id	sid	tid	token	lemma	pos
ejpam-4822	1	1	european	european	PROPN
ejpam-4822	1	2	journal	journal	PROPN
ejpam-4822	1	3	of	of	ADP
ejpam-4822	1	4	pure	pure	ADJ
ejpam-4822	1	5	and	and	CCONJ
ejpam-4822	1	6	applied	apply	VERB
ejpam-4822	1	7	mathematics	mathematic	NOUN
ejpam-4822	1	8	vol	vol	NOUN
ejpam-4822	1	9	.	.	PUNCT
ejpam-4822	2	1	16	16	NUM
ejpam-4822	2	2	,	,	PUNCT
ejpam-4822	2	3	no	no	INTJ
ejpam-4822	2	4	.	.	NOUN
ejpam-4822	2	5	4	4	NUM
ejpam-4822	2	6	,	,	PUNCT
ejpam-4822	2	7	2023	2023	NUM
ejpam-4822	2	8	,	,	PUNCT
ejpam-4822	2	9	2208	2208	NUM
ejpam-4822	2	10	-	-	SYM
ejpam-4822	2	11	2212	2212	NUM
ejpam-4822	2	12	issn	issn	PROPN
ejpam-4822	2	13	1307	1307	NUM
ejpam-4822	2	14	-	-	SYM
ejpam-4822	2	15	5543	5543	NUM
ejpam-4822	2	16	–	–	PUNCT
ejpam-4822	2	17	ejpam.com	ejpam.com	X
ejpam-4822	2	18	published	publish	VERB
ejpam-4822	2	19	by	by	ADP
ejpam-4822	2	20	new	new	PROPN
ejpam-4822	2	21	york	york	PROPN
ejpam-4822	2	22	business	business	PROPN
ejpam-4822	2	23	global	global	PROPN
ejpam-4822	2	24	on	on	ADP
ejpam-4822	2	25	the	the	DET
ejpam-4822	2	26	diophantine	diophantine	NOUN
ejpam-4822	2	27	equation	equation	NOUN
ejpam-4822	2	28	(	(	PUNCT
ejpam-4822	2	29	p+	p+	NOUN
ejpam-4822	2	30	n)x	n)x	X
ejpam-4822	2	31	+	+	CCONJ
ejpam-4822	2	32	py	py	X
ejpam-4822	2	33	=	=	SYM
ejpam-4822	2	34	z2	z2	PROPN
ejpam-4822	2	35	where	where	SCONJ
ejpam-4822	2	36	p	p	PROPN
ejpam-4822	2	37	and	and	CCONJ
ejpam-4822	2	38	p+	p+	PROPN
ejpam-4822	2	39	n	n	PRON
ejpam-4822	2	40	are	be	AUX
ejpam-4822	2	41	prime	prime	ADJ
ejpam-4822	2	42	numbers	number	NOUN
ejpam-4822	2	43	wachirarak	wachirarak	PROPN
ejpam-4822	2	44	orosram	orosram	PROPN
ejpam-4822	2	45	department	department	PROPN
ejpam-4822	2	46	of	of	ADP
ejpam-4822	2	47	mathematics	mathematic	NOUN
ejpam-4822	2	48	,	,	PUNCT
ejpam-4822	2	49	faculty	faculty	NOUN
ejpam-4822	2	50	of	of	ADP
ejpam-4822	2	51	science	science	NOUN
ejpam-4822	2	52	,	,	PUNCT
ejpam-4822	2	53	buriram	buriram	NOUN
ejpam-4822	2	54	rajabhat	rajabhat	PROPN
ejpam-4822	2	55	university	university	NOUN
ejpam-4822	2	56	,	,	PUNCT
ejpam-4822	2	57	buriram	buriram	NOUN
ejpam-4822	2	58	31000	31000	NUM
ejpam-4822	2	59	,	,	PUNCT
ejpam-4822	2	60	thailand	thailand	PROPN
ejpam-4822	2	61	abstract	abstract	NOUN
ejpam-4822	2	62	.	.	PUNCT
ejpam-4822	3	1	in	in	ADP
ejpam-4822	3	2	this	this	DET
ejpam-4822	3	3	paper	paper	NOUN
ejpam-4822	3	4	,	,	PUNCT
ejpam-4822	3	5	we	we	PRON
ejpam-4822	3	6	study	study	VERB
ejpam-4822	3	7	the	the	DET
ejpam-4822	3	8	diophantine	diophantine	NOUN
ejpam-4822	3	9	equation	equation	NOUN
ejpam-4822	3	10	(	(	PUNCT
ejpam-4822	3	11	p	p	NOUN
ejpam-4822	3	12	+	+	CCONJ
ejpam-4822	3	13	n)x	n)x	NOUN
ejpam-4822	4	1	+	+	CCONJ
ejpam-4822	4	2	py	py	X
ejpam-4822	4	3	=	=	SYM
ejpam-4822	4	4	z2	z2	PROPN
ejpam-4822	4	5	,	,	PUNCT
ejpam-4822	4	6	where	where	SCONJ
ejpam-4822	4	7	p	p	X
ejpam-4822	4	8	,	,	PUNCT
ejpam-4822	4	9	p	p	X
ejpam-4822	4	10	+	+	CCONJ
ejpam-4822	4	11	n	n	CCONJ
ejpam-4822	4	12	are	be	AUX
ejpam-4822	4	13	prime	prime	ADJ
ejpam-4822	4	14	numbers	number	NOUN
ejpam-4822	4	15	and	and	CCONJ
ejpam-4822	4	16	n	n	PRON
ejpam-4822	4	17	is	be	AUX
ejpam-4822	4	18	a	a	DET
ejpam-4822	4	19	positive	positive	ADJ
ejpam-4822	4	20	integer	integer	NOUN
ejpam-4822	5	1	such	such	ADJ
ejpam-4822	5	2	that	that	SCONJ
ejpam-4822	5	3	n	n	NUM
ejpam-4822	5	4	≡	≡	PROPN
ejpam-4822	5	5	0	0	PUNCT
ejpam-4822	5	6	(	(	PUNCT
ejpam-4822	5	7	mod	mod	PROPN
ejpam-4822	5	8	4	4	NUM
ejpam-4822	5	9	)	)	PUNCT
ejpam-4822	5	10	.	.	PUNCT
ejpam-4822	6	1	in	in	ADP
ejpam-4822	6	2	case	case	NOUN
ejpam-4822	6	3	p	p	X
ejpam-4822	6	4	=	=	SYM
ejpam-4822	6	5	3	3	NUM
ejpam-4822	6	6	and	and	CCONJ
ejpam-4822	6	7	n	n	NOUN
ejpam-4822	6	8	=	=	SYM
ejpam-4822	6	9	4	4	NUM
ejpam-4822	6	10	,	,	PUNCT
ejpam-4822	6	11	rao	rao	NOUN
ejpam-4822	6	12	[	[	X
ejpam-4822	6	13	7	7	NUM
ejpam-4822	6	14	]	]	PUNCT
ejpam-4822	6	15	showed	show	VERB
ejpam-4822	6	16	that	that	SCONJ
ejpam-4822	6	17	the	the	DET
ejpam-4822	6	18	non	non	ADJ
ejpam-4822	6	19	-	-	ADJ
ejpam-4822	6	20	negative	negative	ADJ
ejpam-4822	6	21	integer	integer	NOUN
ejpam-4822	6	22	solutions	solution	NOUN
ejpam-4822	6	23	are	be	AUX
ejpam-4822	6	24	(	(	PUNCT
ejpam-4822	6	25	x	x	NOUN
ejpam-4822	6	26	,	,	PUNCT
ejpam-4822	6	27	y	y	PROPN
ejpam-4822	6	28	,	,	PUNCT
ejpam-4822	6	29	z	z	NOUN
ejpam-4822	6	30	)	)	PUNCT
ejpam-4822	6	31	=	=	SYM
ejpam-4822	6	32	(	(	PUNCT
ejpam-4822	6	33	0	0	NUM
ejpam-4822	6	34	,	,	PUNCT
ejpam-4822	6	35	1	1	NUM
ejpam-4822	6	36	,	,	PUNCT
ejpam-4822	6	37	2	2	NUM
ejpam-4822	6	38	)	)	PUNCT
ejpam-4822	6	39	and	and	CCONJ
ejpam-4822	6	40	(	(	PUNCT
ejpam-4822	6	41	1	1	NUM
ejpam-4822	6	42	,	,	PUNCT
ejpam-4822	6	43	2	2	NUM
ejpam-4822	6	44	,	,	PUNCT
ejpam-4822	6	45	4	4	NUM
ejpam-4822	6	46	)	)	PUNCT
ejpam-4822	6	47	.	.	PUNCT
ejpam-4822	7	1	in	in	ADP
ejpam-4822	7	2	case	case	NOUN
ejpam-4822	7	3	p	p	X
ejpam-4822	7	4	>	>	X
ejpam-4822	7	5	3	3	NUM
ejpam-4822	7	6	and	and	CCONJ
ejpam-4822	7	7	p	p	PROPN
ejpam-4822	7	8	≡	≡	PROPN
ejpam-4822	7	9	3	3	NUM
ejpam-4822	7	10	(	(	PUNCT
ejpam-4822	7	11	mod	mod	NOUN
ejpam-4822	7	12	4	4	NUM
ejpam-4822	7	13	)	)	PUNCT
ejpam-4822	7	14	,	,	PUNCT
ejpam-4822	7	15	if	if	SCONJ
ejpam-4822	7	16	n	n	PRON
ejpam-4822	7	17	−	−	PROPN
ejpam-4822	7	18	1	1	NUM
ejpam-4822	7	19	is	be	AUX
ejpam-4822	7	20	a	a	DET
ejpam-4822	7	21	prime	prime	ADJ
ejpam-4822	7	22	number	number	NOUN
ejpam-4822	7	23	and	and	CCONJ
ejpam-4822	7	24	2n	2n	NUM
ejpam-4822	7	25	−	−	NOUN
ejpam-4822	7	26	1	1	NUM
ejpam-4822	7	27	is	be	AUX
ejpam-4822	7	28	not	not	PART
ejpam-4822	7	29	prime	prime	ADJ
ejpam-4822	7	30	number	number	NOUN
ejpam-4822	7	31	,	,	PUNCT
ejpam-4822	7	32	then	then	ADV
ejpam-4822	7	33	the	the	DET
ejpam-4822	7	34	non	non	ADJ
ejpam-4822	7	35	-	-	ADJ
ejpam-4822	7	36	negative	negative	ADJ
ejpam-4822	7	37	integer	integer	NOUN
ejpam-4822	7	38	solution	solution	NOUN
ejpam-4822	7	39	(	(	PUNCT
ejpam-4822	7	40	x	x	X
ejpam-4822	7	41	,	,	PUNCT
ejpam-4822	7	42	y	y	PROPN
ejpam-4822	7	43	,	,	PUNCT
ejpam-4822	7	44	z	z	NOUN
ejpam-4822	7	45	)	)	PUNCT
ejpam-4822	7	46	is	be	AUX
ejpam-4822	7	47	(	(	PUNCT
ejpam-4822	7	48	0	0	NUM
ejpam-4822	7	49	,	,	PUNCT
ejpam-4822	7	50	1	1	NUM
ejpam-4822	7	51	,	,	PUNCT
ejpam-4822	7	52	√	√	PROPN
ejpam-4822	7	53	p+	p+	VERB
ejpam-4822	7	54	1	1	NUM
ejpam-4822	7	55	)	)	PUNCT
ejpam-4822	7	56	or	or	CCONJ
ejpam-4822	7	57	(	(	PUNCT
ejpam-4822	7	58	1	1	NUM
ejpam-4822	7	59	,	,	PUNCT
ejpam-4822	7	60	0	0	NUM
ejpam-4822	7	61	,	,	PUNCT
ejpam-4822	7	62	√	√	PROPN
ejpam-4822	7	63	p+	p+	ADJ
ejpam-4822	7	64	n+	n+	NOUN
ejpam-4822	7	65	1	1	NUM
ejpam-4822	7	66	)	)	PUNCT
ejpam-4822	7	67	.	.	PUNCT
ejpam-4822	8	1	in	in	ADP
ejpam-4822	8	2	case	case	NOUN
ejpam-4822	8	3	p	p	X
ejpam-4822	8	4	≡	≡	PROPN
ejpam-4822	8	5	1	1	NUM
ejpam-4822	8	6	(	(	PUNCT
ejpam-4822	8	7	mod	mod	NOUN
ejpam-4822	8	8	4	4	NUM
ejpam-4822	8	9	)	)	PUNCT
ejpam-4822	8	10	,	,	PUNCT
ejpam-4822	8	11	the	the	DET
ejpam-4822	8	12	non	non	ADJ
ejpam-4822	8	13	-	-	ADJ
ejpam-4822	8	14	negative	negative	ADJ
ejpam-4822	8	15	integer	integer	NOUN
ejpam-4822	8	16	solution	solution	NOUN
ejpam-4822	8	17	(	(	PUNCT
ejpam-4822	8	18	x	x	X
ejpam-4822	8	19	,	,	PUNCT
ejpam-4822	8	20	y	y	PROPN
ejpam-4822	8	21	,	,	PUNCT
ejpam-4822	8	22	z	z	NOUN
ejpam-4822	8	23	)	)	PUNCT
ejpam-4822	8	24	is	be	AUX
ejpam-4822	8	25	also	also	ADV
ejpam-4822	8	26	(	(	PUNCT
ejpam-4822	8	27	0	0	NUM
ejpam-4822	8	28	,	,	PUNCT
ejpam-4822	8	29	1	1	NUM
ejpam-4822	8	30	,	,	PUNCT
ejpam-4822	8	31	√	√	PROPN
ejpam-4822	8	32	p+	p+	VERB
ejpam-4822	8	33	1	1	NUM
ejpam-4822	8	34	)	)	PUNCT
ejpam-4822	8	35	or	or	CCONJ
ejpam-4822	8	36	(	(	PUNCT
ejpam-4822	8	37	1	1	NUM
ejpam-4822	8	38	,	,	PUNCT
ejpam-4822	8	39	0	0	NUM
ejpam-4822	8	40	,	,	PUNCT
ejpam-4822	8	41	√	√	PROPN
ejpam-4822	8	42	p+	p+	ADJ
ejpam-4822	8	43	n+	n+	NOUN
ejpam-4822	8	44	1	1	NUM
ejpam-4822	8	45	)	)	PUNCT
ejpam-4822	8	46	.	.	PUNCT
ejpam-4822	9	1	2020	2020	NUM
ejpam-4822	9	2	mathematics	mathematic	NOUN
ejpam-4822	9	3	subject	subject	NOUN
ejpam-4822	9	4	classifications	classification	NOUN
ejpam-4822	9	5	:	:	PUNCT
ejpam-4822	9	6	11d61	11d61	NUM
ejpam-4822	9	7	key	key	ADJ
ejpam-4822	9	8	words	word	NOUN
ejpam-4822	9	9	and	and	CCONJ
ejpam-4822	9	10	phrases	phrase	NOUN
ejpam-4822	9	11	:	:	PUNCT
ejpam-4822	9	12	diophantine	diophantine	VERB
ejpam-4822	9	13	equation	equation	NOUN
ejpam-4822	9	14	,	,	PUNCT
ejpam-4822	9	15	catalan	catalan	NOUN
ejpam-4822	9	16	’s	’s	PART
ejpam-4822	9	17	conjecture	conjecture	NOUN
ejpam-4822	9	18	1	1	NUM
ejpam-4822	9	19	.	.	PUNCT
ejpam-4822	10	1	introduction	introduction	NOUN
ejpam-4822	10	2	many	many	ADJ
ejpam-4822	10	3	mathematicians	mathematician	NOUN
ejpam-4822	10	4	have	have	AUX
ejpam-4822	10	5	been	be	AUX
ejpam-4822	10	6	studying	study	VERB
ejpam-4822	10	7	the	the	DET
ejpam-4822	10	8	diophantine	diophantine	NOUN
ejpam-4822	10	9	equations	equation	NOUN
ejpam-4822	10	10	of	of	ADP
ejpam-4822	10	11	the	the	DET
ejpam-4822	10	12	type	type	NOUN
ejpam-4822	10	13	(	(	PUNCT
ejpam-4822	10	14	p+	p+	NOUN
ejpam-4822	10	15	n)x+py	n)x+py	PROPN
ejpam-4822	10	16	=	=	SYM
ejpam-4822	10	17	z2	z2	PROPN
ejpam-4822	10	18	with	with	ADP
ejpam-4822	10	19	a	a	DET
ejpam-4822	10	20	constant	constant	ADJ
ejpam-4822	10	21	n	n	NOUN
ejpam-4822	10	22	and	and	CCONJ
ejpam-4822	10	23	a	a	DET
ejpam-4822	10	24	specific	specific	ADJ
ejpam-4822	10	25	condition	condition	NOUN
ejpam-4822	10	26	of	of	ADP
ejpam-4822	10	27	p	p	PRON
ejpam-4822	10	28	,	,	PUNCT
ejpam-4822	10	29	for	for	ADP
ejpam-4822	10	30	example	example	NOUN
ejpam-4822	10	31	,	,	PUNCT
ejpam-4822	10	32	in	in	ADP
ejpam-4822	10	33	case	case	NOUN
ejpam-4822	10	34	that	that	SCONJ
ejpam-4822	10	35	p	p	NOUN
ejpam-4822	10	36	is	be	AUX
ejpam-4822	10	37	a	a	DET
ejpam-4822	10	38	prime	prime	ADJ
ejpam-4822	10	39	number	number	NOUN
ejpam-4822	10	40	.	.	PUNCT
ejpam-4822	11	1	in	in	ADP
ejpam-4822	11	2	2015	2015	NUM
ejpam-4822	11	3	,	,	PUNCT
ejpam-4822	11	4	tatong	tatong	NOUN
ejpam-4822	11	5	and	and	CCONJ
ejpam-4822	11	6	suvarnamani	suvarnamani	NOUN
ejpam-4822	11	7	[	[	X
ejpam-4822	11	8	10	10	NUM
ejpam-4822	11	9	]	]	PUNCT
ejpam-4822	11	10	found	find	VERB
ejpam-4822	11	11	that	that	SCONJ
ejpam-4822	11	12	(	(	PUNCT
ejpam-4822	11	13	p	p	X
ejpam-4822	11	14	,	,	PUNCT
ejpam-4822	11	15	x	x	PROPN
ejpam-4822	11	16	,	,	PUNCT
ejpam-4822	11	17	y	y	PROPN
ejpam-4822	11	18	,	,	PUNCT
ejpam-4822	11	19	z	z	NOUN
ejpam-4822	11	20	)	)	PUNCT
ejpam-4822	11	21	=	=	SYM
ejpam-4822	11	22	(	(	PUNCT
ejpam-4822	11	23	3	3	NUM
ejpam-4822	11	24	,	,	PUNCT
ejpam-4822	11	25	1	1	NUM
ejpam-4822	11	26	,	,	PUNCT
ejpam-4822	11	27	0	0	NUM
ejpam-4822	11	28	,	,	PUNCT
ejpam-4822	11	29	2	2	NUM
ejpam-4822	11	30	)	)	PUNCT
ejpam-4822	11	31	is	be	AUX
ejpam-4822	11	32	a	a	DET
ejpam-4822	11	33	unique	unique	ADJ
ejpam-4822	11	34	non	non	ADJ
ejpam-4822	11	35	-	-	ADJ
ejpam-4822	11	36	negative	negative	ADJ
ejpam-4822	11	37	integer	integer	NOUN
ejpam-4822	11	38	solution	solution	NOUN
ejpam-4822	11	39	of	of	ADP
ejpam-4822	11	40	the	the	DET
ejpam-4822	11	41	diophantine	diophantine	NOUN
ejpam-4822	11	42	equation	equation	NOUN
ejpam-4822	11	43	px+(p+1)y	px+(p+1)y	NOUN
ejpam-4822	11	44	=	=	SYM
ejpam-4822	11	45	z2	z2	PROPN
ejpam-4822	11	46	where	where	SCONJ
ejpam-4822	11	47	p	p	NOUN
ejpam-4822	11	48	is	be	AUX
ejpam-4822	11	49	an	an	DET
ejpam-4822	11	50	odd	odd	ADJ
ejpam-4822	11	51	prime	prime	ADJ
ejpam-4822	11	52	number	number	NOUN
ejpam-4822	11	53	.	.	PUNCT
ejpam-4822	12	1	in	in	ADP
ejpam-4822	12	2	2018	2018	NUM
ejpam-4822	12	3	,	,	PUNCT
ejpam-4822	12	4	burshtein	burshtein	ADV
ejpam-4822	12	5	[	[	X
ejpam-4822	12	6	1	1	X
ejpam-4822	12	7	]	]	PUNCT
ejpam-4822	12	8	showed	show	VERB
ejpam-4822	12	9	that	that	SCONJ
ejpam-4822	12	10	the	the	DET
ejpam-4822	12	11	diophantine	diophantine	NOUN
ejpam-4822	12	12	equation	equation	NOUN
ejpam-4822	12	13	px+(p+4)y	px+(p+4)y	ADJ
ejpam-4822	12	14	=	=	SYM
ejpam-4822	12	15	z2	z2	PROPN
ejpam-4822	12	16	when	when	SCONJ
ejpam-4822	12	17	p	p	X
ejpam-4822	12	18	>	>	X
ejpam-4822	12	19	3	3	NUM
ejpam-4822	12	20	,	,	PUNCT
ejpam-4822	12	21	p+4	p+4	PROPN
ejpam-4822	12	22	are	be	AUX
ejpam-4822	12	23	primes	prime	NOUN
ejpam-4822	12	24	has	have	VERB
ejpam-4822	12	25	no	no	DET
ejpam-4822	12	26	positive	positive	ADJ
ejpam-4822	12	27	integer	integer	NOUN
ejpam-4822	12	28	solution	solution	NOUN
ejpam-4822	12	29	(	(	PUNCT
ejpam-4822	12	30	x	x	X
ejpam-4822	12	31	,	,	PUNCT
ejpam-4822	12	32	y	y	PROPN
ejpam-4822	12	33	,	,	PUNCT
ejpam-4822	12	34	z	z	NOUN
ejpam-4822	12	35	)	)	PUNCT
ejpam-4822	12	36	.	.	PUNCT
ejpam-4822	13	1	in	in	ADP
ejpam-4822	13	2	the	the	DET
ejpam-4822	13	3	same	same	ADJ
ejpam-4822	13	4	year	year	NOUN
ejpam-4822	13	5	,	,	PUNCT
ejpam-4822	13	6	fernando	fernando	PROPN
ejpam-4822	13	7	[	[	X
ejpam-4822	13	8	3	3	NUM
ejpam-4822	13	9	]	]	PUNCT
ejpam-4822	13	10	showed	show	VERB
ejpam-4822	13	11	that	that	SCONJ
ejpam-4822	13	12	px+(p+8)y	px+(p+8)y	NOUN
ejpam-4822	13	13	=	=	SYM
ejpam-4822	13	14	z2	z2	PROPN
ejpam-4822	13	15	has	have	VERB
ejpam-4822	13	16	no	no	DET
ejpam-4822	13	17	positive	positive	ADJ
ejpam-4822	13	18	integer	integer	NOUN
ejpam-4822	13	19	solution	solution	NOUN
ejpam-4822	13	20	,	,	PUNCT
ejpam-4822	13	21	when	when	SCONJ
ejpam-4822	13	22	p	p	NOUN
ejpam-4822	13	23	>	>	X
ejpam-4822	13	24	3	3	NUM
ejpam-4822	13	25	and	and	CCONJ
ejpam-4822	13	26	p+	p+	NOUN
ejpam-4822	13	27	8	8	NUM
ejpam-4822	13	28	are	be	AUX
ejpam-4822	13	29	primes	prime	NOUN
ejpam-4822	13	30	.	.	PUNCT
ejpam-4822	14	1	in	in	ADP
ejpam-4822	14	2	addition	addition	NOUN
ejpam-4822	14	3	,	,	PUNCT
ejpam-4822	14	4	kumar	kumar	PROPN
ejpam-4822	14	5	,	,	PUNCT
ejpam-4822	14	6	gupta	gupta	PROPN
ejpam-4822	14	7	and	and	CCONJ
ejpam-4822	14	8	kishan	kishan	PROPN
ejpam-4822	15	1	[	[	X
ejpam-4822	15	2	5	5	NUM
ejpam-4822	15	3	]	]	PUNCT
ejpam-4822	15	4	proved	prove	VERB
ejpam-4822	15	5	that	that	SCONJ
ejpam-4822	15	6	the	the	DET
ejpam-4822	15	7	solution	solution	NOUN
ejpam-4822	15	8	of	of	ADP
ejpam-4822	15	9	px+(p+12)y	px+(p+12)y	PROPN
ejpam-4822	15	10	=	=	PROPN
ejpam-4822	15	11	z2	z2	PROPN
ejpam-4822	15	12	has	have	VERB
ejpam-4822	15	13	no	no	DET
ejpam-4822	15	14	non	non	ADJ
ejpam-4822	15	15	-	-	ADJ
ejpam-4822	15	16	negative	negative	ADJ
ejpam-4822	15	17	integer	integer	NOUN
ejpam-4822	15	18	solution	solution	NOUN
ejpam-4822	15	19	where	where	SCONJ
ejpam-4822	15	20	p	p	NOUN
ejpam-4822	15	21	and	and	CCONJ
ejpam-4822	15	22	p+12	p+12	NOUN
ejpam-4822	15	23	are	be	AUX
ejpam-4822	15	24	prime	prime	ADJ
ejpam-4822	15	25	numbers	number	NOUN
ejpam-4822	15	26	and	and	CCONJ
ejpam-4822	15	27	p	p	NOUN
ejpam-4822	15	28	=	=	PROPN
ejpam-4822	15	29	6n	6n	NOUN
ejpam-4822	16	1	+	+	CCONJ
ejpam-4822	16	2	1	1	NUM
ejpam-4822	16	3	for	for	ADP
ejpam-4822	16	4	some	some	DET
ejpam-4822	16	5	natural	natural	ADJ
ejpam-4822	16	6	number	number	NOUN
ejpam-4822	16	7	n.	n.	NOUN
ejpam-4822	16	8	in	in	ADP
ejpam-4822	16	9	2021	2021	NUM
ejpam-4822	16	10	,	,	PUNCT
ejpam-4822	16	11	dokchan	dokchan	NOUN
ejpam-4822	16	12	and	and	CCONJ
ejpam-4822	16	13	pakapongpun	pakapongpun	VERB
ejpam-4822	17	1	[	[	X
ejpam-4822	17	2	2	2	NUM
ejpam-4822	17	3	]	]	PUNCT
ejpam-4822	17	4	studied	study	VERB
ejpam-4822	17	5	a	a	DET
ejpam-4822	17	6	diophantine	diophantine	NOUN
ejpam-4822	17	7	equation	equation	NOUN
ejpam-4822	17	8	px	px	X
ejpam-4822	17	9	+	+	CCONJ
ejpam-4822	17	10	(	(	PUNCT
ejpam-4822	17	11	p+	p+	NOUN
ejpam-4822	17	12	20)y	20)y	PROPN
ejpam-4822	17	13	=	=	SYM
ejpam-4822	17	14	z2	z2	PROPN
ejpam-4822	17	15	,	,	PUNCT
ejpam-4822	17	16	when	when	SCONJ
ejpam-4822	17	17	p	p	PROPN
ejpam-4822	17	18	and	and	CCONJ
ejpam-4822	17	19	p+	p+	PROPN
ejpam-4822	17	20	20	20	NUM
ejpam-4822	17	21	are	be	AUX
ejpam-4822	17	22	primes	prime	NOUN
ejpam-4822	17	23	and	and	CCONJ
ejpam-4822	17	24	showed	show	VERB
ejpam-4822	17	25	that	that	SCONJ
ejpam-4822	17	26	the	the	DET
ejpam-4822	17	27	equation	equation	NOUN
ejpam-4822	17	28	has	have	VERB
ejpam-4822	17	29	no	no	DET
ejpam-4822	17	30	positive	positive	ADJ
ejpam-4822	17	31	integer	integer	NOUN
ejpam-4822	17	32	solution	solution	NOUN
ejpam-4822	17	33	(	(	PUNCT
ejpam-4822	17	34	x	x	X
ejpam-4822	17	35	,	,	PUNCT
ejpam-4822	17	36	y	y	PROPN
ejpam-4822	17	37	,	,	PUNCT
ejpam-4822	17	38	z	z	NOUN
ejpam-4822	17	39	)	)	PUNCT
ejpam-4822	17	40	.	.	PUNCT
ejpam-4822	18	1	in	in	ADP
ejpam-4822	18	2	the	the	DET
ejpam-4822	18	3	same	same	ADJ
ejpam-4822	18	4	year	year	NOUN
ejpam-4822	18	5	,	,	PUNCT
ejpam-4822	18	6	gayo	gayo	PROPN
ejpam-4822	18	7	jr	jr	PROPN
ejpam-4822	18	8	and	and	CCONJ
ejpam-4822	18	9	bacani	bacani	PROPN
ejpam-4822	18	10	[	[	X
ejpam-4822	18	11	4	4	NUM
ejpam-4822	18	12	]	]	PUNCT
ejpam-4822	18	13	solved	solve	VERB
ejpam-4822	18	14	the	the	DET
ejpam-4822	18	15	diophantine	diophantine	NOUN
ejpam-4822	18	16	equation	equation	NOUN
ejpam-4822	18	17	mx	mx	PROPN
ejpam-4822	19	1	p	p	PROPN
ejpam-4822	19	2	+	+	X
ejpam-4822	19	3	(	(	PUNCT
ejpam-4822	19	4	mq	mq	NOUN
ejpam-4822	19	5	+1)y	+1)y	NOUN
ejpam-4822	19	6	=	=	SYM
ejpam-4822	19	7	z2	z2	PROPN
ejpam-4822	19	8	where	where	SCONJ
ejpam-4822	19	9	mp	mp	PROPN
ejpam-4822	19	10	and	and	CCONJ
ejpam-4822	19	11	mq	mq	PROPN
ejpam-4822	19	12	are	be	AUX
ejpam-4822	19	13	mersenne	mersenne	NOUN
ejpam-4822	19	14	primes	prime	NOUN
ejpam-4822	19	15	.	.	PUNCT
ejpam-4822	20	1	in	in	ADP
ejpam-4822	20	2	2022	2022	NUM
ejpam-4822	20	3	,	,	PUNCT
ejpam-4822	20	4	tadee	tadee	VERB
ejpam-4822	21	1	[	[	X
ejpam-4822	21	2	8	8	NUM
ejpam-4822	21	3	]	]	PUNCT
ejpam-4822	21	4	gave	give	VERB
ejpam-4822	21	5	the	the	DET
ejpam-4822	21	6	solutions	solution	NOUN
ejpam-4822	21	7	of	of	ADP
ejpam-4822	21	8	equations	equation	NOUN
ejpam-4822	21	9	px+(p+14)y	px+(p+14)y	PROPN
ejpam-4822	21	10	=	=	SYM
ejpam-4822	21	11	z2	z2	PROPN
ejpam-4822	21	12	,	,	PUNCT
ejpam-4822	21	13	where	where	SCONJ
ejpam-4822	21	14	p	p	NOUN
ejpam-4822	21	15	and	and	CCONJ
ejpam-4822	21	16	p+14	p+14	NOUN
ejpam-4822	21	17	are	be	AUX
ejpam-4822	21	18	primes	prime	NOUN
ejpam-4822	21	19	.	.	PUNCT
ejpam-4822	22	1	in	in	ADP
ejpam-4822	22	2	2023	2023	NUM
ejpam-4822	22	3	,	,	PUNCT
ejpam-4822	22	4	viriyapong	viriyapong	ADV
ejpam-4822	22	5	and	and	CCONJ
ejpam-4822	22	6	viriyapong	viriyapong	VERB
ejpam-4822	23	1	[	[	X
ejpam-4822	23	2	11	11	NUM
ejpam-4822	23	3	]	]	PUNCT
ejpam-4822	23	4	studied	study	VERB
ejpam-4822	23	5	the	the	DET
ejpam-4822	23	6	diophantine	diophantine	NOUN
ejpam-4822	23	7	equation	equation	NOUN
ejpam-4822	23	8	ax	ax	NOUN
ejpam-4822	23	9	+	+	CCONJ
ejpam-4822	23	10	(	(	PUNCT
ejpam-4822	23	11	a+	a+	PRON
ejpam-4822	23	12	2)y	2)y	PROPN
ejpam-4822	23	13	=	=	SYM
ejpam-4822	23	14	z2	z2	PROPN
ejpam-4822	23	15	,	,	PUNCT
ejpam-4822	23	16	where	where	SCONJ
ejpam-4822	23	17	a	a	DET
ejpam-4822	23	18	≡	≡	PROPN
ejpam-4822	23	19	5	5	NUM
ejpam-4822	23	20	(	(	PUNCT
ejpam-4822	23	21	mod	mod	PROPN
ejpam-4822	23	22	21	21	NUM
ejpam-4822	23	23	)	)	PUNCT
ejpam-4822	23	24	and	and	CCONJ
ejpam-4822	23	25	showed	show	VERB
ejpam-4822	23	26	doi	doi	NOUN
ejpam-4822	23	27	:	:	PUNCT
ejpam-4822	23	28	https://doi.org/10.29020/nybg.ejpam.v16i4.4822	https://doi.org/10.29020/nybg.ejpam.v16i4.4822	ADJ
ejpam-4822	23	29	email	email	NOUN
ejpam-4822	23	30	address	address	NOUN
ejpam-4822	23	31	:	:	PUNCT
ejpam-4822	23	32	wachirarak.tc@bru.ac.th	wachirarak.tc@bru.ac.th	X
ejpam-4822	23	33	(	(	PUNCT
ejpam-4822	23	34	w.	w.	NOUN
ejpam-4822	23	35	orosram	orosram	PROPN
ejpam-4822	23	36	)	)	PUNCT
ejpam-4822	23	37	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4822	23	38	2208	2208	NUM
ejpam-4822	24	1	©	©	PROPN
ejpam-4822	24	2	2023	2023	NUM
ejpam-4822	24	3	ejpam	ejpam	NOUN
ejpam-4822	24	4	all	all	DET
ejpam-4822	24	5	rights	right	NOUN
ejpam-4822	24	6	reserved	reserve	VERB
ejpam-4822	24	7	.	.	PUNCT
ejpam-4822	25	1	w.	w.	PROPN
ejpam-4822	25	2	orosram	orosram	PROPN
ejpam-4822	25	3	/	/	SYM
ejpam-4822	25	4	eur	eur	PROPN
ejpam-4822	25	5	.	.	PUNCT
ejpam-4822	26	1	j.	j.	PROPN
ejpam-4822	26	2	pure	pure	PROPN
ejpam-4822	26	3	appl	appl	PROPN
ejpam-4822	26	4	.	.	PROPN
ejpam-4822	26	5	math	math	PROPN
ejpam-4822	26	6	,	,	PUNCT
ejpam-4822	26	7	16	16	NUM
ejpam-4822	26	8	(	(	PUNCT
ejpam-4822	26	9	4	4	NUM
ejpam-4822	26	10	)	)	PUNCT
ejpam-4822	26	11	(	(	PUNCT
ejpam-4822	26	12	2023	2023	NUM
ejpam-4822	26	13	)	)	PUNCT
ejpam-4822	26	14	,	,	PUNCT
ejpam-4822	26	15	2208	2208	NUM
ejpam-4822	26	16	-	-	SYM
ejpam-4822	26	17	2212	2212	NUM
ejpam-4822	26	18	2209	2209	NUM
ejpam-4822	26	19	that	that	PRON
ejpam-4822	26	20	the	the	DET
ejpam-4822	26	21	equation	equation	NOUN
ejpam-4822	26	22	has	have	VERB
ejpam-4822	26	23	no	no	DET
ejpam-4822	26	24	non	non	ADJ
ejpam-4822	26	25	-	-	ADJ
ejpam-4822	26	26	negative	negative	ADJ
ejpam-4822	26	27	integer	integer	NOUN
ejpam-4822	26	28	solution	solution	NOUN
ejpam-4822	26	29	(	(	PUNCT
ejpam-4822	26	30	x	x	X
ejpam-4822	26	31	,	,	PUNCT
ejpam-4822	26	32	y	y	PROPN
ejpam-4822	26	33	,	,	PUNCT
ejpam-4822	26	34	z	z	NOUN
ejpam-4822	26	35	)	)	PUNCT
ejpam-4822	26	36	.	.	PUNCT
ejpam-4822	27	1	in	in	ADP
ejpam-4822	27	2	the	the	DET
ejpam-4822	27	3	same	same	ADJ
ejpam-4822	27	4	year	year	NOUN
ejpam-4822	27	5	,	,	PUNCT
ejpam-4822	27	6	tadee	tadee	NOUN
ejpam-4822	27	7	and	and	CCONJ
ejpam-4822	27	8	siraworakun	siraworakun	NOUN
ejpam-4822	28	1	[	[	X
ejpam-4822	28	2	9	9	NUM
ejpam-4822	28	3	]	]	PUNCT
ejpam-4822	28	4	studied	study	VERB
ejpam-4822	28	5	the	the	DET
ejpam-4822	28	6	diophantine	diophantine	NOUN
ejpam-4822	28	7	equation	equation	NOUN
ejpam-4822	28	8	px+(p+2q)y	px+(p+2q)y	NOUN
ejpam-4822	28	9	=	=	SYM
ejpam-4822	28	10	z2	z2	PROPN
ejpam-4822	28	11	,	,	PUNCT
ejpam-4822	28	12	where	where	SCONJ
ejpam-4822	28	13	p	p	X
ejpam-4822	28	14	,	,	PUNCT
ejpam-4822	28	15	q	q	ADJ
ejpam-4822	28	16	,	,	PUNCT
ejpam-4822	28	17	p+2q	p+2q	PROPN
ejpam-4822	28	18	are	be	AUX
ejpam-4822	28	19	prime	prime	ADJ
ejpam-4822	28	20	numbers	number	NOUN
ejpam-4822	28	21	and	and	CCONJ
ejpam-4822	28	22	showed	show	VERB
ejpam-4822	28	23	that	that	SCONJ
ejpam-4822	28	24	the	the	DET
ejpam-4822	28	25	equation	equation	NOUN
ejpam-4822	28	26	has	have	VERB
ejpam-4822	28	27	no	no	DET
ejpam-4822	28	28	positive	positive	ADJ
ejpam-4822	28	29	integer	integer	NOUN
ejpam-4822	28	30	solution	solution	NOUN
ejpam-4822	28	31	.	.	PUNCT
ejpam-4822	29	1	in	in	ADP
ejpam-4822	29	2	this	this	DET
ejpam-4822	29	3	paper	paper	NOUN
ejpam-4822	29	4	,	,	PUNCT
ejpam-4822	29	5	we	we	PRON
ejpam-4822	29	6	give	give	VERB
ejpam-4822	29	7	a	a	DET
ejpam-4822	29	8	solution	solution	NOUN
ejpam-4822	29	9	of	of	ADP
ejpam-4822	29	10	the	the	DET
ejpam-4822	29	11	diophantine	diophantine	NOUN
ejpam-4822	29	12	equation	equation	NOUN
ejpam-4822	29	13	(	(	PUNCT
ejpam-4822	29	14	p+n)x+py	p+n)x+py	PROPN
ejpam-4822	29	15	=	=	SYM
ejpam-4822	29	16	z2	z2	PROPN
ejpam-4822	29	17	,	,	PUNCT
ejpam-4822	29	18	where	where	SCONJ
ejpam-4822	29	19	p	p	X
ejpam-4822	29	20	,	,	PUNCT
ejpam-4822	29	21	p+n	p+n	ADJ
ejpam-4822	29	22	are	be	AUX
ejpam-4822	29	23	odd	odd	ADJ
ejpam-4822	29	24	prime	prime	ADJ
ejpam-4822	29	25	numbers	number	NOUN
ejpam-4822	29	26	such	such	ADJ
ejpam-4822	29	27	that	that	SCONJ
ejpam-4822	29	28	n	n	NUM
ejpam-4822	29	29	≡	≡	PROPN
ejpam-4822	29	30	0	0	PUNCT
ejpam-4822	29	31	(	(	PUNCT
ejpam-4822	29	32	mod	mod	PROPN
ejpam-4822	29	33	4	4	NUM
ejpam-4822	29	34	)	)	PUNCT
ejpam-4822	29	35	.	.	PUNCT
ejpam-4822	30	1	to	to	PART
ejpam-4822	30	2	obtain	obtain	VERB
ejpam-4822	30	3	our	our	PRON
ejpam-4822	30	4	result	result	NOUN
ejpam-4822	30	5	,	,	PUNCT
ejpam-4822	30	6	we	we	PRON
ejpam-4822	30	7	consider	consider	VERB
ejpam-4822	30	8	two	two	NUM
ejpam-4822	30	9	cases	case	NOUN
ejpam-4822	30	10	of	of	ADP
ejpam-4822	30	11	p	p	NOUN
ejpam-4822	30	12	in	in	ADP
ejpam-4822	30	13	modulo	modulo	NOUN
ejpam-4822	30	14	4	4	NUM
ejpam-4822	30	15	,	,	PUNCT
ejpam-4822	30	16	i.e.	i.e.	X
ejpam-4822	30	17	,	,	PUNCT
ejpam-4822	30	18	the	the	DET
ejpam-4822	30	19	case	case	NOUN
ejpam-4822	30	20	that	that	SCONJ
ejpam-4822	30	21	p	p	PROPN
ejpam-4822	30	22	≡	≡	PROPN
ejpam-4822	30	23	1	1	NUM
ejpam-4822	30	24	(	(	PUNCT
ejpam-4822	30	25	mod	mod	NOUN
ejpam-4822	30	26	4	4	NUM
ejpam-4822	30	27	)	)	PUNCT
ejpam-4822	30	28	and	and	CCONJ
ejpam-4822	30	29	the	the	DET
ejpam-4822	30	30	case	case	NOUN
ejpam-4822	30	31	that	that	SCONJ
ejpam-4822	30	32	p	p	PROPN
ejpam-4822	30	33	≡	≡	PROPN
ejpam-4822	30	34	3	3	NUM
ejpam-4822	30	35	(	(	PUNCT
ejpam-4822	30	36	mod	mod	NOUN
ejpam-4822	30	37	4	4	NUM
ejpam-4822	30	38	)	)	PUNCT
ejpam-4822	30	39	.	.	PUNCT
ejpam-4822	31	1	in	in	ADP
ejpam-4822	31	2	case	case	NOUN
ejpam-4822	31	3	p	p	X
ejpam-4822	31	4	≡	≡	PROPN
ejpam-4822	31	5	3	3	NUM
ejpam-4822	31	6	(	(	PUNCT
ejpam-4822	31	7	mod	mod	NOUN
ejpam-4822	31	8	4	4	NUM
ejpam-4822	31	9	)	)	PUNCT
ejpam-4822	31	10	,	,	PUNCT
ejpam-4822	31	11	we	we	PRON
ejpam-4822	31	12	first	first	ADV
ejpam-4822	31	13	consider	consider	VERB
ejpam-4822	31	14	case	case	NOUN
ejpam-4822	31	15	p	p	X
ejpam-4822	31	16	=	=	SYM
ejpam-4822	31	17	3	3	NUM
ejpam-4822	31	18	and	and	CCONJ
ejpam-4822	31	19	n	n	NOUN
ejpam-4822	31	20	=	=	NOUN
ejpam-4822	31	21	4	4	NUM
ejpam-4822	31	22	.	.	PUNCT
ejpam-4822	32	1	the	the	DET
ejpam-4822	32	2	considered	consider	VERB
ejpam-4822	32	3	equation	equation	NOUN
ejpam-4822	32	4	in	in	ADP
ejpam-4822	32	5	this	this	DET
ejpam-4822	32	6	case	case	NOUN
ejpam-4822	32	7	is	be	AUX
ejpam-4822	32	8	3x	3x	NUM
ejpam-4822	32	9	+	+	CCONJ
ejpam-4822	32	10	7y	7y	NOUN
ejpam-4822	32	11	=	=	SYM
ejpam-4822	32	12	z2	z2	PROPN
ejpam-4822	32	13	in	in	ADP
ejpam-4822	32	14	which	which	PRON
ejpam-4822	32	15	the	the	DET
ejpam-4822	32	16	solutions	solution	NOUN
ejpam-4822	32	17	were	be	AUX
ejpam-4822	32	18	given	give	VERB
ejpam-4822	32	19	by	by	ADP
ejpam-4822	32	20	rao	rao	NOUN
ejpam-4822	33	1	[	[	X
ejpam-4822	33	2	7	7	X
ejpam-4822	33	3	]	]	PUNCT
ejpam-4822	33	4	that	that	SCONJ
ejpam-4822	33	5	(	(	PUNCT
ejpam-4822	33	6	x	x	X
ejpam-4822	33	7	,	,	PUNCT
ejpam-4822	33	8	y	y	PROPN
ejpam-4822	33	9	,	,	PUNCT
ejpam-4822	33	10	z	z	NOUN
ejpam-4822	33	11	)	)	PUNCT
ejpam-4822	33	12	=	=	SYM
ejpam-4822	33	13	(	(	PUNCT
ejpam-4822	33	14	0	0	NUM
ejpam-4822	33	15	,	,	PUNCT
ejpam-4822	33	16	1	1	NUM
ejpam-4822	33	17	,	,	PUNCT
ejpam-4822	33	18	2	2	NUM
ejpam-4822	33	19	)	)	PUNCT
ejpam-4822	33	20	or	or	CCONJ
ejpam-4822	33	21	(	(	PUNCT
ejpam-4822	33	22	x	x	X
ejpam-4822	33	23	,	,	PUNCT
ejpam-4822	33	24	y	y	PROPN
ejpam-4822	33	25	,	,	PUNCT
ejpam-4822	33	26	z	z	NOUN
ejpam-4822	33	27	)	)	PUNCT
ejpam-4822	33	28	=	=	SYM
ejpam-4822	33	29	(	(	PUNCT
ejpam-4822	33	30	1	1	NUM
ejpam-4822	33	31	,	,	PUNCT
ejpam-4822	33	32	2	2	NUM
ejpam-4822	33	33	,	,	PUNCT
ejpam-4822	33	34	4	4	NUM
ejpam-4822	33	35	)	)	PUNCT
ejpam-4822	33	36	.	.	PUNCT
ejpam-4822	34	1	next	next	ADV
ejpam-4822	34	2	,	,	PUNCT
ejpam-4822	34	3	we	we	PRON
ejpam-4822	34	4	consider	consider	VERB
ejpam-4822	34	5	p	p	PRON
ejpam-4822	34	6	≡	≡	PROPN
ejpam-4822	34	7	3	3	NUM
ejpam-4822	34	8	(	(	PUNCT
ejpam-4822	34	9	mod	mod	NOUN
ejpam-4822	34	10	4	4	NUM
ejpam-4822	34	11	)	)	PUNCT
ejpam-4822	34	12	such	such	ADJ
ejpam-4822	34	13	that	that	SCONJ
ejpam-4822	34	14	p	p	X
ejpam-4822	34	15	>	>	X
ejpam-4822	34	16	3	3	NUM
ejpam-4822	34	17	with	with	ADP
ejpam-4822	34	18	a	a	DET
ejpam-4822	34	19	specific	specific	ADJ
ejpam-4822	34	20	condition	condition	NOUN
ejpam-4822	34	21	that	that	PRON
ejpam-4822	34	22	n−	n−	NOUN
ejpam-4822	34	23	1	1	NUM
ejpam-4822	34	24	is	be	AUX
ejpam-4822	34	25	a	a	DET
ejpam-4822	34	26	prime	prime	ADJ
ejpam-4822	34	27	number	number	NOUN
ejpam-4822	34	28	and	and	CCONJ
ejpam-4822	34	29	2n−	2n−	PROPN
ejpam-4822	34	30	1	1	NUM
ejpam-4822	34	31	is	be	AUX
ejpam-4822	34	32	not	not	PART
ejpam-4822	34	33	a	a	DET
ejpam-4822	34	34	prime	prime	ADJ
ejpam-4822	34	35	number	number	NOUN
ejpam-4822	34	36	.	.	PUNCT
ejpam-4822	35	1	then	then	ADV
ejpam-4822	35	2	,	,	PUNCT
ejpam-4822	35	3	our	our	PRON
ejpam-4822	35	4	final	final	ADJ
ejpam-4822	35	5	case	case	NOUN
ejpam-4822	35	6	is	be	AUX
ejpam-4822	35	7	when	when	SCONJ
ejpam-4822	35	8	p	p	PRON
ejpam-4822	35	9	≡	≡	PROPN
ejpam-4822	35	10	1	1	NUM
ejpam-4822	35	11	(	(	PUNCT
ejpam-4822	35	12	mod	mod	NOUN
ejpam-4822	35	13	4	4	NUM
ejpam-4822	35	14	)	)	PUNCT
ejpam-4822	35	15	and	and	CCONJ
ejpam-4822	35	16	n	n	PRON
ejpam-4822	35	17	is	be	AUX
ejpam-4822	35	18	a	a	DET
ejpam-4822	35	19	positive	positive	ADJ
ejpam-4822	35	20	integer	integer	NOUN
ejpam-4822	35	21	.	.	PUNCT
ejpam-4822	36	1	2	2	X
ejpam-4822	36	2	.	.	X
ejpam-4822	36	3	preliminaries	preliminary	NOUN
ejpam-4822	36	4	proposition	proposition	NOUN
ejpam-4822	36	5	1	1	NUM
ejpam-4822	36	6	.	.	PUNCT
ejpam-4822	37	1	(	(	PUNCT
ejpam-4822	37	2	catalan	catalan	NOUN
ejpam-4822	37	3	’s	’s	PART
ejpam-4822	37	4	conjecture	conjecture	NOUN
ejpam-4822	37	5	)	)	PUNCT
ejpam-4822	37	6	the	the	DET
ejpam-4822	37	7	diophantine	diophantine	NOUN
ejpam-4822	37	8	equation	equation	NOUN
ejpam-4822	37	9	ax	ax	NOUN
ejpam-4822	37	10	−	−	NOUN
ejpam-4822	37	11	by	by	ADP
ejpam-4822	37	12	=	=	PROPN
ejpam-4822	37	13	1	1	NUM
ejpam-4822	37	14	where	where	SCONJ
ejpam-4822	37	15	min{a	min{a	PROPN
ejpam-4822	37	16	,	,	PUNCT
ejpam-4822	37	17	b	b	PROPN
ejpam-4822	37	18	,	,	PUNCT
ejpam-4822	37	19	x	x	NOUN
ejpam-4822	37	20	,	,	PUNCT
ejpam-4822	37	21	y	y	PROPN
ejpam-4822	37	22	}	}	PUNCT
ejpam-4822	37	23	>	>	X
ejpam-4822	37	24	1	1	NUM
ejpam-4822	37	25	has	have	VERB
ejpam-4822	37	26	a	a	DET
ejpam-4822	37	27	unique	unique	ADJ
ejpam-4822	37	28	solution	solution	NOUN
ejpam-4822	37	29	(	(	PUNCT
ejpam-4822	37	30	a	a	PRON
ejpam-4822	37	31	,	,	PUNCT
ejpam-4822	37	32	b	b	NOUN
ejpam-4822	37	33	,	,	PUNCT
ejpam-4822	37	34	x	x	NOUN
ejpam-4822	37	35	,	,	PUNCT
ejpam-4822	37	36	y	y	NOUN
ejpam-4822	37	37	)	)	PUNCT
ejpam-4822	37	38	=	=	PUNCT
ejpam-4822	38	1	(	(	PUNCT
ejpam-4822	38	2	3	3	NUM
ejpam-4822	38	3	,	,	PUNCT
ejpam-4822	38	4	2	2	NUM
ejpam-4822	38	5	,	,	PUNCT
ejpam-4822	38	6	2	2	NUM
ejpam-4822	38	7	,	,	PUNCT
ejpam-4822	38	8	3	3	NUM
ejpam-4822	38	9	)	)	PUNCT
ejpam-4822	38	10	.	.	PUNCT
ejpam-4822	39	1	this	this	DET
ejpam-4822	39	2	proposition	proposition	NOUN
ejpam-4822	39	3	was	be	AUX
ejpam-4822	39	4	proved	prove	VERB
ejpam-4822	39	5	in	in	ADP
ejpam-4822	39	6	2004	2004	NUM
ejpam-4822	39	7	by	by	ADP
ejpam-4822	39	8	mihailescu	mihailescu	PROPN
ejpam-4822	40	1	[	[	X
ejpam-4822	40	2	6	6	NUM
ejpam-4822	40	3	]	]	PUNCT
ejpam-4822	40	4	.	.	PUNCT
ejpam-4822	41	1	lemma	lemma	PROPN
ejpam-4822	41	2	1	1	X
ejpam-4822	41	3	.	.	PUNCT
ejpam-4822	42	1	let	let	VERB
ejpam-4822	42	2	p	p	PRON
ejpam-4822	42	3	be	be	AUX
ejpam-4822	42	4	odd	odd	ADJ
ejpam-4822	42	5	prime	prime	ADJ
ejpam-4822	42	6	number	number	NOUN
ejpam-4822	42	7	.	.	PUNCT
ejpam-4822	43	1	the	the	DET
ejpam-4822	43	2	non	non	ADJ
ejpam-4822	43	3	-	-	ADJ
ejpam-4822	43	4	negative	negative	ADJ
ejpam-4822	43	5	integer	integer	NOUN
ejpam-4822	43	6	solution	solution	NOUN
ejpam-4822	43	7	to	to	ADP
ejpam-4822	43	8	the	the	DET
ejpam-4822	43	9	diophantine	diophantine	NOUN
ejpam-4822	43	10	equation	equation	NOUN
ejpam-4822	43	11	1	1	NUM
ejpam-4822	43	12	+	+	CCONJ
ejpam-4822	43	13	py	py	PROPN
ejpam-4822	43	14	=	=	SYM
ejpam-4822	43	15	z2	z2	PROPN
ejpam-4822	43	16	is	be	AUX
ejpam-4822	43	17	(	(	PUNCT
ejpam-4822	43	18	y	y	PROPN
ejpam-4822	43	19	,	,	PUNCT
ejpam-4822	43	20	z	z	NOUN
ejpam-4822	43	21	)	)	PUNCT
ejpam-4822	43	22	=	=	SYM
ejpam-4822	43	23	(	(	PUNCT
ejpam-4822	43	24	1	1	NUM
ejpam-4822	43	25	,	,	PUNCT
ejpam-4822	43	26	√	√	PROPN
ejpam-4822	43	27	p+	p+	VERB
ejpam-4822	43	28	1	1	NUM
ejpam-4822	43	29	)	)	PUNCT
ejpam-4822	43	30	if	if	SCONJ
ejpam-4822	43	31	√	√	PRON
ejpam-4822	43	32	p+	p+	VERB
ejpam-4822	43	33	1	1	NUM
ejpam-4822	43	34	is	be	AUX
ejpam-4822	43	35	a	a	DET
ejpam-4822	43	36	positive	positive	ADJ
ejpam-4822	43	37	integer	integer	NOUN
ejpam-4822	43	38	.	.	PUNCT
ejpam-4822	44	1	proof	proof	NOUN
ejpam-4822	44	2	.	.	PUNCT
ejpam-4822	45	1	let	let	VERB
ejpam-4822	45	2	(	(	PUNCT
ejpam-4822	45	3	y	y	NOUN
ejpam-4822	45	4	,	,	PUNCT
ejpam-4822	45	5	z	z	NOUN
ejpam-4822	45	6	)	)	PUNCT
ejpam-4822	45	7	be	be	AUX
ejpam-4822	45	8	a	a	DET
ejpam-4822	45	9	non	non	ADJ
ejpam-4822	45	10	-	-	ADJ
ejpam-4822	45	11	negative	negative	ADJ
ejpam-4822	45	12	integer	integer	NOUN
ejpam-4822	45	13	solution	solution	NOUN
ejpam-4822	45	14	of	of	ADP
ejpam-4822	45	15	1	1	NUM
ejpam-4822	45	16	+	+	CCONJ
ejpam-4822	45	17	py	py	PROPN
ejpam-4822	45	18	=	=	SYM
ejpam-4822	45	19	z2	z2	PROPN
ejpam-4822	45	20	.	.	PUNCT
ejpam-4822	46	1	if	if	SCONJ
ejpam-4822	46	2	y	y	PROPN
ejpam-4822	46	3	=	=	SYM
ejpam-4822	46	4	0	0	PROPN
ejpam-4822	46	5	,	,	PUNCT
ejpam-4822	46	6	then	then	ADV
ejpam-4822	46	7	z2	z2	PROPN
ejpam-4822	46	8	=	=	SYM
ejpam-4822	46	9	2	2	NUM
ejpam-4822	46	10	,	,	PUNCT
ejpam-4822	46	11	which	which	PRON
ejpam-4822	46	12	is	be	AUX
ejpam-4822	46	13	impossible	impossible	ADJ
ejpam-4822	46	14	.	.	PUNCT
ejpam-4822	47	1	if	if	SCONJ
ejpam-4822	47	2	y	y	PROPN
ejpam-4822	47	3	>	>	X
ejpam-4822	47	4	1	1	NUM
ejpam-4822	47	5	,	,	PUNCT
ejpam-4822	47	6	then	then	ADV
ejpam-4822	47	7	z	z	NOUN
ejpam-4822	47	8	>	>	X
ejpam-4822	47	9	1	1	X
ejpam-4822	47	10	.	.	PUNCT
ejpam-4822	48	1	by	by	ADP
ejpam-4822	48	2	catalan	catalan	PROPN
ejpam-4822	48	3	’s	’s	PART
ejpam-4822	48	4	conjecture	conjecture	NOUN
ejpam-4822	48	5	,	,	PUNCT
ejpam-4822	48	6	there	there	PRON
ejpam-4822	48	7	is	be	VERB
ejpam-4822	48	8	no	no	DET
ejpam-4822	48	9	non	non	ADJ
ejpam-4822	48	10	-	-	ADJ
ejpam-4822	48	11	negative	negative	ADJ
ejpam-4822	48	12	integer	integer	NOUN
ejpam-4822	48	13	solution	solution	NOUN
ejpam-4822	48	14	.	.	PUNCT
ejpam-4822	49	1	if	if	SCONJ
ejpam-4822	49	2	y	y	PROPN
ejpam-4822	49	3	=	=	SYM
ejpam-4822	49	4	1	1	NUM
ejpam-4822	49	5	,	,	PUNCT
ejpam-4822	49	6	then	then	ADV
ejpam-4822	49	7	z2	z2	PROPN
ejpam-4822	49	8	=	=	SYM
ejpam-4822	49	9	p+	p+	PROPN
ejpam-4822	49	10	1	1	NUM
ejpam-4822	49	11	.	.	PUNCT
ejpam-4822	50	1	so	so	ADV
ejpam-4822	50	2	z	z	NOUN
ejpam-4822	50	3	=	=	PUNCT
ejpam-4822	50	4	√	√	PROPN
ejpam-4822	50	5	p+	p+	NOUN
ejpam-4822	50	6	1	1	NUM
ejpam-4822	50	7	.	.	PUNCT
ejpam-4822	51	1	this	this	PRON
ejpam-4822	51	2	means	mean	VERB
ejpam-4822	51	3	that√	that√	PROPN
ejpam-4822	51	4	p+	p+	PROPN
ejpam-4822	51	5	1	1	NUM
ejpam-4822	51	6	is	be	AUX
ejpam-4822	51	7	a	a	DET
ejpam-4822	51	8	non	non	ADJ
ejpam-4822	51	9	-	-	ADJ
ejpam-4822	51	10	negative	negative	ADJ
ejpam-4822	51	11	integer	integer	NOUN
ejpam-4822	51	12	as	as	SCONJ
ejpam-4822	51	13	z	z	PROPN
ejpam-4822	51	14	is	be	AUX
ejpam-4822	51	15	a	a	DET
ejpam-4822	51	16	non	non	ADJ
ejpam-4822	51	17	-	-	ADJ
ejpam-4822	51	18	negative	negative	ADJ
ejpam-4822	51	19	integer	integer	NOUN
ejpam-4822	51	20	.	.	PUNCT
ejpam-4822	52	1	lemma	lemma	PROPN
ejpam-4822	52	2	2	2	X
ejpam-4822	52	3	.	.	PUNCT
ejpam-4822	53	1	let	let	VERB
ejpam-4822	53	2	n	n	PRON
ejpam-4822	53	3	be	be	AUX
ejpam-4822	53	4	a	a	DET
ejpam-4822	53	5	positive	positive	ADJ
ejpam-4822	53	6	integer	integer	NOUN
ejpam-4822	54	1	such	such	ADJ
ejpam-4822	54	2	that	that	SCONJ
ejpam-4822	54	3	n	n	NUM
ejpam-4822	54	4	≡	≡	PROPN
ejpam-4822	54	5	0	0	PUNCT
ejpam-4822	54	6	(	(	PUNCT
ejpam-4822	54	7	mod	mod	NOUN
ejpam-4822	54	8	4	4	NUM
ejpam-4822	54	9	)	)	PUNCT
ejpam-4822	54	10	and	and	CCONJ
ejpam-4822	54	11	let	let	VERB
ejpam-4822	54	12	p	p	PRON
ejpam-4822	54	13	,	,	PUNCT
ejpam-4822	54	14	p+	p+	AUX
ejpam-4822	54	15	n	n	ADV
ejpam-4822	54	16	be	be	AUX
ejpam-4822	54	17	prime	prime	ADJ
ejpam-4822	54	18	numbers	number	NOUN
ejpam-4822	54	19	.	.	PUNCT
ejpam-4822	55	1	the	the	DET
ejpam-4822	55	2	non	non	ADJ
ejpam-4822	55	3	-	-	ADJ
ejpam-4822	55	4	negative	negative	ADJ
ejpam-4822	55	5	integer	integer	NOUN
ejpam-4822	55	6	solutions	solution	NOUN
ejpam-4822	55	7	of	of	ADP
ejpam-4822	55	8	the	the	DET
ejpam-4822	55	9	diophantine	diophantine	NOUN
ejpam-4822	55	10	equation	equation	NOUN
ejpam-4822	55	11	1+(p+n)x	1+(p+n)x	NUM
ejpam-4822	55	12	=	=	SYM
ejpam-4822	55	13	z2	z2	PROPN
ejpam-4822	55	14	is	be	AUX
ejpam-4822	55	15	(	(	PUNCT
ejpam-4822	55	16	x	x	X
ejpam-4822	55	17	,	,	PUNCT
ejpam-4822	55	18	z	z	NOUN
ejpam-4822	55	19	)	)	PUNCT
ejpam-4822	55	20	=	=	SYM
ejpam-4822	55	21	(	(	PUNCT
ejpam-4822	55	22	1	1	NUM
ejpam-4822	55	23	,	,	PUNCT
ejpam-4822	55	24	√	√	PROPN
ejpam-4822	55	25	p+	p+	ADJ
ejpam-4822	55	26	n+	n+	NOUN
ejpam-4822	55	27	1	1	X
ejpam-4822	55	28	)	)	PUNCT
ejpam-4822	55	29	if	if	SCONJ
ejpam-4822	55	30	√	√	PROPN
ejpam-4822	55	31	p+	p+	NOUN
ejpam-4822	55	32	n+	n+	NOUN
ejpam-4822	55	33	1	1	NUM
ejpam-4822	55	34	is	be	AUX
ejpam-4822	55	35	a	a	DET
ejpam-4822	55	36	positive	positive	ADJ
ejpam-4822	55	37	integer	integer	NOUN
ejpam-4822	55	38	.	.	PUNCT
ejpam-4822	56	1	proof	proof	NOUN
ejpam-4822	56	2	.	.	PUNCT
ejpam-4822	57	1	let	let	VERB
ejpam-4822	57	2	(	(	PUNCT
ejpam-4822	57	3	x	x	NOUN
ejpam-4822	57	4	,	,	PUNCT
ejpam-4822	57	5	z	z	NOUN
ejpam-4822	57	6	)	)	PUNCT
ejpam-4822	57	7	be	be	AUX
ejpam-4822	57	8	a	a	DET
ejpam-4822	57	9	non	non	ADJ
ejpam-4822	57	10	-	-	ADJ
ejpam-4822	57	11	negative	negative	ADJ
ejpam-4822	57	12	integer	integer	NOUN
ejpam-4822	57	13	solution	solution	NOUN
ejpam-4822	57	14	of	of	ADP
ejpam-4822	57	15	1+(p+n)x	1+(p+n)x	PROPN
ejpam-4822	57	16	=	=	SYM
ejpam-4822	57	17	z2	z2	PROPN
ejpam-4822	57	18	.	.	PUNCT
ejpam-4822	58	1	if	if	SCONJ
ejpam-4822	58	2	x	x	PROPN
ejpam-4822	58	3	=	=	SYM
ejpam-4822	58	4	0	0	NUM
ejpam-4822	58	5	,	,	PUNCT
ejpam-4822	58	6	then	then	ADV
ejpam-4822	58	7	z2	z2	PROPN
ejpam-4822	58	8	=	=	SYM
ejpam-4822	58	9	2	2	NUM
ejpam-4822	58	10	,	,	PUNCT
ejpam-4822	58	11	which	which	PRON
ejpam-4822	58	12	is	be	AUX
ejpam-4822	58	13	impossible	impossible	ADJ
ejpam-4822	58	14	.	.	PUNCT
ejpam-4822	59	1	if	if	SCONJ
ejpam-4822	59	2	x	x	PROPN
ejpam-4822	59	3	>	>	X
ejpam-4822	59	4	1	1	NUM
ejpam-4822	59	5	,	,	PUNCT
ejpam-4822	59	6	then	then	ADV
ejpam-4822	59	7	z	z	NOUN
ejpam-4822	59	8	>	>	X
ejpam-4822	59	9	1	1	X
ejpam-4822	59	10	.	.	PUNCT
ejpam-4822	60	1	by	by	ADP
ejpam-4822	60	2	catalan	catalan	PROPN
ejpam-4822	60	3	’s	’s	PART
ejpam-4822	60	4	conjecture	conjecture	NOUN
ejpam-4822	60	5	,	,	PUNCT
ejpam-4822	60	6	there	there	PRON
ejpam-4822	60	7	is	be	VERB
ejpam-4822	60	8	no	no	PRON
ejpam-4822	60	9	of	of	ADP
ejpam-4822	60	10	a	a	DET
ejpam-4822	60	11	non	non	ADJ
ejpam-4822	60	12	-	-	ADJ
ejpam-4822	60	13	negative	negative	ADJ
ejpam-4822	60	14	integer	integer	NOUN
ejpam-4822	60	15	solution	solution	NOUN
ejpam-4822	60	16	.	.	PUNCT
ejpam-4822	61	1	if	if	SCONJ
ejpam-4822	61	2	x	x	SYM
ejpam-4822	61	3	=	=	SYM
ejpam-4822	61	4	1	1	NUM
ejpam-4822	61	5	,	,	PUNCT
ejpam-4822	61	6	then	then	ADV
ejpam-4822	61	7	z2	z2	PROPN
ejpam-4822	61	8	=	=	PROPN
ejpam-4822	62	1	p	p	X
ejpam-4822	62	2	+	+	NOUN
ejpam-4822	62	3	n	n	PROPN
ejpam-4822	62	4	+	+	NOUN
ejpam-4822	62	5	1	1	NUM
ejpam-4822	62	6	.	.	PUNCT
ejpam-4822	63	1	so	so	ADV
ejpam-4822	63	2	z	z	NOUN
ejpam-4822	63	3	=	=	PUNCT
ejpam-4822	63	4	√	√	PROPN
ejpam-4822	63	5	p+	p+	ADJ
ejpam-4822	63	6	n+	n+	NOUN
ejpam-4822	63	7	1	1	X
ejpam-4822	63	8	.	.	PUNCT
ejpam-4822	64	1	this	this	PRON
ejpam-4822	64	2	means	mean	VERB
ejpam-4822	64	3	that	that	SCONJ
ejpam-4822	64	4	√	√	PROPN
ejpam-4822	64	5	p+	p+	PROPN
ejpam-4822	64	6	n+	n+	NUM
ejpam-4822	64	7	1	1	NUM
ejpam-4822	64	8	is	be	AUX
ejpam-4822	64	9	a	a	DET
ejpam-4822	64	10	non	non	ADJ
ejpam-4822	64	11	-	-	ADJ
ejpam-4822	64	12	negative	negative	ADJ
ejpam-4822	64	13	integer	integer	NOUN
ejpam-4822	64	14	as	as	SCONJ
ejpam-4822	64	15	z	z	PROPN
ejpam-4822	64	16	is	be	AUX
ejpam-4822	64	17	a	a	DET
ejpam-4822	64	18	non	non	ADJ
ejpam-4822	64	19	-	-	ADJ
ejpam-4822	64	20	negative	negative	ADJ
ejpam-4822	64	21	integer	integer	NOUN
ejpam-4822	64	22	.	.	PUNCT
ejpam-4822	65	1	theorem	theorem	NOUN
ejpam-4822	65	2	1	1	NUM
ejpam-4822	65	3	.	.	PUNCT
ejpam-4822	66	1	(	(	PUNCT
ejpam-4822	66	2	[	[	X
ejpam-4822	66	3	7	7	NUM
ejpam-4822	66	4	]	]	PUNCT
ejpam-4822	66	5	)	)	PUNCT
ejpam-4822	66	6	let	let	VERB
ejpam-4822	66	7	n	n	NOUN
ejpam-4822	66	8	=	=	SYM
ejpam-4822	66	9	4	4	NUM
ejpam-4822	66	10	and	and	CCONJ
ejpam-4822	66	11	p	p	NOUN
ejpam-4822	67	1	=	=	ADJ
ejpam-4822	67	2	3	3	X
ejpam-4822	67	3	.	.	PUNCT
ejpam-4822	68	1	the	the	DET
ejpam-4822	68	2	non	non	ADJ
ejpam-4822	68	3	-	-	ADJ
ejpam-4822	68	4	negative	negative	ADJ
ejpam-4822	68	5	integer	integer	NOUN
ejpam-4822	68	6	solutions	solution	NOUN
ejpam-4822	68	7	of	of	ADP
ejpam-4822	68	8	the	the	DET
ejpam-4822	68	9	diophantine	diophantine	NOUN
ejpam-4822	68	10	equation	equation	NOUN
ejpam-4822	68	11	(	(	PUNCT
ejpam-4822	68	12	p+	p+	NOUN
ejpam-4822	68	13	n)x	n)x	X
ejpam-4822	68	14	+	+	CCONJ
ejpam-4822	68	15	py	py	X
ejpam-4822	68	16	=	=	SYM
ejpam-4822	68	17	z2	z2	PROPN
ejpam-4822	68	18	are	be	AUX
ejpam-4822	68	19	(	(	PUNCT
ejpam-4822	68	20	x	x	NOUN
ejpam-4822	68	21	,	,	PUNCT
ejpam-4822	68	22	y	y	PROPN
ejpam-4822	68	23	,	,	PUNCT
ejpam-4822	68	24	z	z	NOUN
ejpam-4822	68	25	)	)	PUNCT
ejpam-4822	68	26	=	=	SYM
ejpam-4822	68	27	(	(	PUNCT
ejpam-4822	68	28	0	0	NUM
ejpam-4822	68	29	,	,	PUNCT
ejpam-4822	68	30	1	1	NUM
ejpam-4822	68	31	,	,	PUNCT
ejpam-4822	68	32	2	2	NUM
ejpam-4822	68	33	)	)	PUNCT
ejpam-4822	68	34	and	and	CCONJ
ejpam-4822	68	35	(	(	PUNCT
ejpam-4822	68	36	1	1	NUM
ejpam-4822	68	37	,	,	PUNCT
ejpam-4822	68	38	2	2	NUM
ejpam-4822	68	39	,	,	PUNCT
ejpam-4822	68	40	4	4	NUM
ejpam-4822	68	41	)	)	PUNCT
ejpam-4822	68	42	.	.	PUNCT
ejpam-4822	69	1	this	this	DET
ejpam-4822	69	2	theorem	theorem	NOUN
ejpam-4822	69	3	was	be	AUX
ejpam-4822	69	4	proved	prove	VERB
ejpam-4822	69	5	in	in	ADP
ejpam-4822	69	6	2017	2017	NUM
ejpam-4822	69	7	by	by	ADP
ejpam-4822	69	8	rao	rao	NOUN
ejpam-4822	70	1	[	[	X
ejpam-4822	70	2	7	7	NUM
ejpam-4822	70	3	]	]	PUNCT
ejpam-4822	70	4	.	.	PUNCT
ejpam-4822	71	1	3	3	X
ejpam-4822	71	2	.	.	X
ejpam-4822	71	3	main	main	ADJ
ejpam-4822	71	4	results	result	NOUN
ejpam-4822	71	5	in	in	ADP
ejpam-4822	71	6	theorem	theorem	NOUN
ejpam-4822	71	7	2	2	NUM
ejpam-4822	71	8	,	,	PUNCT
ejpam-4822	71	9	we	we	PRON
ejpam-4822	71	10	use	use	VERB
ejpam-4822	71	11	the	the	DET
ejpam-4822	71	12	same	same	ADJ
ejpam-4822	71	13	method	method	NOUN
ejpam-4822	71	14	of	of	ADP
ejpam-4822	71	15	proof	proof	NOUN
ejpam-4822	71	16	as	as	SCONJ
ejpam-4822	71	17	appeared	appear	VERB
ejpam-4822	71	18	in	in	ADP
ejpam-4822	71	19	[	[	X
ejpam-4822	71	20	1	1	NUM
ejpam-4822	71	21	,	,	PUNCT
ejpam-4822	71	22	2	2	NUM
ejpam-4822	71	23	]	]	PUNCT
ejpam-4822	71	24	to	to	PART
ejpam-4822	71	25	derive	derive	VERB
ejpam-4822	71	26	the	the	DET
ejpam-4822	71	27	result	result	NOUN
ejpam-4822	71	28	.	.	PUNCT
ejpam-4822	72	1	w.	w.	PROPN
ejpam-4822	72	2	orosram	orosram	PROPN
ejpam-4822	72	3	/	/	SYM
ejpam-4822	72	4	eur	eur	PROPN
ejpam-4822	72	5	.	.	PUNCT
ejpam-4822	73	1	j.	j.	PROPN
ejpam-4822	73	2	pure	pure	PROPN
ejpam-4822	73	3	appl	appl	PROPN
ejpam-4822	73	4	.	.	PROPN
ejpam-4822	73	5	math	math	PROPN
ejpam-4822	73	6	,	,	PUNCT
ejpam-4822	73	7	16	16	NUM
ejpam-4822	73	8	(	(	PUNCT
ejpam-4822	73	9	4	4	NUM
ejpam-4822	73	10	)	)	PUNCT
ejpam-4822	73	11	(	(	PUNCT
ejpam-4822	73	12	2023	2023	NUM
ejpam-4822	73	13	)	)	PUNCT
ejpam-4822	73	14	,	,	PUNCT
ejpam-4822	73	15	2208	2208	NUM
ejpam-4822	73	16	-	-	SYM
ejpam-4822	73	17	2212	2212	NUM
ejpam-4822	73	18	2210	2210	NUM
ejpam-4822	73	19	theorem	theorem	VERB
ejpam-4822	73	20	2	2	NUM
ejpam-4822	73	21	.	.	PUNCT
ejpam-4822	74	1	let	let	VERB
ejpam-4822	74	2	n	n	NOUN
ejpam-4822	74	3	and	and	CCONJ
ejpam-4822	74	4	p	p	NOUN
ejpam-4822	74	5	be	be	AUX
ejpam-4822	74	6	positive	positive	ADJ
ejpam-4822	74	7	integers	integer	NOUN
ejpam-4822	74	8	where	where	SCONJ
ejpam-4822	74	9	n	n	X
ejpam-4822	74	10	≡	≡	PROPN
ejpam-4822	74	11	0	0	PUNCT
ejpam-4822	74	12	(	(	PUNCT
ejpam-4822	74	13	mod	mod	PROPN
ejpam-4822	74	14	4	4	NUM
ejpam-4822	74	15	)	)	PUNCT
ejpam-4822	74	16	,	,	PUNCT
ejpam-4822	74	17	p	p	PROPN
ejpam-4822	74	18	≡	≡	PROPN
ejpam-4822	74	19	3	3	NUM
ejpam-4822	74	20	(	(	PUNCT
ejpam-4822	74	21	mod	mod	NOUN
ejpam-4822	74	22	4	4	NUM
ejpam-4822	74	23	)	)	PUNCT
ejpam-4822	74	24	and	and	CCONJ
ejpam-4822	74	25	p	p	X
ejpam-4822	74	26	>	>	X
ejpam-4822	74	27	3	3	NUM
ejpam-4822	74	28	such	such	ADJ
ejpam-4822	74	29	that	that	SCONJ
ejpam-4822	74	30	p	p	X
ejpam-4822	74	31	,	,	PUNCT
ejpam-4822	74	32	p+n	p+n	ADJ
ejpam-4822	74	33	,	,	PUNCT
ejpam-4822	74	34	n−1	n−1	PROPN
ejpam-4822	74	35	are	be	AUX
ejpam-4822	74	36	prime	prime	ADJ
ejpam-4822	74	37	numbers	number	NOUN
ejpam-4822	74	38	and	and	CCONJ
ejpam-4822	74	39	2n−1	2n−1	NUM
ejpam-4822	74	40	is	be	AUX
ejpam-4822	74	41	not	not	PART
ejpam-4822	74	42	a	a	DET
ejpam-4822	74	43	prime	prime	ADJ
ejpam-4822	74	44	number	number	NOUN
ejpam-4822	74	45	.	.	PUNCT
ejpam-4822	75	1	if	if	SCONJ
ejpam-4822	75	2	√	√	PRON
ejpam-4822	75	3	p+	p+	VERB
ejpam-4822	75	4	1	1	NUM
ejpam-4822	75	5	and	and	CCONJ
ejpam-4822	75	6	√	√	PROPN
ejpam-4822	75	7	p+	p+	PROPN
ejpam-4822	75	8	n+	n+	NUM
ejpam-4822	75	9	1	1	NUM
ejpam-4822	75	10	are	be	AUX
ejpam-4822	75	11	integers	integer	NOUN
ejpam-4822	75	12	,	,	PUNCT
ejpam-4822	75	13	then	then	ADV
ejpam-4822	75	14	all	all	PRON
ejpam-4822	75	15	of	of	ADP
ejpam-4822	75	16	the	the	DET
ejpam-4822	75	17	non	non	ADJ
ejpam-4822	75	18	-	-	ADJ
ejpam-4822	75	19	negative	negative	ADJ
ejpam-4822	75	20	integer	integer	NOUN
ejpam-4822	75	21	solutions	solution	NOUN
ejpam-4822	75	22	of	of	ADP
ejpam-4822	75	23	the	the	DET
ejpam-4822	75	24	diophantine	diophantine	NOUN
ejpam-4822	75	25	equation	equation	NOUN
ejpam-4822	75	26	(	(	PUNCT
ejpam-4822	75	27	p+n)x+py	p+n)x+py	PROPN
ejpam-4822	75	28	=	=	SYM
ejpam-4822	75	29	z2	z2	PROPN
ejpam-4822	75	30	are	be	AUX
ejpam-4822	75	31	given	give	VERB
ejpam-4822	75	32	by	by	ADP
ejpam-4822	75	33	(	(	PUNCT
ejpam-4822	75	34	x	x	PROPN
ejpam-4822	75	35	,	,	PUNCT
ejpam-4822	75	36	y	y	PROPN
ejpam-4822	75	37	,	,	PUNCT
ejpam-4822	75	38	z	z	NOUN
ejpam-4822	75	39	)	)	PUNCT
ejpam-4822	75	40	∈	∈	NOUN
ejpam-4822	75	41	{	{	PUNCT
ejpam-4822	75	42	(	(	PUNCT
ejpam-4822	75	43	0	0	NUM
ejpam-4822	75	44	,	,	PUNCT
ejpam-4822	75	45	1	1	NUM
ejpam-4822	75	46	,	,	PUNCT
ejpam-4822	75	47	√	√	PROPN
ejpam-4822	75	48	p+	p+	ADJ
ejpam-4822	75	49	1	1	NUM
ejpam-4822	75	50	)	)	PUNCT
ejpam-4822	75	51	,	,	PUNCT
ejpam-4822	75	52	(	(	PUNCT
ejpam-4822	75	53	1	1	NUM
ejpam-4822	75	54	,	,	PUNCT
ejpam-4822	75	55	0	0	NUM
ejpam-4822	75	56	,	,	PUNCT
ejpam-4822	75	57	√	√	PROPN
ejpam-4822	75	58	p+	p+	ADJ
ejpam-4822	75	59	n+	n+	NOUN
ejpam-4822	75	60	1	1	NUM
ejpam-4822	75	61	)	)	PUNCT
ejpam-4822	75	62	}	}	PUNCT
ejpam-4822	75	63	,	,	PUNCT
ejpam-4822	75	64	where	where	SCONJ
ejpam-4822	75	65	x	x	X
ejpam-4822	75	66	,	,	PUNCT
ejpam-4822	75	67	y	y	PROPN
ejpam-4822	75	68	and	and	CCONJ
ejpam-4822	75	69	z	z	PROPN
ejpam-4822	75	70	are	be	AUX
ejpam-4822	75	71	non	non	ADJ
ejpam-4822	75	72	-	-	ADJ
ejpam-4822	75	73	negative	negative	ADJ
ejpam-4822	75	74	integer	integer	NOUN
ejpam-4822	75	75	.	.	PUNCT
ejpam-4822	76	1	proof	proof	NOUN
ejpam-4822	76	2	.	.	PUNCT
ejpam-4822	77	1	let	let	AUX
ejpam-4822	77	2	(	(	PUNCT
ejpam-4822	77	3	x	x	X
ejpam-4822	77	4	,	,	PUNCT
ejpam-4822	77	5	y	y	PROPN
ejpam-4822	77	6	,	,	PUNCT
ejpam-4822	77	7	z	z	NOUN
ejpam-4822	77	8	)	)	PUNCT
ejpam-4822	77	9	be	be	AUX
ejpam-4822	77	10	a	a	DET
ejpam-4822	77	11	non	non	ADJ
ejpam-4822	77	12	-	-	ADJ
ejpam-4822	77	13	negative	negative	ADJ
ejpam-4822	77	14	integer	integer	NOUN
ejpam-4822	77	15	solution	solution	NOUN
ejpam-4822	77	16	of	of	ADP
ejpam-4822	77	17	(	(	PUNCT
ejpam-4822	77	18	p	p	X
ejpam-4822	77	19	+	+	PROPN
ejpam-4822	77	20	n)x	n)x	NOUN
ejpam-4822	78	1	+	+	CCONJ
ejpam-4822	78	2	py	py	X
ejpam-4822	78	3	=	=	SYM
ejpam-4822	78	4	z2	z2	PROPN
ejpam-4822	78	5	.	.	PUNCT
ejpam-4822	79	1	if	if	SCONJ
ejpam-4822	79	2	x	x	PROPN
ejpam-4822	79	3	=	=	SYM
ejpam-4822	79	4	0	0	NUM
ejpam-4822	79	5	or	or	CCONJ
ejpam-4822	79	6	y	y	PROPN
ejpam-4822	79	7	=	=	SYM
ejpam-4822	79	8	0	0	PROPN
ejpam-4822	79	9	,	,	PUNCT
ejpam-4822	79	10	then	then	ADV
ejpam-4822	79	11	(	(	PUNCT
ejpam-4822	79	12	x	x	X
ejpam-4822	79	13	,	,	PUNCT
ejpam-4822	79	14	y	y	PROPN
ejpam-4822	79	15	,	,	PUNCT
ejpam-4822	79	16	z	z	NOUN
ejpam-4822	79	17	)	)	PUNCT
ejpam-4822	79	18	=	=	SYM
ejpam-4822	79	19	(	(	PUNCT
ejpam-4822	79	20	0	0	NUM
ejpam-4822	79	21	,	,	PUNCT
ejpam-4822	79	22	1	1	NUM
ejpam-4822	79	23	,	,	PUNCT
ejpam-4822	79	24	√	√	PROPN
ejpam-4822	79	25	p+	p+	VERB
ejpam-4822	79	26	1	1	NUM
ejpam-4822	79	27	)	)	PUNCT
ejpam-4822	79	28	or	or	CCONJ
ejpam-4822	79	29	(	(	PUNCT
ejpam-4822	79	30	x	x	X
ejpam-4822	79	31	,	,	PUNCT
ejpam-4822	79	32	y	y	PROPN
ejpam-4822	79	33	,	,	PUNCT
ejpam-4822	79	34	z	z	NOUN
ejpam-4822	79	35	)	)	PUNCT
ejpam-4822	79	36	=	=	SYM
ejpam-4822	79	37	(	(	PUNCT
ejpam-4822	79	38	1	1	NUM
ejpam-4822	79	39	,	,	PUNCT
ejpam-4822	79	40	0	0	NUM
ejpam-4822	79	41	,	,	PUNCT
ejpam-4822	80	1	√	√	PROPN
ejpam-4822	80	2	p+	p+	ADJ
ejpam-4822	80	3	n+	n+	NOUN
ejpam-4822	80	4	1	1	NUM
ejpam-4822	80	5	)	)	PUNCT
ejpam-4822	80	6	by	by	ADP
ejpam-4822	80	7	lemma	lemma	PROPN
ejpam-4822	80	8	1	1	NUM
ejpam-4822	80	9	and	and	CCONJ
ejpam-4822	80	10	lemma	lemma	PROPN
ejpam-4822	80	11	2	2	NUM
ejpam-4822	80	12	.	.	PUNCT
ejpam-4822	81	1	now	now	ADV
ejpam-4822	81	2	,	,	PUNCT
ejpam-4822	81	3	we	we	PRON
ejpam-4822	81	4	suppose	suppose	VERB
ejpam-4822	81	5	x	x	PUNCT
ejpam-4822	81	6	>	>	X
ejpam-4822	81	7	0	0	PUNCT
ejpam-4822	81	8	and	and	CCONJ
ejpam-4822	81	9	y	y	PROPN
ejpam-4822	81	10	>	>	X
ejpam-4822	81	11	0	0	X
ejpam-4822	81	12	.	.	PUNCT
ejpam-4822	82	1	we	we	PRON
ejpam-4822	82	2	consider	consider	VERB
ejpam-4822	82	3	the	the	DET
ejpam-4822	82	4	following	follow	VERB
ejpam-4822	82	5	cases	case	NOUN
ejpam-4822	82	6	.	.	PUNCT
ejpam-4822	83	1	if	if	SCONJ
ejpam-4822	83	2	x	x	PRON
ejpam-4822	83	3	and	and	CCONJ
ejpam-4822	83	4	y	y	PROPN
ejpam-4822	83	5	are	be	AUX
ejpam-4822	83	6	even	even	ADV
ejpam-4822	83	7	,	,	PUNCT
ejpam-4822	83	8	then	then	ADV
ejpam-4822	83	9	(	(	PUNCT
ejpam-4822	83	10	p+n)x	p+n)x	PROPN
ejpam-4822	83	11	≡	≡	PROPN
ejpam-4822	83	12	1	1	NUM
ejpam-4822	83	13	(	(	PUNCT
ejpam-4822	83	14	mod	mod	NOUN
ejpam-4822	83	15	4	4	NUM
ejpam-4822	83	16	)	)	PUNCT
ejpam-4822	83	17	and	and	CCONJ
ejpam-4822	83	18	py	py	PROPN
ejpam-4822	83	19	≡	≡	PROPN
ejpam-4822	83	20	1	1	NUM
ejpam-4822	83	21	(	(	PUNCT
ejpam-4822	83	22	mod	mod	NOUN
ejpam-4822	83	23	4	4	NUM
ejpam-4822	83	24	)	)	PUNCT
ejpam-4822	83	25	.	.	PUNCT
ejpam-4822	84	1	thus	thus	ADV
ejpam-4822	84	2	(	(	PUNCT
ejpam-4822	84	3	p+n)x+py	p+n)x+py	NOUN
ejpam-4822	84	4	≡	≡	PROPN
ejpam-4822	84	5	2	2	NUM
ejpam-4822	84	6	(	(	PUNCT
ejpam-4822	84	7	mod	mod	NOUN
ejpam-4822	84	8	4	4	NUM
ejpam-4822	84	9	)	)	PUNCT
ejpam-4822	84	10	which	which	PRON
ejpam-4822	84	11	is	be	AUX
ejpam-4822	84	12	impossible	impossible	ADJ
ejpam-4822	84	13	since	since	SCONJ
ejpam-4822	84	14	z2	z2	PROPN
ejpam-4822	84	15	≡	≡	PROPN
ejpam-4822	84	16	0	0	NUM
ejpam-4822	84	17	,	,	PUNCT
ejpam-4822	84	18	1	1	NUM
ejpam-4822	84	19	(	(	PUNCT
ejpam-4822	84	20	mod	mod	NOUN
ejpam-4822	84	21	4	4	NUM
ejpam-4822	84	22	)	)	PUNCT
ejpam-4822	84	23	.	.	PUNCT
ejpam-4822	85	1	if	if	SCONJ
ejpam-4822	85	2	x	x	PRON
ejpam-4822	85	3	and	and	CCONJ
ejpam-4822	85	4	y	y	PROPN
ejpam-4822	85	5	are	be	AUX
ejpam-4822	85	6	odd	odd	ADJ
ejpam-4822	85	7	,	,	PUNCT
ejpam-4822	85	8	then	then	ADV
ejpam-4822	85	9	(	(	PUNCT
ejpam-4822	85	10	p+n)x	p+n)x	PROPN
ejpam-4822	85	11	≡	≡	PROPN
ejpam-4822	85	12	3	3	NUM
ejpam-4822	85	13	(	(	PUNCT
ejpam-4822	85	14	mod	mod	NOUN
ejpam-4822	85	15	4	4	NUM
ejpam-4822	85	16	)	)	PUNCT
ejpam-4822	85	17	and	and	CCONJ
ejpam-4822	85	18	py	py	PROPN
ejpam-4822	85	19	≡	≡	PROPN
ejpam-4822	85	20	3	3	NUM
ejpam-4822	85	21	(	(	PUNCT
ejpam-4822	85	22	mod	mod	NOUN
ejpam-4822	85	23	4	4	NUM
ejpam-4822	85	24	)	)	PUNCT
ejpam-4822	85	25	.	.	PUNCT
ejpam-4822	86	1	thus	thus	ADV
ejpam-4822	86	2	(	(	PUNCT
ejpam-4822	86	3	p+	p+	NOUN
ejpam-4822	86	4	n)x	n)x	X
ejpam-4822	87	1	+	+	CCONJ
ejpam-4822	87	2	py	py	X
ejpam-4822	87	3	≡	≡	PROPN
ejpam-4822	87	4	2	2	NUM
ejpam-4822	87	5	(	(	PUNCT
ejpam-4822	87	6	mod	mod	NOUN
ejpam-4822	87	7	4	4	NUM
ejpam-4822	87	8	)	)	PUNCT
ejpam-4822	87	9	which	which	PRON
ejpam-4822	87	10	is	be	AUX
ejpam-4822	87	11	impossible	impossible	ADJ
ejpam-4822	87	12	since	since	SCONJ
ejpam-4822	87	13	z2	z2	PROPN
ejpam-4822	87	14	≡	≡	PROPN
ejpam-4822	87	15	0	0	NUM
ejpam-4822	87	16	,	,	PUNCT
ejpam-4822	87	17	1	1	NUM
ejpam-4822	87	18	(	(	PUNCT
ejpam-4822	87	19	mod	mod	NOUN
ejpam-4822	87	20	4	4	NUM
ejpam-4822	87	21	)	)	PUNCT
ejpam-4822	87	22	.	.	PUNCT
ejpam-4822	88	1	now	now	ADV
ejpam-4822	88	2	,	,	PUNCT
ejpam-4822	88	3	there	there	PRON
ejpam-4822	88	4	are	be	VERB
ejpam-4822	88	5	two	two	NUM
ejpam-4822	88	6	remaining	remain	VERB
ejpam-4822	88	7	cases	case	NOUN
ejpam-4822	88	8	to	to	PART
ejpam-4822	88	9	be	be	AUX
ejpam-4822	88	10	considered	consider	VERB
ejpam-4822	88	11	.	.	PUNCT
ejpam-4822	89	1	case	case	NOUN
ejpam-4822	89	2	1	1	NUM
ejpam-4822	89	3	.	.	PUNCT
ejpam-4822	90	1	x	x	PRON
ejpam-4822	90	2	is	be	AUX
ejpam-4822	90	3	even	even	ADV
ejpam-4822	90	4	and	and	CCONJ
ejpam-4822	90	5	y	y	PROPN
ejpam-4822	90	6	is	be	AUX
ejpam-4822	90	7	odd	odd	ADJ
ejpam-4822	90	8	.	.	PUNCT
ejpam-4822	91	1	there	there	PRON
ejpam-4822	91	2	exist	exist	VERB
ejpam-4822	91	3	k	k	PROPN
ejpam-4822	91	4	≥	≥	NUM
ejpam-4822	91	5	1	1	NUM
ejpam-4822	91	6	and	and	CCONJ
ejpam-4822	91	7	s	s	X
ejpam-4822	91	8	≥	≥	NOUN
ejpam-4822	91	9	0	0	NUM
ejpam-4822	91	10	such	such	ADJ
ejpam-4822	91	11	that	that	SCONJ
ejpam-4822	91	12	x	x	X
ejpam-4822	91	13	=	=	SYM
ejpam-4822	91	14	2k	2k	NUM
ejpam-4822	91	15	,	,	PUNCT
ejpam-4822	91	16	y	y	PROPN
ejpam-4822	91	17	=	=	SYM
ejpam-4822	91	18	2s+1	2s+1	PROPN
ejpam-4822	91	19	.	.	PUNCT
ejpam-4822	92	1	we	we	PRON
ejpam-4822	92	2	have	have	VERB
ejpam-4822	92	3	(	(	PUNCT
ejpam-4822	92	4	p+n)2k+p2s+1	p+n)2k+p2s+1	NOUN
ejpam-4822	92	5	=	=	SYM
ejpam-4822	92	6	z2	z2	PROPN
ejpam-4822	92	7	,	,	PUNCT
ejpam-4822	92	8	which	which	PRON
ejpam-4822	92	9	can	can	AUX
ejpam-4822	92	10	be	be	AUX
ejpam-4822	92	11	rewritten	rewrite	VERB
ejpam-4822	92	12	as	as	ADP
ejpam-4822	92	13	p2s+1	p2s+1	NOUN
ejpam-4822	92	14	=	=	SYM
ejpam-4822	92	15	z2	z2	PROPN
ejpam-4822	92	16	−	−	PROPN
ejpam-4822	92	17	(	(	PUNCT
ejpam-4822	92	18	p+	p+	NOUN
ejpam-4822	92	19	n)2k	n)2k	ADJ
ejpam-4822	92	20	=	=	PUNCT
ejpam-4822	92	21	[	[	PUNCT
ejpam-4822	92	22	z	z	NOUN
ejpam-4822	92	23	−	−	PROPN
ejpam-4822	92	24	(	(	PUNCT
ejpam-4822	92	25	p+	p+	X
ejpam-4822	92	26	n)k	n)k	X
ejpam-4822	92	27	]	]	PUNCT
ejpam-4822	93	1	[	[	PUNCT
ejpam-4822	93	2	z	z	X
ejpam-4822	93	3	+	+	CCONJ
ejpam-4822	93	4	(	(	PUNCT
ejpam-4822	93	5	p+	p+	X
ejpam-4822	93	6	n)k	n)k	X
ejpam-4822	93	7	]	]	PUNCT
ejpam-4822	93	8	.	.	PUNCT
ejpam-4822	94	1	thus	thus	ADV
ejpam-4822	94	2	,	,	PUNCT
ejpam-4822	94	3	there	there	PRON
ejpam-4822	94	4	exist	exist	VERB
ejpam-4822	94	5	non	non	ADJ
ejpam-4822	94	6	-	-	ADJ
ejpam-4822	94	7	negative	negative	ADJ
ejpam-4822	94	8	integers	integer	NOUN
ejpam-4822	94	9	α	α	NOUN
ejpam-4822	94	10	,	,	PUNCT
ejpam-4822	94	11	β	β	VERB
ejpam-4822	94	12	that	that	SCONJ
ejpam-4822	94	13	pα	pα	NOUN
ejpam-4822	94	14	=	=	SYM
ejpam-4822	94	15	z−	z−	X
ejpam-4822	94	16	(	(	PUNCT
ejpam-4822	94	17	p+	p+	X
ejpam-4822	94	18	n)k	n)k	ADJ
ejpam-4822	94	19	and	and	CCONJ
ejpam-4822	94	20	pβ	pβ	PROPN
ejpam-4822	94	21	=	=	PUNCT
ejpam-4822	94	22	z+(p+	z+(p+	PROPN
ejpam-4822	94	23	n)k	n)k	ADV
ejpam-4822	94	24	,	,	PUNCT
ejpam-4822	94	25	where	where	SCONJ
ejpam-4822	94	26	α	α	PRON
ejpam-4822	94	27	<	<	X
ejpam-4822	94	28	β	β	X
ejpam-4822	94	29	and	and	CCONJ
ejpam-4822	94	30	α+	α+	X
ejpam-4822	94	31	β	β	X
ejpam-4822	94	32	=	=	SYM
ejpam-4822	94	33	2s+	2s+	NUM
ejpam-4822	95	1	1	1	NUM
ejpam-4822	95	2	.	.	PUNCT
ejpam-4822	96	1	hence	hence	ADV
ejpam-4822	96	2	2	2	NUM
ejpam-4822	96	3	(	(	PUNCT
ejpam-4822	96	4	p+	p+	X
ejpam-4822	96	5	n)k	n)k	X
ejpam-4822	96	6	=	=	SYM
ejpam-4822	96	7	pα	pα	X
ejpam-4822	96	8	[	[	PUNCT
ejpam-4822	96	9	pβ−α	pβ−α	NOUN
ejpam-4822	96	10	−	−	PROPN
ejpam-4822	96	11	1	1	NUM
ejpam-4822	96	12	]	]	PUNCT
ejpam-4822	96	13	.	.	PUNCT
ejpam-4822	97	1	if	if	SCONJ
ejpam-4822	97	2	α	α	PRON
ejpam-4822	97	3	≥	≥	NUM
ejpam-4822	97	4	1	1	NUM
ejpam-4822	97	5	,	,	PUNCT
ejpam-4822	97	6	then	then	ADV
ejpam-4822	97	7	p	p	NOUN
ejpam-4822	97	8	|	|	NOUN
ejpam-4822	97	9	(	(	PUNCT
ejpam-4822	97	10	p	p	NOUN
ejpam-4822	97	11	+	+	NOUN
ejpam-4822	97	12	n	n	CCONJ
ejpam-4822	97	13	)	)	PUNCT
ejpam-4822	97	14	which	which	PRON
ejpam-4822	97	15	is	be	AUX
ejpam-4822	97	16	impossible	impossible	ADJ
ejpam-4822	97	17	since	since	SCONJ
ejpam-4822	97	18	p	p	NOUN
ejpam-4822	97	19	and	and	CCONJ
ejpam-4822	97	20	p	p	NOUN
ejpam-4822	98	1	+	+	CCONJ
ejpam-4822	98	2	n	n	CCONJ
ejpam-4822	98	3	are	be	AUX
ejpam-4822	98	4	different	different	ADJ
ejpam-4822	98	5	primes	prime	NOUN
ejpam-4822	98	6	.	.	PUNCT
ejpam-4822	99	1	in	in	ADP
ejpam-4822	99	2	case	case	NOUN
ejpam-4822	99	3	α	α	X
ejpam-4822	99	4	=	=	SYM
ejpam-4822	99	5	0	0	NUM
ejpam-4822	99	6	,	,	PUNCT
ejpam-4822	99	7	we	we	PRON
ejpam-4822	99	8	have	have	VERB
ejpam-4822	99	9	2(p	2(p	NUM
ejpam-4822	99	10	+	+	CCONJ
ejpam-4822	99	11	n)k	n)k	ADJ
ejpam-4822	99	12	=	=	PUNCT
ejpam-4822	99	13	p2s+1	p2s+1	NOUN
ejpam-4822	99	14	−	−	NOUN
ejpam-4822	99	15	1	1	NUM
ejpam-4822	99	16	.	.	PUNCT
ejpam-4822	100	1	if	if	SCONJ
ejpam-4822	100	2	s	s	NOUN
ejpam-4822	100	3	=	=	NOUN
ejpam-4822	100	4	0	0	NUM
ejpam-4822	100	5	,	,	PUNCT
ejpam-4822	100	6	then	then	ADV
ejpam-4822	100	7	2(p	2(p	NUM
ejpam-4822	101	1	+	+	CCONJ
ejpam-4822	101	2	n)k	n)k	X
ejpam-4822	101	3	+	+	CCONJ
ejpam-4822	101	4	1	1	NUM
ejpam-4822	101	5	=	=	SYM
ejpam-4822	101	6	p	p	NOUN
ejpam-4822	101	7	which	which	PRON
ejpam-4822	101	8	is	be	AUX
ejpam-4822	101	9	impossible	impossible	ADJ
ejpam-4822	101	10	.	.	PUNCT
ejpam-4822	102	1	if	if	SCONJ
ejpam-4822	102	2	s	s	X
ejpam-4822	102	3	≥	≥	NOUN
ejpam-4822	102	4	1	1	NUM
ejpam-4822	102	5	,	,	PUNCT
ejpam-4822	102	6	then	then	ADV
ejpam-4822	102	7	we	we	PRON
ejpam-4822	102	8	have	have	VERB
ejpam-4822	102	9	2(p+	2(p+	NUM
ejpam-4822	102	10	n)k	n)k	ADJ
ejpam-4822	103	1	=	=	X
ejpam-4822	103	2	(	(	PUNCT
ejpam-4822	103	3	p−	p−	NOUN
ejpam-4822	103	4	1	1	NUM
ejpam-4822	103	5	)	)	PUNCT
ejpam-4822	103	6	[	[	PUNCT
ejpam-4822	103	7	p2s	p2	NOUN
ejpam-4822	103	8	+	+	CCONJ
ejpam-4822	103	9	p2s−1	p2s−1	NOUN
ejpam-4822	103	10	+	+	CCONJ
ejpam-4822	103	11	·	·	PUNCT
ejpam-4822	103	12	·	·	PUNCT
ejpam-4822	103	13	·	·	PUNCT
ejpam-4822	103	14	+	+	X
ejpam-4822	103	15	p+	p+	VERB
ejpam-4822	103	16	1	1	NUM
ejpam-4822	103	17	]	]	PUNCT
ejpam-4822	103	18	.	.	PUNCT
ejpam-4822	104	1	since	since	SCONJ
ejpam-4822	104	2	p−1	p−1	PROPN
ejpam-4822	104	3	is	be	AUX
ejpam-4822	104	4	even	even	ADV
ejpam-4822	104	5	and	and	CCONJ
ejpam-4822	104	6	p2s+p2s−1	p2s+p2s−1	NUM
ejpam-4822	104	7	+	+	PROPN
ejpam-4822	104	8	·	·	PUNCT
ejpam-4822	104	9	·	·	PUNCT
ejpam-4822	104	10	·	·	PUNCT
ejpam-4822	104	11	+	+	X
ejpam-4822	104	12	p+1	p+1	PROPN
ejpam-4822	104	13	is	be	AUX
ejpam-4822	104	14	odd	odd	ADJ
ejpam-4822	104	15	,	,	PUNCT
ejpam-4822	104	16	it	it	PRON
ejpam-4822	104	17	follows	follow	VERB
ejpam-4822	104	18	that	that	SCONJ
ejpam-4822	104	19	p−1	p−1	PROPN
ejpam-4822	104	20	is	be	AUX
ejpam-4822	104	21	an	an	DET
ejpam-4822	104	22	even	even	ADV
ejpam-4822	104	23	positive	positive	ADJ
ejpam-4822	104	24	divisor	divisor	NOUN
ejpam-4822	104	25	of	of	ADP
ejpam-4822	104	26	2(p	2(p	NUM
ejpam-4822	104	27	+	+	CCONJ
ejpam-4822	104	28	n)k	n)k	ADV
ejpam-4822	104	29	that	that	PRON
ejpam-4822	104	30	is	be	AUX
ejpam-4822	104	31	p	p	NOUN
ejpam-4822	104	32	−	−	PROPN
ejpam-4822	104	33	1	1	NUM
ejpam-4822	104	34	=	=	SYM
ejpam-4822	104	35	2	2	NUM
ejpam-4822	104	36	(	(	PUNCT
ejpam-4822	104	37	p+	p+	NOUN
ejpam-4822	104	38	n)j	n)j	ADJ
ejpam-4822	104	39	,	,	PUNCT
ejpam-4822	104	40	for	for	ADP
ejpam-4822	104	41	some	some	DET
ejpam-4822	104	42	integer	integer	NOUN
ejpam-4822	104	43	j	j	PROPN
ejpam-4822	104	44	such	such	ADJ
ejpam-4822	104	45	that	that	SCONJ
ejpam-4822	104	46	0	0	NUM
ejpam-4822	104	47	≤	≤	NUM
ejpam-4822	104	48	j	j	PROPN
ejpam-4822	104	49	<	<	X
ejpam-4822	104	50	k.	k.	PROPN
ejpam-4822	105	1	if	if	SCONJ
ejpam-4822	105	2	j	j	PROPN
ejpam-4822	105	3	=	=	SYM
ejpam-4822	105	4	0	0	PROPN
ejpam-4822	105	5	,	,	PUNCT
ejpam-4822	105	6	then	then	ADV
ejpam-4822	105	7	p	p	NOUN
ejpam-4822	105	8	=	=	PROPN
ejpam-4822	105	9	3	3	NUM
ejpam-4822	105	10	which	which	PRON
ejpam-4822	105	11	contradicts	contradict	VERB
ejpam-4822	105	12	p	p	PROPN
ejpam-4822	105	13	>	>	X
ejpam-4822	105	14	3	3	NUM
ejpam-4822	105	15	.	.	PUNCT
ejpam-4822	106	1	if	if	SCONJ
ejpam-4822	106	2	1	1	NUM
ejpam-4822	106	3	≤	≤	NUM
ejpam-4822	106	4	j	j	NOUN
ejpam-4822	106	5	<	<	X
ejpam-4822	106	6	k	k	PROPN
ejpam-4822	106	7	,	,	PUNCT
ejpam-4822	106	8	then	then	ADV
ejpam-4822	106	9	2(p+	2(p+	NUM
ejpam-4822	106	10	n)j	n)j	X
ejpam-4822	106	11	+	+	CCONJ
ejpam-4822	106	12	1	1	X
ejpam-4822	106	13	=	=	SYM
ejpam-4822	106	14	p	p	NOUN
ejpam-4822	106	15	which	which	PRON
ejpam-4822	106	16	is	be	AUX
ejpam-4822	106	17	also	also	ADV
ejpam-4822	106	18	impossible	impossible	ADJ
ejpam-4822	106	19	.	.	PUNCT
ejpam-4822	107	1	case	case	NOUN
ejpam-4822	107	2	2	2	NUM
ejpam-4822	107	3	.	.	NUM
ejpam-4822	107	4	x	x	X
ejpam-4822	107	5	is	be	AUX
ejpam-4822	107	6	odd	odd	ADJ
ejpam-4822	107	7	and	and	CCONJ
ejpam-4822	107	8	y	y	PROPN
ejpam-4822	107	9	is	be	AUX
ejpam-4822	107	10	even	even	ADV
ejpam-4822	107	11	.	.	PUNCT
ejpam-4822	108	1	there	there	PRON
ejpam-4822	108	2	exist	exist	VERB
ejpam-4822	108	3	k	k	PROPN
ejpam-4822	108	4	≥	≥	X
ejpam-4822	108	5	0	0	NUM
ejpam-4822	108	6	and	and	CCONJ
ejpam-4822	108	7	s	s	X
ejpam-4822	108	8	≥	≥	NOUN
ejpam-4822	108	9	1	1	NUM
ejpam-4822	108	10	such	such	ADJ
ejpam-4822	108	11	that	that	PRON
ejpam-4822	108	12	x	x	X
ejpam-4822	108	13	=	=	PUNCT
ejpam-4822	108	14	2k	2k	NUM
ejpam-4822	108	15	+	+	CCONJ
ejpam-4822	108	16	1	1	NUM
ejpam-4822	108	17	and	and	CCONJ
ejpam-4822	108	18	y	y	NOUN
ejpam-4822	108	19	=	=	SYM
ejpam-4822	109	1	2s	2s	X
ejpam-4822	109	2	.	.	PUNCT
ejpam-4822	110	1	we	we	PRON
ejpam-4822	110	2	now	now	ADV
ejpam-4822	110	3	have	have	VERB
ejpam-4822	110	4	(	(	PUNCT
ejpam-4822	110	5	p+	p+	NOUN
ejpam-4822	110	6	n)2k+1	n)2k+1	ADJ
ejpam-4822	110	7	+	+	NUM
ejpam-4822	110	8	(	(	PUNCT
ejpam-4822	110	9	p)2s	p)2	NOUN
ejpam-4822	110	10	=	=	SYM
ejpam-4822	110	11	z2	z2	PROPN
ejpam-4822	110	12	,	,	PUNCT
ejpam-4822	110	13	which	which	PRON
ejpam-4822	110	14	can	can	AUX
ejpam-4822	110	15	be	be	AUX
ejpam-4822	110	16	rewritten	rewrite	VERB
ejpam-4822	110	17	as	as	ADP
ejpam-4822	110	18	(	(	PUNCT
ejpam-4822	110	19	p+	p+	NOUN
ejpam-4822	111	1	n)2k+1	n)2k+1	ADJ
ejpam-4822	111	2	=	=	SYM
ejpam-4822	111	3	z2	z2	PROPN
ejpam-4822	111	4	−	−	PROPN
ejpam-4822	111	5	p2s	p2s	PROPN
ejpam-4822	111	6	=	=	SYM
ejpam-4822	111	7	(	(	PUNCT
ejpam-4822	111	8	z	z	NOUN
ejpam-4822	111	9	+	+	NOUN
ejpam-4822	111	10	ps	ps	NOUN
ejpam-4822	111	11	)	)	PUNCT
ejpam-4822	111	12	(	(	PUNCT
ejpam-4822	111	13	z	z	NOUN
ejpam-4822	111	14	−	−	PROPN
ejpam-4822	111	15	ps	ps	PROPN
ejpam-4822	111	16	)	)	PUNCT
ejpam-4822	111	17	.	.	PUNCT
ejpam-4822	112	1	thus	thus	ADV
ejpam-4822	112	2	,	,	PUNCT
ejpam-4822	112	3	there	there	PRON
ejpam-4822	112	4	exist	exist	VERB
ejpam-4822	112	5	non	non	ADJ
ejpam-4822	112	6	-	-	ADJ
ejpam-4822	112	7	negative	negative	ADJ
ejpam-4822	112	8	integers	integer	NOUN
ejpam-4822	112	9	α	α	NOUN
ejpam-4822	112	10	,	,	PUNCT
ejpam-4822	112	11	β	β	VERB
ejpam-4822	112	12	such	such	ADJ
ejpam-4822	112	13	that	that	PRON
ejpam-4822	112	14	(	(	PUNCT
ejpam-4822	112	15	p+	p+	NOUN
ejpam-4822	112	16	n)α	n)α	X
ejpam-4822	112	17	=	=	SYM
ejpam-4822	112	18	z	z	NOUN
ejpam-4822	112	19	−	−	PROPN
ejpam-4822	112	20	ps	ps	INTJ
ejpam-4822	112	21	and	and	CCONJ
ejpam-4822	112	22	(	(	PUNCT
ejpam-4822	112	23	p+	p+	NOUN
ejpam-4822	112	24	n)β	n)β	NOUN
ejpam-4822	112	25	=	=	SYM
ejpam-4822	112	26	z	z	PROPN
ejpam-4822	112	27	+	+	NUM
ejpam-4822	112	28	ps	ps	PROPN
ejpam-4822	112	29	,	,	PUNCT
ejpam-4822	112	30	where	where	SCONJ
ejpam-4822	112	31	α	α	X
ejpam-4822	112	32	<	<	X
ejpam-4822	112	33	β	β	X
ejpam-4822	112	34	and	and	CCONJ
ejpam-4822	112	35	α+	α+	X
ejpam-4822	112	36	β	β	X
ejpam-4822	112	37	=	=	SYM
ejpam-4822	112	38	2k	2k	NUM
ejpam-4822	112	39	+	+	CCONJ
ejpam-4822	112	40	1	1	X
ejpam-4822	112	41	.	.	PUNCT
ejpam-4822	112	42	then	then	ADV
ejpam-4822	112	43	2ps	2ps	NOUN
ejpam-4822	112	44	=	=	SYM
ejpam-4822	112	45	(	(	PUNCT
ejpam-4822	112	46	p+	p+	X
ejpam-4822	112	47	n)α	n)α	X
ejpam-4822	112	48	[	[	PUNCT
ejpam-4822	112	49	(	(	PUNCT
ejpam-4822	112	50	p+	p+	NOUN
ejpam-4822	112	51	n)β−α	n)β−α	NOUN
ejpam-4822	112	52	−	−	NOUN
ejpam-4822	112	53	1	1	NUM
ejpam-4822	112	54	]	]	PUNCT
ejpam-4822	112	55	.	.	PUNCT
ejpam-4822	113	1	w.	w.	PROPN
ejpam-4822	113	2	orosram	orosram	PROPN
ejpam-4822	113	3	/	/	SYM
ejpam-4822	113	4	eur	eur	PROPN
ejpam-4822	113	5	.	.	PUNCT
ejpam-4822	114	1	j.	j.	PROPN
ejpam-4822	114	2	pure	pure	PROPN
ejpam-4822	114	3	appl	appl	PROPN
ejpam-4822	114	4	.	.	PROPN
ejpam-4822	114	5	math	math	PROPN
ejpam-4822	114	6	,	,	PUNCT
ejpam-4822	114	7	16	16	NUM
ejpam-4822	114	8	(	(	PUNCT
ejpam-4822	114	9	4	4	NUM
ejpam-4822	114	10	)	)	PUNCT
ejpam-4822	114	11	(	(	PUNCT
ejpam-4822	114	12	2023	2023	NUM
ejpam-4822	114	13	)	)	PUNCT
ejpam-4822	114	14	,	,	PUNCT
ejpam-4822	114	15	2208	2208	NUM
ejpam-4822	114	16	-	-	SYM
ejpam-4822	114	17	2212	2212	NUM
ejpam-4822	114	18	2211	2211	NUM
ejpam-4822	114	19	if	if	SCONJ
ejpam-4822	114	20	α	α	PRON
ejpam-4822	114	21	≥	≥	NUM
ejpam-4822	114	22	1	1	NUM
ejpam-4822	114	23	,	,	PUNCT
ejpam-4822	114	24	then	then	ADV
ejpam-4822	114	25	(	(	PUNCT
ejpam-4822	114	26	p+n	p+n	PROPN
ejpam-4822	114	27	)	)	PUNCT
ejpam-4822	115	1	|	|	ADV
ejpam-4822	115	2	p	p	X
ejpam-4822	115	3	which	which	PRON
ejpam-4822	115	4	is	be	AUX
ejpam-4822	115	5	impossible	impossible	ADJ
ejpam-4822	115	6	.	.	PUNCT
ejpam-4822	116	1	in	in	ADP
ejpam-4822	116	2	case	case	NOUN
ejpam-4822	116	3	α	α	X
ejpam-4822	116	4	=	=	SYM
ejpam-4822	116	5	0	0	NUM
ejpam-4822	116	6	,	,	PUNCT
ejpam-4822	116	7	we	we	PRON
ejpam-4822	116	8	have	have	VERB
ejpam-4822	116	9	2ps	2ps	ADJ
ejpam-4822	116	10	=	=	SYM
ejpam-4822	116	11	(	(	PUNCT
ejpam-4822	116	12	p+	p+	ADV
ejpam-4822	116	13	n)2k+1−1	n)2k+1−1	PROPN
ejpam-4822	116	14	.	.	PUNCT
ejpam-4822	117	1	if	if	SCONJ
ejpam-4822	117	2	k	k	PROPN
ejpam-4822	117	3	=	=	SYM
ejpam-4822	117	4	0	0	PROPN
ejpam-4822	117	5	,	,	PUNCT
ejpam-4822	117	6	then	then	ADV
ejpam-4822	117	7	2ps−p	2ps−p	NUM
ejpam-4822	118	1	=	=	SYM
ejpam-4822	118	2	n−1	n−1	PROPN
ejpam-4822	118	3	.	.	NOUN
ejpam-4822	119	1	hence	hence	ADV
ejpam-4822	119	2	p	p	X
ejpam-4822	119	3	[	[	PUNCT
ejpam-4822	119	4	2ps−1	2ps−1	NUM
ejpam-4822	119	5	−	−	PROPN
ejpam-4822	119	6	1	1	NUM
ejpam-4822	119	7	]	]	PUNCT
ejpam-4822	120	1	=	=	SYM
ejpam-4822	120	2	n−1	n−1	PROPN
ejpam-4822	120	3	.	.	PUNCT
ejpam-4822	121	1	since	since	SCONJ
ejpam-4822	121	2	n−1	n−1	PROPN
ejpam-4822	121	3	is	be	AUX
ejpam-4822	121	4	prime	prime	ADJ
ejpam-4822	121	5	,	,	PUNCT
ejpam-4822	121	6	it	it	PRON
ejpam-4822	121	7	follows	follow	VERB
ejpam-4822	121	8	that	that	SCONJ
ejpam-4822	121	9	p	p	X
ejpam-4822	121	10	=	=	PUNCT
ejpam-4822	121	11	n−	n−	NOUN
ejpam-4822	121	12	1	1	NUM
ejpam-4822	121	13	this	this	PRON
ejpam-4822	121	14	contradicts	contradict	VERB
ejpam-4822	121	15	the	the	DET
ejpam-4822	121	16	fact	fact	NOUN
ejpam-4822	121	17	that	that	SCONJ
ejpam-4822	121	18	p+	p+	VERB
ejpam-4822	121	19	n	n	X
ejpam-4822	121	20	=	=	SYM
ejpam-4822	122	1	2n−	2n−	NUM
ejpam-4822	122	2	1	1	NUM
ejpam-4822	122	3	is	be	AUX
ejpam-4822	122	4	not	not	PART
ejpam-4822	122	5	prime	prime	ADJ
ejpam-4822	122	6	.	.	PUNCT
ejpam-4822	123	1	if	if	SCONJ
ejpam-4822	123	2	k	k	PROPN
ejpam-4822	123	3	≥	≥	NUM
ejpam-4822	123	4	1	1	NUM
ejpam-4822	123	5	,	,	PUNCT
ejpam-4822	123	6	then	then	ADV
ejpam-4822	123	7	2ps	2ps	NOUN
ejpam-4822	123	8	=	=	SYM
ejpam-4822	123	9	(	(	PUNCT
ejpam-4822	123	10	p+	p+	NOUN
ejpam-4822	123	11	n−	n−	NOUN
ejpam-4822	123	12	1	1	NUM
ejpam-4822	123	13	)	)	PUNCT
ejpam-4822	123	14	[	[	PUNCT
ejpam-4822	123	15	(	(	PUNCT
ejpam-4822	123	16	p+	p+	NOUN
ejpam-4822	123	17	n)2k	n)2k	ADJ
ejpam-4822	123	18	+	+	CCONJ
ejpam-4822	123	19	(	(	PUNCT
ejpam-4822	123	20	p+	p+	X
ejpam-4822	123	21	n)2k−1	n)2k−1	X
ejpam-4822	123	22	+	+	X
ejpam-4822	123	23	·	·	PUNCT
ejpam-4822	123	24	·	·	PUNCT
ejpam-4822	123	25	·	·	PUNCT
ejpam-4822	123	26	+	+	CCONJ
ejpam-4822	123	27	(	(	PUNCT
ejpam-4822	123	28	p+	p+	NOUN
ejpam-4822	123	29	n	n	CCONJ
ejpam-4822	123	30	)	)	PUNCT
ejpam-4822	123	31	+	+	CCONJ
ejpam-4822	123	32	1	1	NUM
ejpam-4822	123	33	]	]	PUNCT
ejpam-4822	123	34	.	.	PUNCT
ejpam-4822	124	1	since	since	SCONJ
ejpam-4822	124	2	p	p	PROPN
ejpam-4822	124	3	+	+	CCONJ
ejpam-4822	124	4	n	n	CCONJ
ejpam-4822	124	5	−	−	NOUN
ejpam-4822	124	6	1	1	NUM
ejpam-4822	124	7	is	be	AUX
ejpam-4822	124	8	even	even	ADV
ejpam-4822	124	9	and	and	CCONJ
ejpam-4822	124	10	(	(	PUNCT
ejpam-4822	124	11	p+	p+	NOUN
ejpam-4822	124	12	n)2k	n)2k	ADJ
ejpam-4822	124	13	+	+	CCONJ
ejpam-4822	124	14	(	(	PUNCT
ejpam-4822	124	15	p+	p+	X
ejpam-4822	124	16	n)2k−1	n)2k−1	X
ejpam-4822	124	17	+	+	X
ejpam-4822	124	18	·	·	PUNCT
ejpam-4822	124	19	·	·	PUNCT
ejpam-4822	124	20	·	·	PUNCT
ejpam-4822	125	1	+	+	CCONJ
ejpam-4822	125	2	(	(	PUNCT
ejpam-4822	125	3	p+	p+	NOUN
ejpam-4822	125	4	n	n	CCONJ
ejpam-4822	125	5	)	)	PUNCT
ejpam-4822	125	6	+	+	CCONJ
ejpam-4822	125	7	1	1	NUM
ejpam-4822	125	8	is	be	AUX
ejpam-4822	125	9	odd	odd	ADJ
ejpam-4822	125	10	,	,	PUNCT
ejpam-4822	125	11	it	it	PRON
ejpam-4822	125	12	follows	follow	VERB
ejpam-4822	125	13	that	that	SCONJ
ejpam-4822	125	14	p	p	PROPN
ejpam-4822	126	1	+	+	NOUN
ejpam-4822	126	2	n	n	CCONJ
ejpam-4822	126	3	−	−	PROPN
ejpam-4822	126	4	1	1	NUM
ejpam-4822	126	5	is	be	AUX
ejpam-4822	126	6	an	an	DET
ejpam-4822	126	7	even	even	ADV
ejpam-4822	126	8	positive	positive	ADJ
ejpam-4822	126	9	divisor	divisor	NOUN
ejpam-4822	126	10	of	of	ADP
ejpam-4822	126	11	2ps	2ps	NOUN
ejpam-4822	126	12	that	that	PRON
ejpam-4822	126	13	is	be	AUX
ejpam-4822	126	14	p	p	NOUN
ejpam-4822	126	15	+	+	CCONJ
ejpam-4822	126	16	n	n	CCONJ
ejpam-4822	126	17	−	−	PROPN
ejpam-4822	126	18	1	1	NUM
ejpam-4822	126	19	=	=	SYM
ejpam-4822	126	20	2pl	2pl	ADJ
ejpam-4822	126	21	,	,	PUNCT
ejpam-4822	126	22	for	for	ADP
ejpam-4822	126	23	some	some	DET
ejpam-4822	126	24	integer	integer	NOUN
ejpam-4822	126	25	l	l	NOUN
ejpam-4822	126	26	such	such	ADJ
ejpam-4822	126	27	that	that	SCONJ
ejpam-4822	126	28	0	0	NUM
ejpam-4822	126	29	≤	≤	NUM
ejpam-4822	126	30	l	l	NOUN
ejpam-4822	126	31	<	<	X
ejpam-4822	126	32	s.	s.	PROPN
ejpam-4822	126	33	if	if	SCONJ
ejpam-4822	126	34	l	l	PROPN
ejpam-4822	126	35	=	=	SYM
ejpam-4822	126	36	0	0	NUM
ejpam-4822	126	37	,	,	PUNCT
ejpam-4822	126	38	then	then	ADV
ejpam-4822	126	39	p+	p+	VERB
ejpam-4822	126	40	n	n	PROPN
ejpam-4822	126	41	=	=	SYM
ejpam-4822	126	42	3	3	NUM
ejpam-4822	126	43	,	,	PUNCT
ejpam-4822	126	44	which	which	PRON
ejpam-4822	126	45	is	be	AUX
ejpam-4822	126	46	impossible	impossible	ADJ
ejpam-4822	126	47	since	since	SCONJ
ejpam-4822	126	48	p	p	X
ejpam-4822	126	49	>	>	X
ejpam-4822	126	50	3	3	NUM
ejpam-4822	126	51	and	and	CCONJ
ejpam-4822	126	52	n	n	PRON
ejpam-4822	126	53	are	be	AUX
ejpam-4822	126	54	positive	positive	ADJ
ejpam-4822	126	55	integer	integer	NOUN
ejpam-4822	126	56	.	.	PUNCT
ejpam-4822	127	1	if	if	SCONJ
ejpam-4822	127	2	1	1	NUM
ejpam-4822	127	3	≤	≤	NUM
ejpam-4822	127	4	l	l	NOUN
ejpam-4822	127	5	<	<	X
ejpam-4822	127	6	s	s	PROPN
ejpam-4822	127	7	,	,	PUNCT
ejpam-4822	127	8	then	then	ADV
ejpam-4822	127	9	p	p	X
ejpam-4822	127	10	[	[	PUNCT
ejpam-4822	127	11	2(p)l−1	2(p)l−1	NUM
ejpam-4822	127	12	−	−	NOUN
ejpam-4822	127	13	1	1	NUM
ejpam-4822	127	14	]	]	PUNCT
ejpam-4822	127	15	=	=	PUNCT
ejpam-4822	127	16	n−	n−	NOUN
ejpam-4822	127	17	1	1	NUM
ejpam-4822	127	18	which	which	PRON
ejpam-4822	127	19	is	be	AUX
ejpam-4822	127	20	also	also	ADV
ejpam-4822	127	21	impossible	impossible	ADJ
ejpam-4822	127	22	.	.	PUNCT
ejpam-4822	128	1	example	example	NOUN
ejpam-4822	129	1	1	1	X
ejpam-4822	129	2	.	.	X
ejpam-4822	129	3	there	there	PRON
ejpam-4822	129	4	are	be	VERB
ejpam-4822	129	5	infinitely	infinitely	ADV
ejpam-4822	129	6	many	many	ADJ
ejpam-4822	129	7	n	n	ADP
ejpam-4822	129	8	,	,	PUNCT
ejpam-4822	129	9	p	p	NOUN
ejpam-4822	129	10	of	of	ADP
ejpam-4822	129	11	the	the	DET
ejpam-4822	129	12	form	form	NOUN
ejpam-4822	129	13	n	n	X
ejpam-4822	129	14	≡	≡	PROPN
ejpam-4822	129	15	0	0	PUNCT
ejpam-4822	129	16	(	(	PUNCT
ejpam-4822	129	17	mod	mod	NOUN
ejpam-4822	129	18	4),p	4),p	PROPN
ejpam-4822	129	19	≡	≡	PROPN
ejpam-4822	129	20	3	3	NUM
ejpam-4822	129	21	(	(	PUNCT
ejpam-4822	129	22	mod	mod	NOUN
ejpam-4822	129	23	4	4	NUM
ejpam-4822	129	24	)	)	PUNCT
ejpam-4822	129	25	where	where	SCONJ
ejpam-4822	129	26	p	p	X
ejpam-4822	129	27	>	>	X
ejpam-4822	129	28	3	3	NUM
ejpam-4822	129	29	such	such	ADJ
ejpam-4822	129	30	that	that	SCONJ
ejpam-4822	129	31	p	p	X
ejpam-4822	129	32	,	,	PUNCT
ejpam-4822	129	33	p+n	p+n	ADJ
ejpam-4822	129	34	,	,	PUNCT
ejpam-4822	129	35	n−1	n−1	PROPN
ejpam-4822	129	36	are	be	AUX
ejpam-4822	129	37	prime	prime	ADJ
ejpam-4822	129	38	numbers	number	NOUN
ejpam-4822	129	39	and	and	CCONJ
ejpam-4822	129	40	2n−1	2n−1	NUM
ejpam-4822	129	41	is	be	AUX
ejpam-4822	129	42	not	not	PART
ejpam-4822	129	43	a	a	DET
ejpam-4822	129	44	prime	prime	ADJ
ejpam-4822	129	45	number	number	NOUN
ejpam-4822	129	46	.	.	PUNCT
ejpam-4822	130	1	some	some	DET
ejpam-4822	130	2	diophantine	diophantine	NOUN
ejpam-4822	130	3	equations	equation	NOUN
ejpam-4822	130	4	of	of	ADP
ejpam-4822	130	5	particular	particular	ADJ
ejpam-4822	130	6	values	value	NOUN
ejpam-4822	130	7	of	of	ADP
ejpam-4822	130	8	n	n	PRON
ejpam-4822	130	9	where	where	SCONJ
ejpam-4822	130	10	n	n	X
ejpam-4822	130	11	is	be	AUX
ejpam-4822	130	12	between	between	ADP
ejpam-4822	130	13	1	1	NUM
ejpam-4822	130	14	to	to	ADP
ejpam-4822	130	15	70	70	NUM
ejpam-4822	130	16	with	with	ADP
ejpam-4822	130	17	positive	positive	ADJ
ejpam-4822	130	18	integers	integer	NOUN
ejpam-4822	130	19	√	√	VERB
ejpam-4822	130	20	p+	p+	NOUN
ejpam-4822	130	21	1	1	NUM
ejpam-4822	130	22	and	and	CCONJ
ejpam-4822	130	23	√	√	PROPN
ejpam-4822	130	24	p+	p+	PROPN
ejpam-4822	130	25	n+	n+	NUM
ejpam-4822	130	26	1	1	NUM
ejpam-4822	130	27	are	be	AUX
ejpam-4822	130	28	given	give	VERB
ejpam-4822	130	29	in	in	ADP
ejpam-4822	130	30	the	the	DET
ejpam-4822	130	31	table	table	NOUN
ejpam-4822	130	32	below	below	ADV
ejpam-4822	130	33	.	.	PUNCT
ejpam-4822	131	1	n	n	PROPN
ejpam-4822	131	2	(	(	PUNCT
ejpam-4822	131	3	p+	p+	NOUN
ejpam-4822	131	4	n)x	n)x	X
ejpam-4822	132	1	+	+	CCONJ
ejpam-4822	132	2	py	py	X
ejpam-4822	132	3	=	=	SYM
ejpam-4822	132	4	z2	z2	PROPN
ejpam-4822	132	5	(	(	PUNCT
ejpam-4822	132	6	x	x	PROPN
ejpam-4822	132	7	,	,	PUNCT
ejpam-4822	132	8	y	y	PROPN
ejpam-4822	132	9	,	,	PUNCT
ejpam-4822	132	10	z	z	NOUN
ejpam-4822	132	11	)	)	PUNCT
ejpam-4822	132	12	8	8	NUM
ejpam-4822	132	13	(	(	PUNCT
ejpam-4822	132	14	p+	p+	NOUN
ejpam-4822	132	15	8)x	8)x	NOUN
ejpam-4822	132	16	+	+	CCONJ
ejpam-4822	132	17	py	py	PROPN
ejpam-4822	132	18	=	=	PROPN
ejpam-4822	132	19	z2	z2	PROPN
ejpam-4822	132	20	{	{	PUNCT
ejpam-4822	132	21	(	(	PUNCT
ejpam-4822	132	22	0	0	NUM
ejpam-4822	132	23	,	,	PUNCT
ejpam-4822	132	24	1	1	NUM
ejpam-4822	132	25	,	,	PUNCT
ejpam-4822	132	26	√	√	PROPN
ejpam-4822	132	27	p+	p+	VERB
ejpam-4822	132	28	1	1	NUM
ejpam-4822	132	29	}	}	PUNCT
ejpam-4822	132	30	∪	∪	X
ejpam-4822	132	31	{	{	PUNCT
ejpam-4822	132	32	(	(	PUNCT
ejpam-4822	132	33	1	1	NUM
ejpam-4822	132	34	,	,	PUNCT
ejpam-4822	132	35	0	0	NUM
ejpam-4822	132	36	,	,	PUNCT
ejpam-4822	132	37	√	√	PROPN
ejpam-4822	132	38	p+	p+	VERB
ejpam-4822	132	39	9	9	NUM
ejpam-4822	132	40	)	)	PUNCT
ejpam-4822	132	41	}	}	PUNCT
ejpam-4822	132	42	20	20	NUM
ejpam-4822	132	43	(	(	PUNCT
ejpam-4822	132	44	p+	p+	NOUN
ejpam-4822	132	45	20)x	20)x	NUM
ejpam-4822	132	46	+	+	NUM
ejpam-4822	132	47	py	py	PROPN
ejpam-4822	132	48	=	=	SYM
ejpam-4822	132	49	z2	z2	PROPN
ejpam-4822	132	50	[	[	X
ejpam-4822	132	51	2	2	X
ejpam-4822	132	52	]	]	PUNCT
ejpam-4822	132	53	{	{	PUNCT
ejpam-4822	132	54	(	(	PUNCT
ejpam-4822	132	55	0	0	NUM
ejpam-4822	132	56	,	,	PUNCT
ejpam-4822	132	57	1	1	NUM
ejpam-4822	132	58	,	,	PUNCT
ejpam-4822	132	59	√	√	PROPN
ejpam-4822	132	60	p+	p+	VERB
ejpam-4822	132	61	1	1	NUM
ejpam-4822	132	62	}	}	PUNCT
ejpam-4822	132	63	∪	∪	X
ejpam-4822	132	64	{	{	PUNCT
ejpam-4822	132	65	(	(	PUNCT
ejpam-4822	132	66	1	1	NUM
ejpam-4822	132	67	,	,	PUNCT
ejpam-4822	132	68	0	0	NUM
ejpam-4822	132	69	,	,	PUNCT
ejpam-4822	132	70	√	√	PROPN
ejpam-4822	132	71	p+	p+	VERB
ejpam-4822	132	72	21	21	NUM
ejpam-4822	132	73	)	)	PUNCT
ejpam-4822	132	74	}	}	PUNCT
ejpam-4822	132	75	32	32	NUM
ejpam-4822	132	76	(	(	PUNCT
ejpam-4822	132	77	p+	p+	NOUN
ejpam-4822	132	78	32)x	32)x	NUM
ejpam-4822	132	79	+	+	NUM
ejpam-4822	132	80	py	py	PROPN
ejpam-4822	132	81	=	=	PROPN
ejpam-4822	132	82	z2	z2	PROPN
ejpam-4822	132	83	{	{	PUNCT
ejpam-4822	132	84	(	(	PUNCT
ejpam-4822	132	85	0	0	NUM
ejpam-4822	132	86	,	,	PUNCT
ejpam-4822	132	87	1	1	NUM
ejpam-4822	132	88	,	,	PUNCT
ejpam-4822	132	89	√	√	PROPN
ejpam-4822	132	90	p+	p+	VERB
ejpam-4822	132	91	1	1	NUM
ejpam-4822	132	92	}	}	PUNCT
ejpam-4822	132	93	∪	∪	X
ejpam-4822	132	94	{	{	PUNCT
ejpam-4822	132	95	(	(	PUNCT
ejpam-4822	132	96	1	1	NUM
ejpam-4822	132	97	,	,	PUNCT
ejpam-4822	132	98	0	0	NUM
ejpam-4822	132	99	,	,	PUNCT
ejpam-4822	132	100	√	√	PROPN
ejpam-4822	132	101	p+	p+	VERB
ejpam-4822	132	102	33	33	NUM
ejpam-4822	132	103	)	)	PUNCT
ejpam-4822	132	104	}	}	PUNCT
ejpam-4822	132	105	44	44	NUM
ejpam-4822	132	106	(	(	PUNCT
ejpam-4822	132	107	p+	p+	NOUN
ejpam-4822	132	108	44)x	44)x	NUM
ejpam-4822	132	109	+	+	CCONJ
ejpam-4822	132	110	py	py	PROPN
ejpam-4822	132	111	=	=	PROPN
ejpam-4822	132	112	z2	z2	PROPN
ejpam-4822	132	113	{	{	PUNCT
ejpam-4822	132	114	(	(	PUNCT
ejpam-4822	132	115	0	0	NUM
ejpam-4822	132	116	,	,	PUNCT
ejpam-4822	132	117	1	1	NUM
ejpam-4822	132	118	,	,	PUNCT
ejpam-4822	132	119	√	√	PROPN
ejpam-4822	132	120	p+	p+	VERB
ejpam-4822	132	121	1	1	NUM
ejpam-4822	132	122	}	}	PUNCT
ejpam-4822	132	123	∪	∪	X
ejpam-4822	132	124	{	{	PUNCT
ejpam-4822	132	125	(	(	PUNCT
ejpam-4822	132	126	1	1	NUM
ejpam-4822	132	127	,	,	PUNCT
ejpam-4822	132	128	0	0	NUM
ejpam-4822	132	129	,	,	PUNCT
ejpam-4822	132	130	√	√	PROPN
ejpam-4822	132	131	p+	p+	VERB
ejpam-4822	132	132	45	45	NUM
ejpam-4822	132	133	)	)	PUNCT
ejpam-4822	132	134	}	}	PUNCT
ejpam-4822	132	135	48	48	NUM
ejpam-4822	132	136	(	(	PUNCT
ejpam-4822	132	137	p+	p+	NOUN
ejpam-4822	132	138	48)x	48)x	NUM
ejpam-4822	132	139	+	+	CCONJ
ejpam-4822	132	140	py	py	PROPN
ejpam-4822	132	141	=	=	PROPN
ejpam-4822	132	142	z2	z2	PROPN
ejpam-4822	132	143	{	{	PUNCT
ejpam-4822	132	144	(	(	PUNCT
ejpam-4822	132	145	0	0	NUM
ejpam-4822	132	146	,	,	PUNCT
ejpam-4822	132	147	1	1	NUM
ejpam-4822	132	148	,	,	PUNCT
ejpam-4822	132	149	√	√	PROPN
ejpam-4822	132	150	p+	p+	VERB
ejpam-4822	132	151	1	1	NUM
ejpam-4822	132	152	}	}	PUNCT
ejpam-4822	132	153	∪	∪	X
ejpam-4822	132	154	{	{	PUNCT
ejpam-4822	132	155	(	(	PUNCT
ejpam-4822	132	156	1	1	NUM
ejpam-4822	132	157	,	,	PUNCT
ejpam-4822	132	158	0	0	NUM
ejpam-4822	132	159	,	,	PUNCT
ejpam-4822	132	160	√	√	PROPN
ejpam-4822	132	161	p+	p+	VERB
ejpam-4822	132	162	49	49	NUM
ejpam-4822	132	163	)	)	PUNCT
ejpam-4822	132	164	}	}	PUNCT
ejpam-4822	132	165	60	60	NUM
ejpam-4822	132	166	(	(	PUNCT
ejpam-4822	132	167	p+	p+	NOUN
ejpam-4822	132	168	60)x	60)x	NUM
ejpam-4822	132	169	+	+	CCONJ
ejpam-4822	132	170	py	py	PROPN
ejpam-4822	132	171	=	=	SYM
ejpam-4822	132	172	z2	z2	PROPN
ejpam-4822	132	173	{	{	PUNCT
ejpam-4822	132	174	(	(	PUNCT
ejpam-4822	132	175	0	0	NUM
ejpam-4822	132	176	,	,	PUNCT
ejpam-4822	132	177	1	1	NUM
ejpam-4822	132	178	,	,	PUNCT
ejpam-4822	132	179	√	√	PROPN
ejpam-4822	132	180	p+	p+	VERB
ejpam-4822	132	181	1	1	NUM
ejpam-4822	132	182	}	}	PUNCT
ejpam-4822	132	183	∪	∪	X
ejpam-4822	132	184	{	{	PUNCT
ejpam-4822	132	185	(	(	PUNCT
ejpam-4822	132	186	1	1	NUM
ejpam-4822	132	187	,	,	PUNCT
ejpam-4822	132	188	0	0	NUM
ejpam-4822	132	189	,	,	PUNCT
ejpam-4822	132	190	√	√	PROPN
ejpam-4822	132	191	p+	p+	PROPN
ejpam-4822	132	192	61	61	NUM
ejpam-4822	132	193	)	)	PUNCT
ejpam-4822	132	194	}	}	PUNCT
ejpam-4822	132	195	68	68	NUM
ejpam-4822	132	196	(	(	PUNCT
ejpam-4822	132	197	p+	p+	NOUN
ejpam-4822	132	198	68)x	68)x	NUM
ejpam-4822	132	199	+	+	NUM
ejpam-4822	132	200	py	py	PROPN
ejpam-4822	132	201	=	=	PROPN
ejpam-4822	132	202	z2	z2	PROPN
ejpam-4822	132	203	{	{	PUNCT
ejpam-4822	132	204	(	(	PUNCT
ejpam-4822	132	205	0	0	NUM
ejpam-4822	132	206	,	,	PUNCT
ejpam-4822	132	207	1	1	NUM
ejpam-4822	132	208	,	,	PUNCT
ejpam-4822	132	209	√	√	PROPN
ejpam-4822	132	210	p+	p+	VERB
ejpam-4822	132	211	1	1	NUM
ejpam-4822	132	212	}	}	PUNCT
ejpam-4822	132	213	∪	∪	X
ejpam-4822	132	214	{	{	PUNCT
ejpam-4822	132	215	(	(	PUNCT
ejpam-4822	132	216	1	1	NUM
ejpam-4822	132	217	,	,	PUNCT
ejpam-4822	132	218	0	0	NUM
ejpam-4822	132	219	,	,	PUNCT
ejpam-4822	132	220	√	√	PROPN
ejpam-4822	132	221	p+	p+	VERB
ejpam-4822	132	222	69	69	NUM
ejpam-4822	132	223	)	)	PUNCT
ejpam-4822	132	224	}	}	PUNCT
ejpam-4822	132	225	table	table	NOUN
ejpam-4822	132	226	1	1	NUM
ejpam-4822	132	227	:	:	PUNCT
ejpam-4822	132	228	diophantine	diophantine	VERB
ejpam-4822	132	229	equations	equation	NOUN
ejpam-4822	132	230	satisfying	satisfy	VERB
ejpam-4822	132	231	the	the	DET
ejpam-4822	132	232	condition	condition	NOUN
ejpam-4822	132	233	in	in	ADP
ejpam-4822	132	234	theorem	theorem	NOUN
ejpam-4822	132	235	2	2	NUM
ejpam-4822	132	236	.	.	PUNCT
ejpam-4822	132	237	theorem	theorem	NOUN
ejpam-4822	132	238	3	3	X
ejpam-4822	132	239	.	.	PUNCT
ejpam-4822	133	1	let	let	VERB
ejpam-4822	133	2	p	p	NOUN
ejpam-4822	133	3	and	and	CCONJ
ejpam-4822	133	4	n	n	CCONJ
ejpam-4822	133	5	be	be	AUX
ejpam-4822	133	6	a	a	DET
ejpam-4822	133	7	positive	positive	ADJ
ejpam-4822	133	8	integer	integer	NOUN
ejpam-4822	133	9	where	where	SCONJ
ejpam-4822	133	10	n	n	X
ejpam-4822	133	11	≡	≡	PROPN
ejpam-4822	133	12	0	0	PUNCT
ejpam-4822	134	1	(	(	PUNCT
ejpam-4822	134	2	mod	mod	PROPN
ejpam-4822	134	3	4	4	NUM
ejpam-4822	134	4	)	)	PUNCT
ejpam-4822	134	5	,	,	PUNCT
ejpam-4822	134	6	p	p	PROPN
ejpam-4822	134	7	≡	≡	PROPN
ejpam-4822	134	8	1	1	NUM
ejpam-4822	134	9	(	(	PUNCT
ejpam-4822	134	10	mod	mod	NOUN
ejpam-4822	134	11	4	4	NUM
ejpam-4822	134	12	)	)	PUNCT
ejpam-4822	134	13	such	such	ADJ
ejpam-4822	134	14	that	that	SCONJ
ejpam-4822	134	15	p	p	PROPN
ejpam-4822	134	16	and	and	CCONJ
ejpam-4822	134	17	p	p	NOUN
ejpam-4822	134	18	+	+	CCONJ
ejpam-4822	134	19	n	n	CCONJ
ejpam-4822	134	20	are	be	AUX
ejpam-4822	134	21	prime	prime	ADJ
ejpam-4822	134	22	numbers	number	NOUN
ejpam-4822	134	23	.	.	PUNCT
ejpam-4822	135	1	if	if	SCONJ
ejpam-4822	135	2	√	√	PRON
ejpam-4822	135	3	p+	p+	VERB
ejpam-4822	135	4	1	1	NUM
ejpam-4822	135	5	and	and	CCONJ
ejpam-4822	135	6	√	√	PROPN
ejpam-4822	135	7	p+	p+	PROPN
ejpam-4822	135	8	n+	n+	NUM
ejpam-4822	135	9	1	1	NUM
ejpam-4822	135	10	are	be	AUX
ejpam-4822	135	11	integers	integer	NOUN
ejpam-4822	135	12	,	,	PUNCT
ejpam-4822	135	13	then	then	ADV
ejpam-4822	135	14	the	the	DET
ejpam-4822	135	15	all	all	PRON
ejpam-4822	135	16	of	of	ADP
ejpam-4822	135	17	the	the	DET
ejpam-4822	135	18	non	non	ADJ
ejpam-4822	135	19	-	-	ADJ
ejpam-4822	135	20	negative	negative	ADJ
ejpam-4822	135	21	integer	integer	NOUN
ejpam-4822	135	22	solutions	solution	NOUN
ejpam-4822	135	23	of	of	ADP
ejpam-4822	135	24	(	(	PUNCT
ejpam-4822	135	25	p	p	X
ejpam-4822	135	26	+	+	PROPN
ejpam-4822	135	27	n)x	n)x	NOUN
ejpam-4822	136	1	+	+	CCONJ
ejpam-4822	136	2	py	py	X
ejpam-4822	136	3	=	=	SYM
ejpam-4822	136	4	z2	z2	PROPN
ejpam-4822	136	5	are	be	AUX
ejpam-4822	136	6	given	give	VERB
ejpam-4822	136	7	by	by	ADP
ejpam-4822	136	8	(	(	PUNCT
ejpam-4822	136	9	x	x	PROPN
ejpam-4822	136	10	,	,	PUNCT
ejpam-4822	136	11	y	y	PROPN
ejpam-4822	136	12	,	,	PUNCT
ejpam-4822	136	13	z	z	NOUN
ejpam-4822	136	14	)	)	PUNCT
ejpam-4822	136	15	∈	∈	NOUN
ejpam-4822	136	16	{	{	PUNCT
ejpam-4822	136	17	(	(	PUNCT
ejpam-4822	136	18	0	0	NUM
ejpam-4822	136	19	,	,	PUNCT
ejpam-4822	136	20	1	1	NUM
ejpam-4822	136	21	,	,	PUNCT
ejpam-4822	136	22	√	√	PROPN
ejpam-4822	136	23	p+	p+	ADJ
ejpam-4822	136	24	1	1	NUM
ejpam-4822	136	25	)	)	PUNCT
ejpam-4822	136	26	,	,	PUNCT
ejpam-4822	136	27	(	(	PUNCT
ejpam-4822	136	28	1	1	NUM
ejpam-4822	136	29	,	,	PUNCT
ejpam-4822	136	30	0	0	NUM
ejpam-4822	136	31	,	,	PUNCT
ejpam-4822	136	32	√	√	PROPN
ejpam-4822	136	33	p+	p+	ADJ
ejpam-4822	136	34	n+	n+	NOUN
ejpam-4822	136	35	1	1	NUM
ejpam-4822	136	36	)	)	PUNCT
ejpam-4822	136	37	}	}	PUNCT
ejpam-4822	136	38	.	.	PUNCT
ejpam-4822	137	1	proof	proof	NOUN
ejpam-4822	137	2	.	.	PUNCT
ejpam-4822	138	1	let	let	AUX
ejpam-4822	138	2	(	(	PUNCT
ejpam-4822	138	3	x	x	X
ejpam-4822	138	4	,	,	PUNCT
ejpam-4822	138	5	y	y	PROPN
ejpam-4822	138	6	,	,	PUNCT
ejpam-4822	138	7	z	z	NOUN
ejpam-4822	138	8	)	)	PUNCT
ejpam-4822	138	9	be	be	AUX
ejpam-4822	138	10	a	a	DET
ejpam-4822	138	11	non	non	ADJ
ejpam-4822	138	12	-	-	ADJ
ejpam-4822	138	13	negative	negative	ADJ
ejpam-4822	138	14	integer	integer	NOUN
ejpam-4822	138	15	solution	solution	NOUN
ejpam-4822	138	16	of	of	ADP
ejpam-4822	138	17	(	(	PUNCT
ejpam-4822	138	18	p	p	X
ejpam-4822	138	19	+	+	PROPN
ejpam-4822	138	20	n)x	n)x	NOUN
ejpam-4822	139	1	+	+	CCONJ
ejpam-4822	139	2	py	py	X
ejpam-4822	139	3	=	=	SYM
ejpam-4822	139	4	z2	z2	PROPN
ejpam-4822	139	5	.	.	PUNCT
ejpam-4822	140	1	if	if	SCONJ
ejpam-4822	140	2	x	x	PROPN
ejpam-4822	140	3	=	=	SYM
ejpam-4822	140	4	0	0	NUM
ejpam-4822	140	5	or	or	CCONJ
ejpam-4822	140	6	y	y	PROPN
ejpam-4822	140	7	=	=	SYM
ejpam-4822	140	8	0	0	PROPN
ejpam-4822	140	9	,	,	PUNCT
ejpam-4822	140	10	then	then	ADV
ejpam-4822	140	11	(	(	PUNCT
ejpam-4822	140	12	x	x	X
ejpam-4822	140	13	,	,	PUNCT
ejpam-4822	140	14	y	y	PROPN
ejpam-4822	140	15	,	,	PUNCT
ejpam-4822	140	16	z	z	NOUN
ejpam-4822	140	17	)	)	PUNCT
ejpam-4822	140	18	=	=	SYM
ejpam-4822	140	19	(	(	PUNCT
ejpam-4822	140	20	0	0	NUM
ejpam-4822	140	21	,	,	PUNCT
ejpam-4822	140	22	1	1	NUM
ejpam-4822	140	23	,	,	PUNCT
ejpam-4822	140	24	√	√	PROPN
ejpam-4822	140	25	p+	p+	VERB
ejpam-4822	140	26	1	1	NUM
ejpam-4822	140	27	)	)	PUNCT
ejpam-4822	140	28	or	or	CCONJ
ejpam-4822	140	29	(	(	PUNCT
ejpam-4822	140	30	x	x	X
ejpam-4822	140	31	,	,	PUNCT
ejpam-4822	140	32	y	y	PROPN
ejpam-4822	140	33	,	,	PUNCT
ejpam-4822	140	34	z	z	NOUN
ejpam-4822	140	35	)	)	PUNCT
ejpam-4822	140	36	=	=	SYM
ejpam-4822	140	37	(	(	PUNCT
ejpam-4822	140	38	1	1	NUM
ejpam-4822	140	39	,	,	PUNCT
ejpam-4822	140	40	0	0	NUM
ejpam-4822	140	41	,	,	PUNCT
ejpam-4822	140	42	2	2	NUM
ejpam-4822	140	43	√	√	PROPN
ejpam-4822	140	44	p+	p+	NOUN
ejpam-4822	140	45	n+	n+	NOUN
ejpam-4822	140	46	1	1	NUM
ejpam-4822	140	47	)	)	PUNCT
ejpam-4822	140	48	by	by	ADP
ejpam-4822	140	49	lemma	lemma	PROPN
ejpam-4822	140	50	1	1	NUM
ejpam-4822	140	51	and	and	CCONJ
ejpam-4822	140	52	lemma	lemma	PROPN
ejpam-4822	140	53	2	2	NUM
ejpam-4822	140	54	.	.	PUNCT
ejpam-4822	141	1	if	if	SCONJ
ejpam-4822	141	2	x	x	PROPN
ejpam-4822	141	3	>	>	X
ejpam-4822	141	4	0	0	PUNCT
ejpam-4822	141	5	and	and	CCONJ
ejpam-4822	141	6	y	y	PROPN
ejpam-4822	141	7	>	>	X
ejpam-4822	141	8	0	0	PROPN
ejpam-4822	141	9	,	,	PUNCT
ejpam-4822	141	10	then	then	ADV
ejpam-4822	141	11	(	(	PUNCT
ejpam-4822	141	12	p	p	X
ejpam-4822	141	13	+	+	CCONJ
ejpam-4822	141	14	n)x	n)x	ADJ
ejpam-4822	141	15	≡	≡	PROPN
ejpam-4822	141	16	1	1	NUM
ejpam-4822	141	17	(	(	PUNCT
ejpam-4822	141	18	mod	mod	NOUN
ejpam-4822	141	19	4	4	NUM
ejpam-4822	141	20	)	)	PUNCT
ejpam-4822	141	21	and	and	CCONJ
ejpam-4822	141	22	py	py	PROPN
ejpam-4822	141	23	≡	≡	PROPN
ejpam-4822	141	24	1	1	NUM
ejpam-4822	141	25	(	(	PUNCT
ejpam-4822	141	26	mod	mod	NOUN
ejpam-4822	141	27	4	4	NUM
ejpam-4822	141	28	)	)	PUNCT
ejpam-4822	141	29	.	.	PUNCT
ejpam-4822	142	1	thus	thus	ADV
ejpam-4822	142	2	(	(	PUNCT
ejpam-4822	142	3	p+	p+	NOUN
ejpam-4822	142	4	n)x	n)x	X
ejpam-4822	143	1	+	+	CCONJ
ejpam-4822	143	2	py	py	X
ejpam-4822	143	3	≡	≡	PROPN
ejpam-4822	143	4	2	2	NUM
ejpam-4822	143	5	(	(	PUNCT
ejpam-4822	143	6	mod	mod	NOUN
ejpam-4822	143	7	4	4	NUM
ejpam-4822	143	8	)	)	PUNCT
ejpam-4822	143	9	which	which	PRON
ejpam-4822	143	10	is	be	AUX
ejpam-4822	143	11	impossible	impossible	ADJ
ejpam-4822	143	12	since	since	SCONJ
ejpam-4822	143	13	z2	z2	PROPN
ejpam-4822	143	14	≡	≡	PROPN
ejpam-4822	143	15	0	0	NUM
ejpam-4822	143	16	,	,	PUNCT
ejpam-4822	143	17	1	1	NUM
ejpam-4822	143	18	(	(	PUNCT
ejpam-4822	143	19	mod	mod	NOUN
ejpam-4822	143	20	4	4	NUM
ejpam-4822	143	21	)	)	PUNCT
ejpam-4822	143	22	.	.	PUNCT
ejpam-4822	144	1	acknowledgements	acknowledgement	NOUN
ejpam-4822	144	2	the	the	DET
ejpam-4822	144	3	authors	author	NOUN
ejpam-4822	144	4	wish	wish	VERB
ejpam-4822	144	5	to	to	PART
ejpam-4822	144	6	thank	thank	VERB
ejpam-4822	144	7	the	the	DET
ejpam-4822	144	8	referees	referee	NOUN
ejpam-4822	144	9	for	for	ADP
ejpam-4822	144	10	their	their	PRON
ejpam-4822	144	11	kind	kind	ADJ
ejpam-4822	144	12	suggestions	suggestion	NOUN
ejpam-4822	144	13	and	and	CCONJ
ejpam-4822	144	14	comments	comment	NOUN
ejpam-4822	144	15	to	to	PART
ejpam-4822	144	16	improve	improve	VERB
ejpam-4822	144	17	the	the	DET
ejpam-4822	144	18	article	article	NOUN
ejpam-4822	144	19	.	.	PUNCT
ejpam-4822	145	1	references	reference	NOUN
ejpam-4822	145	2	2212	2212	NUM
ejpam-4822	145	3	references	reference	NOUN
ejpam-4822	145	4	[	[	X
ejpam-4822	145	5	1	1	NUM
ejpam-4822	145	6	]	]	PUNCT
ejpam-4822	145	7	nechemia	nechemia	NOUN
ejpam-4822	145	8	burshtein	burshtein	PROPN
ejpam-4822	145	9	.	.	PUNCT
ejpam-4822	146	1	on	on	ADP
ejpam-4822	146	2	the	the	DET
ejpam-4822	146	3	diophantine	diophantine	NOUN
ejpam-4822	146	4	equation	equation	NOUN
ejpam-4822	146	5	px+(p+4)y	px+(p+4)y	ADJ
ejpam-4822	146	6	=	=	SYM
ejpam-4822	146	7	z2	z2	PROPN
ejpam-4822	146	8	when	when	SCONJ
ejpam-4822	146	9	p	p	X
ejpam-4822	146	10	>	>	X
ejpam-4822	146	11	3	3	NUM
ejpam-4822	146	12	,	,	PUNCT
ejpam-4822	146	13	p+4	p+4	PROPN
ejpam-4822	146	14	are	be	AUX
ejpam-4822	146	15	primes	prime	NOUN
ejpam-4822	146	16	is	be	AUX
ejpam-4822	146	17	insolvable	insolvable	ADJ
ejpam-4822	146	18	in	in	ADP
ejpam-4822	146	19	positive	positive	ADJ
ejpam-4822	146	20	integers	integer	NOUN
ejpam-4822	146	21	.	.	PUNCT
ejpam-4822	147	1	annals	annal	NOUN
ejpam-4822	147	2	of	of	ADP
ejpam-4822	147	3	pure	pure	ADJ
ejpam-4822	147	4	and	and	CCONJ
ejpam-4822	147	5	applied	applied	ADJ
ejpam-4822	147	6	mathematics	mathematic	NOUN
ejpam-4822	147	7	,	,	PUNCT
ejpam-4822	147	8	16(2):283–286	16(2):283–286	NUM
ejpam-4822	147	9	,	,	PUNCT
ejpam-4822	147	10	2018	2018	NUM
ejpam-4822	147	11	.	.	PUNCT
ejpam-4822	148	1	[	[	X
ejpam-4822	148	2	2	2	NUM
ejpam-4822	148	3	]	]	PUNCT
ejpam-4822	148	4	rakporn	rakporn	NOUN
ejpam-4822	148	5	dokchan	dokchan	NOUN
ejpam-4822	148	6	and	and	CCONJ
ejpam-4822	148	7	apisit	apisit	NOUN
ejpam-4822	148	8	pakapongpun	pakapongpun	NOUN
ejpam-4822	148	9	.	.	PUNCT
ejpam-4822	149	1	on	on	ADP
ejpam-4822	149	2	the	the	DET
ejpam-4822	149	3	diophantine	diophantine	NOUN
ejpam-4822	149	4	px	px	X
ejpam-4822	149	5	+	+	CCONJ
ejpam-4822	149	6	(	(	PUNCT
ejpam-4822	149	7	p+	p+	NOUN
ejpam-4822	149	8	20)y	20)y	PROPN
ejpam-4822	149	9	=	=	SYM
ejpam-4822	149	10	z2	z2	PROPN
ejpam-4822	149	11	when	when	SCONJ
ejpam-4822	149	12	p	p	PROPN
ejpam-4822	149	13	and	and	CCONJ
ejpam-4822	149	14	p+	p+	PROPN
ejpam-4822	149	15	20	20	NUM
ejpam-4822	149	16	are	be	AUX
ejpam-4822	149	17	primes	prime	NOUN
ejpam-4822	149	18	.	.	PUNCT
ejpam-4822	150	1	international	international	ADJ
ejpam-4822	150	2	journal	journal	PROPN
ejpam-4822	150	3	of	of	ADP
ejpam-4822	150	4	mathematics	mathematic	NOUN
ejpam-4822	150	5	and	and	CCONJ
ejpam-4822	150	6	computer	computer	NOUN
ejpam-4822	150	7	science	science	NOUN
ejpam-4822	150	8	,	,	PUNCT
ejpam-4822	150	9	16(1):179–183	16(1):179–183	NUM
ejpam-4822	150	10	,	,	PUNCT
ejpam-4822	150	11	2021	2021	NUM
ejpam-4822	150	12	.	.	PUNCT
ejpam-4822	151	1	[	[	X
ejpam-4822	151	2	3	3	X
ejpam-4822	151	3	]	]	PUNCT
ejpam-4822	151	4	n	n	DET
ejpam-4822	151	5	fernando	fernando	NOUN
ejpam-4822	151	6	.	.	PUNCT
ejpam-4822	152	1	on	on	ADP
ejpam-4822	152	2	the	the	DET
ejpam-4822	152	3	solvability	solvability	NOUN
ejpam-4822	152	4	of	of	ADP
ejpam-4822	152	5	the	the	DET
ejpam-4822	152	6	diophantine	diophantine	NOUN
ejpam-4822	152	7	equation	equation	NOUN
ejpam-4822	152	8	px	px	X
ejpam-4822	152	9	+	+	CCONJ
ejpam-4822	152	10	(	(	PUNCT
ejpam-4822	152	11	p+	p+	NOUN
ejpam-4822	152	12	8)y	8)y	X
ejpam-4822	152	13	=	=	SYM
ejpam-4822	152	14	z2	z2	PROPN
ejpam-4822	152	15	when	when	SCONJ
ejpam-4822	152	16	p	p	PROPN
ejpam-4822	152	17	>	>	X
ejpam-4822	152	18	3	3	NUM
ejpam-4822	152	19	and	and	CCONJ
ejpam-4822	152	20	p	p	PRON
ejpam-4822	153	1	+	+	NOUN
ejpam-4822	153	2	8	8	NUM
ejpam-4822	153	3	are	be	AUX
ejpam-4822	153	4	primes	prime	NOUN
ejpam-4822	153	5	.	.	PUNCT
ejpam-4822	154	1	annals	annal	NOUN
ejpam-4822	154	2	of	of	ADP
ejpam-4822	154	3	pure	pure	ADJ
ejpam-4822	154	4	and	and	CCONJ
ejpam-4822	154	5	applied	applied	ADJ
ejpam-4822	154	6	mathematics	mathematic	NOUN
ejpam-4822	154	7	,	,	PUNCT
ejpam-4822	154	8	18(1):9–13	18(1):9–13	NUM
ejpam-4822	154	9	,	,	PUNCT
ejpam-4822	154	10	2018	2018	NUM
ejpam-4822	154	11	.	.	PUNCT
ejpam-4822	155	1	[	[	X
ejpam-4822	155	2	4	4	X
ejpam-4822	155	3	]	]	X
ejpam-4822	155	4	william	william	PROPN
ejpam-4822	155	5	sobredo	sobredo	PROPN
ejpam-4822	155	6	gayo	gayo	PROPN
ejpam-4822	155	7	jr	jr	PROPN
ejpam-4822	155	8	and	and	CCONJ
ejpam-4822	155	9	jerico	jerico	PROPN
ejpam-4822	155	10	bravo	bravo	PROPN
ejpam-4822	155	11	bacani	bacani	PROPN
ejpam-4822	155	12	.	.	PUNCT
ejpam-4822	156	1	on	on	ADP
ejpam-4822	156	2	the	the	DET
ejpam-4822	156	3	diophantine	diophantine	NOUN
ejpam-4822	156	4	equation	equation	NOUN
ejpam-4822	156	5	mx	mx	PROPN
ejpam-4822	156	6	p+(mq+1)y	p+(mq+1)y	PROPN
ejpam-4822	156	7	=	=	SYM
ejpam-4822	156	8	z2	z2	PROPN
ejpam-4822	156	9	.	.	PUNCT
ejpam-4822	157	1	european	european	PROPN
ejpam-4822	157	2	journal	journal	PROPN
ejpam-4822	157	3	of	of	ADP
ejpam-4822	157	4	pure	pure	ADJ
ejpam-4822	157	5	and	and	CCONJ
ejpam-4822	157	6	applied	applied	ADJ
ejpam-4822	157	7	mathematics	mathematic	NOUN
ejpam-4822	157	8	,	,	PUNCT
ejpam-4822	157	9	14(2):396	14(2):396	NUM
ejpam-4822	157	10	–	–	PUNCT
ejpam-4822	157	11	403	403	NUM
ejpam-4822	157	12	,	,	PUNCT
ejpam-4822	157	13	2021	2021	NUM
ejpam-4822	157	14	.	.	PUNCT
ejpam-4822	158	1	[	[	X
ejpam-4822	158	2	5	5	NUM
ejpam-4822	158	3	]	]	PUNCT
ejpam-4822	158	4	s	s	PART
ejpam-4822	158	5	kumar	kumar	PROPN
ejpam-4822	158	6	,	,	PUNCT
ejpam-4822	158	7	d	d	PROPN
ejpam-4822	158	8	gupta	gupta	PROPN
ejpam-4822	158	9	,	,	PUNCT
ejpam-4822	158	10	and	and	CCONJ
ejpam-4822	158	11	h	h	PROPN
ejpam-4822	158	12	kishan	kishan	PROPN
ejpam-4822	158	13	.	.	PUNCT
ejpam-4822	159	1	on	on	ADP
ejpam-4822	159	2	the	the	DET
ejpam-4822	159	3	solution	solution	NOUN
ejpam-4822	159	4	of	of	ADP
ejpam-4822	159	5	exponential	exponential	ADJ
ejpam-4822	159	6	diophantine	diophantine	NOUN
ejpam-4822	159	7	equation	equation	NOUN
ejpam-4822	159	8	px	px	X
ejpam-4822	159	9	+	+	CCONJ
ejpam-4822	159	10	(	(	PUNCT
ejpam-4822	159	11	p	p	X
ejpam-4822	159	12	+	+	NOUN
ejpam-4822	159	13	12)y	12)y	NUM
ejpam-4822	159	14	=	=	SYM
ejpam-4822	159	15	z2	z2	PROPN
ejpam-4822	159	16	.	.	PUNCT
ejpam-4822	160	1	international	international	ADJ
ejpam-4822	160	2	transactions	transaction	NOUN
ejpam-4822	160	3	in	in	ADP
ejpam-4822	160	4	mathematical	mathematical	ADJ
ejpam-4822	160	5	sciences	science	NOUN
ejpam-4822	160	6	and	and	CCONJ
ejpam-4822	160	7	computer	computer	NOUN
ejpam-4822	160	8	,	,	PUNCT
ejpam-4822	160	9	11(1):1–4	11(1):1–4	NOUN
ejpam-4822	160	10	,	,	PUNCT
ejpam-4822	160	11	2018	2018	NUM
ejpam-4822	160	12	.	.	PUNCT
ejpam-4822	161	1	[	[	X
ejpam-4822	161	2	6	6	NUM
ejpam-4822	161	3	]	]	PUNCT
ejpam-4822	161	4	preda	preda	PROPN
ejpam-4822	161	5	mihailescu	mihailescu	PROPN
ejpam-4822	161	6	.	.	PUNCT
ejpam-4822	162	1	primary	primary	ADJ
ejpam-4822	162	2	cyclotomic	cyclotomic	ADJ
ejpam-4822	162	3	units	unit	NOUN
ejpam-4822	162	4	and	and	CCONJ
ejpam-4822	162	5	a	a	DET
ejpam-4822	162	6	proof	proof	NOUN
ejpam-4822	162	7	of	of	ADP
ejpam-4822	162	8	catalans	catalan	NOUN
ejpam-4822	162	9	conjecture	conjecture	VERB
ejpam-4822	162	10	.	.	PUNCT
ejpam-4822	163	1	2004	2004	NUM
ejpam-4822	163	2	.	.	PUNCT
ejpam-4822	164	1	[	[	X
ejpam-4822	164	2	7	7	X
ejpam-4822	164	3	]	]	X
ejpam-4822	164	4	cg	cg	NOUN
ejpam-4822	164	5	rao	rao	PROPN
ejpam-4822	164	6	.	.	PUNCT
ejpam-4822	165	1	on	on	ADP
ejpam-4822	165	2	the	the	DET
ejpam-4822	165	3	diophantine	diophantine	NOUN
ejpam-4822	165	4	equation	equation	NOUN
ejpam-4822	165	5	3x	3x	NUM
ejpam-4822	165	6	+7y	+7y	NUM
ejpam-4822	165	7	=	=	SYM
ejpam-4822	165	8	z2	z2	PROPN
ejpam-4822	165	9	.	.	PUNCT
ejpam-4822	166	1	epra	epra	PROPN
ejpam-4822	166	2	international	international	PROPN
ejpam-4822	166	3	journal	journal	PROPN
ejpam-4822	166	4	of	of	ADP
ejpam-4822	166	5	research	research	NOUN
ejpam-4822	166	6	and	and	CCONJ
ejpam-4822	166	7	development	development	NOUN
ejpam-4822	166	8	,	,	PUNCT
ejpam-4822	166	9	3(6):93–95	3(6):93–95	NUM
ejpam-4822	166	10	,	,	PUNCT
ejpam-4822	166	11	2018	2018	NUM
ejpam-4822	166	12	.	.	PUNCT
ejpam-4822	167	1	[	[	X
ejpam-4822	167	2	8	8	NUM
ejpam-4822	167	3	]	]	X
ejpam-4822	167	4	suton	suton	NOUN
ejpam-4822	167	5	tadee	tadee	PROPN
ejpam-4822	167	6	.	.	PUNCT
ejpam-4822	168	1	on	on	ADP
ejpam-4822	168	2	the	the	DET
ejpam-4822	168	3	diophantine	diophantine	NOUN
ejpam-4822	168	4	equation	equation	NOUN
ejpam-4822	168	5	px	px	X
ejpam-4822	168	6	+	+	CCONJ
ejpam-4822	168	7	(	(	PUNCT
ejpam-4822	168	8	p	p	X
ejpam-4822	168	9	+	+	NOUN
ejpam-4822	168	10	14)y	14)y	NUM
ejpam-4822	168	11	=	=	SYM
ejpam-4822	168	12	z2	z2	PROPN
ejpam-4822	168	13	where	where	SCONJ
ejpam-4822	168	14	p	p	NOUN
ejpam-4822	168	15	and	and	CCONJ
ejpam-4822	168	16	p	p	NOUN
ejpam-4822	168	17	+	+	NOUN
ejpam-4822	168	18	14	14	NUM
ejpam-4822	168	19	are	be	AUX
ejpam-4822	168	20	prime	prime	ADJ
ejpam-4822	168	21	numbers	number	NOUN
ejpam-4822	168	22	.	.	PUNCT
ejpam-4822	169	1	annals	annal	NOUN
ejpam-4822	169	2	of	of	ADP
ejpam-4822	169	3	pure	pure	ADJ
ejpam-4822	169	4	and	and	CCONJ
ejpam-4822	169	5	applied	applied	ADJ
ejpam-4822	169	6	mathematics	mathematic	NOUN
ejpam-4822	169	7	,	,	PUNCT
ejpam-4822	169	8	26(2):125–130	26(2):125–130	PROPN
ejpam-4822	169	9	,	,	PUNCT
ejpam-4822	169	10	2022	2022	NUM
ejpam-4822	169	11	.	.	PUNCT
ejpam-4822	170	1	[	[	X
ejpam-4822	170	2	9	9	NUM
ejpam-4822	170	3	]	]	X
ejpam-4822	170	4	suton	suton	NOUN
ejpam-4822	170	5	tadee	tadee	PROPN
ejpam-4822	170	6	and	and	CCONJ
ejpam-4822	170	7	apirat	apirat	NOUN
ejpam-4822	170	8	siraworakun	siraworakun	PROPN
ejpam-4822	170	9	.	.	PUNCT
ejpam-4822	171	1	non	non	ADJ
ejpam-4822	171	2	-	-	NOUN
ejpam-4822	171	3	existence	existence	NOUN
ejpam-4822	171	4	of	of	ADP
ejpam-4822	171	5	positive	positive	ADJ
ejpam-4822	171	6	integer	integer	NOUN
ejpam-4822	171	7	solutions	solution	NOUN
ejpam-4822	171	8	of	of	ADP
ejpam-4822	171	9	the	the	DET
ejpam-4822	171	10	diophantine	diophantine	NOUN
ejpam-4822	171	11	equation	equation	NOUN
ejpam-4822	171	12	px+(p+2q)y	px+(p+2q)y	NOUN
ejpam-4822	171	13	=	=	SYM
ejpam-4822	171	14	z2	z2	PROPN
ejpam-4822	171	15	where	where	SCONJ
ejpam-4822	171	16	p	p	X
ejpam-4822	171	17	,	,	PUNCT
ejpam-4822	171	18	q	q	PUNCT
ejpam-4822	171	19	and	and	CCONJ
ejpam-4822	171	20	p+2q	p+2q	NOUN
ejpam-4822	171	21	are	be	AUX
ejpam-4822	171	22	prime	prime	ADJ
ejpam-4822	171	23	numbers	number	NOUN
ejpam-4822	171	24	.	.	PUNCT
ejpam-4822	172	1	european	european	ADJ
ejpam-4822	172	2	journal	journal	PROPN
ejpam-4822	172	3	of	of	ADP
ejpam-4822	172	4	pure	pure	ADJ
ejpam-4822	172	5	and	and	CCONJ
ejpam-4822	172	6	applied	applied	ADJ
ejpam-4822	172	7	mathematics	mathematic	NOUN
ejpam-4822	172	8	,	,	PUNCT
ejpam-4822	172	9	16(2):724–735	16(2):724–735	PROPN
ejpam-4822	172	10	,	,	PUNCT
ejpam-4822	172	11	2023	2023	NUM
ejpam-4822	172	12	.	.	PUNCT
ejpam-4822	173	1	[	[	X
ejpam-4822	173	2	10	10	NUM
ejpam-4822	173	3	]	]	X
ejpam-4822	173	4	m	m	NOUN
ejpam-4822	173	5	tatong	tatong	NOUN
ejpam-4822	173	6	and	and	CCONJ
ejpam-4822	173	7	a	a	DET
ejpam-4822	173	8	suvarnamani	suvarnamani	NOUN
ejpam-4822	173	9	.	.	PUNCT
ejpam-4822	174	1	on	on	ADP
ejpam-4822	174	2	the	the	DET
ejpam-4822	174	3	diophantine	diophantine	NOUN
ejpam-4822	174	4	equation	equation	NOUN
ejpam-4822	174	5	px	px	X
ejpam-4822	174	6	+	+	CCONJ
ejpam-4822	174	7	(	(	PUNCT
ejpam-4822	174	8	p	p	X
ejpam-4822	174	9	+	+	NUM
ejpam-4822	174	10	1)y	1)y	NUM
ejpam-4822	174	11	=	=	SYM
ejpam-4822	174	12	z2	z2	PROPN
ejpam-4822	174	13	.	.	PUNCT
ejpam-4822	175	1	international	international	ADJ
ejpam-4822	175	2	journal	journal	NOUN
ejpam-4822	175	3	of	of	ADP
ejpam-4822	175	4	pure	pure	ADJ
ejpam-4822	175	5	and	and	CCONJ
ejpam-4822	175	6	applied	applied	ADJ
ejpam-4822	175	7	mathematics	mathematic	NOUN
ejpam-4822	175	8	,	,	PUNCT
ejpam-4822	175	9	103(2):155–158	103(2):155–158	NUM
ejpam-4822	175	10	,	,	PUNCT
ejpam-4822	175	11	2015	2015	NUM
ejpam-4822	175	12	.	.	PUNCT
ejpam-4822	176	1	[	[	X
ejpam-4822	176	2	11	11	NUM
ejpam-4822	176	3	]	]	X
ejpam-4822	176	4	chokchai	chokchai	ADJ
ejpam-4822	176	5	viriyapong	viriyapong	PROPN
ejpam-4822	176	6	and	and	CCONJ
ejpam-4822	176	7	nongluk	nongluk	PROPN
ejpam-4822	176	8	viriyapong	viriyapong	PROPN
ejpam-4822	176	9	.	.	PUNCT
ejpam-4822	177	1	on	on	ADP
ejpam-4822	177	2	the	the	DET
ejpam-4822	177	3	diophantine	diophantine	NOUN
ejpam-4822	177	4	equation	equation	NOUN
ejpam-4822	177	5	ax+(a+	ax+(a+	PROPN
ejpam-4822	177	6	2)y	2)y	PROPN
ejpam-4822	177	7	=	=	SYM
ejpam-4822	177	8	z2	z2	PROPN
ejpam-4822	177	9	,	,	PUNCT
ejpam-4822	177	10	where	where	SCONJ
ejpam-4822	177	11	a	a	DET
ejpam-4822	177	12	≡	≡	PROPN
ejpam-4822	177	13	5	5	NUM
ejpam-4822	177	14	(	(	PUNCT
ejpam-4822	177	15	mod	mod	PROPN
ejpam-4822	177	16	21	21	NUM
ejpam-4822	177	17	)	)	PUNCT
ejpam-4822	177	18	.	.	PUNCT
ejpam-4822	178	1	international	international	ADJ
ejpam-4822	178	2	journal	journal	PROPN
ejpam-4822	178	3	of	of	ADP
ejpam-4822	178	4	mathematics	mathematics	PROPN
ejpam-4822	178	5	&	&	CCONJ
ejpam-4822	178	6	computer	computer	PROPN
ejpam-4822	178	7	science	science	PROPN
ejpam-4822	178	8	,	,	PUNCT
ejpam-4822	178	9	18(3	18(3	NUM
ejpam-4822	178	10	)	)	PUNCT
ejpam-4822	178	11	,	,	PUNCT
ejpam-4822	178	12	2023	2023	NUM
ejpam-4822	178	13	.	.	PUNCT