id	sid	tid	token	lemma	pos
ejpam-6605	1	1	european	european	PROPN
ejpam-6605	1	2	journal	journal	PROPN
ejpam-6605	1	3	of	of	ADP
ejpam-6605	1	4	pure	pure	ADJ
ejpam-6605	1	5	and	and	CCONJ
ejpam-6605	1	6	applied	applied	ADJ
ejpam-6605	1	7	mathematics	mathematic	NOUN
ejpam-6605	1	8	2025	2025	NUM
ejpam-6605	1	9	,	,	PUNCT
ejpam-6605	1	10	vol	vol	NOUN
ejpam-6605	1	11	.	.	PROPN
ejpam-6605	1	12	18	18	NUM
ejpam-6605	1	13	,	,	PUNCT
ejpam-6605	1	14	issue	issue	NOUN
ejpam-6605	1	15	4	4	NUM
ejpam-6605	1	16	,	,	PUNCT
ejpam-6605	1	17	article	article	NOUN
ejpam-6605	1	18	number	number	NOUN
ejpam-6605	1	19	6605	6605	NUM
ejpam-6605	1	20	issn	issn	VERB
ejpam-6605	1	21	1307	1307	NUM
ejpam-6605	1	22	-	-	SYM
ejpam-6605	1	23	5543	5543	NUM
ejpam-6605	1	24	–	–	PUNCT
ejpam-6605	1	25	ejpam.com	ejpam.com	X
ejpam-6605	1	26	published	publish	VERB
ejpam-6605	1	27	by	by	ADP
ejpam-6605	1	28	new	new	PROPN
ejpam-6605	1	29	york	york	PROPN
ejpam-6605	1	30	business	business	PROPN
ejpam-6605	1	31	global	global	PROPN
ejpam-6605	1	32	on	on	ADP
ejpam-6605	1	33	generalized	generalized	ADJ
ejpam-6605	1	34	mersenne	mersenne	NOUN
ejpam-6605	1	35	numbers	number	NOUN
ejpam-6605	1	36	and	and	CCONJ
ejpam-6605	1	37	extended	extend	VERB
ejpam-6605	1	38	fermat	fermat	PROPN
ejpam-6605	1	39	numbers	number	NOUN
ejpam-6605	1	40	shefa	shefa	PROPN
ejpam-6605	1	41	a.	a.	PROPN
ejpam-6605	1	42	bani	bani	PROPN
ejpam-6605	1	43	melhem1,∗	melhem1,∗	PROPN
ejpam-6605	1	44	,	,	PUNCT
ejpam-6605	1	45	ala’a	ala’a	PUNCT
ejpam-6605	1	46	al	al	PROPN
ejpam-6605	1	47	-	-	PUNCT
ejpam-6605	1	48	kateeb1,∗	kateeb1,∗	PROPN
ejpam-6605	1	49	,	,	PUNCT
ejpam-6605	1	50	afnan	afnan	NOUN
ejpam-6605	1	51	dagher1	dagher1	PROPN
ejpam-6605	1	52	1	1	NUM
ejpam-6605	1	53	department	department	NOUN
ejpam-6605	1	54	of	of	ADP
ejpam-6605	1	55	mathematics	mathematic	NOUN
ejpam-6605	1	56	,	,	PUNCT
ejpam-6605	1	57	faculty	faculty	NOUN
ejpam-6605	1	58	of	of	ADP
ejpam-6605	1	59	science	science	NOUN
ejpam-6605	1	60	,	,	PUNCT
ejpam-6605	1	61	yarmouk	yarmouk	CCONJ
ejpam-6605	1	62	university	university	NOUN
ejpam-6605	1	63	,	,	PUNCT
ejpam-6605	1	64	irbid	irbid	PROPN
ejpam-6605	1	65	,	,	PUNCT
ejpam-6605	1	66	jordan	jordan	PROPN
ejpam-6605	1	67	abstract	abstract	PROPN
ejpam-6605	1	68	.	.	PUNCT
ejpam-6605	2	1	in	in	ADP
ejpam-6605	2	2	this	this	DET
ejpam-6605	2	3	paper	paper	NOUN
ejpam-6605	2	4	,	,	PUNCT
ejpam-6605	2	5	we	we	PRON
ejpam-6605	2	6	study	study	VERB
ejpam-6605	2	7	a	a	DET
ejpam-6605	2	8	generalization	generalization	NOUN
ejpam-6605	2	9	of	of	ADP
ejpam-6605	2	10	mersenne	mersenne	NOUN
ejpam-6605	2	11	numbers	number	NOUN
ejpam-6605	2	12	and	and	CCONJ
ejpam-6605	2	13	we	we	PRON
ejpam-6605	2	14	introduce	introduce	VERB
ejpam-6605	2	15	an	an	DET
ejpam-6605	2	16	extension	extension	NOUN
ejpam-6605	2	17	of	of	ADP
ejpam-6605	2	18	fermat	fermat	PROPN
ejpam-6605	2	19	numbers	number	NOUN
ejpam-6605	2	20	,	,	PUNCT
ejpam-6605	2	21	we	we	PRON
ejpam-6605	2	22	find	find	VERB
ejpam-6605	2	23	their	their	PRON
ejpam-6605	2	24	generating	generating	NOUN
ejpam-6605	2	25	functions	function	NOUN
ejpam-6605	2	26	binet	binet	NOUN
ejpam-6605	2	27	formulas	formula	NOUN
ejpam-6605	2	28	,	,	PUNCT
ejpam-6605	2	29	related	related	ADJ
ejpam-6605	2	30	matrix	matrix	NOUN
ejpam-6605	2	31	representation	representation	NOUN
ejpam-6605	2	32	and	and	CCONJ
ejpam-6605	2	33	many	many	ADJ
ejpam-6605	2	34	other	other	ADJ
ejpam-6605	2	35	properties	property	NOUN
ejpam-6605	2	36	.	.	PUNCT
ejpam-6605	3	1	also	also	ADV
ejpam-6605	3	2	,	,	PUNCT
ejpam-6605	3	3	we	we	PRON
ejpam-6605	3	4	provide	provide	VERB
ejpam-6605	3	5	some	some	DET
ejpam-6605	3	6	applications	application	NOUN
ejpam-6605	3	7	in	in	ADP
ejpam-6605	3	8	cryptography	cryptography	NOUN
ejpam-6605	3	9	.	.	PUNCT
ejpam-6605	4	1	2020	2020	NUM
ejpam-6605	4	2	mathematics	mathematic	NOUN
ejpam-6605	4	3	subject	subject	NOUN
ejpam-6605	4	4	classifications	classification	NOUN
ejpam-6605	4	5	:	:	PUNCT
ejpam-6605	4	6	11b39	11b39	NUM
ejpam-6605	4	7	,	,	PUNCT
ejpam-6605	4	8	11b83	11b83	NUM
ejpam-6605	4	9	key	key	ADJ
ejpam-6605	4	10	words	word	NOUN
ejpam-6605	4	11	and	and	CCONJ
ejpam-6605	4	12	phrases	phrase	NOUN
ejpam-6605	4	13	:	:	PUNCT
ejpam-6605	4	14	mersenne	mersenne	NOUN
ejpam-6605	4	15	and	and	CCONJ
ejpam-6605	4	16	fermat	fermat	PROPN
ejpam-6605	4	17	numbers	number	NOUN
ejpam-6605	4	18	,	,	PUNCT
ejpam-6605	4	19	generating	generate	VERB
ejpam-6605	4	20	function	function	NOUN
ejpam-6605	4	21	,	,	PUNCT
ejpam-6605	4	22	binet	binet	NOUN
ejpam-6605	4	23	formula	formula	NOUN
ejpam-6605	4	24	,	,	PUNCT
ejpam-6605	4	25	key	key	ADJ
ejpam-6605	4	26	exchange	exchange	NOUN
ejpam-6605	4	27	and	and	CCONJ
ejpam-6605	4	28	authentication	authentication	NOUN
ejpam-6605	4	29	protocols	protocol	NOUN
ejpam-6605	4	30	1	1	NUM
ejpam-6605	4	31	.	.	PUNCT
ejpam-6605	4	32	introduction	introduction	NOUN
ejpam-6605	4	33	fibonacci	fibonacci	PROPN
ejpam-6605	4	34	and	and	CCONJ
ejpam-6605	4	35	lucas	lucas	PROPN
ejpam-6605	4	36	integer	integer	PROPN
ejpam-6605	4	37	sequences	sequence	NOUN
ejpam-6605	4	38	and	and	CCONJ
ejpam-6605	4	39	their	their	PRON
ejpam-6605	4	40	generalization/	generalization/	NUM
ejpam-6605	4	41	extensions	extension	NOUN
ejpam-6605	4	42	have	have	VERB
ejpam-6605	4	43	many	many	ADJ
ejpam-6605	4	44	interesting	interesting	ADJ
ejpam-6605	4	45	properties	property	NOUN
ejpam-6605	4	46	and	and	CCONJ
ejpam-6605	4	47	have	have	AUX
ejpam-6605	4	48	been	be	AUX
ejpam-6605	4	49	heavily	heavily	ADV
ejpam-6605	4	50	studied	study	VERB
ejpam-6605	4	51	[	[	X
ejpam-6605	4	52	1–5	1–5	X
ejpam-6605	4	53	]	]	X
ejpam-6605	4	54	.	.	PUNCT
ejpam-6605	5	1	the	the	DET
ejpam-6605	5	2	fibonacci/	fibonacci/	NUM
ejpam-6605	5	3	lucas	lucas	PROPN
ejpam-6605	5	4	sequences	sequence	NOUN
ejpam-6605	5	5	are	be	AUX
ejpam-6605	5	6	given	give	VERB
ejpam-6605	5	7	by	by	ADP
ejpam-6605	5	8	the	the	DET
ejpam-6605	5	9	following	follow	VERB
ejpam-6605	5	10	recurrence	recurrence	NOUN
ejpam-6605	5	11	relations	relation	NOUN
ejpam-6605	5	12	:	:	PUNCT
ejpam-6605	5	13	fn	fn	NOUN
ejpam-6605	5	14	=	=	PUNCT
ejpam-6605	5	15	fn−1	fn−1	PROPN
ejpam-6605	5	16	+	+	CCONJ
ejpam-6605	5	17	fn−2	fn−2	ADJ
ejpam-6605	5	18	,	,	PUNCT
ejpam-6605	5	19	ln	ln	NOUN
ejpam-6605	5	20	=	=	PROPN
ejpam-6605	5	21	ln−1	ln−1	PROPN
ejpam-6605	5	22	+	+	CCONJ
ejpam-6605	5	23	ln−2	ln−2	PROPN
ejpam-6605	5	24	where	where	SCONJ
ejpam-6605	5	25	n	n	PRON
ejpam-6605	5	26	≥	≥	X
ejpam-6605	5	27	2	2	NUM
ejpam-6605	5	28	,	,	PUNCT
ejpam-6605	5	29	f0	f0	PROPN
ejpam-6605	5	30	=	=	SYM
ejpam-6605	5	31	0	0	NUM
ejpam-6605	5	32	,	,	PUNCT
ejpam-6605	5	33	f1	f1	NOUN
ejpam-6605	5	34	=	=	SYM
ejpam-6605	5	35	1	1	NUM
ejpam-6605	5	36	and	and	CCONJ
ejpam-6605	5	37	l0	l0	PROPN
ejpam-6605	5	38	=	=	SYM
ejpam-6605	5	39	2	2	NUM
ejpam-6605	5	40	,	,	PUNCT
ejpam-6605	5	41	l1	l1	PROPN
ejpam-6605	5	42	=	=	PROPN
ejpam-6605	5	43	1	1	X
ejpam-6605	5	44	.	.	X
ejpam-6605	6	1	there	there	PRON
ejpam-6605	6	2	are	be	VERB
ejpam-6605	6	3	other	other	ADJ
ejpam-6605	6	4	fibonacci	fibonacci	PROPN
ejpam-6605	6	5	and	and	CCONJ
ejpam-6605	6	6	lucas	lucas	PROPN
ejpam-6605	6	7	type	type	NOUN
ejpam-6605	6	8	sequences	sequence	NOUN
ejpam-6605	6	9	such	such	ADJ
ejpam-6605	6	10	as	as	ADP
ejpam-6605	6	11	:	:	PUNCT
ejpam-6605	6	12	•	•	NOUN
ejpam-6605	6	13	pell	pell	NOUN
ejpam-6605	6	14	and	and	CCONJ
ejpam-6605	6	15	pell	pell	NOUN
ejpam-6605	6	16	-	-	PUNCT
ejpam-6605	6	17	lucas	lucas	NOUN
ejpam-6605	6	18	numbers	number	NOUN
ejpam-6605	6	19	:	:	PUNCT
ejpam-6605	6	20	pn	pn	PROPN
ejpam-6605	6	21	=	=	PROPN
ejpam-6605	6	22	2pn−1	2pn−1	NUM
ejpam-6605	6	23	+	+	NUM
ejpam-6605	6	24	pn−2;qn	pn−2;qn	NOUN
ejpam-6605	6	25	=	=	SYM
ejpam-6605	6	26	2qn−1	2qn−1	PROPN
ejpam-6605	6	27	+	+	CCONJ
ejpam-6605	6	28	qn−2	qn−2	PROPN
ejpam-6605	6	29	,	,	PUNCT
ejpam-6605	6	30	where	where	SCONJ
ejpam-6605	6	31	n	n	PRON
ejpam-6605	6	32	≥	≥	NOUN
ejpam-6605	6	33	2	2	NUM
ejpam-6605	6	34	,	,	PUNCT
ejpam-6605	6	35	p0	p0	NOUN
ejpam-6605	6	36	=	=	SYM
ejpam-6605	6	37	0	0	NUM
ejpam-6605	6	38	,	,	PUNCT
ejpam-6605	6	39	p1	p1	NOUN
ejpam-6605	6	40	=	=	SYM
ejpam-6605	6	41	1	1	NUM
ejpam-6605	6	42	,	,	PUNCT
ejpam-6605	6	43	q0	q0	PROPN
ejpam-6605	6	44	=	=	PROPN
ejpam-6605	6	45	q1	q1	PROPN
ejpam-6605	6	46	=	=	SYM
ejpam-6605	6	47	1	1	NUM
ejpam-6605	6	48	.	.	NOUN
ejpam-6605	6	49	•	•	NUM
ejpam-6605	6	50	jacobsthal	jacobsthal	ADJ
ejpam-6605	6	51	and	and	CCONJ
ejpam-6605	6	52	jacobsthal	jacobsthal	ADJ
ejpam-6605	6	53	-	-	PUNCT
ejpam-6605	6	54	lucas	lucas	NOUN
ejpam-6605	6	55	numbers	number	NOUN
ejpam-6605	6	56	:	:	PUNCT
ejpam-6605	6	57	jn	jn	PROPN
ejpam-6605	6	58	=	=	PROPN
ejpam-6605	6	59	jn−1	jn−1	PROPN
ejpam-6605	6	60	+	+	CCONJ
ejpam-6605	6	61	2jn−2	2jn−2	NOUN
ejpam-6605	6	62	;	;	PUNCT
ejpam-6605	6	63	jn	jn	PROPN
ejpam-6605	6	64	=	=	PROPN
ejpam-6605	6	65	jn−1	jn−1	PROPN
ejpam-6605	6	66	+	+	CCONJ
ejpam-6605	6	67	2jn−2	2jn−2	NOUN
ejpam-6605	6	68	,	,	PUNCT
ejpam-6605	6	69	where	where	SCONJ
ejpam-6605	6	70	n	n	PRON
ejpam-6605	6	71	≥	≥	NOUN
ejpam-6605	6	72	2	2	NUM
ejpam-6605	6	73	,	,	PUNCT
ejpam-6605	6	74	j0	j0	PROPN
ejpam-6605	6	75	=	=	SYM
ejpam-6605	6	76	0	0	NUM
ejpam-6605	6	77	,	,	PUNCT
ejpam-6605	6	78	j1	j1	PROPN
ejpam-6605	6	79	=	=	SYM
ejpam-6605	6	80	1	1	NUM
ejpam-6605	6	81	,	,	PUNCT
ejpam-6605	6	82	j0	j0	PROPN
ejpam-6605	6	83	=	=	PROPN
ejpam-6605	6	84	j1	j1	PROPN
ejpam-6605	6	85	=	=	SYM
ejpam-6605	6	86	2	2	X
ejpam-6605	6	87	.	.	PUNCT
ejpam-6605	6	88	∗corresponding	∗corresponde	VERB
ejpam-6605	6	89	author	author	NOUN
ejpam-6605	6	90	.	.	PUNCT
ejpam-6605	7	1	∗corresponding	∗corresponde	VERB
ejpam-6605	7	2	author	author	NOUN
ejpam-6605	7	3	.	.	PUNCT
ejpam-6605	8	1	doi	doi	NOUN
ejpam-6605	8	2	:	:	PUNCT
ejpam-6605	8	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6605	https://doi.org/10.29020/nybg.ejpam.v18i4.6605	PROPN
ejpam-6605	8	4	email	email	NOUN
ejpam-6605	8	5	addresses	address	NOUN
ejpam-6605	8	6	:	:	PUNCT
ejpam-6605	8	7	shefa.bm@yu.edu.jo	shefa.bm@yu.edu.jo	PUNCT
ejpam-6605	8	8	(	(	PUNCT
ejpam-6605	8	9	sh	sh	PROPN
ejpam-6605	8	10	.	.	PROPN
ejpam-6605	8	11	a.	a.	PROPN
ejpam-6605	8	12	bani	bani	PROPN
ejpam-6605	8	13	melhem	melhem	PROPN
ejpam-6605	8	14	)	)	PUNCT
ejpam-6605	8	15	,	,	PUNCT
ejpam-6605	8	16	alaa.kateeb@yu.edu.jo	alaa.kateeb@yu.edu.jo	NOUN
ejpam-6605	8	17	(	(	PUNCT
ejpam-6605	8	18	al	al	PROPN
ejpam-6605	8	19	-	-	PUNCT
ejpam-6605	8	20	kateeb	kateeb	PROPN
ejpam-6605	8	21	)	)	PUNCT
ejpam-6605	8	22	,	,	PUNCT
ejpam-6605	8	23	afnand@yu.edu.jo	afnand@yu.edu.jo	PROPN
ejpam-6605	8	24	(	(	PUNCT
ejpam-6605	8	25	a.	a.	NOUN
ejpam-6605	8	26	dagher	dagher	PROPN
ejpam-6605	8	27	)	)	PUNCT
ejpam-6605	8	28	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6605	9	1	1	1	NUM
ejpam-6605	9	2	copyright	copyright	NOUN
ejpam-6605	9	3	:	:	PUNCT
ejpam-6605	9	4	©	©	PROPN
ejpam-6605	9	5	2025	2025	NUM
ejpam-6605	9	6	the	the	DET
ejpam-6605	9	7	author(s	author(s	NOUN
ejpam-6605	9	8	)	)	PUNCT
ejpam-6605	9	9	.	.	PUNCT
ejpam-6605	10	1	(	(	PUNCT
ejpam-6605	10	2	cc	cc	NOUN
ejpam-6605	10	3	by	by	ADP
ejpam-6605	10	4	-	-	PUNCT
ejpam-6605	10	5	nc	nc	PROPN
ejpam-6605	10	6	4.0	4.0	NUM
ejpam-6605	10	7	)	)	PUNCT
ejpam-6605	10	8	sh	sh	PROPN
ejpam-6605	10	9	.	.	PROPN
ejpam-6605	10	10	a.	a.	PROPN
ejpam-6605	10	11	bani	bani	PROPN
ejpam-6605	10	12	melhem	melhem	PROPN
ejpam-6605	10	13	,	,	PUNCT
ejpam-6605	10	14	al	al	PROPN
ejpam-6605	10	15	-	-	PUNCT
ejpam-6605	10	16	kateeb	kateeb	PROPN
ejpam-6605	10	17	,	,	PUNCT
ejpam-6605	10	18	a.	a.	PROPN
ejpam-6605	10	19	dagher	dagher	PROPN
ejpam-6605	10	20	/	/	SYM
ejpam-6605	10	21	eur	eur	PROPN
ejpam-6605	10	22	.	.	PUNCT
ejpam-6605	11	1	j.	j.	PROPN
ejpam-6605	11	2	pure	pure	PROPN
ejpam-6605	11	3	appl	appl	PROPN
ejpam-6605	11	4	.	.	PROPN
ejpam-6605	11	5	math	math	PROPN
ejpam-6605	11	6	,	,	PUNCT
ejpam-6605	11	7	18	18	NUM
ejpam-6605	11	8	(	(	PUNCT
ejpam-6605	11	9	4	4	NUM
ejpam-6605	11	10	)	)	PUNCT
ejpam-6605	11	11	(	(	PUNCT
ejpam-6605	11	12	2025	2025	NUM
ejpam-6605	11	13	)	)	PUNCT
ejpam-6605	11	14	,	,	PUNCT
ejpam-6605	11	15	6605	6605	NUM
ejpam-6605	11	16	2	2	NUM
ejpam-6605	11	17	of	of	ADP
ejpam-6605	11	18	15	15	NUM
ejpam-6605	11	19	all	all	PRON
ejpam-6605	11	20	listed	list	VERB
ejpam-6605	11	21	above	above	ADP
ejpam-6605	11	22	sequences	sequence	NOUN
ejpam-6605	11	23	satisfy	satisfy	VERB
ejpam-6605	11	24	a	a	DET
ejpam-6605	11	25	set	set	NOUN
ejpam-6605	11	26	of	of	ADP
ejpam-6605	11	27	common	common	ADJ
ejpam-6605	11	28	properties	property	NOUN
ejpam-6605	11	29	and	and	CCONJ
ejpam-6605	11	30	identities	identity	NOUN
ejpam-6605	11	31	,	,	PUNCT
ejpam-6605	11	32	for	for	ADP
ejpam-6605	11	33	example	example	NOUN
ejpam-6605	11	34	binet	binet	NOUN
ejpam-6605	11	35	formulas	formula	NOUN
ejpam-6605	11	36	,	,	PUNCT
ejpam-6605	11	37	catalan	catalan	NOUN
ejpam-6605	11	38	and	and	CCONJ
ejpam-6605	11	39	cassini	cassini	NOUN
ejpam-6605	11	40	’s	’s	PART
ejpam-6605	11	41	identities	identity	NOUN
ejpam-6605	11	42	.	.	PUNCT
ejpam-6605	12	1	recently	recently	ADV
ejpam-6605	12	2	,	,	PUNCT
ejpam-6605	12	3	these	these	DET
ejpam-6605	12	4	sequences	sequence	NOUN
ejpam-6605	12	5	were	be	AUX
ejpam-6605	12	6	generalized	generalize	VERB
ejpam-6605	12	7	or	or	CCONJ
ejpam-6605	12	8	extended	extend	VERB
ejpam-6605	12	9	by	by	ADP
ejpam-6605	12	10	many	many	ADJ
ejpam-6605	12	11	authors	author	NOUN
ejpam-6605	12	12	.	.	PUNCT
ejpam-6605	13	1	mersenne	mersenne	NOUN
ejpam-6605	13	2	numbers	number	NOUN
ejpam-6605	13	3	are	be	AUX
ejpam-6605	13	4	given	give	VERB
ejpam-6605	13	5	by	by	ADP
ejpam-6605	13	6	the	the	DET
ejpam-6605	13	7	formula	formula	NOUN
ejpam-6605	13	8	mn	mn	NOUN
ejpam-6605	13	9	=	=	SYM
ejpam-6605	13	10	2n	2n	NUM
ejpam-6605	14	1	−	−	NOUN
ejpam-6605	14	2	1	1	NUM
ejpam-6605	14	3	or	or	CCONJ
ejpam-6605	14	4	using	use	VERB
ejpam-6605	14	5	the	the	DET
ejpam-6605	14	6	recurrence	recurrence	NOUN
ejpam-6605	14	7	relation	relation	NOUN
ejpam-6605	14	8	mn+2	mn+2	PROPN
ejpam-6605	14	9	=	=	SYM
ejpam-6605	14	10	3mn+1−2mn	3mn+1−2mn	PROPN
ejpam-6605	14	11	,	,	PUNCT
ejpam-6605	14	12	where	where	SCONJ
ejpam-6605	14	13	n	n	X
ejpam-6605	14	14	≥	≥	NOUN
ejpam-6605	14	15	2,m0	2,m0	NUM
ejpam-6605	14	16	=	=	SYM
ejpam-6605	14	17	0	0	NUM
ejpam-6605	14	18	and	and	CCONJ
ejpam-6605	14	19	m1	m1	PROPN
ejpam-6605	14	20	=	=	SYM
ejpam-6605	14	21	1	1	X
ejpam-6605	14	22	.	.	PUNCT
ejpam-6605	15	1	also	also	ADV
ejpam-6605	15	2	,	,	PUNCT
ejpam-6605	15	3	fermat	fermat	PROPN
ejpam-6605	15	4	numbers	number	NOUN
ejpam-6605	15	5	are	be	AUX
ejpam-6605	15	6	given	give	VERB
ejpam-6605	15	7	by	by	ADP
ejpam-6605	15	8	fn	fn	NOUN
ejpam-6605	15	9	=	=	SYM
ejpam-6605	15	10	22	22	NUM
ejpam-6605	15	11	n	n	NUM
ejpam-6605	15	12	+1	+1	PROPN
ejpam-6605	15	13	.	.	PUNCT
ejpam-6605	16	1	next	next	ADV
ejpam-6605	16	2	we	we	PRON
ejpam-6605	16	3	define	define	VERB
ejpam-6605	16	4	the	the	DET
ejpam-6605	16	5	generalized	generalized	ADJ
ejpam-6605	16	6	mersenne	mersenne	NOUN
ejpam-6605	16	7	and	and	CCONJ
ejpam-6605	16	8	extended	extend	VERB
ejpam-6605	16	9	fermat	fermat	PROPN
ejpam-6605	16	10	numbers	number	NOUN
ejpam-6605	16	11	,	,	PUNCT
ejpam-6605	16	12	which	which	PRON
ejpam-6605	16	13	are	be	AUX
ejpam-6605	16	14	the	the	DET
ejpam-6605	16	15	main	main	ADJ
ejpam-6605	16	16	interests	interest	NOUN
ejpam-6605	16	17	of	of	ADP
ejpam-6605	16	18	this	this	DET
ejpam-6605	16	19	paper	paper	NOUN
ejpam-6605	16	20	.	.	PUNCT
ejpam-6605	17	1	definition	definition	NOUN
ejpam-6605	17	2	1	1	NUM
ejpam-6605	17	3	.	.	PUNCT
ejpam-6605	18	1	let	let	VERB
ejpam-6605	18	2	k	k	PROPN
ejpam-6605	18	3	≥	≥	PROPN
ejpam-6605	18	4	3	3	NUM
ejpam-6605	18	5	,	,	PUNCT
ejpam-6605	18	6	n	n	PRON
ejpam-6605	18	7	≥	≥	NOUN
ejpam-6605	18	8	2	2	NUM
ejpam-6605	18	9	be	be	AUX
ejpam-6605	18	10	two	two	NUM
ejpam-6605	18	11	integers	integer	NOUN
ejpam-6605	18	12	.	.	PUNCT
ejpam-6605	19	1	we	we	PRON
ejpam-6605	19	2	define	define	VERB
ejpam-6605	19	3	the	the	DET
ejpam-6605	19	4	generalized	generalized	ADJ
ejpam-6605	19	5	mersenne	mersenne	NOUN
ejpam-6605	19	6	and	and	CCONJ
ejpam-6605	19	7	extended	extend	VERB
ejpam-6605	19	8	fermat	fermat	PROPN
ejpam-6605	19	9	numbers	number	NOUN
ejpam-6605	19	10	respectively	respectively	ADV
ejpam-6605	19	11	by	by	ADP
ejpam-6605	19	12	mk	mk	PROPN
ejpam-6605	19	13	,	,	PUNCT
ejpam-6605	19	14	n	n	PROPN
ejpam-6605	19	15	=	=	SYM
ejpam-6605	19	16	kmk	kmk	PROPN
ejpam-6605	19	17	,	,	PUNCT
ejpam-6605	19	18	n−1	n−1	PROPN
ejpam-6605	19	19	+	+	CCONJ
ejpam-6605	19	20	(	(	PUNCT
ejpam-6605	19	21	1	1	NUM
ejpam-6605	19	22	−	−	PROPN
ejpam-6605	19	23	k)mk	k)mk	PROPN
ejpam-6605	19	24	,	,	PUNCT
ejpam-6605	19	25	n−2	n−2	PROPN
ejpam-6605	19	26	,	,	PUNCT
ejpam-6605	19	27	fk	fk	INTJ
ejpam-6605	19	28	,	,	PUNCT
ejpam-6605	19	29	n	n	PROPN
ejpam-6605	19	30	=	=	SYM
ejpam-6605	19	31	kfk	kfk	NOUN
ejpam-6605	19	32	,	,	PUNCT
ejpam-6605	19	33	n−1	n−1	PROPN
ejpam-6605	19	34	+	+	CCONJ
ejpam-6605	19	35	(	(	PUNCT
ejpam-6605	19	36	1	1	NUM
ejpam-6605	19	37	−	−	PROPN
ejpam-6605	19	38	k)fk	k)fk	PROPN
ejpam-6605	19	39	,	,	PUNCT
ejpam-6605	19	40	n−2	n−2	PROPN
ejpam-6605	19	41	where	where	SCONJ
ejpam-6605	19	42	mk,0	mk,0	PROPN
ejpam-6605	19	43	=	=	PROPN
ejpam-6605	19	44	0,mk,1	0,mk,1	SYM
ejpam-6605	19	45	=	=	SYM
ejpam-6605	19	46	1	1	NUM
ejpam-6605	19	47	and	and	CCONJ
ejpam-6605	19	48	fk,0	fk,0	PROPN
ejpam-6605	19	49	=	=	SYM
ejpam-6605	19	50	2	2	NUM
ejpam-6605	19	51	,	,	PUNCT
ejpam-6605	19	52	fk,1	fk,1	NOUN
ejpam-6605	19	53	=	=	SYM
ejpam-6605	19	54	3	3	X
ejpam-6605	19	55	.	.	NOUN
ejpam-6605	19	56	remark	remark	NOUN
ejpam-6605	19	57	1	1	NUM
ejpam-6605	19	58	.	.	PUNCT
ejpam-6605	20	1	the	the	DET
ejpam-6605	20	2	sequence	sequence	NOUN
ejpam-6605	20	3	mk	mk	PROPN
ejpam-6605	20	4	,	,	PUNCT
ejpam-6605	20	5	n	n	PRON
ejpam-6605	20	6	was	be	AUX
ejpam-6605	20	7	introduced	introduce	VERB
ejpam-6605	20	8	and	and	CCONJ
ejpam-6605	20	9	studied	study	VERB
ejpam-6605	20	10	before	before	ADV
ejpam-6605	20	11	in	in	ADP
ejpam-6605	20	12	[	[	X
ejpam-6605	20	13	6	6	NUM
ejpam-6605	20	14	]	]	PUNCT
ejpam-6605	20	15	.	.	PUNCT
ejpam-6605	21	1	the	the	DET
ejpam-6605	21	2	search	search	NOUN
ejpam-6605	21	3	for	for	ADP
ejpam-6605	21	4	mersenne	mersenne	NOUN
ejpam-6605	21	5	primes	prime	NOUN
ejpam-6605	21	6	is	be	AUX
ejpam-6605	21	7	an	an	DET
ejpam-6605	21	8	active	active	ADJ
ejpam-6605	21	9	field	field	NOUN
ejpam-6605	21	10	in	in	ADP
ejpam-6605	21	11	number	number	NOUN
ejpam-6605	21	12	theory	theory	NOUN
ejpam-6605	21	13	,	,	PUNCT
ejpam-6605	21	14	since	since	SCONJ
ejpam-6605	21	15	each	each	DET
ejpam-6605	21	16	even	even	ADV
ejpam-6605	21	17	perfect	perfect	ADJ
ejpam-6605	21	18	number	number	NOUN
ejpam-6605	21	19	equals	equal	VERB
ejpam-6605	21	20	2k−1mk	2k−1mk	PROPN
ejpam-6605	21	21	,	,	PUNCT
ejpam-6605	21	22	where	where	SCONJ
ejpam-6605	21	23	mk	mk	PROPN
ejpam-6605	21	24	is	be	AUX
ejpam-6605	21	25	a	a	DET
ejpam-6605	21	26	prime	prime	ADJ
ejpam-6605	21	27	mersenne	mersenne	NOUN
ejpam-6605	21	28	number	number	NOUN
ejpam-6605	21	29	.	.	PUNCT
ejpam-6605	22	1	fermat	fermat	PROPN
ejpam-6605	22	2	primes	prime	NOUN
ejpam-6605	22	3	are	be	AUX
ejpam-6605	22	4	useful	useful	ADJ
ejpam-6605	22	5	in	in	ADP
ejpam-6605	22	6	generating	generate	VERB
ejpam-6605	22	7	pseudo	pseudo	NOUN
ejpam-6605	22	8	-	-	ADJ
ejpam-6605	22	9	random	random	ADJ
ejpam-6605	22	10	sequences	sequence	NOUN
ejpam-6605	22	11	of	of	ADP
ejpam-6605	22	12	numbers	number	NOUN
ejpam-6605	22	13	an	an	DET
ejpam-6605	22	14	important	important	ADJ
ejpam-6605	22	15	application	application	NOUN
ejpam-6605	22	16	in	in	ADP
ejpam-6605	22	17	computer	computer	NOUN
ejpam-6605	22	18	science	science	NOUN
ejpam-6605	22	19	and	and	CCONJ
ejpam-6605	22	20	cryptography	cryptography	NOUN
ejpam-6605	22	21	,	,	PUNCT
ejpam-6605	22	22	also	also	ADV
ejpam-6605	22	23	they	they	PRON
ejpam-6605	22	24	are	be	AUX
ejpam-6605	22	25	important	important	ADJ
ejpam-6605	22	26	for	for	ADP
ejpam-6605	22	27	some	some	DET
ejpam-6605	22	28	integer	integer	NOUN
ejpam-6605	22	29	factorization	factorization	NOUN
ejpam-6605	22	30	algorithms	algorithm	NOUN
ejpam-6605	22	31	like	like	ADP
ejpam-6605	22	32	in	in	ADP
ejpam-6605	22	33	[	[	X
ejpam-6605	22	34	7	7	NUM
ejpam-6605	22	35	,	,	PUNCT
ejpam-6605	22	36	8	8	NUM
ejpam-6605	22	37	]	]	PUNCT
ejpam-6605	22	38	,	,	PUNCT
ejpam-6605	22	39	the	the	DET
ejpam-6605	22	40	new	new	ADJ
ejpam-6605	22	41	defined	define	VERB
ejpam-6605	22	42	sequences	sequence	NOUN
ejpam-6605	22	43	maybe	maybe	ADV
ejpam-6605	22	44	used	use	VERB
ejpam-6605	22	45	to	to	PART
ejpam-6605	22	46	improve	improve	VERB
ejpam-6605	22	47	such	such	ADJ
ejpam-6605	22	48	algorithms	algorithm	NOUN
ejpam-6605	22	49	.	.	PUNCT
ejpam-6605	23	1	in	in	ADP
ejpam-6605	23	2	this	this	DET
ejpam-6605	23	3	paper	paper	NOUN
ejpam-6605	23	4	we	we	PRON
ejpam-6605	23	5	introduce	introduce	VERB
ejpam-6605	23	6	and	and	CCONJ
ejpam-6605	23	7	study	study	VERB
ejpam-6605	23	8	a	a	DET
ejpam-6605	23	9	generalization	generalization	NOUN
ejpam-6605	23	10	to	to	ADP
ejpam-6605	23	11	the	the	DET
ejpam-6605	23	12	mersenne	mersenne	NOUN
ejpam-6605	23	13	and	and	CCONJ
ejpam-6605	23	14	extended	extend	VERB
ejpam-6605	23	15	fermat	fermat	PROPN
ejpam-6605	23	16	numbers	number	NOUN
ejpam-6605	23	17	.	.	PUNCT
ejpam-6605	24	1	this	this	DET
ejpam-6605	24	2	paper	paper	NOUN
ejpam-6605	24	3	is	be	AUX
ejpam-6605	24	4	structured	structure	VERB
ejpam-6605	24	5	as	as	SCONJ
ejpam-6605	24	6	follows	follow	VERB
ejpam-6605	24	7	in	in	ADP
ejpam-6605	24	8	section	section	NOUN
ejpam-6605	24	9	2	2	NUM
ejpam-6605	24	10	we	we	PRON
ejpam-6605	24	11	introduce	introduce	VERB
ejpam-6605	24	12	the	the	DET
ejpam-6605	24	13	generalized	generalized	ADJ
ejpam-6605	24	14	mersenne	mersenne	NOUN
ejpam-6605	24	15	and	and	CCONJ
ejpam-6605	24	16	extended	extend	VERB
ejpam-6605	24	17	fermat	fermat	PROPN
ejpam-6605	24	18	numbers	number	NOUN
ejpam-6605	24	19	and	and	CCONJ
ejpam-6605	24	20	derive	derive	VERB
ejpam-6605	24	21	their	their	PRON
ejpam-6605	24	22	generating	generating	NOUN
ejpam-6605	24	23	functions	function	NOUN
ejpam-6605	24	24	and	and	CCONJ
ejpam-6605	24	25	binet	binet	NOUN
ejpam-6605	24	26	formulas	formula	NOUN
ejpam-6605	24	27	,	,	PUNCT
ejpam-6605	24	28	in	in	ADP
ejpam-6605	24	29	section	section	NOUN
ejpam-6605	24	30	3	3	NUM
ejpam-6605	24	31	we	we	PRON
ejpam-6605	24	32	find	find	VERB
ejpam-6605	24	33	more	more	ADJ
ejpam-6605	24	34	other	other	ADJ
ejpam-6605	24	35	properties	property	NOUN
ejpam-6605	24	36	,	,	PUNCT
ejpam-6605	24	37	in	in	ADP
ejpam-6605	24	38	section	section	NOUN
ejpam-6605	24	39	4	4	NUM
ejpam-6605	24	40	we	we	PRON
ejpam-6605	24	41	find	find	VERB
ejpam-6605	24	42	the	the	DET
ejpam-6605	24	43	generating	generate	VERB
ejpam-6605	24	44	matrices	matrix	NOUN
ejpam-6605	24	45	of	of	ADP
ejpam-6605	24	46	the	the	DET
ejpam-6605	24	47	generalized	generalized	ADJ
ejpam-6605	24	48	mersenne	mersenne	NOUN
ejpam-6605	24	49	and	and	CCONJ
ejpam-6605	24	50	extended	extend	VERB
ejpam-6605	24	51	fermat	fermat	PROPN
ejpam-6605	24	52	numbers	number	NOUN
ejpam-6605	24	53	,	,	PUNCT
ejpam-6605	24	54	also	also	ADV
ejpam-6605	24	55	we	we	PRON
ejpam-6605	24	56	present	present	VERB
ejpam-6605	24	57	some	some	DET
ejpam-6605	24	58	results	result	NOUN
ejpam-6605	24	59	involving	involve	VERB
ejpam-6605	24	60	mersenne	mersenne	NOUN
ejpam-6605	24	61	numbers	number	NOUN
ejpam-6605	24	62	and	and	CCONJ
ejpam-6605	24	63	some	some	DET
ejpam-6605	24	64	tridiagonal	tridiagonal	ADJ
ejpam-6605	24	65	and	and	CCONJ
ejpam-6605	24	66	hessenberg	hessenberg	NOUN
ejpam-6605	24	67	matrices	matrix	NOUN
ejpam-6605	24	68	,	,	PUNCT
ejpam-6605	24	69	finally	finally	ADV
ejpam-6605	24	70	,	,	PUNCT
ejpam-6605	24	71	in	in	ADP
ejpam-6605	24	72	the	the	DET
ejpam-6605	24	73	last	last	ADJ
ejpam-6605	24	74	section	section	NOUN
ejpam-6605	24	75	we	we	PRON
ejpam-6605	24	76	gave	give	VERB
ejpam-6605	24	77	two	two	NUM
ejpam-6605	24	78	applications	application	NOUN
ejpam-6605	24	79	of	of	ADP
ejpam-6605	24	80	the	the	DET
ejpam-6605	24	81	generalized	generalized	ADJ
ejpam-6605	24	82	mersenne	mersenne	NOUN
ejpam-6605	24	83	numbers	number	NOUN
ejpam-6605	24	84	matrices	matrix	NOUN
ejpam-6605	24	85	in	in	ADP
ejpam-6605	24	86	cryptography	cryptography	NOUN
ejpam-6605	24	87	,	,	PUNCT
ejpam-6605	24	88	namely	namely	ADV
ejpam-6605	24	89	we	we	PRON
ejpam-6605	24	90	present	present	VERB
ejpam-6605	24	91	a	a	DET
ejpam-6605	24	92	key	key	ADJ
ejpam-6605	24	93	-	-	PUNCT
ejpam-6605	24	94	exchange	exchange	NOUN
ejpam-6605	24	95	protocol	protocol	NOUN
ejpam-6605	24	96	and	and	CCONJ
ejpam-6605	24	97	an	an	DET
ejpam-6605	24	98	authentication	authentication	NOUN
ejpam-6605	24	99	scheme	scheme	NOUN
ejpam-6605	24	100	using	use	VERB
ejpam-6605	24	101	matrices	matrix	NOUN
ejpam-6605	24	102	.	.	PUNCT
ejpam-6605	25	1	2	2	X
ejpam-6605	25	2	.	.	X
ejpam-6605	25	3	basic	basic	ADJ
ejpam-6605	25	4	properties	property	NOUN
ejpam-6605	25	5	theorem	theorem	VERB
ejpam-6605	25	6	1	1	NUM
ejpam-6605	25	7	(	(	PUNCT
ejpam-6605	25	8	generating	generating	NOUN
ejpam-6605	25	9	functions	function	NOUN
ejpam-6605	25	10	)	)	PUNCT
ejpam-6605	25	11	.	.	PUNCT
ejpam-6605	26	1	the	the	DET
ejpam-6605	26	2	generating	generate	VERB
ejpam-6605	26	3	functions	function	NOUN
ejpam-6605	26	4	of	of	ADP
ejpam-6605	26	5	the	the	DET
ejpam-6605	26	6	sequences	sequence	NOUN
ejpam-6605	26	7	mk	mk	PROPN
ejpam-6605	26	8	,	,	PUNCT
ejpam-6605	26	9	n	n	PROPN
ejpam-6605	26	10	and	and	CCONJ
ejpam-6605	26	11	fk	fk	INTJ
ejpam-6605	26	12	,	,	PUNCT
ejpam-6605	26	13	n	n	CCONJ
ejpam-6605	26	14	respectively	respectively	ADV
ejpam-6605	26	15	are	be	AUX
ejpam-6605	26	16	(	(	PUNCT
ejpam-6605	26	17	i	i	NOUN
ejpam-6605	26	18	)	)	PUNCT
ejpam-6605	26	19	m(x	m(x	PROPN
ejpam-6605	26	20	)	)	PUNCT
ejpam-6605	27	1	=	=	PUNCT
ejpam-6605	27	2	x	x	SYM
ejpam-6605	27	3	1−kx+(k−1)x2	1−kx+(k−1)x2	NUM
ejpam-6605	27	4	(	(	PUNCT
ejpam-6605	27	5	ii	ii	PROPN
ejpam-6605	27	6	)	)	PUNCT
ejpam-6605	27	7	f	f	PROPN
ejpam-6605	27	8	(	(	PUNCT
ejpam-6605	27	9	x	x	X
ejpam-6605	27	10	)	)	PUNCT
ejpam-6605	27	11	=	=	SYM
ejpam-6605	28	1	2+(3−2k)x	2+(3−2k)x	NUM
ejpam-6605	28	2	1−kx+(k−1)x2	1−kx+(k−1)x2	NUM
ejpam-6605	28	3	proof	proof	NOUN
ejpam-6605	28	4	.	.	PUNCT
ejpam-6605	29	1	let	let	VERB
ejpam-6605	29	2	m(x	m(x	PROPN
ejpam-6605	29	3	)	)	PUNCT
ejpam-6605	29	4	represents	represent	VERB
ejpam-6605	29	5	the	the	DET
ejpam-6605	29	6	generating	generate	VERB
ejpam-6605	29	7	functions	function	NOUN
ejpam-6605	29	8	of	of	ADP
ejpam-6605	29	9	mk	mk	PROPN
ejpam-6605	29	10	,	,	PUNCT
ejpam-6605	29	11	n.	n.	PROPN
ejpam-6605	29	12	note	note	NOUN
ejpam-6605	29	13	,	,	PUNCT
ejpam-6605	29	14	m(x	m(x	PROPN
ejpam-6605	29	15	)	)	PUNCT
ejpam-6605	30	1	=	=	PUNCT
ejpam-6605	31	1	∞∑	∞∑	NUM
ejpam-6605	31	2	n=0	n=0	NUM
ejpam-6605	31	3	mk	mk	NOUN
ejpam-6605	31	4	,	,	PUNCT
ejpam-6605	31	5	nx	nx	PROPN
ejpam-6605	31	6	n	n	PROPN
ejpam-6605	31	7	sh	sh	PROPN
ejpam-6605	31	8	.	.	PROPN
ejpam-6605	31	9	a.	a.	PROPN
ejpam-6605	31	10	bani	bani	PROPN
ejpam-6605	31	11	melhem	melhem	PROPN
ejpam-6605	31	12	,	,	PUNCT
ejpam-6605	31	13	al	al	PROPN
ejpam-6605	31	14	-	-	PUNCT
ejpam-6605	31	15	kateeb	kateeb	PROPN
ejpam-6605	31	16	,	,	PUNCT
ejpam-6605	31	17	a.	a.	PROPN
ejpam-6605	31	18	dagher	dagher	PROPN
ejpam-6605	31	19	/	/	SYM
ejpam-6605	31	20	eur	eur	PROPN
ejpam-6605	31	21	.	.	PUNCT
ejpam-6605	32	1	j.	j.	PROPN
ejpam-6605	32	2	pure	pure	PROPN
ejpam-6605	32	3	appl	appl	PROPN
ejpam-6605	32	4	.	.	PROPN
ejpam-6605	32	5	math	math	PROPN
ejpam-6605	32	6	,	,	PUNCT
ejpam-6605	32	7	18	18	NUM
ejpam-6605	32	8	(	(	PUNCT
ejpam-6605	32	9	4	4	NUM
ejpam-6605	32	10	)	)	PUNCT
ejpam-6605	32	11	(	(	PUNCT
ejpam-6605	32	12	2025	2025	NUM
ejpam-6605	32	13	)	)	PUNCT
ejpam-6605	32	14	,	,	PUNCT
ejpam-6605	32	15	6605	6605	NUM
ejpam-6605	32	16	3	3	NUM
ejpam-6605	32	17	of	of	ADP
ejpam-6605	32	18	15	15	NUM
ejpam-6605	32	19	=	=	SYM
ejpam-6605	32	20	mk,0	mk,0	PROPN
ejpam-6605	32	21	+	+	CCONJ
ejpam-6605	32	22	mk,1x	mk,1x	NOUN
ejpam-6605	32	23	+	+	CCONJ
ejpam-6605	32	24	∞∑	∞∑	PROPN
ejpam-6605	32	25	n=2	n=2	X
ejpam-6605	32	26	mk	mk	NOUN
ejpam-6605	32	27	,	,	PUNCT
ejpam-6605	32	28	nx	nx	PROPN
ejpam-6605	32	29	n	n	NOUN
ejpam-6605	32	30	=	=	SYM
ejpam-6605	32	31	x	x	NOUN
ejpam-6605	33	1	+	+	CCONJ
ejpam-6605	33	2	∞∑	∞∑	NUM
ejpam-6605	33	3	n=2	n=2	PRON
ejpam-6605	33	4	(	(	PUNCT
ejpam-6605	33	5	kmk	kmk	PROPN
ejpam-6605	33	6	,	,	PUNCT
ejpam-6605	33	7	n−1	n−1	PROPN
ejpam-6605	33	8	+	+	CCONJ
ejpam-6605	33	9	(	(	PUNCT
ejpam-6605	33	10	1	1	NUM
ejpam-6605	33	11	−	−	PROPN
ejpam-6605	33	12	k)mk	k)mk	PROPN
ejpam-6605	33	13	,	,	PUNCT
ejpam-6605	33	14	n−2)x	n−2)x	ADV
ejpam-6605	33	15	n	n	NOUN
ejpam-6605	33	16	=	=	SYM
ejpam-6605	33	17	x	x	PROPN
ejpam-6605	34	1	+	+	NUM
ejpam-6605	34	2	kx	kx	PROPN
ejpam-6605	34	3	∞∑	∞∑	ADJ
ejpam-6605	34	4	n=0	n=0	PROPN
ejpam-6605	34	5	mk	mk	PROPN
ejpam-6605	34	6	,	,	PUNCT
ejpam-6605	34	7	nx	nx	PROPN
ejpam-6605	34	8	n	n	NOUN
ejpam-6605	34	9	+	+	CCONJ
ejpam-6605	34	10	(	(	PUNCT
ejpam-6605	34	11	1	1	NUM
ejpam-6605	34	12	−	−	PROPN
ejpam-6605	34	13	k)x2	k)x2	PROPN
ejpam-6605	34	14	∞∑	∞∑	PROPN
ejpam-6605	34	15	n=0	n=0	PROPN
ejpam-6605	34	16	mk	mk	NOUN
ejpam-6605	34	17	,	,	PUNCT
ejpam-6605	34	18	nx	nx	PROPN
ejpam-6605	34	19	n	n	PRON
ejpam-6605	34	20	thus	thus	ADV
ejpam-6605	34	21	,	,	PUNCT
ejpam-6605	34	22	x	x	SYM
ejpam-6605	34	23	=	=	SYM
ejpam-6605	34	24	(	(	PUNCT
ejpam-6605	34	25	1−	1−	NUM
ejpam-6605	34	26	kx−	kx−	X
ejpam-6605	34	27	(	(	PUNCT
ejpam-6605	34	28	1−	1−	NUM
ejpam-6605	34	29	k)x2)m(x	k)x2)m(x	PROPN
ejpam-6605	34	30	)	)	PUNCT
ejpam-6605	34	31	⇒	⇒	NOUN
ejpam-6605	34	32	m(x	m(x	PROPN
ejpam-6605	34	33	)	)	PUNCT
ejpam-6605	35	1	=	=	PUNCT
ejpam-6605	35	2	x	x	SYM
ejpam-6605	36	1	1−kx+(k−1)x2	1−kx+(k−1)x2	X
ejpam-6605	36	2	.	.	PUNCT
ejpam-6605	37	1	similarly	similarly	ADV
ejpam-6605	37	2	we	we	PRON
ejpam-6605	37	3	can	can	AUX
ejpam-6605	37	4	prove	prove	VERB
ejpam-6605	37	5	the	the	DET
ejpam-6605	37	6	theorem	theorem	NOUN
ejpam-6605	37	7	for	for	ADP
ejpam-6605	37	8	f	f	PROPN
ejpam-6605	37	9	(	(	PUNCT
ejpam-6605	37	10	x	x	NOUN
ejpam-6605	37	11	)	)	PUNCT
ejpam-6605	37	12	.	.	PUNCT
ejpam-6605	38	1	f	f	PROPN
ejpam-6605	38	2	(	(	PUNCT
ejpam-6605	38	3	x	x	X
ejpam-6605	38	4	)	)	PUNCT
ejpam-6605	38	5	=	=	PUNCT
ejpam-6605	39	1	∞∑	∞∑	PROPN
ejpam-6605	39	2	n=0	n=0	NUM
ejpam-6605	39	3	fk	fk	INTJ
ejpam-6605	39	4	,	,	PUNCT
ejpam-6605	39	5	nx	nx	PROPN
ejpam-6605	39	6	n	n	PROPN
ejpam-6605	39	7	=	=	PROPN
ejpam-6605	39	8	fk,0	fk,0	PROPN
ejpam-6605	39	9	+	+	CCONJ
ejpam-6605	39	10	fk,1x	fk,1x	NUM
ejpam-6605	39	11	+	+	NOUN
ejpam-6605	39	12	∞∑	∞∑	PROPN
ejpam-6605	39	13	n=2	n=2	X
ejpam-6605	39	14	fk	fk	INTJ
ejpam-6605	39	15	,	,	PUNCT
ejpam-6605	39	16	nx	nx	PROPN
ejpam-6605	39	17	n	n	NOUN
ejpam-6605	39	18	=	=	SYM
ejpam-6605	39	19	2	2	NUM
ejpam-6605	39	20	+	+	NUM
ejpam-6605	39	21	3x	3x	PRON
ejpam-6605	39	22	+	+	CCONJ
ejpam-6605	39	23	∞∑	∞∑	NUM
ejpam-6605	39	24	n=2	n=2	PRON
ejpam-6605	39	25	(	(	PUNCT
ejpam-6605	39	26	kfk	kfk	NOUN
ejpam-6605	39	27	,	,	PUNCT
ejpam-6605	39	28	n−1	n−1	PROPN
ejpam-6605	39	29	+	+	CCONJ
ejpam-6605	39	30	(	(	PUNCT
ejpam-6605	39	31	1	1	NUM
ejpam-6605	39	32	−	−	PROPN
ejpam-6605	39	33	k)fk	k)fk	PROPN
ejpam-6605	39	34	,	,	PUNCT
ejpam-6605	39	35	n−2)x	n−2)x	ADV
ejpam-6605	39	36	n	n	NOUN
ejpam-6605	39	37	=	=	SYM
ejpam-6605	39	38	2	2	NUM
ejpam-6605	39	39	+	+	CCONJ
ejpam-6605	39	40	3x−	3x−	NUM
ejpam-6605	39	41	2kx	2kx	NOUN
ejpam-6605	40	1	+	+	CCONJ
ejpam-6605	40	2	kx	kx	PROPN
ejpam-6605	40	3	∞∑	∞∑	PRON
ejpam-6605	40	4	n=0	n=0	PROPN
ejpam-6605	40	5	fk	fk	INTJ
ejpam-6605	40	6	,	,	PUNCT
ejpam-6605	40	7	nx	nx	PROPN
ejpam-6605	40	8	n	n	NOUN
ejpam-6605	40	9	+	+	CCONJ
ejpam-6605	40	10	(	(	PUNCT
ejpam-6605	40	11	1	1	NUM
ejpam-6605	40	12	−	−	PROPN
ejpam-6605	41	1	k)x2	k)x2	PROPN
ejpam-6605	41	2	∞∑	∞∑	PROPN
ejpam-6605	41	3	n=0	n=0	PROPN
ejpam-6605	41	4	fk	fk	INTJ
ejpam-6605	41	5	,	,	PUNCT
ejpam-6605	41	6	nx	nx	PROPN
ejpam-6605	41	7	n	n	PRON
ejpam-6605	41	8	thus	thus	ADV
ejpam-6605	41	9	,	,	PUNCT
ejpam-6605	41	10	2	2	NUM
ejpam-6605	41	11	+	+	CCONJ
ejpam-6605	41	12	(	(	PUNCT
ejpam-6605	41	13	3	3	NUM
ejpam-6605	41	14	−	−	PROPN
ejpam-6605	41	15	2k)x	2k)x	NUM
ejpam-6605	41	16	=	=	SYM
ejpam-6605	41	17	(	(	PUNCT
ejpam-6605	41	18	1	1	NUM
ejpam-6605	41	19	−	−	PROPN
ejpam-6605	41	20	kx−	kx−	X
ejpam-6605	41	21	(	(	PUNCT
ejpam-6605	41	22	1	1	NUM
ejpam-6605	41	23	−	−	PROPN
ejpam-6605	41	24	k)x2)f	k)x2)f	NOUN
ejpam-6605	41	25	(	(	PUNCT
ejpam-6605	41	26	x	x	NOUN
ejpam-6605	41	27	)	)	PUNCT
ejpam-6605	41	28	⇒	⇒	PROPN
ejpam-6605	41	29	f	f	PROPN
ejpam-6605	41	30	(	(	PUNCT
ejpam-6605	41	31	x	x	X
ejpam-6605	41	32	)	)	PUNCT
ejpam-6605	41	33	=	=	SYM
ejpam-6605	41	34	2+(3−2k)x	2+(3−2k)x	NUM
ejpam-6605	41	35	1−kx+(k−1)x2	1−kx+(k−1)x2	NUM
ejpam-6605	41	36	.	.	PUNCT
ejpam-6605	42	1	theorem	theorem	ADJ
ejpam-6605	42	2	2	2	NUM
ejpam-6605	42	3	(	(	PUNCT
ejpam-6605	42	4	binet	binet	NOUN
ejpam-6605	42	5	formula	formula	NOUN
ejpam-6605	42	6	)	)	PUNCT
ejpam-6605	42	7	.	.	PUNCT
ejpam-6605	43	1	the	the	DET
ejpam-6605	43	2	n	n	ADV
ejpam-6605	43	3	-	-	PUNCT
ejpam-6605	43	4	th	th	NOUN
ejpam-6605	43	5	terms	term	NOUN
ejpam-6605	43	6	of	of	ADP
ejpam-6605	43	7	the	the	DET
ejpam-6605	43	8	generalized	generalized	ADJ
ejpam-6605	43	9	mersenne	mersenne	NOUN
ejpam-6605	43	10	and	and	CCONJ
ejpam-6605	43	11	extended	extend	VERB
ejpam-6605	43	12	fermat	fermat	PROPN
ejpam-6605	43	13	sequences	sequence	NOUN
ejpam-6605	43	14	are	be	AUX
ejpam-6605	43	15	given	give	VERB
ejpam-6605	43	16	by	by	ADP
ejpam-6605	43	17	mk	mk	PROPN
ejpam-6605	43	18	,	,	PUNCT
ejpam-6605	43	19	n	n	NOUN
ejpam-6605	43	20	=	=	SYM
ejpam-6605	43	21	(	(	PUNCT
ejpam-6605	43	22	k	k	X
ejpam-6605	43	23	−	−	PROPN
ejpam-6605	43	24	1)n	1)n	NUM
ejpam-6605	43	25	−	−	PROPN
ejpam-6605	43	26	1	1	NUM
ejpam-6605	43	27	k	k	NOUN
ejpam-6605	43	28	−	−	PROPN
ejpam-6605	43	29	2	2	NUM
ejpam-6605	43	30	and	and	CCONJ
ejpam-6605	43	31	fk	fk	INTJ
ejpam-6605	43	32	,	,	PUNCT
ejpam-6605	43	33	n	n	NOUN
ejpam-6605	43	34	=	=	SYM
ejpam-6605	43	35	(	(	PUNCT
ejpam-6605	43	36	k	k	NOUN
ejpam-6605	43	37	−	−	PROPN
ejpam-6605	43	38	1)n	1)n	PROPN
ejpam-6605	43	39	+	+	PUNCT
ejpam-6605	43	40	2k	2k	NUM
ejpam-6605	43	41	−	−	NUM
ejpam-6605	43	42	5	5	NUM
ejpam-6605	44	1	k	k	NOUN
ejpam-6605	44	2	−	−	NOUN
ejpam-6605	44	3	2	2	NUM
ejpam-6605	44	4	proof	proof	NOUN
ejpam-6605	44	5	.	.	PUNCT
ejpam-6605	45	1	a	a	DET
ejpam-6605	45	2	proof	proof	NOUN
ejpam-6605	45	3	for	for	ADP
ejpam-6605	45	4	mk	mk	PROPN
ejpam-6605	45	5	,	,	PUNCT
ejpam-6605	45	6	n	n	PRON
ejpam-6605	45	7	can	can	AUX
ejpam-6605	45	8	be	be	AUX
ejpam-6605	45	9	found	find	VERB
ejpam-6605	45	10	in	in	ADP
ejpam-6605	45	11	[	[	X
ejpam-6605	45	12	6	6	NUM
ejpam-6605	45	13	]	]	PUNCT
ejpam-6605	45	14	,	,	PUNCT
ejpam-6605	45	15	the	the	DET
ejpam-6605	45	16	formula	formula	NOUN
ejpam-6605	45	17	for	for	ADP
ejpam-6605	45	18	fk	fk	INTJ
ejpam-6605	45	19	,	,	PUNCT
ejpam-6605	45	20	n	n	PRON
ejpam-6605	45	21	can	can	AUX
ejpam-6605	45	22	be	be	AUX
ejpam-6605	45	23	proved	prove	VERB
ejpam-6605	45	24	easily	easily	ADV
ejpam-6605	45	25	by	by	ADP
ejpam-6605	45	26	induction	induction	NOUN
ejpam-6605	45	27	.	.	PUNCT
ejpam-6605	46	1	proposition	proposition	NOUN
ejpam-6605	46	2	1	1	NUM
ejpam-6605	46	3	.	.	PUNCT
ejpam-6605	47	1	for	for	ADP
ejpam-6605	47	2	n	n	PROPN
ejpam-6605	47	3	>	>	SYM
ejpam-6605	47	4	1	1	NUM
ejpam-6605	47	5	we	we	PRON
ejpam-6605	47	6	have	have	VERB
ejpam-6605	47	7	fk	fk	INTJ
ejpam-6605	47	8	,	,	PUNCT
ejpam-6605	47	9	n	n	PROPN
ejpam-6605	47	10	=	=	SYM
ejpam-6605	47	11	mk	mk	PROPN
ejpam-6605	47	12	,	,	PUNCT
ejpam-6605	47	13	n	n	PROPN
ejpam-6605	47	14	+	+	CCONJ
ejpam-6605	47	15	2	2	NUM
ejpam-6605	47	16	proof	proof	NOUN
ejpam-6605	47	17	.	.	PUNCT
ejpam-6605	48	1	immediate	immediate	ADJ
ejpam-6605	48	2	from	from	ADP
ejpam-6605	48	3	the	the	DET
ejpam-6605	48	4	binet	binet	NOUN
ejpam-6605	48	5	formulas	formula	NOUN
ejpam-6605	48	6	.	.	PUNCT
ejpam-6605	49	1	theorem	theorem	ADJ
ejpam-6605	49	2	3	3	NUM
ejpam-6605	49	3	(	(	PUNCT
ejpam-6605	49	4	catalan	catalan	NOUN
ejpam-6605	49	5	’s	’s	PART
ejpam-6605	49	6	identity	identity	NOUN
ejpam-6605	49	7	)	)	PUNCT
ejpam-6605	49	8	.	.	PUNCT
ejpam-6605	50	1	we	we	PRON
ejpam-6605	50	2	have	have	VERB
ejpam-6605	50	3	sh	sh	PROPN
ejpam-6605	50	4	.	.	PUNCT
ejpam-6605	50	5	a.	a.	PROPN
ejpam-6605	50	6	bani	bani	PROPN
ejpam-6605	50	7	melhem	melhem	PROPN
ejpam-6605	50	8	,	,	PUNCT
ejpam-6605	50	9	al	al	PROPN
ejpam-6605	50	10	-	-	PUNCT
ejpam-6605	50	11	kateeb	kateeb	PROPN
ejpam-6605	50	12	,	,	PUNCT
ejpam-6605	50	13	a.	a.	PROPN
ejpam-6605	50	14	dagher	dagher	PROPN
ejpam-6605	50	15	/	/	SYM
ejpam-6605	50	16	eur	eur	PROPN
ejpam-6605	50	17	.	.	PUNCT
ejpam-6605	51	1	j.	j.	PROPN
ejpam-6605	51	2	pure	pure	PROPN
ejpam-6605	51	3	appl	appl	PROPN
ejpam-6605	51	4	.	.	PROPN
ejpam-6605	51	5	math	math	PROPN
ejpam-6605	51	6	,	,	PUNCT
ejpam-6605	51	7	18	18	NUM
ejpam-6605	51	8	(	(	PUNCT
ejpam-6605	51	9	4	4	NUM
ejpam-6605	51	10	)	)	PUNCT
ejpam-6605	51	11	(	(	PUNCT
ejpam-6605	51	12	2025	2025	NUM
ejpam-6605	51	13	)	)	PUNCT
ejpam-6605	51	14	,	,	PUNCT
ejpam-6605	51	15	6605	6605	NUM
ejpam-6605	51	16	4	4	NUM
ejpam-6605	51	17	of	of	ADP
ejpam-6605	51	18	15	15	NUM
ejpam-6605	51	19	•	•	NUM
ejpam-6605	51	20	mk	mk	PROPN
ejpam-6605	51	21	,	,	PUNCT
ejpam-6605	51	22	n−rmk	n−rmk	NOUN
ejpam-6605	51	23	,	,	PUNCT
ejpam-6605	51	24	n+r	n+r	PROPN
ejpam-6605	51	25	−m2	−m2	NOUN
ejpam-6605	51	26	k	k	NOUN
ejpam-6605	51	27	,	,	PUNCT
ejpam-6605	51	28	n	n	PROPN
ejpam-6605	51	29	=	=	PUNCT
ejpam-6605	51	30	−(k	−(k	PROPN
ejpam-6605	52	1	−	−	PROPN
ejpam-6605	52	2	1)n−rm2	1)n−rm2	PROPN
ejpam-6605	52	3	k	k	NOUN
ejpam-6605	52	4	,	,	PUNCT
ejpam-6605	52	5	r	r	NOUN
ejpam-6605	52	6	•	•	NUM
ejpam-6605	52	7	fk	fk	INTJ
ejpam-6605	52	8	,	,	PUNCT
ejpam-6605	52	9	n−rfk	n−rfk	NOUN
ejpam-6605	52	10	,	,	PUNCT
ejpam-6605	52	11	n+r	n+r	PROPN
ejpam-6605	52	12	−	−	PROPN
ejpam-6605	52	13	f	f	PROPN
ejpam-6605	52	14	2	2	NUM
ejpam-6605	52	15	k	k	NOUN
ejpam-6605	52	16	,	,	PUNCT
ejpam-6605	52	17	n	n	NOUN
ejpam-6605	52	18	=	=	SYM
ejpam-6605	52	19	(	(	PUNCT
ejpam-6605	52	20	2k	2k	NOUN
ejpam-6605	52	21	−	−	PROPN
ejpam-6605	52	22	5)(k	5)(k	NUM
ejpam-6605	52	23	−	−	PROPN
ejpam-6605	52	24	1)n−rm2	1)n−rm2	PROPN
ejpam-6605	52	25	k	k	NOUN
ejpam-6605	52	26	,	,	PUNCT
ejpam-6605	52	27	r	r	NOUN
ejpam-6605	52	28	proof	proof	NOUN
ejpam-6605	52	29	.	.	PUNCT
ejpam-6605	53	1	•	•	NUM
ejpam-6605	53	2	mk	mk	PROPN
ejpam-6605	53	3	,	,	PUNCT
ejpam-6605	53	4	n−rmk	n−rmk	NOUN
ejpam-6605	53	5	,	,	PUNCT
ejpam-6605	53	6	n+r	n+r	PROPN
ejpam-6605	53	7	−m2	−m2	NOUN
ejpam-6605	53	8	k	k	NOUN
ejpam-6605	53	9	,	,	PUNCT
ejpam-6605	53	10	n	n	NOUN
ejpam-6605	53	11	=	=	SYM
ejpam-6605	53	12	(	(	PUNCT
ejpam-6605	53	13	k	k	X
ejpam-6605	53	14	−	−	PROPN
ejpam-6605	53	15	1)n−r	1)n−r	NUM
ejpam-6605	53	16	−	−	NOUN
ejpam-6605	53	17	1	1	NUM
ejpam-6605	53	18	(	(	PUNCT
ejpam-6605	53	19	k	k	NOUN
ejpam-6605	53	20	−	−	PROPN
ejpam-6605	53	21	2	2	NUM
ejpam-6605	53	22	)	)	PUNCT
ejpam-6605	53	23	(	(	PUNCT
ejpam-6605	53	24	k	k	NOUN
ejpam-6605	53	25	−	−	PROPN
ejpam-6605	54	1	1)n+r	1)n+r	NOUN
ejpam-6605	54	2	−	−	NOUN
ejpam-6605	54	3	1	1	NUM
ejpam-6605	54	4	(	(	PUNCT
ejpam-6605	54	5	k	k	NOUN
ejpam-6605	54	6	−	−	PROPN
ejpam-6605	54	7	2	2	NUM
ejpam-6605	54	8	)	)	PUNCT
ejpam-6605	54	9	−	−	PROPN
ejpam-6605	54	10	(	(	PUNCT
ejpam-6605	54	11	(	(	PUNCT
ejpam-6605	54	12	k	k	X
ejpam-6605	54	13	−	−	PROPN
ejpam-6605	54	14	1)n	1)n	NUM
ejpam-6605	54	15	−	−	PROPN
ejpam-6605	54	16	1	1	NUM
ejpam-6605	54	17	(	(	PUNCT
ejpam-6605	54	18	k	k	NOUN
ejpam-6605	54	19	−	−	PROPN
ejpam-6605	54	20	2	2	NUM
ejpam-6605	54	21	)	)	PUNCT
ejpam-6605	54	22	)	)	PUNCT
ejpam-6605	54	23	2	2	NUM
ejpam-6605	54	24	=	=	SYM
ejpam-6605	54	25	(	(	PUNCT
ejpam-6605	54	26	k	k	NOUN
ejpam-6605	54	27	−	−	PROPN
ejpam-6605	54	28	1)2n	1)2n	PROPN
ejpam-6605	54	29	−	−	PROPN
ejpam-6605	54	30	(	(	PUNCT
ejpam-6605	54	31	k	k	NOUN
ejpam-6605	54	32	−	−	PROPN
ejpam-6605	54	33	1)n−r	1)n−r	NUM
ejpam-6605	54	34	−	−	PROPN
ejpam-6605	54	35	(	(	PUNCT
ejpam-6605	54	36	k	k	NOUN
ejpam-6605	54	37	−	−	PROPN
ejpam-6605	54	38	1)n+r	1)n+r	PROPN
ejpam-6605	55	1	+	+	CCONJ
ejpam-6605	55	2	1	1	NUM
ejpam-6605	55	3	(	(	PUNCT
ejpam-6605	55	4	k	k	PROPN
ejpam-6605	55	5	−	−	PROPN
ejpam-6605	55	6	2)2	2)2	NUM
ejpam-6605	55	7	−	−	PROPN
ejpam-6605	55	8	(	(	PUNCT
ejpam-6605	55	9	k	k	PROPN
ejpam-6605	55	10	−	−	PROPN
ejpam-6605	55	11	1)2n	1)2n	NUM
ejpam-6605	55	12	−	−	NOUN
ejpam-6605	55	13	2(k	2(k	NUM
ejpam-6605	55	14	−	−	NOUN
ejpam-6605	55	15	1)n	1)n	NUM
ejpam-6605	56	1	+	+	CCONJ
ejpam-6605	56	2	1	1	NUM
ejpam-6605	56	3	(	(	PUNCT
ejpam-6605	56	4	k	k	PROPN
ejpam-6605	56	5	−	−	PROPN
ejpam-6605	56	6	2)2	2)2	NUM
ejpam-6605	56	7	=	=	SYM
ejpam-6605	56	8	−(k	−(k	NOUN
ejpam-6605	56	9	−	−	PROPN
ejpam-6605	56	10	1)n−r	1)n−r	NUM
ejpam-6605	57	1	−	−	PROPN
ejpam-6605	57	2	(	(	PUNCT
ejpam-6605	57	3	k	k	NOUN
ejpam-6605	57	4	−	−	PROPN
ejpam-6605	58	1	1)n+r	1)n+r	PROPN
ejpam-6605	59	1	+	+	CCONJ
ejpam-6605	59	2	2(k	2(k	NUM
ejpam-6605	59	3	−	−	NOUN
ejpam-6605	59	4	1)n	1)n	NUM
ejpam-6605	59	5	(	(	PUNCT
ejpam-6605	59	6	k	k	PROPN
ejpam-6605	59	7	−	−	PROPN
ejpam-6605	59	8	2)2	2)2	NUM
ejpam-6605	59	9	=	=	SYM
ejpam-6605	59	10	−(k	−(k	NOUN
ejpam-6605	60	1	−	−	NOUN
ejpam-6605	60	2	1)n−r	1)n−r	NUM
ejpam-6605	60	3	1	1	NUM
ejpam-6605	60	4	+	+	CCONJ
ejpam-6605	60	5	(	(	PUNCT
ejpam-6605	60	6	k	k	NOUN
ejpam-6605	60	7	−	−	PROPN
ejpam-6605	61	1	1)2r	1)2r	PROPN
ejpam-6605	61	2	−	−	NOUN
ejpam-6605	61	3	2(k	2(k	NUM
ejpam-6605	61	4	−	−	NOUN
ejpam-6605	61	5	1)r	1)r	NUM
ejpam-6605	61	6	(	(	PUNCT
ejpam-6605	61	7	k	k	PROPN
ejpam-6605	61	8	−	−	PROPN
ejpam-6605	61	9	2)2	2)2	NUM
ejpam-6605	61	10	=	=	SYM
ejpam-6605	61	11	−(k	−(k	NOUN
ejpam-6605	61	12	−	−	PROPN
ejpam-6605	61	13	1)n−rm2	1)n−rm2	PROPN
ejpam-6605	62	1	k	k	NOUN
ejpam-6605	62	2	,	,	PUNCT
ejpam-6605	62	3	r	r	NOUN
ejpam-6605	62	4	•	•	NUM
ejpam-6605	62	5	fk	fk	INTJ
ejpam-6605	62	6	,	,	PUNCT
ejpam-6605	62	7	n−rfk	n−rfk	NOUN
ejpam-6605	62	8	,	,	PUNCT
ejpam-6605	62	9	n+r	n+r	PROPN
ejpam-6605	62	10	−	−	PROPN
ejpam-6605	62	11	f	f	PROPN
ejpam-6605	62	12	2	2	NUM
ejpam-6605	62	13	k	k	NOUN
ejpam-6605	62	14	,	,	PUNCT
ejpam-6605	62	15	n	n	NOUN
ejpam-6605	62	16	=	=	SYM
ejpam-6605	62	17	(	(	PUNCT
ejpam-6605	62	18	k	k	NOUN
ejpam-6605	62	19	−	−	PROPN
ejpam-6605	62	20	1)n−r	1)n−r	NUM
ejpam-6605	63	1	+	+	NUM
ejpam-6605	63	2	2k	2k	NUM
ejpam-6605	63	3	−	−	NUM
ejpam-6605	63	4	5	5	NUM
ejpam-6605	64	1	k	k	NOUN
ejpam-6605	64	2	−	−	PROPN
ejpam-6605	64	3	2	2	NUM
ejpam-6605	64	4	(	(	PUNCT
ejpam-6605	64	5	k	k	NOUN
ejpam-6605	64	6	−	−	PROPN
ejpam-6605	65	1	1)n+r	1)n+r	PROPN
ejpam-6605	66	1	+	+	CCONJ
ejpam-6605	66	2	2k	2k	NUM
ejpam-6605	66	3	−	−	NUM
ejpam-6605	66	4	5	5	NUM
ejpam-6605	67	1	k	k	NOUN
ejpam-6605	67	2	−	−	PROPN
ejpam-6605	67	3	2	2	NUM
ejpam-6605	67	4	−	−	PROPN
ejpam-6605	67	5	(	(	PUNCT
ejpam-6605	67	6	(	(	PUNCT
ejpam-6605	67	7	k	k	X
ejpam-6605	67	8	−	−	PROPN
ejpam-6605	67	9	1)n	1)n	PROPN
ejpam-6605	68	1	+	+	PUNCT
ejpam-6605	68	2	2k	2k	NUM
ejpam-6605	68	3	−	−	NUM
ejpam-6605	68	4	5	5	NUM
ejpam-6605	68	5	k	k	NOUN
ejpam-6605	68	6	−	−	PROPN
ejpam-6605	68	7	2	2	NUM
ejpam-6605	68	8	)	)	SYM
ejpam-6605	68	9	2	2	NUM
ejpam-6605	68	10	=	=	SYM
ejpam-6605	68	11	(	(	PUNCT
ejpam-6605	68	12	k	k	NOUN
ejpam-6605	68	13	−	−	PROPN
ejpam-6605	68	14	1)2n	1)2n	PROPN
ejpam-6605	68	15	+	+	CCONJ
ejpam-6605	68	16	(	(	PUNCT
ejpam-6605	68	17	2k	2k	NUM
ejpam-6605	68	18	−	−	PROPN
ejpam-6605	68	19	5)(k	5)(k	NUM
ejpam-6605	68	20	−	−	NUM
ejpam-6605	68	21	1)n−r	1)n−r	NUM
ejpam-6605	69	1	+	+	CCONJ
ejpam-6605	69	2	(	(	PUNCT
ejpam-6605	69	3	2k	2k	NUM
ejpam-6605	69	4	+	+	CCONJ
ejpam-6605	69	5	5)(k	5)(k	NUM
ejpam-6605	69	6	−	−	PROPN
ejpam-6605	69	7	1)n+r	1)n+r	NOUN
ejpam-6605	70	1	+	+	CCONJ
ejpam-6605	70	2	(	(	PUNCT
ejpam-6605	70	3	2k	2k	NUM
ejpam-6605	70	4	+	+	CCONJ
ejpam-6605	70	5	5)2	5)2	NUM
ejpam-6605	70	6	(	(	PUNCT
ejpam-6605	70	7	k	k	PROPN
ejpam-6605	70	8	−	−	PROPN
ejpam-6605	70	9	2)2	2)2	NUM
ejpam-6605	70	10	−	−	PROPN
ejpam-6605	70	11	(	(	PUNCT
ejpam-6605	70	12	k	k	PROPN
ejpam-6605	70	13	−	−	PROPN
ejpam-6605	70	14	1)2n	1)2n	PROPN
ejpam-6605	71	1	+	+	CCONJ
ejpam-6605	71	2	2(2k	2(2k	NUM
ejpam-6605	71	3	−	−	NUM
ejpam-6605	71	4	5)(k	5)(k	NUM
ejpam-6605	71	5	−	−	PROPN
ejpam-6605	71	6	1)n	1)n	PROPN
ejpam-6605	71	7	+	+	CCONJ
ejpam-6605	71	8	(	(	PUNCT
ejpam-6605	71	9	2k	2k	NOUN
ejpam-6605	71	10	−	−	PROPN
ejpam-6605	71	11	5)2	5)2	NUM
ejpam-6605	71	12	(	(	PUNCT
ejpam-6605	71	13	k	k	PROPN
ejpam-6605	71	14	−	−	PROPN
ejpam-6605	71	15	2)2	2)2	NUM
ejpam-6605	71	16	=	=	SYM
ejpam-6605	71	17	(	(	PUNCT
ejpam-6605	71	18	2k	2k	NOUN
ejpam-6605	71	19	−	−	PROPN
ejpam-6605	71	20	5)(k	5)(k	NUM
ejpam-6605	71	21	−	−	NUM
ejpam-6605	71	22	1)n−r	1)n−r	NUM
ejpam-6605	71	23	+	+	CCONJ
ejpam-6605	71	24	(	(	PUNCT
ejpam-6605	71	25	2k	2k	NUM
ejpam-6605	71	26	+	+	CCONJ
ejpam-6605	71	27	5)(k	5)(k	NUM
ejpam-6605	71	28	−	−	PROPN
ejpam-6605	71	29	1)n+r	1)n+r	NOUN
ejpam-6605	72	1	−	−	PROPN
ejpam-6605	72	2	2(2k	2(2k	NUM
ejpam-6605	72	3	−	−	PROPN
ejpam-6605	72	4	5)(k	5)(k	NUM
ejpam-6605	72	5	−	−	PROPN
ejpam-6605	72	6	1)n	1)n	NUM
ejpam-6605	72	7	(	(	PUNCT
ejpam-6605	72	8	k	k	PROPN
ejpam-6605	72	9	−	−	PROPN
ejpam-6605	72	10	2)2	2)2	NUM
ejpam-6605	72	11	=	=	SYM
ejpam-6605	72	12	(	(	PUNCT
ejpam-6605	72	13	2k	2k	NOUN
ejpam-6605	72	14	−	−	PROPN
ejpam-6605	72	15	5)(k	5)(k	NUM
ejpam-6605	72	16	−	−	NUM
ejpam-6605	72	17	1)n−r	1)n−r	NUM
ejpam-6605	72	18	1	1	NUM
ejpam-6605	73	1	+	+	CCONJ
ejpam-6605	73	2	(	(	PUNCT
ejpam-6605	73	3	k	k	NOUN
ejpam-6605	73	4	−	−	PROPN
ejpam-6605	73	5	1)2r	1)2r	PROPN
ejpam-6605	73	6	−	−	NOUN
ejpam-6605	73	7	2(k	2(k	NUM
ejpam-6605	73	8	−	−	NOUN
ejpam-6605	73	9	1)r	1)r	NUM
ejpam-6605	73	10	(	(	PUNCT
ejpam-6605	73	11	k	k	PROPN
ejpam-6605	73	12	−	−	PROPN
ejpam-6605	73	13	2)2	2)2	NUM
ejpam-6605	73	14	=	=	SYM
ejpam-6605	73	15	(	(	PUNCT
ejpam-6605	73	16	2k	2k	NOUN
ejpam-6605	73	17	−	−	PROPN
ejpam-6605	73	18	5)(k	5)(k	NUM
ejpam-6605	73	19	−	−	PROPN
ejpam-6605	73	20	1)n−rm2	1)n−rm2	PROPN
ejpam-6605	74	1	k	k	PROPN
ejpam-6605	74	2	,	,	PUNCT
ejpam-6605	74	3	r.	r.	PROPN
ejpam-6605	74	4	theorem	theorem	VERB
ejpam-6605	74	5	4	4	NUM
ejpam-6605	74	6	(	(	PUNCT
ejpam-6605	74	7	d’ocagne	d’ocagne	PROPN
ejpam-6605	74	8	’s	’s	PART
ejpam-6605	74	9	identity	identity	NOUN
ejpam-6605	74	10	)	)	PUNCT
ejpam-6605	74	11	.	.	PUNCT
ejpam-6605	75	1	if	if	SCONJ
ejpam-6605	75	2	ℓ	ℓ	PROPN
ejpam-6605	75	3	≥	≥	X
ejpam-6605	75	4	n	n	CCONJ
ejpam-6605	75	5	,	,	PUNCT
ejpam-6605	75	6	then	then	ADV
ejpam-6605	75	7	•	•	NUM
ejpam-6605	75	8	mk,ℓmk	mk,ℓmk	PROPN
ejpam-6605	75	9	,	,	PUNCT
ejpam-6605	75	10	n+1	n+1	NUM
ejpam-6605	75	11	−mk,ℓ+1mk	−mk,ℓ+1mk	NOUN
ejpam-6605	75	12	,	,	PUNCT
ejpam-6605	75	13	n	n	NOUN
ejpam-6605	75	14	=	=	SYM
ejpam-6605	75	15	(	(	PUNCT
ejpam-6605	75	16	k	k	X
ejpam-6605	75	17	−	−	PROPN
ejpam-6605	75	18	1)nmk,ℓ−n	1)nmk,ℓ−n	NUM
ejpam-6605	75	19	.	.	PROPN
ejpam-6605	75	20	•	•	NUM
ejpam-6605	75	21	fk,ℓfk	fk,ℓfk	NOUN
ejpam-6605	75	22	,	,	PUNCT
ejpam-6605	75	23	n+1	n+1	PROPN
ejpam-6605	75	24	−	−	PROPN
ejpam-6605	75	25	fk,ℓ+1fk	fk,ℓ+1fk	NOUN
ejpam-6605	75	26	,	,	PUNCT
ejpam-6605	75	27	n	n	NOUN
ejpam-6605	75	28	=	=	SYM
ejpam-6605	75	29	−(5	−(5	PROPN
ejpam-6605	75	30	−	−	PROPN
ejpam-6605	75	31	2k)(k	2k)(k	NUM
ejpam-6605	75	32	−	−	PROPN
ejpam-6605	75	33	1)nmk,ℓ−n	1)nmk,ℓ−n	NUM
ejpam-6605	75	34	.	.	PUNCT
ejpam-6605	76	1	proof	proof	NOUN
ejpam-6605	76	2	.	.	PUNCT
ejpam-6605	77	1	•	•	NUM
ejpam-6605	77	2	mk,ℓmk	mk,ℓmk	PROPN
ejpam-6605	77	3	,	,	PUNCT
ejpam-6605	77	4	n+1	n+1	NUM
ejpam-6605	77	5	−mk,ℓ+1mk	−mk,ℓ+1mk	NOUN
ejpam-6605	77	6	,	,	PUNCT
ejpam-6605	77	7	n	n	NOUN
ejpam-6605	77	8	=	=	SYM
ejpam-6605	77	9	(	(	PUNCT
ejpam-6605	77	10	k	k	X
ejpam-6605	77	11	−	−	PROPN
ejpam-6605	77	12	1)ℓ	1)ℓ	NUM
ejpam-6605	77	13	−	−	PROPN
ejpam-6605	77	14	1	1	NUM
ejpam-6605	77	15	(	(	PUNCT
ejpam-6605	77	16	k	k	NOUN
ejpam-6605	77	17	−	−	PROPN
ejpam-6605	77	18	2	2	NUM
ejpam-6605	77	19	)	)	PUNCT
ejpam-6605	77	20	(	(	PUNCT
ejpam-6605	77	21	k	k	PROPN
ejpam-6605	77	22	−	−	PROPN
ejpam-6605	77	23	1)n+1	1)n+1	NUM
ejpam-6605	78	1	−	−	NUM
ejpam-6605	78	2	1	1	NUM
ejpam-6605	78	3	(	(	PUNCT
ejpam-6605	78	4	k	k	NOUN
ejpam-6605	78	5	−	−	PROPN
ejpam-6605	78	6	2	2	NUM
ejpam-6605	78	7	)	)	PUNCT
ejpam-6605	78	8	−	−	PROPN
ejpam-6605	79	1	(	(	PUNCT
ejpam-6605	79	2	k	k	NOUN
ejpam-6605	79	3	−	−	PROPN
ejpam-6605	79	4	1)ℓ+1	1)ℓ+1	NUM
ejpam-6605	80	1	−	−	NOUN
ejpam-6605	80	2	1	1	NUM
ejpam-6605	80	3	(	(	PUNCT
ejpam-6605	80	4	k	k	NOUN
ejpam-6605	80	5	−	−	PROPN
ejpam-6605	80	6	2	2	NUM
ejpam-6605	80	7	)	)	PUNCT
ejpam-6605	80	8	(	(	PUNCT
ejpam-6605	80	9	k	k	NOUN
ejpam-6605	80	10	−	−	PROPN
ejpam-6605	80	11	1)n	1)n	NUM
ejpam-6605	80	12	−	−	PROPN
ejpam-6605	80	13	1	1	NUM
ejpam-6605	80	14	(	(	PUNCT
ejpam-6605	80	15	k	k	NOUN
ejpam-6605	80	16	−	−	PROPN
ejpam-6605	80	17	2	2	X
ejpam-6605	80	18	)	)	PUNCT
ejpam-6605	80	19	sh	sh	PROPN
ejpam-6605	80	20	.	.	PROPN
ejpam-6605	80	21	a.	a.	PROPN
ejpam-6605	80	22	bani	bani	PROPN
ejpam-6605	80	23	melhem	melhem	PROPN
ejpam-6605	80	24	,	,	PUNCT
ejpam-6605	80	25	al	al	PROPN
ejpam-6605	80	26	-	-	PUNCT
ejpam-6605	80	27	kateeb	kateeb	PROPN
ejpam-6605	80	28	,	,	PUNCT
ejpam-6605	80	29	a.	a.	PROPN
ejpam-6605	80	30	dagher	dagher	PROPN
ejpam-6605	80	31	/	/	SYM
ejpam-6605	80	32	eur	eur	PROPN
ejpam-6605	80	33	.	.	PUNCT
ejpam-6605	81	1	j.	j.	PROPN
ejpam-6605	81	2	pure	pure	PROPN
ejpam-6605	81	3	appl	appl	PROPN
ejpam-6605	81	4	.	.	PROPN
ejpam-6605	81	5	math	math	PROPN
ejpam-6605	81	6	,	,	PUNCT
ejpam-6605	81	7	18	18	NUM
ejpam-6605	81	8	(	(	PUNCT
ejpam-6605	81	9	4	4	NUM
ejpam-6605	81	10	)	)	PUNCT
ejpam-6605	81	11	(	(	PUNCT
ejpam-6605	81	12	2025	2025	NUM
ejpam-6605	81	13	)	)	PUNCT
ejpam-6605	81	14	,	,	PUNCT
ejpam-6605	81	15	6605	6605	NUM
ejpam-6605	81	16	5	5	NUM
ejpam-6605	81	17	of	of	ADP
ejpam-6605	81	18	15	15	NUM
ejpam-6605	81	19	=	=	SYM
ejpam-6605	81	20	(	(	PUNCT
ejpam-6605	81	21	k	k	NOUN
ejpam-6605	81	22	−	−	PROPN
ejpam-6605	82	1	1)ℓ+1	1)ℓ+1	NUM
ejpam-6605	82	2	−	−	PROPN
ejpam-6605	82	3	(	(	PUNCT
ejpam-6605	82	4	k	k	PROPN
ejpam-6605	82	5	−	−	PROPN
ejpam-6605	82	6	1)ℓ	1)ℓ	NUM
ejpam-6605	82	7	−	−	PROPN
ejpam-6605	82	8	(	(	PUNCT
ejpam-6605	82	9	k	k	PROPN
ejpam-6605	82	10	−	−	PROPN
ejpam-6605	82	11	1)n+1	1)n+1	NUM
ejpam-6605	83	1	+	+	CCONJ
ejpam-6605	83	2	(	(	PUNCT
ejpam-6605	83	3	k	k	PROPN
ejpam-6605	83	4	−	−	PROPN
ejpam-6605	83	5	1)n	1)n	NUM
ejpam-6605	83	6	(	(	PUNCT
ejpam-6605	83	7	k	k	PROPN
ejpam-6605	83	8	−	−	PROPN
ejpam-6605	83	9	2)2	2)2	NUM
ejpam-6605	83	10	=	=	SYM
ejpam-6605	83	11	(	(	PUNCT
ejpam-6605	83	12	k	k	NOUN
ejpam-6605	83	13	−	−	PROPN
ejpam-6605	83	14	1)ℓ(k	1)ℓ(k	NUM
ejpam-6605	83	15	−	−	PROPN
ejpam-6605	83	16	2	2	NUM
ejpam-6605	83	17	)	)	PUNCT
ejpam-6605	83	18	−	−	PROPN
ejpam-6605	84	1	(	(	PUNCT
ejpam-6605	84	2	k	k	NOUN
ejpam-6605	84	3	−	−	PROPN
ejpam-6605	85	1	1)n(k	1)n(k	NUM
ejpam-6605	86	1	−	−	NOUN
ejpam-6605	86	2	2	2	NUM
ejpam-6605	86	3	)	)	PUNCT
ejpam-6605	86	4	(	(	PUNCT
ejpam-6605	86	5	k	k	NOUN
ejpam-6605	86	6	−	−	PROPN
ejpam-6605	86	7	2)2	2)2	NUM
ejpam-6605	86	8	=	=	SYM
ejpam-6605	86	9	(	(	PUNCT
ejpam-6605	86	10	k	k	NOUN
ejpam-6605	86	11	−	−	PROPN
ejpam-6605	86	12	1)n	1)n	NUM
ejpam-6605	86	13	(	(	PUNCT
ejpam-6605	86	14	k	k	NOUN
ejpam-6605	86	15	−	−	PROPN
ejpam-6605	87	1	1)ℓ−n	1)ℓ−n	NUM
ejpam-6605	88	1	−	−	NOUN
ejpam-6605	88	2	1	1	NUM
ejpam-6605	89	1	k	k	NOUN
ejpam-6605	89	2	−	−	PROPN
ejpam-6605	89	3	2	2	NUM
ejpam-6605	89	4	=	=	SYM
ejpam-6605	89	5	(	(	PUNCT
ejpam-6605	89	6	k	k	NOUN
ejpam-6605	89	7	−	−	PROPN
ejpam-6605	89	8	1)nmk,ℓ−n	1)nmk,ℓ−n	NUM
ejpam-6605	89	9	•	•	NUM
ejpam-6605	89	10	fk,ℓfk	fk,ℓfk	NOUN
ejpam-6605	89	11	,	,	PUNCT
ejpam-6605	89	12	n+1	n+1	PROPN
ejpam-6605	89	13	−	−	PROPN
ejpam-6605	89	14	fk,ℓ+1fk	fk,ℓ+1fk	NOUN
ejpam-6605	89	15	,	,	PUNCT
ejpam-6605	89	16	n	n	X
ejpam-6605	89	17	=	=	SYM
ejpam-6605	89	18	(	(	PUNCT
ejpam-6605	89	19	k	k	X
ejpam-6605	89	20	−	−	PROPN
ejpam-6605	89	21	1)ℓ	1)ℓ	NUM
ejpam-6605	89	22	+	+	CCONJ
ejpam-6605	89	23	2k	2k	NUM
ejpam-6605	89	24	−	−	NUM
ejpam-6605	89	25	5	5	NUM
ejpam-6605	90	1	(	(	PUNCT
ejpam-6605	90	2	k	k	NOUN
ejpam-6605	90	3	−	−	PROPN
ejpam-6605	90	4	2	2	NUM
ejpam-6605	90	5	)	)	PUNCT
ejpam-6605	90	6	(	(	PUNCT
ejpam-6605	90	7	k	k	PROPN
ejpam-6605	90	8	−	−	PROPN
ejpam-6605	90	9	1)n+1	1)n+1	NUM
ejpam-6605	91	1	+	+	NUM
ejpam-6605	91	2	2k	2k	NUM
ejpam-6605	91	3	−	−	NUM
ejpam-6605	91	4	5	5	NUM
ejpam-6605	91	5	(	(	PUNCT
ejpam-6605	91	6	k	k	NOUN
ejpam-6605	91	7	−	−	PROPN
ejpam-6605	91	8	2	2	NUM
ejpam-6605	91	9	)	)	PUNCT
ejpam-6605	91	10	−	−	PROPN
ejpam-6605	92	1	(	(	PUNCT
ejpam-6605	92	2	k	k	NOUN
ejpam-6605	92	3	−	−	PROPN
ejpam-6605	92	4	1)ℓ+1	1)ℓ+1	NUM
ejpam-6605	93	1	+	+	PUNCT
ejpam-6605	93	2	2k	2k	NUM
ejpam-6605	93	3	−	−	NOUN
ejpam-6605	93	4	5	5	NUM
ejpam-6605	93	5	(	(	PUNCT
ejpam-6605	93	6	k	k	NOUN
ejpam-6605	93	7	−	−	PROPN
ejpam-6605	93	8	2	2	NUM
ejpam-6605	93	9	)	)	PUNCT
ejpam-6605	93	10	(	(	PUNCT
ejpam-6605	93	11	k	k	NOUN
ejpam-6605	93	12	−	−	PROPN
ejpam-6605	93	13	1)n	1)n	PROPN
ejpam-6605	94	1	+	+	PUNCT
ejpam-6605	94	2	2k	2k	NUM
ejpam-6605	94	3	−	−	NUM
ejpam-6605	94	4	5	5	NUM
ejpam-6605	94	5	(	(	PUNCT
ejpam-6605	94	6	k	k	NOUN
ejpam-6605	94	7	−	−	PROPN
ejpam-6605	94	8	2	2	NUM
ejpam-6605	94	9	)	)	PUNCT
ejpam-6605	94	10	=	=	SYM
ejpam-6605	94	11	(	(	PUNCT
ejpam-6605	94	12	2k	2k	NOUN
ejpam-6605	94	13	−	−	NOUN
ejpam-6605	94	14	5	5	X
ejpam-6605	94	15	)	)	PUNCT
ejpam-6605	94	16	−(k	−(k	NOUN
ejpam-6605	94	17	−	−	PROPN
ejpam-6605	94	18	1)ℓ+1	1)ℓ+1	NUM
ejpam-6605	95	1	+	+	CCONJ
ejpam-6605	95	2	(	(	PUNCT
ejpam-6605	95	3	k	k	PROPN
ejpam-6605	95	4	−	−	PROPN
ejpam-6605	95	5	1)ℓ	1)ℓ	NUM
ejpam-6605	95	6	+	+	CCONJ
ejpam-6605	95	7	(	(	PUNCT
ejpam-6605	95	8	k	k	PROPN
ejpam-6605	95	9	−	−	PROPN
ejpam-6605	95	10	1)n+1	1)n+1	NUM
ejpam-6605	96	1	−	−	PROPN
ejpam-6605	96	2	(	(	PUNCT
ejpam-6605	96	3	k	k	PROPN
ejpam-6605	96	4	−	−	PROPN
ejpam-6605	96	5	1)n	1)n	NUM
ejpam-6605	96	6	(	(	PUNCT
ejpam-6605	96	7	k	k	PROPN
ejpam-6605	96	8	−	−	PROPN
ejpam-6605	96	9	2)2	2)2	NUM
ejpam-6605	96	10	=	=	SYM
ejpam-6605	96	11	(	(	PUNCT
ejpam-6605	96	12	2k	2k	NOUN
ejpam-6605	96	13	−	−	PROPN
ejpam-6605	96	14	5	5	NUM
ejpam-6605	96	15	)	)	PUNCT
ejpam-6605	96	16	(	(	PUNCT
ejpam-6605	96	17	k	k	NOUN
ejpam-6605	96	18	−	−	PROPN
ejpam-6605	96	19	1)ℓ(2	1)ℓ(2	NOUN
ejpam-6605	96	20	−	−	PROPN
ejpam-6605	96	21	k	k	NOUN
ejpam-6605	96	22	)	)	PUNCT
ejpam-6605	97	1	+	+	CCONJ
ejpam-6605	97	2	(	(	PUNCT
ejpam-6605	97	3	k	k	X
ejpam-6605	97	4	−	−	PROPN
ejpam-6605	97	5	1)n(k	1)n(k	NUM
ejpam-6605	97	6	−	−	NOUN
ejpam-6605	97	7	2	2	NUM
ejpam-6605	97	8	)	)	PUNCT
ejpam-6605	97	9	(	(	PUNCT
ejpam-6605	97	10	k	k	NOUN
ejpam-6605	97	11	−	−	PROPN
ejpam-6605	97	12	2)2	2)2	NUM
ejpam-6605	97	13	=	=	SYM
ejpam-6605	97	14	(	(	PUNCT
ejpam-6605	97	15	2k	2k	NOUN
ejpam-6605	97	16	−	−	PROPN
ejpam-6605	97	17	5	5	NUM
ejpam-6605	97	18	)	)	PUNCT
ejpam-6605	97	19	(	(	PUNCT
ejpam-6605	97	20	k	k	NOUN
ejpam-6605	97	21	−	−	PROPN
ejpam-6605	97	22	1)n	1)n	NUM
ejpam-6605	97	23	−	−	PROPN
ejpam-6605	98	1	(	(	PUNCT
ejpam-6605	98	2	k	k	PROPN
ejpam-6605	98	3	−	−	PROPN
ejpam-6605	98	4	1)ℓ	1)ℓ	NUM
ejpam-6605	98	5	(	(	PUNCT
ejpam-6605	98	6	k	k	NOUN
ejpam-6605	98	7	−	−	PROPN
ejpam-6605	98	8	2	2	NUM
ejpam-6605	98	9	)	)	PUNCT
ejpam-6605	98	10	=	=	SYM
ejpam-6605	98	11	(	(	PUNCT
ejpam-6605	98	12	2k	2k	NOUN
ejpam-6605	98	13	−	−	PROPN
ejpam-6605	98	14	5)(k	5)(k	NUM
ejpam-6605	98	15	−	−	PROPN
ejpam-6605	98	16	1)n	1)n	SYM
ejpam-6605	98	17	1	1	NUM
ejpam-6605	98	18	−	−	PROPN
ejpam-6605	98	19	(	(	PUNCT
ejpam-6605	98	20	k	k	PROPN
ejpam-6605	98	21	−	−	PROPN
ejpam-6605	99	1	1)ℓ−n	1)ℓ−n	NUM
ejpam-6605	99	2	(	(	PUNCT
ejpam-6605	99	3	k	k	NOUN
ejpam-6605	99	4	−	−	PROPN
ejpam-6605	99	5	2	2	NUM
ejpam-6605	99	6	)	)	PUNCT
ejpam-6605	99	7	=	=	PUNCT
ejpam-6605	100	1	−(5	−(5	PROPN
ejpam-6605	100	2	−	−	PROPN
ejpam-6605	100	3	2k)(k	2k)(k	NUM
ejpam-6605	100	4	−	−	PROPN
ejpam-6605	100	5	1)nmk,ℓ−n	1)nmk,ℓ−n	NUM
ejpam-6605	100	6	.	.	PUNCT
ejpam-6605	101	1	theorem	theorem	NOUN
ejpam-6605	101	2	5	5	NUM
ejpam-6605	101	3	(	(	PUNCT
ejpam-6605	101	4	vajda	vajda	PROPN
ejpam-6605	101	5	’s	’s	PART
ejpam-6605	101	6	identity	identity	NOUN
ejpam-6605	101	7	)	)	PUNCT
ejpam-6605	101	8	.	.	PUNCT
ejpam-6605	102	1	(	(	PUNCT
ejpam-6605	102	2	i	i	NOUN
ejpam-6605	102	3	)	)	PUNCT
ejpam-6605	102	4	(	(	PUNCT
ejpam-6605	102	5	formulation	formulation	NOUN
ejpam-6605	102	6	1	1	NUM
ejpam-6605	102	7	)	)	PUNCT
ejpam-6605	102	8	mk	mk	NOUN
ejpam-6605	102	9	,	,	PUNCT
ejpam-6605	102	10	n+imk	n+imk	SYM
ejpam-6605	102	11	,	,	PUNCT
ejpam-6605	102	12	n+j	n+j	PROPN
ejpam-6605	102	13	−mk	−mk	PROPN
ejpam-6605	102	14	,	,	PUNCT
ejpam-6605	102	15	nmk	nmk	PROPN
ejpam-6605	102	16	,	,	PUNCT
ejpam-6605	102	17	n+i+j	n+i+j	X
ejpam-6605	103	1	=	=	SYM
ejpam-6605	104	1	(	(	PUNCT
ejpam-6605	104	2	k	k	PROPN
ejpam-6605	104	3	−	−	PROPN
ejpam-6605	104	4	1)nmk	1)nmk	NUM
ejpam-6605	104	5	,	,	PUNCT
ejpam-6605	104	6	imk	imk	PROPN
ejpam-6605	104	7	,	,	PUNCT
ejpam-6605	104	8	j	j	PROPN
ejpam-6605	104	9	(	(	PUNCT
ejpam-6605	104	10	ii	ii	PROPN
ejpam-6605	104	11	)	)	PUNCT
ejpam-6605	104	12	(	(	PUNCT
ejpam-6605	104	13	formulation	formulation	NOUN
ejpam-6605	104	14	2	2	NUM
ejpam-6605	104	15	)	)	PUNCT
ejpam-6605	104	16	mk	mk	NOUN
ejpam-6605	104	17	,	,	PUNCT
ejpam-6605	104	18	n+jmk	n+jmk	PROPN
ejpam-6605	104	19	,	,	PUNCT
ejpam-6605	104	20	m−j	m−j	PROPN
ejpam-6605	104	21	−mk	−mk	PROPN
ejpam-6605	104	22	,	,	PUNCT
ejpam-6605	104	23	nmk	nmk	PRON
ejpam-6605	104	24	,	,	PUNCT
ejpam-6605	104	25	m	m	VERB
ejpam-6605	104	26	=	=	SYM
ejpam-6605	104	27	(	(	PUNCT
ejpam-6605	104	28	k	k	PROPN
ejpam-6605	104	29	−	−	PROPN
ejpam-6605	104	30	1)nmk	1)nmk	NUM
ejpam-6605	104	31	,	,	PUNCT
ejpam-6605	104	32	m−n−jmk	m−n−jmk	PROPN
ejpam-6605	104	33	,	,	PUNCT
ejpam-6605	104	34	j	j	PROPN
ejpam-6605	104	35	proof	proof	NOUN
ejpam-6605	104	36	.	.	PUNCT
ejpam-6605	105	1	(	(	PUNCT
ejpam-6605	105	2	i	i	NOUN
ejpam-6605	105	3	)	)	PUNCT
ejpam-6605	105	4	(	(	PUNCT
ejpam-6605	105	5	formulation	formulation	NOUN
ejpam-6605	105	6	1	1	NUM
ejpam-6605	105	7	)	)	PUNCT
ejpam-6605	105	8	mk	mk	NOUN
ejpam-6605	105	9	,	,	PUNCT
ejpam-6605	105	10	n+imk	n+imk	SYM
ejpam-6605	105	11	,	,	PUNCT
ejpam-6605	105	12	n+j	n+j	PROPN
ejpam-6605	105	13	−mk	−mk	PROPN
ejpam-6605	105	14	,	,	PUNCT
ejpam-6605	105	15	nmk	nmk	PROPN
ejpam-6605	105	16	,	,	PUNCT
ejpam-6605	105	17	n+i+j	n+i+j	X
ejpam-6605	106	1	=	=	SYM
ejpam-6605	107	1	(	(	PUNCT
ejpam-6605	107	2	k	k	NOUN
ejpam-6605	107	3	−	−	PROPN
ejpam-6605	107	4	1)n+i	1)n+i	NUM
ejpam-6605	107	5	−	−	PROPN
ejpam-6605	107	6	1	1	NUM
ejpam-6605	107	7	(	(	PUNCT
ejpam-6605	107	8	k	k	NOUN
ejpam-6605	107	9	−	−	PROPN
ejpam-6605	107	10	2	2	NUM
ejpam-6605	107	11	)	)	PUNCT
ejpam-6605	107	12	(	(	PUNCT
ejpam-6605	107	13	k	k	NOUN
ejpam-6605	107	14	−	−	PROPN
ejpam-6605	107	15	1)n+j	1)n+j	NUM
ejpam-6605	107	16	−	−	PROPN
ejpam-6605	107	17	1	1	NUM
ejpam-6605	107	18	(	(	PUNCT
ejpam-6605	107	19	k	k	NOUN
ejpam-6605	107	20	−	−	PROPN
ejpam-6605	107	21	2	2	NUM
ejpam-6605	107	22	)	)	PUNCT
ejpam-6605	107	23	−	−	PROPN
ejpam-6605	108	1	(	(	PUNCT
ejpam-6605	108	2	k	k	NOUN
ejpam-6605	108	3	−	−	PROPN
ejpam-6605	108	4	1)n	1)n	NUM
ejpam-6605	108	5	−	−	PROPN
ejpam-6605	108	6	1	1	NUM
ejpam-6605	108	7	(	(	PUNCT
ejpam-6605	108	8	k	k	NOUN
ejpam-6605	108	9	−	−	PROPN
ejpam-6605	108	10	2	2	NUM
ejpam-6605	108	11	)	)	PUNCT
ejpam-6605	108	12	(	(	PUNCT
ejpam-6605	108	13	k	k	PROPN
ejpam-6605	109	1	−	−	PROPN
ejpam-6605	109	2	1)n+i+j	1)n+i+j	NUM
ejpam-6605	110	1	−	−	NOUN
ejpam-6605	110	2	1	1	NUM
ejpam-6605	110	3	(	(	PUNCT
ejpam-6605	110	4	k	k	NOUN
ejpam-6605	110	5	−	−	PROPN
ejpam-6605	110	6	2	2	NUM
ejpam-6605	110	7	)	)	PUNCT
ejpam-6605	110	8	=	=	SYM
ejpam-6605	110	9	(	(	PUNCT
ejpam-6605	110	10	k	k	NOUN
ejpam-6605	110	11	−	−	PROPN
ejpam-6605	110	12	1)n	1)n	NUM
ejpam-6605	110	13	−	−	PROPN
ejpam-6605	110	14	(	(	PUNCT
ejpam-6605	110	15	k	k	NOUN
ejpam-6605	110	16	−	−	PROPN
ejpam-6605	110	17	1)n+i	1)n+i	NUM
ejpam-6605	110	18	−	−	PROPN
ejpam-6605	110	19	(	(	PUNCT
ejpam-6605	110	20	k	k	NOUN
ejpam-6605	110	21	−	−	PROPN
ejpam-6605	110	22	1)n+j	1)n+j	PROPN
ejpam-6605	111	1	+	+	CCONJ
ejpam-6605	111	2	(	(	PUNCT
ejpam-6605	111	3	k	k	PROPN
ejpam-6605	111	4	−	−	PROPN
ejpam-6605	111	5	1)n+i+j	1)n+i+j	NUM
ejpam-6605	111	6	(	(	PUNCT
ejpam-6605	111	7	k	k	PROPN
ejpam-6605	112	1	−	−	PROPN
ejpam-6605	112	2	2)2	2)2	NUM
ejpam-6605	112	3	=	=	SYM
ejpam-6605	112	4	(	(	PUNCT
ejpam-6605	112	5	k	k	NOUN
ejpam-6605	112	6	−	−	PROPN
ejpam-6605	112	7	1)n	1)n	NUM
ejpam-6605	112	8	1	1	NUM
ejpam-6605	112	9	−	−	PROPN
ejpam-6605	112	10	(	(	PUNCT
ejpam-6605	112	11	k	k	PROPN
ejpam-6605	112	12	−	−	PROPN
ejpam-6605	112	13	1)i	1)i	NUM
ejpam-6605	112	14	−	−	PROPN
ejpam-6605	113	1	(	(	PUNCT
ejpam-6605	113	2	k	k	NOUN
ejpam-6605	113	3	−	−	PROPN
ejpam-6605	113	4	1)j	1)j	NUM
ejpam-6605	114	1	+	+	CCONJ
ejpam-6605	114	2	(	(	PUNCT
ejpam-6605	114	3	k	k	PROPN
ejpam-6605	114	4	−	−	PROPN
ejpam-6605	114	5	1)i+j	1)i+j	NUM
ejpam-6605	114	6	(	(	PUNCT
ejpam-6605	114	7	k	k	PROPN
ejpam-6605	114	8	−	−	PROPN
ejpam-6605	114	9	2)2	2)2	NUM
ejpam-6605	114	10	=	=	SYM
ejpam-6605	114	11	(	(	PUNCT
ejpam-6605	114	12	k	k	NOUN
ejpam-6605	114	13	−	−	PROPN
ejpam-6605	114	14	1)n	1)n	NUM
ejpam-6605	114	15	1	1	NUM
ejpam-6605	114	16	−	−	PROPN
ejpam-6605	114	17	(	(	PUNCT
ejpam-6605	114	18	k	k	PROPN
ejpam-6605	114	19	−	−	PROPN
ejpam-6605	114	20	1)i	1)i	NUM
ejpam-6605	114	21	−	−	PROPN
ejpam-6605	114	22	(	(	PUNCT
ejpam-6605	114	23	k	k	NOUN
ejpam-6605	114	24	−	−	PROPN
ejpam-6605	114	25	1)j(1	1)j(1	NOUN
ejpam-6605	114	26	−	−	PROPN
ejpam-6605	114	27	(	(	PUNCT
ejpam-6605	114	28	k	k	NOUN
ejpam-6605	114	29	−	−	PROPN
ejpam-6605	114	30	1)i	1)i	NUM
ejpam-6605	114	31	)	)	PUNCT
ejpam-6605	114	32	(	(	PUNCT
ejpam-6605	114	33	k	k	PROPN
ejpam-6605	114	34	−	−	PROPN
ejpam-6605	114	35	2)2	2)2	NUM
ejpam-6605	114	36	sh	sh	PROPN
ejpam-6605	114	37	.	.	PUNCT
ejpam-6605	114	38	a.	a.	PROPN
ejpam-6605	114	39	bani	bani	PROPN
ejpam-6605	114	40	melhem	melhem	PROPN
ejpam-6605	114	41	,	,	PUNCT
ejpam-6605	114	42	al	al	PROPN
ejpam-6605	114	43	-	-	PUNCT
ejpam-6605	114	44	kateeb	kateeb	PROPN
ejpam-6605	114	45	,	,	PUNCT
ejpam-6605	114	46	a.	a.	PROPN
ejpam-6605	114	47	dagher	dagher	PROPN
ejpam-6605	114	48	/	/	SYM
ejpam-6605	114	49	eur	eur	PROPN
ejpam-6605	114	50	.	.	PUNCT
ejpam-6605	115	1	j.	j.	PROPN
ejpam-6605	115	2	pure	pure	PROPN
ejpam-6605	115	3	appl	appl	PROPN
ejpam-6605	115	4	.	.	PROPN
ejpam-6605	115	5	math	math	PROPN
ejpam-6605	115	6	,	,	PUNCT
ejpam-6605	115	7	18	18	NUM
ejpam-6605	115	8	(	(	PUNCT
ejpam-6605	115	9	4	4	NUM
ejpam-6605	115	10	)	)	PUNCT
ejpam-6605	115	11	(	(	PUNCT
ejpam-6605	115	12	2025	2025	NUM
ejpam-6605	115	13	)	)	PUNCT
ejpam-6605	115	14	,	,	PUNCT
ejpam-6605	115	15	6605	6605	NUM
ejpam-6605	115	16	6	6	NUM
ejpam-6605	115	17	of	of	ADP
ejpam-6605	115	18	15	15	NUM
ejpam-6605	115	19	=	=	SYM
ejpam-6605	115	20	(	(	PUNCT
ejpam-6605	115	21	k	k	NOUN
ejpam-6605	115	22	−	−	PROPN
ejpam-6605	115	23	1)n	1)n	X
ejpam-6605	115	24	(	(	PUNCT
ejpam-6605	115	25	1	1	NUM
ejpam-6605	115	26	−	−	NOUN
ejpam-6605	115	27	(	(	PUNCT
ejpam-6605	115	28	k	k	NOUN
ejpam-6605	115	29	−	−	PROPN
ejpam-6605	115	30	1)i)(1	1)i)(1	NUM
ejpam-6605	115	31	−	−	PROPN
ejpam-6605	116	1	(	(	PUNCT
ejpam-6605	116	2	k	k	NOUN
ejpam-6605	116	3	−	−	PROPN
ejpam-6605	116	4	1)j	1)j	NUM
ejpam-6605	116	5	)	)	PUNCT
ejpam-6605	116	6	(	(	PUNCT
ejpam-6605	116	7	k	k	NOUN
ejpam-6605	116	8	−	−	PROPN
ejpam-6605	116	9	2)2	2)2	NUM
ejpam-6605	116	10	=	=	SYM
ejpam-6605	116	11	(	(	PUNCT
ejpam-6605	116	12	k	k	PROPN
ejpam-6605	116	13	−	−	PROPN
ejpam-6605	116	14	1)nmk	1)nmk	NUM
ejpam-6605	116	15	,	,	PUNCT
ejpam-6605	116	16	imk	imk	PROPN
ejpam-6605	116	17	,	,	PUNCT
ejpam-6605	116	18	j	j	PROPN
ejpam-6605	116	19	(	(	PUNCT
ejpam-6605	116	20	ii	ii	PROPN
ejpam-6605	116	21	)	)	PUNCT
ejpam-6605	116	22	(	(	PUNCT
ejpam-6605	116	23	formulation	formulation	NOUN
ejpam-6605	116	24	2	2	NUM
ejpam-6605	116	25	)	)	PUNCT
ejpam-6605	116	26	mk	mk	NOUN
ejpam-6605	116	27	,	,	PUNCT
ejpam-6605	116	28	n+imk	n+imk	NOUN
ejpam-6605	116	29	,	,	PUNCT
ejpam-6605	116	30	m−j	m−j	NOUN
ejpam-6605	116	31	−mk	−mk	PROPN
ejpam-6605	116	32	,	,	PUNCT
ejpam-6605	116	33	nmk	nmk	PRON
ejpam-6605	116	34	,	,	PUNCT
ejpam-6605	116	35	m	m	VERB
ejpam-6605	116	36	=	=	SYM
ejpam-6605	116	37	(	(	PUNCT
ejpam-6605	116	38	k	k	NOUN
ejpam-6605	116	39	−	−	PROPN
ejpam-6605	116	40	1)n+j	1)n+j	NUM
ejpam-6605	116	41	−	−	PROPN
ejpam-6605	116	42	1	1	NUM
ejpam-6605	116	43	(	(	PUNCT
ejpam-6605	116	44	k	k	NOUN
ejpam-6605	116	45	−	−	PROPN
ejpam-6605	116	46	2	2	NUM
ejpam-6605	116	47	)	)	PUNCT
ejpam-6605	116	48	(	(	PUNCT
ejpam-6605	116	49	k	k	NOUN
ejpam-6605	116	50	−	−	PROPN
ejpam-6605	117	1	1)m−j	1)m−j	NUM
ejpam-6605	117	2	−	−	NOUN
ejpam-6605	117	3	1	1	NUM
ejpam-6605	117	4	(	(	PUNCT
ejpam-6605	117	5	k	k	NOUN
ejpam-6605	117	6	−	−	PROPN
ejpam-6605	117	7	2	2	NUM
ejpam-6605	117	8	)	)	PUNCT
ejpam-6605	117	9	−	−	PROPN
ejpam-6605	118	1	(	(	PUNCT
ejpam-6605	118	2	k	k	NOUN
ejpam-6605	118	3	−	−	PROPN
ejpam-6605	118	4	1)n	1)n	NUM
ejpam-6605	118	5	−	−	PROPN
ejpam-6605	118	6	1	1	NUM
ejpam-6605	118	7	(	(	PUNCT
ejpam-6605	118	8	k	k	NOUN
ejpam-6605	118	9	−	−	PROPN
ejpam-6605	118	10	2	2	NUM
ejpam-6605	118	11	)	)	PUNCT
ejpam-6605	118	12	(	(	PUNCT
ejpam-6605	118	13	k	k	NOUN
ejpam-6605	118	14	−	−	PROPN
ejpam-6605	118	15	1)m	1)m	NUM
ejpam-6605	118	16	−	−	NOUN
ejpam-6605	118	17	1	1	NUM
ejpam-6605	118	18	(	(	PUNCT
ejpam-6605	118	19	k	k	NOUN
ejpam-6605	118	20	−	−	PROPN
ejpam-6605	118	21	2	2	NUM
ejpam-6605	118	22	)	)	PUNCT
ejpam-6605	118	23	=	=	SYM
ejpam-6605	119	1	(	(	PUNCT
ejpam-6605	119	2	k	k	NOUN
ejpam-6605	119	3	−	−	PROPN
ejpam-6605	119	4	1)m	1)m	NUM
ejpam-6605	119	5	−	−	PROPN
ejpam-6605	119	6	(	(	PUNCT
ejpam-6605	119	7	k	k	NOUN
ejpam-6605	119	8	−	−	PROPN
ejpam-6605	119	9	1)m−j	1)m−j	NUM
ejpam-6605	119	10	−	−	PROPN
ejpam-6605	120	1	(	(	PUNCT
ejpam-6605	120	2	k	k	NOUN
ejpam-6605	120	3	−	−	PROPN
ejpam-6605	120	4	1)n+j	1)n+j	PROPN
ejpam-6605	121	1	+	+	CCONJ
ejpam-6605	121	2	(	(	PUNCT
ejpam-6605	121	3	k	k	PROPN
ejpam-6605	121	4	−	−	PROPN
ejpam-6605	121	5	1)n	1)n	NUM
ejpam-6605	121	6	(	(	PUNCT
ejpam-6605	121	7	k	k	PROPN
ejpam-6605	121	8	−	−	PROPN
ejpam-6605	121	9	2)2	2)2	NUM
ejpam-6605	121	10	=	=	SYM
ejpam-6605	121	11	(	(	PUNCT
ejpam-6605	121	12	k	k	NOUN
ejpam-6605	121	13	−	−	PROPN
ejpam-6605	121	14	1)n	1)n	NUM
ejpam-6605	121	15	1	1	NUM
ejpam-6605	121	16	−	−	PROPN
ejpam-6605	121	17	(	(	PUNCT
ejpam-6605	121	18	k	k	PROPN
ejpam-6605	121	19	−	−	PROPN
ejpam-6605	121	20	1)m−n−j	1)m−n−j	NUM
ejpam-6605	122	1	+	+	CCONJ
ejpam-6605	122	2	(	(	PUNCT
ejpam-6605	122	3	k	k	X
ejpam-6605	122	4	−	−	PROPN
ejpam-6605	122	5	1)j((k	1)j((k	NUM
ejpam-6605	123	1	−	−	PROPN
ejpam-6605	123	2	1)m−n−j	1)m−n−j	NUM
ejpam-6605	123	3	−	−	NOUN
ejpam-6605	123	4	1	1	NUM
ejpam-6605	123	5	)	)	PUNCT
ejpam-6605	123	6	(	(	PUNCT
ejpam-6605	123	7	k	k	NOUN
ejpam-6605	123	8	−	−	PROPN
ejpam-6605	123	9	2)2	2)2	NUM
ejpam-6605	123	10	=	=	SYM
ejpam-6605	123	11	(	(	PUNCT
ejpam-6605	123	12	k	k	PROPN
ejpam-6605	123	13	−	−	PROPN
ejpam-6605	123	14	1)nmk	1)nmk	NUM
ejpam-6605	123	15	,	,	PUNCT
ejpam-6605	123	16	m−n−jmk	m−n−jmk	PROPN
ejpam-6605	123	17	,	,	PUNCT
ejpam-6605	123	18	j	j	PROPN
ejpam-6605	123	19	theorem	theorem	VERB
ejpam-6605	123	20	6	6	NUM
ejpam-6605	123	21	(	(	PUNCT
ejpam-6605	123	22	sum	sum	NOUN
ejpam-6605	123	23	of	of	ADP
ejpam-6605	123	24	terms	term	NOUN
ejpam-6605	123	25	)	)	PUNCT
ejpam-6605	123	26	.	.	PUNCT
ejpam-6605	124	1	if	if	SCONJ
ejpam-6605	124	2	n	n	PRON
ejpam-6605	124	3	≥	≥	NOUN
ejpam-6605	124	4	2	2	NUM
ejpam-6605	124	5	,	,	PUNCT
ejpam-6605	124	6	then	then	ADV
ejpam-6605	124	7	(	(	PUNCT
ejpam-6605	124	8	i	i	NOUN
ejpam-6605	124	9	)	)	PUNCT
ejpam-6605	124	10	∑n	∑n	PROPN
ejpam-6605	124	11	i=0mk	i=0mk	NOUN
ejpam-6605	124	12	,	,	PUNCT
ejpam-6605	124	13	i	i	PRON
ejpam-6605	124	14	=	=	NOUN
ejpam-6605	124	15	1	1	NUM
ejpam-6605	124	16	k−2(mk	k−2(mk	PROPN
ejpam-6605	124	17	,	,	PUNCT
ejpam-6605	124	18	n+1	n+1	PROPN
ejpam-6605	124	19	−	−	PROPN
ejpam-6605	124	20	n−	n−	NOUN
ejpam-6605	124	21	1	1	NUM
ejpam-6605	124	22	)	)	PUNCT
ejpam-6605	124	23	(	(	PUNCT
ejpam-6605	124	24	ii	ii	NOUN
ejpam-6605	124	25	)	)	PUNCT
ejpam-6605	124	26	∑n	∑n	PROPN
ejpam-6605	124	27	i=0	i=0	PROPN
ejpam-6605	124	28	fk	fk	INTJ
ejpam-6605	124	29	,	,	PUNCT
ejpam-6605	124	30	i	i	PROPN
ejpam-6605	124	31	=	=	NOUN
ejpam-6605	124	32	1	1	NUM
ejpam-6605	124	33	k−2(fk	k−2(fk	PROPN
ejpam-6605	124	34	,	,	PUNCT
ejpam-6605	124	35	n+1	n+1	PROPN
ejpam-6605	124	36	−	−	PROPN
ejpam-6605	124	37	2	2	NUM
ejpam-6605	124	38	+	+	CCONJ
ejpam-6605	124	39	(	(	PUNCT
ejpam-6605	124	40	n	n	PROPN
ejpam-6605	124	41	+	+	CCONJ
ejpam-6605	124	42	1)(2k	1)(2k	NUM
ejpam-6605	124	43	−	−	NOUN
ejpam-6605	124	44	5	5	NUM
ejpam-6605	124	45	)	)	PUNCT
ejpam-6605	124	46	)	)	PUNCT
ejpam-6605	125	1	=	=	SYM
ejpam-6605	125	2	1	1	NUM
ejpam-6605	125	3	k−2(mk	k−2(mk	PROPN
ejpam-6605	125	4	,	,	PUNCT
ejpam-6605	125	5	n+1	n+1	PROPN
ejpam-6605	125	6	+	+	PUNCT
ejpam-6605	125	7	(	(	PUNCT
ejpam-6605	125	8	n	n	PROPN
ejpam-6605	125	9	+	+	CCONJ
ejpam-6605	125	10	1)(2k	1)(2k	NUM
ejpam-6605	125	11	−	−	NOUN
ejpam-6605	125	12	5	5	NUM
ejpam-6605	125	13	)	)	PUNCT
ejpam-6605	125	14	)	)	PUNCT
ejpam-6605	125	15	(	(	PUNCT
ejpam-6605	125	16	iii	iii	X
ejpam-6605	125	17	)	)	PUNCT
ejpam-6605	125	18	∑n	∑n	PROPN
ejpam-6605	125	19	i=0mk,2i	i=0mk,2i	NOUN
ejpam-6605	125	20	=	=	PROPN
ejpam-6605	125	21	1	1	NUM
ejpam-6605	125	22	k−2	k−2	PROPN
ejpam-6605	125	23	(	(	PUNCT
ejpam-6605	125	24	1kmk,2(n+1	1kmk,2(n+1	NUM
ejpam-6605	125	25	)	)	PUNCT
ejpam-6605	125	26	−	−	PROPN
ejpam-6605	125	27	n−	n−	NOUN
ejpam-6605	125	28	1	1	NUM
ejpam-6605	125	29	)	)	PUNCT
ejpam-6605	125	30	(	(	PUNCT
ejpam-6605	125	31	iv	iv	X
ejpam-6605	125	32	)	)	PUNCT
ejpam-6605	125	33	∑n	∑n	PROPN
ejpam-6605	125	34	i=0	i=0	PROPN
ejpam-6605	125	35	fk,2i	fk,2i	NUM
ejpam-6605	125	36	=	=	SYM
ejpam-6605	125	37	1	1	NUM
ejpam-6605	125	38	k−2	k−2	PROPN
ejpam-6605	125	39	(	(	PUNCT
ejpam-6605	125	40	1kmk,2(n+1)+(n+1)(2k−5	1kmk,2(n+1)+(n+1)(2k−5	NUM
ejpam-6605	125	41	)	)	PUNCT
ejpam-6605	125	42	)	)	PUNCT
ejpam-6605	126	1	=	=	SYM
ejpam-6605	126	2	1	1	NUM
ejpam-6605	126	3	k−2	k−2	PROPN
ejpam-6605	126	4	(	(	PUNCT
ejpam-6605	126	5	1k	1k	PROPN
ejpam-6605	126	6	(	(	PUNCT
ejpam-6605	126	7	fk,2(n+1)−2)+(n+1)(2k−5	fk,2(n+1)−2)+(n+1)(2k−5	NOUN
ejpam-6605	126	8	)	)	PUNCT
ejpam-6605	126	9	)	)	PUNCT
ejpam-6605	126	10	proof	proof	NOUN
ejpam-6605	126	11	.	.	PUNCT
ejpam-6605	127	1	(	(	PUNCT
ejpam-6605	127	2	i	i	NOUN
ejpam-6605	127	3	)	)	PUNCT
ejpam-6605	127	4	n∑	n∑	PROPN
ejpam-6605	128	1	i=0	i=0	PROPN
ejpam-6605	128	2	mk	mk	PROPN
ejpam-6605	128	3	,	,	PUNCT
ejpam-6605	128	4	i	i	PRON
ejpam-6605	128	5	=	=	PUNCT
ejpam-6605	128	6	n∑	n∑	PROPN
ejpam-6605	128	7	i=0	i=0	PROPN
ejpam-6605	128	8	(	(	PUNCT
ejpam-6605	128	9	k	k	PROPN
ejpam-6605	128	10	−	−	PROPN
ejpam-6605	128	11	1)i	1)i	NUM
ejpam-6605	128	12	−	−	PROPN
ejpam-6605	128	13	1	1	NUM
ejpam-6605	128	14	k	k	NOUN
ejpam-6605	128	15	−	−	PROPN
ejpam-6605	128	16	2	2	NUM
ejpam-6605	128	17	=	=	SYM
ejpam-6605	128	18	1	1	NUM
ejpam-6605	128	19	(	(	PUNCT
ejpam-6605	128	20	k	k	NOUN
ejpam-6605	128	21	−	−	PROPN
ejpam-6605	128	22	2	2	NUM
ejpam-6605	128	23	)	)	PUNCT
ejpam-6605	128	24	(	(	PUNCT
ejpam-6605	128	25	1	1	NUM
ejpam-6605	128	26	−	−	PROPN
ejpam-6605	128	27	(	(	PUNCT
ejpam-6605	128	28	k	k	PROPN
ejpam-6605	128	29	−	−	PROPN
ejpam-6605	129	1	1)n+1	1)n+1	NUM
ejpam-6605	129	2	2	2	NUM
ejpam-6605	129	3	−	−	PROPN
ejpam-6605	129	4	k	k	NOUN
ejpam-6605	129	5	−	−	PROPN
ejpam-6605	129	6	(	(	PUNCT
ejpam-6605	129	7	n	n	PROPN
ejpam-6605	129	8	+	+	NUM
ejpam-6605	129	9	1	1	NUM
ejpam-6605	129	10	)	)	PUNCT
ejpam-6605	129	11	)	)	PUNCT
ejpam-6605	129	12	,	,	PUNCT
ejpam-6605	129	13	geometric	geometric	ADJ
ejpam-6605	129	14	series	series	NOUN
ejpam-6605	129	15	=	=	NOUN
ejpam-6605	129	16	1	1	NUM
ejpam-6605	129	17	k	k	NOUN
ejpam-6605	129	18	−	−	PROPN
ejpam-6605	129	19	2	2	NUM
ejpam-6605	129	20	(	(	PUNCT
ejpam-6605	129	21	mk	mk	PROPN
ejpam-6605	129	22	,	,	PUNCT
ejpam-6605	129	23	n+1	n+1	PROPN
ejpam-6605	129	24	−	−	PROPN
ejpam-6605	129	25	n−	n−	NOUN
ejpam-6605	129	26	1	1	NUM
ejpam-6605	129	27	)	)	PUNCT
ejpam-6605	129	28	(	(	PUNCT
ejpam-6605	129	29	ii	ii	NOUN
ejpam-6605	129	30	)	)	PUNCT
ejpam-6605	129	31	n∑	n∑	PROPN
ejpam-6605	129	32	i=0	i=0	PROPN
ejpam-6605	129	33	fk	fk	INTJ
ejpam-6605	129	34	,	,	PUNCT
ejpam-6605	129	35	i	i	PROPN
ejpam-6605	129	36	=	=	PROPN
ejpam-6605	129	37	n∑	n∑	PROPN
ejpam-6605	129	38	i=0	i=0	PROPN
ejpam-6605	129	39	(	(	PUNCT
ejpam-6605	129	40	k	k	NOUN
ejpam-6605	129	41	−	−	PROPN
ejpam-6605	129	42	1)i	1)i	NUM
ejpam-6605	129	43	+	+	CCONJ
ejpam-6605	129	44	(	(	PUNCT
ejpam-6605	129	45	2k	2k	NOUN
ejpam-6605	129	46	−	−	NOUN
ejpam-6605	129	47	5	5	NUM
ejpam-6605	129	48	)	)	PUNCT
ejpam-6605	129	49	k	k	NOUN
ejpam-6605	130	1	−	−	NOUN
ejpam-6605	130	2	2	2	NUM
ejpam-6605	130	3	=	=	SYM
ejpam-6605	130	4	1	1	NUM
ejpam-6605	130	5	(	(	PUNCT
ejpam-6605	130	6	k	k	NOUN
ejpam-6605	130	7	−	−	PROPN
ejpam-6605	130	8	2	2	NUM
ejpam-6605	130	9	)	)	PUNCT
ejpam-6605	130	10	(	(	PUNCT
ejpam-6605	130	11	1	1	NUM
ejpam-6605	130	12	−	−	PROPN
ejpam-6605	130	13	(	(	PUNCT
ejpam-6605	130	14	k	k	PROPN
ejpam-6605	130	15	−	−	PROPN
ejpam-6605	130	16	1)n+1	1)n+1	NUM
ejpam-6605	130	17	2	2	NUM
ejpam-6605	130	18	−	−	PROPN
ejpam-6605	130	19	k	k	X
ejpam-6605	131	1	+	+	CCONJ
ejpam-6605	131	2	(	(	PUNCT
ejpam-6605	131	3	n	n	PROPN
ejpam-6605	131	4	+	+	CCONJ
ejpam-6605	131	5	1)(2k	1)(2k	NUM
ejpam-6605	131	6	−	−	NOUN
ejpam-6605	131	7	5	5	NUM
ejpam-6605	131	8	)	)	PUNCT
ejpam-6605	131	9	)	)	PUNCT
ejpam-6605	131	10	,	,	PUNCT
ejpam-6605	131	11	geometric	geometric	ADJ
ejpam-6605	131	12	series	series	NOUN
ejpam-6605	131	13	=	=	NOUN
ejpam-6605	131	14	1	1	NUM
ejpam-6605	131	15	k	k	NOUN
ejpam-6605	131	16	−	−	PROPN
ejpam-6605	131	17	2	2	NUM
ejpam-6605	131	18	(	(	PUNCT
ejpam-6605	131	19	fk	fk	INTJ
ejpam-6605	131	20	,	,	PUNCT
ejpam-6605	131	21	n+1	n+1	PROPN
ejpam-6605	131	22	−	−	PROPN
ejpam-6605	131	23	2	2	NUM
ejpam-6605	131	24	+	+	CCONJ
ejpam-6605	131	25	(	(	PUNCT
ejpam-6605	131	26	n	n	PROPN
ejpam-6605	131	27	+	+	CCONJ
ejpam-6605	131	28	1)(2k	1)(2k	NUM
ejpam-6605	131	29	−	−	NOUN
ejpam-6605	131	30	5	5	NUM
ejpam-6605	131	31	)	)	PUNCT
ejpam-6605	131	32	)	)	PUNCT
ejpam-6605	132	1	=	=	SYM
ejpam-6605	133	1	1	1	NUM
ejpam-6605	133	2	k	k	NOUN
ejpam-6605	133	3	−	−	PROPN
ejpam-6605	133	4	2	2	NUM
ejpam-6605	133	5	(	(	PUNCT
ejpam-6605	133	6	mk	mk	NOUN
ejpam-6605	133	7	,	,	PUNCT
ejpam-6605	133	8	n+1	n+1	PROPN
ejpam-6605	133	9	+	+	PUNCT
ejpam-6605	133	10	(	(	PUNCT
ejpam-6605	133	11	n	n	PROPN
ejpam-6605	133	12	+	+	CCONJ
ejpam-6605	133	13	1)(2k	1)(2k	NUM
ejpam-6605	133	14	−	−	NOUN
ejpam-6605	133	15	5	5	NUM
ejpam-6605	133	16	)	)	PUNCT
ejpam-6605	133	17	)	)	PUNCT
ejpam-6605	134	1	sh	sh	PROPN
ejpam-6605	134	2	.	.	PROPN
ejpam-6605	134	3	a.	a.	PROPN
ejpam-6605	134	4	bani	bani	PROPN
ejpam-6605	134	5	melhem	melhem	PROPN
ejpam-6605	134	6	,	,	PUNCT
ejpam-6605	134	7	al	al	PROPN
ejpam-6605	134	8	-	-	PUNCT
ejpam-6605	134	9	kateeb	kateeb	PROPN
ejpam-6605	134	10	,	,	PUNCT
ejpam-6605	134	11	a.	a.	PROPN
ejpam-6605	134	12	dagher	dagher	PROPN
ejpam-6605	134	13	/	/	SYM
ejpam-6605	134	14	eur	eur	PROPN
ejpam-6605	134	15	.	.	PUNCT
ejpam-6605	135	1	j.	j.	PROPN
ejpam-6605	135	2	pure	pure	PROPN
ejpam-6605	135	3	appl	appl	PROPN
ejpam-6605	135	4	.	.	PROPN
ejpam-6605	135	5	math	math	PROPN
ejpam-6605	135	6	,	,	PUNCT
ejpam-6605	135	7	18	18	NUM
ejpam-6605	135	8	(	(	PUNCT
ejpam-6605	135	9	4	4	NUM
ejpam-6605	135	10	)	)	PUNCT
ejpam-6605	135	11	(	(	PUNCT
ejpam-6605	135	12	2025	2025	NUM
ejpam-6605	135	13	)	)	PUNCT
ejpam-6605	135	14	,	,	PUNCT
ejpam-6605	135	15	6605	6605	NUM
ejpam-6605	135	16	7	7	NUM
ejpam-6605	135	17	of	of	ADP
ejpam-6605	135	18	15	15	NUM
ejpam-6605	135	19	(	(	PUNCT
ejpam-6605	135	20	iii	iii	NOUN
ejpam-6605	135	21	)	)	PUNCT
ejpam-6605	135	22	n∑	n∑	PROPN
ejpam-6605	135	23	i=0	i=0	PROPN
ejpam-6605	135	24	mk,2i	mk,2i	PROPN
ejpam-6605	135	25	=	=	SYM
ejpam-6605	135	26	n∑	n∑	PROPN
ejpam-6605	135	27	i=0	i=0	PROPN
ejpam-6605	135	28	(	(	PUNCT
ejpam-6605	135	29	(	(	PUNCT
ejpam-6605	135	30	k	k	X
ejpam-6605	135	31	−	−	PROPN
ejpam-6605	135	32	1)2)i	1)2)i	NUM
ejpam-6605	135	33	−	−	PROPN
ejpam-6605	135	34	1	1	NUM
ejpam-6605	135	35	k	k	NOUN
ejpam-6605	135	36	−	−	PROPN
ejpam-6605	135	37	2	2	NUM
ejpam-6605	135	38	=	=	SYM
ejpam-6605	135	39	1	1	NUM
ejpam-6605	135	40	(	(	PUNCT
ejpam-6605	135	41	k	k	NOUN
ejpam-6605	135	42	−	−	PROPN
ejpam-6605	135	43	2	2	NUM
ejpam-6605	135	44	)	)	PUNCT
ejpam-6605	135	45	(	(	PUNCT
ejpam-6605	135	46	1	1	NUM
ejpam-6605	135	47	−	−	NOUN
ejpam-6605	135	48	(	(	PUNCT
ejpam-6605	135	49	(	(	PUNCT
ejpam-6605	135	50	k	k	PROPN
ejpam-6605	135	51	−	−	PROPN
ejpam-6605	135	52	1)2)n+1	1)2)n+1	NUM
ejpam-6605	135	53	1	1	NUM
ejpam-6605	135	54	−	−	PROPN
ejpam-6605	136	1	(	(	PUNCT
ejpam-6605	136	2	k	k	PROPN
ejpam-6605	136	3	−	−	PROPN
ejpam-6605	137	1	1)2	1)2	NUM
ejpam-6605	137	2	−	−	PROPN
ejpam-6605	137	3	(	(	PUNCT
ejpam-6605	137	4	n	n	NOUN
ejpam-6605	137	5	+	+	NUM
ejpam-6605	137	6	1	1	NUM
ejpam-6605	137	7	)	)	PUNCT
ejpam-6605	137	8	)	)	PUNCT
ejpam-6605	137	9	,	,	PUNCT
ejpam-6605	137	10	geometric	geometric	ADJ
ejpam-6605	137	11	series	series	NOUN
ejpam-6605	137	12	=	=	SYM
ejpam-6605	137	13	1	1	NUM
ejpam-6605	137	14	(	(	PUNCT
ejpam-6605	137	15	k	k	NOUN
ejpam-6605	137	16	−	−	PROPN
ejpam-6605	137	17	2	2	NUM
ejpam-6605	137	18	)	)	PUNCT
ejpam-6605	137	19	(	(	PUNCT
ejpam-6605	137	20	1	1	NUM
ejpam-6605	137	21	−	−	NOUN
ejpam-6605	137	22	(	(	PUNCT
ejpam-6605	137	23	(	(	PUNCT
ejpam-6605	137	24	k	k	NOUN
ejpam-6605	137	25	−	−	PROPN
ejpam-6605	137	26	1)2n+2	1)2n+2	NUM
ejpam-6605	137	27	k(2	k(2	NOUN
ejpam-6605	137	28	−	−	PROPN
ejpam-6605	137	29	k	k	NOUN
ejpam-6605	137	30	)	)	PUNCT
ejpam-6605	137	31	−	−	PROPN
ejpam-6605	138	1	(	(	PUNCT
ejpam-6605	138	2	n	n	NOUN
ejpam-6605	138	3	+	+	NUM
ejpam-6605	138	4	1	1	NUM
ejpam-6605	138	5	)	)	PUNCT
ejpam-6605	138	6	)	)	PUNCT
ejpam-6605	139	1	=	=	SYM
ejpam-6605	140	1	1	1	NUM
ejpam-6605	140	2	k	k	NOUN
ejpam-6605	140	3	−	−	PROPN
ejpam-6605	140	4	2	2	NUM
ejpam-6605	140	5	(	(	PUNCT
ejpam-6605	140	6	1	1	NUM
ejpam-6605	140	7	k	k	PROPN
ejpam-6605	140	8	mk	mk	PROPN
ejpam-6605	140	9	,	,	PUNCT
ejpam-6605	140	10	n+1	n+1	PROPN
ejpam-6605	140	11	−	−	PROPN
ejpam-6605	140	12	n−	n−	NOUN
ejpam-6605	140	13	1	1	NUM
ejpam-6605	140	14	)	)	PUNCT
ejpam-6605	140	15	(	(	PUNCT
ejpam-6605	140	16	iv	iv	X
ejpam-6605	140	17	)	)	PUNCT
ejpam-6605	140	18	n∑	n∑	NOUN
ejpam-6605	141	1	i=0	i=0	PROPN
ejpam-6605	141	2	fk,2i	fk,2i	NUM
ejpam-6605	141	3	=	=	SYM
ejpam-6605	141	4	n∑	n∑	PROPN
ejpam-6605	141	5	i=0	i=0	PROPN
ejpam-6605	141	6	(	(	PUNCT
ejpam-6605	141	7	(	(	PUNCT
ejpam-6605	141	8	k	k	NOUN
ejpam-6605	141	9	−	−	PROPN
ejpam-6605	141	10	1)2)i	1)2)i	NUM
ejpam-6605	141	11	+	+	CCONJ
ejpam-6605	141	12	(	(	PUNCT
ejpam-6605	141	13	2k	2k	NOUN
ejpam-6605	141	14	−	−	NOUN
ejpam-6605	141	15	5	5	NUM
ejpam-6605	141	16	)	)	PUNCT
ejpam-6605	141	17	k	k	NOUN
ejpam-6605	141	18	−	−	NOUN
ejpam-6605	141	19	2	2	NUM
ejpam-6605	141	20	=	=	SYM
ejpam-6605	141	21	1	1	NUM
ejpam-6605	141	22	(	(	PUNCT
ejpam-6605	141	23	k	k	NOUN
ejpam-6605	141	24	−	−	PROPN
ejpam-6605	141	25	2	2	NUM
ejpam-6605	141	26	)	)	PUNCT
ejpam-6605	141	27	(	(	PUNCT
ejpam-6605	141	28	1	1	NUM
ejpam-6605	141	29	−	−	NOUN
ejpam-6605	141	30	(	(	PUNCT
ejpam-6605	141	31	(	(	PUNCT
ejpam-6605	141	32	k	k	PROPN
ejpam-6605	141	33	−	−	PROPN
ejpam-6605	141	34	1)2)n+1	1)2)n+1	NUM
ejpam-6605	141	35	1	1	NUM
ejpam-6605	141	36	−	−	PROPN
ejpam-6605	141	37	(	(	PUNCT
ejpam-6605	141	38	k	k	PROPN
ejpam-6605	141	39	−	−	PROPN
ejpam-6605	141	40	1)2	1)2	NUM
ejpam-6605	141	41	+	+	CCONJ
ejpam-6605	141	42	(	(	PUNCT
ejpam-6605	141	43	n	n	X
ejpam-6605	141	44	+	+	CCONJ
ejpam-6605	141	45	1)(2k	1)(2k	NUM
ejpam-6605	141	46	−	−	NOUN
ejpam-6605	141	47	5	5	NUM
ejpam-6605	141	48	)	)	PUNCT
ejpam-6605	141	49	)	)	PUNCT
ejpam-6605	141	50	,	,	PUNCT
ejpam-6605	141	51	geometric	geometric	ADJ
ejpam-6605	141	52	series	series	NOUN
ejpam-6605	141	53	=	=	SYM
ejpam-6605	141	54	1	1	NUM
ejpam-6605	141	55	(	(	PUNCT
ejpam-6605	141	56	k	k	NOUN
ejpam-6605	141	57	−	−	PROPN
ejpam-6605	141	58	2	2	NUM
ejpam-6605	141	59	)	)	PUNCT
ejpam-6605	141	60	(	(	PUNCT
ejpam-6605	141	61	1	1	NUM
ejpam-6605	141	62	−	−	NOUN
ejpam-6605	141	63	(	(	PUNCT
ejpam-6605	141	64	(	(	PUNCT
ejpam-6605	141	65	k	k	NOUN
ejpam-6605	141	66	−	−	PROPN
ejpam-6605	141	67	1)2n+2	1)2n+2	NUM
ejpam-6605	141	68	k(2	k(2	NOUN
ejpam-6605	141	69	−	−	PROPN
ejpam-6605	141	70	k	k	NOUN
ejpam-6605	141	71	)	)	PUNCT
ejpam-6605	142	1	+	+	CCONJ
ejpam-6605	142	2	(	(	PUNCT
ejpam-6605	142	3	n	n	X
ejpam-6605	142	4	+	+	CCONJ
ejpam-6605	142	5	1)(2k	1)(2k	NUM
ejpam-6605	142	6	−	−	NOUN
ejpam-6605	142	7	5	5	NUM
ejpam-6605	142	8	)	)	PUNCT
ejpam-6605	142	9	)	)	PUNCT
ejpam-6605	142	10	=	=	SYM
ejpam-6605	143	1	1	1	NUM
ejpam-6605	143	2	k	k	NOUN
ejpam-6605	143	3	−	−	PROPN
ejpam-6605	143	4	2	2	NUM
ejpam-6605	143	5	(	(	PUNCT
ejpam-6605	143	6	1	1	NUM
ejpam-6605	143	7	k	k	NOUN
ejpam-6605	143	8	mk,2(n+1	mk,2(n+1	PROPN
ejpam-6605	143	9	)	)	PUNCT
ejpam-6605	144	1	+	+	CCONJ
ejpam-6605	144	2	(	(	PUNCT
ejpam-6605	144	3	n	n	X
ejpam-6605	144	4	+	+	CCONJ
ejpam-6605	144	5	1)(2k	1)(2k	NUM
ejpam-6605	144	6	−	−	NOUN
ejpam-6605	144	7	5	5	NUM
ejpam-6605	144	8	)	)	PUNCT
ejpam-6605	144	9	)	)	PUNCT
ejpam-6605	144	10	=	=	SYM
ejpam-6605	145	1	1	1	NUM
ejpam-6605	145	2	k	k	NOUN
ejpam-6605	145	3	−	−	PROPN
ejpam-6605	145	4	2	2	NUM
ejpam-6605	145	5	(	(	PUNCT
ejpam-6605	145	6	1	1	NUM
ejpam-6605	145	7	k	k	NOUN
ejpam-6605	145	8	(	(	PUNCT
ejpam-6605	145	9	fk,2(n+1	fk,2(n+1	NUM
ejpam-6605	145	10	)	)	PUNCT
ejpam-6605	145	11	−	−	ADP
ejpam-6605	145	12	2	2	NUM
ejpam-6605	145	13	)	)	PUNCT
ejpam-6605	145	14	+	+	CCONJ
ejpam-6605	145	15	(	(	PUNCT
ejpam-6605	145	16	n	n	X
ejpam-6605	145	17	+	+	CCONJ
ejpam-6605	145	18	1)(2k	1)(2k	NUM
ejpam-6605	145	19	−	−	NOUN
ejpam-6605	145	20	5	5	NUM
ejpam-6605	145	21	)	)	PUNCT
ejpam-6605	145	22	)	)	PUNCT
ejpam-6605	145	23	lemma	lemma	PROPN
ejpam-6605	146	1	1	1	X
ejpam-6605	146	2	.	.	PUNCT
ejpam-6605	147	1	we	we	PRON
ejpam-6605	147	2	have	have	VERB
ejpam-6605	147	3	limn→∞	limn→∞	PROPN
ejpam-6605	147	4	mk	mk	X
ejpam-6605	147	5	,	,	PUNCT
ejpam-6605	147	6	n+1	n+1	PROPN
ejpam-6605	147	7	mk	mk	PROPN
ejpam-6605	147	8	,	,	PUNCT
ejpam-6605	147	9	n	n	NOUN
ejpam-6605	147	10	=	=	SYM
ejpam-6605	147	11	k	k	NOUN
ejpam-6605	148	1	−	−	NOUN
ejpam-6605	148	2	1	1	X
ejpam-6605	148	3	.	.	PUNCT
ejpam-6605	149	1	proof	proof	NOUN
ejpam-6605	149	2	.	.	PUNCT
ejpam-6605	150	1	limn→∞	limn→∞	PROPN
ejpam-6605	150	2	mk	mk	PROPN
ejpam-6605	150	3	,	,	PUNCT
ejpam-6605	150	4	n+1	n+1	PROPN
ejpam-6605	150	5	mk	mk	PROPN
ejpam-6605	150	6	,	,	PUNCT
ejpam-6605	150	7	n	n	PROPN
ejpam-6605	150	8	=	=	SYM
ejpam-6605	150	9	limn→∞	limn→∞	PROPN
ejpam-6605	150	10	(	(	PUNCT
ejpam-6605	150	11	k−1)n+1−1	k−1)n+1−1	PROPN
ejpam-6605	150	12	k−2	k−2	PROPN
ejpam-6605	150	13	·	·	PUNCT
ejpam-6605	150	14	k−2	k−2	PROPN
ejpam-6605	150	15	(	(	PUNCT
ejpam-6605	150	16	k−1)n−1	k−1)n−1	PROPN
ejpam-6605	150	17	=	=	SYM
ejpam-6605	150	18	limn→∞	limn→∞	PROPN
ejpam-6605	150	19	(	(	PUNCT
ejpam-6605	150	20	k−1)n+1(1−	k−1)n+1(1−	NOUN
ejpam-6605	150	21	1	1	NUM
ejpam-6605	150	22	(	(	PUNCT
ejpam-6605	150	23	k−1)n+1	k−1)n+1	PROPN
ejpam-6605	150	24	)	)	PUNCT
ejpam-6605	150	25	(	(	PUNCT
ejpam-6605	150	26	k−1)n(1−	k−1)n(1−	PROPN
ejpam-6605	150	27	1	1	NUM
ejpam-6605	150	28	(	(	PUNCT
ejpam-6605	150	29	k−1)n	k−1)n	PROPN
ejpam-6605	150	30	)	)	PUNCT
ejpam-6605	150	31	=	=	PUNCT
ejpam-6605	151	1	k	k	X
ejpam-6605	152	1	−	−	PROPN
ejpam-6605	152	2	1	1	NUM
ejpam-6605	152	3	lemma	lemma	PROPN
ejpam-6605	152	4	2	2	NUM
ejpam-6605	152	5	.	.	PUNCT
ejpam-6605	153	1	the	the	DET
ejpam-6605	153	2	series	series	PROPN
ejpam-6605	153	3	∑∞	∑∞	PROPN
ejpam-6605	153	4	n=0	n=0	X
ejpam-6605	153	5	1	1	NUM
ejpam-6605	153	6	mk	mk	NOUN
ejpam-6605	153	7	,	,	PUNCT
ejpam-6605	153	8	n	n	X
ejpam-6605	153	9	is	be	AUX
ejpam-6605	153	10	a	a	DET
ejpam-6605	153	11	convergent	convergent	NOUN
ejpam-6605	153	12	series	series	NOUN
ejpam-6605	153	13	.	.	PUNCT
ejpam-6605	154	1	proof	proof	NOUN
ejpam-6605	154	2	.	.	PUNCT
ejpam-6605	155	1	by	by	ADP
ejpam-6605	155	2	ratio	ratio	NOUN
ejpam-6605	155	3	test	test	NOUN
ejpam-6605	155	4	limn→∞	limn→∞	PROPN
ejpam-6605	155	5	mk	mk	PROPN
ejpam-6605	155	6	,	,	PUNCT
ejpam-6605	155	7	n	n	PROPN
ejpam-6605	155	8	mk	mk	NOUN
ejpam-6605	155	9	,	,	PUNCT
ejpam-6605	155	10	n+1	n+1	PROPN
ejpam-6605	155	11	=	=	SYM
ejpam-6605	155	12	1	1	NUM
ejpam-6605	155	13	k−1	k−1	PROPN
ejpam-6605	155	14	<	<	X
ejpam-6605	155	15	1	1	NUM
ejpam-6605	155	16	,	,	PUNCT
ejpam-6605	155	17	so	so	ADV
ejpam-6605	155	18	the	the	DET
ejpam-6605	155	19	series	series	NOUN
ejpam-6605	155	20	is	be	AUX
ejpam-6605	155	21	convergent	convergent	ADJ
ejpam-6605	155	22	,	,	PUNCT
ejpam-6605	155	23	lemma	lemma	PROPN
ejpam-6605	155	24	3	3	NUM
ejpam-6605	155	25	.	.	PUNCT
ejpam-6605	156	1	the	the	DET
ejpam-6605	156	2	series	series	PROPN
ejpam-6605	156	3	∑∞	∑∞	PROPN
ejpam-6605	156	4	n=1	n=1	PROPN
ejpam-6605	156	5	mk	mk	PROPN
ejpam-6605	156	6	,	,	PUNCT
ejpam-6605	156	7	n	n	PRON
ejpam-6605	156	8	kn	kn	NOUN
ejpam-6605	157	1	=	=	PROPN
ejpam-6605	157	2	k	k	PROPN
ejpam-6605	157	3	k−1	k−1	PROPN
ejpam-6605	157	4	.	.	PUNCT
ejpam-6605	158	1	proof	proof	NOUN
ejpam-6605	158	2	.	.	PUNCT
ejpam-6605	159	1	let	let	VERB
ejpam-6605	159	2	s	s	NOUN
ejpam-6605	159	3	=	=	NOUN
ejpam-6605	159	4	∑∞	∑∞	X
ejpam-6605	159	5	n=1	n=1	PROPN
ejpam-6605	159	6	mk	mk	PROPN
ejpam-6605	159	7	,	,	PUNCT
ejpam-6605	159	8	n	n	PRON
ejpam-6605	159	9	kn	kn	NOUN
ejpam-6605	159	10	.	.	PUNCT
ejpam-6605	160	1	then	then	ADV
ejpam-6605	160	2	∞∑	∞∑	NUM
ejpam-6605	160	3	n=1	n=1	PROPN
ejpam-6605	160	4	mk	mk	PROPN
ejpam-6605	160	5	,	,	PUNCT
ejpam-6605	160	6	n	n	PRON
ejpam-6605	160	7	kn	kn	NOUN
ejpam-6605	160	8	=	=	NOUN
ejpam-6605	160	9	1	1	NUM
ejpam-6605	160	10	k	k	NOUN
ejpam-6605	160	11	+	+	CCONJ
ejpam-6605	160	12	∞∑	∞∑	PROPN
ejpam-6605	160	13	n=2	n=2	X
ejpam-6605	160	14	mk	mk	NOUN
ejpam-6605	160	15	,	,	PUNCT
ejpam-6605	160	16	n	n	PRON
ejpam-6605	160	17	kn	kn	PROPN
ejpam-6605	160	18	sh	sh	PROPN
ejpam-6605	160	19	.	.	PROPN
ejpam-6605	160	20	a.	a.	PROPN
ejpam-6605	160	21	bani	bani	PROPN
ejpam-6605	160	22	melhem	melhem	PROPN
ejpam-6605	160	23	,	,	PUNCT
ejpam-6605	160	24	al	al	PROPN
ejpam-6605	160	25	-	-	PUNCT
ejpam-6605	160	26	kateeb	kateeb	PROPN
ejpam-6605	160	27	,	,	PUNCT
ejpam-6605	160	28	a.	a.	PROPN
ejpam-6605	160	29	dagher	dagher	PROPN
ejpam-6605	160	30	/	/	SYM
ejpam-6605	160	31	eur	eur	PROPN
ejpam-6605	160	32	.	.	PUNCT
ejpam-6605	161	1	j.	j.	PROPN
ejpam-6605	161	2	pure	pure	PROPN
ejpam-6605	161	3	appl	appl	PROPN
ejpam-6605	161	4	.	.	PROPN
ejpam-6605	161	5	math	math	PROPN
ejpam-6605	161	6	,	,	PUNCT
ejpam-6605	161	7	18	18	NUM
ejpam-6605	161	8	(	(	PUNCT
ejpam-6605	161	9	4	4	NUM
ejpam-6605	161	10	)	)	PUNCT
ejpam-6605	161	11	(	(	PUNCT
ejpam-6605	161	12	2025	2025	NUM
ejpam-6605	161	13	)	)	PUNCT
ejpam-6605	161	14	,	,	PUNCT
ejpam-6605	161	15	6605	6605	NUM
ejpam-6605	161	16	8	8	NUM
ejpam-6605	161	17	of	of	ADP
ejpam-6605	161	18	15	15	NUM
ejpam-6605	161	19	=	=	SYM
ejpam-6605	161	20	1	1	NUM
ejpam-6605	161	21	k	k	NOUN
ejpam-6605	161	22	+	+	CCONJ
ejpam-6605	161	23	∞∑	∞∑	PROPN
ejpam-6605	161	24	n=1	n=1	PROPN
ejpam-6605	161	25	mk	mk	PROPN
ejpam-6605	161	26	,	,	PUNCT
ejpam-6605	161	27	n+1	n+1	PROPN
ejpam-6605	161	28	kn+1	kn+1	PROPN
ejpam-6605	161	29	=	=	SYM
ejpam-6605	161	30	1	1	NUM
ejpam-6605	161	31	k	k	NOUN
ejpam-6605	161	32	+	+	CCONJ
ejpam-6605	161	33	∞∑	∞∑	PROPN
ejpam-6605	161	34	n=1	n=1	PROPN
ejpam-6605	161	35	kmk	kmk	PROPN
ejpam-6605	161	36	,	,	PUNCT
ejpam-6605	161	37	n	n	PROPN
ejpam-6605	161	38	+	+	CCONJ
ejpam-6605	161	39	(	(	PUNCT
ejpam-6605	161	40	1	1	NUM
ejpam-6605	161	41	−	−	PROPN
ejpam-6605	161	42	k)mk	k)mk	PROPN
ejpam-6605	161	43	,	,	PUNCT
ejpam-6605	161	44	n−1	n−1	PROPN
ejpam-6605	161	45	kn+1	kn+1	PROPN
ejpam-6605	161	46	=	=	SYM
ejpam-6605	161	47	1	1	NUM
ejpam-6605	161	48	k	k	NOUN
ejpam-6605	161	49	+	+	CCONJ
ejpam-6605	161	50	∞∑	∞∑	PROPN
ejpam-6605	161	51	n=1	n=1	PROPN
ejpam-6605	161	52	mk	mk	PROPN
ejpam-6605	161	53	,	,	PUNCT
ejpam-6605	161	54	n	n	PRON
ejpam-6605	161	55	kn	kn	PROPN
ejpam-6605	161	56	+	+	CCONJ
ejpam-6605	161	57	(	(	PUNCT
ejpam-6605	161	58	1	1	NUM
ejpam-6605	161	59	−	−	PROPN
ejpam-6605	161	60	k	k	X
ejpam-6605	161	61	)	)	PUNCT
ejpam-6605	161	62	k2	k2	NOUN
ejpam-6605	161	63	∞∑	∞∑	PROPN
ejpam-6605	161	64	n=1	n=1	PROPN
ejpam-6605	161	65	mk	mk	PROPN
ejpam-6605	161	66	,	,	PUNCT
ejpam-6605	161	67	n−1	n−1	PROPN
ejpam-6605	161	68	kn−1	kn−1	PROPN
ejpam-6605	161	69	=	=	NOUN
ejpam-6605	162	1	1	1	NUM
ejpam-6605	162	2	k	k	NOUN
ejpam-6605	162	3	+	+	PRON
ejpam-6605	162	4	s	s	X
ejpam-6605	162	5	+	+	X
ejpam-6605	162	6	(	(	PUNCT
ejpam-6605	162	7	1	1	NUM
ejpam-6605	162	8	−	−	PROPN
ejpam-6605	162	9	k	k	X
ejpam-6605	162	10	)	)	PUNCT
ejpam-6605	162	11	k2	k2	NOUN
ejpam-6605	162	12	∞∑	∞∑	PROPN
ejpam-6605	162	13	n=0	n=0	PROPN
ejpam-6605	162	14	mk	mk	NOUN
ejpam-6605	162	15	,	,	PUNCT
ejpam-6605	162	16	n	n	PROPN
ejpam-6605	162	17	kn	kn	NOUN
ejpam-6605	162	18	=	=	NOUN
ejpam-6605	162	19	1	1	NUM
ejpam-6605	163	1	k	k	NOUN
ejpam-6605	163	2	+	+	PRON
ejpam-6605	163	3	s	s	X
ejpam-6605	163	4	+	+	X
ejpam-6605	163	5	(	(	PUNCT
ejpam-6605	163	6	1	1	NUM
ejpam-6605	163	7	−	−	PROPN
ejpam-6605	163	8	k	k	X
ejpam-6605	163	9	)	)	PUNCT
ejpam-6605	163	10	k2	k2	PROPN
ejpam-6605	163	11	s	s	PART
ejpam-6605	163	12	thus	thus	ADV
ejpam-6605	163	13	,	,	PUNCT
ejpam-6605	163	14	s	s	PART
ejpam-6605	163	15	=	=	SYM
ejpam-6605	163	16	k	k	PROPN
ejpam-6605	163	17	k−1	k−1	PROPN
ejpam-6605	163	18	.	.	PUNCT
ejpam-6605	164	1	we	we	PRON
ejpam-6605	164	2	need	need	VERB
ejpam-6605	164	3	the	the	DET
ejpam-6605	164	4	next	next	ADJ
ejpam-6605	164	5	remark	remark	NOUN
ejpam-6605	164	6	in	in	ADP
ejpam-6605	164	7	the	the	DET
ejpam-6605	164	8	proof	proof	NOUN
ejpam-6605	164	9	of	of	ADP
ejpam-6605	164	10	the	the	DET
ejpam-6605	164	11	next	next	ADJ
ejpam-6605	164	12	theorem	theorem	NOUN
ejpam-6605	164	13	.	.	PUNCT
ejpam-6605	165	1	in	in	ADP
ejpam-6605	165	2	fact	fact	NOUN
ejpam-6605	165	3	it	it	PRON
ejpam-6605	165	4	is	be	AUX
ejpam-6605	165	5	exercise	exercise	NOUN
ejpam-6605	165	6	16	16	NUM
ejpam-6605	165	7	in	in	ADP
ejpam-6605	165	8	section	section	NOUN
ejpam-6605	165	9	3.3	3.3	NUM
ejpam-6605	165	10	in	in	ADP
ejpam-6605	165	11	[	[	X
ejpam-6605	165	12	9	9	NUM
ejpam-6605	165	13	]	]	PUNCT
ejpam-6605	165	14	.	.	PUNCT
ejpam-6605	166	1	remark	remark	PROPN
ejpam-6605	166	2	2	2	NUM
ejpam-6605	166	3	.	.	PUNCT
ejpam-6605	167	1	for	for	ADP
ejpam-6605	167	2	any	any	DET
ejpam-6605	167	3	three	three	NUM
ejpam-6605	167	4	integers	integer	NOUN
ejpam-6605	167	5	a	a	DET
ejpam-6605	167	6	,	,	PUNCT
ejpam-6605	167	7	b	b	NOUN
ejpam-6605	167	8	and	and	CCONJ
ejpam-6605	167	9	c	c	X
ejpam-6605	167	10	such	such	ADJ
ejpam-6605	168	1	that	that	SCONJ
ejpam-6605	168	2	gcd(a	gcd(a	PROPN
ejpam-6605	168	3	,	,	PUNCT
ejpam-6605	168	4	b	b	NOUN
ejpam-6605	168	5	)	)	PUNCT
ejpam-6605	168	6	=	=	SYM
ejpam-6605	168	7	gcd(a	gcd(a	PROPN
ejpam-6605	168	8	,	,	PUNCT
ejpam-6605	168	9	c	c	NOUN
ejpam-6605	168	10	)	)	PUNCT
ejpam-6605	168	11	=	=	SYM
ejpam-6605	168	12	1	1	NUM
ejpam-6605	168	13	,	,	PUNCT
ejpam-6605	168	14	we	we	PRON
ejpam-6605	168	15	have	have	VERB
ejpam-6605	168	16	gcd(a	gcd(a	PROPN
ejpam-6605	168	17	,	,	PUNCT
ejpam-6605	168	18	bc	bc	PROPN
ejpam-6605	168	19	)	)	PUNCT
ejpam-6605	168	20	=	=	SYM
ejpam-6605	168	21	1	1	NUM
ejpam-6605	168	22	theorem	theorem	VERB
ejpam-6605	168	23	7	7	NUM
ejpam-6605	168	24	.	.	NOUN
ejpam-6605	168	25	for	for	ADP
ejpam-6605	168	26	n	n	PRON
ejpam-6605	168	27	≥	≥	NUM
ejpam-6605	168	28	1	1	NUM
ejpam-6605	168	29	,	,	PUNCT
ejpam-6605	168	30	we	we	PRON
ejpam-6605	168	31	have	have	VERB
ejpam-6605	168	32	(	(	PUNCT
ejpam-6605	168	33	i	i	NOUN
ejpam-6605	168	34	)	)	PUNCT
ejpam-6605	168	35	gcd(mk	gcd(mk	PROPN
ejpam-6605	168	36	,	,	PUNCT
ejpam-6605	168	37	n	n	CCONJ
ejpam-6605	168	38	,	,	PUNCT
ejpam-6605	168	39	k	k	PROPN
ejpam-6605	169	1	−	−	PROPN
ejpam-6605	169	2	1	1	X
ejpam-6605	169	3	)	)	PUNCT
ejpam-6605	169	4	=	=	SYM
ejpam-6605	169	5	1	1	NUM
ejpam-6605	169	6	(	(	PUNCT
ejpam-6605	169	7	ii	ii	NOUN
ejpam-6605	169	8	)	)	PUNCT
ejpam-6605	169	9	gcd(mk	gcd(mk	NOUN
ejpam-6605	169	10	,	,	PUNCT
ejpam-6605	169	11	n	n	CCONJ
ejpam-6605	169	12	,	,	PUNCT
ejpam-6605	169	13	k	k	NOUN
ejpam-6605	169	14	)	)	PUNCT
ejpam-6605	169	15	=	=	NOUN
ejpam-6605	169	16	{	{	PUNCT
ejpam-6605	169	17	1	1	NUM
ejpam-6605	169	18	,	,	PUNCT
ejpam-6605	169	19	if	if	SCONJ
ejpam-6605	169	20	n	n	PRON
ejpam-6605	169	21	is	be	AUX
ejpam-6605	169	22	odd	odd	ADJ
ejpam-6605	169	23	k	k	NOUN
ejpam-6605	169	24	,	,	PUNCT
ejpam-6605	169	25	if	if	SCONJ
ejpam-6605	169	26	n	n	PRON
ejpam-6605	169	27	is	be	AUX
ejpam-6605	169	28	even	even	ADV
ejpam-6605	169	29	(	(	PUNCT
ejpam-6605	169	30	iii	iii	NOUN
ejpam-6605	169	31	)	)	PUNCT
ejpam-6605	169	32	gcd(mk	gcd(mk	NOUN
ejpam-6605	169	33	,	,	PUNCT
ejpam-6605	169	34	n	n	CCONJ
ejpam-6605	169	35	,	,	PUNCT
ejpam-6605	169	36	mk	mk	PROPN
ejpam-6605	169	37	,	,	PUNCT
ejpam-6605	169	38	n+1	n+1	PROPN
ejpam-6605	169	39	)	)	PUNCT
ejpam-6605	169	40	=	=	SYM
ejpam-6605	169	41	1	1	NUM
ejpam-6605	169	42	(	(	PUNCT
ejpam-6605	169	43	iv	iv	X
ejpam-6605	169	44	)	)	PUNCT
ejpam-6605	169	45	gcd(fk	gcd(fk	NOUN
ejpam-6605	169	46	,	,	PUNCT
ejpam-6605	169	47	n	n	CCONJ
ejpam-6605	169	48	,	,	PUNCT
ejpam-6605	169	49	k	k	PROPN
ejpam-6605	170	1	−	−	PROPN
ejpam-6605	170	2	1	1	X
ejpam-6605	170	3	)	)	PUNCT
ejpam-6605	170	4	=	=	SYM
ejpam-6605	170	5	1	1	NUM
ejpam-6605	170	6	(	(	PUNCT
ejpam-6605	170	7	v	v	NOUN
ejpam-6605	170	8	)	)	PUNCT
ejpam-6605	170	9	gcd(fk	gcd(fk	NOUN
ejpam-6605	170	10	,	,	PUNCT
ejpam-6605	170	11	n	n	CCONJ
ejpam-6605	170	12	,	,	PUNCT
ejpam-6605	170	13	k	k	NOUN
ejpam-6605	170	14	)	)	PUNCT
ejpam-6605	170	15	=	=	SYM
ejpam-6605	170	16	{	{	PUNCT
ejpam-6605	170	17	gcd(3	gcd(3	NOUN
ejpam-6605	170	18	,	,	PUNCT
ejpam-6605	170	19	k	k	NOUN
ejpam-6605	170	20	)	)	PUNCT
ejpam-6605	170	21	,	,	PUNCT
ejpam-6605	170	22	if	if	SCONJ
ejpam-6605	170	23	n	n	PRON
ejpam-6605	170	24	is	be	AUX
ejpam-6605	170	25	odd	odd	ADJ
ejpam-6605	170	26	gcd(2	gcd(2	NOUN
ejpam-6605	170	27	,	,	PUNCT
ejpam-6605	170	28	k	k	NOUN
ejpam-6605	170	29	)	)	PUNCT
ejpam-6605	170	30	,	,	PUNCT
ejpam-6605	170	31	if	if	SCONJ
ejpam-6605	170	32	n	n	PRON
ejpam-6605	170	33	is	be	AUX
ejpam-6605	170	34	even	even	ADV
ejpam-6605	170	35	(	(	PUNCT
ejpam-6605	170	36	vi	vi	NOUN
ejpam-6605	170	37	)	)	PUNCT
ejpam-6605	170	38	gcd(fk	gcd(fk	NOUN
ejpam-6605	170	39	,	,	PUNCT
ejpam-6605	170	40	n	n	CCONJ
ejpam-6605	170	41	,	,	PUNCT
ejpam-6605	170	42	fk	fk	INTJ
ejpam-6605	170	43	,	,	PUNCT
ejpam-6605	170	44	n+1	n+1	PROPN
ejpam-6605	170	45	)	)	PUNCT
ejpam-6605	170	46	=	=	SYM
ejpam-6605	170	47	1	1	NUM
ejpam-6605	170	48	proof	proof	NOUN
ejpam-6605	170	49	.	.	PUNCT
ejpam-6605	171	1	(	(	PUNCT
ejpam-6605	171	2	i	i	NOUN
ejpam-6605	171	3	)	)	PUNCT
ejpam-6605	171	4	we	we	PRON
ejpam-6605	171	5	prove	prove	VERB
ejpam-6605	171	6	this	this	DET
ejpam-6605	171	7	property	property	NOUN
ejpam-6605	171	8	using	use	VERB
ejpam-6605	171	9	mathematical	mathematical	ADJ
ejpam-6605	171	10	induction	induction	NOUN
ejpam-6605	171	11	.	.	PUNCT
ejpam-6605	172	1	at	at	ADP
ejpam-6605	172	2	first	first	PROPN
ejpam-6605	172	3	gcd(mk,1	gcd(mk,1	PROPN
ejpam-6605	172	4	,	,	PUNCT
ejpam-6605	172	5	k	k	PROPN
ejpam-6605	172	6	−	−	PROPN
ejpam-6605	172	7	1	1	NUM
ejpam-6605	172	8	)	)	PUNCT
ejpam-6605	172	9	=	=	PUNCT
ejpam-6605	172	10	gcd(1	gcd(1	PROPN
ejpam-6605	172	11	,	,	PUNCT
ejpam-6605	172	12	k	k	PROPN
ejpam-6605	172	13	−	−	PROPN
ejpam-6605	172	14	1	1	X
ejpam-6605	172	15	)	)	PUNCT
ejpam-6605	172	16	=	=	SYM
ejpam-6605	172	17	1	1	X
ejpam-6605	172	18	.	.	X
ejpam-6605	172	19	assume	assume	VERB
ejpam-6605	172	20	that	that	SCONJ
ejpam-6605	172	21	gcd(mk	gcd(mk	NOUN
ejpam-6605	172	22	,	,	PUNCT
ejpam-6605	172	23	n	n	CCONJ
ejpam-6605	172	24	,	,	PUNCT
ejpam-6605	172	25	k	k	PROPN
ejpam-6605	172	26	−	−	PROPN
ejpam-6605	172	27	1	1	X
ejpam-6605	172	28	)	)	PUNCT
ejpam-6605	172	29	=	=	SYM
ejpam-6605	172	30	1	1	NUM
ejpam-6605	172	31	,	,	PUNCT
ejpam-6605	172	32	consider	consider	VERB
ejpam-6605	172	33	gcd(mk	gcd(mk	NOUN
ejpam-6605	172	34	,	,	PUNCT
ejpam-6605	172	35	n+1	n+1	PROPN
ejpam-6605	172	36	,	,	PUNCT
ejpam-6605	172	37	k	k	PROPN
ejpam-6605	173	1	−	−	PROPN
ejpam-6605	173	2	1	1	NUM
ejpam-6605	173	3	)	)	PUNCT
ejpam-6605	173	4	=	=	NOUN
ejpam-6605	173	5	gcd(kmk	gcd(kmk	NOUN
ejpam-6605	173	6	,	,	PUNCT
ejpam-6605	173	7	n	n	X
ejpam-6605	173	8	+	+	CCONJ
ejpam-6605	173	9	(	(	PUNCT
ejpam-6605	173	10	1−k)mk	1−k)mk	NUM
ejpam-6605	173	11	,	,	PUNCT
ejpam-6605	173	12	n−1	n−1	PROPN
ejpam-6605	173	13	,	,	PUNCT
ejpam-6605	173	14	k−1	k−1	PROPN
ejpam-6605	173	15	)	)	PUNCT
ejpam-6605	173	16	=	=	SYM
ejpam-6605	173	17	gcd(kmk	gcd(kmk	NOUN
ejpam-6605	173	18	,	,	PUNCT
ejpam-6605	173	19	n	n	CCONJ
ejpam-6605	173	20	,	,	PUNCT
ejpam-6605	173	21	k−1	k−1	PROPN
ejpam-6605	173	22	)	)	PUNCT
ejpam-6605	173	23	=	=	SYM
ejpam-6605	173	24	gcd(mk	gcd(mk	NOUN
ejpam-6605	173	25	,	,	PUNCT
ejpam-6605	173	26	n	n	CCONJ
ejpam-6605	173	27	,	,	PUNCT
ejpam-6605	173	28	k−1	k−1	PROPN
ejpam-6605	173	29	)	)	PUNCT
ejpam-6605	173	30	=	=	SYM
ejpam-6605	173	31	1	1	NUM
ejpam-6605	173	32	,	,	PUNCT
ejpam-6605	173	33	using	use	VERB
ejpam-6605	173	34	the	the	DET
ejpam-6605	173	35	well	well	ADV
ejpam-6605	173	36	-	-	PUNCT
ejpam-6605	173	37	known	know	VERB
ejpam-6605	173	38	property	property	NOUN
ejpam-6605	173	39	gcd(a	gcd(a	PROPN
ejpam-6605	173	40	+	+	CCONJ
ejpam-6605	173	41	bc	bc	PROPN
ejpam-6605	173	42	,	,	PUNCT
ejpam-6605	173	43	b	b	NOUN
ejpam-6605	173	44	)	)	PUNCT
ejpam-6605	173	45	=	=	SYM
ejpam-6605	173	46	gcd(a	gcd(a	PROPN
ejpam-6605	173	47	,	,	PUNCT
ejpam-6605	173	48	b	b	NOUN
ejpam-6605	173	49	)	)	PUNCT
ejpam-6605	173	50	sh	sh	PROPN
ejpam-6605	173	51	.	.	PROPN
ejpam-6605	173	52	a.	a.	PROPN
ejpam-6605	173	53	bani	bani	PROPN
ejpam-6605	173	54	melhem	melhem	PROPN
ejpam-6605	173	55	,	,	PUNCT
ejpam-6605	173	56	al	al	PROPN
ejpam-6605	173	57	-	-	PUNCT
ejpam-6605	173	58	kateeb	kateeb	PROPN
ejpam-6605	173	59	,	,	PUNCT
ejpam-6605	173	60	a.	a.	PROPN
ejpam-6605	173	61	dagher	dagher	PROPN
ejpam-6605	173	62	/	/	SYM
ejpam-6605	173	63	eur	eur	PROPN
ejpam-6605	173	64	.	.	PUNCT
ejpam-6605	174	1	j.	j.	PROPN
ejpam-6605	174	2	pure	pure	PROPN
ejpam-6605	174	3	appl	appl	PROPN
ejpam-6605	174	4	.	.	PROPN
ejpam-6605	174	5	math	math	PROPN
ejpam-6605	174	6	,	,	PUNCT
ejpam-6605	174	7	18	18	NUM
ejpam-6605	174	8	(	(	PUNCT
ejpam-6605	174	9	4	4	NUM
ejpam-6605	174	10	)	)	PUNCT
ejpam-6605	174	11	(	(	PUNCT
ejpam-6605	174	12	2025	2025	NUM
ejpam-6605	174	13	)	)	PUNCT
ejpam-6605	174	14	,	,	PUNCT
ejpam-6605	174	15	6605	6605	NUM
ejpam-6605	174	16	9	9	NUM
ejpam-6605	174	17	of	of	ADP
ejpam-6605	174	18	15	15	NUM
ejpam-6605	174	19	(	(	PUNCT
ejpam-6605	174	20	ii	ii	NOUN
ejpam-6605	174	21	)	)	PUNCT
ejpam-6605	175	1	we	we	PRON
ejpam-6605	175	2	prove	prove	VERB
ejpam-6605	175	3	this	this	DET
ejpam-6605	175	4	property	property	NOUN
ejpam-6605	175	5	using	use	VERB
ejpam-6605	175	6	mathematical	mathematical	ADJ
ejpam-6605	175	7	induction	induction	NOUN
ejpam-6605	175	8	.	.	PUNCT
ejpam-6605	176	1	at	at	ADP
ejpam-6605	176	2	first	first	PROPN
ejpam-6605	176	3	gcd(mk,1	gcd(mk,1	PROPN
ejpam-6605	176	4	,	,	PUNCT
ejpam-6605	176	5	k	k	NOUN
ejpam-6605	176	6	)	)	PUNCT
ejpam-6605	176	7	=	=	SYM
ejpam-6605	176	8	1	1	NUM
ejpam-6605	176	9	and	and	CCONJ
ejpam-6605	176	10	gcd(mk,2	gcd(mk,2	PROPN
ejpam-6605	176	11	,	,	PUNCT
ejpam-6605	176	12	k	k	NOUN
ejpam-6605	176	13	)	)	PUNCT
ejpam-6605	176	14	=	=	SYM
ejpam-6605	176	15	2	2	X
ejpam-6605	176	16	.	.	X
ejpam-6605	176	17	assume	assume	VERB
ejpam-6605	176	18	that	that	SCONJ
ejpam-6605	176	19	gcd(mk	gcd(mk	NOUN
ejpam-6605	176	20	,	,	PUNCT
ejpam-6605	176	21	n	n	CCONJ
ejpam-6605	176	22	,	,	PUNCT
ejpam-6605	176	23	k	k	NOUN
ejpam-6605	176	24	)	)	PUNCT
ejpam-6605	176	25	=	=	NOUN
ejpam-6605	176	26	{	{	PUNCT
ejpam-6605	177	1	1	1	NUM
ejpam-6605	177	2	,	,	PUNCT
ejpam-6605	177	3	if	if	SCONJ
ejpam-6605	177	4	n	n	PRON
ejpam-6605	177	5	is	be	AUX
ejpam-6605	177	6	odd	odd	ADJ
ejpam-6605	177	7	k	k	NOUN
ejpam-6605	177	8	,	,	PUNCT
ejpam-6605	177	9	if	if	SCONJ
ejpam-6605	177	10	n	n	PRON
ejpam-6605	177	11	is	be	AUX
ejpam-6605	177	12	even	even	ADV
ejpam-6605	177	13	,	,	PUNCT
ejpam-6605	177	14	now	now	ADV
ejpam-6605	177	15	consider	consider	VERB
ejpam-6605	177	16	gcd(mk	gcd(mk	NOUN
ejpam-6605	177	17	,	,	PUNCT
ejpam-6605	177	18	n+1	n+1	PROPN
ejpam-6605	177	19	,	,	PUNCT
ejpam-6605	177	20	k	k	NOUN
ejpam-6605	177	21	)	)	PUNCT
ejpam-6605	177	22	=	=	SYM
ejpam-6605	177	23	gcd(kmk	gcd(kmk	NOUN
ejpam-6605	177	24	,	,	PUNCT
ejpam-6605	177	25	n	n	X
ejpam-6605	177	26	+	+	CCONJ
ejpam-6605	177	27	(	(	PUNCT
ejpam-6605	177	28	1	1	NUM
ejpam-6605	177	29	−	−	PROPN
ejpam-6605	177	30	k)mk	k)mk	PROPN
ejpam-6605	177	31	,	,	PUNCT
ejpam-6605	177	32	n−1	n−1	PROPN
ejpam-6605	177	33	,	,	PUNCT
ejpam-6605	177	34	k	k	NOUN
ejpam-6605	177	35	)	)	PUNCT
ejpam-6605	178	1	=	=	SYM
ejpam-6605	178	2	gcd((1	gcd((1	VERB
ejpam-6605	178	3	−	−	PROPN
ejpam-6605	179	1	k)mk	k)mk	PROPN
ejpam-6605	179	2	,	,	PUNCT
ejpam-6605	179	3	n−1	n−1	PROPN
ejpam-6605	179	4	,	,	PUNCT
ejpam-6605	179	5	k	k	NOUN
ejpam-6605	179	6	)	)	PUNCT
ejpam-6605	179	7	=	=	SYM
ejpam-6605	179	8	gcd(mk	gcd(mk	NOUN
ejpam-6605	179	9	,	,	PUNCT
ejpam-6605	179	10	n−1	n−1	PROPN
ejpam-6605	179	11	,	,	PUNCT
ejpam-6605	179	12	k	k	NOUN
ejpam-6605	179	13	)	)	PUNCT
ejpam-6605	179	14	=	=	NOUN
ejpam-6605	179	15	{	{	PUNCT
ejpam-6605	179	16	1	1	NUM
ejpam-6605	179	17	,	,	PUNCT
ejpam-6605	179	18	if	if	SCONJ
ejpam-6605	179	19	n−	n−	PROPN
ejpam-6605	179	20	1	1	NUM
ejpam-6605	179	21	is	be	AUX
ejpam-6605	179	22	odd	odd	ADJ
ejpam-6605	179	23	k	k	NOUN
ejpam-6605	179	24	,	,	PUNCT
ejpam-6605	179	25	if	if	SCONJ
ejpam-6605	179	26	n−	n−	NOUN
ejpam-6605	179	27	1	1	NUM
ejpam-6605	179	28	is	be	AUX
ejpam-6605	179	29	even	even	ADV
ejpam-6605	179	30	=	=	PUNCT
ejpam-6605	179	31	{	{	PUNCT
ejpam-6605	179	32	1	1	NUM
ejpam-6605	179	33	,	,	PUNCT
ejpam-6605	179	34	if	if	SCONJ
ejpam-6605	179	35	n	n	PRON
ejpam-6605	179	36	+	+	SYM
ejpam-6605	179	37	1	1	NUM
ejpam-6605	179	38	is	be	AUX
ejpam-6605	179	39	odd	odd	ADJ
ejpam-6605	179	40	k	k	NOUN
ejpam-6605	179	41	,	,	PUNCT
ejpam-6605	179	42	if	if	SCONJ
ejpam-6605	179	43	n	n	PROPN
ejpam-6605	179	44	+	+	SYM
ejpam-6605	179	45	1	1	NUM
ejpam-6605	179	46	is	be	AUX
ejpam-6605	179	47	even	even	ADV
ejpam-6605	179	48	as	as	SCONJ
ejpam-6605	179	49	desired	desire	VERB
ejpam-6605	179	50	.	.	PUNCT
ejpam-6605	180	1	(	(	PUNCT
ejpam-6605	180	2	iii	iii	X
ejpam-6605	180	3	)	)	PUNCT
ejpam-6605	180	4	the	the	DET
ejpam-6605	180	5	result	result	NOUN
ejpam-6605	180	6	is	be	AUX
ejpam-6605	180	7	clear	clear	ADJ
ejpam-6605	180	8	for	for	ADP
ejpam-6605	180	9	n	n	NOUN
ejpam-6605	180	10	=	=	SYM
ejpam-6605	180	11	1	1	NUM
ejpam-6605	180	12	,	,	PUNCT
ejpam-6605	180	13	so	so	SCONJ
ejpam-6605	180	14	we	we	PRON
ejpam-6605	180	15	proceed	proceed	VERB
ejpam-6605	180	16	by	by	ADP
ejpam-6605	180	17	mathematical	mathematical	ADJ
ejpam-6605	180	18	induction	induction	NOUN
ejpam-6605	180	19	.	.	PUNCT
ejpam-6605	181	1	let	let	VERB
ejpam-6605	181	2	d	d	NOUN
ejpam-6605	181	3	=	=	SYM
ejpam-6605	181	4	gcd(mk	gcd(mk	NOUN
ejpam-6605	181	5	,	,	PUNCT
ejpam-6605	181	6	n+1,mk	n+1,mk	NOUN
ejpam-6605	181	7	,	,	PUNCT
ejpam-6605	181	8	n+2	n+2	PRON
ejpam-6605	181	9	)	)	PUNCT
ejpam-6605	181	10	.	.	PUNCT
ejpam-6605	182	1	we	we	PRON
ejpam-6605	182	2	have	have	VERB
ejpam-6605	182	3	d|mk	d|mk	PROPN
ejpam-6605	182	4	,	,	PUNCT
ejpam-6605	182	5	n+1	n+1	PROPN
ejpam-6605	182	6	and	and	CCONJ
ejpam-6605	182	7	d|mk	d|mk	PROPN
ejpam-6605	182	8	,	,	PUNCT
ejpam-6605	182	9	n+2	n+2	PRON
ejpam-6605	183	1	so	so	SCONJ
ejpam-6605	183	2	it	it	PRON
ejpam-6605	183	3	divides	divide	VERB
ejpam-6605	183	4	any	any	DET
ejpam-6605	183	5	linear	linear	ADJ
ejpam-6605	183	6	combination	combination	NOUN
ejpam-6605	183	7	of	of	ADP
ejpam-6605	183	8	them	they	PRON
ejpam-6605	183	9	that	that	PRON
ejpam-6605	183	10	is	be	AUX
ejpam-6605	183	11	d|(mk	d|(mk	PROPN
ejpam-6605	183	12	,	,	PUNCT
ejpam-6605	183	13	n+2	n+2	PROPN
ejpam-6605	183	14	−	−	PROPN
ejpam-6605	183	15	kmk	kmk	PROPN
ejpam-6605	183	16	,	,	PUNCT
ejpam-6605	183	17	n+1	n+1	PROPN
ejpam-6605	183	18	)	)	PUNCT
ejpam-6605	183	19	=	=	PUNCT
ejpam-6605	184	1	(	(	PUNCT
ejpam-6605	184	2	1	1	NUM
ejpam-6605	184	3	−	−	PROPN
ejpam-6605	184	4	k)mk	k)mk	PROPN
ejpam-6605	184	5	,	,	PUNCT
ejpam-6605	184	6	n	n	PRON
ejpam-6605	184	7	thus	thus	ADV
ejpam-6605	184	8	,	,	PUNCT
ejpam-6605	184	9	d|(gcd(mk	d|(gcd(mk	NOUN
ejpam-6605	184	10	,	,	PUNCT
ejpam-6605	184	11	n+1	n+1	PROPN
ejpam-6605	184	12	,	,	PUNCT
ejpam-6605	184	13	(	(	PUNCT
ejpam-6605	184	14	1	1	NUM
ejpam-6605	184	15	−	−	PROPN
ejpam-6605	184	16	k)mk	k)mk	PROPN
ejpam-6605	184	17	,	,	PUNCT
ejpam-6605	184	18	n	n	CCONJ
ejpam-6605	184	19	)	)	PUNCT
ejpam-6605	184	20	)	)	PUNCT
ejpam-6605	184	21	.	.	PUNCT
ejpam-6605	185	1	now	now	ADV
ejpam-6605	185	2	,	,	PUNCT
ejpam-6605	185	3	from	from	ADP
ejpam-6605	185	4	remark	remark	NOUN
ejpam-6605	185	5	2	2	NUM
ejpam-6605	185	6	and	and	CCONJ
ejpam-6605	185	7	part	part	NOUN
ejpam-6605	185	8	1	1	NUM
ejpam-6605	185	9	we	we	PRON
ejpam-6605	185	10	have	have	VERB
ejpam-6605	185	11	gcd(mk	gcd(mk	NOUN
ejpam-6605	185	12	,	,	PUNCT
ejpam-6605	185	13	n+1	n+1	PROPN
ejpam-6605	185	14	,	,	PUNCT
ejpam-6605	185	15	(	(	PUNCT
ejpam-6605	185	16	1	1	NUM
ejpam-6605	185	17	−	−	PROPN
ejpam-6605	185	18	k)mk	k)mk	PROPN
ejpam-6605	185	19	,	,	PUNCT
ejpam-6605	185	20	n	n	CCONJ
ejpam-6605	185	21	)	)	PUNCT
ejpam-6605	185	22	=	=	SYM
ejpam-6605	185	23	1	1	NUM
ejpam-6605	185	24	which	which	PRON
ejpam-6605	185	25	leads	lead	VERB
ejpam-6605	185	26	to	to	ADP
ejpam-6605	185	27	the	the	DET
ejpam-6605	185	28	fact	fact	NOUN
ejpam-6605	185	29	that	that	SCONJ
ejpam-6605	185	30	d	d	NOUN
ejpam-6605	185	31	=	=	SYM
ejpam-6605	185	32	1	1	X
ejpam-6605	185	33	.	.	PUNCT
ejpam-6605	185	34	(	(	PUNCT
ejpam-6605	185	35	iv	iv	X
ejpam-6605	185	36	)	)	PUNCT
ejpam-6605	185	37	similar	similar	ADJ
ejpam-6605	185	38	to	to	ADP
ejpam-6605	185	39	number	number	NOUN
ejpam-6605	185	40	1	1	NUM
ejpam-6605	185	41	above	above	ADV
ejpam-6605	185	42	.	.	PUNCT
ejpam-6605	186	1	(	(	PUNCT
ejpam-6605	186	2	v	v	NOUN
ejpam-6605	186	3	)	)	PUNCT
ejpam-6605	186	4	similar	similar	ADJ
ejpam-6605	186	5	to	to	ADP
ejpam-6605	186	6	number	number	NOUN
ejpam-6605	186	7	2	2	NUM
ejpam-6605	186	8	above	above	ADV
ejpam-6605	186	9	.	.	PUNCT
ejpam-6605	187	1	(	(	PUNCT
ejpam-6605	187	2	vi	vi	NOUN
ejpam-6605	187	3	)	)	PUNCT
ejpam-6605	187	4	similar	similar	ADJ
ejpam-6605	187	5	to	to	ADP
ejpam-6605	187	6	number	number	NOUN
ejpam-6605	187	7	3	3	NUM
ejpam-6605	187	8	above	above	ADV
ejpam-6605	187	9	.	.	PUNCT
ejpam-6605	188	1	lemma	lemma	PROPN
ejpam-6605	188	2	4	4	X
ejpam-6605	188	3	.	.	PUNCT
ejpam-6605	189	1	if	if	SCONJ
ejpam-6605	189	2	k	k	PROPN
ejpam-6605	189	3	is	be	AUX
ejpam-6605	189	4	even	even	ADV
ejpam-6605	189	5	,	,	PUNCT
ejpam-6605	189	6	then	then	ADV
ejpam-6605	189	7	gcd(mk	gcd(mk	NOUN
ejpam-6605	189	8	,	,	PUNCT
ejpam-6605	189	9	n	n	CCONJ
ejpam-6605	189	10	,	,	PUNCT
ejpam-6605	189	11	fk	fk	INTJ
ejpam-6605	189	12	,	,	PUNCT
ejpam-6605	189	13	n	n	CCONJ
ejpam-6605	189	14	)	)	PUNCT
ejpam-6605	189	15	=	=	PRON
ejpam-6605	189	16	{	{	PUNCT
ejpam-6605	189	17	1	1	NUM
ejpam-6605	189	18	,	,	PUNCT
ejpam-6605	189	19	if	if	SCONJ
ejpam-6605	189	20	n	n	PRON
ejpam-6605	189	21	is	be	AUX
ejpam-6605	189	22	odd	odd	ADJ
ejpam-6605	189	23	2	2	NUM
ejpam-6605	189	24	,	,	PUNCT
ejpam-6605	189	25	if	if	SCONJ
ejpam-6605	189	26	n	n	PRON
ejpam-6605	189	27	is	be	AUX
ejpam-6605	189	28	even	even	ADV
ejpam-6605	189	29	proof	proof	ADJ
ejpam-6605	189	30	.	.	PUNCT
ejpam-6605	190	1	recall	recall	VERB
ejpam-6605	190	2	that	that	PRON
ejpam-6605	190	3	fk	fk	INTJ
ejpam-6605	190	4	,	,	PUNCT
ejpam-6605	190	5	n	n	PROPN
ejpam-6605	190	6	=	=	SYM
ejpam-6605	190	7	mk	mk	PROPN
ejpam-6605	190	8	,	,	PUNCT
ejpam-6605	190	9	n	n	PROPN
ejpam-6605	190	10	+	+	NUM
ejpam-6605	190	11	2	2	NUM
ejpam-6605	190	12	(	(	PUNCT
ejpam-6605	190	13	proposition	proposition	NOUN
ejpam-6605	190	14	1	1	NUM
ejpam-6605	190	15	)	)	PUNCT
ejpam-6605	190	16	,	,	PUNCT
ejpam-6605	190	17	also	also	ADV
ejpam-6605	190	18	if	if	SCONJ
ejpam-6605	190	19	k	k	PROPN
ejpam-6605	190	20	is	be	AUX
ejpam-6605	190	21	even	even	ADV
ejpam-6605	190	22	we	we	PRON
ejpam-6605	190	23	have	have	VERB
ejpam-6605	190	24	mk	mk	NOUN
ejpam-6605	190	25	,	,	PUNCT
ejpam-6605	190	26	n	n	PROPN
ejpam-6605	190	27	≡	≡	PROPN
ejpam-6605	190	28	n	n	PRON
ejpam-6605	190	29	mod	mod	NOUN
ejpam-6605	190	30	2	2	NUM
ejpam-6605	190	31	,	,	PUNCT
ejpam-6605	190	32	thus	thus	ADV
ejpam-6605	190	33	gcd(mk	gcd(mk	NOUN
ejpam-6605	190	34	,	,	PUNCT
ejpam-6605	190	35	n	n	CCONJ
ejpam-6605	190	36	,	,	PUNCT
ejpam-6605	190	37	fk	fk	INTJ
ejpam-6605	190	38	,	,	PUNCT
ejpam-6605	190	39	n	n	CCONJ
ejpam-6605	190	40	)	)	PUNCT
ejpam-6605	191	1	=	=	PRON
ejpam-6605	191	2	{	{	PUNCT
ejpam-6605	191	3	1	1	NUM
ejpam-6605	191	4	,	,	PUNCT
ejpam-6605	191	5	if	if	SCONJ
ejpam-6605	191	6	n	n	PRON
ejpam-6605	191	7	is	be	AUX
ejpam-6605	191	8	odd	odd	ADJ
ejpam-6605	191	9	2	2	NUM
ejpam-6605	191	10	,	,	PUNCT
ejpam-6605	191	11	if	if	SCONJ
ejpam-6605	191	12	n	n	PRON
ejpam-6605	191	13	is	be	AUX
ejpam-6605	191	14	even	even	ADV
ejpam-6605	191	15	,	,	PUNCT
ejpam-6605	191	16	as	as	SCONJ
ejpam-6605	191	17	desired	desire	VERB
ejpam-6605	191	18	.	.	PUNCT
ejpam-6605	192	1	sh	sh	PROPN
ejpam-6605	192	2	.	.	PROPN
ejpam-6605	192	3	a.	a.	PROPN
ejpam-6605	192	4	bani	bani	PROPN
ejpam-6605	192	5	melhem	melhem	PROPN
ejpam-6605	192	6	,	,	PUNCT
ejpam-6605	192	7	al	al	PROPN
ejpam-6605	192	8	-	-	PUNCT
ejpam-6605	192	9	kateeb	kateeb	PROPN
ejpam-6605	192	10	,	,	PUNCT
ejpam-6605	192	11	a.	a.	PROPN
ejpam-6605	192	12	dagher	dagher	PROPN
ejpam-6605	192	13	/	/	SYM
ejpam-6605	192	14	eur	eur	PROPN
ejpam-6605	192	15	.	.	PUNCT
ejpam-6605	193	1	j.	j.	PROPN
ejpam-6605	193	2	pure	pure	PROPN
ejpam-6605	193	3	appl	appl	PROPN
ejpam-6605	193	4	.	.	PROPN
ejpam-6605	193	5	math	math	PROPN
ejpam-6605	193	6	,	,	PUNCT
ejpam-6605	193	7	18	18	NUM
ejpam-6605	193	8	(	(	PUNCT
ejpam-6605	193	9	4	4	NUM
ejpam-6605	193	10	)	)	PUNCT
ejpam-6605	193	11	(	(	PUNCT
ejpam-6605	193	12	2025	2025	NUM
ejpam-6605	193	13	)	)	PUNCT
ejpam-6605	193	14	,	,	PUNCT
ejpam-6605	193	15	6605	6605	NUM
ejpam-6605	193	16	10	10	NUM
ejpam-6605	193	17	of	of	ADP
ejpam-6605	193	18	15	15	NUM
ejpam-6605	193	19	3	3	NUM
ejpam-6605	193	20	.	.	NOUN
ejpam-6605	193	21	matrix	matrix	NOUN
ejpam-6605	193	22	representations	representation	NOUN
ejpam-6605	193	23	theorem	theorem	VERB
ejpam-6605	193	24	8	8	NUM
ejpam-6605	193	25	(	(	PUNCT
ejpam-6605	193	26	matrix	matrix	NOUN
ejpam-6605	193	27	of	of	ADP
ejpam-6605	193	28	generalized	generalized	ADJ
ejpam-6605	193	29	mersenne	mersenne	NOUN
ejpam-6605	193	30	numbers	number	NOUN
ejpam-6605	193	31	)	)	PUNCT
ejpam-6605	193	32	.	.	PUNCT
ejpam-6605	194	1	let	let	VERB
ejpam-6605	194	2	qk	qk	VERB
ejpam-6605	194	3	=	=	PUNCT
ejpam-6605	195	1	[	[	PUNCT
ejpam-6605	195	2	0	0	NUM
ejpam-6605	195	3	1	1	NUM
ejpam-6605	195	4	1	1	NUM
ejpam-6605	195	5	−	−	PROPN
ejpam-6605	195	6	k	k	NOUN
ejpam-6605	196	1	k	k	PROPN
ejpam-6605	196	2	]	]	PUNCT
ejpam-6605	196	3	.	.	PUNCT
ejpam-6605	197	1	then	then	ADV
ejpam-6605	197	2	for	for	ADP
ejpam-6605	197	3	n	n	PROPN
ejpam-6605	197	4	≥	≥	NUM
ejpam-6605	197	5	2	2	NUM
ejpam-6605	197	6	we	we	PRON
ejpam-6605	197	7	have	have	VERB
ejpam-6605	197	8	qn	qn	NOUN
ejpam-6605	197	9	k	k	NOUN
ejpam-6605	198	1	=	=	PRON
ejpam-6605	198	2	[	[	PUNCT
ejpam-6605	198	3	(	(	PUNCT
ejpam-6605	198	4	1	1	NUM
ejpam-6605	198	5	−	−	PROPN
ejpam-6605	198	6	k)mk	k)mk	PROPN
ejpam-6605	198	7	,	,	PUNCT
ejpam-6605	198	8	n−1	n−1	PROPN
ejpam-6605	198	9	mk	mk	PROPN
ejpam-6605	198	10	,	,	PUNCT
ejpam-6605	198	11	n	n	PROPN
ejpam-6605	198	12	(	(	PUNCT
ejpam-6605	198	13	1	1	NUM
ejpam-6605	198	14	−	−	PROPN
ejpam-6605	198	15	k)mk	k)mk	PROPN
ejpam-6605	198	16	,	,	PUNCT
ejpam-6605	198	17	n	n	PRON
ejpam-6605	198	18	mk	mk	NOUN
ejpam-6605	198	19	,	,	PUNCT
ejpam-6605	198	20	n+1	n+1	NUM
ejpam-6605	198	21	]	]	PUNCT
ejpam-6605	198	22	proof	proof	NOUN
ejpam-6605	198	23	.	.	PUNCT
ejpam-6605	199	1	we	we	PRON
ejpam-6605	199	2	prove	prove	VERB
ejpam-6605	199	3	the	the	DET
ejpam-6605	199	4	result	result	NOUN
ejpam-6605	199	5	by	by	ADP
ejpam-6605	199	6	mathematical	mathematical	ADJ
ejpam-6605	199	7	induction	induction	NOUN
ejpam-6605	199	8	:	:	PUNCT
ejpam-6605	199	9	•	•	ADP
ejpam-6605	199	10	if	if	SCONJ
ejpam-6605	199	11	n	n	X
ejpam-6605	199	12	=	=	SYM
ejpam-6605	199	13	2	2	NUM
ejpam-6605	199	14	,	,	PUNCT
ejpam-6605	199	15	we	we	PRON
ejpam-6605	199	16	have	have	VERB
ejpam-6605	199	17	q2	q2	NOUN
ejpam-6605	199	18	k	k	PUNCT
ejpam-6605	200	1	=	=	PUNCT
ejpam-6605	200	2	[	[	PUNCT
ejpam-6605	200	3	1	1	NUM
ejpam-6605	200	4	−	−	PROPN
ejpam-6605	200	5	k	k	PROPN
ejpam-6605	200	6	k	k	PROPN
ejpam-6605	200	7	k(1	k(1	PROPN
ejpam-6605	200	8	−	−	PROPN
ejpam-6605	200	9	k	k	PROPN
ejpam-6605	200	10	)	)	PUNCT
ejpam-6605	200	11	k2	k2	NOUN
ejpam-6605	200	12	+	+	CCONJ
ejpam-6605	200	13	(	(	PUNCT
ejpam-6605	200	14	1	1	NUM
ejpam-6605	200	15	−	−	PROPN
ejpam-6605	200	16	k)2	k)2	X
ejpam-6605	200	17	]	]	PUNCT
ejpam-6605	201	1	=	=	PUNCT
ejpam-6605	202	1	[	[	PUNCT
ejpam-6605	202	2	(	(	PUNCT
ejpam-6605	202	3	1	1	NUM
ejpam-6605	202	4	−	−	NOUN
ejpam-6605	202	5	k)mk,1	k)mk,1	NOUN
ejpam-6605	202	6	mk,2	mk,2	NOUN
ejpam-6605	202	7	(	(	PUNCT
ejpam-6605	202	8	1	1	NUM
ejpam-6605	202	9	−	−	NOUN
ejpam-6605	202	10	k)mk,2	k)mk,2	NOUN
ejpam-6605	202	11	mk,3	mk,3	PROPN
ejpam-6605	202	12	]	]	PUNCT
ejpam-6605	202	13	•	•	ADP
ejpam-6605	202	14	assuming	assume	VERB
ejpam-6605	202	15	that	that	SCONJ
ejpam-6605	202	16	the	the	DET
ejpam-6605	202	17	result	result	NOUN
ejpam-6605	202	18	is	be	AUX
ejpam-6605	202	19	true	true	ADJ
ejpam-6605	202	20	for	for	ADP
ejpam-6605	202	21	all	all	DET
ejpam-6605	202	22	2	2	NUM
ejpam-6605	202	23	≤	≤	NUM
ejpam-6605	202	24	m	m	VERB
ejpam-6605	202	25	≤	≤	X
ejpam-6605	202	26	n.	n.	NOUN
ejpam-6605	202	27	•	•	ADP
ejpam-6605	202	28	consider	consider	VERB
ejpam-6605	202	29	qn+1	qn+1	NUM
ejpam-6605	202	30	k	k	NOUN
ejpam-6605	202	31	=	=	PUNCT
ejpam-6605	202	32	qkq	qkq	PROPN
ejpam-6605	202	33	n	n	X
ejpam-6605	202	34	k	k	NOUN
ejpam-6605	202	35	=	=	PUNCT
ejpam-6605	203	1	[	[	PUNCT
ejpam-6605	203	2	0	0	NUM
ejpam-6605	203	3	1	1	NUM
ejpam-6605	203	4	1	1	NUM
ejpam-6605	203	5	−	−	PROPN
ejpam-6605	204	1	k	k	NOUN
ejpam-6605	204	2	k	k	X
ejpam-6605	204	3	]	]	X
ejpam-6605	205	1	[	[	PUNCT
ejpam-6605	205	2	(	(	PUNCT
ejpam-6605	205	3	1	1	NUM
ejpam-6605	205	4	−	−	PROPN
ejpam-6605	205	5	k)mk	k)mk	PROPN
ejpam-6605	205	6	,	,	PUNCT
ejpam-6605	205	7	n−1	n−1	PROPN
ejpam-6605	205	8	mk	mk	PROPN
ejpam-6605	205	9	,	,	PUNCT
ejpam-6605	205	10	n	n	PROPN
ejpam-6605	205	11	(	(	PUNCT
ejpam-6605	205	12	1	1	NUM
ejpam-6605	205	13	−	−	PROPN
ejpam-6605	205	14	k)mk	k)mk	PROPN
ejpam-6605	205	15	,	,	PUNCT
ejpam-6605	205	16	n	n	PRON
ejpam-6605	205	17	mk	mk	NOUN
ejpam-6605	205	18	,	,	PUNCT
ejpam-6605	205	19	n+1	n+1	PROPN
ejpam-6605	205	20	]	]	PUNCT
ejpam-6605	205	21	=	=	PUNCT
ejpam-6605	205	22	[	[	PUNCT
ejpam-6605	205	23	(	(	PUNCT
ejpam-6605	205	24	1	1	NUM
ejpam-6605	205	25	−	−	PROPN
ejpam-6605	205	26	k)mk	k)mk	PROPN
ejpam-6605	205	27	,	,	PUNCT
ejpam-6605	205	28	n	n	PROPN
ejpam-6605	205	29	mk	mk	NOUN
ejpam-6605	205	30	,	,	PUNCT
ejpam-6605	205	31	n+1	n+1	PROPN
ejpam-6605	205	32	(	(	PUNCT
ejpam-6605	205	33	1	1	NUM
ejpam-6605	205	34	−	−	PROPN
ejpam-6605	205	35	k)mk	k)mk	PROPN
ejpam-6605	205	36	,	,	PUNCT
ejpam-6605	205	37	n+1	n+1	PROPN
ejpam-6605	205	38	mk	mk	PROPN
ejpam-6605	205	39	,	,	PUNCT
ejpam-6605	205	40	n+2	n+2	PRON
ejpam-6605	205	41	]	]	PUNCT
ejpam-6605	205	42	as	as	SCONJ
ejpam-6605	205	43	desired	desire	VERB
ejpam-6605	205	44	.	.	PUNCT
ejpam-6605	206	1	lemma	lemma	PROPN
ejpam-6605	206	2	5	5	NUM
ejpam-6605	206	3	.	.	PUNCT
ejpam-6605	207	1	for	for	ADP
ejpam-6605	207	2	any	any	DET
ejpam-6605	207	3	integers	integer	NOUN
ejpam-6605	207	4	m	m	VERB
ejpam-6605	207	5	and	and	CCONJ
ejpam-6605	207	6	n	n	PROPN
ejpam-6605	207	7	and	and	CCONJ
ejpam-6605	207	8	k	k	PROPN
ejpam-6605	207	9	≥	≥	NUM
ejpam-6605	207	10	2	2	NUM
ejpam-6605	207	11	we	we	PRON
ejpam-6605	207	12	have	have	VERB
ejpam-6605	207	13	(	(	PUNCT
ejpam-6605	207	14	i	i	NOUN
ejpam-6605	207	15	)	)	PUNCT
ejpam-6605	207	16	mk	mk	PROPN
ejpam-6605	207	17	,	,	PUNCT
ejpam-6605	207	18	n+m	n+m	NUM
ejpam-6605	207	19	=	=	SYM
ejpam-6605	207	20	(	(	PUNCT
ejpam-6605	207	21	1	1	NUM
ejpam-6605	207	22	−	−	PROPN
ejpam-6605	207	23	k)mk	k)mk	PROPN
ejpam-6605	207	24	,	,	PUNCT
ejpam-6605	207	25	n−1mk	n−1mk	PROPN
ejpam-6605	207	26	,	,	PUNCT
ejpam-6605	207	27	m	m	VERB
ejpam-6605	207	28	+	+	X
ejpam-6605	207	29	mk	mk	PROPN
ejpam-6605	207	30	,	,	PUNCT
ejpam-6605	207	31	nmk	nmk	PRON
ejpam-6605	207	32	,	,	PUNCT
ejpam-6605	207	33	m+1	m+1	PRON
ejpam-6605	207	34	.	.	PUNCT
ejpam-6605	208	1	(	(	PUNCT
ejpam-6605	208	2	ii	ii	X
ejpam-6605	208	3	)	)	PUNCT
ejpam-6605	208	4	mk	mk	PROPN
ejpam-6605	208	5	,	,	PUNCT
ejpam-6605	208	6	n+m+1	n+m+1	PROPN
ejpam-6605	208	7	=	=	PUNCT
ejpam-6605	208	8	(	(	PUNCT
ejpam-6605	208	9	1	1	NUM
ejpam-6605	208	10	−	−	PROPN
ejpam-6605	208	11	k)mk	k)mk	PROPN
ejpam-6605	208	12	,	,	PUNCT
ejpam-6605	208	13	nmk	nmk	PRON
ejpam-6605	208	14	,	,	PUNCT
ejpam-6605	208	15	m	m	VERB
ejpam-6605	208	16	+	+	X
ejpam-6605	208	17	mk	mk	NOUN
ejpam-6605	208	18	,	,	PUNCT
ejpam-6605	208	19	n+1mk	n+1mk	NOUN
ejpam-6605	208	20	,	,	PUNCT
ejpam-6605	208	21	m+1	m+1	PRON
ejpam-6605	208	22	.	.	PUNCT
ejpam-6605	209	1	(	(	PUNCT
ejpam-6605	209	2	iii	iii	X
ejpam-6605	209	3	)	)	PUNCT
ejpam-6605	209	4	mk,2n	mk,2n	X
ejpam-6605	209	5	=	=	PUNCT
ejpam-6605	210	1	(	(	PUNCT
ejpam-6605	210	2	1	1	NUM
ejpam-6605	210	3	−	−	PROPN
ejpam-6605	210	4	k)mk	k)mk	PROPN
ejpam-6605	210	5	,	,	PUNCT
ejpam-6605	210	6	n−1mk	n−1mk	PROPN
ejpam-6605	210	7	,	,	PUNCT
ejpam-6605	210	8	n	n	PROPN
ejpam-6605	210	9	+	+	CCONJ
ejpam-6605	210	10	mk	mk	PROPN
ejpam-6605	210	11	,	,	PUNCT
ejpam-6605	210	12	nmk	nmk	PROPN
ejpam-6605	210	13	,	,	PUNCT
ejpam-6605	210	14	n+1	n+1	PROPN
ejpam-6605	210	15	.	.	PROPN
ejpam-6605	210	16	(	(	PUNCT
ejpam-6605	210	17	iv	iv	X
ejpam-6605	210	18	)	)	PUNCT
ejpam-6605	210	19	mk,2n+1	mk,2n+1	NOUN
ejpam-6605	210	20	=	=	SYM
ejpam-6605	210	21	(	(	PUNCT
ejpam-6605	210	22	1	1	NUM
ejpam-6605	210	23	−	−	PROPN
ejpam-6605	210	24	k)m2	k)m2	PROPN
ejpam-6605	210	25	k	k	PROPN
ejpam-6605	210	26	,	,	PUNCT
ejpam-6605	210	27	n	n	PROPN
ejpam-6605	210	28	+	+	NUM
ejpam-6605	210	29	m2	m2	PROPN
ejpam-6605	210	30	k	k	PROPN
ejpam-6605	210	31	,	,	PUNCT
ejpam-6605	210	32	n+1	n+1	PROPN
ejpam-6605	210	33	.	.	PUNCT
ejpam-6605	210	34	proof	proof	NOUN
ejpam-6605	210	35	.	.	PUNCT
ejpam-6605	211	1	consider	consider	VERB
ejpam-6605	211	2	qn+m	qn+m	VERB
ejpam-6605	211	3	k	k	NOUN
ejpam-6605	212	1	=	=	PUNCT
ejpam-6605	212	2	qn	qn	PROPN
ejpam-6605	212	3	kq	kq	PROPN
ejpam-6605	212	4	m	m	PROPN
ejpam-6605	212	5	k	k	NOUN
ejpam-6605	213	1	=	=	PUNCT
ejpam-6605	213	2	[	[	PUNCT
ejpam-6605	213	3	(	(	PUNCT
ejpam-6605	213	4	1	1	NUM
ejpam-6605	213	5	−	−	PROPN
ejpam-6605	213	6	k)mk	k)mk	PROPN
ejpam-6605	213	7	,	,	PUNCT
ejpam-6605	213	8	n+m+1	n+m+1	PROPN
ejpam-6605	213	9	mk	mk	PROPN
ejpam-6605	213	10	,	,	PUNCT
ejpam-6605	213	11	n+m	n+m	NUM
ejpam-6605	213	12	(	(	PUNCT
ejpam-6605	213	13	1	1	NUM
ejpam-6605	213	14	−	−	PROPN
ejpam-6605	213	15	k)mk	k)mk	PROPN
ejpam-6605	213	16	,	,	PUNCT
ejpam-6605	213	17	n+m	n+m	PROPN
ejpam-6605	213	18	mk	mk	PROPN
ejpam-6605	213	19	,	,	PUNCT
ejpam-6605	213	20	n+m+1	n+m+1	PROPN
ejpam-6605	213	21	]	]	PUNCT
ejpam-6605	213	22	=	=	PUNCT
ejpam-6605	213	23	[	[	PUNCT
ejpam-6605	213	24	(	(	PUNCT
ejpam-6605	213	25	1	1	NUM
ejpam-6605	213	26	−	−	PROPN
ejpam-6605	213	27	k)mk	k)mk	PROPN
ejpam-6605	213	28	,	,	PUNCT
ejpam-6605	213	29	n−1	n−1	PROPN
ejpam-6605	213	30	mk	mk	PROPN
ejpam-6605	213	31	,	,	PUNCT
ejpam-6605	213	32	n	n	PROPN
ejpam-6605	213	33	(	(	PUNCT
ejpam-6605	213	34	1	1	NUM
ejpam-6605	213	35	−	−	PROPN
ejpam-6605	213	36	k)mk	k)mk	PROPN
ejpam-6605	213	37	,	,	PUNCT
ejpam-6605	213	38	n	n	PRON
ejpam-6605	213	39	mk	mk	NOUN
ejpam-6605	213	40	,	,	PUNCT
ejpam-6605	213	41	n+1	n+1	PROPN
ejpam-6605	213	42	]	]	PUNCT
ejpam-6605	213	43	[	[	PUNCT
ejpam-6605	213	44	(	(	PUNCT
ejpam-6605	213	45	1	1	NUM
ejpam-6605	213	46	−	−	PROPN
ejpam-6605	213	47	k)mk	k)mk	PROPN
ejpam-6605	213	48	,	,	PUNCT
ejpam-6605	213	49	m−1	m−1	PROPN
ejpam-6605	213	50	mk	mk	PROPN
ejpam-6605	213	51	,	,	PUNCT
ejpam-6605	213	52	m	m	PROPN
ejpam-6605	213	53	(	(	PUNCT
ejpam-6605	213	54	1	1	NUM
ejpam-6605	213	55	−	−	PROPN
ejpam-6605	213	56	k)mk	k)mk	PROPN
ejpam-6605	213	57	,	,	PUNCT
ejpam-6605	213	58	m	m	PROPN
ejpam-6605	213	59	mk	mk	NOUN
ejpam-6605	213	60	,	,	PUNCT
ejpam-6605	213	61	m+1	m+1	NUM
ejpam-6605	213	62	]	]	PUNCT
ejpam-6605	213	63	we	we	PRON
ejpam-6605	213	64	get	get	VERB
ejpam-6605	213	65	1	1	NUM
ejpam-6605	213	66	and	and	CCONJ
ejpam-6605	213	67	2	2	NUM
ejpam-6605	213	68	from	from	ADP
ejpam-6605	213	69	equating	equate	VERB
ejpam-6605	213	70	the	the	DET
ejpam-6605	213	71	corresponding	corresponding	ADJ
ejpam-6605	213	72	entries	entry	NOUN
ejpam-6605	213	73	of	of	ADP
ejpam-6605	213	74	the	the	DET
ejpam-6605	213	75	equal	equal	ADJ
ejpam-6605	213	76	matrices	matrix	NOUN
ejpam-6605	213	77	.	.	PUNCT
ejpam-6605	214	1	also	also	ADV
ejpam-6605	214	2	,	,	PUNCT
ejpam-6605	214	3	we	we	PRON
ejpam-6605	214	4	get	get	VERB
ejpam-6605	214	5	3	3	NUM
ejpam-6605	214	6	and	and	CCONJ
ejpam-6605	214	7	4	4	NUM
ejpam-6605	214	8	by	by	ADP
ejpam-6605	214	9	letting	let	VERB
ejpam-6605	214	10	m	m	PROPN
ejpam-6605	214	11	=	=	SYM
ejpam-6605	214	12	n	n	PROPN
ejpam-6605	214	13	in	in	ADP
ejpam-6605	214	14	1	1	NUM
ejpam-6605	214	15	and	and	CCONJ
ejpam-6605	214	16	2	2	NUM
ejpam-6605	214	17	.	.	X
ejpam-6605	215	1	lemma	lemma	PROPN
ejpam-6605	215	2	6	6	NUM
ejpam-6605	215	3	(	(	PUNCT
ejpam-6605	215	4	matrix	matrix	NOUN
ejpam-6605	215	5	of	of	ADP
ejpam-6605	215	6	extended	extended	ADJ
ejpam-6605	215	7	fermat	fermat	PROPN
ejpam-6605	215	8	numbers	number	NOUN
ejpam-6605	215	9	)	)	PUNCT
ejpam-6605	215	10	.	.	PUNCT
ejpam-6605	216	1	let	let	VERB
ejpam-6605	216	2	rk	rk	VERB
ejpam-6605	216	3	=	=	PUNCT
ejpam-6605	216	4	[	[	PUNCT
ejpam-6605	216	5	2	2	NUM
ejpam-6605	216	6	3	3	NUM
ejpam-6605	216	7	3	3	NUM
ejpam-6605	216	8	2	2	NUM
ejpam-6605	216	9	+	+	CCONJ
ejpam-6605	216	10	k	k	X
ejpam-6605	216	11	]	]	PUNCT
ejpam-6605	216	12	.	.	PUNCT
ejpam-6605	217	1	then	then	ADV
ejpam-6605	217	2	qn	qn	PROPN
ejpam-6605	217	3	krk	krk	PROPN
ejpam-6605	217	4	=	=	PUNCT
ejpam-6605	218	1	[	[	PUNCT
ejpam-6605	218	2	fk	fk	INTJ
ejpam-6605	218	3	,	,	PUNCT
ejpam-6605	218	4	n	n	X
ejpam-6605	218	5	fk	fk	INTJ
ejpam-6605	218	6	,	,	PUNCT
ejpam-6605	218	7	n+1	n+1	PROPN
ejpam-6605	218	8	fk	fk	INTJ
ejpam-6605	218	9	,	,	PUNCT
ejpam-6605	218	10	n+1	n+1	PROPN
ejpam-6605	218	11	fk	fk	INTJ
ejpam-6605	218	12	,	,	PUNCT
ejpam-6605	218	13	n+2	n+2	PRON
ejpam-6605	218	14	]	]	PUNCT
ejpam-6605	218	15	proof	proof	NOUN
ejpam-6605	218	16	.	.	PUNCT
ejpam-6605	219	1	can	can	AUX
ejpam-6605	219	2	be	be	AUX
ejpam-6605	219	3	proved	prove	VERB
ejpam-6605	219	4	easily	easily	ADV
ejpam-6605	219	5	by	by	ADP
ejpam-6605	219	6	mathematical	mathematical	ADJ
ejpam-6605	219	7	induction	induction	NOUN
ejpam-6605	219	8	.	.	PUNCT
ejpam-6605	220	1	sh	sh	PROPN
ejpam-6605	220	2	.	.	PROPN
ejpam-6605	220	3	a.	a.	PROPN
ejpam-6605	220	4	bani	bani	PROPN
ejpam-6605	220	5	melhem	melhem	PROPN
ejpam-6605	220	6	,	,	PUNCT
ejpam-6605	220	7	al	al	PROPN
ejpam-6605	220	8	-	-	PUNCT
ejpam-6605	220	9	kateeb	kateeb	PROPN
ejpam-6605	220	10	,	,	PUNCT
ejpam-6605	220	11	a.	a.	PROPN
ejpam-6605	220	12	dagher	dagher	PROPN
ejpam-6605	220	13	/	/	SYM
ejpam-6605	220	14	eur	eur	PROPN
ejpam-6605	220	15	.	.	PUNCT
ejpam-6605	221	1	j.	j.	PROPN
ejpam-6605	221	2	pure	pure	PROPN
ejpam-6605	221	3	appl	appl	PROPN
ejpam-6605	221	4	.	.	PROPN
ejpam-6605	221	5	math	math	PROPN
ejpam-6605	221	6	,	,	PUNCT
ejpam-6605	221	7	18	18	NUM
ejpam-6605	221	8	(	(	PUNCT
ejpam-6605	221	9	4	4	NUM
ejpam-6605	221	10	)	)	PUNCT
ejpam-6605	221	11	(	(	PUNCT
ejpam-6605	221	12	2025	2025	NUM
ejpam-6605	221	13	)	)	PUNCT
ejpam-6605	221	14	,	,	PUNCT
ejpam-6605	221	15	6605	6605	NUM
ejpam-6605	221	16	11	11	NUM
ejpam-6605	221	17	of	of	ADP
ejpam-6605	221	18	15	15	NUM
ejpam-6605	221	19	4	4	NUM
ejpam-6605	221	20	.	.	PUNCT
ejpam-6605	221	21	special	special	ADJ
ejpam-6605	221	22	kind	kind	NOUN
ejpam-6605	221	23	of	of	ADP
ejpam-6605	221	24	tridiagonal	tridiagonal	ADJ
ejpam-6605	221	25	and	and	CCONJ
ejpam-6605	221	26	hessenberg	hessenberg	NOUN
ejpam-6605	221	27	matrices	matrice	VERB
ejpam-6605	221	28	a	a	DET
ejpam-6605	221	29	tridiagonal	tridiagonal	ADJ
ejpam-6605	221	30	matrix	matrix	NOUN
ejpam-6605	221	31	is	be	AUX
ejpam-6605	221	32	a	a	DET
ejpam-6605	221	33	matrix	matrix	NOUN
ejpam-6605	221	34	that	that	PRON
ejpam-6605	221	35	has	have	VERB
ejpam-6605	221	36	nonzero	nonzero	ADJ
ejpam-6605	221	37	elements	element	NOUN
ejpam-6605	221	38	only	only	ADV
ejpam-6605	221	39	on	on	ADP
ejpam-6605	221	40	the	the	DET
ejpam-6605	221	41	main	main	ADJ
ejpam-6605	221	42	diagonal	diagonal	NOUN
ejpam-6605	221	43	and	and	CCONJ
ejpam-6605	221	44	on	on	ADP
ejpam-6605	221	45	the	the	DET
ejpam-6605	221	46	first	first	ADJ
ejpam-6605	221	47	diagonal	diagonal	ADJ
ejpam-6605	221	48	below	below	ADV
ejpam-6605	221	49	and	and	CCONJ
ejpam-6605	221	50	above	above	ADP
ejpam-6605	221	51	the	the	DET
ejpam-6605	221	52	main	main	ADJ
ejpam-6605	221	53	diagonal	diagonal	NOUN
ejpam-6605	221	54	.	.	PUNCT
ejpam-6605	222	1	in	in	ADP
ejpam-6605	222	2	this	this	DET
ejpam-6605	222	3	subsection	subsection	NOUN
ejpam-6605	222	4	we	we	PRON
ejpam-6605	222	5	represent	represent	VERB
ejpam-6605	222	6	some	some	DET
ejpam-6605	222	7	tridiagonal	tridiagonal	ADJ
ejpam-6605	222	8	matrices	matrix	NOUN
ejpam-6605	222	9	whose	whose	DET
ejpam-6605	222	10	determinant	determinant	ADJ
ejpam-6605	222	11	or	or	CCONJ
ejpam-6605	222	12	permanent	permanent	ADJ
ejpam-6605	222	13	is	be	AUX
ejpam-6605	222	14	a	a	DET
ejpam-6605	222	15	generalized	generalized	ADJ
ejpam-6605	222	16	mersenne	mersenne	NOUN
ejpam-6605	222	17	number	number	NOUN
ejpam-6605	222	18	.	.	PUNCT
ejpam-6605	223	1	lemma	lemma	PROPN
ejpam-6605	223	2	7	7	X
ejpam-6605	223	3	.	.	PUNCT
ejpam-6605	223	4	suppose	suppose	VERB
ejpam-6605	223	5	that	that	SCONJ
ejpam-6605	223	6	n	n	PROPN
ejpam-6605	223	7	≥	≥	NUM
ejpam-6605	223	8	1	1	NUM
ejpam-6605	223	9	is	be	AUX
ejpam-6605	223	10	an	an	DET
ejpam-6605	223	11	integer	integer	NOUN
ejpam-6605	223	12	.	.	PUNCT
ejpam-6605	224	1	(	(	PUNCT
ejpam-6605	224	2	i	i	NOUN
ejpam-6605	224	3	)	)	PUNCT
ejpam-6605	224	4	let	let	VERB
ejpam-6605	224	5	nn(k	nn(k	NUM
ejpam-6605	224	6	)	)	PUNCT
ejpam-6605	224	7	=	=	SYM
ejpam-6605	224	8			NOUN
ejpam-6605	225	1	k	k	PROPN
ejpam-6605	225	2	k	k	PROPN
ejpam-6605	226	1	−	−	PROPN
ejpam-6605	226	2	1	1	NUM
ejpam-6605	226	3	0	0	NUM
ejpam-6605	226	4	·	·	PUNCT
ejpam-6605	226	5	·	·	PUNCT
ejpam-6605	226	6	·	·	PUNCT
ejpam-6605	226	7	·	·	PUNCT
ejpam-6605	226	8	·	·	PUNCT
ejpam-6605	226	9	·	·	PUNCT
ejpam-6605	226	10	·	·	PUNCT
ejpam-6605	226	11	·	·	PUNCT
ejpam-6605	226	12	·	·	PUNCT
ejpam-6605	226	13	·	·	PUNCT
ejpam-6605	226	14	·	·	PUNCT
ejpam-6605	226	15	·	·	PUNCT
ejpam-6605	226	16	0	0	NUM
ejpam-6605	227	1	−1	−1	NOUN
ejpam-6605	227	2	k	k	NOUN
ejpam-6605	228	1	1	1	NUM
ejpam-6605	228	2	−	−	PROPN
ejpam-6605	228	3	k	k	NOUN
ejpam-6605	228	4	0	0	PUNCT
ejpam-6605	228	5	·	·	PUNCT
ejpam-6605	228	6	·	·	PUNCT
ejpam-6605	228	7	·	·	PUNCT
ejpam-6605	228	8	·	·	PUNCT
ejpam-6605	228	9	·	·	PUNCT
ejpam-6605	228	10	·	·	PUNCT
ejpam-6605	228	11	·	·	PUNCT
ejpam-6605	228	12	·	·	PUNCT
ejpam-6605	228	13	·	·	PUNCT
ejpam-6605	228	14	0	0	NUM
ejpam-6605	228	15	0	0	NUM
ejpam-6605	228	16	−1	−1	NOUN
ejpam-6605	229	1	k	k	NOUN
ejpam-6605	229	2	1	1	NUM
ejpam-6605	229	3	−	−	PROPN
ejpam-6605	229	4	k	k	PROPN
ejpam-6605	229	5	·	·	PUNCT
ejpam-6605	229	6	·	·	PUNCT
ejpam-6605	229	7	·	·	PUNCT
ejpam-6605	229	8	·	·	PUNCT
ejpam-6605	229	9	·	·	PUNCT
ejpam-6605	229	10	·	·	PUNCT
ejpam-6605	229	11	·	·	PUNCT
ejpam-6605	229	12	·	·	PUNCT
ejpam-6605	229	13	·	·	PUNCT
ejpam-6605	229	14	0	0	NUM
ejpam-6605	229	15	0	0	NUM
ejpam-6605	229	16	0	0	NUM
ejpam-6605	230	1	−1	−1	NOUN
ejpam-6605	231	1	k	k	NOUN
ejpam-6605	231	2	1	1	NUM
ejpam-6605	231	3	−	−	PROPN
ejpam-6605	231	4	k	k	PROPN
ejpam-6605	231	5	·	·	PUNCT
ejpam-6605	231	6	·	·	PUNCT
ejpam-6605	231	7	·	·	PUNCT
ejpam-6605	231	8	·	·	PUNCT
ejpam-6605	231	9	·	·	PUNCT
ejpam-6605	231	10	·	·	PUNCT
ejpam-6605	231	11	0	0	NUM
ejpam-6605	231	12	...	...	PUNCT
ejpam-6605	231	13	...	...	PUNCT
ejpam-6605	231	14	...	...	PUNCT
ejpam-6605	231	15	...	...	PUNCT
ejpam-6605	231	16	...	...	PUNCT
ejpam-6605	231	17	...	...	PUNCT
ejpam-6605	231	18	...	...	PUNCT
ejpam-6605	231	19	...	...	PUNCT
ejpam-6605	232	1	0	0	NUM
ejpam-6605	232	2	...	...	PUNCT
ejpam-6605	233	1	−1	−1	NOUN
ejpam-6605	234	1	k	k	NOUN
ejpam-6605	234	2			VERB
ejpam-6605	234	3	then	then	ADV
ejpam-6605	234	4	det(nn	det(nn	ADJ
ejpam-6605	234	5	)	)	PUNCT
ejpam-6605	234	6	=	=	SYM
ejpam-6605	234	7	mk	mk	PROPN
ejpam-6605	234	8	,	,	PUNCT
ejpam-6605	234	9	n+1	n+1	PROPN
ejpam-6605	234	10	.	.	PUNCT
ejpam-6605	234	11	(	(	PUNCT
ejpam-6605	234	12	ii	ii	NOUN
ejpam-6605	234	13	)	)	PUNCT
ejpam-6605	234	14	let	let	VERB
ejpam-6605	234	15	hn(k	hn(k	PRON
ejpam-6605	234	16	)	)	PUNCT
ejpam-6605	234	17	=	=	SYM
ejpam-6605	234	18			NOUN
ejpam-6605	234	19	0	0	NUM
ejpam-6605	234	20	1	1	NUM
ejpam-6605	234	21	0	0	NUM
ejpam-6605	234	22	·	·	PUNCT
ejpam-6605	234	23	·	·	PUNCT
ejpam-6605	234	24	·	·	PUNCT
ejpam-6605	234	25	·	·	PUNCT
ejpam-6605	234	26	·	·	PUNCT
ejpam-6605	234	27	·	·	PUNCT
ejpam-6605	234	28	·	·	PUNCT
ejpam-6605	234	29	·	·	PUNCT
ejpam-6605	234	30	·	·	PUNCT
ejpam-6605	234	31	·	·	PUNCT
ejpam-6605	234	32	·	·	PUNCT
ejpam-6605	234	33	·	·	PUNCT
ejpam-6605	234	34	0	0	NUM
ejpam-6605	235	1	−1	−1	NOUN
ejpam-6605	235	2	0	0	NUM
ejpam-6605	235	3	1	1	NUM
ejpam-6605	235	4	−	−	PROPN
ejpam-6605	235	5	k	k	NOUN
ejpam-6605	235	6	0	0	PUNCT
ejpam-6605	235	7	·	·	PUNCT
ejpam-6605	235	8	·	·	PUNCT
ejpam-6605	235	9	·	·	PUNCT
ejpam-6605	235	10	·	·	PUNCT
ejpam-6605	235	11	·	·	PUNCT
ejpam-6605	235	12	·	·	PUNCT
ejpam-6605	235	13	·	·	PUNCT
ejpam-6605	235	14	·	·	PUNCT
ejpam-6605	235	15	·	·	PUNCT
ejpam-6605	235	16	0	0	NUM
ejpam-6605	235	17	0	0	NUM
ejpam-6605	235	18	−1	−1	NOUN
ejpam-6605	236	1	k	k	NOUN
ejpam-6605	236	2	1	1	NUM
ejpam-6605	236	3	−	−	PROPN
ejpam-6605	236	4	k	k	PROPN
ejpam-6605	236	5	·	·	PUNCT
ejpam-6605	236	6	·	·	PUNCT
ejpam-6605	236	7	·	·	PUNCT
ejpam-6605	236	8	·	·	PUNCT
ejpam-6605	236	9	·	·	PUNCT
ejpam-6605	236	10	·	·	PUNCT
ejpam-6605	236	11	·	·	PUNCT
ejpam-6605	236	12	·	·	PUNCT
ejpam-6605	236	13	·	·	PUNCT
ejpam-6605	236	14	0	0	NUM
ejpam-6605	236	15	0	0	NUM
ejpam-6605	236	16	0	0	NUM
ejpam-6605	237	1	−1	−1	NOUN
ejpam-6605	238	1	k	k	NOUN
ejpam-6605	238	2	1	1	NUM
ejpam-6605	238	3	−	−	PROPN
ejpam-6605	238	4	k	k	PROPN
ejpam-6605	238	5	·	·	PUNCT
ejpam-6605	238	6	·	·	PUNCT
ejpam-6605	238	7	·	·	PUNCT
ejpam-6605	238	8	·	·	PUNCT
ejpam-6605	238	9	·	·	PUNCT
ejpam-6605	238	10	·	·	PUNCT
ejpam-6605	238	11	0	0	NUM
ejpam-6605	238	12	...	...	PUNCT
ejpam-6605	238	13	...	...	PUNCT
ejpam-6605	238	14	...	...	PUNCT
ejpam-6605	238	15	...	...	PUNCT
ejpam-6605	238	16	...	...	PUNCT
ejpam-6605	238	17	...	...	PUNCT
ejpam-6605	238	18	...	...	PUNCT
ejpam-6605	239	1	0	0	NUM
ejpam-6605	239	2	0	0	NUM
ejpam-6605	239	3	·	·	PUNCT
ejpam-6605	239	4	·	·	PUNCT
ejpam-6605	239	5	·	·	PUNCT
ejpam-6605	239	6	·	·	PUNCT
ejpam-6605	239	7	·	·	PUNCT
ejpam-6605	239	8	·	·	PUNCT
ejpam-6605	239	9	·	·	PUNCT
ejpam-6605	239	10	·	·	PUNCT
ejpam-6605	239	11	·	·	PUNCT
ejpam-6605	239	12	·	·	PUNCT
ejpam-6605	239	13	·	·	PUNCT
ejpam-6605	239	14	·	·	PUNCT
ejpam-6605	239	15	·	·	PUNCT
ejpam-6605	239	16	·	·	PUNCT
ejpam-6605	239	17	·	·	PUNCT
ejpam-6605	239	18	−1	−1	NOUN
ejpam-6605	240	1	k	k	NOUN
ejpam-6605	240	2			NOUN
ejpam-6605	240	3	.	.	PUNCT
ejpam-6605	241	1	then	then	ADV
ejpam-6605	241	2	det(hn	det(hn	NOUN
ejpam-6605	241	3	)	)	PUNCT
ejpam-6605	241	4	=	=	SYM
ejpam-6605	241	5	mk	mk	PROPN
ejpam-6605	241	6	,	,	PUNCT
ejpam-6605	241	7	n.	n.	NOUN
ejpam-6605	241	8	proof	proof	NOUN
ejpam-6605	241	9	.	.	PUNCT
ejpam-6605	242	1	clear	clear	ADJ
ejpam-6605	242	2	from	from	ADP
ejpam-6605	242	3	section	section	NOUN
ejpam-6605	242	4	2.1	2.1	NUM
ejpam-6605	242	5	and	and	CCONJ
ejpam-6605	242	6	2.2	2.2	NUM
ejpam-6605	242	7	in	in	ADP
ejpam-6605	242	8	[	[	X
ejpam-6605	242	9	3	3	X
ejpam-6605	242	10	]	]	X
ejpam-6605	242	11	lemma	lemma	PROPN
ejpam-6605	242	12	8	8	NUM
ejpam-6605	242	13	.	.	PUNCT
ejpam-6605	242	14	suppose	suppose	VERB
ejpam-6605	242	15	that	that	SCONJ
ejpam-6605	242	16	n	n	PROPN
ejpam-6605	242	17	≥	≥	NUM
ejpam-6605	242	18	1	1	NUM
ejpam-6605	242	19	is	be	AUX
ejpam-6605	242	20	an	an	DET
ejpam-6605	242	21	integer	integer	NOUN
ejpam-6605	242	22	.	.	PUNCT
ejpam-6605	243	1	let	let	VERB
ejpam-6605	243	2	tn(k	tn(k	NOUN
ejpam-6605	243	3	)	)	PUNCT
ejpam-6605	244	1	=	=	SYM
ejpam-6605	244	2			NOUN
ejpam-6605	245	1	k	k	NOUN
ejpam-6605	245	2	1	1	NUM
ejpam-6605	245	3	0	0	NUM
ejpam-6605	245	4	·	·	PUNCT
ejpam-6605	245	5	·	·	PUNCT
ejpam-6605	245	6	·	·	PUNCT
ejpam-6605	245	7	·	·	PUNCT
ejpam-6605	245	8	·	·	PUNCT
ejpam-6605	245	9	·	·	PUNCT
ejpam-6605	245	10	·	·	PUNCT
ejpam-6605	245	11	·	·	PUNCT
ejpam-6605	245	12	·	·	PUNCT
ejpam-6605	245	13	·	·	PUNCT
ejpam-6605	245	14	·	·	PUNCT
ejpam-6605	245	15	·	·	PUNCT
ejpam-6605	245	16	0	0	NUM
ejpam-6605	246	1	k	k	X
ejpam-6605	247	1	−	−	PROPN
ejpam-6605	247	2	1	1	NUM
ejpam-6605	247	3	k	k	NOUN
ejpam-6605	247	4	1	1	NUM
ejpam-6605	247	5	0	0	NUM
ejpam-6605	247	6	·	·	PUNCT
ejpam-6605	247	7	·	·	PUNCT
ejpam-6605	247	8	·	·	PUNCT
ejpam-6605	247	9	0	0	NUM
ejpam-6605	247	10	0	0	NUM
ejpam-6605	248	1	k	k	NOUN
ejpam-6605	248	2	−	−	PROPN
ejpam-6605	249	1	1	1	NUM
ejpam-6605	249	2	k	k	NOUN
ejpam-6605	249	3	1	1	NUM
ejpam-6605	249	4	0	0	NUM
ejpam-6605	249	5	...	...	SYM
ejpam-6605	249	6	0	0	NUM
ejpam-6605	249	7	...	...	PUNCT
ejpam-6605	249	8	...	...	PUNCT
ejpam-6605	249	9	...	...	PUNCT
ejpam-6605	249	10	...	...	PUNCT
ejpam-6605	249	11	...	...	PUNCT
ejpam-6605	249	12	0	0	NUM
ejpam-6605	249	13	...	...	PUNCT
ejpam-6605	250	1	k	k	X
ejpam-6605	251	1	−	−	PROPN
ejpam-6605	251	2	1	1	NUM
ejpam-6605	251	3	k	k	NOUN
ejpam-6605	251	4	.	.	NOUN
ejpam-6605	251	5	then	then	ADV
ejpam-6605	251	6	det(tn	det(tn	X
ejpam-6605	251	7	)	)	PUNCT
ejpam-6605	251	8	=	=	SYM
ejpam-6605	251	9	mk	mk	PROPN
ejpam-6605	251	10	,	,	PUNCT
ejpam-6605	251	11	n+1	n+1	PROPN
ejpam-6605	251	12	.	.	PUNCT
ejpam-6605	252	1	proof	proof	NOUN
ejpam-6605	252	2	.	.	PUNCT
ejpam-6605	253	1	let	let	VERB
ejpam-6605	253	2	α	α	NOUN
ejpam-6605	253	3	=	=	PUNCT
ejpam-6605	254	1	k	k	NOUN
ejpam-6605	254	2	−	−	PROPN
ejpam-6605	254	3	1	1	NUM
ejpam-6605	254	4	,	,	PUNCT
ejpam-6605	254	5	β	β	X
ejpam-6605	254	6	=	=	SYM
ejpam-6605	254	7	1	1	X
ejpam-6605	254	8	.	.	PUNCT
ejpam-6605	255	1	then	then	ADV
ejpam-6605	255	2	mk	mk	PROPN
ejpam-6605	255	3	,	,	PUNCT
ejpam-6605	255	4	n	n	X
ejpam-6605	255	5	=	=	PUNCT
ejpam-6605	255	6	αn−βn	αn−βn	NUM
ejpam-6605	255	7	α−β	α−β	PROPN
ejpam-6605	255	8	,	,	PUNCT
ejpam-6605	255	9	following	follow	VERB
ejpam-6605	255	10	the	the	DET
ejpam-6605	255	11	work	work	NOUN
ejpam-6605	255	12	of	of	ADP
ejpam-6605	255	13	kilic	kilic	NOUN
ejpam-6605	255	14	and	and	CCONJ
ejpam-6605	255	15	tasci	tasci	NOUN
ejpam-6605	255	16	in	in	ADP
ejpam-6605	255	17	[	[	X
ejpam-6605	255	18	10	10	NUM
ejpam-6605	255	19	,	,	PUNCT
ejpam-6605	255	20	11	11	NUM
ejpam-6605	255	21	]	]	PUNCT
ejpam-6605	255	22	we	we	PRON
ejpam-6605	255	23	have	have	VERB
ejpam-6605	255	24	det(tn	det(tn	NOUN
ejpam-6605	255	25	)	)	PUNCT
ejpam-6605	255	26	=	=	SYM
ejpam-6605	255	27	mk	mk	PROPN
ejpam-6605	255	28	,	,	PUNCT
ejpam-6605	255	29	n+1	n+1	PROPN
ejpam-6605	255	30	.	.	PUNCT
ejpam-6605	256	1	finally	finally	ADV
ejpam-6605	256	2	,	,	PUNCT
ejpam-6605	256	3	we	we	PRON
ejpam-6605	256	4	use	use	VERB
ejpam-6605	256	5	theorems	theorem	NOUN
ejpam-6605	256	6	1	1	NUM
ejpam-6605	256	7	-	-	SYM
ejpam-6605	256	8	3	3	NUM
ejpam-6605	256	9	from	from	ADP
ejpam-6605	256	10	[	[	X
ejpam-6605	256	11	10	10	NUM
ejpam-6605	256	12	]	]	PUNCT
ejpam-6605	256	13	to	to	PART
ejpam-6605	256	14	get	get	VERB
ejpam-6605	256	15	the	the	DET
ejpam-6605	256	16	following	follow	VERB
ejpam-6605	256	17	result	result	NOUN
ejpam-6605	256	18	.	.	PUNCT
ejpam-6605	257	1	lemma	lemma	PROPN
ejpam-6605	257	2	9	9	NUM
ejpam-6605	257	3	.	.	PUNCT
ejpam-6605	258	1	we	we	PRON
ejpam-6605	258	2	have	have	VERB
ejpam-6605	258	3	(	(	PUNCT
ejpam-6605	258	4	i	i	NOUN
ejpam-6605	258	5	)	)	PUNCT
ejpam-6605	258	6	let	let	VERB
ejpam-6605	258	7	an(k	an(k	NOUN
ejpam-6605	258	8	)	)	PUNCT
ejpam-6605	259	1	=	=	PRON
ejpam-6605	259	2			NOUN
ejpam-6605	260	1	k	k	NOUN
ejpam-6605	260	2	1	1	NUM
ejpam-6605	260	3	−	−	PROPN
ejpam-6605	260	4	k	k	NOUN
ejpam-6605	260	5	0	0	NUM
ejpam-6605	260	6	...	...	PUNCT
ejpam-6605	260	7	...	...	PUNCT
ejpam-6605	260	8	...	...	PUNCT
ejpam-6605	261	1	0	0	NUM
ejpam-6605	261	2	1	1	NUM
ejpam-6605	261	3	k	k	NOUN
ejpam-6605	261	4	1	1	NUM
ejpam-6605	261	5	−	−	PROPN
ejpam-6605	261	6	k	k	NOUN
ejpam-6605	261	7	0	0	PUNCT
ejpam-6605	261	8	...	...	PUNCT
ejpam-6605	261	9	0	0	NUM
ejpam-6605	261	10	0	0	NUM
ejpam-6605	261	11	1	1	NUM
ejpam-6605	261	12	k	k	NOUN
ejpam-6605	261	13	1	1	NUM
ejpam-6605	261	14	−	−	PROPN
ejpam-6605	261	15	k	k	NOUN
ejpam-6605	261	16	0	0	NUM
ejpam-6605	261	17	...	...	PUNCT
ejpam-6605	261	18	0	0	NUM
ejpam-6605	261	19	...	...	PUNCT
ejpam-6605	261	20	...	...	PUNCT
ejpam-6605	261	21	...	...	PUNCT
ejpam-6605	261	22	...	...	PUNCT
ejpam-6605	261	23	...	...	PUNCT
ejpam-6605	261	24	0	0	X
ejpam-6605	261	25	...	...	SYM
ejpam-6605	261	26	1	1	NUM
ejpam-6605	261	27	k	k	X
ejpam-6605	261	28	.	.	NOUN
ejpam-6605	261	29	then	then	ADV
ejpam-6605	261	30	per(an	per(an	NOUN
ejpam-6605	261	31	)	)	PUNCT
ejpam-6605	261	32	=	=	SYM
ejpam-6605	261	33	mk	mk	PROPN
ejpam-6605	261	34	,	,	PUNCT
ejpam-6605	261	35	n+1	n+1	PROPN
ejpam-6605	261	36	.	.	PROPN
ejpam-6605	262	1	sh	sh	PROPN
ejpam-6605	262	2	.	.	PROPN
ejpam-6605	262	3	a.	a.	PROPN
ejpam-6605	262	4	bani	bani	PROPN
ejpam-6605	262	5	melhem	melhem	PROPN
ejpam-6605	262	6	,	,	PUNCT
ejpam-6605	262	7	al	al	PROPN
ejpam-6605	262	8	-	-	PUNCT
ejpam-6605	262	9	kateeb	kateeb	PROPN
ejpam-6605	262	10	,	,	PUNCT
ejpam-6605	262	11	a.	a.	PROPN
ejpam-6605	262	12	dagher	dagher	PROPN
ejpam-6605	262	13	/	/	SYM
ejpam-6605	262	14	eur	eur	PROPN
ejpam-6605	262	15	.	.	PUNCT
ejpam-6605	263	1	j.	j.	PROPN
ejpam-6605	263	2	pure	pure	PROPN
ejpam-6605	263	3	appl	appl	PROPN
ejpam-6605	263	4	.	.	PROPN
ejpam-6605	263	5	math	math	PROPN
ejpam-6605	263	6	,	,	PUNCT
ejpam-6605	263	7	18	18	NUM
ejpam-6605	263	8	(	(	PUNCT
ejpam-6605	263	9	4	4	NUM
ejpam-6605	263	10	)	)	PUNCT
ejpam-6605	263	11	(	(	PUNCT
ejpam-6605	263	12	2025	2025	NUM
ejpam-6605	263	13	)	)	PUNCT
ejpam-6605	263	14	,	,	PUNCT
ejpam-6605	263	15	6605	6605	NUM
ejpam-6605	263	16	12	12	NUM
ejpam-6605	263	17	of	of	ADP
ejpam-6605	263	18	15	15	NUM
ejpam-6605	263	19	(	(	PUNCT
ejpam-6605	263	20	ii	ii	NOUN
ejpam-6605	263	21	)	)	PUNCT
ejpam-6605	263	22	let	let	VERB
ejpam-6605	263	23	hn(k	hn(k	PRON
ejpam-6605	263	24	)	)	PUNCT
ejpam-6605	264	1	=	=	SYM
ejpam-6605	264	2			NOUN
ejpam-6605	265	1	k	k	NOUN
ejpam-6605	265	2	1	1	X
ejpam-6605	265	3	−	−	PROPN
ejpam-6605	265	4	k	k	NOUN
ejpam-6605	265	5	0	0	NUM
ejpam-6605	265	6	...	...	PUNCT
ejpam-6605	265	7	...	...	PUNCT
ejpam-6605	266	1	0	0	NUM
ejpam-6605	267	1	1	1	NUM
ejpam-6605	267	2	0	0	NUM
ejpam-6605	267	3	0	0	NUM
ejpam-6605	267	4	0	0	NUM
ejpam-6605	267	5	0	0	NUM
ejpam-6605	267	6	0	0	NUM
ejpam-6605	267	7	0	0	NUM
ejpam-6605	267	8	an(k	an(k	NUM
ejpam-6605	267	9	)	)	PUNCT
ejpam-6605	267	10	0	0	NUM
ejpam-6605	267	11	·	·	PUNCT
ejpam-6605	267	12	·	·	PUNCT
ejpam-6605	267	13	·	·	PUNCT
ejpam-6605	267	14	0	0	NUM
ejpam-6605	267	15	0	0	NUM
ejpam-6605	267	16	0	0	NUM
ejpam-6605	267	17	·	·	PUNCT
ejpam-6605	267	18	·	·	PUNCT
ejpam-6605	267	19	·	·	PUNCT
ejpam-6605	267	20	0	0	X
ejpam-6605	268	1	.	.	PROPN
ejpam-6605	268	2	then	then	ADV
ejpam-6605	268	3	per(hn	per(hn	NOUN
ejpam-6605	268	4	)	)	PUNCT
ejpam-6605	268	5	=	=	SYM
ejpam-6605	268	6	∑i=0	∑i=0	PROPN
ejpam-6605	268	7	n	n	NUM
ejpam-6605	268	8	mk	mk	NOUN
ejpam-6605	268	9	,	,	PUNCT
ejpam-6605	268	10	i	i	PRON
ejpam-6605	268	11	where	where	SCONJ
ejpam-6605	268	12	n	n	PRON
ejpam-6605	268	13	≥	≥	X
ejpam-6605	268	14	2	2	NUM
ejpam-6605	268	15	and	and	CCONJ
ejpam-6605	268	16	an(k	an(k	NUM
ejpam-6605	268	17	)	)	PUNCT
ejpam-6605	268	18	defined	define	VERB
ejpam-6605	268	19	as	as	ADP
ejpam-6605	268	20	the	the	DET
ejpam-6605	268	21	last	last	ADJ
ejpam-6605	268	22	part	part	NOUN
ejpam-6605	268	23	.	.	PUNCT
ejpam-6605	269	1	(	(	PUNCT
ejpam-6605	269	2	iii	iii	X
ejpam-6605	269	3	)	)	PUNCT
ejpam-6605	269	4	let	let	VERB
ejpam-6605	269	5	gn(k	gn(k	PRON
ejpam-6605	269	6	)	)	PUNCT
ejpam-6605	269	7	=	=	SYM
ejpam-6605	269	8			VERB
ejpam-6605	269	9	1	1	NUM
ejpam-6605	269	10	1	1	NUM
ejpam-6605	269	11	1	1	NUM
ejpam-6605	269	12	...	...	PUNCT
ejpam-6605	269	13	...	...	PUNCT
ejpam-6605	270	1	...	...	PUNCT
ejpam-6605	271	1	1	1	NUM
ejpam-6605	271	2	−1	−1	NOUN
ejpam-6605	271	3	k	k	NOUN
ejpam-6605	272	1	1	1	NUM
ejpam-6605	272	2	−	−	PROPN
ejpam-6605	272	3	k	k	NOUN
ejpam-6605	272	4	0	0	PUNCT
ejpam-6605	272	5	...	...	PUNCT
ejpam-6605	273	1	0	0	NUM
ejpam-6605	273	2	0	0	NUM
ejpam-6605	273	3	−1	−1	NOUN
ejpam-6605	273	4	k	k	NOUN
ejpam-6605	274	1	1	1	NUM
ejpam-6605	274	2	−	−	PROPN
ejpam-6605	274	3	k	k	NOUN
ejpam-6605	274	4	0	0	NUM
ejpam-6605	274	5	...	...	PUNCT
ejpam-6605	274	6	0	0	NUM
ejpam-6605	274	7	...	...	PUNCT
ejpam-6605	274	8	...	...	PUNCT
ejpam-6605	274	9	...	...	PUNCT
ejpam-6605	274	10	...	...	PUNCT
ejpam-6605	274	11	...	...	PUNCT
ejpam-6605	275	1	0	0	NUM
ejpam-6605	275	2	...	...	PUNCT
ejpam-6605	275	3	−1	−1	NOUN
ejpam-6605	276	1	k	k	X
ejpam-6605	276	2	.	.	NOUN
ejpam-6605	276	3	then	then	ADV
ejpam-6605	276	4	det(gn	det(gn	ADJ
ejpam-6605	276	5	)	)	PUNCT
ejpam-6605	276	6	=	=	SYM
ejpam-6605	276	7	∑i=0	∑i=0	PROPN
ejpam-6605	276	8	n	n	NUM
ejpam-6605	276	9	mk	mk	NOUN
ejpam-6605	276	10	,	,	PUNCT
ejpam-6605	276	11	i	i	PRON
ejpam-6605	276	12	where	where	SCONJ
ejpam-6605	276	13	n	n	PRON
ejpam-6605	276	14	≥	≥	NOUN
ejpam-6605	276	15	2	2	NUM
ejpam-6605	276	16	.	.	PUNCT
ejpam-6605	276	17	proof	proof	NOUN
ejpam-6605	276	18	.	.	PUNCT
ejpam-6605	277	1	using	use	VERB
ejpam-6605	277	2	α	α	PROPN
ejpam-6605	277	3	=	=	SYM
ejpam-6605	277	4	k	k	NOUN
ejpam-6605	278	1	−	−	PROPN
ejpam-6605	278	2	1	1	NUM
ejpam-6605	278	3	,	,	PUNCT
ejpam-6605	278	4	β	β	X
ejpam-6605	278	5	=	=	SYM
ejpam-6605	278	6	1	1	NUM
ejpam-6605	278	7	and	and	CCONJ
ejpam-6605	278	8	mk	mk	PROPN
ejpam-6605	278	9	,	,	PUNCT
ejpam-6605	278	10	n	n	PRON
ejpam-6605	278	11	=	=	PUNCT
ejpam-6605	278	12	αn−βn	αn−βn	NUM
ejpam-6605	278	13	α−β	α−β	X
ejpam-6605	278	14	(	(	PUNCT
ejpam-6605	278	15	i	i	NOUN
ejpam-6605	278	16	)	)	PUNCT
ejpam-6605	278	17	statement	statement	NOUN
ejpam-6605	278	18	1	1	NUM
ejpam-6605	278	19	is	be	AUX
ejpam-6605	278	20	true	true	ADJ
ejpam-6605	278	21	by	by	ADP
ejpam-6605	278	22	theorem	theorem	NOUN
ejpam-6605	278	23	1	1	NUM
ejpam-6605	278	24	from	from	ADP
ejpam-6605	278	25	[	[	X
ejpam-6605	278	26	10	10	NUM
ejpam-6605	278	27	]	]	PUNCT
ejpam-6605	278	28	.	.	PUNCT
ejpam-6605	279	1	(	(	PUNCT
ejpam-6605	279	2	ii	ii	NOUN
ejpam-6605	279	3	)	)	PUNCT
ejpam-6605	279	4	statement	statement	NOUN
ejpam-6605	279	5	2	2	NUM
ejpam-6605	279	6	is	be	AUX
ejpam-6605	279	7	true	true	ADJ
ejpam-6605	279	8	by	by	ADP
ejpam-6605	279	9	theorem	theorem	NOUN
ejpam-6605	279	10	2	2	NUM
ejpam-6605	279	11	from	from	ADP
ejpam-6605	279	12	[	[	X
ejpam-6605	279	13	10	10	NUM
ejpam-6605	279	14	]	]	PUNCT
ejpam-6605	279	15	.	.	PUNCT
ejpam-6605	280	1	(	(	PUNCT
ejpam-6605	280	2	iii	iii	X
ejpam-6605	280	3	)	)	PUNCT
ejpam-6605	280	4	statement	statement	NOUN
ejpam-6605	280	5	3	3	NUM
ejpam-6605	280	6	is	be	AUX
ejpam-6605	280	7	true	true	ADJ
ejpam-6605	280	8	by	by	ADP
ejpam-6605	280	9	theorem	theorem	NOUN
ejpam-6605	280	10	3	3	NUM
ejpam-6605	280	11	from	from	ADP
ejpam-6605	280	12	[	[	X
ejpam-6605	280	13	10	10	NUM
ejpam-6605	280	14	]	]	PUNCT
ejpam-6605	280	15	.	.	PUNCT
ejpam-6605	281	1	5	5	X
ejpam-6605	281	2	.	.	X
ejpam-6605	282	1	some	some	DET
ejpam-6605	282	2	applications	application	NOUN
ejpam-6605	282	3	in	in	ADP
ejpam-6605	282	4	this	this	DET
ejpam-6605	282	5	section	section	NOUN
ejpam-6605	282	6	we	we	PRON
ejpam-6605	282	7	give	give	VERB
ejpam-6605	282	8	two	two	NUM
ejpam-6605	282	9	applications	application	NOUN
ejpam-6605	282	10	in	in	ADP
ejpam-6605	282	11	cryptography	cryptography	NOUN
ejpam-6605	282	12	for	for	ADP
ejpam-6605	282	13	the	the	DET
ejpam-6605	282	14	matrix	matrix	NOUN
ejpam-6605	282	15	representation	representation	NOUN
ejpam-6605	282	16	of	of	ADP
ejpam-6605	282	17	mk	mk	PROPN
ejpam-6605	282	18	,	,	PUNCT
ejpam-6605	282	19	m	m	PROPN
ejpam-6605	282	20	,	,	PUNCT
ejpam-6605	282	21	which	which	PRON
ejpam-6605	282	22	was	be	AUX
ejpam-6605	282	23	found	find	VERB
ejpam-6605	282	24	in	in	ADP
ejpam-6605	282	25	section	section	NOUN
ejpam-6605	282	26	3	3	NUM
ejpam-6605	282	27	.	.	PROPN
ejpam-6605	282	28	5.1	5.1	NUM
ejpam-6605	282	29	.	.	PUNCT
ejpam-6605	283	1	an	an	DET
ejpam-6605	283	2	authentication	authentication	NOUN
ejpam-6605	283	3	protocol	protocol	NOUN
ejpam-6605	283	4	in	in	ADP
ejpam-6605	283	5	this	this	DET
ejpam-6605	283	6	section	section	NOUN
ejpam-6605	283	7	we	we	PRON
ejpam-6605	283	8	will	will	AUX
ejpam-6605	283	9	introduce	introduce	VERB
ejpam-6605	283	10	an	an	DET
ejpam-6605	283	11	authentication	authentication	NOUN
ejpam-6605	283	12	protocol	protocol	NOUN
ejpam-6605	283	13	based	base	VERB
ejpam-6605	283	14	on	on	ADP
ejpam-6605	283	15	matrices	matrix	NOUN
ejpam-6605	283	16	.	.	PUNCT
ejpam-6605	284	1	at	at	ADP
ejpam-6605	284	2	first	first	ADV
ejpam-6605	284	3	,	,	PUNCT
ejpam-6605	284	4	alice	alice	PROPN
ejpam-6605	284	5	chooses	choose	VERB
ejpam-6605	284	6	a	a	DET
ejpam-6605	284	7	large	large	ADJ
ejpam-6605	284	8	integer	integer	NOUN
ejpam-6605	284	9	n	n	PROPN
ejpam-6605	284	10	=	=	SYM
ejpam-6605	284	11	pq	pq	NOUN
ejpam-6605	284	12	a	a	DET
ejpam-6605	284	13	product	product	NOUN
ejpam-6605	284	14	of	of	ADP
ejpam-6605	284	15	two	two	NUM
ejpam-6605	284	16	primes	prime	NOUN
ejpam-6605	284	17	and	and	CCONJ
ejpam-6605	285	1	an	an	DET
ejpam-6605	285	2	integer	integer	NOUN
ejpam-6605	285	3	k	k	PROPN
ejpam-6605	285	4	>	>	X
ejpam-6605	285	5	2	2	X
ejpam-6605	285	6	.	.	PUNCT
ejpam-6605	285	7	then	then	ADV
ejpam-6605	285	8	alice	alice	PROPN
ejpam-6605	285	9	chooses	choose	VERB
ejpam-6605	285	10	two	two	NUM
ejpam-6605	285	11	matrices	matrix	NOUN
ejpam-6605	285	12	a	a	DET
ejpam-6605	285	13	=	=	PUNCT
ejpam-6605	285	14	qn1	qn1	PROPN
ejpam-6605	285	15	k	k	PROPN
ejpam-6605	285	16	and	and	CCONJ
ejpam-6605	285	17	b	b	X
ejpam-6605	285	18	=	=	NOUN
ejpam-6605	285	19	qn2	qn2	NOUN
ejpam-6605	285	20	k	k	PROPN
ejpam-6605	285	21	and	and	CCONJ
ejpam-6605	285	22	computes	compute	VERB
ejpam-6605	285	23	their	their	PRON
ejpam-6605	285	24	squares	square	NOUN
ejpam-6605	285	25	modulo	modulo	PROPN
ejpam-6605	285	26	n.	n.	PROPN
ejpam-6605	285	27	namely	namely	ADV
ejpam-6605	285	28	,	,	PUNCT
ejpam-6605	285	29	c	c	PROPN
ejpam-6605	285	30	=	=	SYM
ejpam-6605	285	31	a2	a2	PROPN
ejpam-6605	285	32	=	=	PUNCT
ejpam-6605	286	1	q2n1	q2n1	PROPN
ejpam-6605	286	2	k	k	PROPN
ejpam-6605	286	3	mod	mod	PROPN
ejpam-6605	286	4	n	n	PROPN
ejpam-6605	286	5	and	and	CCONJ
ejpam-6605	286	6	d	d	NOUN
ejpam-6605	286	7	=	=	SYM
ejpam-6605	286	8	b2	b2	NOUN
ejpam-6605	286	9	=	=	SYM
ejpam-6605	286	10	q2n2	q2n2	PROPN
ejpam-6605	286	11	k	k	PROPN
ejpam-6605	286	12	mod	mod	PROPN
ejpam-6605	286	13	n.	n.	PROPN
ejpam-6605	286	14	alice	alice	PROPN
ejpam-6605	286	15	publishes	publish	VERB
ejpam-6605	286	16	c	c	PROPN
ejpam-6605	286	17	and	and	CCONJ
ejpam-6605	286	18	d.	d.	PROPN
ejpam-6605	286	19	the	the	DET
ejpam-6605	286	20	method	method	NOUN
ejpam-6605	286	21	works	work	VERB
ejpam-6605	286	22	as	as	SCONJ
ejpam-6605	286	23	follows	follow	VERB
ejpam-6605	286	24	:	:	PUNCT
ejpam-6605	286	25	algorithm	algorithm	NOUN
ejpam-6605	286	26	1	1	NUM
ejpam-6605	286	27	.	.	PUNCT
ejpam-6605	287	1	(	(	PUNCT
ejpam-6605	287	2	i	i	NOUN
ejpam-6605	287	3	)	)	PUNCT
ejpam-6605	287	4	alice	alice	PROPN
ejpam-6605	287	5	chooses	choose	VERB
ejpam-6605	287	6	two	two	NUM
ejpam-6605	287	7	random	random	ADJ
ejpam-6605	287	8	integers	integer	NOUN
ejpam-6605	287	9	m1,m2	m1,m2	PROPN
ejpam-6605	287	10	and	and	CCONJ
ejpam-6605	287	11	finds	find	VERB
ejpam-6605	287	12	the	the	DET
ejpam-6605	287	13	matrices	matrix	NOUN
ejpam-6605	287	14	x1	x1	NOUN
ejpam-6605	288	1	=	=	PUNCT
ejpam-6605	288	2	qm1	qm1	PROPN
ejpam-6605	288	3	k	k	PROPN
ejpam-6605	288	4	,	,	PUNCT
ejpam-6605	288	5	x2	x2	PROPN
ejpam-6605	289	1	=	=	PUNCT
ejpam-6605	289	2	qm2	qm2	NOUN
ejpam-6605	290	1	k	k	INTJ
ejpam-6605	290	2	.	.	PUNCT
ejpam-6605	291	1	then	then	ADV
ejpam-6605	291	2	she	she	PRON
ejpam-6605	291	3	computes	compute	VERB
ejpam-6605	291	4	y1	y1	NOUN
ejpam-6605	291	5	=	=	SYM
ejpam-6605	291	6	x2	x2	PROPN
ejpam-6605	291	7	1	1	NUM
ejpam-6605	291	8	mod	mod	NOUN
ejpam-6605	291	9	n	n	PROPN
ejpam-6605	291	10	and	and	CCONJ
ejpam-6605	291	11	y2	y2	PROPN
ejpam-6605	291	12	=	=	SYM
ejpam-6605	292	1	x2	x2	PROPN
ejpam-6605	292	2	2	2	NUM
ejpam-6605	292	3	mod	mod	NOUN
ejpam-6605	292	4	n	n	PROPN
ejpam-6605	292	5	and	and	CCONJ
ejpam-6605	292	6	sends	send	VERB
ejpam-6605	292	7	y1	y1	PROPN
ejpam-6605	292	8	,	,	PUNCT
ejpam-6605	292	9	y2	y2	PROPN
ejpam-6605	292	10	to	to	ADP
ejpam-6605	292	11	bob	bob	PROPN
ejpam-6605	292	12	.	.	PUNCT
ejpam-6605	293	1	(	(	PUNCT
ejpam-6605	293	2	ii	ii	X
ejpam-6605	293	3	)	)	PUNCT
ejpam-6605	293	4	bob	bob	PROPN
ejpam-6605	293	5	chooses	choose	VERB
ejpam-6605	293	6	two	two	NUM
ejpam-6605	293	7	random	random	ADJ
ejpam-6605	293	8	numbers	number	NOUN
ejpam-6605	293	9	v1	v1	NOUN
ejpam-6605	293	10	,	,	PUNCT
ejpam-6605	293	11	v2	v2	PROPN
ejpam-6605	293	12	∈	∈	PROPN
ejpam-6605	293	13	{	{	PUNCT
ejpam-6605	293	14	0	0	NUM
ejpam-6605	293	15	,	,	PUNCT
ejpam-6605	293	16	1	1	NUM
ejpam-6605	293	17	}	}	PUNCT
ejpam-6605	293	18	and	and	CCONJ
ejpam-6605	293	19	sends	send	VERB
ejpam-6605	293	20	them	they	PRON
ejpam-6605	293	21	to	to	ADP
ejpam-6605	293	22	alice	alice	PROPN
ejpam-6605	293	23	.	.	PUNCT
ejpam-6605	294	1	(	(	PUNCT
ejpam-6605	294	2	iii	iii	X
ejpam-6605	294	3	)	)	PUNCT
ejpam-6605	294	4	alice	alice	PROPN
ejpam-6605	294	5	computes	compute	VERB
ejpam-6605	294	6	z	z	NOUN
ejpam-6605	294	7	=	=	SYM
ejpam-6605	294	8	x1x2a	x1x2a	PUNCT
ejpam-6605	294	9	v1bv2	v1bv2	PROPN
ejpam-6605	294	10	mod	mod	PROPN
ejpam-6605	294	11	n	n	CCONJ
ejpam-6605	294	12	and	and	CCONJ
ejpam-6605	294	13	send	send	VERB
ejpam-6605	294	14	it	it	PRON
ejpam-6605	294	15	to	to	ADP
ejpam-6605	294	16	bob	bob	PROPN
ejpam-6605	294	17	.	.	PUNCT
ejpam-6605	295	1	(	(	PUNCT
ejpam-6605	295	2	iv	iv	X
ejpam-6605	295	3	)	)	PUNCT
ejpam-6605	295	4	bob	bob	NOUN
ejpam-6605	295	5	verifies	verifie	NOUN
ejpam-6605	295	6	the	the	DET
ejpam-6605	295	7	identity	identity	NOUN
ejpam-6605	295	8	of	of	ADP
ejpam-6605	295	9	alice	alice	PROPN
ejpam-6605	295	10	by	by	ADP
ejpam-6605	295	11	checking	check	VERB
ejpam-6605	295	12	that	that	SCONJ
ejpam-6605	295	13	z2	z2	PROPN
ejpam-6605	295	14	=	=	SYM
ejpam-6605	295	15	y1y2c	y1y2c	NUM
ejpam-6605	295	16	v1dv2	v1dv2	PROPN
ejpam-6605	295	17	(	(	PUNCT
ejpam-6605	295	18	v	v	NOUN
ejpam-6605	295	19	)	)	PUNCT
ejpam-6605	295	20	bob	bob	PROPN
ejpam-6605	295	21	asks	ask	VERB
ejpam-6605	295	22	alice	alice	PROPN
ejpam-6605	295	23	to	to	PART
ejpam-6605	295	24	send	send	VERB
ejpam-6605	295	25	him	he	PRON
ejpam-6605	295	26	one	one	NUM
ejpam-6605	295	27	of	of	ADP
ejpam-6605	295	28	x1	x1	NUM
ejpam-6605	295	29	or	or	CCONJ
ejpam-6605	295	30	x2	x2	NOUN
ejpam-6605	296	1	and	and	CCONJ
ejpam-6605	296	2	he	he	PRON
ejpam-6605	296	3	checks	check	VERB
ejpam-6605	296	4	that	that	PRON
ejpam-6605	296	5	y1	y1	NOUN
ejpam-6605	297	1	=	=	SYM
ejpam-6605	297	2	x2	x2	PROPN
ejpam-6605	297	3	1	1	NUM
ejpam-6605	297	4	or	or	CCONJ
ejpam-6605	297	5	y2	y2	NOUN
ejpam-6605	297	6	=	=	SYM
ejpam-6605	297	7	x2	x2	PROPN
ejpam-6605	297	8	2	2	X
ejpam-6605	297	9	.	.	PUNCT
ejpam-6605	298	1	sh	sh	PROPN
ejpam-6605	298	2	.	.	PROPN
ejpam-6605	298	3	a.	a.	PROPN
ejpam-6605	298	4	bani	bani	PROPN
ejpam-6605	298	5	melhem	melhem	PROPN
ejpam-6605	298	6	,	,	PUNCT
ejpam-6605	298	7	al	al	PROPN
ejpam-6605	298	8	-	-	PUNCT
ejpam-6605	298	9	kateeb	kateeb	PROPN
ejpam-6605	298	10	,	,	PUNCT
ejpam-6605	298	11	a.	a.	PROPN
ejpam-6605	298	12	dagher	dagher	PROPN
ejpam-6605	298	13	/	/	SYM
ejpam-6605	298	14	eur	eur	PROPN
ejpam-6605	298	15	.	.	PUNCT
ejpam-6605	299	1	j.	j.	PROPN
ejpam-6605	299	2	pure	pure	PROPN
ejpam-6605	299	3	appl	appl	PROPN
ejpam-6605	299	4	.	.	PROPN
ejpam-6605	299	5	math	math	PROPN
ejpam-6605	299	6	,	,	PUNCT
ejpam-6605	299	7	18	18	NUM
ejpam-6605	299	8	(	(	PUNCT
ejpam-6605	299	9	4	4	NUM
ejpam-6605	299	10	)	)	PUNCT
ejpam-6605	299	11	(	(	PUNCT
ejpam-6605	299	12	2025	2025	NUM
ejpam-6605	299	13	)	)	PUNCT
ejpam-6605	299	14	,	,	PUNCT
ejpam-6605	299	15	6605	6605	NUM
ejpam-6605	299	16	13	13	NUM
ejpam-6605	299	17	of	of	ADP
ejpam-6605	299	18	15	15	NUM
ejpam-6605	299	19	example	example	NOUN
ejpam-6605	299	20	1	1	NUM
ejpam-6605	299	21	.	.	PUNCT
ejpam-6605	300	1	let	let	VERB
ejpam-6605	300	2	n	n	NOUN
ejpam-6605	300	3	=	=	SYM
ejpam-6605	300	4	11	11	NUM
ejpam-6605	300	5	·	·	SYM
ejpam-6605	300	6	13	13	NUM
ejpam-6605	300	7	=	=	SYM
ejpam-6605	300	8	143	143	NUM
ejpam-6605	300	9	,	,	PUNCT
ejpam-6605	300	10	and	and	CCONJ
ejpam-6605	300	11	k	k	X
ejpam-6605	301	1	=	=	SYM
ejpam-6605	301	2	5	5	X
ejpam-6605	301	3	.	.	PUNCT
ejpam-6605	302	1	if	if	SCONJ
ejpam-6605	302	2	alice	alice	PROPN
ejpam-6605	302	3	takes	take	VERB
ejpam-6605	302	4	on	on	ADP
ejpam-6605	302	5	n1	n1	PROPN
ejpam-6605	302	6	=	=	SYM
ejpam-6605	302	7	2	2	NUM
ejpam-6605	302	8	and	and	CCONJ
ejpam-6605	302	9	n2	n2	NOUN
ejpam-6605	302	10	=	=	ADJ
ejpam-6605	303	1	3	3	X
ejpam-6605	303	2	.	.	PUNCT
ejpam-6605	303	3	then	then	ADV
ejpam-6605	303	4	a	a	PRON
ejpam-6605	303	5	=	=	X
ejpam-6605	303	6	[	[	PUNCT
ejpam-6605	303	7	139	139	NUM
ejpam-6605	303	8	5	5	NUM
ejpam-6605	303	9	123	123	NUM
ejpam-6605	303	10	21	21	NUM
ejpam-6605	303	11	]	]	PUNCT
ejpam-6605	303	12	and	and	CCONJ
ejpam-6605	303	13	b	b	X
ejpam-6605	304	1	=	=	SYM
ejpam-6605	304	2	[	[	PUNCT
ejpam-6605	304	3	123	123	NUM
ejpam-6605	304	4	21	21	NUM
ejpam-6605	304	5	59	59	NUM
ejpam-6605	304	6	85	85	NUM
ejpam-6605	304	7	]	]	PUNCT
ejpam-6605	304	8	.	.	PUNCT
ejpam-6605	305	1	also	also	ADV
ejpam-6605	305	2	,	,	PUNCT
ejpam-6605	305	3	we	we	PRON
ejpam-6605	305	4	have	have	VERB
ejpam-6605	305	5	c	c	NOUN
ejpam-6605	305	6	=	=	SYM
ejpam-6605	305	7	a2	a2	PROPN
ejpam-6605	305	8	=	=	PUNCT
ejpam-6605	306	1	[	[	PUNCT
ejpam-6605	306	2	59	59	NUM
ejpam-6605	306	3	85	85	NUM
ejpam-6605	306	4	89	89	NUM
ejpam-6605	306	5	55	55	NUM
ejpam-6605	306	6	]	]	PUNCT
ejpam-6605	306	7	and	and	CCONJ
ejpam-6605	306	8	d	d	NOUN
ejpam-6605	306	9	=	=	SYM
ejpam-6605	306	10	b2	b2	NOUN
ejpam-6605	306	11	=	=	SYM
ejpam-6605	306	12	[	[	PUNCT
ejpam-6605	306	13	66	66	NUM
ejpam-6605	306	14	78	78	NUM
ejpam-6605	306	15	117	117	NUM
ejpam-6605	306	16	27	27	NUM
ejpam-6605	306	17	]	]	PUNCT
ejpam-6605	306	18	(	(	PUNCT
ejpam-6605	306	19	i	i	NOUN
ejpam-6605	306	20	)	)	PUNCT
ejpam-6605	306	21	alice	alice	PROPN
ejpam-6605	306	22	chooses	choose	VERB
ejpam-6605	306	23	two	two	NUM
ejpam-6605	306	24	random	random	ADJ
ejpam-6605	306	25	integers	integer	NOUN
ejpam-6605	306	26	m1	m1	NOUN
ejpam-6605	306	27	=	=	SYM
ejpam-6605	307	1	3,m2	3,m2	NUM
ejpam-6605	307	2	=	=	SYM
ejpam-6605	307	3	4	4	NUM
ejpam-6605	308	1	and	and	CCONJ
ejpam-6605	308	2	finds	find	VERB
ejpam-6605	308	3	the	the	DET
ejpam-6605	308	4	matrices	matrix	NOUN
ejpam-6605	309	1	x1	x1	NOUN
ejpam-6605	310	1	=	=	PUNCT
ejpam-6605	310	2	qm1	qm1	PROPN
ejpam-6605	310	3	5	5	NUM
ejpam-6605	311	1	=	=	SYM
ejpam-6605	311	2	[	[	PUNCT
ejpam-6605	311	3	123	123	NUM
ejpam-6605	311	4	21	21	NUM
ejpam-6605	311	5	59	59	NUM
ejpam-6605	311	6	85	85	NUM
ejpam-6605	311	7	]	]	PUNCT
ejpam-6605	311	8	x2	x2	NOUN
ejpam-6605	311	9	=	=	PUNCT
ejpam-6605	312	1	qm2	qm2	NOUN
ejpam-6605	312	2	5	5	NUM
ejpam-6605	313	1	=	=	SYM
ejpam-6605	313	2	[	[	PUNCT
ejpam-6605	313	3	59	59	NUM
ejpam-6605	313	4	85	85	NUM
ejpam-6605	313	5	89	89	NUM
ejpam-6605	313	6	55	55	NUM
ejpam-6605	313	7	]	]	PUNCT
ejpam-6605	313	8	then	then	ADV
ejpam-6605	313	9	she	she	PRON
ejpam-6605	313	10	computes	compute	VERB
ejpam-6605	313	11	y1	y1	NOUN
ejpam-6605	313	12	=	=	SYM
ejpam-6605	313	13	x2	x2	PROPN
ejpam-6605	313	14	1	1	NUM
ejpam-6605	313	15	=	=	SYM
ejpam-6605	313	16	[	[	PUNCT
ejpam-6605	313	17	66	66	NUM
ejpam-6605	313	18	78	78	NUM
ejpam-6605	313	19	117	117	NUM
ejpam-6605	313	20	27	27	NUM
ejpam-6605	313	21	]	]	PUNCT
ejpam-6605	313	22	and	and	CCONJ
ejpam-6605	313	23	y2	y2	NOUN
ejpam-6605	313	24	=	=	SYM
ejpam-6605	314	1	x2	x2	PROPN
ejpam-6605	314	2	2	2	NUM
ejpam-6605	315	1	=	=	SYM
ejpam-6605	315	2	[	[	PUNCT
ejpam-6605	315	3	35	35	NUM
ejpam-6605	315	4	109	109	NUM
ejpam-6605	315	5	136	136	NUM
ejpam-6605	315	6	8	8	NUM
ejpam-6605	315	7	]	]	PUNCT
ejpam-6605	315	8	and	and	CCONJ
ejpam-6605	315	9	sends	send	VERB
ejpam-6605	315	10	y1	y1	PROPN
ejpam-6605	315	11	,	,	PUNCT
ejpam-6605	315	12	y2	y2	PROPN
ejpam-6605	315	13	to	to	ADP
ejpam-6605	315	14	bob	bob	PROPN
ejpam-6605	315	15	.	.	PUNCT
ejpam-6605	316	1	(	(	PUNCT
ejpam-6605	316	2	ii	ii	X
ejpam-6605	316	3	)	)	PUNCT
ejpam-6605	316	4	bob	bob	PROPN
ejpam-6605	316	5	chooses	choose	VERB
ejpam-6605	316	6	two	two	NUM
ejpam-6605	316	7	random	random	ADJ
ejpam-6605	316	8	numbers	number	NOUN
ejpam-6605	316	9	v1	v1	NOUN
ejpam-6605	316	10	=	=	SYM
ejpam-6605	316	11	0	0	NUM
ejpam-6605	316	12	,	,	PUNCT
ejpam-6605	316	13	v2	v2	NOUN
ejpam-6605	316	14	=	=	SYM
ejpam-6605	316	15	1	1	NUM
ejpam-6605	316	16	and	and	CCONJ
ejpam-6605	316	17	sends	send	VERB
ejpam-6605	316	18	them	they	PRON
ejpam-6605	316	19	to	to	ADP
ejpam-6605	316	20	alice	alice	PROPN
ejpam-6605	316	21	.	.	PUNCT
ejpam-6605	317	1	(	(	PUNCT
ejpam-6605	317	2	iii	iii	X
ejpam-6605	317	3	)	)	PUNCT
ejpam-6605	317	4	alice	alice	PROPN
ejpam-6605	317	5	computes	compute	VERB
ejpam-6605	317	6	z	z	NOUN
ejpam-6605	317	7	=	=	SYM
ejpam-6605	317	8	x1x2a	x1x2a	PUNCT
ejpam-6605	317	9	v1bv2	v1bv2	PROPN
ejpam-6605	317	10	mod	mod	PROPN
ejpam-6605	318	1	n	n	PROPN
ejpam-6605	319	1	=	=	PRON
ejpam-6605	320	1	[	[	PUNCT
ejpam-6605	320	2	111	111	NUM
ejpam-6605	320	3	33	33	NUM
ejpam-6605	320	4	11	11	NUM
ejpam-6605	320	5	133	133	NUM
ejpam-6605	320	6	]	]	PUNCT
ejpam-6605	321	1	and	and	CCONJ
ejpam-6605	321	2	send	send	VERB
ejpam-6605	321	3	it	it	PRON
ejpam-6605	321	4	to	to	ADP
ejpam-6605	321	5	bob	bob	PROPN
ejpam-6605	321	6	.	.	PUNCT
ejpam-6605	322	1	(	(	PUNCT
ejpam-6605	322	2	iv	iv	X
ejpam-6605	322	3	)	)	PUNCT
ejpam-6605	322	4	bob	bob	NOUN
ejpam-6605	322	5	verifies	verifie	NOUN
ejpam-6605	322	6	the	the	DET
ejpam-6605	322	7	identity	identity	NOUN
ejpam-6605	322	8	of	of	ADP
ejpam-6605	322	9	alice	alice	PROPN
ejpam-6605	322	10	by	by	ADP
ejpam-6605	322	11	checking	check	VERB
ejpam-6605	322	12	that	that	SCONJ
ejpam-6605	322	13	z2	z2	PROPN
ejpam-6605	322	14	=	=	SYM
ejpam-6605	322	15	y1y2c	y1y2c	NUM
ejpam-6605	322	16	v1dv2	v1dv2	NOUN
ejpam-6605	322	17	=	=	PUNCT
ejpam-6605	323	1	[	[	PUNCT
ejpam-6605	323	2	100	100	NUM
ejpam-6605	323	3	44	44	NUM
ejpam-6605	323	4	110	110	NUM
ejpam-6605	323	5	34	34	NUM
ejpam-6605	323	6	]	]	PUNCT
ejpam-6605	323	7	(	(	PUNCT
ejpam-6605	323	8	v	v	NOUN
ejpam-6605	323	9	)	)	PUNCT
ejpam-6605	323	10	bob	bob	PROPN
ejpam-6605	323	11	asks	ask	VERB
ejpam-6605	323	12	alice	alice	PROPN
ejpam-6605	323	13	to	to	PART
ejpam-6605	323	14	send	send	VERB
ejpam-6605	323	15	him	he	PRON
ejpam-6605	323	16	one	one	NUM
ejpam-6605	323	17	of	of	ADP
ejpam-6605	323	18	x1	x1	NUM
ejpam-6605	323	19	or	or	CCONJ
ejpam-6605	323	20	x2	x2	NOUN
ejpam-6605	323	21	and	and	CCONJ
ejpam-6605	323	22	he	he	PRON
ejpam-6605	323	23	checks	check	VERB
ejpam-6605	323	24	that	that	PRON
ejpam-6605	323	25	y1	y1	NOUN
ejpam-6605	324	1	=	=	SYM
ejpam-6605	324	2	x2	x2	PROPN
ejpam-6605	324	3	1	1	NUM
ejpam-6605	324	4	or	or	CCONJ
ejpam-6605	324	5	y2	y2	NOUN
ejpam-6605	324	6	=	=	SYM
ejpam-6605	324	7	x2	x2	PROPN
ejpam-6605	324	8	2	2	X
ejpam-6605	324	9	.	.	PUNCT
ejpam-6605	325	1	we	we	PRON
ejpam-6605	325	2	should	should	AUX
ejpam-6605	325	3	mention	mention	VERB
ejpam-6605	325	4	that	that	SCONJ
ejpam-6605	325	5	it	it	PRON
ejpam-6605	325	6	is	be	AUX
ejpam-6605	325	7	very	very	ADV
ejpam-6605	325	8	hard	hard	ADJ
ejpam-6605	325	9	to	to	PART
ejpam-6605	325	10	know	know	VERB
ejpam-6605	325	11	the	the	DET
ejpam-6605	325	12	matrices	matrix	NOUN
ejpam-6605	325	13	a	a	PRON
ejpam-6605	325	14	and	and	CCONJ
ejpam-6605	325	15	b	b	NOUN
ejpam-6605	325	16	from	from	ADP
ejpam-6605	325	17	c	c	PROPN
ejpam-6605	325	18	and	and	CCONJ
ejpam-6605	325	19	d.	d.	PROPN
ejpam-6605	325	20	also	also	ADV
ejpam-6605	325	21	,	,	PUNCT
ejpam-6605	325	22	be	be	AUX
ejpam-6605	325	23	choosing	choose	VERB
ejpam-6605	325	24	a	a	DET
ejpam-6605	325	25	very	very	ADV
ejpam-6605	325	26	large	large	ADJ
ejpam-6605	325	27	number	number	NOUN
ejpam-6605	325	28	the	the	DET
ejpam-6605	325	29	problem	problem	NOUN
ejpam-6605	325	30	will	will	AUX
ejpam-6605	325	31	be	be	AUX
ejpam-6605	325	32	more	more	ADV
ejpam-6605	325	33	and	and	CCONJ
ejpam-6605	325	34	more	more	ADV
ejpam-6605	325	35	harder	hard	ADV
ejpam-6605	325	36	.	.	PUNCT
ejpam-6605	326	1	5.2	5.2	NUM
ejpam-6605	326	2	.	.	PUNCT
ejpam-6605	327	1	a	a	DET
ejpam-6605	327	2	key	key	ADJ
ejpam-6605	327	3	exchange	exchange	NOUN
ejpam-6605	327	4	protocol	protocol	NOUN
ejpam-6605	327	5	in	in	ADP
ejpam-6605	327	6	this	this	DET
ejpam-6605	327	7	section	section	NOUN
ejpam-6605	327	8	we	we	PRON
ejpam-6605	327	9	propose	propose	VERB
ejpam-6605	327	10	a	a	DET
ejpam-6605	327	11	key	key	ADJ
ejpam-6605	327	12	exchange	exchange	NOUN
ejpam-6605	327	13	protocol	protocol	NOUN
ejpam-6605	327	14	based	base	VERB
ejpam-6605	327	15	on	on	ADP
ejpam-6605	327	16	matrices	matrix	NOUN
ejpam-6605	327	17	at	at	ADP
ejpam-6605	327	18	first	first	ADJ
ejpam-6605	327	19	alice	alice	PROPN
ejpam-6605	327	20	and	and	CCONJ
ejpam-6605	327	21	bob	bob	PROPN
ejpam-6605	327	22	choose	choose	VERB
ejpam-6605	327	23	and	and	CCONJ
ejpam-6605	327	24	integer	integer	PROPN
ejpam-6605	327	25	n	n	PROPN
ejpam-6605	327	26	=	=	SYM
ejpam-6605	327	27	pq	pq	PROPN
ejpam-6605	327	28	and	and	CCONJ
ejpam-6605	327	29	k	k	X
ejpam-6605	327	30	>	>	X
ejpam-6605	327	31	2	2	X
ejpam-6605	327	32	.	.	PUNCT
ejpam-6605	328	1	then	then	ADV
ejpam-6605	328	2	they	they	PRON
ejpam-6605	328	3	choose	choose	VERB
ejpam-6605	328	4	a	a	DET
ejpam-6605	328	5	2	2	NUM
ejpam-6605	328	6	×	×	NOUN
ejpam-6605	328	7	2	2	NUM
ejpam-6605	328	8	matrix	matrix	NOUN
ejpam-6605	328	9	a	a	DET
ejpam-6605	328	10	the	the	DET
ejpam-6605	328	11	protocol	protocol	NOUN
ejpam-6605	328	12	works	work	NOUN
ejpam-6605	328	13	as	as	SCONJ
ejpam-6605	328	14	follows	follow	VERB
ejpam-6605	328	15	:	:	PUNCT
ejpam-6605	328	16	algorithm	algorithm	NOUN
ejpam-6605	328	17	2	2	NUM
ejpam-6605	328	18	.	.	PUNCT
ejpam-6605	329	1	(	(	PUNCT
ejpam-6605	329	2	i	i	NOUN
ejpam-6605	329	3	)	)	PUNCT
ejpam-6605	329	4	alice	alice	PROPN
ejpam-6605	329	5	selects	select	VERB
ejpam-6605	329	6	an	an	DET
ejpam-6605	329	7	integer	integer	NOUN
ejpam-6605	329	8	t	t	PROPN
ejpam-6605	329	9	>	>	X
ejpam-6605	329	10	0	0	PUNCT
ejpam-6605	330	1	and	and	CCONJ
ejpam-6605	330	2	a	a	DET
ejpam-6605	330	3	secret	secret	ADJ
ejpam-6605	330	4	matrix	matrix	NOUN
ejpam-6605	330	5	b	b	NOUN
ejpam-6605	331	1	=	=	PUNCT
ejpam-6605	331	2	qn1	qn1	PROPN
ejpam-6605	331	3	k	k	PROPN
ejpam-6605	331	4	mod	mod	PROPN
ejpam-6605	331	5	n	n	PROPN
ejpam-6605	331	6	that	that	PRON
ejpam-6605	331	7	does	do	AUX
ejpam-6605	331	8	n’t	not	PART
ejpam-6605	331	9	commute	commute	VERB
ejpam-6605	331	10	with	with	ADP
ejpam-6605	331	11	a.	a.	NOUN
ejpam-6605	331	12	she	she	PRON
ejpam-6605	331	13	computes	compute	VERB
ejpam-6605	331	14	x1	x1	NOUN
ejpam-6605	331	15	=	=	SYM
ejpam-6605	331	16	atb	atb	PROPN
ejpam-6605	331	17	mod	mod	PROPN
ejpam-6605	331	18	n	n	PROPN
ejpam-6605	331	19	and	and	CCONJ
ejpam-6605	331	20	send	send	VERB
ejpam-6605	331	21	it	it	PRON
ejpam-6605	331	22	to	to	ADP
ejpam-6605	331	23	bob	bob	PROPN
ejpam-6605	331	24	.	.	PUNCT
ejpam-6605	332	1	(	(	PUNCT
ejpam-6605	332	2	ii	ii	X
ejpam-6605	332	3	)	)	PUNCT
ejpam-6605	332	4	bob	bob	PROPN
ejpam-6605	332	5	chooses	choose	VERB
ejpam-6605	332	6	an	an	DET
ejpam-6605	332	7	integer	integer	NOUN
ejpam-6605	332	8	s	s	PROPN
ejpam-6605	332	9	>	>	X
ejpam-6605	332	10	0	0	PROPN
ejpam-6605	332	11	and	and	CCONJ
ejpam-6605	332	12	a	a	DET
ejpam-6605	332	13	secret	secret	ADJ
ejpam-6605	332	14	matrix	matrix	NOUN
ejpam-6605	332	15	c	c	PUNCT
ejpam-6605	332	16	=	=	PUNCT
ejpam-6605	332	17	qn2	qn2	PROPN
ejpam-6605	332	18	k	k	PROPN
ejpam-6605	332	19	mod	mod	PROPN
ejpam-6605	332	20	n	n	CCONJ
ejpam-6605	332	21	that	that	PRON
ejpam-6605	332	22	does	do	AUX
ejpam-6605	332	23	n’t	not	PART
ejpam-6605	332	24	commute	commute	VERB
ejpam-6605	332	25	with	with	ADP
ejpam-6605	332	26	a	a	PRON
ejpam-6605	332	27	and	and	CCONJ
ejpam-6605	332	28	computes	compute	VERB
ejpam-6605	332	29	x2	x2	PROPN
ejpam-6605	332	30	=	=	SYM
ejpam-6605	332	31	asc	asc	PROPN
ejpam-6605	332	32	mod	mod	PROPN
ejpam-6605	332	33	n	n	PROPN
ejpam-6605	332	34	and	and	CCONJ
ejpam-6605	332	35	send	send	VERB
ejpam-6605	332	36	it	it	PRON
ejpam-6605	332	37	to	to	ADP
ejpam-6605	332	38	alice	alice	PROPN
ejpam-6605	332	39	.	.	PUNCT
ejpam-6605	333	1	(	(	PUNCT
ejpam-6605	333	2	iii	iii	X
ejpam-6605	333	3	)	)	PUNCT
ejpam-6605	333	4	alice	alice	PROPN
ejpam-6605	333	5	computes	compute	VERB
ejpam-6605	333	6	ka	ka	X
ejpam-6605	334	1	=	=	SYM
ejpam-6605	334	2	atx2b	atx2b	PROPN
ejpam-6605	334	3	mod	mod	PROPN
ejpam-6605	334	4	n.	n.	PROPN
ejpam-6605	334	5	sh	sh	PROPN
ejpam-6605	334	6	.	.	PROPN
ejpam-6605	334	7	a.	a.	PROPN
ejpam-6605	334	8	bani	bani	PROPN
ejpam-6605	334	9	melhem	melhem	PROPN
ejpam-6605	334	10	,	,	PUNCT
ejpam-6605	334	11	al	al	PROPN
ejpam-6605	334	12	-	-	PUNCT
ejpam-6605	334	13	kateeb	kateeb	PROPN
ejpam-6605	334	14	,	,	PUNCT
ejpam-6605	334	15	a.	a.	PROPN
ejpam-6605	334	16	dagher	dagher	PROPN
ejpam-6605	334	17	/	/	SYM
ejpam-6605	334	18	eur	eur	PROPN
ejpam-6605	334	19	.	.	PUNCT
ejpam-6605	335	1	j.	j.	PROPN
ejpam-6605	335	2	pure	pure	PROPN
ejpam-6605	335	3	appl	appl	PROPN
ejpam-6605	335	4	.	.	PROPN
ejpam-6605	335	5	math	math	PROPN
ejpam-6605	335	6	,	,	PUNCT
ejpam-6605	335	7	18	18	NUM
ejpam-6605	335	8	(	(	PUNCT
ejpam-6605	335	9	4	4	NUM
ejpam-6605	335	10	)	)	PUNCT
ejpam-6605	335	11	(	(	PUNCT
ejpam-6605	335	12	2025	2025	NUM
ejpam-6605	335	13	)	)	PUNCT
ejpam-6605	335	14	,	,	PUNCT
ejpam-6605	335	15	6605	6605	NUM
ejpam-6605	335	16	14	14	NUM
ejpam-6605	335	17	of	of	ADP
ejpam-6605	335	18	15	15	NUM
ejpam-6605	335	19	(	(	PUNCT
ejpam-6605	335	20	iv	iv	X
ejpam-6605	335	21	)	)	PUNCT
ejpam-6605	335	22	bob	bob	PROPN
ejpam-6605	335	23	computes	compute	VERB
ejpam-6605	335	24	kb	kb	PROPN
ejpam-6605	335	25	=	=	PUNCT
ejpam-6605	336	1	asx1c	asx1c	PROPN
ejpam-6605	336	2	mod	mod	PROPN
ejpam-6605	337	1	n	n	CCONJ
ejpam-6605	337	2	we	we	PRON
ejpam-6605	337	3	have	have	VERB
ejpam-6605	337	4	ka	ka	PROPN
ejpam-6605	337	5	=	=	SYM
ejpam-6605	337	6	kb	kb	PROPN
ejpam-6605	337	7	=	=	PUNCT
ejpam-6605	337	8	k.	k.	PROPN
ejpam-6605	337	9	example	example	NOUN
ejpam-6605	338	1	2	2	X
ejpam-6605	338	2	.	.	PUNCT
ejpam-6605	338	3	let	let	VERB
ejpam-6605	338	4	k	k	NOUN
ejpam-6605	338	5	=	=	PUNCT
ejpam-6605	338	6	4	4	NUM
ejpam-6605	338	7	and	and	CCONJ
ejpam-6605	338	8	a	a	PRON
ejpam-6605	338	9	=	=	X
ejpam-6605	338	10	[	[	PUNCT
ejpam-6605	338	11	1	1	NUM
ejpam-6605	338	12	2	2	NUM
ejpam-6605	338	13	3	3	NUM
ejpam-6605	338	14	4	4	NUM
ejpam-6605	338	15	]	]	PUNCT
ejpam-6605	338	16	.	.	PUNCT
ejpam-6605	339	1	(	(	PUNCT
ejpam-6605	339	2	i	i	NOUN
ejpam-6605	339	3	)	)	PUNCT
ejpam-6605	339	4	alice	alice	PROPN
ejpam-6605	339	5	selects	select	VERB
ejpam-6605	339	6	an	an	DET
ejpam-6605	339	7	integer	integer	NOUN
ejpam-6605	339	8	t	t	PROPN
ejpam-6605	339	9	=	=	SYM
ejpam-6605	339	10	3	3	NUM
ejpam-6605	339	11	and	and	CCONJ
ejpam-6605	339	12	computes	compute	VERB
ejpam-6605	339	13	b	b	NOUN
ejpam-6605	339	14	=	=	SYM
ejpam-6605	339	15	q3	q3	NOUN
ejpam-6605	339	16	k	k	PROPN
ejpam-6605	340	1	=	=	PUNCT
ejpam-6605	340	2	[	[	PUNCT
ejpam-6605	340	3	131	131	NUM
ejpam-6605	340	4	13	13	NUM
ejpam-6605	340	5	104	104	NUM
ejpam-6605	340	6	40	40	NUM
ejpam-6605	340	7	]	]	PUNCT
ejpam-6605	340	8	which	which	PRON
ejpam-6605	340	9	does	do	AUX
ejpam-6605	340	10	n’t	not	PART
ejpam-6605	340	11	commute	commute	VERB
ejpam-6605	340	12	with	with	ADP
ejpam-6605	340	13	a.	a.	NOUN
ejpam-6605	340	14	she	she	PRON
ejpam-6605	340	15	computes	compute	VERB
ejpam-6605	340	16	x1	x1	NOUN
ejpam-6605	340	17	=	=	SYM
ejpam-6605	340	18	atb	atb	NOUN
ejpam-6605	341	1	=	=	PUNCT
ejpam-6605	341	2	[	[	PUNCT
ejpam-6605	341	3	24	24	NUM
ejpam-6605	341	4	67	67	NUM
ejpam-6605	341	5	3	3	NUM
ejpam-6605	341	6	53	53	NUM
ejpam-6605	341	7	]	]	PUNCT
ejpam-6605	342	1	and	and	CCONJ
ejpam-6605	342	2	send	send	VERB
ejpam-6605	342	3	it	it	PRON
ejpam-6605	342	4	to	to	ADP
ejpam-6605	342	5	bob	bob	PROPN
ejpam-6605	342	6	.	.	PUNCT
ejpam-6605	343	1	(	(	PUNCT
ejpam-6605	343	2	ii	ii	X
ejpam-6605	343	3	)	)	PUNCT
ejpam-6605	343	4	bob	bob	PROPN
ejpam-6605	343	5	chooses	choose	VERB
ejpam-6605	343	6	s	s	PART
ejpam-6605	343	7	=	=	SYM
ejpam-6605	343	8	7	7	NUM
ejpam-6605	343	9	and	and	CCONJ
ejpam-6605	343	10	find	find	VERB
ejpam-6605	343	11	c	c	NOUN
ejpam-6605	343	12	=	=	PROPN
ejpam-6605	343	13	q5	q5	PROPN
ejpam-6605	343	14	k	k	PROPN
ejpam-6605	343	15	mod	mod	PROPN
ejpam-6605	344	1	n	n	PROPN
ejpam-6605	345	1	=	=	PRON
ejpam-6605	346	1	[	[	PUNCT
ejpam-6605	346	2	23	23	NUM
ejpam-6605	346	3	121	121	NUM
ejpam-6605	346	4	66	66	NUM
ejpam-6605	346	5	78	78	NUM
ejpam-6605	346	6	]	]	PUNCT
ejpam-6605	346	7	which	which	PRON
ejpam-6605	346	8	does	do	AUX
ejpam-6605	346	9	n’t	not	PART
ejpam-6605	346	10	commute	commute	VERB
ejpam-6605	346	11	with	with	ADP
ejpam-6605	346	12	a	a	PRON
ejpam-6605	346	13	and	and	CCONJ
ejpam-6605	346	14	computes	compute	VERB
ejpam-6605	346	15	x2	x2	PROPN
ejpam-6605	346	16	=	=	PUNCT
ejpam-6605	346	17	asc	asc	PROPN
ejpam-6605	346	18	=	=	PROPN
ejpam-6605	347	1	[	[	PUNCT
ejpam-6605	347	2	130	130	NUM
ejpam-6605	347	3	42	42	NUM
ejpam-6605	347	4	85	85	NUM
ejpam-6605	347	5	72	72	NUM
ejpam-6605	347	6	]	]	PUNCT
ejpam-6605	348	1	and	and	CCONJ
ejpam-6605	348	2	send	send	VERB
ejpam-6605	348	3	it	it	PRON
ejpam-6605	348	4	to	to	ADP
ejpam-6605	348	5	alice	alice	PROPN
ejpam-6605	348	6	.	.	PUNCT
ejpam-6605	349	1	(	(	PUNCT
ejpam-6605	349	2	iii	iii	X
ejpam-6605	349	3	)	)	PUNCT
ejpam-6605	349	4	alice	alice	PROPN
ejpam-6605	349	5	computes	compute	VERB
ejpam-6605	349	6	ka	ka	X
ejpam-6605	350	1	=	=	PUNCT
ejpam-6605	350	2	atx2b	atx2b	PROPN
ejpam-6605	350	3	=	=	PUNCT
ejpam-6605	351	1	[	[	PUNCT
ejpam-6605	351	2	1	1	NUM
ejpam-6605	351	3	112	112	NUM
ejpam-6605	351	4	111	111	NUM
ejpam-6605	351	5	29	29	NUM
ejpam-6605	351	6	]	]	PUNCT
ejpam-6605	351	7	.	.	PUNCT
ejpam-6605	352	1	(	(	PUNCT
ejpam-6605	352	2	iv	iv	X
ejpam-6605	352	3	)	)	PUNCT
ejpam-6605	352	4	bob	bob	PROPN
ejpam-6605	352	5	computes	compute	VERB
ejpam-6605	352	6	kb	kb	PROPN
ejpam-6605	352	7	=	=	PUNCT
ejpam-6605	352	8	asx1c	asx1c	PROPN
ejpam-6605	353	1	=	=	PUNCT
ejpam-6605	353	2	[	[	PUNCT
ejpam-6605	353	3	1	1	NUM
ejpam-6605	353	4	112	112	NUM
ejpam-6605	353	5	111	111	NUM
ejpam-6605	353	6	29	29	NUM
ejpam-6605	353	7	]	]	SYM
ejpam-6605	353	8	6	6	NUM
ejpam-6605	353	9	.	.	X
ejpam-6605	353	10	conclusion	conclusion	NOUN
ejpam-6605	353	11	in	in	ADP
ejpam-6605	353	12	this	this	DET
ejpam-6605	353	13	paper	paper	NOUN
ejpam-6605	353	14	we	we	PRON
ejpam-6605	353	15	consider	consider	VERB
ejpam-6605	353	16	a	a	DET
ejpam-6605	353	17	generalization	generalization	NOUN
ejpam-6605	353	18	of	of	ADP
ejpam-6605	353	19	merssen	merssen	PROPN
ejpam-6605	353	20	and	and	CCONJ
ejpam-6605	353	21	fermat	fermat	PROPN
ejpam-6605	353	22	numbers	number	NOUN
ejpam-6605	353	23	into	into	ADP
ejpam-6605	353	24	complex	complex	ADJ
ejpam-6605	353	25	numbers	number	NOUN
ejpam-6605	353	26	,	,	PUNCT
ejpam-6605	353	27	we	we	PRON
ejpam-6605	353	28	derive	derive	VERB
ejpam-6605	353	29	some	some	DET
ejpam-6605	353	30	properties	property	NOUN
ejpam-6605	353	31	of	of	ADP
ejpam-6605	353	32	the	the	DET
ejpam-6605	353	33	new	new	ADJ
ejpam-6605	353	34	sequence	sequence	NOUN
ejpam-6605	353	35	.	.	PUNCT
ejpam-6605	354	1	for	for	ADP
ejpam-6605	354	2	future	future	ADJ
ejpam-6605	354	3	work	work	NOUN
ejpam-6605	354	4	we	we	PRON
ejpam-6605	354	5	may	may	AUX
ejpam-6605	354	6	consider	consider	VERB
ejpam-6605	354	7	more	more	ADJ
ejpam-6605	354	8	generalizations	generalization	NOUN
ejpam-6605	354	9	and	and	CCONJ
ejpam-6605	354	10	extensions	extension	NOUN
ejpam-6605	354	11	of	of	ADP
ejpam-6605	354	12	such	such	ADJ
ejpam-6605	354	13	sequence	sequence	NOUN
ejpam-6605	354	14	and	and	CCONJ
ejpam-6605	354	15	try	try	VERB
ejpam-6605	354	16	to	to	PART
ejpam-6605	354	17	relate	relate	VERB
ejpam-6605	354	18	them	they	PRON
ejpam-6605	354	19	with	with	ADP
ejpam-6605	354	20	real	real	ADJ
ejpam-6605	354	21	life	life	NOUN
ejpam-6605	354	22	applications	application	NOUN
ejpam-6605	354	23	.	.	PUNCT
ejpam-6605	355	1	acknowledgements	acknowledgement	VERB
ejpam-6605	355	2	the	the	DET
ejpam-6605	355	3	publication	publication	NOUN
ejpam-6605	355	4	of	of	ADP
ejpam-6605	355	5	this	this	DET
ejpam-6605	355	6	paper	paper	NOUN
ejpam-6605	355	7	was	be	AUX
ejpam-6605	355	8	supported	support	VERB
ejpam-6605	355	9	by	by	ADP
ejpam-6605	355	10	the	the	DET
ejpam-6605	355	11	yarmouk	yarmouk	PROPN
ejpam-6605	355	12	university	university	NOUN
ejpam-6605	355	13	research	research	NOUN
ejpam-6605	355	14	council	council	PROPN
ejpam-6605	355	15	.	.	PUNCT
ejpam-6605	356	1	references	reference	NOUN
ejpam-6605	356	2	[	[	X
ejpam-6605	356	3	1	1	X
ejpam-6605	356	4	]	]	PUNCT
ejpam-6605	356	5	i	i	PROPN
ejpam-6605	356	6	d	d	PROPN
ejpam-6605	356	7	bruggles	bruggle	NOUN
ejpam-6605	356	8	and	and	CCONJ
ejpam-6605	356	9	ve	ve	VERB
ejpam-6605	356	10	hoggatt	hoggatt	PROPN
ejpam-6605	356	11	jr	jr	PROPN
ejpam-6605	356	12	.	.	PROPN
ejpam-6605	356	13	a	a	DET
ejpam-6605	356	14	primer	primer	NOUN
ejpam-6605	356	15	on	on	ADP
ejpam-6605	356	16	the	the	DET
ejpam-6605	356	17	fibonacci	fibonacci	NOUN
ejpam-6605	356	18	numbers	number	NOUN
ejpam-6605	356	19	-	-	PUNCT
ejpam-6605	356	20	part	part	NOUN
ejpam-6605	356	21	iv	iv	NOUN
ejpam-6605	356	22	.	.	PUNCT
ejpam-6605	357	1	the	the	DET
ejpam-6605	357	2	fibonacci	fibonacci	NOUN
ejpam-6605	357	3	quarterly	quarterly	ADV
ejpam-6605	357	4	,	,	PUNCT
ejpam-6605	357	5	1(4):65–71	1(4):65–71	NUM
ejpam-6605	357	6	,	,	PUNCT
ejpam-6605	357	7	1963	1963	NUM
ejpam-6605	357	8	.	.	PUNCT
ejpam-6605	358	1	[	[	X
ejpam-6605	358	2	2	2	X
ejpam-6605	358	3	]	]	PUNCT
ejpam-6605	358	4	marcia	marcia	PROPN
ejpam-6605	358	5	edson	edson	PROPN
ejpam-6605	358	6	and	and	CCONJ
ejpam-6605	358	7	omer	omer	PROPN
ejpam-6605	358	8	yayenie	yayenie	PROPN
ejpam-6605	358	9	.	.	PUNCT
ejpam-6605	359	1	a	a	DET
ejpam-6605	359	2	new	new	ADJ
ejpam-6605	359	3	generalization	generalization	NOUN
ejpam-6605	359	4	of	of	ADP
ejpam-6605	359	5	fibonacci	fibonacci	PROPN
ejpam-6605	359	6	sequence	sequence	NOUN
ejpam-6605	359	7	&	&	CCONJ
ejpam-6605	359	8	extended	extend	VERB
ejpam-6605	359	9	binet	binet	NOUN
ejpam-6605	359	10	’s	’s	PART
ejpam-6605	359	11	formula	formula	NOUN
ejpam-6605	359	12	.	.	PUNCT
ejpam-6605	360	1	2009	2009	NUM
ejpam-6605	360	2	.	.	PUNCT
ejpam-6605	361	1	[	[	X
ejpam-6605	361	2	3	3	X
ejpam-6605	361	3	]	]	X
ejpam-6605	361	4	sergio	sergio	PROPN
ejpam-6605	361	5	falcón	falcón	PROPN
ejpam-6605	361	6	and	and	CCONJ
ejpam-6605	361	7	ángel	ángel	PROPN
ejpam-6605	361	8	plaza	plaza	PROPN
ejpam-6605	361	9	.	.	PUNCT
ejpam-6605	362	1	on	on	ADP
ejpam-6605	362	2	the	the	DET
ejpam-6605	362	3	fibonacci	fibonacci	NOUN
ejpam-6605	362	4	k	k	NOUN
ejpam-6605	362	5	-	-	PUNCT
ejpam-6605	362	6	numbers	number	NOUN
ejpam-6605	362	7	.	.	PUNCT
ejpam-6605	363	1	chaos	chaos	NOUN
ejpam-6605	363	2	,	,	PUNCT
ejpam-6605	363	3	solitons	soliton	NOUN
ejpam-6605	363	4	&	&	CCONJ
ejpam-6605	363	5	fractals	fractal	NOUN
ejpam-6605	363	6	,	,	PUNCT
ejpam-6605	363	7	32(5):1615–1624	32(5):1615–1624	NUM
ejpam-6605	363	8	,	,	PUNCT
ejpam-6605	363	9	2007	2007	NUM
ejpam-6605	363	10	.	.	PUNCT
ejpam-6605	364	1	[	[	X
ejpam-6605	364	2	4	4	X
ejpam-6605	364	3	]	]	X
ejpam-6605	364	4	henry	henry	PROPN
ejpam-6605	364	5	w	w	PROPN
ejpam-6605	364	6	gould	gould	PROPN
ejpam-6605	364	7	.	.	PUNCT
ejpam-6605	365	1	a	a	DET
ejpam-6605	365	2	history	history	NOUN
ejpam-6605	365	3	of	of	ADP
ejpam-6605	365	4	the	the	DET
ejpam-6605	365	5	fibonacci	fibonacci	NOUN
ejpam-6605	365	6	q	q	NOUN
ejpam-6605	365	7	-	-	PUNCT
ejpam-6605	365	8	matrix	matrix	NOUN
ejpam-6605	365	9	and	and	CCONJ
ejpam-6605	365	10	a	a	DET
ejpam-6605	365	11	higher	higher	ADV
ejpam-6605	365	12	-	-	PUNCT
ejpam-6605	365	13	dimensional	dimensional	ADJ
ejpam-6605	365	14	problem	problem	NOUN
ejpam-6605	365	15	.	.	PUNCT
ejpam-6605	366	1	the	the	DET
ejpam-6605	366	2	fibonacci	fibonacci	NOUN
ejpam-6605	366	3	quarterly	quarterly	PROPN
ejpam-6605	366	4	,	,	PUNCT
ejpam-6605	366	5	19(3):250–257	19(3):250–257	NOUN
ejpam-6605	366	6	,	,	PUNCT
ejpam-6605	366	7	1981	1981	NUM
ejpam-6605	366	8	.	.	PUNCT
ejpam-6605	367	1	sh	sh	PROPN
ejpam-6605	367	2	.	.	PROPN
ejpam-6605	367	3	a.	a.	PROPN
ejpam-6605	367	4	bani	bani	PROPN
ejpam-6605	367	5	melhem	melhem	PROPN
ejpam-6605	367	6	,	,	PUNCT
ejpam-6605	367	7	al	al	PROPN
ejpam-6605	367	8	-	-	PUNCT
ejpam-6605	367	9	kateeb	kateeb	PROPN
ejpam-6605	367	10	,	,	PUNCT
ejpam-6605	367	11	a.	a.	PROPN
ejpam-6605	367	12	dagher	dagher	PROPN
ejpam-6605	367	13	/	/	SYM
ejpam-6605	367	14	eur	eur	PROPN
ejpam-6605	367	15	.	.	PUNCT
ejpam-6605	368	1	j.	j.	PROPN
ejpam-6605	368	2	pure	pure	PROPN
ejpam-6605	368	3	appl	appl	PROPN
ejpam-6605	368	4	.	.	PROPN
ejpam-6605	368	5	math	math	PROPN
ejpam-6605	368	6	,	,	PUNCT
ejpam-6605	368	7	18	18	NUM
ejpam-6605	368	8	(	(	PUNCT
ejpam-6605	368	9	4	4	NUM
ejpam-6605	368	10	)	)	PUNCT
ejpam-6605	368	11	(	(	PUNCT
ejpam-6605	368	12	2025	2025	NUM
ejpam-6605	368	13	)	)	PUNCT
ejpam-6605	368	14	,	,	PUNCT
ejpam-6605	368	15	6605	6605	NUM
ejpam-6605	368	16	15	15	NUM
ejpam-6605	368	17	of	of	ADP
ejpam-6605	368	18	15	15	NUM
ejpam-6605	368	19	[	[	SYM
ejpam-6605	368	20	5	5	NUM
ejpam-6605	368	21	]	]	PUNCT
ejpam-6605	368	22	ve	ve	NOUN
ejpam-6605	368	23	hoggat	hoggat	NOUN
ejpam-6605	368	24	.	.	PUNCT
ejpam-6605	369	1	fibonacci	fibonacci	NOUN
ejpam-6605	369	2	and	and	CCONJ
ejpam-6605	369	3	lucas	lucas	PROPN
ejpam-6605	369	4	numbers	number	NOUN
ejpam-6605	369	5	,	,	PUNCT
ejpam-6605	369	6	houghton	houghton	PROPN
ejpam-6605	369	7	-	-	PUNCT
ejpam-6605	369	8	mifflin	mifflin	PROPN
ejpam-6605	369	9	.	.	PUNCT
ejpam-6605	370	1	palo	palo	PROPN
ejpam-6605	370	2	alto	alto	PROPN
ejpam-6605	370	3	,	,	PUNCT
ejpam-6605	370	4	california	california	PROPN
ejpam-6605	370	5	,	,	PUNCT
ejpam-6605	370	6	1969	1969	NUM
ejpam-6605	370	7	.	.	PUNCT
ejpam-6605	371	1	[	[	X
ejpam-6605	371	2	6	6	NUM
ejpam-6605	371	3	]	]	PUNCT
ejpam-6605	371	4	pawe	pawe	NOUN
ejpam-6605	371	5	l	l	NOUN
ejpam-6605	371	6	ochalik	ochalik	PROPN
ejpam-6605	371	7	and	and	CCONJ
ejpam-6605	371	8	andrzej	andrzej	PROPN
ejpam-6605	371	9	w	w	PROPN
ejpam-6605	371	10	loch	loch	PROPN
ejpam-6605	371	11	.	.	PUNCT
ejpam-6605	372	1	on	on	ADP
ejpam-6605	372	2	generalized	generalized	ADJ
ejpam-6605	372	3	mersenne	mersenne	NOUN
ejpam-6605	372	4	numbers	number	NOUN
ejpam-6605	372	5	,	,	PUNCT
ejpam-6605	372	6	their	their	PRON
ejpam-6605	372	7	interpretations	interpretation	NOUN
ejpam-6605	372	8	and	and	CCONJ
ejpam-6605	372	9	matrix	matrix	NOUN
ejpam-6605	372	10	generators	generator	NOUN
ejpam-6605	372	11	.	.	PUNCT
ejpam-6605	373	1	annales	annales	PROPN
ejpam-6605	373	2	universitatis	universitatis	PROPN
ejpam-6605	373	3	mariae	mariae	PROPN
ejpam-6605	373	4	curie	curie	PROPN
ejpam-6605	373	5	-	-	PUNCT
ejpam-6605	373	6	sk	sk	NOUN
ejpam-6605	373	7	lodowska	lodowska	NOUN
ejpam-6605	373	8	,	,	PUNCT
ejpam-6605	373	9	sectio	sectio	X
ejpam-6605	373	10	a	a	DET
ejpam-6605	373	11	–	–	PUNCT
ejpam-6605	373	12	mathematica	mathematica	PROPN
ejpam-6605	373	13	,	,	PUNCT
ejpam-6605	373	14	72(1	72(1	NOUN
ejpam-6605	373	15	)	)	PUNCT
ejpam-6605	373	16	,	,	PUNCT
ejpam-6605	373	17	2018	2018	NUM
ejpam-6605	373	18	.	.	PUNCT
ejpam-6605	374	1	[	[	X
ejpam-6605	374	2	7	7	NUM
ejpam-6605	374	3	]	]	X
ejpam-6605	374	4	tian	tian	PROPN
ejpam-6605	374	5	-	-	PUNCT
ejpam-6605	374	6	xiao	xiao	PROPN
ejpam-6605	374	7	he	he	PROPN
ejpam-6605	374	8	,	,	PUNCT
ejpam-6605	374	9	peter	peter	PROPN
ejpam-6605	374	10	js	js	PROPN
ejpam-6605	374	11	shiue	shiue	VERB
ejpam-6605	374	12	,	,	PUNCT
ejpam-6605	374	13	and	and	CCONJ
ejpam-6605	374	14	yaotsu	yaotsu	PROPN
ejpam-6605	374	15	chang	chang	PROPN
ejpam-6605	374	16	.	.	PUNCT
ejpam-6605	375	1	computation	computation	NOUN
ejpam-6605	375	2	of	of	ADP
ejpam-6605	375	3	fermat	fermat	PROPN
ejpam-6605	375	4	’s	’s	PART
ejpam-6605	375	5	pseudoprimes	pseudoprime	NOUN
ejpam-6605	375	6	(	(	PUNCT
ejpam-6605	375	7	dedicated	dedicate	VERB
ejpam-6605	375	8	to	to	ADP
ejpam-6605	375	9	the	the	DET
ejpam-6605	375	10	memory	memory	NOUN
ejpam-6605	375	11	of	of	ADP
ejpam-6605	375	12	professor	professor	PROPN
ejpam-6605	375	13	leetsch	leetsch	PROPN
ejpam-6605	375	14	c.	c.	PROPN
ejpam-6605	375	15	hsu	hsu	PROPN
ejpam-6605	375	16	)	)	PUNCT
ejpam-6605	375	17	.	.	PUNCT
ejpam-6605	376	1	journal	journal	PROPN
ejpam-6605	376	2	of	of	ADP
ejpam-6605	376	3	discrete	discrete	ADJ
ejpam-6605	376	4	mathematical	mathematical	ADJ
ejpam-6605	376	5	sciences	science	NOUN
ejpam-6605	376	6	and	and	CCONJ
ejpam-6605	376	7	cryptography	cryptography	NOUN
ejpam-6605	376	8	,	,	PUNCT
ejpam-6605	376	9	25(2):335–352	25(2):335–352	PROPN
ejpam-6605	376	10	,	,	PUNCT
ejpam-6605	376	11	2022	2022	NUM
ejpam-6605	376	12	.	.	PUNCT
ejpam-6605	377	1	[	[	X
ejpam-6605	377	2	8	8	NUM
ejpam-6605	377	3	]	]	PUNCT
ejpam-6605	377	4	kritsanapong	kritsanapong	NOUN
ejpam-6605	377	5	somsuk	somsuk	NOUN
ejpam-6605	377	6	.	.	PUNCT
ejpam-6605	378	1	the	the	DET
ejpam-6605	378	2	improvement	improvement	NOUN
ejpam-6605	378	3	of	of	ADP
ejpam-6605	378	4	initial	initial	ADJ
ejpam-6605	378	5	value	value	NOUN
ejpam-6605	378	6	closer	close	ADV
ejpam-6605	378	7	to	to	ADP
ejpam-6605	378	8	the	the	DET
ejpam-6605	378	9	target	target	NOUN
ejpam-6605	378	10	for	for	ADP
ejpam-6605	378	11	fermat	fermat	PROPN
ejpam-6605	378	12	’s	’s	PART
ejpam-6605	378	13	factorization	factorization	NOUN
ejpam-6605	378	14	algorithm	algorithm	NOUN
ejpam-6605	378	15	.	.	PUNCT
ejpam-6605	379	1	journal	journal	NOUN
ejpam-6605	379	2	of	of	ADP
ejpam-6605	379	3	discrete	discrete	ADJ
ejpam-6605	379	4	mathematical	mathematical	ADJ
ejpam-6605	379	5	sciences	science	NOUN
ejpam-6605	379	6	and	and	CCONJ
ejpam-6605	379	7	cryptography	cryptography	NOUN
ejpam-6605	379	8	,	,	PUNCT
ejpam-6605	379	9	21(7	21(7	PROPN
ejpam-6605	379	10	-	-	PUNCT
ejpam-6605	379	11	8):1573–1580	8):1573–1580	NOUN
ejpam-6605	379	12	,	,	PUNCT
ejpam-6605	379	13	2018	2018	NUM
ejpam-6605	379	14	.	.	PUNCT
ejpam-6605	380	1	[	[	X
ejpam-6605	380	2	9	9	NUM
ejpam-6605	380	3	]	]	PUNCT
ejpam-6605	380	4	kenneth	kenneth	PROPN
ejpam-6605	380	5	h	h	PROPN
ejpam-6605	380	6	rosen	rosen	PROPN
ejpam-6605	380	7	.	.	PUNCT
ejpam-6605	381	1	elementary	elementary	ADJ
ejpam-6605	381	2	number	number	NOUN
ejpam-6605	381	3	theory	theory	NOUN
ejpam-6605	381	4	.	.	PUNCT
ejpam-6605	382	1	pearson	pearson	PROPN
ejpam-6605	382	2	education	education	PROPN
ejpam-6605	382	3	london	london	PROPN
ejpam-6605	382	4	,	,	PUNCT
ejpam-6605	382	5	2011	2011	NUM
ejpam-6605	382	6	.	.	PUNCT
ejpam-6605	383	1	[	[	X
ejpam-6605	383	2	10	10	NUM
ejpam-6605	383	3	]	]	X
ejpam-6605	383	4	e	e	X
ejpam-6605	383	5	kilic	kilic	NOUN
ejpam-6605	383	6	and	and	CCONJ
ejpam-6605	383	7	d	d	NOUN
ejpam-6605	383	8	taşci	taşci	PROPN
ejpam-6605	383	9	.	.	PUNCT
ejpam-6605	384	1	on	on	ADP
ejpam-6605	384	2	sums	sum	NOUN
ejpam-6605	384	3	of	of	ADP
ejpam-6605	384	4	second	second	ADJ
ejpam-6605	384	5	order	order	NOUN
ejpam-6605	384	6	linear	linear	NOUN
ejpam-6605	384	7	recurrences	recurrence	NOUN
ejpam-6605	384	8	by	by	ADP
ejpam-6605	384	9	hessenberg	hessenberg	PROPN
ejpam-6605	384	10	matrices	matrix	NOUN
ejpam-6605	384	11	.	.	PUNCT
ejpam-6605	385	1	the	the	DET
ejpam-6605	385	2	rocky	rocky	ADJ
ejpam-6605	385	3	mountain	mountain	NOUN
ejpam-6605	385	4	journal	journal	NOUN
ejpam-6605	385	5	of	of	ADP
ejpam-6605	385	6	mathematics	mathematic	NOUN
ejpam-6605	385	7	,	,	PUNCT
ejpam-6605	385	8	pages	page	NOUN
ejpam-6605	385	9	531–544	531–544	NUM
ejpam-6605	385	10	,	,	PUNCT
ejpam-6605	385	11	2008	2008	NUM
ejpam-6605	385	12	.	.	PUNCT
ejpam-6605	386	1	[	[	X
ejpam-6605	386	2	11	11	NUM
ejpam-6605	386	3	]	]	PUNCT
ejpam-6605	386	4	emrah	emrah	VERB
ejpam-6605	386	5	kilic	kilic	NOUN
ejpam-6605	386	6	and	and	CCONJ
ejpam-6605	386	7	dursun	dursun	NOUN
ejpam-6605	386	8	tasci	tasci	PROPN
ejpam-6605	386	9	.	.	PUNCT
ejpam-6605	387	1	on	on	ADP
ejpam-6605	387	2	the	the	DET
ejpam-6605	387	3	second	second	ADJ
ejpam-6605	387	4	order	order	NOUN
ejpam-6605	387	5	linear	linear	NOUN
ejpam-6605	387	6	recurrences	recurrence	NOUN
ejpam-6605	387	7	by	by	ADP
ejpam-6605	387	8	tridiagonal	tridiagonal	ADJ
ejpam-6605	387	9	matrices	matrix	NOUN
ejpam-6605	387	10	.	.	PUNCT
ejpam-6605	388	1	ars	ars	PROPN
ejpam-6605	388	2	combin	combin	PROPN
ejpam-6605	388	3	,	,	PUNCT
ejpam-6605	388	4	91:11–18	91:11–18	NUM
ejpam-6605	388	5	,	,	PUNCT
ejpam-6605	388	6	2009	2009	NUM
ejpam-6605	388	7	.	.	PUNCT