852	444	18	14	14	NUM
ejpam-3852	444	19	5	5	NUM
ejpam-3852	444	20	.	.	PUNCT
ejpam-3852	445	1	further	further	ADJ
ejpam-3852	445	2	comments	comment	NOUN
ejpam-3852	445	3	and	and	CCONJ
ejpam-3852	445	4	research	research	NOUN
ejpam-3852	445	5	problems	problem	NOUN
ejpam-3852	445	6	we	we	PRON
ejpam-3852	445	7	wondered	wonder	VERB
ejpam-3852	445	8	whether	whether	SCONJ
ejpam-3852	445	9	,	,	PUNCT
ejpam-3852	445	10	besides	besides	SCONJ
ejpam-3852	445	11	the	the	DET
ejpam-3852	445	12	stochastic	stochastic	ADJ
ejpam-3852	445	13	uses	use	NOUN
ejpam-3852	445	14	of	of	ADP
ejpam-3852	445	15	hicg	hicg	NOUN
ejpam-3852	445	16	(	(	PUNCT
ejpam-3852	445	17	and	and	CCONJ
ejpam-3852	445	18	from	from	ADP
ejpam-3852	445	19	our	our	PRON
ejpam-3852	445	20	experiments	experiment	NOUN
ejpam-3852	445	21	,	,	PUNCT
ejpam-3852	445	22	it	it	PRON
ejpam-3852	445	23	seems	seem	VERB
ejpam-3852	445	24	that	that	SCONJ
ejpam-3852	445	25	taking	take	VERB
ejpam-3852	445	26	m	m	NOUN
ejpam-3852	445	27	=	=	NOUN
ejpam-3852	445	28	264	264	NUM
ejpam-3852	445	29	performs	perform	VERB
ejpam-3852	445	30	very	very	ADV
ejpam-3852	445	31	well	well	ADV
ejpam-3852	445	32	)	)	PUNCT
ejpam-3852	445	33	,	,	PUNCT
ejpam-3852	445	34	if	if	SCONJ
ejpam-3852	445	35	one	one	PRON
ejpam-3852	445	36	can	can	AUX
ejpam-3852	445	37	also	also	ADV
ejpam-3852	445	38	have	have	VERB
ejpam-3852	445	39	some	some	DET
ejpam-3852	445	40	cryptographic	cryptographic	ADJ
ejpam-3852	445	41	applications	application	NOUN
ejpam-3852	445	42	of	of	ADP
ejpam-3852	445	43	our	our	PRON
ejpam-3852	445	44	sequence	sequence	NOUN
ejpam-3852	445	45	.	.	PUNCT
ejpam-3852	446	1	taking	take	VERB
ejpam-3852	446	2	the	the	DET
ejpam-3852	446	3	least	least	ADJ
ejpam-3852	446	4	significant	significant	ADJ
ejpam-3852	446	5	bit	bit	NOUN
ejpam-3852	446	6	of	of	ADP
ejpam-3852	446	7	every	every	DET
ejpam-3852	446	8	residues	residue	NOUN
ejpam-3852	446	9	of	of	ADP
ejpam-3852	446	10	{	{	PUNCT
ejpam-3852	446	11	yn	yn	NOUN
ejpam-3852	446	12	}	}	PUNCT
ejpam-3852	446	13	and	and	CCONJ
ejpam-3852	446	14	applying	apply	VERB
ejpam-3852	446	15	randomness	randomness	NOUN
ejpam-3852	446	16	tests	test	NOUN
ejpam-3852	446	17	on	on	ADP
ejpam-3852	446	18	it	it	PRON
ejpam-3852	446	19	,	,	PUNCT
ejpam-3852	446	20	revealed	reveal	VERB
ejpam-3852	446	21	too	too	ADV
ejpam-3852	446	22	many	many	ADJ
ejpam-3852	446	23	patterns	pattern	NOUN
ejpam-3852	446	24	and	and	CCONJ
ejpam-3852	446	25	the	the	DET
ejpam-3852	446	26	p	p	NOUN
ejpam-3852	446	27	-	-	PUNCT
ejpam-3852	446	28	values	value	NOUN
ejpam-3852	446	29	were	be	AUX
ejpam-3852	446	30	low	low	ADJ
ejpam-3852	446	31	.	.	PUNCT
ejpam-3852	447	1	however	however	ADV
ejpam-3852	447	2	,	,	PUNCT
ejpam-3852	447	3	by	by	ADP
ejpam-3852	447	4	taking	take	VERB
ejpam-3852	447	5	the	the	DET
ejpam-3852	447	6	most	most	ADV
ejpam-3852	447	7	significant	significant	ADJ
ejpam-3852	447	8	bit	bit	NOUN
ejpam-3852	447	9	(	(	PUNCT
ejpam-3852	447	10	see	see	VERB
ejpam-3852	447	11	the	the	DET
ejpam-3852	447	12	previous	previous	ADJ
ejpam-3852	447	13	section	section	NOUN
ejpam-3852	447	14	)	)	PUNCT
ejpam-3852	447	15	up	up	ADP
ejpam-3852	447	16	to	to	PART
ejpam-3852	447	17	half	half	DET
ejpam-3852	447	18	the	the	DET
ejpam-3852	447	19	period	period	NOUN
ejpam-3852	447	20	(	(	PUNCT
ejpam-3852	447	21	because	because	SCONJ
ejpam-3852	447	22	for	for	ADP
ejpam-3852	447	23	a	a	DET
ejpam-3852	447	24	hicg	hicg	NOUN
ejpam-3852	447	25	of	of	ADP
ejpam-3852	447	26	period	period	NOUN
ejpam-3852	447	27	2	2	NUM
ejpam-3852	447	28	m	m	NOUN
ejpam-3852	447	29	,	,	PUNCT
ejpam-3852	447	30	ym+k	ym+k	PROPN
ejpam-3852	447	31	≡	≡	PROPN
ejpam-3852	447	32	yk	yk	PROPN
ejpam-3852	448	1	+	+	PROPN
ejpam-3852	448	2	m	m	PROPN
ejpam-3852	448	3	(	(	PUNCT
ejpam-3852	448	4	mod	mod	PROPN
ejpam-3852	448	5	2	2	NUM
ejpam-3852	448	6	m	m	NOUN
ejpam-3852	448	7	)	)	PUNCT
ejpam-3852	448	8	)	)	PUNCT
ejpam-3852	448	9	,	,	PUNCT
ejpam-3852	448	10	we	we	PRON
ejpam-3852	448	11	were	be	AUX
ejpam-3852	448	12	pleasantly	pleasantly	ADV
ejpam-3852	448	13	surprised	surprised	ADJ
ejpam-3852	448	14	to	to	PART
ejpam-3852	448	15	see	see	VERB
ejpam-3852	448	16	that	that	PRON
ejpam-3852	448	17	for	for	ADP
ejpam-3852	448	18	that	that	DET
ejpam-3852	448	19	bit	bit	NOUN
ejpam-3852	448	20	sequence	sequence	NOUN
ejpam-3852	448	21	corresponding	correspond	VERB
ejpam-3852	448	22	to	to	ADP
ejpam-3852	448	23	half	half	NOUN
ejpam-3852	448	24	of	of	ADP
ejpam-3852	448	25	a	a	DET
ejpam-3852	448	26	period	period	NOUN
ejpam-3852	448	27	and	and	CCONJ
ejpam-3852	448	28	applying	apply	VERB
ejpam-3852	448	29	the	the	DET
ejpam-3852	448	30	nist	nist	NOUN
ejpam-3852	448	31	randomness	randomness	NOUN
ejpam-3852	448	32	suite	suite	NOUN
ejpam-3852	448	33	tests	test	NOUN
ejpam-3852	448	34	(	(	PUNCT
ejpam-3852	448	35	sts	st	NOUN
ejpam-3852	448	36	)	)	PUNCT
ejpam-3852	448	37	,	,	PUNCT
ejpam-3852	448	38	our	our	PRON
ejpam-3852	448	39	sequence	sequence	NOUN
ejpam-3852	448	40	passed	pass	VERB
ejpam-3852	448	41	all	all	PRON
ejpam-3852	448	42	of	of	ADP
ejpam-3852	448	43	the	the	DET
ejpam-3852	448	44	tests	test	NOUN
ejpam-3852	448	45	in	in	ADP
ejpam-3852	448	46	multiple	multiple	ADJ
ejpam-3852	448	47	runs	run	NOUN
ejpam-3852	448	48	,	,	PUNCT
ejpam-3852	448	49	and	and	CCONJ
ejpam-3852	448	50	the	the	DET
ejpam-3852	448	51	p	p	NOUN
ejpam-3852	448	52	-	-	PUNCT
ejpam-3852	448	53	values	value	NOUN
ejpam-3852	448	54	were	be	AUX
ejpam-3852	448	55	above	above	ADP
ejpam-3852	448	56	the	the	DET
ejpam-3852	448	57	0.01	0.01	NUM
ejpam-3852	448	58	significance	significance	NOUN
ejpam-3852	448	59	level	level	NOUN
ejpam-3852	448	60	(	(	PUNCT
ejpam-3852	448	61	we	we	PRON
ejpam-3852	448	62	do	do	AUX
ejpam-3852	448	63	not	not	PART
ejpam-3852	448	64	go	go	VERB
ejpam-3852	448	65	into	into	ADP
ejpam-3852	448	66	details	detail	NOUN
ejpam-3852	448	67	of	of	ADP
ejpam-3852	448	68	the	the	DET
ejpam-3852	448	69	sts	st	NOUN
ejpam-3852	448	70	suite	suite	NOUN
ejpam-3852	448	71	and	and	CCONJ
ejpam-3852	448	72	the	the	DET
ejpam-3852	448	73	randomness	randomness	NOUN
ejpam-3852	448	74	requirements	requirement	NOUN
ejpam-3852	448	75	here	here	ADV
ejpam-3852	448	76	)	)	PUNCT
ejpam-3852	448	77	.	.	PUNCT
ejpam-3852	449	1	we	we	PRON
ejpam-3852	449	2	visually	visually	ADV
ejpam-3852	449	3	display	display	VERB
ejpam-3852	449	4	in	in	ADP
ejpam-3852	449	5	figure	figure	NOUN
ejpam-3852	449	6	1	1	NUM
ejpam-3852	449	7	below	below	ADP
ejpam-3852	449	8	the	the	DET
ejpam-3852	449	9	outcome	outcome	NOUN
ejpam-3852	449	10	of	of	ADP
ejpam-3852	449	11	such	such	DET
ejpam-3852	449	12	an	an	DET
ejpam-3852	449	13	experiment	experiment	NOUN
ejpam-3852	449	14	run	run	VERB
ejpam-3852	449	15	with	with	ADP
ejpam-3852	449	16	the	the	DET
ejpam-3852	449	17	parameters	parameter	NOUN
ejpam-3852	449	18	ω	ω	NOUN
ejpam-3852	449	19	=	=	SYM
ejpam-3852	449	20	64	64	NUM
ejpam-3852	449	21	,	,	PUNCT
ejpam-3852	449	22	a	a	DET
ejpam-3852	449	23	=	=	SYM
ejpam-3852	449	24	1886906	1886906	NUM
ejpam-3852	449	25	,	,	PUNCT
ejpam-3852	449	26	b	b	X
ejpam-3852	449	27	=	=	SYM
ejpam-3852	449	28	706715	706715	NUM
ejpam-3852	449	29	,	,	PUNCT
ejpam-3852	449	30	c	c	NOUN
ejpam-3852	449	31	=	=	SYM
ejpam-3852	449	32	807782	807782	NUM
ejpam-3852	449	33	,	,	PUNCT
ejpam-3852	449	34	y0	y0	PROPN
ejpam-3852	449	35	=	=	SYM
ejpam-3852	449	36	430227	430227	NUM
ejpam-3852	449	37	and	and	CCONJ
ejpam-3852	449	38	y1	y1	NOUN
ejpam-3852	449	39	=	=	SYM
ejpam-3852	449	40	1725239	1725239	NUM
ejpam-3852	449	41	and	and	CCONJ
ejpam-3852	449	42	108	108	NUM
ejpam-3852	449	43	prns	prn	NOUN
ejpam-3852	449	44	.	.	PUNCT
ejpam-3852	450	1	also	also	ADV
ejpam-3852	450	2	with	with	ADP
ejpam-3852	450	3	the	the	DET
ejpam-3852	450	4	same	same	ADJ
ejpam-3852	450	5	random	random	ADJ
ejpam-3852	450	6	number	number	NOUN
ejpam-3852	450	7	test	test	NOUN
ejpam-3852	450	8	0.0	0.0	NUM
ejpam-3852	450	9	0.2	0.2	NUM
ejpam-3852	450	10	0.4	0.4	NUM
ejpam-3852	450	11	0.6	0.6	NUM
ejpam-3852	450	12	0.8	0.8	NUM
ejpam-3852	450	13	1.0	1.0	NUM
ejpam-3852	450	14	p	p	NOUN
ejpam-3852	450	15	-v	-v	PUNCT
ejpam-3852	450	16	a	a	DET
ejpam-3852	450	17	lu	lu	NOUN
ejpam-3852	450	18	e	e	NOUN
ejpam-3852	450	19	a	a	PRON
ejpam-3852	450	20	p	p	X
ejpam-3852	450	21	p	p	NOUN
ejpam-3852	450	22	r	r	NOUN
ejpam-3852	450	23	o	o	NOUN
ejpam-3852	450	24	x	x	X
ejpam-3852	451	1	i	i	PRON
ejpam-3852	451	2	m	m	VERB
ejpam-3852	451	3	a	a	DET
ejpam-3852	451	4	t	t	NOUN
ejpam-3852	451	5	e	e	X
ejpam-3852	451	6	e	e	X
ejpam-3852	451	7	n	n	X
ejpam-3852	451	8	t	t	NOUN
ejpam-3852	451	9	r	r	NOUN
ejpam-3852	451	10	o	o	X
ejpam-3852	452	1	p	p	X
ejpam-3852	452	2	y	y	PROPN
ejpam-3852	452	3	t	t	PROPN
ejpam-3852	452	4	e	e	PROPN
ejpam-3852	452	5	s	s	PROPN
ejpam-3852	452	6	t	t	PROPN
ejpam-3852	452	7	b	b	PROPN
ejpam-3852	452	8	l	l	NOUN
ejpam-3852	453	1	o	o	X
ejpam-3852	453	2	c	c	NOUN
ejpam-3852	454	1	k	k	NOUN
ejpam-3852	454	2	f	f	NOUN
ejpam-3852	454	3	r	r	NOUN
ejpam-3852	454	4	e	e	X
ejpam-3852	454	5	q	q	X
ejpam-3852	454	6	u	u	X
ejpam-3852	454	7	e	e	NOUN
ejpam-3852	454	8	n	n	PROPN
ejpam-3852	454	9	c	c	PROPN
ejpam-3852	454	10	y	y	PROPN
ejpam-3852	454	11	t	t	PROPN
ejpam-3852	454	12	e	e	X
ejpam-3852	454	13	s	s	PROPN
ejpam-3852	454	14	t	t	PROPN
ejpam-3852	454	15	c	c	NOUN
ejpam-3852	454	16	u	u	NOUN
ejpam-3852	454	17	m	m	NOUN
ejpam-3852	454	18	u	u	NOUN
ejpam-3852	454	19	l	l	NOUN
ejpam-3852	454	20	a	a	PROPN
ejpam-3852	454	21	t	t	NOUN
ejpam-3852	454	22	iv	iv	NUM
ejpam-3852	455	1	e	e	NOUN
ejpam-3852	455	2	s	s	VERB
ejpam-3852	455	3	u	u	X
ejpam-3852	455	4	m	m	NOUN
ejpam-3852	455	5	s	s	X
ejpam-3852	455	6	(	(	PUNCT
ejpam-3852	455	7	f	f	NOUN
ejpam-3852	455	8	o	o	NOUN
ejpam-3852	456	1	r	r	NOUN
ejpam-3852	456	2	w	w	NOUN
ejpam-3852	456	3	a	a	DET
ejpam-3852	456	4	r	r	NOUN
ejpam-3852	456	5	d	d	NOUN
ejpam-3852	456	6	)	)	PUNCT
ejpam-3852	456	7	t	t	PROPN
ejpam-3852	456	8	e	e	NOUN
ejpam-3852	456	9	s	s	PROPN
ejpam-3852	456	10	t	t	X
ejpam-3852	457	1	f	f	PROPN
ejpam-3852	457	2	f	f	PROPN
ejpam-3852	457	3	t	t	PROPN
ejpam-3852	457	4	t	t	X
ejpam-3852	457	5	e	e	X
ejpam-3852	457	6	s	s	PROPN
ejpam-3852	457	7	t	t	X
ejpam-3852	457	8	f	f	NOUN
ejpam-3852	457	9	r	r	NOUN
ejpam-3852	457	10	e	e	NOUN
ejpam-3852	457	11	q	q	X
ejpam-3852	457	12	u	u	X
ejpam-3852	457	13	e	e	NOUN
ejpam-3852	457	14	n	n	PROPN
ejpam-3852	457	15	c	c	PROPN
ejpam-3852	457	16	y	y	PROPN
ejpam-3852	457	17	t	t	PROPN
ejpam-3852	457	18	e	e	X
ejpam-3852	457	19	s	s	PROPN
ejpam-3852	457	20	t	t	X
ejpam-3852	457	21	l	l	NOUN
ejpam-3852	457	22	in	in	ADP
ejpam-3852	457	23	e	e	PROPN
ejpam-3852	457	24	a	a	DET
ejpam-3852	457	25	r	r	NOUN
ejpam-3852	457	26	c	c	NOUN
ejpam-3852	457	27	o	o	NOUN
ejpam-3852	457	28	m	m	VERB
ejpam-3852	457	29	p	p	NOUN
ejpam-3852	457	30	l	l	NOUN
ejpam-3852	457	31	e	e	NOUN
ejpam-3852	457	32	x	x	X
ejpam-3852	457	33	it	it	PRON
ejpam-3852	457	34	y	y	NOUN
ejpam-3852	457	35	l	l	NOUN
ejpam-3852	457	36	o	o	NOUN
ejpam-3852	457	37	n	n	CCONJ
ejpam-3852	457	38	g	g	NOUN
ejpam-3852	457	39	e	e	PROPN
ejpam-3852	457	40	s	s	PROPN
ejpam-3852	457	41	t	t	PROPN
ejpam-3852	457	42	r	r	NOUN
ejpam-3852	457	43	u	u	NOUN
ejpam-3852	457	44	n	n	PROPN
ejpam-3852	457	45	s	s	NOUN
ejpam-3852	457	46	o	o	NOUN
ejpam-3852	457	47	f	f	X
ejpam-3852	457	48	o	o	NOUN
ejpam-3852	457	49	n	n	ADP
ejpam-3852	457	50	e	e	NOUN
ejpam-3852	457	51	s	s	PROPN
ejpam-3852	457	52	t	t	PROPN
ejpam-3852	457	53	e	e	NOUN
ejpam-3852	457	54	s	s	PROPN
ejpam-3852	457	55	t	t	PROPN
ejpam-3852	457	56	n	n	NOUN
ejpam-3852	457	57	o	o	NOUN
ejpam-3852	457	58	n	n	CCONJ
ejpam-3852	457	59	o	o	X
ejpam-3852	457	60	v	v	NOUN
ejpam-3852	457	61	e	e	NOUN
ejpam-3852	457	62	r	r	NOUN
ejpam-3852	457	63	l	l	NOUN
ejpam-3852	457	64	a	a	DET
ejpam-3852	457	65	p	p	X
ejpam-3852	457	66	p	p	NOUN
ejpam-3852	457	67	in	in	ADP
ejpam-3852	457	68	g	g	PROPN
ejpam-3852	457	69	t	t	PROPN
ejpam-3852	457	70	e	e	NOUN
ejpam-3852	457	71	m	m	PROPN
ejpam-3852	457	72	p	p	NOUN
ejpam-3852	457	73	l	l	NOUN
ejpam-3852	457	74	a	a	DET
ejpam-3852	457	75	t	t	NOUN
ejpam-3852	457	76	e	e	NOUN
ejpam-3852	457	77	s	s	PROPN
ejpam-3852	457	78	t	t	PROPN
ejpam-3852	457	79	e	e	NOUN
ejpam-3852	457	80	s	s	PROPN
ejpam-3852	457	81	t	t	X
ejpam-3852	457	82	o	o	X
ejpam-3852	457	83	v	v	ADP
ejpam-3852	457	84	e	e	NOUN
ejpam-3852	457	85	r	r	NOUN
ejpam-3852	457	86	l	l	NOUN
ejpam-3852	457	87	a	a	DET
ejpam-3852	457	88	p	p	X
ejpam-3852	457	89	p	p	NOUN
ejpam-3852	457	90	in	in	ADP
ejpam-3852	457	91	g	g	PROPN
ejpam-3852	457	92	t	t	PROPN
ejpam-3852	457	93	e	e	NOUN
ejpam-3852	457	94	m	m	PROPN
ejpam-3852	457	95	p	p	NOUN
ejpam-3852	457	96	l	l	NOUN
ejpam-3852	457	97	a	a	DET
ejpam-3852	457	98	t	t	NOUN
ejpam-3852	457	99	e	e	X
ejpam-3852	457	100	o	o	NOUN
ejpam-3852	457	101	f	f	X
ejpam-3852	457	102	a	a	DET
ejpam-3852	457	103	l	l	NOUN
ejpam-3852	457	104	l	l	NOUN
ejpam-3852	457	105	o	o	NOUN
ejpam-3852	457	106	n	n	ADP
ejpam-3852	457	107	e	e	NOUN
ejpam-3852	457	108	s	s	PROPN
ejpam-3852	457	109	t	t	PROPN
ejpam-3852	457	110	e	e	NOUN
ejpam-3852	457	111	s	s	PROPN
ejpam-3852	457	112	t	t	PROPN
ejpam-3852	457	113	r	r	NOUN
ejpam-3852	457	114	a	a	DET
ejpam-3852	457	115	n	n	NOUN
ejpam-3852	457	116	d	d	X
ejpam-3852	457	117	o	o	NOUN
ejpam-3852	457	118	m	m	VERB
ejpam-3852	457	119	e	e	NOUN
ejpam-3852	457	120	x	x	X
ejpam-3852	457	121	c	c	NOUN
ejpam-3852	457	122	u	u	NOUN
ejpam-3852	457	123	r	r	NOUN
ejpam-3852	457	124	s	s	PROPN
ejpam-3852	457	125	io	io	X
ejpam-3852	457	126	n	n	PROPN
ejpam-3852	457	127	s	s	PROPN
ejpam-3852	457	128	v	v	NOUN
ejpam-3852	457	129	a	a	DET
ejpam-3852	457	130	r	r	NOUN
ejpam-3852	457	131	ia	ia	PROPN
ejpam-3852	457	132	n	n	ADP
ejpam-3852	457	133	t	t	NOUN
ejpam-3852	457	134	t	t	X
ejpam-3852	457	135	e	e	X
ejpam-3852	457	136	s	s	PROPN
ejpam-3852	457	137	t	t	PROPN
ejpam-3852	457	138	r	r	NOUN
ejpam-3852	457	139	a	a	DET
ejpam-3852	457	140	n	n	NOUN
ejpam-3852	457	141	d	d	X
ejpam-3852	457	142	o	o	NOUN
ejpam-3852	457	143	m	m	VERB
ejpam-3852	457	144	e	e	NOUN
ejpam-3852	457	145	x	x	X
ejpam-3852	457	146	c	c	NOUN
ejpam-3852	457	147	u	u	NOUN
ejpam-3852	457	148	r	r	NOUN
ejpam-3852	457	149	s	s	PROPN
ejpam-3852	457	150	io	io	X
ejpam-3852	457	151	n	n	PROPN
ejpam-3852	457	152	s	s	PROPN
ejpam-3852	457	153	t	t	NOUN
ejpam-3852	457	154	e	e	NOUN
ejpam-3852	457	155	s	s	PROPN
ejpam-3852	457	156	t	t	PROPN
ejpam-3852	457	157	r	r	NOUN
ejpam-3852	457	158	a	a	DET
ejpam-3852	457	159	n	n	NOUN
ejpam-3852	457	160	k	k	PROPN
ejpam-3852	457	161	t	t	PROPN
ejpam-3852	457	162	e	e	PROPN
ejpam-3852	457	163	s	s	PROPN
ejpam-3852	457	164	t	t	PROPN
ejpam-3852	457	165	r	r	NOUN
ejpam-3852	457	166	u	u	PROPN
ejpam-3852	457	167	n	n	PROPN
ejpam-3852	457	168	s	s	PROPN
ejpam-3852	457	169	t	t	NOUN
ejpam-3852	457	170	e	e	NOUN
ejpam-3852	457	171	s	s	PROPN
ejpam-3852	457	172	t	t	NOUN
ejpam-3852	457	173	s	s	X
ejpam-3852	457	174	e	e	NOUN
ejpam-3852	457	175	r	r	PROPN
ejpam-3852	457	176	ia	ia	PROPN
ejpam-3852	457	177	l	l	NOUN
ejpam-3852	457	178	t	t	NOUN
ejpam-3852	457	179	e	e	X
ejpam-3852	457	180	s	s	PROPN
ejpam-3852	457	181	t	t	PROPN
ejpam-3852	457	182	u	u	NOUN
ejpam-3852	457	183	n	n	ADP
ejpam-3852	457	184	iv	iv	NOUN
ejpam-3852	457	185	e	e	NOUN
ejpam-3852	457	186	r	r	NOUN
ejpam-3852	457	187	s	s	PROPN
ejpam-3852	457	188	a	a	DET
ejpam-3852	457	189	l	l	NOUN
ejpam-3852	457	190	s	s	ADP
ejpam-3852	457	191	t	t	PROPN
ejpam-3852	457	192	a	a	DET
ejpam-3852	457	193	t	t	PROPN
ejpam-3852	457	194	is	be	AUX
ejpam-3852	457	195	t	t	PROPN
ejpam-3852	457	196	ic	ic	PROPN
ejpam-3852	457	197	a	a	DET
ejpam-3852	457	198	l	l	NOUN
ejpam-3852	457	199	t	t	NOUN
ejpam-3852	457	200	e	e	X
ejpam-3852	457	201	s	s	PROPN
ejpam-3852	457	202	t	t	PROPN
ejpam-3852	457	203	significance	significance	NOUN
ejpam-3852	457	204	level=0.01	level=0.01	VERB
ejpam-3852	457	205	nist	nist	NOUN
ejpam-3852	457	206	random	random	ADJ
ejpam-3852	457	207	number	number	NOUN
ejpam-3852	457	208	test	test	NOUN
ejpam-3852	457	209	suite	suite	NOUN
ejpam-3852	457	210	for	for	ADP
ejpam-3852	457	211	108	108	NUM
ejpam-3852	457	212	digits	digit	NOUN
ejpam-3852	457	213	of	of	ADP
ejpam-3852	457	214	hicg	hicg	ADJ
ejpam-3852	457	215	figure	figure	NOUN
ejpam-3852	457	216	1	1	NUM
ejpam-3852	457	217	:	:	PUNCT
ejpam-3852	457	218	the	the	DET
ejpam-3852	457	219	nist	nist	NOUN
ejpam-3852	457	220	sts	st	NOUN
ejpam-3852	457	221	applied	apply	VERB
ejpam-3852	457	222	to	to	ADP
ejpam-3852	457	223	hicg	hicg	ADJ
ejpam-3852	457	224	parameters	parameter	NOUN
ejpam-3852	457	225	and	and	CCONJ
ejpam-3852	457	226	109	109	NUM
ejpam-3852	457	227	prns	prn	NOUN
ejpam-3852	457	228	we	we	PRON
ejpam-3852	457	229	ran	run	VERB
ejpam-3852	457	230	the	the	DET
ejpam-3852	457	231	dieharder	dieharder	NOUN
ejpam-3852	457	232	test	test	NOUN
ejpam-3852	457	233	which	which	PRON
ejpam-3852	457	234	also	also	ADV
ejpam-3852	457	235	showed	show	VERB
ejpam-3852	457	236	promising	promising	ADJ
ejpam-3852	457	237	results	result	NOUN
ejpam-3852	457	238	which	which	PRON
ejpam-3852	457	239	are	be	AUX
ejpam-3852	457	240	being	be	AUX
ejpam-3852	457	241	visually	visually	ADV
ejpam-3852	457	242	displayed	display	VERB
ejpam-3852	457	243	in	in	ADP
ejpam-3852	457	244	figure	figure	NOUN
ejpam-3852	457	245	2	2	NUM
ejpam-3852	457	246	(	(	PUNCT
ejpam-3852	457	247	here	here	ADV
ejpam-3852	457	248	the	the	DET
ejpam-3852	457	249	109	109	NUM
ejpam-3852	457	250	bits	bit	NOUN
ejpam-3852	457	251	are	be	AUX
ejpam-3852	457	252	partitioned	partition	VERB
ejpam-3852	457	253	into	into	ADP
ejpam-3852	457	254	31249999	31249999	NUM
ejpam-3852	457	255	32	32	NUM
ejpam-3852	457	256	-	-	PUNCT
ejpam-3852	457	257	bit	bit	NOUN
ejpam-3852	457	258	numbers	number	NOUN
ejpam-3852	457	259	which	which	PRON
ejpam-3852	457	260	are	be	AUX
ejpam-3852	457	261	further	far	ADV
ejpam-3852	457	262	converted	convert	VERB
ejpam-3852	457	263	to	to	ADP
ejpam-3852	457	264	decimal	decimal	ADJ
ejpam-3852	457	265	numbers	number	NOUN
ejpam-3852	457	266	and	and	CCONJ
ejpam-3852	457	267	then	then	ADV
ejpam-3852	457	268	the	the	DET
ejpam-3852	457	269	dieharder	dieharder	NOUN
ejpam-3852	457	270	test	test	NOUN
ejpam-3852	457	271	is	be	AUX
ejpam-3852	457	272	run	run	VERB
ejpam-3852	457	273	)	)	PUNCT
ejpam-3852	457	274	.	.	PUNCT
ejpam-3852	458	1	we	we	PRON
ejpam-3852	458	2	further	far	ADV
ejpam-3852	458	3	computed	compute	VERB
ejpam-3852	458	4	the	the	DET
ejpam-3852	458	5	linear	linear	ADJ
ejpam-3852	458	6	complexity	complexity	NOUN
ejpam-3852	458	7	profile	profile	NOUN
ejpam-3852	458	8	of	of	ADP
ejpam-3852	458	9	such	such	DET
ejpam-3852	458	10	a	a	DET
ejpam-3852	458	11	binary	binary	ADJ
ejpam-3852	458	12	sequence	sequence	NOUN
ejpam-3852	458	13	for	for	ADP
ejpam-3852	458	14	105	105	NUM
ejpam-3852	458	15	bits	bit	NOUN
ejpam-3852	458	16	and	and	CCONJ
ejpam-3852	458	17	found	find	VERB
ejpam-3852	458	18	an	an	DET
ejpam-3852	458	19	excellent	excellent	ADJ
ejpam-3852	458	20	profile	profile	NOUN
ejpam-3852	458	21	.	.	PUNCT
ejpam-3852	459	1	we	we	PRON
ejpam-3852	459	2	display	display	VERB
ejpam-3852	459	3	such	such	DET
ejpam-3852	459	4	an	an	DET
ejpam-3852	459	5	experiment	experiment	NOUN
ejpam-3852	459	6	in	in	ADP
ejpam-3852	459	7	figure	figure	NOUN
ejpam-3852	459	8	3	3	NUM
ejpam-3852	459	9	.	.	PUNCT
ejpam-3852	460	1	while	while	SCONJ
ejpam-3852	460	2	these	these	DET
ejpam-3852	460	3	observations	observation	NOUN
ejpam-3852	460	4	were	be	AUX
ejpam-3852	460	5	not	not	PART
ejpam-3852	460	6	initially	initially	ADV
ejpam-3852	460	7	the	the	DET
ejpam-3852	460	8	purpose	purpose	NOUN
ejpam-3852	460	9	of	of	ADP
ejpam-3852	460	10	the	the	DET
ejpam-3852	460	11	paper	paper	NOUN
ejpam-3852	460	12	,	,	PUNCT
ejpam-3852	460	13	we	we	PRON
ejpam-3852	460	14	just	just	ADV
ejpam-3852	460	15	want	want	VERB
ejpam-3852	460	16	to	to	PART
ejpam-3852	460	17	point	point	VERB
ejpam-3852	460	18	them	they	PRON
ejpam-3852	460	19	out	out	ADP
ejpam-3852	460	20	as	as	ADP
ejpam-3852	460	21	by	by	ADP
ejpam-3852	460	22	-	-	PUNCT
ejpam-3852	460	23	products	product	NOUN
ejpam-3852	460	24	.	.	PUNCT
ejpam-3852	461	1	further	further	ADJ
ejpam-3852	461	2	investigation	investigation	NOUN
ejpam-3852	461	3	is	be	AUX
ejpam-3852	461	4	warranted	warrant	VERB
ejpam-3852	461	5	.	.	PUNCT
ejpam-3852	462	1	there	there	PRON
ejpam-3852	462	2	are	be	VERB
ejpam-3852	462	3	several	several	ADJ
ejpam-3852	462	4	works	work	NOUN
ejpam-3852	462	5	(	(	PUNCT
ejpam-3852	462	6	see	see	VERB
ejpam-3852	462	7	[	[	X
ejpam-3852	462	8	20	20	NUM
ejpam-3852	462	9	]	]	PUNCT
ejpam-3852	462	10	and	and	CCONJ
ejpam-3852	462	11	the	the	DET
ejpam-3852	462	12	references	reference	NOUN
ejpam-3852	462	13	therein	therein	ADV
ejpam-3852	462	14	)	)	PUNCT
ejpam-3852	462	15	devoted	devote	VERB
ejpam-3852	462	16	to	to	ADP
ejpam-3852	462	17	the	the	DET
ejpam-3852	462	18	computation	computation	NOUN
ejpam-3852	462	19	of	of	ADP
ejpam-3852	462	20	the	the	DET
ejpam-3852	462	21	discrepancy	discrepancy	NOUN
ejpam-3852	462	22	of	of	ADP
ejpam-3852	462	23	the	the	DET
ejpam-3852	462	24	inversive	inversive	ADJ
ejpam-3852	462	25	congruential	congruential	ADJ
ejpam-3852	462	26	generator	generator	NOUN
ejpam-3852	462	27	.	.	PUNCT
ejpam-3852	463	1	certainly	certainly	ADV
ejpam-3852	463	2	,	,	PUNCT
ejpam-3852	463	3	a	a	DET
ejpam-3852	463	4	similar	similar	ADJ
ejpam-3852	463	5	inquiry	inquiry	NOUN
ejpam-3852	463	6	can	can	AUX
ejpam-3852	463	7	be	be	AUX
ejpam-3852	463	8	addressed	address	VERB
ejpam-3852	463	9	for	for	ADP
ejpam-3852	463	10	our	our	PRON
ejpam-3852	463	11	generator	generator	NOUN
ejpam-3852	463	12	,	,	PUNCT
ejpam-3852	463	13	and	and	CCONJ
ejpam-3852	463	14	we	we	PRON
ejpam-3852	463	15	leave	leave	VERB
ejpam-3852	463	16	the	the	DET
ejpam-3852	463	17	computation	computation	NOUN
ejpam-3852	463	18	of	of	ADP
ejpam-3852	463	19	the	the	DET
ejpam-3852	463	20	discrepancy	discrepancy	NOUN
ejpam-3852	463	21	(	(	PUNCT
ejpam-3852	463	22	and	and	CCONJ
ejpam-3852	463	23	its	its	PRON
ejpam-3852	463	24	bounds	bound	NOUN
ejpam-3852	463	25	)	)	PUNCT
ejpam-3852	463	26	for	for	ADP
ejpam-3852	463	27	our	our	PRON
ejpam-3852	463	28	hicg	hicg	NOUN
ejpam-3852	463	29	for	for	ADP
ejpam-3852	463	30	a	a	DET
ejpam-3852	463	31	subsequent	subsequent	ADJ
ejpam-3852	463	32	project	project	NOUN
ejpam-3852	463	33	,	,	PUNCT
ejpam-3852	463	34	or	or	CCONJ
ejpam-3852	463	35	to	to	ADP
ejpam-3852	463	36	the	the	DET
ejpam-3852	463	37	interested	interested	ADJ
ejpam-3852	463	38	reader	reader	NOUN
ejpam-3852	463	39	.	.	PUNCT
ejpam-3852	464	1	references	reference	NOUN
ejpam-3852	464	2	15	15	NUM
ejpam-3852	464	3	random	random	ADJ
ejpam-3852	464	4	number	number	NOUN
ejpam-3852	464	5	test	test	NOUN
ejpam-3852	464	6	0.0	0.0	NUM
ejpam-3852	464	7	0.2	0.2	NUM
ejpam-3852	464	8	0.4	0.4	NUM
ejpam-3852	464	9	0.6	0.6	NUM
ejpam-3852	464	10	0.8	0.8	NUM
ejpam-3852	464	11	1.0	1.0	NUM
ejpam-3852	464	12	p	p	NOUN
ejpam-3852	464	13	-v	-v	PUNCT
ejpam-3852	464	14	a	a	DET
ejpam-3852	464	15	lu	lu	NOUN
ejpam-3852	464	16	e	e	NOUN
ejpam-3852	464	17	b	b	X
ejpam-3852	464	18	ir	ir	X
ejpam-3852	464	19	th	th	X
ejpam-3852	464	20	d	d	X
ejpam-3852	464	21	a	a	DET
ejpam-3852	464	22	y	y	PROPN
ejpam-3852	464	23	s	s	PROPN
ejpam-3852	464	24	t	t	NOUN
ejpam-3852	464	25	e	e	NOUN
ejpam-3852	464	26	s	s	PROPN
ejpam-3852	464	27	t	t	X
ejpam-3852	464	28	o	o	X
ejpam-3852	464	29	v	v	INTJ
ejpam-3852	464	30	e	e	X
ejpam-3852	464	31	rl	rl	ADP
ejpam-3852	464	32	a	a	DET
ejpam-3852	464	33	p	p	X
ejpam-3852	464	34	p	p	NOUN
ejpam-3852	464	35	in	in	ADP
ejpam-3852	464	36	g	g	PROPN
ejpam-3852	464	37	5	5	NUM
ejpam-3852	464	38	p	p	NOUN
ejpam-3852	464	39	e	e	PROPN
ejpam-3852	464	40	rm	rm	NOUN
ejpam-3852	464	41	u	u	NOUN
ejpam-3852	464	42	ta	ta	X
ejpam-3852	464	43	ti	ti	X
ejpam-3852	464	44	o	o	PROPN
ejpam-3852	464	45	n	n	PROPN
ejpam-3852	464	46	s	s	PROPN
ejpam-3852	464	47	t	t	NOUN
ejpam-3852	464	48	e	e	NOUN
ejpam-3852	464	49	s	s	PROPN
ejpam-3852	464	50	t	t	PROPN
ejpam-3852	464	51	3	3	NUM
ejpam-3852	464	52	2	2	NUM
ejpam-3852	464	53	x	x	SYM
ejpam-3852	464	54	3	3	NUM
ejpam-3852	464	55	2	2	NUM
ejpam-3852	464	56	b	b	NOUN
ejpam-3852	464	57	in	in	ADP
ejpam-3852	464	58	a	a	DET
ejpam-3852	464	59	ry	ry	NOUN
ejpam-3852	464	60	r	r	NOUN
ejpam-3852	464	61	a	a	PRON
ejpam-3852	464	62	n	n	NOUN
ejpam-3852	464	63	k	k	PROPN
ejpam-3852	464	64	t	t	PROPN
ejpam-3852	464	65	e	e	PROPN
ejpam-3852	464	66	s	s	PROPN
ejpam-3852	464	67	t	t	PROPN
ejpam-3852	464	68	b	b	PROPN
ejpam-3852	465	1	it	it	PRON
ejpam-3852	465	2	s	s	VERB
ejpam-3852	465	3	tr	tr	VERB
ejpam-3852	465	4	e	e	PROPN
ejpam-3852	465	5	a	a	DET
ejpam-3852	465	6	m	m	NOUN
ejpam-3852	465	7	t	t	NOUN
ejpam-3852	465	8	e	e	NOUN
ejpam-3852	465	9	s	s	PROPN
ejpam-3852	465	10	t	t	X
ejpam-3852	465	11	o	o	X
ejpam-3852	465	12	v	v	INTJ
ejpam-3852	465	13	e	e	X
ejpam-3852	465	14	rl	rl	ADP
ejpam-3852	465	15	a	a	DET
ejpam-3852	465	16	p	p	X
ejpam-3852	465	17	p	p	NOUN
ejpam-3852	465	18	in	in	ADP
ejpam-3852	465	19	g	g	PROPN
ejpam-3852	465	20	p	p	PROPN
ejpam-3852	465	21	a	a	DET
ejpam-3852	465	22	ir	ir	PROPN
ejpam-3852	465	23	s	s	PROPN
ejpam-3852	465	24	t	t	NOUN
ejpam-3852	465	25	e	e	NOUN
ejpam-3852	465	26	s	s	PROPN
ejpam-3852	465	27	t	t	X
ejpam-3852	465	28	o	o	X
ejpam-3852	465	29	v	v	INTJ
ejpam-3852	465	30	e	e	X
ejpam-3852	465	31	rl	rl	ADP
ejpam-3852	465	32	a	a	DET
ejpam-3852	465	33	p	p	X
ejpam-3852	465	34	p	p	NOUN
ejpam-3852	465	35	in	in	ADP
ejpam-3852	465	36	g	g	PROPN
ejpam-3852	465	37	q	q	PROPN
ejpam-3852	465	38	u	u	PROPN
ejpam-3852	465	39	a	a	PROPN
ejpam-3852	465	40	d	d	X
ejpam-3852	465	41	ru	ru	PROPN
ejpam-3852	465	42	p	p	PROPN
ejpam-3852	465	43	le	le	PROPN
ejpam-3852	465	44	s	s	PROPN
ejpam-3852	465	45	t	t	PROPN
ejpam-3852	465	46	e	e	NOUN
ejpam-3852	465	47	s	s	PROPN
ejpam-3852	465	48	t	t	PROPN
ejpam-3852	465	49	d	d	PROPN
ejpam-3852	465	50	n	n	PROPN
ejpam-3852	465	51	a	a	DET
ejpam-3852	465	52	t	t	NOUN
ejpam-3852	465	53	e	e	X
ejpam-3852	465	54	s	s	PROPN
ejpam-3852	465	55	t	t	NOUN
ejpam-3852	465	56	c	c	NOUN
ejpam-3852	465	57	o	o	X
ejpam-3852	465	58	u	u	NOUN
ejpam-3852	465	59	n	n	ADP
ejpam-3852	465	60	t	t	NOUN
ejpam-3852	465	61	th	th	X
ejpam-3852	465	62	e	e	PROPN
ejpam-3852	465	63	1	1	NUM
ejpam-3852	465	64	's	's	PART
ejpam-3852	465	65	(	(	PUNCT
ejpam-3852	465	66	s	s	X
ejpam-3852	465	67	tr	tr	VERB
ejpam-3852	465	68	e	e	PROPN
ejpam-3852	465	69	a	a	DET
ejpam-3852	465	70	m	m	NOUN
ejpam-3852	465	71	)	)	PUNCT
ejpam-3852	465	72	t	t	PROPN
ejpam-3852	465	73	e	e	NOUN
ejpam-3852	465	74	s	s	PROPN
ejpam-3852	465	75	t	t	NOUN
ejpam-3852	465	76	c	c	NOUN
ejpam-3852	465	77	o	o	X
ejpam-3852	465	78	u	u	NOUN
ejpam-3852	465	79	n	n	ADP
ejpam-3852	465	80	t	t	NOUN
ejpam-3852	465	81	th	th	X
ejpam-3852	465	82	e	e	PROPN
ejpam-3852	465	83	1	1	NUM
ejpam-3852	465	84	's	's	PART
ejpam-3852	465	85	(	(	PUNCT
ejpam-3852	465	86	b	b	NOUN
ejpam-3852	465	87	y	y	PROPN
ejpam-3852	465	88	te	te	PROPN
ejpam-3852	465	89	)	)	PUNCT
ejpam-3852	465	90	t	t	PROPN
ejpam-3852	465	91	e	e	NOUN
ejpam-3852	465	92	s	s	PROPN
ejpam-3852	465	93	t	t	PROPN
ejpam-3852	465	94	p	p	NOUN
ejpam-3852	465	95	a	a	DET
ejpam-3852	465	96	rk	rk	NOUN
ejpam-3852	465	97	in	in	ADP
ejpam-3852	465	98	g	g	PROPN
ejpam-3852	465	99	l	l	NOUN
ejpam-3852	465	100	o	o	NOUN
ejpam-3852	466	1	t	t	NOUN
ejpam-3852	466	2	t	t	X
ejpam-3852	466	3	e	e	X
ejpam-3852	466	4	s	s	PROPN
ejpam-3852	466	5	t	t	PROPN
ejpam-3852	466	6	2	2	NUM
ejpam-3852	467	1	d	d	NOUN
ejpam-3852	467	2	c	c	X
ejpam-3852	467	3	ir	ir	PROPN
ejpam-3852	467	4	c	c	X
ejpam-3852	467	5	le	le	X
ejpam-3852	467	6	(	(	PUNCT
ejpam-3852	467	7	m	m	VERB
ejpam-3852	467	8	in	in	ADP
ejpam-3852	467	9	i	i	PRON
ejpam-3852	467	10	m	m	VERB
ejpam-3852	467	11	u	u	NOUN
ejpam-3852	467	12	m	m	PROPN
ejpam-3852	467	13	d	d	NOUN
ejpam-3852	467	14	is	be	AUX
ejpam-3852	467	15	ta	ta	ADP
ejpam-3852	467	16	n	n	ADV
ejpam-3852	467	17	c	c	NOUN
ejpam-3852	467	18	e	e	X
ejpam-3852	467	19	)	)	PUNCT
ejpam-3852	467	20	t	t	PROPN
ejpam-3852	467	21	e	e	NOUN
ejpam-3852	467	22	s	s	PROPN
ejpam-3852	467	23	t	t	PROPN
ejpam-3852	467	24	3	3	NUM
ejpam-3852	467	25	d	d	PROPN
ejpam-3852	467	26	s	s	X
ejpam-3852	467	27	p	p	NOUN
ejpam-3852	467	28	h	h	NOUN
ejpam-3852	467	29	e	e	X
ejpam-3852	467	30	re	re	X
ejpam-3852	467	31	(	(	PUNCT
ejpam-3852	467	32	m	m	VERB
ejpam-3852	467	33	in	in	ADP
ejpam-3852	467	34	i	i	PRON
ejpam-3852	467	35	m	m	VERB
ejpam-3852	467	36	u	u	NOUN
ejpam-3852	467	37	m	m	PROPN
ejpam-3852	467	38	d	d	NOUN
ejpam-3852	467	39	is	be	AUX
ejpam-3852	467	40	ta	ta	ADP
ejpam-3852	467	41	n	n	ADV
ejpam-3852	467	42	c	c	NOUN
ejpam-3852	467	43	e	e	X
ejpam-3852	467	44	)	)	PUNCT
ejpam-3852	467	45	t	t	PROPN
ejpam-3852	467	46	e	e	NOUN
ejpam-3852	467	47	s	s	PROPN
ejpam-3852	467	48	t	t	PROPN
ejpam-3852	467	49	s	s	PART
ejpam-3852	467	50	q	q	X
ejpam-3852	467	51	u	u	X
ejpam-3852	467	52	e	e	X
ejpam-3852	467	53	e	e	X
ejpam-3852	467	54	z	z	NOUN
ejpam-3852	467	55	e	e	PROPN
ejpam-3852	467	56	t	t	PROPN
ejpam-3852	467	57	e	e	PROPN
ejpam-3852	467	58	s	s	PROPN
ejpam-3852	467	59	t	t	PROPN
ejpam-3852	467	60	s	s	X
ejpam-3852	467	61	u	u	NOUN
ejpam-3852	467	62	m	m	PROPN
ejpam-3852	467	63	s	s	PROPN
ejpam-3852	467	64	t	t	NOUN
ejpam-3852	467	65	e	e	NOUN
ejpam-3852	467	66	s	s	PROPN
ejpam-3852	467	67	t	t	PROPN
ejpam-3852	467	68	r	r	NOUN
ejpam-3852	467	69	u	u	PROPN
ejpam-3852	467	70	n	n	PROPN
ejpam-3852	467	71	s	s	PROPN
ejpam-3852	467	72	t	t	NOUN
ejpam-3852	467	73	e	e	PROPN
ejpam-3852	467	74	s	s	PROPN
ejpam-3852	467	75	t	t	PROPN
ejpam-3852	467	76	significance	significance	NOUN
ejpam-3852	467	77	level=0.01	level=0.01	NOUN
ejpam-3852	467	78	dieharder	dieharder	VERB
ejpam-3852	467	79	random	random	ADJ
ejpam-3852	467	80	number	number	NOUN
ejpam-3852	467	81	test	test	NOUN
ejpam-3852	467	82	suite	suite	NOUN
ejpam-3852	467	83	for	for	ADP
ejpam-3852	467	84	109	109	NUM
ejpam-3852	467	85	bits	bit	NOUN
ejpam-3852	467	86	of	of	ADP
ejpam-3852	467	87	hicg	hicg	ADJ
ejpam-3852	467	88	figure	figure	NOUN
ejpam-3852	467	89	2	2	NUM
ejpam-3852	467	90	:	:	PUNCT
ejpam-3852	467	91	the	the	DET
ejpam-3852	467	92	dieharder	dieharder	NOUN
ejpam-3852	467	93	test	test	NOUN
ejpam-3852	467	94	applied	apply	VERB
ejpam-3852	467	95	to	to	ADP
ejpam-3852	467	96	hicg	hicg	VERB
ejpam-3852	467	97	0	0	NUM
ejpam-3852	467	98	20000	20000	NUM
ejpam-3852	467	99	40000	40000	NUM
ejpam-3852	467	100	60000	60000	NUM
ejpam-3852	467	101	80000	80000	NUM
ejpam-3852	467	102	100000	100000	NUM
ejpam-3852	467	103	bits	bit	NOUN
ejpam-3852	467	104	0	0	NUM
ejpam-3852	467	105	10000	10000	NUM
ejpam-3852	467	106	20000	20000	NUM
ejpam-3852	467	107	30000	30000	NUM
ejpam-3852	467	108	40000	40000	NUM
ejpam-3852	467	109	50000	50000	NUM
ejpam-3852	467	110	l	l	NOUN
ejpam-3852	467	111	in	in	ADP
ejpam-3852	467	112	e	e	PROPN
ejpam-3852	467	113	a	a	DET
ejpam-3852	467	114	r	r	NOUN
ejpam-3852	467	115	c	c	NOUN
ejpam-3852	467	116	o	o	NOUN
ejpam-3852	467	117	m	m	VERB
ejpam-3852	467	118	p	p	X
ejpam-3852	467	119	le	le	X
ejpam-3852	467	120	x	x	X
ejpam-3852	468	1	it	it	PRON
ejpam-3852	468	2	y	y	PRON
ejpam-3852	468	3	figure	figure	VERB
ejpam-3852	468	4	3	3	NUM
ejpam-3852	468	5	:	:	PUNCT
ejpam-3852	468	6	the	the	DET
ejpam-3852	468	7	linear	linear	ADJ
ejpam-3852	468	8	complexity	complexity	NOUN
ejpam-3852	468	9	profile	profile	NOUN
ejpam-3852	468	10	of	of	ADP
ejpam-3852	468	11	hicg	hicg	NOUN
ejpam-3852	468	12	in	in	ADP
ejpam-3852	468	13	the	the	DET
ejpam-3852	468	14	spirit	spirit	NOUN
ejpam-3852	468	15	of	of	ADP
ejpam-3852	468	16	our	our	PRON
ejpam-3852	468	17	paper	paper	NOUN
ejpam-3852	468	18	,	,	PUNCT
ejpam-3852	468	19	for	for	ADP
ejpam-3852	468	20	a	a	DET
ejpam-3852	468	21	modulus	modulus	ADJ
ejpam-3852	468	22	m	m	NOUN
ejpam-3852	468	23	=	=	SYM
ejpam-3852	468	24	2ω	2ω	NUM
ejpam-3852	468	25	and	and	CCONJ
ejpam-3852	468	26	y0	y0	NOUN
ejpam-3852	468	27	,	,	PUNCT
ejpam-3852	468	28	y1	y1	PROPN
ejpam-3852	468	29	∈	∈	PROPN
ejpam-3852	468	30	gm	gm	PROPN
ejpam-3852	468	31	,	,	PUNCT
ejpam-3852	468	32	one	one	PRON
ejpam-3852	468	33	can	can	AUX
ejpam-3852	468	34	define	define	VERB
ejpam-3852	468	35	yn+2	yn+2	NUM
ejpam-3852	468	36	≡	≡	PROPN
ejpam-3852	468	37	ay−1n+1	ay−1n+1	PROPN
ejpam-3852	469	1	+	+	CCONJ
ejpam-3852	470	1	by−1n	by−1n	PROPN
ejpam-3852	470	2	+	+	CCONJ
ejpam-3852	470	3	cyn+1	cyn+1	PROPN
ejpam-3852	470	4	+	+	CCONJ
ejpam-3852	470	5	dyn	dyn	NOUN
ejpam-3852	470	6	+	+	CCONJ
ejpam-3852	470	7	e	e	X
ejpam-3852	470	8	(	(	PUNCT
ejpam-3852	470	9	mod	mod	PROPN
ejpam-3852	470	10	m	m	PROPN
ejpam-3852	470	11	)	)	PUNCT
ejpam-3852	470	12	,	,	PUNCT
ejpam-3852	470	13	n	n	PROPN
ejpam-3852	470	14	=	=	SYM
ejpam-3852	470	15	0	0	NUM
ejpam-3852	470	16	,	,	PUNCT
ejpam-3852	470	17	1	1	NUM
ejpam-3852	470	18	,	,	PUNCT
ejpam-3852	470	19	.	.	PUNCT
ejpam-3852	470	20	.	.	PUNCT
ejpam-3852	471	1	.	.	PUNCT
ejpam-3852	472	1	,	,	PUNCT
ejpam-3852	472	2	(	(	PUNCT
ejpam-3852	472	3	9	9	X
ejpam-3852	472	4	)	)	PUNCT
ejpam-3852	472	5	where	where	SCONJ
ejpam-3852	472	6	a	a	DET
ejpam-3852	472	7	,	,	PUNCT
ejpam-3852	472	8	b	b	NOUN
ejpam-3852	472	9	,	,	PUNCT
ejpam-3852	472	10	c	c	NOUN
ejpam-3852	472	11	,	,	PUNCT
ejpam-3852	472	12	d	d	NOUN
ejpam-3852	472	13	,	,	PUNCT
ejpam-3852	472	14	e	e	PROPN
ejpam-3852	472	15	∈	∈	PROPN
ejpam-3852	472	16	zm	zm	PROPN
ejpam-3852	472	17	are	be	AUX
ejpam-3852	472	18	such	such	ADJ
ejpam-3852	472	19	that	that	SCONJ
ejpam-3852	472	20	yn+2	yn+2	NUM
ejpam-3852	472	21	∈	∈	PROPN
ejpam-3852	472	22	gm	gm	PROPN
ejpam-3852	472	23	,	,	PUNCT
ejpam-3852	472	24	whenever	whenever	SCONJ
ejpam-3852	472	25	yn	yn	X
ejpam-3852	472	26	,	,	PUNCT
ejpam-3852	472	27	yn+1	yn+1	PROPN
ejpam-3852	472	28	∈	∈	PROPN
ejpam-3852	472	29	gm	gm	PROPN
ejpam-3852	472	30	.	.	PUNCT
ejpam-3852	473	1	the	the	DET
ejpam-3852	473	2	study	study	NOUN
ejpam-3852	473	3	of	of	ADP
ejpam-3852	473	4	such	such	DET
ejpam-3852	473	5	a	a	DET
ejpam-3852	473	6	generator	generator	NOUN
ejpam-3852	473	7	(	(	PUNCT
ejpam-3852	473	8	which	which	PRON
ejpam-3852	473	9	includes	include	VERB
ejpam-3852	473	10	as	as	ADP
ejpam-3852	473	11	particular	particular	ADJ
ejpam-3852	473	12	cases	case	NOUN
ejpam-3852	473	13	every	every	DET
ejpam-3852	473	14	other	other	ADJ
ejpam-3852	473	15	type	type	NOUN
ejpam-3852	473	16	of	of	ADP
ejpam-3852	473	17	first	first	ADJ
ejpam-3852	473	18	-	-	PUNCT
ejpam-3852	473	19	order	order	NOUN
ejpam-3852	473	20	linear	linear	ADJ
ejpam-3852	473	21	and	and	CCONJ
ejpam-3852	473	22	inversive	inversive	ADJ
ejpam-3852	473	23	congruential	congruential	ADJ
ejpam-3852	473	24	generator	generator	NOUN
ejpam-3852	473	25	)	)	PUNCT
ejpam-3852	473	26	is	be	AUX
ejpam-3852	473	27	certainly	certainly	ADV
ejpam-3852	473	28	an	an	DET
ejpam-3852	473	29	intriguing	intriguing	ADJ
ejpam-3852	473	30	problem	problem	NOUN
ejpam-3852	473	31	.	.	PUNCT
ejpam-3852	474	1	finally	finally	ADV
ejpam-3852	474	2	,	,	PUNCT
ejpam-3852	474	3	all	all	PRON
ejpam-3852	474	4	of	of	ADP
ejpam-3852	474	5	our	our	PRON
ejpam-3852	474	6	considerations	consideration	NOUN
ejpam-3852	474	7	,	,	PUNCT
ejpam-3852	474	8	results	result	NOUN
ejpam-3852	474	9	and	and	CCONJ
ejpam-3852	474	10	inquiries	inquiry	NOUN
ejpam-3852	474	11	can	can	AUX
ejpam-3852	474	12	be	be	AUX
ejpam-3852	474	13	investigated	investigate	VERB
ejpam-3852	474	14	for	for	ADP
ejpam-3852	474	15	an	an	DET
ejpam-3852	474	16	odd	odd	ADJ
ejpam-3852	474	17	characteristic	characteristic	NOUN
ejpam-3852	474	18	.	.	PUNCT
ejpam-3852	475	1	references	reference	NOUN
ejpam-3852	475	2	[	[	X
ejpam-3852	475	3	1	1	NUM
ejpam-3852	475	4	]	]	PUNCT
ejpam-3852	475	5	manuel	manuel	PROPN
ejpam-3852	475	6	blum	blum	PROPN
ejpam-3852	475	7	and	and	CCONJ
ejpam-3852	475	8	silvio	silvio	PROPN
ejpam-3852	475	9	micali	micali	PROPN
ejpam-3852	475	10	.	.	PUNCT
ejpam-3852	476	1	how	how	SCONJ
ejpam-3852	476	2	to	to	PART
ejpam-3852	476	3	generate	generate	VERB
ejpam-3852	476	4	cryptographically	cryptographically	ADV
ejpam-3852	476	5	strong	strong	ADJ
ejpam-3852	476	6	sequences	sequence	NOUN
ejpam-3852	476	7	of	of	ADP
ejpam-3852	476	8	pseudorandom	pseudorandom	PROPN
ejpam-3852	476	9	bits	bit	NOUN
ejpam-3852	476	10	.	.	PUNCT
ejpam-3852	477	1	siam	siam	PROPN
ejpam-3852	477	2	j.	j.	PROPN
ejpam-3852	477	3	comput	comput	PROPN
ejpam-3852	477	4	.	.	PUNCT
ejpam-3852	477	5	,	,	PUNCT
ejpam-3852	477	6	13(4):850–864	13(4):850–864	PROPN
ejpam-3852	477	7	,	,	PUNCT
ejpam-3852	477	8	1984	1984	NUM
ejpam-3852	477	9	.	.	PUNCT
ejpam-3852	478	1	[	[	X
ejpam-3852	478	2	2	2	NUM
ejpam-3852	478	3	]	]	PUNCT
ejpam-3852	478	4	gerhard	gerhard	PROPN
ejpam-3852	478	5	dorfer	dorfer	NOUN
ejpam-3852	478	6	and	and	CCONJ
ejpam-3852	478	7	arne	arne	VERB
ejpam-3852	478	8	winterhof	winterhof	NOUN
ejpam-3852	478	9	.	.	PUNCT
ejpam-3852	479	1	lattice	lattice	NOUN
ejpam-3852	479	2	structure	structure	NOUN
ejpam-3852	479	3	and	and	CCONJ
ejpam-3852	479	4	linear	linear	PROPN
ejpam-3852	479	5	complexity	complexity	NOUN
ejpam-3852	479	6	profile	profile	NOUN
ejpam-3852	479	7	of	of	ADP
ejpam-3852	479	8	references	reference	NOUN
ejpam-3852	479	9	16	16	NUM
ejpam-3852	479	10	nonlinear	nonlinear	ADJ
ejpam-3852	479	11	pseudorandom	pseudorandom	NOUN
ejpam-3852	479	12	number	number	NOUN
ejpam-3852	479	13	generators	generator	NOUN
ejpam-3852	479	14	.	.	PUNCT
ejpam-3852	480	1	appl	appl	PROPN
ejpam-3852	480	2	.	.	PUNCT
ejpam-3852	481	1	algebra	algebra	PROPN
ejpam-3852	481	2	engrg	engrg	PROPN
ejpam-3852	481	3	.	.	PROPN
ejpam-3852	481	4	comm	comm	NOUN
ejpam-3852	481	5	.	.	PUNCT
ejpam-3852	482	1	comput	comput	NOUN
ejpam-3852	482	2	.	.	PUNCT
ejpam-3852	482	3	,	,	PUNCT
ejpam-3852	482	4	13(6):499–508	13(6):499–508	NUM
ejpam-3852	482	5	,	,	PUNCT
ejpam-3852	482	6	2003	2003	NUM
ejpam-3852	482	7	.	.	PUNCT
ejpam-3852	483	1	[	[	X
ejpam-3852	483	2	3	3	X
ejpam-3852	483	3	]	]	X
ejpam-3852	483	4	jürgen	jürgen	PROPN
ejpam-3852	483	5	eichenauer	eichenauer	PROPN
ejpam-3852	483	6	,	,	PUNCT
ejpam-3852	483	7	jürgen	jürgen	PROPN
ejpam-3852	483	8	lehn	lehn	NOUN
ejpam-3852	483	9	,	,	PUNCT
ejpam-3852	483	10	and	and	CCONJ
ejpam-3852	483	11	alev	alev	ADJ
ejpam-3852	483	12	topuzoğlu	topuzoğlu	NOUN
ejpam-3852	483	13	.	.	PUNCT
ejpam-3852	484	1	a	a	DET
ejpam-3852	484	2	nonlinear	nonlinear	ADJ
ejpam-3852	484	3	congruential	congruential	ADJ
ejpam-3852	484	4	pseudorandom	pseudorandom	NOUN
ejpam-3852	484	5	number	number	NOUN
ejpam-3852	484	6	generator	generator	NOUN
ejpam-3852	484	7	with	with	ADP
ejpam-3852	484	8	power	power	NOUN
ejpam-3852	484	9	of	of	ADP
ejpam-3852	484	10	two	two	NUM
ejpam-3852	484	11	modulus	modulus	NOUN
ejpam-3852	484	12	.	.	PUNCT
ejpam-3852	484	13	math	math	NOUN
ejpam-3852	484	14	.	.	PUNCT
ejpam-3852	485	1	comp	comp	PROPN
ejpam-3852	485	2	.	.	PUNCT
ejpam-3852	485	3	,	,	PUNCT
ejpam-3852	485	4	51(184):757	51(184):757	NUM
ejpam-3852	485	5	–	–	PUNCT
ejpam-3852	485	6	759	759	NUM
ejpam-3852	485	7	,	,	PUNCT
ejpam-3852	485	8	1988	1988	NUM
ejpam-3852	485	9	.	.	PUNCT
ejpam-3852	486	1	[	[	X
ejpam-3852	486	2	4	4	X
ejpam-3852	486	3	]	]	PUNCT
ejpam-3852	486	4	j.	j.	PROPN
ejpam-3852	486	5	eichenauer	eichenauer	PROPN
ejpam-3852	486	6	-	-	PUNCT
ejpam-3852	486	7	herrmann	herrmann	PROPN
ejpam-3852	486	8	,	,	PUNCT
ejpam-3852	486	9	h.	h.	PROPN
ejpam-3852	486	10	grothe	grothe	PROPN
ejpam-3852	486	11	,	,	PUNCT
ejpam-3852	486	12	h.	h.	PROPN
ejpam-3852	486	13	niederreiter	niederreiter	PROPN
ejpam-3852	486	14	,	,	PUNCT
ejpam-3852	486	15	and	and	CCONJ
ejpam-3852	486	16	a.	a.	NOUN
ejpam-3852	486	17	topuzoğlu	topuzoğlu	PROPN
ejpam-3852	486	18	.	.	PUNCT
ejpam-3852	487	1	on	on	ADP
ejpam-3852	487	2	the	the	DET
ejpam-3852	487	3	lattice	lattice	NOUN
ejpam-3852	487	4	structure	structure	NOUN
ejpam-3852	487	5	of	of	ADP
ejpam-3852	487	6	a	a	DET
ejpam-3852	487	7	nonlinear	nonlinear	ADJ
ejpam-3852	487	8	generator	generator	NOUN
ejpam-3852	487	9	with	with	ADP
ejpam-3852	487	10	modulus	modulus	ADJ
ejpam-3852	487	11	2α	2α	NOUN
ejpam-3852	487	12	.	.	PUNCT
ejpam-3852	488	1	j.	j.	PROPN
ejpam-3852	488	2	comput	comput	PROPN
ejpam-3852	488	3	.	.	PUNCT
ejpam-3852	489	1	appl	appl	PROPN
ejpam-3852	489	2	.	.	PROPN
ejpam-3852	489	3	math	math	PROPN
ejpam-3852	489	4	.	.	PUNCT
ejpam-3852	489	5	,	,	PUNCT
ejpam-3852	490	1	31(1):81–85	31(1):81–85	NUM
ejpam-3852	490	2	,	,	PUNCT
ejpam-3852	490	3	1990	1990	NUM
ejpam-3852	490	4	.	.	PUNCT
ejpam-3852	491	1	random	random	ADJ
ejpam-3852	491	2	numbers	number	NOUN
ejpam-3852	491	3	and	and	CCONJ
ejpam-3852	491	4	simulation	simulation	NOUN
ejpam-3852	491	5	(	(	PUNCT
ejpam-3852	491	6	lambrecht	lambrecht	NOUN
ejpam-3852	491	7	,	,	PUNCT
ejpam-3852	491	8	1988	1988	NUM
ejpam-3852	491	9	)	)	PUNCT
ejpam-3852	491	10	.	.	PUNCT
ejpam-3852	492	1	[	[	X
ejpam-3852	492	2	5	5	NUM
ejpam-3852	492	3	]	]	X
ejpam-3852	492	4	jürgen	jürgen	PROPN
ejpam-3852	492	5	eichenauer	eichenauer	PROPN
ejpam-3852	492	6	-	-	PUNCT
ejpam-3852	492	7	herrmann	herrmann	PROPN
ejpam-3852	492	8	.	.	PUNCT
ejpam-3852	493	1	inversive	inversive	ADJ
ejpam-3852	493	2	congruential	congruential	ADJ
ejpam-3852	493	3	pseudorandom	pseudorandom	NOUN
ejpam-3852	493	4	numbers	number	NOUN
ejpam-3852	493	5	avoid	avoid	VERB
ejpam-3852	493	6	the	the	DET
ejpam-3852	493	7	planes	plane	NOUN
ejpam-3852	493	8	.	.	PUNCT
ejpam-3852	494	1	math	math	NOUN
ejpam-3852	494	2	.	.	PUNCT
ejpam-3852	495	1	comp	comp	PROPN
ejpam-3852	495	2	.	.	PUNCT
ejpam-3852	495	3	,	,	PUNCT
ejpam-3852	495	4	56(193):297–301	56(193):297–301	PROPN
ejpam-3852	495	5	,	,	PUNCT
ejpam-3852	495	6	1991	1991	NUM
ejpam-3852	495	7	.	.	PUNCT
ejpam-3852	496	1	[	[	X
ejpam-3852	496	2	6	6	NUM
ejpam-3852	496	3	]	]	X
ejpam-3852	496	4	jürgen	jürgen	PROPN
ejpam-3852	496	5	eichenauer	eichenauer	PROPN
ejpam-3852	496	6	-	-	PUNCT
ejpam-3852	496	7	herrmann	herrmann	PROPN
ejpam-3852	496	8	.	.	PUNCT
ejpam-3852	497	1	inversive	inversive	ADJ
ejpam-3852	497	2	congruential	congruential	ADJ
ejpam-3852	497	3	pseudorandom	pseudorandom	NOUN
ejpam-3852	497	4	numbers	number	NOUN
ejpam-3852	497	5	:	:	PUNCT
ejpam-3852	497	6	a	a	DET
ejpam-3852	497	7	tutorial	tutorial	NOUN
ejpam-3852	497	8	.	.	PUNCT
ejpam-3852	498	1	international	international	ADJ
ejpam-3852	498	2	statistical	statistical	ADJ
ejpam-3852	498	3	review	review	NOUN
ejpam-3852	498	4	,	,	PUNCT
ejpam-3852	498	5	560:2(193):167–176	560:2(193):167–176	NUM
ejpam-3852	498	6	,	,	PUNCT
ejpam-3852	498	7	1992	1992	NUM
ejpam-3852	498	8	.	.	PUNCT
ejpam-3852	499	1	[	[	X
ejpam-3852	499	2	7	7	X
ejpam-3852	499	3	]	]	X
ejpam-3852	499	4	jürgen	jürgen	X
ejpam-3852	499	5	eichenauer	eichenauer	PROPN
ejpam-3852	499	6	-	-	PUNCT
ejpam-3852	499	7	herrmann	herrmann	PROPN
ejpam-3852	499	8	.	.	PUNCT
ejpam-3852	500	1	statistical	statistical	ADJ
ejpam-3852	500	2	independence	independence	NOUN
ejpam-3852	500	3	of	of	ADP
ejpam-3852	500	4	a	a	DET
ejpam-3852	500	5	new	new	ADJ
ejpam-3852	500	6	class	class	NOUN
ejpam-3852	500	7	of	of	ADP
ejpam-3852	500	8	inversive	inversive	ADJ
ejpam-3852	500	9	congruential	congruential	ADJ
ejpam-3852	500	10	pseudorandom	pseudorandom	NOUN
ejpam-3852	500	11	numbers	number	NOUN
ejpam-3852	500	12	.	.	PUNCT
ejpam-3852	501	1	math	math	NOUN
ejpam-3852	501	2	.	.	PUNCT
ejpam-3852	502	1	comp	comp	PROPN
ejpam-3852	502	2	.	.	PUNCT
ejpam-3852	502	3	,	,	PUNCT
ejpam-3852	502	4	60(201):375–384	60(201):375–384	PROPN
ejpam-3852	502	5	,	,	PUNCT
ejpam-3852	502	6	1993	1993	NUM
ejpam-3852	502	7	.	.	PUNCT
ejpam-3852	503	1	[	[	X
ejpam-3852	503	2	8	8	NUM
ejpam-3852	503	3	]	]	X
ejpam-3852	503	4	jürgen	jürgen	PROPN
ejpam-3852	503	5	eichenauer	eichenauer	PROPN
ejpam-3852	503	6	-	-	PUNCT
ejpam-3852	503	7	herrmann	herrmann	PROPN
ejpam-3852	503	8	.	.	PUNCT
ejpam-3852	504	1	on	on	ADP
ejpam-3852	504	2	generalized	generalized	ADJ
ejpam-3852	504	3	inversive	inversive	ADJ
ejpam-3852	504	4	congruential	congruential	ADJ
ejpam-3852	504	5	pseudorandom	pseudorandom	NOUN
ejpam-3852	504	6	numbers	number	NOUN
ejpam-3852	504	7	.	.	PUNCT
ejpam-3852	505	1	math	math	NOUN
ejpam-3852	505	2	.	.	PUNCT
ejpam-3852	506	1	comp	comp	PROPN
ejpam-3852	506	2	.	.	PUNCT
ejpam-3852	506	3	,	,	PUNCT
ejpam-3852	507	1	63(207):293–299	63(207):293–299	PROPN
ejpam-3852	507	2	,	,	PUNCT
ejpam-3852	507	3	1994	1994	NUM
ejpam-3852	507	4	.	.	PUNCT
ejpam-3852	508	1	[	[	X
ejpam-3852	508	2	9	9	NUM
ejpam-3852	508	3	]	]	X
ejpam-3852	508	4	jürgen	jürgen	X
ejpam-3852	508	5	eichenauer	eichenauer	PROPN
ejpam-3852	508	6	-	-	PUNCT
ejpam-3852	508	7	herrmann	herrmann	PROPN
ejpam-3852	508	8	and	and	CCONJ
ejpam-3852	508	9	harald	harald	PROPN
ejpam-3852	508	10	niederreiter	niederreiter	PROPN
ejpam-3852	508	11	.	.	PUNCT
ejpam-3852	509	1	lower	low	ADJ
ejpam-3852	509	2	bounds	bound	NOUN
ejpam-3852	509	3	for	for	ADP
ejpam-3852	509	4	the	the	DET
ejpam-3852	509	5	discrepancy	discrepancy	NOUN
ejpam-3852	509	6	of	of	ADP
ejpam-3852	509	7	inversive	inversive	ADJ
ejpam-3852	509	8	congruential	congruential	ADJ
ejpam-3852	509	9	pseudorandom	pseudorandom	NOUN
ejpam-3852	509	10	numbers	number	NOUN
ejpam-3852	509	11	with	with	ADP
ejpam-3852	509	12	power	power	NOUN
ejpam-3852	509	13	of	of	ADP
ejpam-3852	509	14	two	two	NUM
ejpam-3852	509	15	modulus	modulus	NOUN
ejpam-3852	509	16	.	.	PUNCT
ejpam-3852	509	17	math	math	NOUN
ejpam-3852	509	18	.	.	PUNCT
ejpam-3852	510	1	comp	comp	PROPN
ejpam-3852	510	2	.	.	PUNCT
ejpam-3852	510	3	,	,	PUNCT
ejpam-3852	510	4	58(198):775–779	58(198):775–779	PROPN
ejpam-3852	510	5	,	,	PUNCT
ejpam-3852	510	6	1992	1992	NUM
ejpam-3852	510	7	.	.	PUNCT
ejpam-3852	511	1	[	[	X
ejpam-3852	511	2	10	10	NUM
ejpam-3852	511	3	]	]	X
ejpam-3852	511	4	reza	reza	PROPN
ejpam-3852	511	5	rezaeian	rezaeian	ADJ
ejpam-3852	511	6	farashahi	farashahi	NOUN
ejpam-3852	511	7	and	and	CCONJ
ejpam-3852	511	8	igor	igor	PROPN
ejpam-3852	511	9	e.	e.	PROPN
ejpam-3852	511	10	shparlinski	shparlinski	PROPN
ejpam-3852	511	11	.	.	PUNCT
ejpam-3852	512	1	pseudorandom	pseudorandom	PROPN
ejpam-3852	512	2	bits	bit	NOUN
ejpam-3852	512	3	from	from	ADP
ejpam-3852	512	4	points	point	NOUN
ejpam-3852	512	5	on	on	ADP
ejpam-3852	512	6	elliptic	elliptic	ADJ
ejpam-3852	512	7	curves	curve	NOUN
ejpam-3852	512	8	.	.	PUNCT
ejpam-3852	513	1	ieee	ieee	PROPN
ejpam-3852	513	2	trans	trans	PROPN
ejpam-3852	513	3	.	.	PUNCT
ejpam-3852	514	1	inform	inform	NOUN
ejpam-3852	514	2	.	.	PUNCT
ejpam-3852	515	1	theory	theory	NOUN
ejpam-3852	515	2	,	,	PUNCT
ejpam-3852	515	3	58(2):1242–1247	58(2):1242–1247	NUM
ejpam-3852	515	4	,	,	PUNCT
ejpam-3852	515	5	2012	2012	NUM
ejpam-3852	515	6	.	.	PUNCT
ejpam-3852	516	1	[	[	X
ejpam-3852	516	2	11	11	NUM
ejpam-3852	516	3	]	]	SYM
ejpam-3852	516	4	domingo	domingo	PROPN
ejpam-3852	516	5	gómez	gómez	PROPN
ejpam-3852	516	6	,	,	PUNCT
ejpam-3852	516	7	jaime	jaime	NOUN
ejpam-3852	516	8	gutierrez	gutierrez	PROPN
ejpam-3852	516	9	,	,	PUNCT
ejpam-3852	516	10	and	and	CCONJ
ejpam-3852	516	11	álvar	álvar	PROPN
ejpam-3852	516	12	ibeas	ibea	NOUN
ejpam-3852	516	13	.	.	PUNCT
ejpam-3852	517	1	attacking	attack	VERB
ejpam-3852	517	2	the	the	DET
ejpam-3852	517	3	pollard	pollard	PROPN
ejpam-3852	517	4	generator	generator	PROPN
ejpam-3852	517	5	.	.	PUNCT
ejpam-3852	518	1	ieee	ieee	PROPN
ejpam-3852	518	2	trans	trans	PROPN
ejpam-3852	518	3	.	.	PUNCT
ejpam-3852	519	1	inform	inform	NOUN
ejpam-3852	519	2	.	.	PUNCT
ejpam-3852	520	1	theory	theory	NOUN
ejpam-3852	520	2	,	,	PUNCT
ejpam-3852	520	3	52(12):5518–5523	52(12):5518–5523	PROPN
ejpam-3852	520	4	,	,	PUNCT
ejpam-3852	520	5	2006	2006	NUM
ejpam-3852	520	6	.	.	PUNCT
ejpam-3852	521	1	[	[	X
ejpam-3852	521	2	12	12	NUM
ejpam-3852	521	3	]	]	X
ejpam-3852	521	4	honggang	honggang	PROPN
ejpam-3852	521	5	hu	hu	PROPN
ejpam-3852	521	6	,	,	PUNCT
ejpam-3852	521	7	lei	lei	PROPN
ejpam-3852	521	8	hu	hu	PROPN
ejpam-3852	521	9	,	,	PUNCT
ejpam-3852	521	10	and	and	CCONJ
ejpam-3852	521	11	dengguo	dengguo	PROPN
ejpam-3852	521	12	feng	feng	PROPN
ejpam-3852	521	13	.	.	PUNCT
ejpam-3852	522	1	on	on	ADP
ejpam-3852	522	2	a	a	DET
ejpam-3852	522	3	class	class	NOUN
ejpam-3852	522	4	of	of	ADP
ejpam-3852	522	5	pseudorandom	pseudorandom	NOUN
ejpam-3852	522	6	sequences	sequence	NOUN
ejpam-3852	522	7	from	from	ADP
ejpam-3852	522	8	elliptic	elliptic	ADJ
ejpam-3852	522	9	curves	curve	NOUN
ejpam-3852	522	10	over	over	ADP
ejpam-3852	522	11	finite	finite	ADJ
ejpam-3852	522	12	fields	field	NOUN
ejpam-3852	522	13	.	.	PUNCT
ejpam-3852	523	1	ieee	ieee	PROPN
ejpam-3852	523	2	trans	trans	PROPN
ejpam-3852	523	3	.	.	PUNCT
ejpam-3852	524	1	inform	inform	NOUN
ejpam-3852	524	2	.	.	PUNCT
ejpam-3852	525	1	theory	theory	NOUN
ejpam-3852	525	2	,	,	PUNCT
ejpam-3852	525	3	53(7):2598–2605	53(7):2598–2605	NUM
ejpam-3852	525	4	,	,	PUNCT
ejpam-3852	525	5	2007	2007	NUM
ejpam-3852	525	6	.	.	PUNCT
ejpam-3852	526	1	[	[	X
ejpam-3852	526	2	13	13	NUM
ejpam-3852	526	3	]	]	PUNCT
ejpam-3852	526	4	a.	a.	NOUN
ejpam-3852	526	5	w.	w.	PROPN
ejpam-3852	526	6	ingleton	ingleton	PROPN
ejpam-3852	526	7	.	.	PUNCT
ejpam-3852	527	1	the	the	DET
ejpam-3852	527	2	rank	rank	NOUN
ejpam-3852	527	3	of	of	ADP
ejpam-3852	527	4	circulant	circulant	ADJ
ejpam-3852	527	5	matrices	matrix	NOUN
ejpam-3852	527	6	.	.	PUNCT
ejpam-3852	528	1	j.	j.	PROPN
ejpam-3852	528	2	london	london	PROPN
ejpam-3852	528	3	math	math	PROPN
ejpam-3852	528	4	.	.	PUNCT
ejpam-3852	529	1	soc	soc	PROPN
ejpam-3852	529	2	.	.	PROPN
ejpam-3852	529	3	,	,	PUNCT
ejpam-3852	529	4	31:632–635	31:632–635	PROPN
ejpam-3852	529	5	,	,	PUNCT
ejpam-3852	529	6	1956	1956	NUM
ejpam-3852	529	7	.	.	PUNCT
ejpam-3852	530	1	[	[	X
ejpam-3852	530	2	14	14	NUM
ejpam-3852	530	3	]	]	X
ejpam-3852	530	4	takashi	takashi	PROPN
ejpam-3852	530	5	kato	kato	PROPN
ejpam-3852	530	6	,	,	PUNCT
ejpam-3852	530	7	li	li	PROPN
ejpam-3852	530	8	-	-	PROPN
ejpam-3852	530	9	ming	ming	PROPN
ejpam-3852	530	10	wu	wu	PROPN
ejpam-3852	530	11	,	,	PUNCT
ejpam-3852	530	12	and	and	CCONJ
ejpam-3852	530	13	niro	niro	PROPN
ejpam-3852	530	14	yanagihara	yanagihara	NOUN
ejpam-3852	530	15	.	.	PUNCT
ejpam-3852	531	1	on	on	ADP
ejpam-3852	531	2	a	a	DET
ejpam-3852	531	3	nonlinear	nonlinear	ADJ
ejpam-3852	531	4	congruential	congruential	ADJ
ejpam-3852	531	5	pseudorandom	pseudorandom	NOUN
ejpam-3852	531	6	number	number	NOUN
ejpam-3852	531	7	generator	generator	PROPN
ejpam-3852	531	8	.	.	PUNCT
ejpam-3852	531	9	math	math	NOUN
ejpam-3852	531	10	.	.	PUNCT
ejpam-3852	532	1	comp	comp	PROPN
ejpam-3852	532	2	.	.	PUNCT
ejpam-3852	532	3	,	,	PUNCT
ejpam-3852	533	1	65(213):227–233	65(213):227–233	PROPN
ejpam-3852	533	2	,	,	PUNCT
ejpam-3852	533	3	1996	1996	NUM
ejpam-3852	533	4	.	.	PUNCT
ejpam-3852	534	1	[	[	X
ejpam-3852	534	2	15	15	NUM
ejpam-3852	534	3	]	]	X
ejpam-3852	534	4	donald	donald	PROPN
ejpam-3852	534	5	e.	e.	PROPN
ejpam-3852	534	6	knuth	knuth	PROPN
ejpam-3852	534	7	.	.	PUNCT
ejpam-3852	535	1	the	the	DET
ejpam-3852	535	2	art	art	NOUN
ejpam-3852	535	3	of	of	ADP
ejpam-3852	535	4	computer	computer	NOUN
ejpam-3852	535	5	programming	programming	NOUN
ejpam-3852	535	6	,	,	PUNCT
ejpam-3852	535	7	volume	volume	NOUN
ejpam-3852	535	8	ii	ii	PROPN
ejpam-3852	535	9	:	:	PUNCT
ejpam-3852	535	10	seminumerical	seminumerical	ADJ
ejpam-3852	535	11	algorithms	algorithm	NOUN
ejpam-3852	535	12	,	,	PUNCT
ejpam-3852	535	13	2nd	2nd	PROPN
ejpam-3852	535	14	edition	edition	PROPN
ejpam-3852	535	15	.	.	PUNCT
ejpam-3852	536	1	addison	addison	PROPN
ejpam-3852	536	2	-	-	PUNCT
ejpam-3852	536	3	wesley	wesley	PROPN
ejpam-3852	536	4	,	,	PUNCT
ejpam-3852	536	5	reading	reading	NOUN
ejpam-3852	536	6	,	,	PUNCT
ejpam-3852	536	7	ma	ma	PROPN
ejpam-3852	536	8	,	,	PUNCT
ejpam-3852	536	9	1981	1981	NUM
ejpam-3852	536	10	.	.	PUNCT
ejpam-3852	537	1	[	[	X
ejpam-3852	537	2	16	16	NUM
ejpam-3852	537	3	]	]	PUNCT
ejpam-3852	537	4	j.	j.	PROPN
ejpam-3852	537	5	mc	mc	PROPN
ejpam-3852	537	6	laughlin	laughlin	PROPN
ejpam-3852	537	7	.	.	PUNCT
ejpam-3852	538	1	combinatorial	combinatorial	ADJ
ejpam-3852	538	2	identities	identity	NOUN
ejpam-3852	538	3	deriving	derive	VERB
ejpam-3852	538	4	from	from	ADP
ejpam-3852	538	5	the	the	DET
ejpam-3852	538	6	nth	nth	NOUN
ejpam-3852	538	7	power	power	NOUN
ejpam-3852	538	8	of	of	ADP
ejpam-3852	538	9	a	a	DET
ejpam-3852	538	10	2	2	NUM
ejpam-3852	538	11	×	×	NOUN
ejpam-3852	538	12	2	2	NUM
ejpam-3852	538	13	matrix	matrix	NOUN
ejpam-3852	538	14	.	.	PUNCT
ejpam-3852	539	1	integers	integer	NOUN
ejpam-3852	539	2	,	,	PUNCT
ejpam-3852	539	3	4	4	NUM
ejpam-3852	539	4	:	:	PUNCT
ejpam-3852	539	5	a19	a19	PROPN
ejpam-3852	539	6	,	,	PUNCT
ejpam-3852	539	7	15	15	NUM
ejpam-3852	539	8	,	,	PUNCT
ejpam-3852	539	9	2004	2004	NUM
ejpam-3852	539	10	.	.	PUNCT
ejpam-3852	540	1	appendix	appendix	VERB
ejpam-3852	540	2	17	17	NUM
ejpam-3852	540	3	[	[	SYM
ejpam-3852	540	4	17	17	NUM
ejpam-3852	540	5	]	]	X
ejpam-3852	540	6	harald	harald	PROPN
ejpam-3852	540	7	niederreiter	niederreiter	PROPN
ejpam-3852	540	8	.	.	PUNCT
ejpam-3852	541	1	the	the	DET
ejpam-3852	541	2	serial	serial	ADJ
ejpam-3852	541	3	test	test	NOUN
ejpam-3852	541	4	for	for	ADP
ejpam-3852	541	5	congruential	congruential	ADJ
ejpam-3852	541	6	pseudorandom	pseudorandom	NOUN
ejpam-3852	541	7	numbers	number	NOUN
ejpam-3852	541	8	generated	generate	VERB
ejpam-3852	541	9	by	by	ADP
ejpam-3852	541	10	inversions	inversion	NOUN
ejpam-3852	541	11	.	.	PUNCT
ejpam-3852	542	1	math	math	NOUN
ejpam-3852	542	2	.	.	PUNCT
ejpam-3852	543	1	comp	comp	PROPN
ejpam-3852	543	2	.	.	PUNCT
ejpam-3852	543	3	,	,	PUNCT
ejpam-3852	543	4	52(185):135–144	52(185):135–144	PROPN
ejpam-3852	543	5	,	,	PUNCT
ejpam-3852	543	6	1989	1989	NUM
ejpam-3852	543	7	.	.	PUNCT
ejpam-3852	544	1	[	[	X
ejpam-3852	544	2	18	18	NUM
ejpam-3852	544	3	]	]	X
ejpam-3852	544	4	harald	harald	PROPN
ejpam-3852	544	5	niederreiter	niederreiter	PROPN
ejpam-3852	544	6	.	.	PUNCT
ejpam-3852	545	1	recent	recent	ADJ
ejpam-3852	545	2	trends	trend	NOUN
ejpam-3852	545	3	in	in	ADP
ejpam-3852	545	4	random	random	ADJ
ejpam-3852	545	5	number	number	NOUN
ejpam-3852	545	6	and	and	CCONJ
ejpam-3852	545	7	random	random	ADJ
ejpam-3852	545	8	vector	vector	NOUN
ejpam-3852	545	9	generation	generation	NOUN
ejpam-3852	545	10	.	.	PUNCT
ejpam-3852	546	1	ann	ann	PROPN
ejpam-3852	546	2	.	.	PUNCT
ejpam-3852	546	3	oper	oper	PROPN
ejpam-3852	546	4	.	.	PUNCT
ejpam-3852	546	5	res	res	PROPN
ejpam-3852	546	6	.	.	PROPN
ejpam-3852	546	7	,	,	PUNCT
ejpam-3852	546	8	31(1	31(1	NUM
ejpam-3852	546	9	-	-	SYM
ejpam-3852	546	10	4):323–345	4):323–345	NUM
ejpam-3852	546	11	,	,	PUNCT
ejpam-3852	546	12	1991	1991	NUM
ejpam-3852	546	13	.	.	PUNCT
ejpam-3852	547	1	stochastic	stochastic	ADJ
ejpam-3852	547	2	programming	programming	NOUN
ejpam-3852	547	3	,	,	PUNCT
ejpam-3852	547	4	part	part	PROPN
ejpam-3852	547	5	ii	ii	PROPN
ejpam-3852	547	6	(	(	PUNCT
ejpam-3852	547	7	ann	ann	PROPN
ejpam-3852	547	8	arbor	arbor	PROPN
ejpam-3852	547	9	,	,	PUNCT
ejpam-3852	547	10	mi	mi	PROPN
ejpam-3852	547	11	,	,	PUNCT
ejpam-3852	547	12	1989	1989	NUM
ejpam-3852	547	13	)	)	PUNCT
ejpam-3852	547	14	.	.	PUNCT
ejpam-3852	548	1	[	[	X
ejpam-3852	548	2	19	19	NUM
ejpam-3852	548	3	]	]	X
ejpam-3852	548	4	harald	harald	PROPN
ejpam-3852	548	5	niederreiter	niederreiter	PROPN
ejpam-3852	548	6	.	.	PUNCT
ejpam-3852	549	1	random	random	ADJ
ejpam-3852	549	2	number	number	NOUN
ejpam-3852	549	3	generation	generation	NOUN
ejpam-3852	549	4	and	and	CCONJ
ejpam-3852	549	5	quasi	quasi	ADJ
ejpam-3852	549	6	-	-	ADJ
ejpam-3852	549	7	monte	monte	ADJ
ejpam-3852	549	8	carlo	carlo	NOUN
ejpam-3852	549	9	methods	method	NOUN
ejpam-3852	549	10	,	,	PUNCT
ejpam-3852	549	11	volume	volume	NOUN
ejpam-3852	549	12	63	63	NUM
ejpam-3852	549	13	of	of	ADP
ejpam-3852	549	14	cbms	cbms	ADJ
ejpam-3852	549	15	-	-	PUNCT
ejpam-3852	549	16	nsf	nsf	ADJ
ejpam-3852	549	17	regional	regional	ADJ
ejpam-3852	549	18	conference	conference	NOUN
ejpam-3852	549	19	series	series	NOUN
ejpam-3852	549	20	in	in	ADP
ejpam-3852	549	21	applied	applied	ADJ
ejpam-3852	549	22	mathematics	mathematic	NOUN
ejpam-3852	549	23	.	.	PUNCT
ejpam-3852	550	1	society	society	NOUN
ejpam-3852	550	2	for	for	ADP
ejpam-3852	550	3	industrial	industrial	ADJ
ejpam-3852	550	4	and	and	CCONJ
ejpam-3852	550	5	applied	applied	ADJ
ejpam-3852	550	6	mathematics	mathematic	NOUN
ejpam-3852	550	7	(	(	PUNCT
ejpam-3852	550	8	siam	siam	NOUN
ejpam-3852	550	9	)	)	PUNCT
ejpam-3852	550	10	,	,	PUNCT
ejpam-3852	550	11	philadelphia	philadelphia	PROPN
ejpam-3852	550	12	,	,	PUNCT
ejpam-3852	550	13	pa	pa	PROPN
ejpam-3852	550	14	,	,	PUNCT
ejpam-3852	550	15	1992	1992	NUM
ejpam-3852	550	16	.	.	PUNCT
ejpam-3852	551	1	[	[	X
ejpam-3852	551	2	20	20	NUM
ejpam-3852	551	3	]	]	X
ejpam-3852	551	4	harald	harald	PROPN
ejpam-3852	551	5	niederreiter	niederreiter	PROPN
ejpam-3852	551	6	and	and	CCONJ
ejpam-3852	551	7	igor	igor	PROPN
ejpam-3852	551	8	e.	e.	PROPN
ejpam-3852	551	9	shparlinski	shparlinski	PROPN
ejpam-3852	551	10	.	.	PUNCT
ejpam-3852	552	1	exponential	exponential	ADJ
ejpam-3852	552	2	sums	sum	NOUN
ejpam-3852	552	3	and	and	CCONJ
ejpam-3852	552	4	the	the	DET
ejpam-3852	552	5	distribution	distribution	NOUN
ejpam-3852	552	6	of	of	ADP
ejpam-3852	552	7	inversive	inversive	ADJ
ejpam-3852	552	8	congruential	congruential	ADJ
ejpam-3852	552	9	pseudorandom	pseudorandom	NOUN
ejpam-3852	552	10	numbers	number	NOUN
ejpam-3852	552	11	with	with	ADP
ejpam-3852	552	12	prime	prime	ADJ
ejpam-3852	552	13	-	-	PUNCT
ejpam-3852	552	14	power	power	NOUN
ejpam-3852	552	15	modulus	modulus	NOUN
ejpam-3852	552	16	.	.	PUNCT
ejpam-3852	553	1	acta	acta	PROPN
ejpam-3852	553	2	arith	arith	PROPN
ejpam-3852	553	3	.	.	PUNCT
ejpam-3852	553	4	,	,	PUNCT
ejpam-3852	554	1	92(1):89–98	92(1):89–98	NUM
ejpam-3852	554	2	,	,	PUNCT
ejpam-3852	554	3	2000	2000	NUM
ejpam-3852	554	4	.	.	PUNCT
ejpam-3852	555	1	[	[	X
ejpam-3852	555	2	21	21	NUM
ejpam-3852	555	3	]	]	X
ejpam-3852	555	4	oystein	oystein	PROPN
ejpam-3852	555	5	ore	ore	PROPN
ejpam-3852	555	6	.	.	PUNCT
ejpam-3852	556	1	some	some	DET
ejpam-3852	556	2	studies	study	NOUN
ejpam-3852	556	3	on	on	ADP
ejpam-3852	556	4	cyclic	cyclic	ADJ
ejpam-3852	556	5	determinants	determinant	NOUN
ejpam-3852	556	6	.	.	PUNCT
ejpam-3852	557	1	duke	duke	PROPN
ejpam-3852	557	2	math	math	PROPN
ejpam-3852	557	3	.	.	PUNCT
ejpam-3852	558	1	j.	j.	PROPN
ejpam-3852	558	2	,	,	PUNCT
ejpam-3852	558	3	18:343–354	18:343–354	PROPN
ejpam-3852	558	4	,	,	PUNCT
ejpam-3852	558	5	1951	1951	NUM
ejpam-3852	558	6	.	.	PUNCT
ejpam-3852	559	1	appendix	appendix	VERB
ejpam-3852	559	2	sage	sage	NOUN
ejpam-3852	559	3	code	code	NOUN
ejpam-3852	559	4	with	with	ADP
ejpam-3852	559	5	the	the	DET
ejpam-3852	559	6	parameters	parameter	NOUN
ejpam-3852	559	7	ω	ω	NOUN
ejpam-3852	559	8	=	=	SYM
ejpam-3852	559	9	64	64	NUM
ejpam-3852	559	10	,	,	PUNCT
ejpam-3852	559	11	a	a	DET
ejpam-3852	559	12	=	=	SYM
ejpam-3852	559	13	1886906	1886906	NUM
ejpam-3852	559	14	,	,	PUNCT
ejpam-3852	559	15	b	b	X
ejpam-3852	559	16	=	=	SYM
ejpam-3852	559	17	706715	706715	NUM
ejpam-3852	559	18	,	,	PUNCT
ejpam-3852	559	19	c	c	NOUN
ejpam-3852	559	20	=	=	SYM
ejpam-3852	559	21	807782	807782	NUM
ejpam-3852	559	22	,	,	PUNCT
ejpam-3852	559	23	y0	y0	PROPN
ejpam-3852	559	24	=	=	SYM
ejpam-3852	559	25	430227	430227	NUM
ejpam-3852	559	26	and	and	CCONJ
ejpam-3852	559	27	y1	y1	NOUN
ejpam-3852	559	28	=	=	SYM
ejpam-3852	559	29	1725239	1725239	NUM
ejpam-3852	559	30	:	:	PUNCT
ejpam-3852	559	31	n=64	n=64	PROPN
ejpam-3852	559	32	n=2ˆn	n=2ˆn	VERB
ejpam-3852	559	33	a	a	DET
ejpam-3852	559	34	=	=	NOUN
ejpam-3852	559	35	1886906	1886906	NUM
ejpam-3852	559	36	b	b	X
ejpam-3852	560	1	=	=	SYM
ejpam-3852	560	2	706715	706715	NUM
ejpam-3852	560	3	c	c	NOUN
ejpam-3852	560	4	=	=	NOUN
ejpam-3852	560	5	807782	807782	NUM
ejpam-3852	560	6	y0	y0	PROPN
ejpam-3852	560	7	=	=	SYM
ejpam-3852	560	8	430227	430227	NUM
ejpam-3852	560	9	y1	y1	NOUN
ejpam-3852	560	10	=	=	VERB
ejpam-3852	560	11	1725239	1725239	NUM
ejpam-3852	560	12	y	y	NOUN
ejpam-3852	560	13	=	=	NOUN
ejpam-3852	560	14	y0	y0	ADJ
ejpam-3852	560	15	z	z	NOUN
ejpam-3852	560	16	=	=	NOUN
ejpam-3852	560	17	y1	y1	ADJ
ejpam-3852	560	18	pr	pr	NOUN
ejpam-3852	560	19	in	in	ADP
ejpam-3852	560	20	t	t	PROPN
ejpam-3852	560	21	(	(	PUNCT
ejpam-3852	560	22	”	"	PUNCT
ejpam-3852	560	23	0	0	NUM
ejpam-3852	560	24	,	,	PUNCT
ejpam-3852	560	25	0	0	NUM
ejpam-3852	560	26	,	,	PUNCT
ejpam-3852	560	27	”	"	PUNCT
ejpam-3852	560	28	,	,	PUNCT
ejpam-3852	560	29	end	end	NOUN
ejpam-3852	560	30	=	=	PUNCT
ejpam-3852	560	31	’	'	PUNCT
ejpam-3852	560	32	’	'	PUNCT
ejpam-3852	560	33	)	)	PUNCT
ejpam-3852	560	34	,	,	PUNCT
ejpam-3852	560	35	#	#	NOUN
ejpam-3852	560	36	as	as	ADP
ejpam-3852	560	37	y0	y0	NOUN
ejpam-3852	560	38	and	and	CCONJ
ejpam-3852	560	39	y1	y1	NOUN
ejpam-3852	560	40	are	be	AUX
ejpam-3852	560	41	l	l	NOUN
ejpam-3852	560	42	e	e	NOUN
ejpam-3852	560	43	s	s	X
ejpam-3852	560	44	s	s	X
ejpam-3852	560	45	than	than	ADP
ejpam-3852	560	46	n/2	n/2	NOUN
ejpam-3852	560	47	,	,	PUNCT
ejpam-3852	561	1	i	i	PRON
ejpam-3852	561	2	n	n	VERB
ejpam-3852	562	1	i	i	PRON
ejpam-3852	562	2	t	t	VERB
ejpam-3852	562	3	i	i	PRON
ejpam-3852	562	4	a	a	DET
ejpam-3852	562	5	l	l	NOUN
ejpam-3852	562	6	two	two	NUM
ejpam-3852	562	7	prns	prn	NOUN
ejpam-3852	562	8	are	be	AUX
ejpam-3852	562	9	s	s	X
ejpam-3852	562	10	e	e	NOUN
ejpam-3852	562	11	t	t	NOUN
ejpam-3852	562	12	to	to	PART
ejpam-3852	562	13	be	be	AUX
ejpam-3852	562	14	0	0	NUM
ejpam-3852	562	15	.	.	PUNCT
ejpam-3852	563	1	f	f	X
ejpam-3852	564	1	o	o	NOUN
ejpam-3852	564	2	r	r	NOUN
ejpam-3852	564	3	i	i	PRON
ejpam-3852	564	4	in	in	ADP
ejpam-3852	564	5	range	range	NOUN
ejpam-3852	564	6	(	(	PUNCT
ejpam-3852	564	7	2	2	NUM
ejpam-3852	564	8	,	,	PUNCT
ejpam-3852	564	9	1	1	NUM
ejpam-3852	564	10	0	0	NUM
ejpam-3852	564	11	0	0	NUM
ejpam-3852	564	12	)	)	PUNCT
ejpam-3852	564	13	:	:	PUNCT
ejpam-3852	565	1	w	w	X
ejpam-3852	565	2	=	=	X
ejpam-3852	565	3	a∗z	a∗z	X
ejpam-3852	565	4	.	.	PUNCT
ejpam-3852	566	1	inverse	inverse	PROPN
ejpam-3852	566	2	mod	mod	PROPN
ejpam-3852	566	3	(	(	PUNCT
ejpam-3852	566	4	n)+b∗y+c	n)+b∗y+c	PROPN
ejpam-3852	566	5	w	w	X
ejpam-3852	566	6	=	=	NOUN
ejpam-3852	566	7	w%n	w%n	NOUN
ejpam-3852	567	1	i	i	PRON
ejpam-3852	567	2	f	f	PROPN
ejpam-3852	568	1	(	(	PUNCT
ejpam-3852	568	2	w	w	NOUN
ejpam-3852	568	3	<	<	X
ejpam-3852	568	4	n/	n/	ADJ
ejpam-3852	568	5	2	2	NUM
ejpam-3852	568	6	)	)	PUNCT
ejpam-3852	569	1	:	:	PUNCT
ejpam-3852	569	2	p	p	X
ejpam-3852	569	3	r	r	NOUN
ejpam-3852	569	4	in	in	ADP
ejpam-3852	569	5	t	t	PROPN
ejpam-3852	569	6	(	(	PUNCT
ejpam-3852	569	7	”	"	PUNCT
ejpam-3852	569	8	0	0	NUM
ejpam-3852	569	9	,	,	PUNCT
ejpam-3852	569	10	”	"	PUNCT
ejpam-3852	569	11	,	,	PUNCT
ejpam-3852	569	12	end	end	NOUN
ejpam-3852	569	13	=	=	PUNCT
ejpam-3852	569	14	’	'	PUNCT
ejpam-3852	569	15	’	'	PUNCT
ejpam-3852	569	16	)	)	PUNCT
ejpam-3852	570	1	e	e	X
ejpam-3852	570	2	l	l	NOUN
ejpam-3852	570	3	s	s	X
ejpam-3852	570	4	e	e	NOUN
ejpam-3852	570	5	:	:	PUNCT
ejpam-3852	570	6	p	p	X
ejpam-3852	570	7	r	r	NOUN
ejpam-3852	570	8	in	in	ADP
ejpam-3852	570	9	t	t	PROPN
ejpam-3852	570	10	(	(	PUNCT
ejpam-3852	570	11	”	"	PUNCT
ejpam-3852	570	12	1	1	NUM
ejpam-3852	570	13	,	,	PUNCT
ejpam-3852	570	14	”	"	PUNCT
ejpam-3852	570	15	,	,	PUNCT
ejpam-3852	570	16	end	end	NOUN
ejpam-3852	570	17	=	=	PUNCT
ejpam-3852	570	18	’	'	PUNCT
ejpam-3852	570	19	’	'	PUNCT
ejpam-3852	570	20	)	)	PUNCT
ejpam-3852	571	1	y	y	PUNCT
ejpam-3852	571	2	=	=	NOUN
ejpam-3852	571	3	z	z	NOUN
ejpam-3852	571	4	appendix	appendix	VERB
ejpam-3852	571	5	18	18	NUM
ejpam-3852	571	6	z	z	NOUN
ejpam-3852	571	7	=	=	NOUN
ejpam-3852	571	8	w	w	NOUN