id	sid	tid	token	lemma	pos
ejpam-5323	1	1	european	european	PROPN
ejpam-5323	1	2	journal	journal	PROPN
ejpam-5323	1	3	of	of	ADP
ejpam-5323	1	4	pure	pure	ADJ
ejpam-5323	1	5	and	and	CCONJ
ejpam-5323	1	6	applied	apply	VERB
ejpam-5323	1	7	mathematics	mathematic	NOUN
ejpam-5323	1	8	vol	vol	NOUN
ejpam-5323	1	9	.	.	PROPN
ejpam-5323	2	1	17	17	NUM
ejpam-5323	2	2	,	,	PUNCT
ejpam-5323	2	3	no	no	INTJ
ejpam-5323	2	4	.	.	NOUN
ejpam-5323	2	5	3	3	NUM
ejpam-5323	2	6	,	,	PUNCT
ejpam-5323	2	7	2024	2024	NUM
ejpam-5323	2	8	,	,	PUNCT
ejpam-5323	2	9	2127	2127	NUM
ejpam-5323	2	10	-	-	SYM
ejpam-5323	2	11	2141	2141	NUM
ejpam-5323	2	12	issn	issn	VERB
ejpam-5323	2	13	1307	1307	NUM
ejpam-5323	2	14	-	-	SYM
ejpam-5323	2	15	5543	5543	NUM
ejpam-5323	2	16	–	–	PUNCT
ejpam-5323	2	17	ejpam.com	ejpam.com	X
ejpam-5323	2	18	published	publish	VERB
ejpam-5323	2	19	by	by	ADP
ejpam-5323	2	20	new	new	PROPN
ejpam-5323	2	21	york	york	PROPN
ejpam-5323	2	22	business	business	PROPN
ejpam-5323	2	23	global	global	ADJ
ejpam-5323	2	24	structure	structure	NOUN
ejpam-5323	2	25	of	of	ADP
ejpam-5323	2	26	primitive	primitive	ADJ
ejpam-5323	2	27	pythagorean	pythagorean	ADJ
ejpam-5323	2	28	triples	triple	NOUN
ejpam-5323	2	29	in	in	ADP
ejpam-5323	2	30	generating	generate	VERB
ejpam-5323	2	31	trees	tree	NOUN
ejpam-5323	2	32	lucia	lucia	PROPN
ejpam-5323	3	1	kőszegyová	kőszegyová	PROPN
ejpam-5323	3	2	1,∗	1,∗	PROPN
ejpam-5323	3	3	,	,	PUNCT
ejpam-5323	3	4	evelin	evelin	PROPN
ejpam-5323	3	5	csókási1	csókási1	PROPN
ejpam-5323	3	6	,	,	PUNCT
ejpam-5323	3	7	juraj	juraj	VERB
ejpam-5323	3	8	hirjak1	hirjak1	PROPN
ejpam-5323	3	9	1	1	NUM
ejpam-5323	3	10	institute	institute	PROPN
ejpam-5323	3	11	of	of	ADP
ejpam-5323	3	12	mathematics	mathematic	NOUN
ejpam-5323	3	13	,	,	PUNCT
ejpam-5323	3	14	faculty	faculty	NOUN
ejpam-5323	3	15	of	of	ADP
ejpam-5323	3	16	science	science	NOUN
ejpam-5323	3	17	,	,	PUNCT
ejpam-5323	3	18	p.j	p.j	PROPN
ejpam-5323	3	19	.	.	PROPN
ejpam-5323	3	20	šafárik	šafárik	PROPN
ejpam-5323	3	21	university	university	PROPN
ejpam-5323	3	22	in	in	ADP
ejpam-5323	3	23	košice	košice	PROPN
ejpam-5323	3	24	,	,	PUNCT
ejpam-5323	3	25	košice	košice	PROPN
ejpam-5323	3	26	,	,	PUNCT
ejpam-5323	3	27	slovakia	slovakia	PROPN
ejpam-5323	3	28	abstract	abstract	PROPN
ejpam-5323	3	29	.	.	PUNCT
ejpam-5323	4	1	a	a	DET
ejpam-5323	4	2	pythagorean	pythagorean	PROPN
ejpam-5323	4	3	triple	triple	NOUN
ejpam-5323	4	4	is	be	AUX
ejpam-5323	4	5	a	a	DET
ejpam-5323	4	6	triple	triple	NOUN
ejpam-5323	4	7	of	of	ADP
ejpam-5323	4	8	positive	positive	ADJ
ejpam-5323	4	9	integers	integer	NOUN
ejpam-5323	4	10	(	(	PUNCT
ejpam-5323	4	11	a	a	PRON
ejpam-5323	4	12	,	,	PUNCT
ejpam-5323	4	13	b	b	NOUN
ejpam-5323	4	14	,	,	PUNCT
ejpam-5323	4	15	c	c	NOUN
ejpam-5323	4	16	)	)	PUNCT
ejpam-5323	4	17	such	such	ADJ
ejpam-5323	4	18	that	that	PRON
ejpam-5323	4	19	a2	a2	PROPN
ejpam-5323	4	20	+	+	CCONJ
ejpam-5323	4	21	b2	b2	NOUN
ejpam-5323	4	22	=	=	PROPN
ejpam-5323	4	23	c2	c2	PROPN
ejpam-5323	4	24	.	.	PUNCT
ejpam-5323	5	1	if	if	SCONJ
ejpam-5323	5	2	a	a	DET
ejpam-5323	5	3	,	,	PUNCT
ejpam-5323	5	4	b	b	NOUN
ejpam-5323	5	5	are	be	AUX
ejpam-5323	5	6	coprime	coprime	ADJ
ejpam-5323	5	7	,	,	PUNCT
ejpam-5323	5	8	then	then	ADV
ejpam-5323	5	9	it	it	PRON
ejpam-5323	5	10	is	be	AUX
ejpam-5323	5	11	called	call	VERB
ejpam-5323	5	12	a	a	DET
ejpam-5323	5	13	primitive	primitive	ADJ
ejpam-5323	5	14	pythagorean	pythagorean	NOUN
ejpam-5323	5	15	triple	triple	NOUN
ejpam-5323	5	16	.	.	PUNCT
ejpam-5323	6	1	it	it	PRON
ejpam-5323	6	2	is	be	AUX
ejpam-5323	6	3	known	know	VERB
ejpam-5323	6	4	that	that	SCONJ
ejpam-5323	6	5	every	every	DET
ejpam-5323	6	6	primitive	primitive	ADJ
ejpam-5323	6	7	pythagorean	pythagorean	NOUN
ejpam-5323	6	8	triple	triple	NOUN
ejpam-5323	6	9	can	can	AUX
ejpam-5323	6	10	be	be	AUX
ejpam-5323	6	11	generated	generate	VERB
ejpam-5323	6	12	from	from	ADP
ejpam-5323	6	13	the	the	DET
ejpam-5323	6	14	triple	triple	ADJ
ejpam-5323	6	15	(	(	PUNCT
ejpam-5323	6	16	3	3	NUM
ejpam-5323	6	17	,	,	PUNCT
ejpam-5323	6	18	4	4	NUM
ejpam-5323	6	19	,	,	PUNCT
ejpam-5323	6	20	5	5	NUM
ejpam-5323	6	21	)	)	PUNCT
ejpam-5323	6	22	using	use	VERB
ejpam-5323	6	23	multiplication	multiplication	NOUN
ejpam-5323	6	24	by	by	ADP
ejpam-5323	6	25	unique	unique	ADJ
ejpam-5323	6	26	number	number	NOUN
ejpam-5323	6	27	and	and	CCONJ
ejpam-5323	6	28	order	order	NOUN
ejpam-5323	6	29	of	of	ADP
ejpam-5323	6	30	three	three	NUM
ejpam-5323	6	31	specific	specific	ADJ
ejpam-5323	6	32	3	3	NUM
ejpam-5323	6	33	×	×	NOUN
ejpam-5323	6	34	3	3	NUM
ejpam-5323	6	35	matrices	matrix	NOUN
ejpam-5323	6	36	,	,	PUNCT
ejpam-5323	6	37	which	which	PRON
ejpam-5323	6	38	yields	yield	VERB
ejpam-5323	6	39	a	a	DET
ejpam-5323	6	40	ternary	ternary	ADJ
ejpam-5323	6	41	tree	tree	NOUN
ejpam-5323	6	42	of	of	ADP
ejpam-5323	6	43	triplets	triplet	NOUN
ejpam-5323	6	44	.	.	PUNCT
ejpam-5323	7	1	two	two	NUM
ejpam-5323	7	2	such	such	ADJ
ejpam-5323	7	3	trees	tree	NOUN
ejpam-5323	7	4	were	be	AUX
ejpam-5323	7	5	described	describe	VERB
ejpam-5323	7	6	by	by	ADP
ejpam-5323	7	7	berggren	berggren	PROPN
ejpam-5323	7	8	and	and	CCONJ
ejpam-5323	7	9	price	price	NOUN
ejpam-5323	7	10	,	,	PUNCT
ejpam-5323	7	11	respectively	respectively	ADV
ejpam-5323	7	12	.	.	PUNCT
ejpam-5323	8	1	a	a	DET
ejpam-5323	8	2	different	different	ADJ
ejpam-5323	8	3	approach	approach	NOUN
ejpam-5323	8	4	is	be	AUX
ejpam-5323	8	5	to	to	PART
ejpam-5323	8	6	view	view	VERB
ejpam-5323	8	7	the	the	DET
ejpam-5323	8	8	primitive	primitive	ADJ
ejpam-5323	8	9	pythagorean	pythagorean	ADJ
ejpam-5323	8	10	triples	triple	NOUN
ejpam-5323	8	11	as	as	ADP
ejpam-5323	8	12	points	point	NOUN
ejpam-5323	8	13	in	in	ADP
ejpam-5323	8	14	the	the	DET
ejpam-5323	8	15	three	three	NUM
ejpam-5323	8	16	-	-	PUNCT
ejpam-5323	8	17	dimensional	dimensional	ADJ
ejpam-5323	8	18	euclidean	euclidean	ADJ
ejpam-5323	8	19	space	space	NOUN
ejpam-5323	8	20	.	.	PUNCT
ejpam-5323	9	1	in	in	ADP
ejpam-5323	9	2	this	this	DET
ejpam-5323	9	3	paper	paper	NOUN
ejpam-5323	9	4	,	,	PUNCT
ejpam-5323	9	5	we	we	PRON
ejpam-5323	9	6	prove	prove	VERB
ejpam-5323	9	7	that	that	SCONJ
ejpam-5323	9	8	the	the	DET
ejpam-5323	9	9	triple	triple	NOUN
ejpam-5323	9	10	of	of	ADP
ejpam-5323	9	11	descendants	descendant	NOUN
ejpam-5323	9	12	of	of	ADP
ejpam-5323	9	13	any	any	DET
ejpam-5323	9	14	primitive	primitive	ADJ
ejpam-5323	9	15	pythagorean	pythagorean	NOUN
ejpam-5323	9	16	triple	triple	NOUN
ejpam-5323	9	17	in	in	ADP
ejpam-5323	9	18	berggren	berggren	PROPN
ejpam-5323	9	19	’s	’s	PART
ejpam-5323	9	20	or	or	CCONJ
ejpam-5323	9	21	price	price	NOUN
ejpam-5323	9	22	’s	’s	PART
ejpam-5323	9	23	tree	tree	NOUN
ejpam-5323	9	24	forms	form	VERB
ejpam-5323	9	25	a	a	DET
ejpam-5323	9	26	triangle	triangle	NOUN
ejpam-5323	9	27	(	(	PUNCT
ejpam-5323	9	28	and	and	CCONJ
ejpam-5323	9	29	therefore	therefore	ADV
ejpam-5323	9	30	defines	define	VERB
ejpam-5323	9	31	a	a	DET
ejpam-5323	9	32	plane	plane	NOUN
ejpam-5323	9	33	)	)	PUNCT
ejpam-5323	9	34	,	,	PUNCT
ejpam-5323	9	35	and	and	CCONJ
ejpam-5323	9	36	we	we	PRON
ejpam-5323	9	37	present	present	VERB
ejpam-5323	9	38	our	our	PRON
ejpam-5323	9	39	results	result	NOUN
ejpam-5323	9	40	related	relate	VERB
ejpam-5323	9	41	to	to	ADP
ejpam-5323	9	42	these	these	DET
ejpam-5323	9	43	triangles	triangle	NOUN
ejpam-5323	9	44	(	(	PUNCT
ejpam-5323	9	45	and	and	CCONJ
ejpam-5323	9	46	these	these	DET
ejpam-5323	9	47	planes	plane	NOUN
ejpam-5323	9	48	)	)	PUNCT
ejpam-5323	9	49	.	.	PUNCT
ejpam-5323	10	1	2020	2020	NUM
ejpam-5323	10	2	mathematics	mathematic	NOUN
ejpam-5323	10	3	subject	subject	NOUN
ejpam-5323	10	4	classifications	classification	NOUN
ejpam-5323	10	5	:	:	PUNCT
ejpam-5323	10	6	11d09	11d09	NUM
ejpam-5323	10	7	,	,	PUNCT
ejpam-5323	10	8	11a41	11a41	NUM
ejpam-5323	10	9	,	,	PUNCT
ejpam-5323	10	10	11c99	11c99	NUM
ejpam-5323	10	11	key	key	ADJ
ejpam-5323	10	12	words	word	NOUN
ejpam-5323	10	13	and	and	CCONJ
ejpam-5323	10	14	phrases	phrase	NOUN
ejpam-5323	10	15	:	:	PUNCT
ejpam-5323	10	16	primitive	primitive	ADJ
ejpam-5323	10	17	pythagorean	pythagorean	ADJ
ejpam-5323	10	18	triples	triple	NOUN
ejpam-5323	10	19	,	,	PUNCT
ejpam-5323	10	20	berggren	berggren	PROPN
ejpam-5323	10	21	’s	’s	PART
ejpam-5323	10	22	tree	tree	NOUN
ejpam-5323	10	23	,	,	PUNCT
ejpam-5323	10	24	price	price	NOUN
ejpam-5323	10	25	’s	’s	PART
ejpam-5323	10	26	tree	tree	NOUN
ejpam-5323	10	27	,	,	PUNCT
ejpam-5323	10	28	euclid	euclid	PROPN
ejpam-5323	10	29	’s	’s	PART
ejpam-5323	10	30	formula	formula	NOUN
ejpam-5323	10	31	1	1	NUM
ejpam-5323	10	32	.	.	PUNCT
ejpam-5323	11	1	introduction	introduction	NOUN
ejpam-5323	11	2	primitive	primitive	ADJ
ejpam-5323	11	3	pythagorean	pythagorean	PROPN
ejpam-5323	11	4	triples	triple	NOUN
ejpam-5323	11	5	are	be	AUX
ejpam-5323	11	6	an	an	DET
ejpam-5323	11	7	interesting	interesting	ADJ
ejpam-5323	11	8	object	object	NOUN
ejpam-5323	11	9	of	of	ADP
ejpam-5323	11	10	the	the	DET
ejpam-5323	11	11	number	number	NOUN
ejpam-5323	11	12	theory	theory	NOUN
ejpam-5323	11	13	,	,	PUNCT
ejpam-5323	11	14	and	and	CCONJ
ejpam-5323	11	15	they	they	PRON
ejpam-5323	11	16	have	have	VERB
ejpam-5323	11	17	potential	potential	NOUN
ejpam-5323	11	18	to	to	PART
ejpam-5323	11	19	be	be	AUX
ejpam-5323	11	20	also	also	ADV
ejpam-5323	11	21	used	use	VERB
ejpam-5323	11	22	while	while	SCONJ
ejpam-5323	11	23	studying	study	VERB
ejpam-5323	11	24	the	the	DET
ejpam-5323	11	25	properties	property	NOUN
ejpam-5323	11	26	in	in	ADP
ejpam-5323	11	27	other	other	ADJ
ejpam-5323	11	28	areas	area	NOUN
ejpam-5323	11	29	of	of	ADP
ejpam-5323	11	30	the	the	DET
ejpam-5323	11	31	mathematics	mathematic	NOUN
ejpam-5323	11	32	(	(	PUNCT
ejpam-5323	11	33	e.g.	e.g.	ADV
ejpam-5323	11	34	in	in	ADP
ejpam-5323	11	35	geometry	geometry	NOUN
ejpam-5323	11	36	,	,	PUNCT
ejpam-5323	11	37	or	or	CCONJ
ejpam-5323	11	38	in	in	ADP
ejpam-5323	11	39	graph	graph	NOUN
ejpam-5323	11	40	theory	theory	NOUN
ejpam-5323	11	41	)	)	PUNCT
ejpam-5323	11	42	.	.	PUNCT
ejpam-5323	12	1	the	the	DET
ejpam-5323	12	2	description	description	NOUN
ejpam-5323	12	3	and	and	CCONJ
ejpam-5323	12	4	knowledge	knowledge	NOUN
ejpam-5323	12	5	of	of	ADP
ejpam-5323	12	6	their	their	PRON
ejpam-5323	12	7	properties	property	NOUN
ejpam-5323	12	8	can	can	AUX
ejpam-5323	12	9	also	also	ADV
ejpam-5323	12	10	be	be	AUX
ejpam-5323	12	11	used	use	VERB
ejpam-5323	12	12	practically	practically	ADV
ejpam-5323	12	13	,	,	PUNCT
ejpam-5323	12	14	for	for	ADP
ejpam-5323	12	15	example	example	NOUN
ejpam-5323	12	16	in	in	ADP
ejpam-5323	12	17	cryptography	cryptography	NOUN
ejpam-5323	12	18	,	,	PUNCT
ejpam-5323	12	19	considering	consider	VERB
ejpam-5323	12	20	that	that	SCONJ
ejpam-5323	12	21	there	there	PRON
ejpam-5323	12	22	are	be	VERB
ejpam-5323	12	23	infinitely	infinitely	ADV
ejpam-5323	12	24	many	many	ADJ
ejpam-5323	12	25	primitive	primitive	ADJ
ejpam-5323	12	26	pythagorean	pythagorean	ADJ
ejpam-5323	12	27	triples	triple	NOUN
ejpam-5323	12	28	,	,	PUNCT
ejpam-5323	12	29	and	and	CCONJ
ejpam-5323	12	30	the	the	DET
ejpam-5323	12	31	fact	fact	NOUN
ejpam-5323	12	32	that	that	SCONJ
ejpam-5323	12	33	such	such	ADJ
ejpam-5323	12	34	triples	triple	NOUN
ejpam-5323	12	35	have	have	AUX
ejpam-5323	12	36	the	the	DET
ejpam-5323	12	37	ability	ability	NOUN
ejpam-5323	12	38	of	of	ADP
ejpam-5323	12	39	creating	create	VERB
ejpam-5323	12	40	probability	probability	NOUN
ejpam-5323	12	41	events	event	NOUN
ejpam-5323	12	42	[	[	X
ejpam-5323	12	43	15	15	NUM
ejpam-5323	12	44	]	]	PUNCT
ejpam-5323	12	45	.	.	PUNCT
ejpam-5323	13	1	moreover	moreover	ADV
ejpam-5323	13	2	,	,	PUNCT
ejpam-5323	13	3	sufficiently	sufficiently	ADV
ejpam-5323	13	4	large	large	ADJ
ejpam-5323	13	5	primitive	primitive	ADJ
ejpam-5323	13	6	pythagorean	pythagorean	NOUN
ejpam-5323	13	7	triples	triple	NOUN
ejpam-5323	13	8	can	can	AUX
ejpam-5323	13	9	be	be	AUX
ejpam-5323	13	10	used	use	VERB
ejpam-5323	13	11	as	as	ADP
ejpam-5323	13	12	keys	key	NOUN
ejpam-5323	13	13	by	by	ADP
ejpam-5323	13	14	certification	certification	NOUN
ejpam-5323	13	15	authority	authority	NOUN
ejpam-5323	13	16	sending	send	VERB
ejpam-5323	13	17	two	two	NUM
ejpam-5323	13	18	numbers	number	NOUN
ejpam-5323	13	19	to	to	ADP
ejpam-5323	13	20	two	two	NUM
ejpam-5323	13	21	parties	party	NOUN
ejpam-5323	13	22	as	as	ADP
ejpam-5323	13	23	seeds	seed	NOUN
ejpam-5323	13	24	to	to	PART
ejpam-5323	13	25	generate	generate	VERB
ejpam-5323	13	26	the	the	DET
ejpam-5323	13	27	key	key	NOUN
ejpam-5323	13	28	,	,	PUNCT
ejpam-5323	13	29	and	and	CCONJ
ejpam-5323	13	30	keeping	keep	VERB
ejpam-5323	13	31	the	the	DET
ejpam-5323	13	32	third	third	ADJ
ejpam-5323	13	33	number	number	NOUN
ejpam-5323	13	34	for	for	ADP
ejpam-5323	13	35	audit	audit	NOUN
ejpam-5323	13	36	purposes	purpose	NOUN
ejpam-5323	13	37	[	[	X
ejpam-5323	13	38	5	5	NUM
ejpam-5323	13	39	]	]	PUNCT
ejpam-5323	13	40	.	.	PUNCT
ejpam-5323	14	1	to	to	PART
ejpam-5323	14	2	use	use	VERB
ejpam-5323	14	3	primitive	primitive	ADJ
ejpam-5323	14	4	pythagorean	pythagorean	NOUN
ejpam-5323	14	5	triples	triple	NOUN
ejpam-5323	14	6	,	,	PUNCT
ejpam-5323	14	7	we	we	PRON
ejpam-5323	14	8	need	need	VERB
ejpam-5323	14	9	to	to	PART
ejpam-5323	14	10	understand	understand	VERB
ejpam-5323	14	11	them	they	PRON
ejpam-5323	14	12	and	and	CCONJ
ejpam-5323	14	13	their	their	PRON
ejpam-5323	14	14	generating	generating	NOUN
ejpam-5323	14	15	better	well	ADV
ejpam-5323	14	16	.	.	PUNCT
ejpam-5323	15	1	currently	currently	ADV
ejpam-5323	15	2	,	,	PUNCT
ejpam-5323	15	3	there	there	PRON
ejpam-5323	15	4	are	be	VERB
ejpam-5323	15	5	various	various	ADJ
ejpam-5323	15	6	ways	way	NOUN
ejpam-5323	15	7	of	of	ADP
ejpam-5323	15	8	generating	generate	VERB
ejpam-5323	15	9	integer	integer	NOUN
ejpam-5323	15	10	solutions	solution	NOUN
ejpam-5323	15	11	of	of	ADP
ejpam-5323	15	12	pythagorean	pythagorean	PROPN
ejpam-5323	15	13	∗corresponding	∗corresponding	NOUN
ejpam-5323	15	14	author	author	NOUN
ejpam-5323	15	15	.	.	PUNCT
ejpam-5323	16	1	doi	doi	NOUN
ejpam-5323	16	2	:	:	PUNCT
ejpam-5323	16	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5323	https://doi.org/10.29020/nybg.ejpam.v17i3.5323	ADJ
ejpam-5323	16	4	email	email	NOUN
ejpam-5323	16	5	addresses	address	NOUN
ejpam-5323	16	6	:	:	PUNCT
ejpam-5323	16	7	lucia.janickova@upjs.sk	lucia.janickova@upjs.sk	NOUN
ejpam-5323	16	8	(	(	PUNCT
ejpam-5323	16	9	l.	l.	PROPN
ejpam-5323	16	10	kőszegyová	kőszegyová	PROPN
ejpam-5323	16	11	)	)	PUNCT
ejpam-5323	16	12	,	,	PUNCT
ejpam-5323	16	13	csokasi.evelinke@gmail.com	csokasi.evelinke@gmail.com	PROPN
ejpam-5323	16	14	(	(	PUNCT
ejpam-5323	16	15	e.	e.	PROPN
ejpam-5323	16	16	csókási	csókási	PROPN
ejpam-5323	16	17	)	)	PUNCT
ejpam-5323	16	18	,	,	PUNCT
ejpam-5323	16	19	juraj.hirjak@student.upjs.sk	juraj.hirjak@student.upjs.sk	PROPN
ejpam-5323	16	20	(	(	PUNCT
ejpam-5323	16	21	j.	j.	PROPN
ejpam-5323	16	22	hirjak	hirjak	PROPN
ejpam-5323	16	23	)	)	PUNCT
ejpam-5323	16	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5323	16	25	2127	2127	NUM
ejpam-5323	16	26	©	©	ADP
ejpam-5323	16	27	2024	2024	NUM
ejpam-5323	16	28	ejpam	ejpam	NOUN
ejpam-5323	16	29	all	all	DET
ejpam-5323	16	30	rights	right	NOUN
ejpam-5323	16	31	reserved	reserve	VERB
ejpam-5323	16	32	.	.	PUNCT
ejpam-5323	17	1	l.	l.	PROPN
ejpam-5323	17	2	kőszegyová	kőszegyová	PROPN
ejpam-5323	17	3	,	,	PUNCT
ejpam-5323	17	4	e.	e.	PROPN
ejpam-5323	17	5	csókási	csókási	PROPN
ejpam-5323	17	6	,	,	PUNCT
ejpam-5323	17	7	j.	j.	PROPN
ejpam-5323	17	8	hirjak	hirjak	PROPN
ejpam-5323	17	9	/	/	SYM
ejpam-5323	17	10	eur	eur	PROPN
ejpam-5323	17	11	.	.	PUNCT
ejpam-5323	18	1	j.	j.	PROPN
ejpam-5323	18	2	pure	pure	PROPN
ejpam-5323	18	3	appl	appl	PROPN
ejpam-5323	18	4	.	.	PROPN
ejpam-5323	18	5	math	math	PROPN
ejpam-5323	18	6	,	,	PUNCT
ejpam-5323	18	7	17	17	NUM
ejpam-5323	18	8	(	(	PUNCT
ejpam-5323	18	9	3	3	NUM
ejpam-5323	18	10	)	)	PUNCT
ejpam-5323	18	11	(	(	PUNCT
ejpam-5323	18	12	2024	2024	NUM
ejpam-5323	18	13	)	)	PUNCT
ejpam-5323	18	14	,	,	PUNCT
ejpam-5323	18	15	2127	2127	NUM
ejpam-5323	18	16	-	-	SYM
ejpam-5323	18	17	2141	2141	NUM
ejpam-5323	18	18	2128	2128	NUM
ejpam-5323	18	19	equation	equation	NOUN
ejpam-5323	18	20	a2	a2	NOUN
ejpam-5323	18	21	+	+	CCONJ
ejpam-5323	18	22	b2	b2	NOUN
ejpam-5323	18	23	=	=	PROPN
ejpam-5323	18	24	c2	c2	PROPN
ejpam-5323	18	25	.	.	PUNCT
ejpam-5323	19	1	euclid	euclid	PROPN
ejpam-5323	19	2	’s	’s	PART
ejpam-5323	19	3	formula	formula	NOUN
ejpam-5323	19	4	,	,	PUNCT
ejpam-5323	19	5	berggren	berggren	PROPN
ejpam-5323	19	6	’s	’s	PART
ejpam-5323	19	7	tree	tree	NOUN
ejpam-5323	19	8	and	and	CCONJ
ejpam-5323	19	9	price	price	NOUN
ejpam-5323	19	10	’s	’s	PART
ejpam-5323	19	11	tree	tree	NOUN
ejpam-5323	19	12	are	be	AUX
ejpam-5323	19	13	among	among	ADP
ejpam-5323	19	14	the	the	DET
ejpam-5323	19	15	best	well	ADV
ejpam-5323	19	16	known	know	VERB
ejpam-5323	19	17	ones	one	NOUN
ejpam-5323	19	18	,	,	PUNCT
ejpam-5323	19	19	however	however	ADV
ejpam-5323	19	20	there	there	PRON
ejpam-5323	19	21	are	be	VERB
ejpam-5323	19	22	many	many	ADJ
ejpam-5323	19	23	others	other	NOUN
ejpam-5323	19	24	.	.	PUNCT
ejpam-5323	20	1	some	some	DET
ejpam-5323	20	2	examples	example	NOUN
ejpam-5323	20	3	can	can	AUX
ejpam-5323	20	4	be	be	AUX
ejpam-5323	20	5	found	find	VERB
ejpam-5323	20	6	e.g.	e.g.	ADV
ejpam-5323	20	7	in	in	ADP
ejpam-5323	20	8	[	[	X
ejpam-5323	20	9	13	13	NUM
ejpam-5323	20	10	]	]	PUNCT
ejpam-5323	20	11	.	.	PUNCT
ejpam-5323	21	1	the	the	DET
ejpam-5323	21	2	matrices	matrix	NOUN
ejpam-5323	21	3	used	use	VERB
ejpam-5323	21	4	to	to	PART
ejpam-5323	21	5	generate	generate	VERB
ejpam-5323	21	6	berggren	berggren	PROPN
ejpam-5323	21	7	’s	’s	PART
ejpam-5323	21	8	tree	tree	NOUN
ejpam-5323	21	9	produce	produce	VERB
ejpam-5323	21	10	solutions	solution	NOUN
ejpam-5323	21	11	(	(	PUNCT
ejpam-5323	21	12	a	a	DET
ejpam-5323	21	13	,	,	PUNCT
ejpam-5323	21	14	b	b	NOUN
ejpam-5323	21	15	,	,	PUNCT
ejpam-5323	21	16	c	c	NOUN
ejpam-5323	21	17	)	)	PUNCT
ejpam-5323	21	18	with	with	ADP
ejpam-5323	21	19	coprime	coprime	NOUN
ejpam-5323	21	20	elements	element	NOUN
ejpam-5323	21	21	,	,	PUNCT
ejpam-5323	21	22	i.e.	i.e.	X
ejpam-5323	21	23	the	the	DET
ejpam-5323	21	24	primitive	primitive	ADJ
ejpam-5323	21	25	pythagorean	pythagorean	ADJ
ejpam-5323	21	26	triples	triple	NOUN
ejpam-5323	21	27	,	,	PUNCT
ejpam-5323	21	28	which	which	PRON
ejpam-5323	21	29	can	can	AUX
ejpam-5323	21	30	be	be	AUX
ejpam-5323	21	31	viewed	view	VERB
ejpam-5323	21	32	as	as	ADP
ejpam-5323	21	33	lengths	length	NOUN
ejpam-5323	21	34	of	of	ADP
ejpam-5323	21	35	the	the	DET
ejpam-5323	21	36	sides	side	NOUN
ejpam-5323	21	37	of	of	ADP
ejpam-5323	21	38	pythagorean	pythagorean	PROPN
ejpam-5323	21	39	triangles	triangle	NOUN
ejpam-5323	21	40	.	.	PUNCT
ejpam-5323	22	1	another	another	DET
ejpam-5323	22	2	methods	method	NOUN
ejpam-5323	22	3	of	of	ADP
ejpam-5323	22	4	gerating	gerate	VERB
ejpam-5323	22	5	these	these	DET
ejpam-5323	22	6	triples	triple	NOUN
ejpam-5323	22	7	use	use	VERB
ejpam-5323	22	8	sequences	sequence	NOUN
ejpam-5323	22	9	,	,	PUNCT
ejpam-5323	22	10	generating	generate	VERB
ejpam-5323	22	11	the	the	DET
ejpam-5323	22	12	following	follow	VERB
ejpam-5323	22	13	triples	triple	NOUN
ejpam-5323	22	14	from	from	ADP
ejpam-5323	22	15	a	a	DET
ejpam-5323	22	16	starting	start	VERB
ejpam-5323	22	17	triple	triple	NOUN
ejpam-5323	22	18	.	.	PUNCT
ejpam-5323	23	1	one	one	NUM
ejpam-5323	23	2	of	of	ADP
ejpam-5323	23	3	the	the	DET
ejpam-5323	23	4	newest	new	ADJ
ejpam-5323	23	5	of	of	ADP
ejpam-5323	23	6	these	these	DET
ejpam-5323	23	7	appraoches	appraoche	NOUN
ejpam-5323	23	8	is	be	AUX
ejpam-5323	23	9	described	describe	VERB
ejpam-5323	23	10	by	by	ADP
ejpam-5323	23	11	[	[	X
ejpam-5323	23	12	5	5	NUM
ejpam-5323	23	13	]	]	PUNCT
ejpam-5323	23	14	.	.	PUNCT
ejpam-5323	24	1	other	other	ADJ
ejpam-5323	24	2	approaches	approach	NOUN
ejpam-5323	24	3	to	to	ADP
ejpam-5323	24	4	primitive	primitive	ADJ
ejpam-5323	24	5	pythagorean	pythagorean	NOUN
ejpam-5323	24	6	triples	triple	NOUN
ejpam-5323	24	7	were	be	AUX
ejpam-5323	24	8	introduced	introduce	VERB
ejpam-5323	24	9	e.g.	e.g.	ADV
ejpam-5323	24	10	by	by	ADP
ejpam-5323	24	11	[	[	X
ejpam-5323	24	12	2	2	NUM
ejpam-5323	24	13	]	]	PUNCT
ejpam-5323	24	14	.	.	PUNCT
ejpam-5323	25	1	some	some	DET
ejpam-5323	25	2	properties	property	NOUN
ejpam-5323	25	3	of	of	ADP
ejpam-5323	25	4	the	the	DET
ejpam-5323	25	5	pythagorean	pythagorean	PROPN
ejpam-5323	25	6	triangles	triangle	NOUN
ejpam-5323	25	7	were	be	AUX
ejpam-5323	25	8	already	already	ADV
ejpam-5323	25	9	described	describe	VERB
ejpam-5323	25	10	.	.	PUNCT
ejpam-5323	26	1	e.g.	e.g.	ADV
ejpam-5323	26	2	,	,	PUNCT
ejpam-5323	26	3	the	the	DET
ejpam-5323	26	4	number	number	NOUN
ejpam-5323	26	5	of	of	ADP
ejpam-5323	26	6	primitive	primitive	ADJ
ejpam-5323	26	7	pythagorean	pythagorean	ADJ
ejpam-5323	26	8	triples	triple	NOUN
ejpam-5323	26	9	with	with	ADP
ejpam-5323	26	10	a	a	DET
ejpam-5323	26	11	given	give	VERB
ejpam-5323	26	12	inradius	inradius	NOUN
ejpam-5323	26	13	[	[	X
ejpam-5323	26	14	11	11	NUM
ejpam-5323	26	15	]	]	PUNCT
ejpam-5323	26	16	,	,	PUNCT
ejpam-5323	26	17	triples	triple	NOUN
ejpam-5323	26	18	with	with	ADP
ejpam-5323	26	19	common	common	ADJ
ejpam-5323	26	20	lengths	length	NOUN
ejpam-5323	26	21	of	of	ADP
ejpam-5323	26	22	leg	leg	NOUN
ejpam-5323	26	23	[	[	X
ejpam-5323	26	24	6	6	NUM
ejpam-5323	26	25	]	]	PUNCT
ejpam-5323	26	26	or	or	CCONJ
ejpam-5323	26	27	height	height	NOUN
ejpam-5323	26	28	of	of	ADP
ejpam-5323	26	29	primitive	primitive	ADJ
ejpam-5323	26	30	pythagorean	pythagorean	ADJ
ejpam-5323	26	31	triples	triple	NOUN
ejpam-5323	26	32	(	(	PUNCT
ejpam-5323	26	33	the	the	DET
ejpam-5323	26	34	difference	difference	NOUN
ejpam-5323	26	35	between	between	ADP
ejpam-5323	26	36	length	length	NOUN
ejpam-5323	26	37	of	of	ADP
ejpam-5323	26	38	the	the	DET
ejpam-5323	26	39	hypotenuse	hypotenuse	NOUN
ejpam-5323	26	40	and	and	CCONJ
ejpam-5323	26	41	length	length	NOUN
ejpam-5323	26	42	of	of	ADP
ejpam-5323	26	43	even	even	ADV
ejpam-5323	26	44	leg	leg	NOUN
ejpam-5323	26	45	)	)	PUNCT
ejpam-5323	27	1	[	[	X
ejpam-5323	27	2	4	4	NUM
ejpam-5323	27	3	]	]	PUNCT
ejpam-5323	27	4	.	.	PUNCT
ejpam-5323	28	1	further	far	ADV
ejpam-5323	28	2	,	,	PUNCT
ejpam-5323	28	3	it	it	PRON
ejpam-5323	28	4	was	be	AUX
ejpam-5323	28	5	described	describe	VERB
ejpam-5323	28	6	how	how	SCONJ
ejpam-5323	28	7	to	to	PART
ejpam-5323	28	8	find	find	VERB
ejpam-5323	28	9	the	the	DET
ejpam-5323	28	10	pairs	pair	NOUN
ejpam-5323	28	11	of	of	ADP
ejpam-5323	28	12	pythagorean	pythagorean	PROPN
ejpam-5323	28	13	triangles	triangle	NOUN
ejpam-5323	28	14	with	with	ADP
ejpam-5323	28	15	equal	equal	ADJ
ejpam-5323	28	16	areas	area	NOUN
ejpam-5323	28	17	,	,	PUNCT
ejpam-5323	28	18	or	or	CCONJ
ejpam-5323	28	19	primitive	primitive	ADJ
ejpam-5323	28	20	pythagorean	pythagorean	ADJ
ejpam-5323	28	21	triangles	triangle	NOUN
ejpam-5323	28	22	having	have	VERB
ejpam-5323	28	23	the	the	DET
ejpam-5323	28	24	same	same	ADJ
ejpam-5323	28	25	perimeter	perimeter	NOUN
ejpam-5323	28	26	[	[	X
ejpam-5323	28	27	1	1	NUM
ejpam-5323	28	28	]	]	PUNCT
ejpam-5323	28	29	.	.	PUNCT
ejpam-5323	29	1	also	also	ADV
ejpam-5323	29	2	,	,	PUNCT
ejpam-5323	29	3	some	some	DET
ejpam-5323	29	4	numerical	numerical	ADJ
ejpam-5323	29	5	properties	property	NOUN
ejpam-5323	29	6	of	of	ADP
ejpam-5323	29	7	primitive	primitive	ADJ
ejpam-5323	29	8	pythagorean	pythagorean	NOUN
ejpam-5323	29	9	triples	triple	NOUN
ejpam-5323	29	10	were	be	AUX
ejpam-5323	29	11	studied	study	VERB
ejpam-5323	29	12	e.g.	e.g.	ADV
ejpam-5323	29	13	in	in	ADP
ejpam-5323	29	14	[	[	X
ejpam-5323	29	15	3	3	NUM
ejpam-5323	29	16	]	]	PUNCT
ejpam-5323	29	17	,	,	PUNCT
ejpam-5323	29	18	[	[	X
ejpam-5323	29	19	8	8	NUM
ejpam-5323	29	20	]	]	PUNCT
ejpam-5323	29	21	.	.	PUNCT
ejpam-5323	30	1	the	the	DET
ejpam-5323	30	2	primitive	primitive	ADJ
ejpam-5323	30	3	pythagorean	pythagorean	NOUN
ejpam-5323	30	4	triples	triple	NOUN
ejpam-5323	30	5	can	can	AUX
ejpam-5323	30	6	be	be	AUX
ejpam-5323	30	7	also	also	ADV
ejpam-5323	30	8	viewed	view	VERB
ejpam-5323	30	9	as	as	ADP
ejpam-5323	30	10	coordinates	coordinate	NOUN
ejpam-5323	30	11	of	of	ADP
ejpam-5323	30	12	the	the	DET
ejpam-5323	30	13	points	point	NOUN
ejpam-5323	30	14	in	in	ADP
ejpam-5323	30	15	the	the	DET
ejpam-5323	30	16	three	three	NUM
ejpam-5323	30	17	-	-	PUNCT
ejpam-5323	30	18	dimensional	dimensional	ADJ
ejpam-5323	30	19	euclidean	euclidean	ADJ
ejpam-5323	30	20	space	space	NOUN
ejpam-5323	30	21	.	.	PUNCT
ejpam-5323	31	1	in	in	ADP
ejpam-5323	31	2	this	this	DET
ejpam-5323	31	3	paper	paper	NOUN
ejpam-5323	31	4	,	,	PUNCT
ejpam-5323	31	5	we	we	PRON
ejpam-5323	31	6	consider	consider	VERB
ejpam-5323	31	7	the	the	DET
ejpam-5323	31	8	triples	triple	NOUN
ejpam-5323	31	9	which	which	PRON
ejpam-5323	31	10	are	be	AUX
ejpam-5323	31	11	generated	generate	VERB
ejpam-5323	31	12	from	from	ADP
ejpam-5323	31	13	a	a	DET
ejpam-5323	31	14	given	give	VERB
ejpam-5323	31	15	triple	triple	NOUN
ejpam-5323	31	16	in	in	ADP
ejpam-5323	31	17	either	either	CCONJ
ejpam-5323	31	18	berggren	berggren	PROPN
ejpam-5323	31	19	’s	’s	PART
ejpam-5323	31	20	or	or	CCONJ
ejpam-5323	31	21	price	price	NOUN
ejpam-5323	31	22	’s	’s	PART
ejpam-5323	31	23	tree	tree	NOUN
ejpam-5323	31	24	of	of	ADP
ejpam-5323	31	25	primitive	primitive	ADJ
ejpam-5323	31	26	pythagorean	pythagorean	NOUN
ejpam-5323	31	27	triples	triple	NOUN
ejpam-5323	31	28	(	(	PUNCT
ejpam-5323	31	29	such	such	ADJ
ejpam-5323	31	30	trees	tree	NOUN
ejpam-5323	31	31	always	always	ADV
ejpam-5323	31	32	produce	produce	VERB
ejpam-5323	31	33	three	three	NUM
ejpam-5323	31	34	descendant	descendant	ADJ
ejpam-5323	31	35	triples	triple	NOUN
ejpam-5323	31	36	from	from	ADP
ejpam-5323	31	37	a	a	DET
ejpam-5323	31	38	given	give	VERB
ejpam-5323	31	39	triple	triple	ADJ
ejpam-5323	31	40	)	)	PUNCT
ejpam-5323	31	41	.	.	PUNCT
ejpam-5323	32	1	then	then	ADV
ejpam-5323	32	2	we	we	PRON
ejpam-5323	32	3	assign	assign	VERB
ejpam-5323	32	4	these	these	DET
ejpam-5323	32	5	descendant	descendant	ADJ
ejpam-5323	32	6	triples	triple	NOUN
ejpam-5323	32	7	the	the	DET
ejpam-5323	32	8	vertices	vertex	NOUN
ejpam-5323	32	9	in	in	ADP
ejpam-5323	32	10	three	three	NUM
ejpam-5323	32	11	-	-	PUNCT
ejpam-5323	32	12	dimensional	dimensional	ADJ
ejpam-5323	32	13	space	space	NOUN
ejpam-5323	32	14	and	and	CCONJ
ejpam-5323	32	15	prove	prove	VERB
ejpam-5323	32	16	that	that	SCONJ
ejpam-5323	32	17	these	these	DET
ejpam-5323	32	18	points	point	NOUN
ejpam-5323	32	19	are	be	AUX
ejpam-5323	32	20	not	not	PART
ejpam-5323	32	21	colinear	colinear	ADJ
ejpam-5323	32	22	,	,	PUNCT
ejpam-5323	32	23	therefore	therefore	ADV
ejpam-5323	32	24	they	they	PRON
ejpam-5323	32	25	form	form	VERB
ejpam-5323	32	26	a	a	DET
ejpam-5323	32	27	triangle	triangle	NOUN
ejpam-5323	32	28	(	(	PUNCT
ejpam-5323	32	29	or	or	CCONJ
ejpam-5323	32	30	a	a	DET
ejpam-5323	32	31	plane	plane	NOUN
ejpam-5323	32	32	)	)	PUNCT
ejpam-5323	32	33	.	.	PUNCT
ejpam-5323	33	1	we	we	PRON
ejpam-5323	33	2	focus	focus	VERB
ejpam-5323	33	3	on	on	ADP
ejpam-5323	33	4	these	these	DET
ejpam-5323	33	5	triangles	triangle	NOUN
ejpam-5323	33	6	formed	form	VERB
ejpam-5323	33	7	by	by	ADP
ejpam-5323	33	8	the	the	DET
ejpam-5323	33	9	descendant	descendant	ADJ
ejpam-5323	33	10	triples	triple	NOUN
ejpam-5323	33	11	in	in	ADP
ejpam-5323	33	12	either	either	CCONJ
ejpam-5323	33	13	berggren	berggren	PROPN
ejpam-5323	33	14	’s	’s	PART
ejpam-5323	33	15	or	or	CCONJ
ejpam-5323	33	16	price	price	NOUN
ejpam-5323	33	17	’s	’s	PART
ejpam-5323	33	18	tree	tree	NOUN
ejpam-5323	33	19	of	of	ADP
ejpam-5323	33	20	primitive	primitive	ADJ
ejpam-5323	33	21	pythagorean	pythagorean	NOUN
ejpam-5323	33	22	triples	triple	NOUN
ejpam-5323	33	23	,	,	PUNCT
ejpam-5323	33	24	and	and	CCONJ
ejpam-5323	33	25	describe	describe	VERB
ejpam-5323	33	26	some	some	PRON
ejpam-5323	33	27	of	of	ADP
ejpam-5323	33	28	their	their	PRON
ejpam-5323	33	29	properties	property	NOUN
ejpam-5323	33	30	.	.	PUNCT
ejpam-5323	34	1	namely	namely	ADV
ejpam-5323	34	2	we	we	PRON
ejpam-5323	34	3	study	study	VERB
ejpam-5323	34	4	the	the	DET
ejpam-5323	34	5	planes	plane	NOUN
ejpam-5323	34	6	containing	contain	VERB
ejpam-5323	34	7	these	these	DET
ejpam-5323	34	8	triangles	triangle	NOUN
ejpam-5323	34	9	;	;	PUNCT
ejpam-5323	34	10	and	and	CCONJ
ejpam-5323	34	11	the	the	DET
ejpam-5323	34	12	types	type	NOUN
ejpam-5323	34	13	of	of	ADP
ejpam-5323	34	14	these	these	DET
ejpam-5323	34	15	triangles	triangle	NOUN
ejpam-5323	34	16	.	.	PUNCT
ejpam-5323	35	1	2	2	X
ejpam-5323	35	2	.	.	X
ejpam-5323	35	3	preliminary	preliminary	ADJ
ejpam-5323	35	4	first	first	ADV
ejpam-5323	35	5	,	,	PUNCT
ejpam-5323	35	6	we	we	PRON
ejpam-5323	35	7	present	present	VERB
ejpam-5323	35	8	some	some	DET
ejpam-5323	35	9	basic	basic	ADJ
ejpam-5323	35	10	notations	notation	NOUN
ejpam-5323	35	11	and	and	CCONJ
ejpam-5323	35	12	definitions	definition	NOUN
ejpam-5323	35	13	which	which	PRON
ejpam-5323	35	14	we	we	PRON
ejpam-5323	35	15	use	use	VERB
ejpam-5323	35	16	through	through	ADP
ejpam-5323	35	17	the	the	DET
ejpam-5323	35	18	paper	paper	NOUN
ejpam-5323	35	19	.	.	PUNCT
ejpam-5323	36	1	let	let	VERB
ejpam-5323	36	2	us	we	PRON
ejpam-5323	36	3	denote	denote	VERB
ejpam-5323	36	4	n	n	PROPN
ejpam-5323	36	5	:	:	PUNCT
ejpam-5323	36	6	=	=	SYM
ejpam-5323	36	7	{	{	PUNCT
ejpam-5323	36	8	1	1	NUM
ejpam-5323	36	9	,	,	PUNCT
ejpam-5323	36	10	2	2	NUM
ejpam-5323	36	11	,	,	PUNCT
ejpam-5323	36	12	3	3	NUM
ejpam-5323	36	13	,	,	PUNCT
ejpam-5323	36	14	.	.	PUNCT
ejpam-5323	36	15	.	.	PUNCT
ejpam-5323	36	16	.	.	PUNCT
ejpam-5323	37	1	}	}	PUNCT
ejpam-5323	38	1	and	and	CCONJ
ejpam-5323	38	2	n0	n0	NUM
ejpam-5323	38	3	:	:	PUNCT
ejpam-5323	39	1	=	=	NOUN
ejpam-5323	39	2	n	n	PRON
ejpam-5323	39	3	∪	∪	X
ejpam-5323	39	4	{	{	PUNCT
ejpam-5323	39	5	0	0	NUM
ejpam-5323	39	6	}	}	PUNCT
ejpam-5323	39	7	.	.	PUNCT
ejpam-5323	40	1	for	for	ADP
ejpam-5323	40	2	a	a	DET
ejpam-5323	40	3	matrix	matrix	NOUN
ejpam-5323	40	4	m	m	NOUN
ejpam-5323	40	5	,	,	PUNCT
ejpam-5323	40	6	denote	denote	VERB
ejpam-5323	40	7	its	its	PRON
ejpam-5323	40	8	transpose	transpose	NOUN
ejpam-5323	40	9	as	as	ADP
ejpam-5323	40	10	m⊤.	m⊤.	PROPN
ejpam-5323	40	11	for	for	ADP
ejpam-5323	40	12	a	a	DET
ejpam-5323	40	13	vector	vector	NOUN
ejpam-5323	40	14	u⃗	u⃗	PROPN
ejpam-5323	40	15	,	,	PUNCT
ejpam-5323	40	16	we	we	PRON
ejpam-5323	40	17	denote	denote	VERB
ejpam-5323	40	18	its	its	PRON
ejpam-5323	40	19	norm	norm	NOUN
ejpam-5323	40	20	as	as	ADP
ejpam-5323	40	21	|u⃗|	|u⃗|	X
ejpam-5323	40	22	.	.	PUNCT
ejpam-5323	41	1	definition	definition	NOUN
ejpam-5323	41	2	1	1	NUM
ejpam-5323	41	3	.	.	PUNCT
ejpam-5323	42	1	a	a	DET
ejpam-5323	42	2	triple	triple	NOUN
ejpam-5323	42	3	of	of	ADP
ejpam-5323	42	4	positive	positive	ADJ
ejpam-5323	42	5	integers	integer	NOUN
ejpam-5323	42	6	(	(	PUNCT
ejpam-5323	42	7	a	a	DET
ejpam-5323	42	8	,	,	PUNCT
ejpam-5323	42	9	b	b	NOUN
ejpam-5323	42	10	,	,	PUNCT
ejpam-5323	42	11	c	c	NOUN
ejpam-5323	42	12	)	)	PUNCT
ejpam-5323	42	13	is	be	AUX
ejpam-5323	42	14	called	call	VERB
ejpam-5323	42	15	a	a	DET
ejpam-5323	42	16	pythagorean	pythagorean	NOUN
ejpam-5323	42	17	triple	triple	NOUN
ejpam-5323	42	18	if	if	SCONJ
ejpam-5323	42	19	a2+b2	a2+b2	PROPN
ejpam-5323	42	20	=	=	SYM
ejpam-5323	42	21	c2	c2	PROPN
ejpam-5323	42	22	.	.	PUNCT
ejpam-5323	43	1	moreover	moreover	ADV
ejpam-5323	43	2	,	,	PUNCT
ejpam-5323	43	3	if	if	SCONJ
ejpam-5323	43	4	gcd(a	gcd(a	PROPN
ejpam-5323	43	5	,	,	PUNCT
ejpam-5323	43	6	b	b	NOUN
ejpam-5323	43	7	)	)	PUNCT
ejpam-5323	43	8	=	=	SYM
ejpam-5323	43	9	1	1	NUM
ejpam-5323	43	10	,	,	PUNCT
ejpam-5323	43	11	then	then	ADV
ejpam-5323	43	12	we	we	PRON
ejpam-5323	43	13	call	call	VERB
ejpam-5323	43	14	(	(	PUNCT
ejpam-5323	43	15	a	a	DET
ejpam-5323	43	16	,	,	PUNCT
ejpam-5323	43	17	b	b	NOUN
ejpam-5323	43	18	,	,	PUNCT
ejpam-5323	43	19	c	c	NOUN
ejpam-5323	43	20	)	)	PUNCT
ejpam-5323	43	21	a	a	DET
ejpam-5323	43	22	primitive	primitive	ADJ
ejpam-5323	43	23	pythagorean	pythagorean	NOUN
ejpam-5323	43	24	triple	triple	NOUN
ejpam-5323	43	25	.	.	PUNCT
ejpam-5323	44	1	definition	definition	NOUN
ejpam-5323	44	2	2	2	NUM
ejpam-5323	44	3	.	.	PUNCT
ejpam-5323	45	1	if	if	SCONJ
ejpam-5323	45	2	(	(	PUNCT
ejpam-5323	45	3	a	a	DET
ejpam-5323	45	4	,	,	PUNCT
ejpam-5323	45	5	b	b	NOUN
ejpam-5323	45	6	,	,	PUNCT
ejpam-5323	45	7	c	c	NOUN
ejpam-5323	45	8	)	)	PUNCT
ejpam-5323	45	9	is	be	AUX
ejpam-5323	45	10	a	a	DET
ejpam-5323	45	11	pythagorean	pythagorean	PROPN
ejpam-5323	45	12	triple	triple	NOUN
ejpam-5323	45	13	,	,	PUNCT
ejpam-5323	45	14	we	we	PRON
ejpam-5323	45	15	say	say	VERB
ejpam-5323	45	16	that	that	SCONJ
ejpam-5323	45	17	a	a	DET
ejpam-5323	45	18	triangle	triangle	NOUN
ejpam-5323	45	19	corresponds	correspond	VERB
ejpam-5323	45	20	to	to	ADP
ejpam-5323	45	21	this	this	DET
ejpam-5323	45	22	triple	triple	NOUN
ejpam-5323	45	23	if	if	SCONJ
ejpam-5323	45	24	its	its	PRON
ejpam-5323	45	25	sides	side	NOUN
ejpam-5323	45	26	have	have	VERB
ejpam-5323	45	27	lengths	length	NOUN
ejpam-5323	45	28	a	a	DET
ejpam-5323	45	29	,	,	PUNCT
ejpam-5323	45	30	b	b	NOUN
ejpam-5323	45	31	,	,	PUNCT
ejpam-5323	45	32	c.	c.	NOUN
ejpam-5323	45	33	a	a	DET
ejpam-5323	45	34	triangle	triangle	NOUN
ejpam-5323	45	35	corresponding	correspond	VERB
ejpam-5323	45	36	to	to	ADP
ejpam-5323	45	37	a	a	DET
ejpam-5323	45	38	(	(	PUNCT
ejpam-5323	45	39	primitive	primitive	ADJ
ejpam-5323	45	40	)	)	PUNCT
ejpam-5323	45	41	pythagorean	pythagorean	NOUN
ejpam-5323	45	42	triple	triple	NOUN
ejpam-5323	45	43	is	be	AUX
ejpam-5323	45	44	called	call	VERB
ejpam-5323	45	45	a	a	DET
ejpam-5323	45	46	(	(	PUNCT
ejpam-5323	45	47	primitive	primitive	ADJ
ejpam-5323	45	48	)	)	PUNCT
ejpam-5323	45	49	pythagorean	pythagorean	NOUN
ejpam-5323	45	50	triangle	triangle	NOUN
ejpam-5323	45	51	.	.	PUNCT
ejpam-5323	46	1	for	for	ADP
ejpam-5323	46	2	convenience	convenience	NOUN
ejpam-5323	46	3	,	,	PUNCT
ejpam-5323	46	4	we	we	PRON
ejpam-5323	46	5	use	use	VERB
ejpam-5323	46	6	the	the	DET
ejpam-5323	46	7	abbreviation	abbreviation	NOUN
ejpam-5323	46	8	ppt	ppt	NOUN
ejpam-5323	46	9	for	for	ADP
ejpam-5323	46	10	both	both	DET
ejpam-5323	46	11	primitive	primitive	ADJ
ejpam-5323	46	12	pythagorean	pythagorean	NOUN
ejpam-5323	46	13	triple	triple	ADJ
ejpam-5323	46	14	and	and	CCONJ
ejpam-5323	46	15	primitive	primitive	ADJ
ejpam-5323	46	16	pythagorean	pythagorean	ADJ
ejpam-5323	46	17	triangle	triangle	NOUN
ejpam-5323	46	18	.	.	PUNCT
ejpam-5323	47	1	it	it	PRON
ejpam-5323	47	2	is	be	AUX
ejpam-5323	47	3	easy	easy	ADJ
ejpam-5323	47	4	to	to	PART
ejpam-5323	47	5	see	see	VERB
ejpam-5323	47	6	the	the	DET
ejpam-5323	47	7	parity	parity	NOUN
ejpam-5323	47	8	of	of	ADP
ejpam-5323	47	9	the	the	DET
ejpam-5323	47	10	individual	individual	ADJ
ejpam-5323	47	11	components	component	NOUN
ejpam-5323	47	12	of	of	ADP
ejpam-5323	47	13	a	a	DET
ejpam-5323	47	14	ppt	ppt	NOUN
ejpam-5323	47	15	,	,	PUNCT
ejpam-5323	47	16	see	see	VERB
ejpam-5323	48	1	e.g.	e.g.	ADV
ejpam-5323	48	2	[	[	X
ejpam-5323	48	3	8	8	NUM
ejpam-5323	48	4	]	]	PUNCT
ejpam-5323	48	5	:	:	PUNCT
ejpam-5323	48	6	lemma	lemma	PROPN
ejpam-5323	48	7	1	1	X
ejpam-5323	48	8	.	.	PUNCT
ejpam-5323	49	1	if	if	SCONJ
ejpam-5323	49	2	(	(	PUNCT
ejpam-5323	49	3	a	a	DET
ejpam-5323	49	4	,	,	PUNCT
ejpam-5323	49	5	b	b	NOUN
ejpam-5323	49	6	,	,	PUNCT
ejpam-5323	49	7	c	c	NOUN
ejpam-5323	49	8	)	)	PUNCT
ejpam-5323	49	9	is	be	AUX
ejpam-5323	49	10	a	a	DET
ejpam-5323	49	11	primitive	primitive	ADJ
ejpam-5323	49	12	pythagorean	pythagorean	NOUN
ejpam-5323	49	13	triple	triple	NOUN
ejpam-5323	49	14	,	,	PUNCT
ejpam-5323	49	15	then	then	ADV
ejpam-5323	49	16	one	one	NUM
ejpam-5323	49	17	of	of	ADP
ejpam-5323	49	18	a	a	PRON
ejpam-5323	49	19	,	,	PUNCT
ejpam-5323	49	20	b	b	NOUN
ejpam-5323	49	21	is	be	AUX
ejpam-5323	49	22	even	even	ADV
ejpam-5323	49	23	and	and	CCONJ
ejpam-5323	49	24	the	the	DET
ejpam-5323	49	25	other	other	ADJ
ejpam-5323	49	26	one	one	NUM
ejpam-5323	49	27	is	be	AUX
ejpam-5323	49	28	odd	odd	ADJ
ejpam-5323	49	29	,	,	PUNCT
ejpam-5323	49	30	and	and	CCONJ
ejpam-5323	49	31	c	c	PROPN
ejpam-5323	49	32	is	be	AUX
ejpam-5323	49	33	odd	odd	ADJ
ejpam-5323	49	34	.	.	PUNCT
ejpam-5323	50	1	l.	l.	PROPN
ejpam-5323	50	2	kőszegyová	kőszegyová	PROPN
ejpam-5323	50	3	,	,	PUNCT
ejpam-5323	50	4	e.	e.	PROPN
ejpam-5323	50	5	csókási	csókási	PROPN
ejpam-5323	50	6	,	,	PUNCT
ejpam-5323	50	7	j.	j.	PROPN
ejpam-5323	50	8	hirjak	hirjak	PROPN
ejpam-5323	50	9	/	/	SYM
ejpam-5323	50	10	eur	eur	PROPN
ejpam-5323	50	11	.	.	PUNCT
ejpam-5323	51	1	j.	j.	PROPN
ejpam-5323	51	2	pure	pure	PROPN
ejpam-5323	51	3	appl	appl	PROPN
ejpam-5323	51	4	.	.	PROPN
ejpam-5323	51	5	math	math	PROPN
ejpam-5323	51	6	,	,	PUNCT
ejpam-5323	51	7	17	17	NUM
ejpam-5323	51	8	(	(	PUNCT
ejpam-5323	51	9	3	3	NUM
ejpam-5323	51	10	)	)	PUNCT
ejpam-5323	51	11	(	(	PUNCT
ejpam-5323	51	12	2024	2024	NUM
ejpam-5323	51	13	)	)	PUNCT
ejpam-5323	51	14	,	,	PUNCT
ejpam-5323	51	15	2127	2127	NUM
ejpam-5323	51	16	-	-	SYM
ejpam-5323	51	17	2141	2141	NUM
ejpam-5323	51	18	2129	2129	NUM
ejpam-5323	51	19	in	in	ADP
ejpam-5323	51	20	the	the	DET
ejpam-5323	51	21	following	follow	VERB
ejpam-5323	51	22	sections	section	NOUN
ejpam-5323	52	1	,	,	PUNCT
ejpam-5323	52	2	we	we	PRON
ejpam-5323	52	3	consider	consider	VERB
ejpam-5323	52	4	generating	generate	VERB
ejpam-5323	52	5	the	the	DET
ejpam-5323	52	6	primitive	primitive	ADJ
ejpam-5323	52	7	pythagorean	pythagorean	NOUN
ejpam-5323	52	8	triples	triple	NOUN
ejpam-5323	52	9	using	use	VERB
ejpam-5323	52	10	the	the	DET
ejpam-5323	52	11	trees	tree	NOUN
ejpam-5323	52	12	described	describe	VERB
ejpam-5323	52	13	by	by	ADP
ejpam-5323	52	14	berggren	berggren	PROPN
ejpam-5323	52	15	and	and	CCONJ
ejpam-5323	52	16	price	price	NOUN
ejpam-5323	52	17	,	,	PUNCT
ejpam-5323	52	18	respectively	respectively	ADV
ejpam-5323	52	19	.	.	PUNCT
ejpam-5323	53	1	in	in	ADP
ejpam-5323	53	2	these	these	DET
ejpam-5323	53	3	trees	tree	NOUN
ejpam-5323	53	4	,	,	PUNCT
ejpam-5323	53	5	the	the	DET
ejpam-5323	53	6	components	component	NOUN
ejpam-5323	53	7	of	of	ADP
ejpam-5323	53	8	ppt	ppt	PROPN
ejpam-5323	53	9	(	(	PUNCT
ejpam-5323	53	10	a	a	DET
ejpam-5323	53	11	,	,	PUNCT
ejpam-5323	53	12	b	b	NOUN
ejpam-5323	53	13	,	,	PUNCT
ejpam-5323	53	14	c	c	NOUN
ejpam-5323	53	15	)	)	PUNCT
ejpam-5323	53	16	are	be	AUX
ejpam-5323	53	17	ordered	order	VERB
ejpam-5323	53	18	such	such	ADJ
ejpam-5323	53	19	that	that	SCONJ
ejpam-5323	53	20	a	a	PRON
ejpam-5323	53	21	is	be	AUX
ejpam-5323	53	22	odd	odd	ADJ
ejpam-5323	53	23	and	and	CCONJ
ejpam-5323	53	24	b	b	NOUN
ejpam-5323	53	25	is	be	AUX
ejpam-5323	53	26	even	even	ADV
ejpam-5323	53	27	.	.	PUNCT
ejpam-5323	54	1	we	we	PRON
ejpam-5323	54	2	use	use	VERB
ejpam-5323	54	3	this	this	DET
ejpam-5323	54	4	order	order	NOUN
ejpam-5323	54	5	of	of	ADP
ejpam-5323	54	6	components	component	NOUN
ejpam-5323	54	7	in	in	ADP
ejpam-5323	54	8	the	the	DET
ejpam-5323	54	9	rest	rest	NOUN
ejpam-5323	54	10	of	of	ADP
ejpam-5323	54	11	our	our	PRON
ejpam-5323	54	12	article	article	NOUN
ejpam-5323	54	13	.	.	PUNCT
ejpam-5323	55	1	in	in	ADP
ejpam-5323	55	2	the	the	DET
ejpam-5323	55	3	proofs	proof	NOUN
ejpam-5323	55	4	concerning	concern	VERB
ejpam-5323	55	5	ppts	ppt	NOUN
ejpam-5323	55	6	,	,	PUNCT
ejpam-5323	55	7	it	it	PRON
ejpam-5323	55	8	is	be	AUX
ejpam-5323	55	9	often	often	ADV
ejpam-5323	55	10	useful	useful	ADJ
ejpam-5323	55	11	to	to	PART
ejpam-5323	55	12	express	express	VERB
ejpam-5323	55	13	the	the	DET
ejpam-5323	55	14	primitive	primitive	ADJ
ejpam-5323	55	15	pythagorean	pythagorean	NOUN
ejpam-5323	55	16	triples	triple	NOUN
ejpam-5323	55	17	using	use	VERB
ejpam-5323	55	18	euclid	euclid	PROPN
ejpam-5323	55	19	’s	’s	PART
ejpam-5323	55	20	formula	formula	NOUN
ejpam-5323	55	21	[	[	X
ejpam-5323	55	22	10	10	NUM
ejpam-5323	55	23	]	]	NUM
ejpam-5323	55	24	:	:	PUNCT
ejpam-5323	55	25	theorem	theorem	ADJ
ejpam-5323	55	26	1	1	NUM
ejpam-5323	55	27	(	(	PUNCT
ejpam-5323	55	28	euclid	euclid	PROPN
ejpam-5323	55	29	’s	’s	PART
ejpam-5323	55	30	formula	formula	NOUN
ejpam-5323	55	31	)	)	PUNCT
ejpam-5323	55	32	.	.	PUNCT
ejpam-5323	56	1	triple	triple	ADV
ejpam-5323	56	2	(	(	PUNCT
ejpam-5323	56	3	a	a	DET
ejpam-5323	56	4	,	,	PUNCT
ejpam-5323	56	5	b	b	NOUN
ejpam-5323	56	6	,	,	PUNCT
ejpam-5323	56	7	c	c	NOUN
ejpam-5323	56	8	)	)	PUNCT
ejpam-5323	56	9	is	be	AUX
ejpam-5323	56	10	a	a	DET
ejpam-5323	56	11	primitive	primitive	ADJ
ejpam-5323	56	12	pythagorean	pythagorean	NOUN
ejpam-5323	56	13	triple	triple	NOUN
ejpam-5323	56	14	with	with	ADP
ejpam-5323	56	15	odd	odd	ADJ
ejpam-5323	56	16	a	a	DET
ejpam-5323	56	17	if	if	NOUN
ejpam-5323	57	1	and	and	CCONJ
ejpam-5323	57	2	only	only	ADV
ejpam-5323	57	3	if	if	SCONJ
ejpam-5323	57	4	there	there	PRON
ejpam-5323	57	5	exist	exist	VERB
ejpam-5323	57	6	m	m	PRON
ejpam-5323	57	7	,	,	PUNCT
ejpam-5323	57	8	n	n	PROPN
ejpam-5323	57	9	∈	∈	PROPN
ejpam-5323	57	10	n	n	NOUN
ejpam-5323	57	11	of	of	ADP
ejpam-5323	57	12	different	different	ADJ
ejpam-5323	57	13	parity	parity	NOUN
ejpam-5323	57	14	,	,	PUNCT
ejpam-5323	57	15	such	such	ADJ
ejpam-5323	57	16	that	that	DET
ejpam-5323	57	17	gcd(m	gcd(m	NOUN
ejpam-5323	57	18	,	,	PUNCT
ejpam-5323	57	19	n	n	CCONJ
ejpam-5323	57	20	)	)	PUNCT
ejpam-5323	57	21	=	=	SYM
ejpam-5323	57	22	1	1	NUM
ejpam-5323	57	23	,	,	PUNCT
ejpam-5323	57	24	m	m	VERB
ejpam-5323	57	25	>	>	X
ejpam-5323	57	26	n	n	PROPN
ejpam-5323	58	1	and	and	CCONJ
ejpam-5323	58	2	a	a	DET
ejpam-5323	58	3	=	=	PROPN
ejpam-5323	58	4	m2	m2	PROPN
ejpam-5323	58	5	−	−	PROPN
ejpam-5323	58	6	n2	n2	PROPN
ejpam-5323	58	7	,	,	PUNCT
ejpam-5323	58	8	b	b	X
ejpam-5323	58	9	=	=	SYM
ejpam-5323	58	10	2mn	2mn	X
ejpam-5323	58	11	,	,	PUNCT
ejpam-5323	58	12	c	c	X
ejpam-5323	58	13	=	=	SYM
ejpam-5323	58	14	n2	n2	PROPN
ejpam-5323	58	15	+	+	PROPN
ejpam-5323	58	16	m2	m2	PROPN
ejpam-5323	58	17	.	.	PUNCT
ejpam-5323	59	1	(	(	PUNCT
ejpam-5323	59	2	1	1	NUM
ejpam-5323	59	3	)	)	PUNCT
ejpam-5323	59	4	3	3	NUM
ejpam-5323	59	5	.	.	PUNCT
ejpam-5323	60	1	descendants	descendant	NOUN
ejpam-5323	60	2	in	in	ADP
ejpam-5323	60	3	berggren	berggren	PROPN
ejpam-5323	60	4	’s	’s	PART
ejpam-5323	60	5	tree	tree	NOUN
ejpam-5323	60	6	according	accord	VERB
ejpam-5323	60	7	to	to	ADP
ejpam-5323	60	8	berggren	berggren	PROPN
ejpam-5323	60	9	,	,	PUNCT
ejpam-5323	60	10	every	every	DET
ejpam-5323	60	11	primitive	primitive	ADJ
ejpam-5323	60	12	pythagorean	pythagorean	NOUN
ejpam-5323	60	13	triple	triple	NOUN
ejpam-5323	60	14	(	(	PUNCT
ejpam-5323	60	15	a	a	DET
ejpam-5323	60	16	,	,	PUNCT
ejpam-5323	60	17	b	b	NOUN
ejpam-5323	60	18	,	,	PUNCT
ejpam-5323	60	19	c	c	NOUN
ejpam-5323	60	20	)	)	PUNCT
ejpam-5323	60	21	with	with	ADP
ejpam-5323	60	22	odd	odd	ADJ
ejpam-5323	60	23	a	a	PRON
ejpam-5323	60	24	can	can	AUX
ejpam-5323	60	25	be	be	AUX
ejpam-5323	60	26	generated	generate	VERB
ejpam-5323	60	27	from	from	ADP
ejpam-5323	60	28	the	the	DET
ejpam-5323	60	29	triple	triple	ADJ
ejpam-5323	60	30	(	(	PUNCT
ejpam-5323	60	31	3	3	NUM
ejpam-5323	60	32	,	,	PUNCT
ejpam-5323	60	33	4	4	NUM
ejpam-5323	60	34	,	,	PUNCT
ejpam-5323	60	35	5	5	NUM
ejpam-5323	60	36	)	)	PUNCT
ejpam-5323	60	37	by	by	ADP
ejpam-5323	60	38	unique	unique	ADJ
ejpam-5323	60	39	three	three	NUM
ejpam-5323	60	40	-	-	ADJ
ejpam-5323	60	41	fold	fold	ADJ
ejpam-5323	60	42	ascent	ascent	NOUN
ejpam-5323	60	43	using	use	VERB
ejpam-5323	60	44	the	the	DET
ejpam-5323	60	45	three	three	NUM
ejpam-5323	60	46	matrices	matrix	NOUN
ejpam-5323	60	47	u	u	NOUN
ejpam-5323	60	48	,	,	PUNCT
ejpam-5323	60	49	a	a	PRON
ejpam-5323	60	50	,	,	PUNCT
ejpam-5323	60	51	d	d	X
ejpam-5323	61	1	[	[	X
ejpam-5323	61	2	7	7	NUM
ejpam-5323	61	3	]	]	SYM
ejpam-5323	61	4	:	:	PUNCT
ejpam-5323	61	5	u	u	SYM
ejpam-5323	61	6	=	=	PUNCT
ejpam-5323	61	7	1	1	PROPN
ejpam-5323	61	8	−2	−2	NOUN
ejpam-5323	61	9	2	2	NUM
ejpam-5323	61	10	2	2	NUM
ejpam-5323	61	11	−1	−1	NOUN
ejpam-5323	61	12	2	2	NUM
ejpam-5323	61	13	2	2	NUM
ejpam-5323	61	14	−2	−2	NOUN
ejpam-5323	61	15	3	3	NUM
ejpam-5323	61	16			PROPN
ejpam-5323	61	17	,	,	PUNCT
ejpam-5323	61	18	a	a	DET
ejpam-5323	61	19	=	=	SYM
ejpam-5323	61	20	1	1	PROPN
ejpam-5323	61	21	2	2	NUM
ejpam-5323	61	22	2	2	NUM
ejpam-5323	61	23	2	2	NUM
ejpam-5323	61	24	1	1	NUM
ejpam-5323	61	25	2	2	NUM
ejpam-5323	61	26	2	2	NUM
ejpam-5323	61	27	2	2	NUM
ejpam-5323	61	28	3	3	NUM
ejpam-5323	61	29			PROPN
ejpam-5323	61	30	,	,	PUNCT
ejpam-5323	61	31	d	d	PROPN
ejpam-5323	61	32	=	=	SYM
ejpam-5323	61	33	−1	−1	PROPN
ejpam-5323	61	34	2	2	NUM
ejpam-5323	61	35	2	2	NUM
ejpam-5323	61	36	−2	−2	NOUN
ejpam-5323	61	37	1	1	NUM
ejpam-5323	61	38	2	2	NUM
ejpam-5323	61	39	−2	−2	NOUN
ejpam-5323	61	40	2	2	NUM
ejpam-5323	61	41	3	3	NUM
ejpam-5323	61	42			PROPN
ejpam-5323	61	43	.	.	PUNCT
ejpam-5323	62	1	further	far	ADV
ejpam-5323	62	2	,	,	PUNCT
ejpam-5323	62	3	it	it	PRON
ejpam-5323	62	4	is	be	AUX
ejpam-5323	62	5	easy	easy	ADJ
ejpam-5323	62	6	to	to	PART
ejpam-5323	62	7	show	show	VERB
ejpam-5323	62	8	that	that	SCONJ
ejpam-5323	62	9	for	for	ADP
ejpam-5323	62	10	every	every	DET
ejpam-5323	62	11	n	n	PRON
ejpam-5323	62	12	∈	∈	PROPN
ejpam-5323	62	13	n	n	PRON
ejpam-5323	62	14	the	the	DET
ejpam-5323	62	15	following	follow	VERB
ejpam-5323	62	16	holds	hold	NOUN
ejpam-5323	62	17	:	:	PUNCT
ejpam-5323	63	1	un	un	PROPN
ejpam-5323	63	2	=	=	PROPN
ejpam-5323	63	3			PROPN
ejpam-5323	63	4	1	1	NUM
ejpam-5323	63	5	−2n	−2n	PROPN
ejpam-5323	63	6	2n	2n	NUM
ejpam-5323	63	7	2n	2n	NUM
ejpam-5323	63	8	1−	1−	NUM
ejpam-5323	63	9	2n2	2n2	NUM
ejpam-5323	63	10	2n2	2n2	NUM
ejpam-5323	63	11	2n	2n	NUM
ejpam-5323	63	12	−2n2	−2n2	NUM
ejpam-5323	63	13	2n2	2n2	NUM
ejpam-5323	63	14	+	+	CCONJ
ejpam-5323	63	15	1	1	NUM
ejpam-5323	63	16			PROPN
ejpam-5323	63	17	,	,	PUNCT
ejpam-5323	63	18	an	an	DET
ejpam-5323	63	19	=	=	X
ejpam-5323	63	20			X
ejpam-5323	63	21	(	(	PUNCT
ejpam-5323	63	22	−1)n	−1)n	PROPN
ejpam-5323	63	23	2	2	NUM
ejpam-5323	63	24	+	+	CCONJ
ejpam-5323	63	25	a1	a1	NOUN
ejpam-5323	63	26	(	(	PUNCT
ejpam-5323	63	27	−1)n+1	−1)n+1	NOUN
ejpam-5323	63	28	2	2	NUM
ejpam-5323	63	29	+	+	CCONJ
ejpam-5323	63	30	a1	a1	NOUN
ejpam-5323	63	31	a2	a2	PROPN
ejpam-5323	63	32	(	(	PUNCT
ejpam-5323	63	33	−1)n+1	−1)n+1	NOUN
ejpam-5323	63	34	2	2	NUM
ejpam-5323	63	35	+	+	CCONJ
ejpam-5323	63	36	a1	a1	NOUN
ejpam-5323	63	37	(	(	PUNCT
ejpam-5323	63	38	−1)n	−1)n	PROPN
ejpam-5323	63	39	2	2	NUM
ejpam-5323	63	40	+	+	CCONJ
ejpam-5323	63	41	a1	a1	NOUN
ejpam-5323	63	42	a2	a2	PROPN
ejpam-5323	63	43	a2	a2	PROPN
ejpam-5323	63	44	a2	a2	PROPN
ejpam-5323	63	45	2a1	2a1	PROPN
ejpam-5323	63	46			NOUN
ejpam-5323	63	47	,	,	PUNCT
ejpam-5323	63	48	dn	dn	NOUN
ejpam-5323	63	49	=	=	PUNCT
ejpam-5323	63	50	1−	1−	PRON
ejpam-5323	63	51	2n2	2n2	NUM
ejpam-5323	63	52	2n	2n	NUM
ejpam-5323	63	53	2n2	2n2	NUM
ejpam-5323	63	54	−2n	−2n	PROPN
ejpam-5323	63	55	1	1	NUM
ejpam-5323	63	56	2n	2n	NUM
ejpam-5323	63	57	−2n2	−2n2	NUM
ejpam-5323	63	58	2n	2n	NUM
ejpam-5323	63	59	2n2	2n2	NUM
ejpam-5323	63	60	+	+	CCONJ
ejpam-5323	63	61	1	1	NUM
ejpam-5323	63	62			PROPN
ejpam-5323	63	63	,	,	PUNCT
ejpam-5323	63	64	where	where	SCONJ
ejpam-5323	63	65	a1	a1	NOUN
ejpam-5323	63	66	=	=	NOUN
ejpam-5323	63	67	1	1	NUM
ejpam-5323	63	68	4	4	NUM
ejpam-5323	63	69	[	[	X
ejpam-5323	63	70	(	(	PUNCT
ejpam-5323	63	71	3−	3−	NUM
ejpam-5323	63	72	2	2	NUM
ejpam-5323	63	73	√	√	NUM
ejpam-5323	63	74	2)n	2)n	NUM
ejpam-5323	63	75	+	+	CCONJ
ejpam-5323	63	76	(	(	PUNCT
ejpam-5323	63	77	3	3	NUM
ejpam-5323	63	78	+	+	SYM
ejpam-5323	63	79	2	2	NUM
ejpam-5323	63	80	√	√	NUM
ejpam-5323	63	81	2)n	2)n	NUM
ejpam-5323	63	82	]	]	PUNCT
ejpam-5323	63	83	,	,	PUNCT
ejpam-5323	63	84	a2	a2	PROPN
ejpam-5323	63	85	=	=	PUNCT
ejpam-5323	63	86	−(3−2	−(3−2	PROPN
ejpam-5323	63	87	√	√	ADV
ejpam-5323	63	88	2	2	NUM
ejpam-5323	63	89	)	)	PUNCT
ejpam-5323	63	90	n	n	PRON
ejpam-5323	63	91	2	2	NUM
ejpam-5323	63	92	√	√	NUM
ejpam-5323	63	93	2	2	NUM
ejpam-5323	63	94	+	+	CCONJ
ejpam-5323	63	95	(	(	PUNCT
ejpam-5323	63	96	3	3	NUM
ejpam-5323	63	97	+	+	NOUN
ejpam-5323	63	98	2	2	NUM
ejpam-5323	63	99	√	√	NUM
ejpam-5323	63	100	2	2	NUM
ejpam-5323	63	101	)	)	PUNCT
ejpam-5323	63	102	n	n	DET
ejpam-5323	63	103	2	2	NUM
ejpam-5323	63	104	√	√	NUM
ejpam-5323	63	105	2	2	NUM
ejpam-5323	63	106	.	.	PUNCT
ejpam-5323	64	1	theorem	theorem	NOUN
ejpam-5323	64	2	2	2	NUM
ejpam-5323	64	3	.	.	PUNCT
ejpam-5323	65	1	if	if	SCONJ
ejpam-5323	65	2	(	(	PUNCT
ejpam-5323	65	3	a	a	DET
ejpam-5323	65	4	,	,	PUNCT
ejpam-5323	65	5	b	b	NOUN
ejpam-5323	65	6	,	,	PUNCT
ejpam-5323	65	7	c	c	NOUN
ejpam-5323	65	8	)	)	PUNCT
ejpam-5323	65	9	is	be	AUX
ejpam-5323	65	10	a	a	DET
ejpam-5323	65	11	primitive	primitive	ADJ
ejpam-5323	65	12	pythagorean	pythagorean	NOUN
ejpam-5323	65	13	triple	triple	NOUN
ejpam-5323	65	14	with	with	ADP
ejpam-5323	65	15	odd	odd	ADJ
ejpam-5323	65	16	a	a	PRON
ejpam-5323	65	17	,	,	PUNCT
ejpam-5323	65	18	and	and	CCONJ
ejpam-5323	65	19	m	m	PROPN
ejpam-5323	65	20	is	be	AUX
ejpam-5323	65	21	a	a	DET
ejpam-5323	65	22	matrix	matrix	NOUN
ejpam-5323	65	23	such	such	ADJ
ejpam-5323	65	24	that	that	SCONJ
ejpam-5323	65	25	m	m	PROPN
ejpam-5323	65	26	∈	∈	PROPN
ejpam-5323	65	27	{	{	PUNCT
ejpam-5323	65	28	u	u	NOUN
ejpam-5323	65	29	,	,	PUNCT
ejpam-5323	65	30	a	a	PRON
ejpam-5323	65	31	,	,	PUNCT
ejpam-5323	65	32	d	d	NOUN
ejpam-5323	65	33	}	}	PUNCT
ejpam-5323	65	34	,	,	PUNCT
ejpam-5323	65	35	then	then	ADV
ejpam-5323	65	36	m	m	VERB
ejpam-5323	65	37	·	·	PUNCT
ejpam-5323	65	38	(	(	PUNCT
ejpam-5323	65	39	a	a	DET
ejpam-5323	65	40	,	,	PUNCT
ejpam-5323	65	41	b	b	NOUN
ejpam-5323	65	42	,	,	PUNCT
ejpam-5323	65	43	c)⊤	c)⊤	NOUN
ejpam-5323	65	44	is	be	AUX
ejpam-5323	65	45	a	a	DET
ejpam-5323	65	46	primitive	primitive	ADJ
ejpam-5323	65	47	pythagorean	pythagorean	NOUN
ejpam-5323	65	48	triple	triple	NOUN
ejpam-5323	65	49	with	with	ADP
ejpam-5323	65	50	an	an	DET
ejpam-5323	65	51	odd	odd	ADJ
ejpam-5323	65	52	first	first	ADJ
ejpam-5323	65	53	component	component	NOUN
ejpam-5323	65	54	.	.	PUNCT
ejpam-5323	66	1	berggren	berggren	PROPN
ejpam-5323	66	2	’s	’s	PART
ejpam-5323	66	3	tree	tree	NOUN
ejpam-5323	66	4	of	of	ADP
ejpam-5323	66	5	ppt	ppt	PROPN
ejpam-5323	66	6	contains	contain	VERB
ejpam-5323	66	7	all	all	DET
ejpam-5323	66	8	ppts	ppt	NOUN
ejpam-5323	66	9	,	,	PUNCT
ejpam-5323	66	10	and	and	CCONJ
ejpam-5323	66	11	each	each	DET
ejpam-5323	66	12	ppt	ppt	NOUN
ejpam-5323	66	13	is	be	AUX
ejpam-5323	66	14	generated	generate	VERB
ejpam-5323	66	15	by	by	ADP
ejpam-5323	66	16	a	a	DET
ejpam-5323	66	17	unique	unique	ADJ
ejpam-5323	66	18	sequence	sequence	NOUN
ejpam-5323	66	19	of	of	ADP
ejpam-5323	66	20	matrix	matrix	NOUN
ejpam-5323	66	21	multiplication	multiplication	NOUN
ejpam-5323	66	22	[	[	X
ejpam-5323	66	23	7	7	NUM
ejpam-5323	66	24	]	]	PUNCT
ejpam-5323	66	25	.	.	PUNCT
ejpam-5323	67	1	the	the	DET
ejpam-5323	67	2	first	first	ADJ
ejpam-5323	67	3	few	few	ADJ
ejpam-5323	67	4	levels	level	NOUN
ejpam-5323	67	5	of	of	ADP
ejpam-5323	67	6	berggren	berggren	PROPN
ejpam-5323	67	7	’s	’s	PART
ejpam-5323	67	8	tree	tree	NOUN
ejpam-5323	67	9	can	can	AUX
ejpam-5323	67	10	be	be	AUX
ejpam-5323	67	11	seen	see	VERB
ejpam-5323	67	12	in	in	ADP
ejpam-5323	67	13	the	the	DET
ejpam-5323	67	14	figure	figure	NOUN
ejpam-5323	67	15	1	1	NUM
ejpam-5323	67	16	.	.	PUNCT
ejpam-5323	68	1	l.	l.	PROPN
ejpam-5323	68	2	kőszegyová	kőszegyová	PROPN
ejpam-5323	68	3	,	,	PUNCT
ejpam-5323	68	4	e.	e.	PROPN
ejpam-5323	68	5	csókási	csókási	PROPN
ejpam-5323	68	6	,	,	PUNCT
ejpam-5323	68	7	j.	j.	PROPN
ejpam-5323	68	8	hirjak	hirjak	PROPN
ejpam-5323	68	9	/	/	SYM
ejpam-5323	68	10	eur	eur	PROPN
ejpam-5323	68	11	.	.	PUNCT
ejpam-5323	69	1	j.	j.	PROPN
ejpam-5323	69	2	pure	pure	PROPN
ejpam-5323	69	3	appl	appl	PROPN
ejpam-5323	69	4	.	.	PROPN
ejpam-5323	69	5	math	math	PROPN
ejpam-5323	69	6	,	,	PUNCT
ejpam-5323	69	7	17	17	NUM
ejpam-5323	69	8	(	(	PUNCT
ejpam-5323	69	9	3	3	NUM
ejpam-5323	69	10	)	)	PUNCT
ejpam-5323	69	11	(	(	PUNCT
ejpam-5323	69	12	2024	2024	NUM
ejpam-5323	69	13	)	)	PUNCT
ejpam-5323	69	14	,	,	PUNCT
ejpam-5323	69	15	2127	2127	NUM
ejpam-5323	69	16	-	-	SYM
ejpam-5323	69	17	2141	2141	NUM
ejpam-5323	69	18	2130	2130	NUM
ejpam-5323	69	19	(	(	PUNCT
ejpam-5323	69	20	3	3	NUM
ejpam-5323	69	21	,	,	PUNCT
ejpam-5323	69	22	4	4	NUM
ejpam-5323	69	23	,	,	PUNCT
ejpam-5323	69	24	5	5	NUM
ejpam-5323	69	25	)	)	PUNCT
ejpam-5323	69	26	(	(	PUNCT
ejpam-5323	69	27	5	5	NUM
ejpam-5323	69	28	,	,	PUNCT
ejpam-5323	69	29	12	12	NUM
ejpam-5323	69	30	,	,	PUNCT
ejpam-5323	69	31	13	13	NUM
ejpam-5323	69	32	)	)	PUNCT
ejpam-5323	69	33	(	(	PUNCT
ejpam-5323	69	34	21	21	NUM
ejpam-5323	69	35	,	,	PUNCT
ejpam-5323	69	36	20	20	NUM
ejpam-5323	69	37	,	,	PUNCT
ejpam-5323	69	38	29	29	NUM
ejpam-5323	69	39	)	)	PUNCT
ejpam-5323	69	40	(	(	PUNCT
ejpam-5323	69	41	15	15	NUM
ejpam-5323	69	42	,	,	PUNCT
ejpam-5323	69	43	8	8	NUM
ejpam-5323	69	44	,	,	PUNCT
ejpam-5323	69	45	17	17	NUM
ejpam-5323	69	46	)	)	PUNCT
ejpam-5323	69	47	(	(	PUNCT
ejpam-5323	69	48	7	7	NUM
ejpam-5323	69	49	,	,	PUNCT
ejpam-5323	69	50	24	24	NUM
ejpam-5323	69	51	,	,	PUNCT
ejpam-5323	69	52	25	25	NUM
ejpam-5323	69	53	)	)	PUNCT
ejpam-5323	69	54	(	(	PUNCT
ejpam-5323	69	55	55	55	NUM
ejpam-5323	69	56	,	,	PUNCT
ejpam-5323	69	57	48	48	NUM
ejpam-5323	69	58	,	,	PUNCT
ejpam-5323	69	59	73	73	NUM
ejpam-5323	69	60	)	)	PUNCT
ejpam-5323	69	61	(	(	PUNCT
ejpam-5323	69	62	45	45	NUM
ejpam-5323	69	63	,	,	PUNCT
ejpam-5323	69	64	28	28	NUM
ejpam-5323	69	65	,	,	PUNCT
ejpam-5323	69	66	53	53	NUM
ejpam-5323	69	67	)	)	PUNCT
ejpam-5323	69	68	(	(	PUNCT
ejpam-5323	69	69	39	39	NUM
ejpam-5323	69	70	,	,	PUNCT
ejpam-5323	69	71	80	80	NUM
ejpam-5323	69	72	,	,	PUNCT
ejpam-5323	69	73	89	89	NUM
ejpam-5323	69	74	)	)	PUNCT
ejpam-5323	69	75	(	(	PUNCT
ejpam-5323	69	76	119	119	NUM
ejpam-5323	69	77	,	,	PUNCT
ejpam-5323	69	78	120	120	NUM
ejpam-5323	69	79	,	,	PUNCT
ejpam-5323	69	80	169	169	NUM
ejpam-5323	69	81	)	)	PUNCT
ejpam-5323	69	82	(	(	PUNCT
ejpam-5323	69	83	77	77	NUM
ejpam-5323	69	84	,	,	PUNCT
ejpam-5323	69	85	36	36	NUM
ejpam-5323	69	86	,	,	PUNCT
ejpam-5323	69	87	85	85	NUM
ejpam-5323	69	88	)	)	PUNCT
ejpam-5323	69	89	(	(	PUNCT
ejpam-5323	69	90	33	33	NUM
ejpam-5323	69	91	,	,	PUNCT
ejpam-5323	69	92	56	56	NUM
ejpam-5323	69	93	,	,	PUNCT
ejpam-5323	69	94	65	65	NUM
ejpam-5323	69	95	)	)	PUNCT
ejpam-5323	69	96	(	(	PUNCT
ejpam-5323	69	97	65	65	NUM
ejpam-5323	69	98	,	,	PUNCT
ejpam-5323	69	99	72	72	NUM
ejpam-5323	69	100	,	,	PUNCT
ejpam-5323	69	101	97	97	NUM
ejpam-5323	69	102	)	)	PUNCT
ejpam-5323	69	103	(	(	PUNCT
ejpam-5323	69	104	35	35	NUM
ejpam-5323	69	105	,	,	PUNCT
ejpam-5323	69	106	12	12	NUM
ejpam-5323	69	107	,	,	PUNCT
ejpam-5323	69	108	37	37	NUM
ejpam-5323	69	109	)	)	PUNCT
ejpam-5323	69	110	u	u	NOUN
ejpam-5323	69	111	a	a	X
ejpam-5323	69	112	d	d	X
ejpam-5323	69	113	u	u	NOUN
ejpam-5323	69	114	a	a	PROPN
ejpam-5323	69	115	d	d	X
ejpam-5323	69	116	u	u	NOUN
ejpam-5323	69	117	a	a	PROPN
ejpam-5323	69	118	d	d	X
ejpam-5323	69	119	u	u	NOUN
ejpam-5323	69	120	a	a	DET
ejpam-5323	69	121	d	d	NOUN
ejpam-5323	69	122	figure	figure	NOUN
ejpam-5323	69	123	1	1	NUM
ejpam-5323	69	124	:	:	PUNCT
ejpam-5323	69	125	berggren	berggren	PROPN
ejpam-5323	69	126	’s	’s	PART
ejpam-5323	69	127	tree	tree	NOUN
ejpam-5323	69	128	of	of	ADP
ejpam-5323	69	129	ppts	ppt	NOUN
ejpam-5323	69	130	.	.	PUNCT
ejpam-5323	70	1	definition	definition	NOUN
ejpam-5323	70	2	3	3	X
ejpam-5323	70	3	.	.	PUNCT
ejpam-5323	71	1	let	let	VERB
ejpam-5323	71	2	p	p	PRON
ejpam-5323	71	3	be	be	AUX
ejpam-5323	71	4	a	a	DET
ejpam-5323	71	5	primitive	primitive	ADJ
ejpam-5323	71	6	pythagorean	pythagorean	NOUN
ejpam-5323	71	7	triple	triple	NOUN
ejpam-5323	71	8	.	.	PUNCT
ejpam-5323	72	1	we	we	PRON
ejpam-5323	72	2	say	say	VERB
ejpam-5323	72	3	that	that	SCONJ
ejpam-5323	72	4	p	p	PROPN
ejpam-5323	72	5	is	be	AUX
ejpam-5323	72	6	the	the	DET
ejpam-5323	72	7	parent	parent	NOUN
ejpam-5323	72	8	of	of	ADP
ejpam-5323	72	9	the	the	DET
ejpam-5323	72	10	triples	triple	NOUN
ejpam-5323	72	11	up⊤	up⊤	ADJ
ejpam-5323	72	12	,	,	PUNCT
ejpam-5323	72	13	ap⊤	ap⊤	VERB
ejpam-5323	72	14	,	,	PUNCT
ejpam-5323	72	15	dp⊤.	dp⊤.	VERB
ejpam-5323	72	16	the	the	DET
ejpam-5323	72	17	triples	triple	NOUN
ejpam-5323	72	18	up⊤	up⊤	ADJ
ejpam-5323	72	19	,	,	PUNCT
ejpam-5323	72	20	ap⊤	ap⊤	NOUN
ejpam-5323	72	21	,	,	PUNCT
ejpam-5323	72	22	dp⊤	dp⊤	NOUN
ejpam-5323	72	23	are	be	AUX
ejpam-5323	72	24	called	call	VERB
ejpam-5323	72	25	the	the	DET
ejpam-5323	72	26	descendants	descendant	NOUN
ejpam-5323	72	27	of	of	ADP
ejpam-5323	72	28	p	p	NOUN
ejpam-5323	72	29	in	in	ADP
ejpam-5323	72	30	berggren	berggren	PROPN
ejpam-5323	72	31	’s	’s	PART
ejpam-5323	72	32	tree	tree	NOUN
ejpam-5323	72	33	.	.	PUNCT
ejpam-5323	73	1	proposition	proposition	NOUN
ejpam-5323	73	2	1	1	NUM
ejpam-5323	73	3	.	.	PUNCT
ejpam-5323	74	1	let	let	VERB
ejpam-5323	74	2	p	p	PRON
ejpam-5323	74	3	be	be	AUX
ejpam-5323	74	4	a	a	DET
ejpam-5323	74	5	primitive	primitive	ADJ
ejpam-5323	74	6	pythagorean	pythagorean	NOUN
ejpam-5323	74	7	triple	triple	NOUN
ejpam-5323	74	8	.	.	PUNCT
ejpam-5323	75	1	then	then	ADV
ejpam-5323	75	2	the	the	DET
ejpam-5323	75	3	points	point	NOUN
ejpam-5323	75	4	with	with	ADP
ejpam-5323	75	5	the	the	DET
ejpam-5323	75	6	coordinates	coordinate	NOUN
ejpam-5323	75	7	up⊤	up⊤	VERB
ejpam-5323	75	8	,	,	PUNCT
ejpam-5323	75	9	ap⊤	ap⊤	NOUN
ejpam-5323	75	10	,	,	PUNCT
ejpam-5323	75	11	dp⊤	dp⊤	NOUN
ejpam-5323	75	12	are	be	AUX
ejpam-5323	75	13	not	not	PART
ejpam-5323	75	14	collinear	collinear	ADJ
ejpam-5323	75	15	.	.	PUNCT
ejpam-5323	76	1	proof	proof	NOUN
ejpam-5323	76	2	.	.	PUNCT
ejpam-5323	77	1	let	let	VERB
ejpam-5323	77	2	p	p	NOUN
ejpam-5323	77	3	=	=	X
ejpam-5323	77	4	(	(	PUNCT
ejpam-5323	77	5	a	a	PRON
ejpam-5323	77	6	,	,	PUNCT
ejpam-5323	77	7	b	b	NOUN
ejpam-5323	77	8	,	,	PUNCT
ejpam-5323	77	9	c	c	NOUN
ejpam-5323	77	10	)	)	PUNCT
ejpam-5323	77	11	.	.	PUNCT
ejpam-5323	78	1	we	we	PRON
ejpam-5323	78	2	consider	consider	VERB
ejpam-5323	78	3	the	the	DET
ejpam-5323	78	4	vectors	vector	NOUN
ejpam-5323	78	5	u⃗	u⃗	PROPN
ejpam-5323	78	6	=	=	PUNCT
ejpam-5323	78	7	ap⊤	ap⊤	X
ejpam-5323	78	8	−	−	PROPN
ejpam-5323	78	9	up⊤	up⊤	ADJ
ejpam-5323	78	10	and	and	CCONJ
ejpam-5323	78	11	v⃗	v⃗	ADJ
ejpam-5323	78	12	=	=	PUNCT
ejpam-5323	78	13	dp⊤	dp⊤	NOUN
ejpam-5323	78	14	−	−	ADP
ejpam-5323	78	15	up⊤.	up⊤.	NOUN
ejpam-5323	78	16	it	it	PRON
ejpam-5323	78	17	is	be	AUX
ejpam-5323	78	18	easy	easy	ADJ
ejpam-5323	78	19	to	to	PART
ejpam-5323	78	20	show	show	VERB
ejpam-5323	78	21	that	that	SCONJ
ejpam-5323	78	22	u⃗	u⃗	PROPN
ejpam-5323	78	23	=	=	SYM
ejpam-5323	78	24	(	(	PUNCT
ejpam-5323	78	25	a−	a−	PROPN
ejpam-5323	78	26	u)p⊤	u)p⊤	ADJ
ejpam-5323	78	27	=	=	PUNCT
ejpam-5323	78	28	0	0	ADP
ejpam-5323	78	29	4	4	NUM
ejpam-5323	78	30	0	0	NUM
ejpam-5323	78	31	0	0	NUM
ejpam-5323	78	32	2	2	NUM
ejpam-5323	78	33	0	0	NUM
ejpam-5323	78	34	0	0	NUM
ejpam-5323	78	35	4	4	NUM
ejpam-5323	78	36	0	0	NUM
ejpam-5323	78	37			PROPN
ejpam-5323	78	38	·	·	PUNCT
ejpam-5323	78	39	a	a	NOUN
ejpam-5323	78	40	b	b	X
ejpam-5323	78	41	c	c	X
ejpam-5323	78	42			PROPN
ejpam-5323	78	43	=	=	SYM
ejpam-5323	78	44	4b	4b	ADJ
ejpam-5323	78	45	2b	2b	NUM
ejpam-5323	78	46	4b	4b	X
ejpam-5323	78	47			PROPN
ejpam-5323	78	48	,	,	PUNCT
ejpam-5323	78	49	v⃗	v⃗	VERB
ejpam-5323	78	50	=	=	SYM
ejpam-5323	78	51	(	(	PUNCT
ejpam-5323	78	52	d	d	NOUN
ejpam-5323	78	53	−	−	NOUN
ejpam-5323	78	54	u)p⊤	u)p⊤	ADJ
ejpam-5323	78	55	=	=	SYM
ejpam-5323	78	56	−2	−2	PROPN
ejpam-5323	78	57	4	4	NUM
ejpam-5323	78	58	0	0	NUM
ejpam-5323	78	59	−4	−4	NOUN
ejpam-5323	78	60	2	2	NUM
ejpam-5323	78	61	0	0	NUM
ejpam-5323	78	62	−4	−4	NOUN
ejpam-5323	78	63	4	4	NUM
ejpam-5323	78	64	0	0	NUM
ejpam-5323	78	65			PROPN
ejpam-5323	78	66	·	·	PUNCT
ejpam-5323	78	67	a	a	NOUN
ejpam-5323	78	68	b	b	X
ejpam-5323	78	69	c	c	X
ejpam-5323	78	70			PROPN
ejpam-5323	78	71	=	=	PUNCT
ejpam-5323	78	72	−2a+	−2a+	PROPN
ejpam-5323	78	73	4b	4b	X
ejpam-5323	79	1	−4a+	−4a+	PROPN
ejpam-5323	79	2	2b	2b	NUM
ejpam-5323	79	3	−4a+	−4a+	PROPN
ejpam-5323	79	4	4b	4b	X
ejpam-5323	79	5			PROPN
ejpam-5323	79	6	.	.	PUNCT
ejpam-5323	80	1	by	by	ADP
ejpam-5323	80	2	way	way	NOUN
ejpam-5323	80	3	of	of	ADP
ejpam-5323	80	4	contradiction	contradiction	NOUN
ejpam-5323	80	5	,	,	PUNCT
ejpam-5323	80	6	assume	assume	VERB
ejpam-5323	80	7	that	that	SCONJ
ejpam-5323	80	8	these	these	DET
ejpam-5323	80	9	vectors	vector	NOUN
ejpam-5323	80	10	are	be	AUX
ejpam-5323	80	11	linearly	linearly	ADV
ejpam-5323	80	12	dependent	dependent	ADJ
ejpam-5323	80	13	,	,	PUNCT
ejpam-5323	80	14	i.e.	i.e.	X
ejpam-5323	80	15	,	,	PUNCT
ejpam-5323	80	16	that	that	SCONJ
ejpam-5323	80	17	there	there	PRON
ejpam-5323	80	18	exists	exist	VERB
ejpam-5323	80	19	nonzero	nonzero	ADJ
ejpam-5323	80	20	real	real	ADJ
ejpam-5323	80	21	number	number	NOUN
ejpam-5323	80	22	k	k	NOUN
ejpam-5323	80	23	such	such	ADJ
ejpam-5323	80	24	that	that	SCONJ
ejpam-5323	80	25	u⃗	u⃗	PROPN
ejpam-5323	80	26	=	=	PUNCT
ejpam-5323	80	27	kv⃗.	kv⃗.	PUNCT
ejpam-5323	80	28	then	then	ADV
ejpam-5323	80	29	(	(	PUNCT
ejpam-5323	80	30	4b	4b	X
ejpam-5323	80	31	,	,	PUNCT
ejpam-5323	80	32	2b	2b	NUM
ejpam-5323	80	33	,	,	PUNCT
ejpam-5323	80	34	4b	4b	NUM
ejpam-5323	80	35	)	)	PUNCT
ejpam-5323	80	36	=	=	SYM
ejpam-5323	80	37	k(−2a+4b,−4a+	k(−2a+4b,−4a+	PROPN
ejpam-5323	80	38	2b,−4a+	2b,−4a+	NUM
ejpam-5323	80	39	4b	4b	NOUN
ejpam-5323	80	40	)	)	PUNCT
ejpam-5323	80	41	,	,	PUNCT
ejpam-5323	80	42	hence	hence	ADV
ejpam-5323	80	43	4b	4b	X
ejpam-5323	80	44	=	=	SYM
ejpam-5323	80	45	k(−2a+	k(−2a+	PROPN
ejpam-5323	80	46	4b	4b	X
ejpam-5323	80	47	)	)	PUNCT
ejpam-5323	80	48	and	and	CCONJ
ejpam-5323	80	49	4b	4b	X
ejpam-5323	80	50	=	=	SYM
ejpam-5323	80	51	k(−4a+	k(−4a+	PROPN
ejpam-5323	80	52	4b	4b	PROPN
ejpam-5323	80	53	)	)	PUNCT
ejpam-5323	80	54	.	.	PUNCT
ejpam-5323	81	1	this	this	PRON
ejpam-5323	81	2	implies	imply	VERB
ejpam-5323	81	3	that	that	SCONJ
ejpam-5323	81	4	k(−2a+	k(−2a+	PROPN
ejpam-5323	81	5	4b	4b	X
ejpam-5323	81	6	)	)	PUNCT
ejpam-5323	81	7	=	=	SYM
ejpam-5323	81	8	k(−4a+	k(−4a+	PROPN
ejpam-5323	81	9	4b	4b	X
ejpam-5323	81	10	)	)	PUNCT
ejpam-5323	82	1	−2a+	−2a+	PROPN
ejpam-5323	82	2	4b	4b	X
ejpam-5323	83	1	=	=	PUNCT
ejpam-5323	83	2	−4a+	−4a+	PROPN
ejpam-5323	83	3	4b	4b	X
ejpam-5323	83	4	2a	2a	NUM
ejpam-5323	83	5	=	=	SYM
ejpam-5323	83	6	0	0	NUM
ejpam-5323	83	7	which	which	PRON
ejpam-5323	83	8	is	be	AUX
ejpam-5323	83	9	a	a	DET
ejpam-5323	83	10	contradiction	contradiction	NOUN
ejpam-5323	83	11	with	with	ADP
ejpam-5323	83	12	a	a	DET
ejpam-5323	83	13	∈	∈	PROPN
ejpam-5323	83	14	n.	n.	NOUN
ejpam-5323	83	15	therefore	therefore	ADV
ejpam-5323	83	16	,	,	PUNCT
ejpam-5323	83	17	u⃗	u⃗	PROPN
ejpam-5323	83	18	,	,	PUNCT
ejpam-5323	83	19	v⃗	v⃗	PROPN
ejpam-5323	83	20	are	be	AUX
ejpam-5323	83	21	linearly	linearly	ADV
ejpam-5323	83	22	independent	independent	ADJ
ejpam-5323	83	23	and	and	CCONJ
ejpam-5323	83	24	the	the	DET
ejpam-5323	83	25	points	point	NOUN
ejpam-5323	83	26	up⊤	up⊤	VERB
ejpam-5323	83	27	,	,	PUNCT
ejpam-5323	83	28	ap⊤	ap⊤	NOUN
ejpam-5323	83	29	,	,	PUNCT
ejpam-5323	83	30	dp⊤	dp⊤	NOUN
ejpam-5323	83	31	are	be	AUX
ejpam-5323	83	32	not	not	PART
ejpam-5323	83	33	collinear	collinear	ADJ
ejpam-5323	83	34	.	.	PUNCT
ejpam-5323	84	1	this	this	PRON
ejpam-5323	84	2	implies	imply	VERB
ejpam-5323	84	3	that	that	SCONJ
ejpam-5323	84	4	the	the	DET
ejpam-5323	84	5	points	point	NOUN
ejpam-5323	84	6	with	with	ADP
ejpam-5323	84	7	the	the	DET
ejpam-5323	84	8	coordinates	coordinate	NOUN
ejpam-5323	84	9	up⊤	up⊤	VERB
ejpam-5323	84	10	,	,	PUNCT
ejpam-5323	84	11	ap⊤	ap⊤	NOUN
ejpam-5323	84	12	,	,	PUNCT
ejpam-5323	84	13	dp⊤	dp⊤	NOUN
ejpam-5323	84	14	determine	determine	VERB
ejpam-5323	84	15	a	a	DET
ejpam-5323	84	16	plane	plane	NOUN
ejpam-5323	84	17	,	,	PUNCT
ejpam-5323	84	18	and	and	CCONJ
ejpam-5323	84	19	a	a	DET
ejpam-5323	84	20	triangle	triangle	NOUN
ejpam-5323	84	21	.	.	PUNCT
ejpam-5323	85	1	in	in	ADP
ejpam-5323	85	2	the	the	DET
ejpam-5323	85	3	following	following	NOUN
ejpam-5323	85	4	,	,	PUNCT
ejpam-5323	85	5	we	we	PRON
ejpam-5323	85	6	prove	prove	VERB
ejpam-5323	85	7	some	some	DET
ejpam-5323	85	8	properties	property	NOUN
ejpam-5323	85	9	of	of	ADP
ejpam-5323	85	10	this	this	DET
ejpam-5323	85	11	plane	plane	NOUN
ejpam-5323	85	12	(	(	PUNCT
ejpam-5323	85	13	and	and	CCONJ
ejpam-5323	85	14	this	this	DET
ejpam-5323	85	15	triangle	triangle	NOUN
ejpam-5323	85	16	)	)	PUNCT
ejpam-5323	85	17	.	.	PUNCT
ejpam-5323	86	1	for	for	ADP
ejpam-5323	86	2	simplicity	simplicity	NOUN
ejpam-5323	86	3	,	,	PUNCT
ejpam-5323	86	4	we	we	PRON
ejpam-5323	86	5	use	use	VERB
ejpam-5323	86	6	the	the	DET
ejpam-5323	86	7	following	following	ADJ
ejpam-5323	86	8	notion	notion	NOUN
ejpam-5323	86	9	:	:	PUNCT
ejpam-5323	86	10	definition	definition	NOUN
ejpam-5323	86	11	4	4	NUM
ejpam-5323	86	12	.	.	PUNCT
ejpam-5323	86	13	let	let	VERB
ejpam-5323	86	14	p	p	PRON
ejpam-5323	86	15	be	be	AUX
ejpam-5323	86	16	a	a	DET
ejpam-5323	86	17	primitive	primitive	ADJ
ejpam-5323	86	18	pythagorean	pythagorean	NOUN
ejpam-5323	86	19	triple	triple	NOUN
ejpam-5323	86	20	and	and	CCONJ
ejpam-5323	86	21	let	let	VERB
ejpam-5323	86	22	up⊤	up⊤	PRON
ejpam-5323	86	23	,	,	PUNCT
ejpam-5323	86	24	ap⊤	ap⊤	ADV
ejpam-5323	86	25	,	,	PUNCT
ejpam-5323	86	26	dp⊤	dp⊤	X
ejpam-5323	86	27	be	be	VERB
ejpam-5323	86	28	its	its	PRON
ejpam-5323	86	29	descendants	descendant	NOUN
ejpam-5323	86	30	in	in	ADP
ejpam-5323	86	31	berggren	berggren	PROPN
ejpam-5323	86	32	’s	’s	PART
ejpam-5323	86	33	tree	tree	NOUN
ejpam-5323	86	34	.	.	PUNCT
ejpam-5323	87	1	the	the	DET
ejpam-5323	87	2	triangle	triangle	NOUN
ejpam-5323	87	3	with	with	ADP
ejpam-5323	87	4	vertices	vertex	NOUN
ejpam-5323	87	5	with	with	ADP
ejpam-5323	87	6	the	the	DET
ejpam-5323	87	7	coordinates	coordinate	NOUN
ejpam-5323	87	8	up⊤	up⊤	VERB
ejpam-5323	87	9	,	,	PUNCT
ejpam-5323	87	10	ap⊤	ap⊤	NOUN
ejpam-5323	87	11	,	,	PUNCT
ejpam-5323	87	12	dp⊤	dp⊤	X
ejpam-5323	87	13	is	be	AUX
ejpam-5323	87	14	called	call	VERB
ejpam-5323	87	15	the	the	DET
ejpam-5323	87	16	descendant	descendant	ADJ
ejpam-5323	87	17	triangle	triangle	NOUN
ejpam-5323	87	18	of	of	ADP
ejpam-5323	87	19	p	p	NOUN
ejpam-5323	87	20	in	in	ADP
ejpam-5323	87	21	berggren	berggren	PROPN
ejpam-5323	87	22	’s	’s	PART
ejpam-5323	87	23	tree	tree	NOUN
ejpam-5323	87	24	,	,	PUNCT
ejpam-5323	87	25	and	and	CCONJ
ejpam-5323	87	26	we	we	PRON
ejpam-5323	87	27	denote	denote	VERB
ejpam-5323	87	28	it	it	PRON
ejpam-5323	87	29	by	by	ADP
ejpam-5323	87	30	△	△	NOUN
ejpam-5323	87	31	b(p	b(p	X
ejpam-5323	87	32	)	)	PUNCT
ejpam-5323	87	33	.	.	PUNCT
ejpam-5323	88	1	l.	l.	PROPN
ejpam-5323	88	2	kőszegyová	kőszegyová	PROPN
ejpam-5323	88	3	,	,	PUNCT
ejpam-5323	88	4	e.	e.	PROPN
ejpam-5323	88	5	csókási	csókási	PROPN
ejpam-5323	88	6	,	,	PUNCT
ejpam-5323	88	7	j.	j.	PROPN
ejpam-5323	88	8	hirjak	hirjak	PROPN
ejpam-5323	88	9	/	/	SYM
ejpam-5323	88	10	eur	eur	PROPN
ejpam-5323	88	11	.	.	PUNCT
ejpam-5323	89	1	j.	j.	PROPN
ejpam-5323	89	2	pure	pure	PROPN
ejpam-5323	89	3	appl	appl	PROPN
ejpam-5323	89	4	.	.	PROPN
ejpam-5323	89	5	math	math	PROPN
ejpam-5323	89	6	,	,	PUNCT
ejpam-5323	89	7	17	17	NUM
ejpam-5323	89	8	(	(	PUNCT
ejpam-5323	89	9	3	3	NUM
ejpam-5323	89	10	)	)	PUNCT
ejpam-5323	89	11	(	(	PUNCT
ejpam-5323	89	12	2024	2024	NUM
ejpam-5323	89	13	)	)	PUNCT
ejpam-5323	89	14	,	,	PUNCT
ejpam-5323	89	15	2127	2127	NUM
ejpam-5323	89	16	-	-	SYM
ejpam-5323	89	17	2141	2141	NUM
ejpam-5323	89	18	2131	2131	NUM
ejpam-5323	89	19	proposition	proposition	NOUN
ejpam-5323	89	20	2	2	NUM
ejpam-5323	89	21	.	.	PUNCT
ejpam-5323	90	1	let	let	VERB
ejpam-5323	90	2	p	p	NOUN
ejpam-5323	90	3	=	=	X
ejpam-5323	90	4	(	(	PUNCT
ejpam-5323	90	5	a	a	DET
ejpam-5323	90	6	,	,	PUNCT
ejpam-5323	90	7	b	b	NOUN
ejpam-5323	90	8	,	,	PUNCT
ejpam-5323	90	9	c	c	NOUN
ejpam-5323	90	10	)	)	PUNCT
ejpam-5323	90	11	be	be	AUX
ejpam-5323	90	12	a	a	DET
ejpam-5323	90	13	primitive	primitive	ADJ
ejpam-5323	90	14	pythagorean	pythagorean	NOUN
ejpam-5323	90	15	triple	triple	NOUN
ejpam-5323	90	16	.	.	PUNCT
ejpam-5323	91	1	then	then	ADV
ejpam-5323	91	2	the	the	DET
ejpam-5323	91	3	triangle	triangle	NOUN
ejpam-5323	91	4	△	△	PUNCT
ejpam-5323	91	5	b(p	b(p	X
ejpam-5323	91	6	)	)	PUNCT
ejpam-5323	91	7	belongs	belong	VERB
ejpam-5323	91	8	to	to	ADP
ejpam-5323	91	9	the	the	DET
ejpam-5323	91	10	plane	plane	NOUN
ejpam-5323	91	11	2x+	2x+	NUM
ejpam-5323	91	12	2y	2y	NUM
ejpam-5323	91	13	−	−	NOUN
ejpam-5323	91	14	3z	3z	ADJ
ejpam-5323	91	15	+	+	PUNCT
ejpam-5323	91	16	c	c	NOUN
ejpam-5323	91	17	=	=	SYM
ejpam-5323	91	18	0	0	PROPN
ejpam-5323	91	19	.	.	PUNCT
ejpam-5323	92	1	(	(	PUNCT
ejpam-5323	92	2	2	2	X
ejpam-5323	92	3	)	)	PUNCT
ejpam-5323	92	4	proof	proof	NOUN
ejpam-5323	92	5	.	.	PUNCT
ejpam-5323	93	1	according	accord	VERB
ejpam-5323	93	2	to	to	ADP
ejpam-5323	93	3	the	the	DET
ejpam-5323	93	4	proposition	proposition	NOUN
ejpam-5323	93	5	1	1	NUM
ejpam-5323	93	6	,	,	PUNCT
ejpam-5323	93	7	vertices	vertice	VERB
ejpam-5323	93	8	up⊤	up⊤	PRON
ejpam-5323	93	9	,	,	PUNCT
ejpam-5323	93	10	ap⊤	ap⊤	NOUN
ejpam-5323	93	11	,	,	PUNCT
ejpam-5323	93	12	dp⊤	dp⊤	NOUN
ejpam-5323	93	13	form	form	VERB
ejpam-5323	93	14	a	a	DET
ejpam-5323	93	15	triangle	triangle	NOUN
ejpam-5323	93	16	,	,	PUNCT
ejpam-5323	93	17	therefore	therefore	ADV
ejpam-5323	93	18	,	,	PUNCT
ejpam-5323	93	19	they	they	PRON
ejpam-5323	93	20	define	define	VERB
ejpam-5323	93	21	a	a	DET
ejpam-5323	93	22	plane	plane	NOUN
ejpam-5323	93	23	.	.	PUNCT
ejpam-5323	94	1	analogously	analogously	ADV
ejpam-5323	94	2	to	to	ADP
ejpam-5323	94	3	the	the	DET
ejpam-5323	94	4	previous	previous	ADJ
ejpam-5323	94	5	proof	proof	NOUN
ejpam-5323	94	6	,	,	PUNCT
ejpam-5323	94	7	we	we	PRON
ejpam-5323	94	8	consider	consider	VERB
ejpam-5323	94	9	vectors	vector	NOUN
ejpam-5323	94	10	u⃗	u⃗	PROPN
ejpam-5323	94	11	=	=	PUNCT
ejpam-5323	94	12	ap⊤	ap⊤	X
ejpam-5323	94	13	−	−	PROPN
ejpam-5323	94	14	up⊤	up⊤	ADV
ejpam-5323	95	1	=	=	SYM
ejpam-5323	95	2	(	(	PUNCT
ejpam-5323	95	3	4b	4b	X
ejpam-5323	95	4	,	,	PUNCT
ejpam-5323	95	5	2b	2b	NUM
ejpam-5323	95	6	,	,	PUNCT
ejpam-5323	95	7	4b	4b	NUM
ejpam-5323	95	8	)	)	PUNCT
ejpam-5323	95	9	and	and	CCONJ
ejpam-5323	95	10	v⃗	v⃗	PROPN
ejpam-5323	95	11	=	=	PUNCT
ejpam-5323	95	12	dp⊤	dp⊤	NOUN
ejpam-5323	95	13	−	−	X
ejpam-5323	95	14	up⊤	up⊤	ADV
ejpam-5323	96	1	=	=	PUNCT
ejpam-5323	97	1	(	(	PUNCT
ejpam-5323	97	2	−2a+	−2a+	PROPN
ejpam-5323	97	3	4b,−4a+	4b,−4a+	PROPN
ejpam-5323	97	4	2b,−4a+	2b,−4a+	NUM
ejpam-5323	97	5	4b	4b	PROPN
ejpam-5323	97	6	)	)	PUNCT
ejpam-5323	97	7	.	.	PUNCT
ejpam-5323	98	1	firstly	firstly	ADV
ejpam-5323	98	2	,	,	PUNCT
ejpam-5323	98	3	we	we	PRON
ejpam-5323	98	4	compute	compute	VERB
ejpam-5323	98	5	the	the	DET
ejpam-5323	98	6	normal	normal	ADJ
ejpam-5323	98	7	vector	vector	NOUN
ejpam-5323	98	8	of	of	ADP
ejpam-5323	98	9	the	the	DET
ejpam-5323	98	10	wanted	wanted	ADJ
ejpam-5323	98	11	plane	plane	NOUN
ejpam-5323	98	12	as	as	ADP
ejpam-5323	98	13	cross	cross	NOUN
ejpam-5323	98	14	product	product	NOUN
ejpam-5323	98	15	of	of	ADP
ejpam-5323	98	16	these	these	DET
ejpam-5323	98	17	vectors	vector	NOUN
ejpam-5323	98	18	:	:	PUNCT
ejpam-5323	99	1	u⃗×	u⃗×	PROPN
ejpam-5323	99	2	v⃗	v⃗	PROPN
ejpam-5323	99	3	=	=	SYM
ejpam-5323	99	4	(	(	PUNCT
ejpam-5323	99	5	8ab	8ab	NOUN
ejpam-5323	99	6	,	,	PUNCT
ejpam-5323	99	7	8ab,−12ab	8ab,−12ab	NUM
ejpam-5323	99	8	)	)	PUNCT
ejpam-5323	100	1	≈	≈	PROPN
ejpam-5323	100	2	(	(	PUNCT
ejpam-5323	100	3	2	2	NUM
ejpam-5323	100	4	,	,	PUNCT
ejpam-5323	100	5	2,−3	2,−3	NUM
ejpam-5323	100	6	)	)	PUNCT
ejpam-5323	100	7	.	.	PUNCT
ejpam-5323	101	1	therefore	therefore	ADV
ejpam-5323	101	2	,	,	PUNCT
ejpam-5323	101	3	2x	2x	NUM
ejpam-5323	101	4	+	+	CCONJ
ejpam-5323	101	5	2y	2y	NUM
ejpam-5323	101	6	−	−	NOUN
ejpam-5323	101	7	3z	3z	ADJ
ejpam-5323	101	8	+	+	CCONJ
ejpam-5323	101	9	d	d	NOUN
ejpam-5323	101	10	=	=	SYM
ejpam-5323	101	11	0	0	NUM
ejpam-5323	101	12	is	be	AUX
ejpam-5323	101	13	the	the	DET
ejpam-5323	101	14	equation	equation	NOUN
ejpam-5323	101	15	of	of	ADP
ejpam-5323	101	16	wanted	wanted	ADJ
ejpam-5323	101	17	plane	plane	NOUN
ejpam-5323	101	18	for	for	ADP
ejpam-5323	101	19	some	some	DET
ejpam-5323	101	20	d	d	PROPN
ejpam-5323	101	21	∈	∈	PROPN
ejpam-5323	101	22	r.	r.	NOUN
ejpam-5323	101	23	since	since	SCONJ
ejpam-5323	101	24	up⊤	up⊤	ADV
ejpam-5323	101	25	belongs	belong	VERB
ejpam-5323	101	26	to	to	ADP
ejpam-5323	101	27	this	this	DET
ejpam-5323	101	28	plane	plane	NOUN
ejpam-5323	101	29	,	,	PUNCT
ejpam-5323	101	30	we	we	PRON
ejpam-5323	101	31	get	get	VERB
ejpam-5323	101	32	2(a−	2(a−	NUM
ejpam-5323	101	33	2b+	2b+	NUM
ejpam-5323	101	34	2c	2c	NUM
ejpam-5323	101	35	)	)	PUNCT
ejpam-5323	102	1	+	+	CCONJ
ejpam-5323	102	2	2(2a−	2(2a−	NUM
ejpam-5323	102	3	b+	b+	ADP
ejpam-5323	102	4	2c)−	2c)−	NUM
ejpam-5323	102	5	3(2a−	3(2a−	NUM
ejpam-5323	102	6	2b+	2b+	NUM
ejpam-5323	102	7	3c	3c	NUM
ejpam-5323	102	8	)	)	PUNCT
ejpam-5323	103	1	+	+	CCONJ
ejpam-5323	103	2	d	d	NOUN
ejpam-5323	103	3	=	=	SYM
ejpam-5323	103	4	0	0	NUM
ejpam-5323	103	5	which	which	PRON
ejpam-5323	103	6	yields	yield	VERB
ejpam-5323	103	7	d	d	PROPN
ejpam-5323	103	8	=	=	SYM
ejpam-5323	103	9	c.	c.	PROPN
ejpam-5323	103	10	hence	hence	ADV
ejpam-5323	103	11	,	,	PUNCT
ejpam-5323	103	12	the	the	DET
ejpam-5323	103	13	wanted	want	VERB
ejpam-5323	103	14	plane	plane	NOUN
ejpam-5323	103	15	is	be	AUX
ejpam-5323	103	16	2x+	2x+	NUM
ejpam-5323	103	17	2y	2y	NUM
ejpam-5323	103	18	−	−	NOUN
ejpam-5323	103	19	3z	3z	ADJ
ejpam-5323	103	20	+	+	PUNCT
ejpam-5323	103	21	c	c	NOUN
ejpam-5323	103	22	=	=	SYM
ejpam-5323	103	23	0	0	X
ejpam-5323	103	24	.	.	PUNCT
ejpam-5323	104	1	it	it	PRON
ejpam-5323	104	2	directly	directly	ADV
ejpam-5323	104	3	follows	follow	VERB
ejpam-5323	104	4	that	that	SCONJ
ejpam-5323	104	5	:	:	PUNCT
ejpam-5323	104	6	corollary	corollary	ADJ
ejpam-5323	104	7	1	1	X
ejpam-5323	104	8	.	.	PUNCT
ejpam-5323	105	1	if	if	SCONJ
ejpam-5323	105	2	p	p	X
ejpam-5323	105	3	,	,	PUNCT
ejpam-5323	105	4	q	q	X
ejpam-5323	105	5	are	be	AUX
ejpam-5323	105	6	primitive	primitive	ADJ
ejpam-5323	105	7	pythagorean	pythagorean	ADJ
ejpam-5323	105	8	triples	triple	NOUN
ejpam-5323	105	9	,	,	PUNCT
ejpam-5323	105	10	then	then	ADV
ejpam-5323	105	11	the	the	DET
ejpam-5323	105	12	planes	plane	NOUN
ejpam-5323	105	13	defined	define	VERB
ejpam-5323	105	14	by	by	ADP
ejpam-5323	105	15	triangles	triangle	NOUN
ejpam-5323	105	16	△	△	NOUN
ejpam-5323	105	17	b(p	b(p	X
ejpam-5323	105	18	)	)	PUNCT
ejpam-5323	105	19	and	and	CCONJ
ejpam-5323	105	20	△	△	NOUN
ejpam-5323	105	21	b(q	b(q	PROPN
ejpam-5323	105	22	)	)	PUNCT
ejpam-5323	105	23	are	be	AUX
ejpam-5323	105	24	parallel	parallel	ADJ
ejpam-5323	105	25	.	.	PUNCT
ejpam-5323	106	1	corollary	corollary	ADJ
ejpam-5323	106	2	2	2	NUM
ejpam-5323	106	3	.	.	PUNCT
ejpam-5323	107	1	each	each	DET
ejpam-5323	107	2	primitive	primitive	ADJ
ejpam-5323	107	3	pythagorean	pythagorean	NOUN
ejpam-5323	107	4	triple	triple	NOUN
ejpam-5323	107	5	belongs	belong	VERB
ejpam-5323	107	6	to	to	ADP
ejpam-5323	107	7	a	a	DET
ejpam-5323	107	8	plane	plane	NOUN
ejpam-5323	107	9	2x+	2x+	NUM
ejpam-5323	107	10	2y	2y	NUM
ejpam-5323	107	11	−	−	NOUN
ejpam-5323	107	12	3z	3z	ADJ
ejpam-5323	107	13	+	+	PUNCT
ejpam-5323	107	14	d	d	NOUN
ejpam-5323	107	15	=	=	SYM
ejpam-5323	107	16	0	0	NUM
ejpam-5323	107	17	for	for	ADP
ejpam-5323	107	18	some	some	DET
ejpam-5323	107	19	odd	odd	ADJ
ejpam-5323	107	20	d	d	PROPN
ejpam-5323	107	21	∈	∈	PROPN
ejpam-5323	107	22	n.	n.	NOUN
ejpam-5323	107	23	proof	proof	NOUN
ejpam-5323	107	24	.	.	PUNCT
ejpam-5323	108	1	according	accord	VERB
ejpam-5323	108	2	to	to	ADP
ejpam-5323	108	3	[	[	X
ejpam-5323	108	4	7	7	NUM
ejpam-5323	108	5	]	]	PUNCT
ejpam-5323	108	6	,	,	PUNCT
ejpam-5323	108	7	berggren	berggren	PROPN
ejpam-5323	108	8	’s	’s	PART
ejpam-5323	108	9	tree	tree	NOUN
ejpam-5323	108	10	contains	contain	VERB
ejpam-5323	108	11	all	all	DET
ejpam-5323	108	12	primitive	primitive	ADJ
ejpam-5323	108	13	pythagorean	pythagorean	ADJ
ejpam-5323	108	14	triples	triple	NOUN
ejpam-5323	108	15	.	.	PUNCT
ejpam-5323	109	1	therefore	therefore	ADV
ejpam-5323	109	2	,	,	PUNCT
ejpam-5323	109	3	if	if	SCONJ
ejpam-5323	109	4	p	p	NOUN
ejpam-5323	109	5	is	be	AUX
ejpam-5323	109	6	a	a	DET
ejpam-5323	109	7	ppt	ppt	NOUN
ejpam-5323	109	8	,	,	PUNCT
ejpam-5323	109	9	then	then	ADV
ejpam-5323	109	10	it	it	PRON
ejpam-5323	109	11	is	be	AUX
ejpam-5323	109	12	either	either	CCONJ
ejpam-5323	109	13	(	(	PUNCT
ejpam-5323	109	14	3	3	NUM
ejpam-5323	109	15	,	,	PUNCT
ejpam-5323	109	16	4	4	NUM
ejpam-5323	109	17	,	,	PUNCT
ejpam-5323	109	18	5	5	NUM
ejpam-5323	109	19	)	)	PUNCT
ejpam-5323	109	20	or	or	CCONJ
ejpam-5323	109	21	it	it	PRON
ejpam-5323	109	22	is	be	AUX
ejpam-5323	109	23	a	a	DET
ejpam-5323	109	24	descendant	descendant	ADJ
ejpam-5323	109	25	triple	triple	NOUN
ejpam-5323	109	26	of	of	ADP
ejpam-5323	109	27	some	some	DET
ejpam-5323	109	28	triple	triple	ADJ
ejpam-5323	109	29	(	(	PUNCT
ejpam-5323	109	30	e	e	NOUN
ejpam-5323	109	31	,	,	PUNCT
ejpam-5323	109	32	f	f	X
ejpam-5323	109	33	,	,	PUNCT
ejpam-5323	109	34	g	g	NOUN
ejpam-5323	109	35	)	)	PUNCT
ejpam-5323	109	36	in	in	ADP
ejpam-5323	109	37	berggren	berggren	PROPN
ejpam-5323	109	38	’s	’s	PART
ejpam-5323	109	39	tree	tree	NOUN
ejpam-5323	109	40	such	such	ADJ
ejpam-5323	109	41	that	that	SCONJ
ejpam-5323	109	42	g	g	PROPN
ejpam-5323	109	43	∈	∈	PROPN
ejpam-5323	110	1	n	n	PRON
ejpam-5323	110	2	is	be	AUX
ejpam-5323	110	3	odd	odd	ADJ
ejpam-5323	110	4	.	.	PUNCT
ejpam-5323	111	1	if	if	SCONJ
ejpam-5323	111	2	p	p	NOUN
ejpam-5323	111	3	=	=	X
ejpam-5323	111	4	(	(	PUNCT
ejpam-5323	111	5	3	3	NUM
ejpam-5323	111	6	,	,	PUNCT
ejpam-5323	111	7	4	4	NUM
ejpam-5323	111	8	,	,	PUNCT
ejpam-5323	111	9	5	5	NUM
ejpam-5323	111	10	)	)	PUNCT
ejpam-5323	111	11	then	then	ADV
ejpam-5323	111	12	it	it	PRON
ejpam-5323	111	13	clearly	clearly	ADV
ejpam-5323	111	14	belongs	belong	VERB
ejpam-5323	111	15	to	to	ADP
ejpam-5323	111	16	the	the	DET
ejpam-5323	111	17	plane	plane	NOUN
ejpam-5323	111	18	2x+	2x+	NUM
ejpam-5323	111	19	2y	2y	NUM
ejpam-5323	111	20	−	−	NOUN
ejpam-5323	111	21	3z	3z	NUM
ejpam-5323	111	22	+	+	CCONJ
ejpam-5323	111	23	1	1	NUM
ejpam-5323	111	24	=	=	SYM
ejpam-5323	111	25	0	0	NUM
ejpam-5323	111	26	.	.	PUNCT
ejpam-5323	112	1	if	if	SCONJ
ejpam-5323	112	2	p	p	NOUN
ejpam-5323	112	3	is	be	AUX
ejpam-5323	112	4	a	a	DET
ejpam-5323	112	5	descendant	descendant	ADJ
ejpam-5323	112	6	triple	triple	NOUN
ejpam-5323	112	7	of	of	ADP
ejpam-5323	112	8	some	some	DET
ejpam-5323	112	9	triple	triple	ADJ
ejpam-5323	112	10	(	(	PUNCT
ejpam-5323	112	11	e	e	NOUN
ejpam-5323	112	12	,	,	PUNCT
ejpam-5323	112	13	f	f	X
ejpam-5323	112	14	,	,	PUNCT
ejpam-5323	112	15	g	g	NOUN
ejpam-5323	112	16	)	)	PUNCT
ejpam-5323	112	17	in	in	ADP
ejpam-5323	112	18	berggren	berggren	PROPN
ejpam-5323	112	19	’s	’s	PART
ejpam-5323	112	20	tree	tree	NOUN
ejpam-5323	112	21	,	,	PUNCT
ejpam-5323	112	22	then	then	ADV
ejpam-5323	112	23	by	by	ADP
ejpam-5323	112	24	proposition	proposition	NOUN
ejpam-5323	112	25	2	2	NUM
ejpam-5323	112	26	,	,	PUNCT
ejpam-5323	112	27	it	it	PRON
ejpam-5323	112	28	belongs	belong	VERB
ejpam-5323	112	29	to	to	ADP
ejpam-5323	112	30	the	the	DET
ejpam-5323	112	31	plane	plane	NOUN
ejpam-5323	112	32	2x+	2x+	NUM
ejpam-5323	112	33	2y	2y	NUM
ejpam-5323	112	34	−	−	NOUN
ejpam-5323	112	35	3z	3z	ADJ
ejpam-5323	112	36	+	+	CCONJ
ejpam-5323	112	37	g	g	NOUN
ejpam-5323	112	38	=	=	NOUN
ejpam-5323	112	39	0	0	NUM
ejpam-5323	113	1	where	where	SCONJ
ejpam-5323	113	2	g	g	PROPN
ejpam-5323	113	3	∈	∈	PROPN
ejpam-5323	113	4	n	n	PRON
ejpam-5323	113	5	is	be	AUX
ejpam-5323	113	6	odd	odd	ADJ
ejpam-5323	113	7	.	.	PUNCT
ejpam-5323	114	1	in	in	ADP
ejpam-5323	114	2	[	[	X
ejpam-5323	114	3	14	14	NUM
ejpam-5323	114	4	]	]	PUNCT
ejpam-5323	114	5	,	,	PUNCT
ejpam-5323	114	6	tripathi	tripathi	PROPN
ejpam-5323	114	7	proved	prove	VERB
ejpam-5323	114	8	the	the	DET
ejpam-5323	114	9	following	follow	VERB
ejpam-5323	114	10	lemma	lemma	PROPN
ejpam-5323	114	11	:	:	PUNCT
ejpam-5323	114	12	lemma	lemma	PROPN
ejpam-5323	114	13	2	2	NUM
ejpam-5323	114	14	.	.	X
ejpam-5323	114	15	for	for	ADP
ejpam-5323	114	16	odd	odd	ADJ
ejpam-5323	114	17	n	n	CCONJ
ejpam-5323	114	18	∈	∈	PROPN
ejpam-5323	114	19	n	n	CCONJ
ejpam-5323	114	20	,	,	PUNCT
ejpam-5323	114	21	the	the	DET
ejpam-5323	114	22	number	number	NOUN
ejpam-5323	114	23	of	of	ADP
ejpam-5323	114	24	primitive	primitive	ADJ
ejpam-5323	114	25	pythagorean	pythagorean	ADJ
ejpam-5323	114	26	triples	triple	NOUN
ejpam-5323	114	27	(	(	PUNCT
ejpam-5323	114	28	a	a	PRON
ejpam-5323	114	29	,	,	PUNCT
ejpam-5323	114	30	b	b	NOUN
ejpam-5323	114	31	,	,	PUNCT
ejpam-5323	114	32	n	n	CCONJ
ejpam-5323	114	33	)	)	PUNCT
ejpam-5323	114	34	is	be	AUX
ejpam-5323	114	35	p∗	p∗	ADJ
ejpam-5323	114	36	2	2	NUM
ejpam-5323	114	37	(	(	PUNCT
ejpam-5323	114	38	n	n	CCONJ
ejpam-5323	114	39	)	)	PUNCT
ejpam-5323	115	1	=	=	NOUN
ejpam-5323	115	2	{	{	PUNCT
ejpam-5323	115	3	2ω(n)−1	2ω(n)−1	NUM
ejpam-5323	115	4	,	,	PUNCT
ejpam-5323	115	5	if	if	SCONJ
ejpam-5323	115	6	n	n	PRON
ejpam-5323	115	7	≥	≥	NOUN
ejpam-5323	115	8	3	3	NUM
ejpam-5323	115	9	and	and	CCONJ
ejpam-5323	115	10	no	no	DET
ejpam-5323	115	11	prime	prime	NOUN
ejpam-5323	115	12	of	of	ADP
ejpam-5323	115	13	the	the	DET
ejpam-5323	115	14	form	form	NOUN
ejpam-5323	115	15	4k	4k	NOUN
ejpam-5323	115	16	+	+	CCONJ
ejpam-5323	115	17	3	3	NUM
ejpam-5323	115	18	divides	divide	NOUN
ejpam-5323	115	19	n	n	CCONJ
ejpam-5323	115	20	,	,	PUNCT
ejpam-5323	115	21	0	0	NUM
ejpam-5323	115	22	,	,	PUNCT
ejpam-5323	115	23	if	if	SCONJ
ejpam-5323	115	24	n	n	NOUN
ejpam-5323	115	25	=	=	SYM
ejpam-5323	115	26	1	1	NUM
ejpam-5323	115	27	or	or	CCONJ
ejpam-5323	115	28	n	n	PROPN
ejpam-5323	115	29	has	have	VERB
ejpam-5323	115	30	a	a	DET
ejpam-5323	115	31	prime	prime	ADJ
ejpam-5323	115	32	divisor	divisor	NOUN
ejpam-5323	115	33	of	of	ADP
ejpam-5323	115	34	the	the	DET
ejpam-5323	115	35	form	form	NOUN
ejpam-5323	115	36	4k	4k	NOUN
ejpam-5323	115	37	+	+	CCONJ
ejpam-5323	115	38	3	3	NUM
ejpam-5323	115	39	,	,	PUNCT
ejpam-5323	115	40	where	where	SCONJ
ejpam-5323	115	41	ω(n	ω(n	NUM
ejpam-5323	115	42	)	)	PUNCT
ejpam-5323	115	43	is	be	AUX
ejpam-5323	115	44	the	the	DET
ejpam-5323	115	45	number	number	NOUN
ejpam-5323	115	46	of	of	ADP
ejpam-5323	115	47	prime	prime	ADJ
ejpam-5323	115	48	divisors	divisor	NOUN
ejpam-5323	115	49	of	of	ADP
ejpam-5323	115	50	n.	n.	NOUN
ejpam-5323	115	51	we	we	PRON
ejpam-5323	115	52	use	use	VERB
ejpam-5323	115	53	lemmas	lemma	NOUN
ejpam-5323	115	54	1	1	NUM
ejpam-5323	115	55	and	and	CCONJ
ejpam-5323	115	56	2	2	NUM
ejpam-5323	115	57	to	to	PART
ejpam-5323	115	58	determine	determine	VERB
ejpam-5323	115	59	the	the	DET
ejpam-5323	115	60	number	number	NOUN
ejpam-5323	115	61	of	of	ADP
ejpam-5323	115	62	descendant	descendant	ADJ
ejpam-5323	115	63	triangles	triangle	NOUN
ejpam-5323	115	64	in	in	ADP
ejpam-5323	115	65	the	the	DET
ejpam-5323	115	66	individual	individual	ADJ
ejpam-5323	115	67	planes	plane	NOUN
ejpam-5323	115	68	.	.	PUNCT
ejpam-5323	116	1	proposition	proposition	NOUN
ejpam-5323	116	2	3	3	NUM
ejpam-5323	116	3	.	.	PUNCT
ejpam-5323	117	1	if	if	SCONJ
ejpam-5323	117	2	c	c	PROPN
ejpam-5323	117	3	∈	∈	PROPN
ejpam-5323	117	4	n	n	VERB
ejpam-5323	117	5	is	be	AUX
ejpam-5323	117	6	odd	odd	ADJ
ejpam-5323	117	7	,	,	PUNCT
ejpam-5323	117	8	then	then	ADV
ejpam-5323	117	9	the	the	DET
ejpam-5323	117	10	plane	plane	NOUN
ejpam-5323	117	11	2x	2x	NUM
ejpam-5323	118	1	+	+	CCONJ
ejpam-5323	118	2	2y	2y	NUM
ejpam-5323	118	3	−	−	NOUN
ejpam-5323	118	4	3z	3z	ADJ
ejpam-5323	118	5	+	+	PUNCT
ejpam-5323	118	6	c	c	NOUN
ejpam-5323	118	7	=	=	SYM
ejpam-5323	118	8	0	0	NUM
ejpam-5323	118	9	contains	contain	VERB
ejpam-5323	118	10	p∗	p∗	NOUN
ejpam-5323	118	11	2	2	NUM
ejpam-5323	118	12	(	(	PUNCT
ejpam-5323	118	13	c	c	NOUN
ejpam-5323	118	14	)	)	PUNCT
ejpam-5323	118	15	descendant	descendant	ADJ
ejpam-5323	118	16	triangles	triangle	NOUN
ejpam-5323	118	17	△	△	PROPN
ejpam-5323	118	18	b.	b.	PROPN
ejpam-5323	118	19	l.	l.	PROPN
ejpam-5323	118	20	kőszegyová	kőszegyová	PROPN
ejpam-5323	118	21	,	,	PUNCT
ejpam-5323	118	22	e.	e.	PROPN
ejpam-5323	118	23	csókási	csókási	PROPN
ejpam-5323	118	24	,	,	PUNCT
ejpam-5323	118	25	j.	j.	PROPN
ejpam-5323	118	26	hirjak	hirjak	PROPN
ejpam-5323	118	27	/	/	SYM
ejpam-5323	118	28	eur	eur	PROPN
ejpam-5323	118	29	.	.	PUNCT
ejpam-5323	119	1	j.	j.	PROPN
ejpam-5323	119	2	pure	pure	PROPN
ejpam-5323	119	3	appl	appl	PROPN
ejpam-5323	119	4	.	.	PROPN
ejpam-5323	119	5	math	math	PROPN
ejpam-5323	119	6	,	,	PUNCT
ejpam-5323	119	7	17	17	NUM
ejpam-5323	119	8	(	(	PUNCT
ejpam-5323	119	9	3	3	NUM
ejpam-5323	119	10	)	)	PUNCT
ejpam-5323	119	11	(	(	PUNCT
ejpam-5323	119	12	2024	2024	NUM
ejpam-5323	119	13	)	)	PUNCT
ejpam-5323	119	14	,	,	PUNCT
ejpam-5323	119	15	2127	2127	NUM
ejpam-5323	119	16	-	-	SYM
ejpam-5323	119	17	2141	2141	NUM
ejpam-5323	119	18	2132	2132	NUM
ejpam-5323	119	19	proof	proof	NOUN
ejpam-5323	119	20	.	.	PUNCT
ejpam-5323	120	1	according	accord	VERB
ejpam-5323	120	2	to	to	ADP
ejpam-5323	120	3	lemma	lemma	PROPN
ejpam-5323	120	4	2	2	NUM
ejpam-5323	120	5	,	,	PUNCT
ejpam-5323	120	6	for	for	ADP
ejpam-5323	120	7	each	each	DET
ejpam-5323	120	8	odd	odd	ADJ
ejpam-5323	120	9	c	c	PROPN
ejpam-5323	120	10	∈	∈	PROPN
ejpam-5323	120	11	n	n	CCONJ
ejpam-5323	120	12	,	,	PUNCT
ejpam-5323	120	13	there	there	PRON
ejpam-5323	120	14	is	be	VERB
ejpam-5323	120	15	p∗	p∗	ADJ
ejpam-5323	120	16	2	2	NUM
ejpam-5323	120	17	(	(	PUNCT
ejpam-5323	120	18	c	c	NOUN
ejpam-5323	120	19	)	)	PUNCT
ejpam-5323	120	20	primitive	primitive	ADJ
ejpam-5323	120	21	pythagorean	pythagorean	ADJ
ejpam-5323	120	22	triples	triple	NOUN
ejpam-5323	120	23	p	p	NOUN
ejpam-5323	120	24	with	with	ADP
ejpam-5323	120	25	the	the	DET
ejpam-5323	120	26	third	third	ADJ
ejpam-5323	120	27	component	component	NOUN
ejpam-5323	120	28	c.	c.	PROPN
ejpam-5323	120	29	further	far	ADV
ejpam-5323	120	30	,	,	PUNCT
ejpam-5323	120	31	the	the	DET
ejpam-5323	120	32	proposition	proposition	NOUN
ejpam-5323	120	33	2	2	NUM
ejpam-5323	120	34	yields	yield	NOUN
ejpam-5323	120	35	that	that	PRON
ejpam-5323	120	36	for	for	ADP
ejpam-5323	120	37	each	each	DET
ejpam-5323	120	38	such	such	ADJ
ejpam-5323	120	39	p	p	NOUN
ejpam-5323	120	40	,	,	PUNCT
ejpam-5323	120	41	the	the	DET
ejpam-5323	120	42	descendant	descendant	ADJ
ejpam-5323	120	43	triangle	triangle	NOUN
ejpam-5323	120	44	△	△	NOUN
ejpam-5323	120	45	b(p	b(p	X
ejpam-5323	120	46	)	)	PUNCT
ejpam-5323	120	47	belongs	belong	VERB
ejpam-5323	120	48	to	to	ADP
ejpam-5323	120	49	the	the	DET
ejpam-5323	120	50	plane	plane	NOUN
ejpam-5323	120	51	2x+	2x+	NUM
ejpam-5323	120	52	2y	2y	NUM
ejpam-5323	120	53	−	−	NOUN
ejpam-5323	120	54	3z	3z	ADJ
ejpam-5323	120	55	+	+	PUNCT
ejpam-5323	120	56	c	c	NOUN
ejpam-5323	120	57	=	=	SYM
ejpam-5323	120	58	0	0	X
ejpam-5323	120	59	.	.	PUNCT
ejpam-5323	121	1	it	it	PRON
ejpam-5323	121	2	is	be	AUX
ejpam-5323	121	3	easy	easy	ADJ
ejpam-5323	121	4	to	to	PART
ejpam-5323	121	5	see	see	VERB
ejpam-5323	121	6	that	that	SCONJ
ejpam-5323	121	7	the	the	DET
ejpam-5323	121	8	plane	plane	NOUN
ejpam-5323	121	9	2x+	2x+	NUM
ejpam-5323	121	10	2y	2y	NUM
ejpam-5323	121	11	−	−	NOUN
ejpam-5323	121	12	3z	3z	ADJ
ejpam-5323	121	13	+	+	PUNCT
ejpam-5323	121	14	c	c	NOUN
ejpam-5323	121	15	=	=	SYM
ejpam-5323	121	16	0	0	PROPN
ejpam-5323	121	17	can	can	AUX
ejpam-5323	121	18	not	not	PART
ejpam-5323	121	19	contain	contain	VERB
ejpam-5323	121	20	more	more	ADJ
ejpam-5323	121	21	descendant	descendant	ADJ
ejpam-5323	121	22	triangles	triangle	NOUN
ejpam-5323	121	23	.	.	PUNCT
ejpam-5323	122	1	assume	assume	VERB
ejpam-5323	122	2	that	that	SCONJ
ejpam-5323	122	3	there	there	PRON
ejpam-5323	122	4	is	be	VERB
ejpam-5323	122	5	a	a	DET
ejpam-5323	122	6	descendant	descendant	ADJ
ejpam-5323	122	7	triangle	triangle	NOUN
ejpam-5323	122	8	△	△	PUNCT
ejpam-5323	122	9	b(q	b(q	PROPN
ejpam-5323	122	10	)	)	PUNCT
ejpam-5323	122	11	in	in	ADP
ejpam-5323	122	12	2x+2y−	2x+2y−	NUM
ejpam-5323	122	13	3z+	3z+	NUM
ejpam-5323	122	14	c	c	NOUN
ejpam-5323	122	15	=	=	SYM
ejpam-5323	122	16	0	0	NUM
ejpam-5323	122	17	such	such	ADJ
ejpam-5323	122	18	that	that	DET
ejpam-5323	122	19	q	q	NOUN
ejpam-5323	123	1	=	=	X
ejpam-5323	123	2	(	(	PUNCT
ejpam-5323	123	3	a	a	PRON
ejpam-5323	123	4	,	,	PUNCT
ejpam-5323	123	5	b	b	NOUN
ejpam-5323	123	6	,	,	PUNCT
ejpam-5323	123	7	n	n	CCONJ
ejpam-5323	123	8	)	)	PUNCT
ejpam-5323	123	9	,	,	PUNCT
ejpam-5323	123	10	n	n	CCONJ
ejpam-5323	123	11	̸=	̸=	PROPN
ejpam-5323	123	12	c.	c.	NOUN
ejpam-5323	123	13	however	however	ADV
ejpam-5323	123	14	,	,	PUNCT
ejpam-5323	123	15	by	by	ADP
ejpam-5323	123	16	the	the	DET
ejpam-5323	123	17	proposition	proposition	NOUN
ejpam-5323	123	18	2	2	NUM
ejpam-5323	123	19	,	,	PUNCT
ejpam-5323	123	20	△	△	NOUN
ejpam-5323	123	21	b(q	b(q	PROPN
ejpam-5323	123	22	)	)	PUNCT
ejpam-5323	123	23	also	also	ADV
ejpam-5323	123	24	belongs	belong	VERB
ejpam-5323	123	25	to	to	ADP
ejpam-5323	123	26	the	the	DET
ejpam-5323	123	27	plane	plane	NOUN
ejpam-5323	123	28	2x+	2x+	NUM
ejpam-5323	123	29	2y	2y	NUM
ejpam-5323	123	30	−	−	NOUN
ejpam-5323	123	31	3z	3z	ADJ
ejpam-5323	123	32	+	+	CCONJ
ejpam-5323	123	33	n	n	CCONJ
ejpam-5323	123	34	=	=	SYM
ejpam-5323	123	35	0	0	NUM
ejpam-5323	123	36	which	which	PRON
ejpam-5323	123	37	yields	yield	VERB
ejpam-5323	123	38	n	n	NOUN
ejpam-5323	123	39	=	=	SYM
ejpam-5323	123	40	c	c	NOUN
ejpam-5323	123	41	,	,	PUNCT
ejpam-5323	123	42	a	a	DET
ejpam-5323	123	43	contradiction	contradiction	NOUN
ejpam-5323	123	44	.	.	PUNCT
ejpam-5323	124	1	corollary	corollary	ADJ
ejpam-5323	124	2	3	3	NUM
ejpam-5323	124	3	.	.	PUNCT
ejpam-5323	125	1	for	for	ADP
ejpam-5323	125	2	each	each	DET
ejpam-5323	125	3	odd	odd	ADJ
ejpam-5323	125	4	integer	integer	NOUN
ejpam-5323	125	5	n	n	PRON
ejpam-5323	125	6	≥	≥	NOUN
ejpam-5323	125	7	3	3	NUM
ejpam-5323	125	8	,	,	PUNCT
ejpam-5323	125	9	the	the	DET
ejpam-5323	125	10	plane	plane	NOUN
ejpam-5323	125	11	2x+2y−3z+n	2x+2y−3z+n	NUM
ejpam-5323	125	12	=	=	SYM
ejpam-5323	125	13	0	0	NUM
ejpam-5323	125	14	contains	contain	VERB
ejpam-5323	125	15	3·p∗	3·p∗	NUM
ejpam-5323	125	16	2	2	NUM
ejpam-5323	125	17	(	(	PUNCT
ejpam-5323	125	18	n	n	CCONJ
ejpam-5323	125	19	)	)	PUNCT
ejpam-5323	125	20	primitive	primitive	ADJ
ejpam-5323	125	21	pythagorean	pythagorean	ADJ
ejpam-5323	125	22	triples	triple	NOUN
ejpam-5323	125	23	.	.	PUNCT
ejpam-5323	126	1	the	the	DET
ejpam-5323	126	2	plane	plane	NOUN
ejpam-5323	126	3	2x+	2x+	NUM
ejpam-5323	126	4	2y	2y	NUM
ejpam-5323	126	5	−	−	NOUN
ejpam-5323	126	6	3z	3z	NUM
ejpam-5323	126	7	+	+	CCONJ
ejpam-5323	126	8	1	1	NUM
ejpam-5323	126	9	=	=	SYM
ejpam-5323	126	10	0	0	NUM
ejpam-5323	126	11	contains	contain	VERB
ejpam-5323	126	12	a	a	DET
ejpam-5323	126	13	single	single	ADJ
ejpam-5323	126	14	primitive	primitive	ADJ
ejpam-5323	126	15	pythagorean	pythagorean	NOUN
ejpam-5323	126	16	triple	triple	NOUN
ejpam-5323	126	17	,	,	PUNCT
ejpam-5323	126	18	(	(	PUNCT
ejpam-5323	126	19	3	3	NUM
ejpam-5323	126	20	,	,	PUNCT
ejpam-5323	126	21	4	4	NUM
ejpam-5323	126	22	,	,	PUNCT
ejpam-5323	126	23	5	5	NUM
ejpam-5323	126	24	)	)	PUNCT
ejpam-5323	126	25	.	.	PUNCT
ejpam-5323	127	1	proof	proof	NOUN
ejpam-5323	127	2	.	.	PUNCT
ejpam-5323	128	1	let	let	VERB
ejpam-5323	128	2	n	n	NOUN
ejpam-5323	128	3	=	=	SYM
ejpam-5323	128	4	1	1	X
ejpam-5323	128	5	.	.	PUNCT
ejpam-5323	129	1	if	if	SCONJ
ejpam-5323	129	2	(	(	PUNCT
ejpam-5323	129	3	a	a	DET
ejpam-5323	129	4	,	,	PUNCT
ejpam-5323	129	5	b	b	NOUN
ejpam-5323	129	6	,	,	PUNCT
ejpam-5323	129	7	c	c	NOUN
ejpam-5323	129	8	)	)	PUNCT
ejpam-5323	129	9	is	be	AUX
ejpam-5323	129	10	a	a	DET
ejpam-5323	129	11	primitive	primitive	ADJ
ejpam-5323	129	12	pythagorean	pythagorean	NOUN
ejpam-5323	129	13	triple	triple	NOUN
ejpam-5323	129	14	belonging	belong	VERB
ejpam-5323	129	15	to	to	ADP
ejpam-5323	129	16	2x+	2x+	NUM
ejpam-5323	129	17	2y	2y	NUM
ejpam-5323	129	18	−	−	NOUN
ejpam-5323	129	19	3z	3z	NUM
ejpam-5323	129	20	+	+	CCONJ
ejpam-5323	129	21	1	1	NUM
ejpam-5323	129	22	=	=	SYM
ejpam-5323	129	23	0	0	NUM
ejpam-5323	129	24	,	,	PUNCT
ejpam-5323	129	25	then	then	ADV
ejpam-5323	129	26	by	by	ADP
ejpam-5323	129	27	euclid	euclid	PROPN
ejpam-5323	129	28	’s	’s	PART
ejpam-5323	129	29	formula	formula	NOUN
ejpam-5323	129	30	we	we	PRON
ejpam-5323	129	31	get	get	VERB
ejpam-5323	129	32	2(m2	2(m2	NUM
ejpam-5323	129	33	−	−	NOUN
ejpam-5323	129	34	n2	n2	NOUN
ejpam-5323	129	35	)	)	PUNCT
ejpam-5323	130	1	+	+	CCONJ
ejpam-5323	130	2	2(2mn)−	2(2mn)−	NUM
ejpam-5323	130	3	3(m2	3(m2	NUM
ejpam-5323	130	4	+	+	CCONJ
ejpam-5323	130	5	n2	n2	ADJ
ejpam-5323	130	6	)	)	PUNCT
ejpam-5323	130	7	+	+	CCONJ
ejpam-5323	130	8	1	1	NUM
ejpam-5323	130	9	=	=	SYM
ejpam-5323	130	10	0	0	NUM
ejpam-5323	130	11	m2	m2	PROPN
ejpam-5323	130	12	−	−	PROPN
ejpam-5323	130	13	4mn+	4mn+	NOUN
ejpam-5323	130	14	5n2	5n2	NUM
ejpam-5323	130	15	−	−	NOUN
ejpam-5323	130	16	1	1	NUM
ejpam-5323	130	17	=	=	SYM
ejpam-5323	130	18	0	0	NUM
ejpam-5323	130	19	assuming	assume	VERB
ejpam-5323	130	20	that	that	SCONJ
ejpam-5323	130	21	m	m	PROPN
ejpam-5323	130	22	is	be	AUX
ejpam-5323	130	23	a	a	DET
ejpam-5323	130	24	variable	variable	NOUN
ejpam-5323	130	25	and	and	CCONJ
ejpam-5323	130	26	n	n	PRON
ejpam-5323	130	27	is	be	AUX
ejpam-5323	130	28	a	a	DET
ejpam-5323	130	29	parameter	parameter	NOUN
ejpam-5323	130	30	,	,	PUNCT
ejpam-5323	130	31	we	we	PRON
ejpam-5323	130	32	get	get	VERB
ejpam-5323	130	33	m	m	VERB
ejpam-5323	130	34	=	=	NOUN
ejpam-5323	130	35	4n±	4n±	NUM
ejpam-5323	131	1	√	√	NUM
ejpam-5323	131	2	4−	4−	NUM
ejpam-5323	131	3	4n2	4n2	NUM
ejpam-5323	131	4	2	2	NUM
ejpam-5323	131	5	according	accord	VERB
ejpam-5323	131	6	to	to	ADP
ejpam-5323	131	7	euclid	euclid	PROPN
ejpam-5323	131	8	’s	’s	PART
ejpam-5323	131	9	formula	formula	NOUN
ejpam-5323	131	10	,	,	PUNCT
ejpam-5323	131	11	n	n	CCONJ
ejpam-5323	131	12	,	,	PUNCT
ejpam-5323	131	13	m	m	PROPN
ejpam-5323	131	14	∈	∈	PROPN
ejpam-5323	131	15	n	n	CCONJ
ejpam-5323	131	16	,	,	PUNCT
ejpam-5323	131	17	which	which	PRON
ejpam-5323	131	18	yields	yield	VERB
ejpam-5323	131	19	4−	4−	PROPN
ejpam-5323	131	20	4n2	4n2	NUM
ejpam-5323	131	21	≥	≥	NOUN
ejpam-5323	131	22	0	0	NUM
ejpam-5323	132	1	⇐	⇐	ADJ
ejpam-5323	132	2	⇒	⇒	PROPN
ejpam-5323	132	3	n	n	NOUN
ejpam-5323	132	4	=	=	SYM
ejpam-5323	132	5	1	1	NUM
ejpam-5323	132	6	,	,	PUNCT
ejpam-5323	132	7	therefore	therefore	ADV
ejpam-5323	132	8	,	,	PUNCT
ejpam-5323	132	9	m	m	VERB
ejpam-5323	132	10	=	=	ADJ
ejpam-5323	132	11	2	2	NUM
ejpam-5323	132	12	.	.	PUNCT
ejpam-5323	133	1	hence	hence	ADV
ejpam-5323	133	2	,	,	PUNCT
ejpam-5323	133	3	a	a	DET
ejpam-5323	133	4	primitive	primitive	ADJ
ejpam-5323	133	5	pythagorean	pythagorean	NOUN
ejpam-5323	133	6	triple	triple	NOUN
ejpam-5323	133	7	(	(	PUNCT
ejpam-5323	133	8	a	a	PRON
ejpam-5323	133	9	,	,	PUNCT
ejpam-5323	133	10	b	b	NOUN
ejpam-5323	133	11	,	,	PUNCT
ejpam-5323	133	12	c	c	NOUN
ejpam-5323	133	13	)	)	PUNCT
ejpam-5323	133	14	belongs	belong	VERB
ejpam-5323	133	15	to	to	ADP
ejpam-5323	133	16	the	the	DET
ejpam-5323	133	17	plane	plane	NOUN
ejpam-5323	133	18	2x+2y−3z+1	2x+2y−3z+1	NUM
ejpam-5323	133	19	=	=	SYM
ejpam-5323	133	20	0	0	NUM
ejpam-5323	133	21	⇐	⇐	ADJ
ejpam-5323	133	22	⇒	⇒	NOUN
ejpam-5323	133	23	[	[	X
ejpam-5323	133	24	(	(	PUNCT
ejpam-5323	133	25	a	a	DET
ejpam-5323	133	26	,	,	PUNCT
ejpam-5323	133	27	b	b	NOUN
ejpam-5323	133	28	,	,	PUNCT
ejpam-5323	133	29	c	c	NOUN
ejpam-5323	133	30	)	)	PUNCT
ejpam-5323	133	31	=	=	SYM
ejpam-5323	133	32	(	(	PUNCT
ejpam-5323	133	33	m2	m2	PROPN
ejpam-5323	133	34	−	−	PROPN
ejpam-5323	133	35	n2	n2	PROPN
ejpam-5323	133	36	,	,	PUNCT
ejpam-5323	133	37	2mn	2mn	PROPN
ejpam-5323	133	38	,	,	PUNCT
ejpam-5323	133	39	m2	m2	PROPN
ejpam-5323	133	40	+	+	CCONJ
ejpam-5323	133	41	n2	n2	NOUN
ejpam-5323	133	42	)	)	PUNCT
ejpam-5323	133	43	where	where	SCONJ
ejpam-5323	133	44	n	n	NOUN
ejpam-5323	133	45	=	=	SYM
ejpam-5323	133	46	1	1	NUM
ejpam-5323	133	47	and	and	CCONJ
ejpam-5323	133	48	m	m	VERB
ejpam-5323	133	49	=	=	ADJ
ejpam-5323	133	50	2	2	NUM
ejpam-5323	133	51	]	]	PUNCT
ejpam-5323	133	52	⇐	⇐	ADJ
ejpam-5323	133	53	⇒	⇒	NOUN
ejpam-5323	133	54	(	(	PUNCT
ejpam-5323	133	55	a	a	DET
ejpam-5323	133	56	,	,	PUNCT
ejpam-5323	133	57	b	b	NOUN
ejpam-5323	133	58	,	,	PUNCT
ejpam-5323	133	59	c	c	NOUN
ejpam-5323	133	60	)	)	PUNCT
ejpam-5323	133	61	=	=	SYM
ejpam-5323	133	62	(	(	PUNCT
ejpam-5323	133	63	3	3	NUM
ejpam-5323	133	64	,	,	PUNCT
ejpam-5323	133	65	4	4	NUM
ejpam-5323	133	66	,	,	PUNCT
ejpam-5323	133	67	5	5	NUM
ejpam-5323	133	68	)	)	PUNCT
ejpam-5323	133	69	.	.	PUNCT
ejpam-5323	134	1	let	let	VERB
ejpam-5323	134	2	n	n	PRON
ejpam-5323	134	3	be	be	AUX
ejpam-5323	134	4	an	an	DET
ejpam-5323	134	5	odd	odd	ADJ
ejpam-5323	134	6	integer	integer	NOUN
ejpam-5323	134	7	,	,	PUNCT
ejpam-5323	134	8	n	n	PRON
ejpam-5323	134	9	≥	≥	NOUN
ejpam-5323	134	10	3	3	NUM
ejpam-5323	134	11	.	.	PUNCT
ejpam-5323	135	1	by	by	ADP
ejpam-5323	135	2	proposition	proposition	NOUN
ejpam-5323	135	3	3	3	NUM
ejpam-5323	135	4	,	,	PUNCT
ejpam-5323	135	5	the	the	DET
ejpam-5323	135	6	plane	plane	NOUN
ejpam-5323	135	7	2x	2x	NUM
ejpam-5323	136	1	+	+	CCONJ
ejpam-5323	136	2	2y	2y	NUM
ejpam-5323	136	3	−	−	NOUN
ejpam-5323	136	4	3z	3z	ADJ
ejpam-5323	136	5	+	+	CCONJ
ejpam-5323	136	6	n	n	CCONJ
ejpam-5323	136	7	=	=	SYM
ejpam-5323	136	8	0	0	NUM
ejpam-5323	136	9	contains	contain	VERB
ejpam-5323	136	10	p∗	p∗	NOUN
ejpam-5323	136	11	2	2	NUM
ejpam-5323	136	12	(	(	PUNCT
ejpam-5323	136	13	n	n	CCONJ
ejpam-5323	136	14	)	)	PUNCT
ejpam-5323	136	15	descendant	descendant	ADJ
ejpam-5323	136	16	triangles	triangle	NOUN
ejpam-5323	136	17	△	△	PROPN
ejpam-5323	136	18	b.	b.	PROPN
ejpam-5323	136	19	each	each	DET
ejpam-5323	136	20	vertex	vertex	NOUN
ejpam-5323	136	21	of	of	ADP
ejpam-5323	136	22	△	△	PROPN
ejpam-5323	136	23	b	b	PROPN
ejpam-5323	136	24	is	be	AUX
ejpam-5323	136	25	a	a	DET
ejpam-5323	136	26	ppt	ppt	NOUN
ejpam-5323	136	27	,	,	PUNCT
ejpam-5323	136	28	hence	hence	ADV
ejpam-5323	136	29	there	there	PRON
ejpam-5323	136	30	are	be	VERB
ejpam-5323	136	31	at	at	ADV
ejpam-5323	136	32	least	least	ADJ
ejpam-5323	136	33	3	3	NUM
ejpam-5323	136	34	·	·	PUNCT
ejpam-5323	136	35	p∗	p∗	ADJ
ejpam-5323	136	36	2	2	NUM
ejpam-5323	136	37	(	(	PUNCT
ejpam-5323	136	38	n	n	CCONJ
ejpam-5323	136	39	)	)	PUNCT
ejpam-5323	136	40	ppts	ppt	NOUN
ejpam-5323	136	41	in	in	ADP
ejpam-5323	136	42	the	the	DET
ejpam-5323	136	43	plane	plane	NOUN
ejpam-5323	136	44	2x+	2x+	NUM
ejpam-5323	136	45	2y	2y	NUM
ejpam-5323	136	46	−	−	NOUN
ejpam-5323	136	47	3z	3z	ADJ
ejpam-5323	136	48	+	+	CCONJ
ejpam-5323	136	49	n	n	NOUN
ejpam-5323	136	50	=	=	SYM
ejpam-5323	136	51	0	0	NUM
ejpam-5323	136	52	.	.	PUNCT
ejpam-5323	137	1	by	by	ADP
ejpam-5323	137	2	way	way	NOUN
ejpam-5323	137	3	of	of	ADP
ejpam-5323	137	4	contradiction	contradiction	NOUN
ejpam-5323	137	5	,	,	PUNCT
ejpam-5323	137	6	we	we	PRON
ejpam-5323	137	7	show	show	VERB
ejpam-5323	137	8	that	that	SCONJ
ejpam-5323	137	9	there	there	PRON
ejpam-5323	137	10	are	be	VERB
ejpam-5323	137	11	no	no	PRON
ejpam-5323	137	12	more	more	ADJ
ejpam-5323	137	13	ppts	ppt	NOUN
ejpam-5323	137	14	in	in	ADP
ejpam-5323	137	15	2x+2y−3z+n	2x+2y−3z+n	NUM
ejpam-5323	137	16	=	=	SYM
ejpam-5323	137	17	0	0	X
ejpam-5323	137	18	.	.	PUNCT
ejpam-5323	138	1	let	let	VERB
ejpam-5323	138	2	us	we	PRON
ejpam-5323	138	3	assume	assume	VERB
ejpam-5323	138	4	that	that	SCONJ
ejpam-5323	138	5	there	there	PRON
ejpam-5323	138	6	is	be	VERB
ejpam-5323	138	7	a	a	DET
ejpam-5323	138	8	ppt	ppt	NOUN
ejpam-5323	138	9	(	(	PUNCT
ejpam-5323	138	10	a	a	DET
ejpam-5323	138	11	,	,	PUNCT
ejpam-5323	138	12	b	b	NOUN
ejpam-5323	138	13	,	,	PUNCT
ejpam-5323	138	14	c	c	NOUN
ejpam-5323	138	15	)	)	PUNCT
ejpam-5323	138	16	in	in	ADP
ejpam-5323	138	17	2x	2x	NUM
ejpam-5323	139	1	+	+	CCONJ
ejpam-5323	139	2	2y	2y	NUM
ejpam-5323	139	3	−	−	NOUN
ejpam-5323	139	4	3z	3z	ADJ
ejpam-5323	139	5	+	+	CCONJ
ejpam-5323	139	6	n	n	CCONJ
ejpam-5323	139	7	=	=	SYM
ejpam-5323	139	8	0	0	NUM
ejpam-5323	139	9	such	such	ADJ
ejpam-5323	139	10	that	that	SCONJ
ejpam-5323	139	11	(	(	PUNCT
ejpam-5323	139	12	a	a	DET
ejpam-5323	139	13	,	,	PUNCT
ejpam-5323	139	14	b	b	NOUN
ejpam-5323	139	15	,	,	PUNCT
ejpam-5323	139	16	c	c	NOUN
ejpam-5323	139	17	)	)	PUNCT
ejpam-5323	139	18	is	be	AUX
ejpam-5323	139	19	not	not	PART
ejpam-5323	139	20	a	a	DET
ejpam-5323	139	21	descendant	descendant	NOUN
ejpam-5323	139	22	of	of	ADP
ejpam-5323	139	23	any	any	DET
ejpam-5323	139	24	ppt	ppt	NOUN
ejpam-5323	139	25	with	with	ADP
ejpam-5323	139	26	the	the	DET
ejpam-5323	139	27	third	third	ADJ
ejpam-5323	139	28	component	component	NOUN
ejpam-5323	139	29	n	n	PROPN
ejpam-5323	139	30	in	in	ADP
ejpam-5323	139	31	berggren	berggren	PROPN
ejpam-5323	139	32	’s	’s	PART
ejpam-5323	139	33	tree	tree	NOUN
ejpam-5323	139	34	.	.	PUNCT
ejpam-5323	140	1	then	then	ADV
ejpam-5323	140	2	(	(	PUNCT
ejpam-5323	140	3	a	a	PRON
ejpam-5323	140	4	,	,	PUNCT
ejpam-5323	140	5	b	b	NOUN
ejpam-5323	140	6	,	,	PUNCT
ejpam-5323	140	7	c	c	NOUN
ejpam-5323	140	8	)	)	PUNCT
ejpam-5323	140	9	=	=	SYM
ejpam-5323	140	10	(	(	PUNCT
ejpam-5323	140	11	3	3	NUM
ejpam-5323	140	12	,	,	PUNCT
ejpam-5323	140	13	4	4	NUM
ejpam-5323	140	14	,	,	PUNCT
ejpam-5323	140	15	5	5	NUM
ejpam-5323	140	16	)	)	PUNCT
ejpam-5323	140	17	or	or	CCONJ
ejpam-5323	140	18	(	(	PUNCT
ejpam-5323	140	19	a	a	DET
ejpam-5323	140	20	,	,	PUNCT
ejpam-5323	140	21	b	b	NOUN
ejpam-5323	140	22	,	,	PUNCT
ejpam-5323	140	23	c	c	NOUN
ejpam-5323	140	24	)	)	PUNCT
ejpam-5323	140	25	is	be	AUX
ejpam-5323	140	26	a	a	DET
ejpam-5323	140	27	descendant	descendant	NOUN
ejpam-5323	140	28	of	of	ADP
ejpam-5323	140	29	some	some	DET
ejpam-5323	140	30	ppt	ppt	NOUN
ejpam-5323	140	31	(	(	PUNCT
ejpam-5323	140	32	d	d	NOUN
ejpam-5323	140	33	,	,	PUNCT
ejpam-5323	140	34	e	e	NOUN
ejpam-5323	140	35	,	,	PUNCT
ejpam-5323	140	36	f	f	X
ejpam-5323	140	37	)	)	PUNCT
ejpam-5323	140	38	such	such	ADJ
ejpam-5323	140	39	that	that	SCONJ
ejpam-5323	140	40	f	f	PROPN
ejpam-5323	140	41	̸=	̸=	PROPN
ejpam-5323	140	42	n.	n.	NOUN
ejpam-5323	140	43	if	if	SCONJ
ejpam-5323	140	44	(	(	PUNCT
ejpam-5323	140	45	a	a	DET
ejpam-5323	140	46	,	,	PUNCT
ejpam-5323	140	47	b	b	NOUN
ejpam-5323	140	48	,	,	PUNCT
ejpam-5323	140	49	c	c	NOUN
ejpam-5323	140	50	)	)	PUNCT
ejpam-5323	140	51	=	=	SYM
ejpam-5323	140	52	(	(	PUNCT
ejpam-5323	140	53	3	3	NUM
ejpam-5323	140	54	,	,	PUNCT
ejpam-5323	140	55	4	4	NUM
ejpam-5323	140	56	,	,	PUNCT
ejpam-5323	140	57	5	5	NUM
ejpam-5323	140	58	)	)	PUNCT
ejpam-5323	140	59	,	,	PUNCT
ejpam-5323	140	60	then	then	ADV
ejpam-5323	140	61	from	from	ADP
ejpam-5323	140	62	(	(	PUNCT
ejpam-5323	140	63	a	a	DET
ejpam-5323	140	64	,	,	PUNCT
ejpam-5323	140	65	b	b	NOUN
ejpam-5323	140	66	,	,	PUNCT
ejpam-5323	140	67	c	c	NOUN
ejpam-5323	140	68	)	)	PUNCT
ejpam-5323	140	69	belonging	belong	VERB
ejpam-5323	140	70	to	to	ADP
ejpam-5323	140	71	2x+2y−3z+n	2x+2y−3z+n	NUM
ejpam-5323	140	72	=	=	SYM
ejpam-5323	140	73	0	0	NUM
ejpam-5323	140	74	,	,	PUNCT
ejpam-5323	140	75	we	we	PRON
ejpam-5323	140	76	get	get	VERB
ejpam-5323	140	77	n	n	PRON
ejpam-5323	140	78	=	=	SYM
ejpam-5323	140	79	1	1	NUM
ejpam-5323	140	80	,	,	PUNCT
ejpam-5323	140	81	a	a	DET
ejpam-5323	140	82	contradiction	contradiction	NOUN
ejpam-5323	140	83	with	with	ADP
ejpam-5323	140	84	n	n	PRON
ejpam-5323	140	85	≥	≥	NUM
ejpam-5323	140	86	3	3	NUM
ejpam-5323	140	87	.	.	PUNCT
ejpam-5323	141	1	if	if	SCONJ
ejpam-5323	141	2	(	(	PUNCT
ejpam-5323	141	3	a	a	DET
ejpam-5323	141	4	,	,	PUNCT
ejpam-5323	141	5	b	b	NOUN
ejpam-5323	141	6	,	,	PUNCT
ejpam-5323	141	7	c	c	NOUN
ejpam-5323	141	8	)	)	PUNCT
ejpam-5323	141	9	is	be	AUX
ejpam-5323	141	10	a	a	DET
ejpam-5323	141	11	descendant	descendant	NOUN
ejpam-5323	141	12	of	of	ADP
ejpam-5323	141	13	some	some	DET
ejpam-5323	141	14	ppt	ppt	NOUN
ejpam-5323	141	15	(	(	PUNCT
ejpam-5323	141	16	d	d	NOUN
ejpam-5323	141	17	,	,	PUNCT
ejpam-5323	141	18	e	e	NOUN
ejpam-5323	141	19	,	,	PUNCT
ejpam-5323	141	20	f	f	PROPN
ejpam-5323	141	21	)	)	PUNCT
ejpam-5323	141	22	,	,	PUNCT
ejpam-5323	141	23	such	such	ADJ
ejpam-5323	141	24	that	that	SCONJ
ejpam-5323	141	25	f	f	PROPN
ejpam-5323	141	26	̸=	̸=	PROPN
ejpam-5323	141	27	n	n	CCONJ
ejpam-5323	141	28	,	,	PUNCT
ejpam-5323	141	29	then	then	ADV
ejpam-5323	141	30	by	by	ADP
ejpam-5323	141	31	proposition	proposition	NOUN
ejpam-5323	141	32	2	2	NUM
ejpam-5323	141	33	,	,	PUNCT
ejpam-5323	141	34	(	(	PUNCT
ejpam-5323	141	35	a	a	DET
ejpam-5323	141	36	,	,	PUNCT
ejpam-5323	141	37	b	b	NOUN
ejpam-5323	141	38	,	,	PUNCT
ejpam-5323	141	39	c	c	NOUN
ejpam-5323	141	40	)	)	PUNCT
ejpam-5323	141	41	belongs	belong	VERB
ejpam-5323	141	42	to	to	ADP
ejpam-5323	141	43	the	the	DET
ejpam-5323	141	44	plane	plane	NOUN
ejpam-5323	142	1	2x	2x	NUM
ejpam-5323	143	1	+	+	CCONJ
ejpam-5323	143	2	2y	2y	NUM
ejpam-5323	143	3	−	−	NOUN
ejpam-5323	143	4	3z	3z	ADJ
ejpam-5323	143	5	+	+	CCONJ
ejpam-5323	143	6	f	f	X
ejpam-5323	143	7	=	=	SYM
ejpam-5323	143	8	0	0	PROPN
ejpam-5323	143	9	.	.	PUNCT
ejpam-5323	144	1	however	however	ADV
ejpam-5323	144	2	,	,	PUNCT
ejpam-5323	144	3	the	the	DET
ejpam-5323	144	4	triple	triple	ADJ
ejpam-5323	144	5	(	(	PUNCT
ejpam-5323	144	6	a	a	PRON
ejpam-5323	144	7	,	,	PUNCT
ejpam-5323	144	8	b	b	NOUN
ejpam-5323	144	9	,	,	PUNCT
ejpam-5323	144	10	c	c	NOUN
ejpam-5323	144	11	)	)	PUNCT
ejpam-5323	144	12	also	also	ADV
ejpam-5323	144	13	belongs	belong	VERB
ejpam-5323	144	14	to	to	ADP
ejpam-5323	144	15	the	the	DET
ejpam-5323	144	16	plane	plane	NOUN
ejpam-5323	144	17	2x+	2x+	NUM
ejpam-5323	144	18	2y	2y	NUM
ejpam-5323	144	19	−	−	NOUN
ejpam-5323	144	20	3z	3z	ADJ
ejpam-5323	144	21	+	+	CCONJ
ejpam-5323	144	22	n	n	CCONJ
ejpam-5323	144	23	=	=	SYM
ejpam-5323	144	24	0	0	NUM
ejpam-5323	144	25	,	,	PUNCT
ejpam-5323	144	26	which	which	PRON
ejpam-5323	144	27	yields	yield	VERB
ejpam-5323	144	28	f	f	PROPN
ejpam-5323	144	29	=	=	SYM
ejpam-5323	144	30	n	n	CCONJ
ejpam-5323	144	31	,	,	PUNCT
ejpam-5323	144	32	a	a	DET
ejpam-5323	144	33	contradiction	contradiction	NOUN
ejpam-5323	144	34	.	.	PUNCT
ejpam-5323	145	1	a	a	DET
ejpam-5323	145	2	primitive	primitive	ADJ
ejpam-5323	145	3	pythagorean	pythagorean	NOUN
ejpam-5323	145	4	triple	triple	NOUN
ejpam-5323	145	5	can	can	AUX
ejpam-5323	145	6	be	be	AUX
ejpam-5323	145	7	viewed	view	VERB
ejpam-5323	145	8	as	as	ADP
ejpam-5323	145	9	a	a	DET
ejpam-5323	145	10	right	right	ADJ
ejpam-5323	145	11	triangle	triangle	NOUN
ejpam-5323	145	12	,	,	PUNCT
ejpam-5323	145	13	and	and	CCONJ
ejpam-5323	145	14	the	the	DET
ejpam-5323	145	15	points	point	NOUN
ejpam-5323	145	16	corresponding	correspond	VERB
ejpam-5323	145	17	to	to	ADP
ejpam-5323	145	18	the	the	DET
ejpam-5323	145	19	descendants	descendant	NOUN
ejpam-5323	145	20	of	of	ADP
ejpam-5323	145	21	a	a	DET
ejpam-5323	145	22	ppt	ppt	NOUN
ejpam-5323	145	23	in	in	ADP
ejpam-5323	145	24	berggren	berggren	PROPN
ejpam-5323	145	25	’s	’s	PART
ejpam-5323	145	26	tree	tree	NOUN
ejpam-5323	145	27	also	also	ADV
ejpam-5323	145	28	form	form	VERB
ejpam-5323	145	29	a	a	DET
ejpam-5323	145	30	triangle	triangle	NOUN
ejpam-5323	145	31	.	.	PUNCT
ejpam-5323	146	1	it	it	PRON
ejpam-5323	146	2	is	be	AUX
ejpam-5323	146	3	natural	natural	ADJ
ejpam-5323	146	4	to	to	PART
ejpam-5323	146	5	ask	ask	VERB
ejpam-5323	146	6	whether	whether	SCONJ
ejpam-5323	146	7	the	the	DET
ejpam-5323	146	8	descendant	descendant	ADJ
ejpam-5323	146	9	triangle	triangle	NOUN
ejpam-5323	146	10	△	△	NOUN
ejpam-5323	146	11	b(p	b(p	X
ejpam-5323	146	12	)	)	PUNCT
ejpam-5323	146	13	can	can	AUX
ejpam-5323	146	14	also	also	ADV
ejpam-5323	146	15	be	be	AUX
ejpam-5323	146	16	a	a	DET
ejpam-5323	146	17	right	right	ADJ
ejpam-5323	146	18	triangle	triangle	NOUN
ejpam-5323	146	19	for	for	ADP
ejpam-5323	146	20	some	some	DET
ejpam-5323	146	21	p	p	NOUN
ejpam-5323	146	22	.	.	PUNCT
ejpam-5323	147	1	the	the	DET
ejpam-5323	147	2	following	follow	VERB
ejpam-5323	147	3	proposition	proposition	NOUN
ejpam-5323	147	4	offers	offer	VERB
ejpam-5323	147	5	the	the	DET
ejpam-5323	147	6	answer	answer	NOUN
ejpam-5323	147	7	to	to	ADP
ejpam-5323	147	8	this	this	DET
ejpam-5323	147	9	question	question	NOUN
ejpam-5323	147	10	.	.	PUNCT
ejpam-5323	148	1	l.	l.	PROPN
ejpam-5323	148	2	kőszegyová	kőszegyová	PROPN
ejpam-5323	148	3	,	,	PUNCT
ejpam-5323	148	4	e.	e.	PROPN
ejpam-5323	148	5	csókási	csókási	PROPN
ejpam-5323	148	6	,	,	PUNCT
ejpam-5323	148	7	j.	j.	PROPN
ejpam-5323	148	8	hirjak	hirjak	PROPN
ejpam-5323	148	9	/	/	SYM
ejpam-5323	148	10	eur	eur	PROPN
ejpam-5323	148	11	.	.	PUNCT
ejpam-5323	149	1	j.	j.	PROPN
ejpam-5323	149	2	pure	pure	PROPN
ejpam-5323	149	3	appl	appl	PROPN
ejpam-5323	149	4	.	.	PROPN
ejpam-5323	149	5	math	math	PROPN
ejpam-5323	149	6	,	,	PUNCT
ejpam-5323	149	7	17	17	NUM
ejpam-5323	149	8	(	(	PUNCT
ejpam-5323	149	9	3	3	NUM
ejpam-5323	149	10	)	)	PUNCT
ejpam-5323	149	11	(	(	PUNCT
ejpam-5323	149	12	2024	2024	NUM
ejpam-5323	149	13	)	)	PUNCT
ejpam-5323	149	14	,	,	PUNCT
ejpam-5323	149	15	2127	2127	NUM
ejpam-5323	149	16	-	-	SYM
ejpam-5323	149	17	2141	2141	NUM
ejpam-5323	149	18	2133	2133	NUM
ejpam-5323	149	19	proposition	proposition	NOUN
ejpam-5323	149	20	4	4	NUM
ejpam-5323	149	21	.	.	PUNCT
ejpam-5323	150	1	let	let	VERB
ejpam-5323	150	2	p	p	PRON
ejpam-5323	150	3	be	be	AUX
ejpam-5323	150	4	a	a	DET
ejpam-5323	150	5	primitive	primitive	ADJ
ejpam-5323	150	6	pythagorean	pythagorean	NOUN
ejpam-5323	150	7	triple	triple	NOUN
ejpam-5323	150	8	.	.	PUNCT
ejpam-5323	151	1	the	the	DET
ejpam-5323	151	2	triangle	triangle	NOUN
ejpam-5323	151	3	△	△	PUNCT
ejpam-5323	151	4	b(p	b(p	X
ejpam-5323	151	5	)	)	PUNCT
ejpam-5323	151	6	is	be	AUX
ejpam-5323	151	7	a	a	DET
ejpam-5323	151	8	nonright	nonright	ADJ
ejpam-5323	151	9	triangle	triangle	NOUN
ejpam-5323	151	10	.	.	PUNCT
ejpam-5323	152	1	proof	proof	NOUN
ejpam-5323	152	2	.	.	PUNCT
ejpam-5323	153	1	let	let	VERB
ejpam-5323	153	2	p	p	NOUN
ejpam-5323	153	3	=	=	X
ejpam-5323	153	4	(	(	PUNCT
ejpam-5323	153	5	a	a	PRON
ejpam-5323	153	6	,	,	PUNCT
ejpam-5323	153	7	b	b	NOUN
ejpam-5323	153	8	,	,	PUNCT
ejpam-5323	153	9	c	c	NOUN
ejpam-5323	153	10	)	)	PUNCT
ejpam-5323	153	11	and	and	CCONJ
ejpam-5323	153	12	let	let	VERB
ejpam-5323	153	13	the	the	DET
ejpam-5323	153	14	vectors	vector	NOUN
ejpam-5323	153	15	u⃗	u⃗	PROPN
ejpam-5323	153	16	,	,	PUNCT
ejpam-5323	153	17	v⃗	v⃗	PROPN
ejpam-5323	153	18	,	,	PUNCT
ejpam-5323	153	19	w⃗	w⃗	VERB
ejpam-5323	153	20	be	be	AUX
ejpam-5323	153	21	as	as	SCONJ
ejpam-5323	153	22	follows	follow	VERB
ejpam-5323	153	23	:	:	PUNCT
ejpam-5323	153	24	u⃗	u⃗	PROPN
ejpam-5323	153	25	=	=	PUNCT
ejpam-5323	153	26	ap⊤	ap⊤	X
ejpam-5323	153	27	−	−	PROPN
ejpam-5323	153	28	up⊤	up⊤	ADJ
ejpam-5323	153	29	,	,	PUNCT
ejpam-5323	153	30	v⃗	v⃗	NOUN
ejpam-5323	153	31	=	=	PUNCT
ejpam-5323	153	32	dp⊤	dp⊤	NOUN
ejpam-5323	153	33	−	−	X
ejpam-5323	153	34	up⊤	up⊤	ADJ
ejpam-5323	153	35	,	,	PUNCT
ejpam-5323	153	36	w⃗	w⃗	VERB
ejpam-5323	153	37	=	=	PUNCT
ejpam-5323	153	38	dp⊤	dp⊤	NOUN
ejpam-5323	153	39	−ap⊤.	−ap⊤.	NOUN
ejpam-5323	153	40	to	to	PART
ejpam-5323	153	41	show	show	VERB
ejpam-5323	153	42	that	that	SCONJ
ejpam-5323	153	43	the	the	DET
ejpam-5323	153	44	triangle	triangle	NOUN
ejpam-5323	153	45	with	with	ADP
ejpam-5323	153	46	the	the	DET
ejpam-5323	153	47	vertices	vertex	NOUN
ejpam-5323	153	48	up⊤	up⊤	PRON
ejpam-5323	153	49	,	,	PUNCT
ejpam-5323	153	50	ap⊤	ap⊤	NOUN
ejpam-5323	153	51	,	,	PUNCT
ejpam-5323	153	52	dp⊤	dp⊤	PROPN
ejpam-5323	153	53	is	be	AUX
ejpam-5323	153	54	a	a	DET
ejpam-5323	153	55	non	non	ADJ
ejpam-5323	153	56	-	-	ADJ
ejpam-5323	153	57	right	right	ADJ
ejpam-5323	153	58	triangle	triangle	NOUN
ejpam-5323	153	59	,	,	PUNCT
ejpam-5323	153	60	it	it	PRON
ejpam-5323	153	61	is	be	AUX
ejpam-5323	153	62	sufficient	sufficient	ADJ
ejpam-5323	153	63	to	to	PART
ejpam-5323	153	64	show	show	VERB
ejpam-5323	153	65	that	that	SCONJ
ejpam-5323	153	66	u⃗	u⃗	PROPN
ejpam-5323	153	67	·	·	PUNCT
ejpam-5323	153	68	v⃗	v⃗	VERB
ejpam-5323	153	69	̸=	̸=	PROPN
ejpam-5323	153	70	0	0	NUM
ejpam-5323	153	71	,	,	PUNCT
ejpam-5323	153	72	u⃗	u⃗	PROPN
ejpam-5323	153	73	·	·	PUNCT
ejpam-5323	153	74	w⃗	w⃗	VERB
ejpam-5323	153	75	̸=	̸=	PROPN
ejpam-5323	153	76	0	0	NUM
ejpam-5323	153	77	,	,	PUNCT
ejpam-5323	153	78	v⃗	v⃗	ADJ
ejpam-5323	153	79	·	·	PUNCT
ejpam-5323	153	80	w⃗	w⃗	VERB
ejpam-5323	153	81	̸=	̸=	PROPN
ejpam-5323	153	82	0	0	NUM
ejpam-5323	153	83	.	.	PUNCT
ejpam-5323	154	1	according	accord	VERB
ejpam-5323	154	2	to	to	ADP
ejpam-5323	154	3	the	the	DET
ejpam-5323	154	4	proof	proof	NOUN
ejpam-5323	154	5	of	of	ADP
ejpam-5323	154	6	proposition	proposition	NOUN
ejpam-5323	154	7	1	1	NUM
ejpam-5323	154	8	,	,	PUNCT
ejpam-5323	154	9	u⃗	u⃗	PROPN
ejpam-5323	154	10	=	=	PUNCT
ejpam-5323	154	11	(	(	PUNCT
ejpam-5323	154	12	4b	4b	X
ejpam-5323	154	13	,	,	PUNCT
ejpam-5323	154	14	2b	2b	NUM
ejpam-5323	154	15	,	,	PUNCT
ejpam-5323	154	16	4b	4b	NUM
ejpam-5323	154	17	)	)	PUNCT
ejpam-5323	154	18	and	and	CCONJ
ejpam-5323	154	19	v⃗	v⃗	PROPN
ejpam-5323	154	20	=	=	PUNCT
ejpam-5323	154	21	(	(	PUNCT
ejpam-5323	154	22	−2a+	−2a+	PROPN
ejpam-5323	154	23	4b,−4a+	4b,−4a+	PROPN
ejpam-5323	154	24	2b,−4a+	2b,−4a+	NUM
ejpam-5323	154	25	4b	4b	PROPN
ejpam-5323	154	26	)	)	PUNCT
ejpam-5323	154	27	.	.	PUNCT
ejpam-5323	155	1	analogously	analogously	ADV
ejpam-5323	155	2	,	,	PUNCT
ejpam-5323	155	3	w⃗	w⃗	VERB
ejpam-5323	155	4	=	=	PUNCT
ejpam-5323	155	5	(	(	PUNCT
ejpam-5323	155	6	d	d	NOUN
ejpam-5323	155	7	−a)p⊤	−a)p⊤	X
ejpam-5323	155	8	=	=	NOUN
ejpam-5323	155	9	−2	−2	X
ejpam-5323	155	10	0	0	NUM
ejpam-5323	155	11	0	0	NUM
ejpam-5323	156	1	−4	−4	NOUN
ejpam-5323	156	2	0	0	SYM
ejpam-5323	156	3	0	0	NUM
ejpam-5323	157	1	−4	−4	NOUN
ejpam-5323	157	2	0	0	SYM
ejpam-5323	157	3	0	0	NUM
ejpam-5323	158	1			PROPN
ejpam-5323	158	2	·	·	PUNCT
ejpam-5323	158	3	a	a	NOUN
ejpam-5323	158	4	b	b	X
ejpam-5323	158	5	c	c	NOUN
ejpam-5323	158	6			PROPN
ejpam-5323	158	7	=	=	SYM
ejpam-5323	158	8	−2a	−2a	ADJ
ejpam-5323	158	9	−4a	−4a	ADJ
ejpam-5323	158	10	−4a	−4a	PUNCT
ejpam-5323	158	11			PROPN
ejpam-5323	158	12	.	.	PUNCT
ejpam-5323	158	13	1	1	NUM
ejpam-5323	158	14	.	.	NUM
ejpam-5323	158	15	)	)	PUNCT
ejpam-5323	159	1	by	by	ADP
ejpam-5323	159	2	way	way	NOUN
ejpam-5323	159	3	of	of	ADP
ejpam-5323	159	4	contradiction	contradiction	NOUN
ejpam-5323	159	5	,	,	PUNCT
ejpam-5323	159	6	assume	assume	VERB
ejpam-5323	159	7	that	that	SCONJ
ejpam-5323	159	8	u⃗	u⃗	PROPN
ejpam-5323	159	9	·	·	PUNCT
ejpam-5323	159	10	v⃗	v⃗	VERB
ejpam-5323	159	11	=	=	SYM
ejpam-5323	159	12	0	0	X
ejpam-5323	159	13	.	.	PUNCT
ejpam-5323	160	1	clearly	clearly	ADV
ejpam-5323	160	2	,	,	PUNCT
ejpam-5323	160	3	u⃗	u⃗	PROPN
ejpam-5323	160	4	·	·	PUNCT
ejpam-5323	160	5	v⃗	v⃗	PROPN
ejpam-5323	160	6	=	=	SYM
ejpam-5323	160	7	(	(	PUNCT
ejpam-5323	160	8	4b	4b	X
ejpam-5323	160	9	,	,	PUNCT
ejpam-5323	160	10	2b	2b	NUM
ejpam-5323	160	11	,	,	PUNCT
ejpam-5323	160	12	4b	4b	X
ejpam-5323	160	13	)	)	PUNCT
ejpam-5323	160	14	·	·	PUNCT
ejpam-5323	161	1	(	(	PUNCT
ejpam-5323	161	2	−2a+	−2a+	NOUN
ejpam-5323	161	3	4b,−4a	4b,−4a	PROPN
ejpam-5323	161	4	+	+	CCONJ
ejpam-5323	161	5	2c,−4a	2c,−4a	PROPN
ejpam-5323	161	6	+	+	CCONJ
ejpam-5323	161	7	4b	4b	X
ejpam-5323	161	8	)	)	PUNCT
ejpam-5323	162	1	=	=	PUNCT
ejpam-5323	162	2	−32ab	−32ab	NOUN
ejpam-5323	162	3	+	+	CCONJ
ejpam-5323	163	1	36b2	36b2	NUM
ejpam-5323	163	2	.	.	PUNCT
ejpam-5323	163	3	since	since	SCONJ
ejpam-5323	163	4	a	a	DET
ejpam-5323	163	5	,	,	PUNCT
ejpam-5323	163	6	b	b	X
ejpam-5323	163	7	>	>	X
ejpam-5323	163	8	0	0	NUM
ejpam-5323	163	9	,	,	PUNCT
ejpam-5323	163	10	we	we	PRON
ejpam-5323	163	11	get	get	VERB
ejpam-5323	163	12	b	b	NOUN
ejpam-5323	163	13	=	=	NOUN
ejpam-5323	163	14	8a	8a	NUM
ejpam-5323	163	15	9	9	NUM
ejpam-5323	163	16	.	.	PUNCT
ejpam-5323	164	1	however	however	ADV
ejpam-5323	164	2	,	,	PUNCT
ejpam-5323	164	3	(	(	PUNCT
ejpam-5323	164	4	a	a	DET
ejpam-5323	164	5	,	,	PUNCT
ejpam-5323	164	6	b	b	NOUN
ejpam-5323	164	7	,	,	PUNCT
ejpam-5323	164	8	c	c	NOUN
ejpam-5323	164	9	)	)	PUNCT
ejpam-5323	164	10	satisfies	satisfy	VERB
ejpam-5323	164	11	the	the	DET
ejpam-5323	164	12	pythagorean	pythagorean	PROPN
ejpam-5323	164	13	equation	equation	NOUN
ejpam-5323	164	14	which	which	PRON
ejpam-5323	164	15	yields	yield	VERB
ejpam-5323	164	16	a2	a2	PROPN
ejpam-5323	164	17	+	+	CCONJ
ejpam-5323	165	1	64a2	64a2	NUM
ejpam-5323	165	2	81	81	NUM
ejpam-5323	165	3	=	=	SYM
ejpam-5323	165	4	c2	c2	PROPN
ejpam-5323	165	5	√	√	VERB
ejpam-5323	165	6	145	145	NUM
ejpam-5323	165	7	a	a	DET
ejpam-5323	165	8	9	9	NUM
ejpam-5323	165	9	=	=	SYM
ejpam-5323	165	10	c	c	NOUN
ejpam-5323	165	11	which	which	PRON
ejpam-5323	165	12	is	be	AUX
ejpam-5323	165	13	a	a	DET
ejpam-5323	165	14	contradiction	contradiction	NOUN
ejpam-5323	165	15	with	with	ADP
ejpam-5323	165	16	a	a	DET
ejpam-5323	165	17	,	,	PUNCT
ejpam-5323	165	18	c	c	PROPN
ejpam-5323	165	19	∈	∈	PROPN
ejpam-5323	165	20	n.	n.	NOUN
ejpam-5323	165	21	2	2	NUM
ejpam-5323	165	22	.	.	PUNCT
ejpam-5323	165	23	)	)	PUNCT
ejpam-5323	165	24	similarly	similarly	ADV
ejpam-5323	165	25	,	,	PUNCT
ejpam-5323	165	26	u⃗	u⃗	PROPN
ejpam-5323	165	27	·	·	PUNCT
ejpam-5323	165	28	w⃗	w⃗	VERB
ejpam-5323	165	29	=	=	SYM
ejpam-5323	165	30	(	(	PUNCT
ejpam-5323	165	31	4b	4b	X
ejpam-5323	165	32	,	,	PUNCT
ejpam-5323	165	33	2b	2b	NUM
ejpam-5323	165	34	,	,	PUNCT
ejpam-5323	165	35	4b	4b	X
ejpam-5323	165	36	)	)	PUNCT
ejpam-5323	165	37	·	·	PUNCT
ejpam-5323	165	38	(	(	PUNCT
ejpam-5323	165	39	−2a,−4a,−4a	−2a,−4a,−4a	NOUN
ejpam-5323	165	40	)	)	PUNCT
ejpam-5323	165	41	=	=	SYM
ejpam-5323	165	42	−32ab	−32ab	PROPN
ejpam-5323	165	43	and	and	CCONJ
ejpam-5323	165	44	from	from	ADP
ejpam-5323	165	45	a	a	DET
ejpam-5323	165	46	,	,	PUNCT
ejpam-5323	165	47	b	b	X
ejpam-5323	165	48	>	>	X
ejpam-5323	165	49	0	0	NUM
ejpam-5323	166	1	it	it	PRON
ejpam-5323	166	2	follows	follow	VERB
ejpam-5323	166	3	that	that	SCONJ
ejpam-5323	166	4	u⃗	u⃗	PROPN
ejpam-5323	166	5	·	·	PUNCT
ejpam-5323	166	6	w⃗	w⃗	VERB
ejpam-5323	166	7	̸=	̸=	PROPN
ejpam-5323	166	8	0	0	NUM
ejpam-5323	166	9	.	.	PUNCT
ejpam-5323	167	1	3	3	NUM
ejpam-5323	167	2	.	.	NUM
ejpam-5323	167	3	)	)	PUNCT
ejpam-5323	167	4	finally	finally	ADV
ejpam-5323	167	5	,	,	PUNCT
ejpam-5323	167	6	v⃗	v⃗	ADJ
ejpam-5323	167	7	·	·	PUNCT
ejpam-5323	167	8	w⃗	w⃗	PROPN
ejpam-5323	167	9	=	=	SYM
ejpam-5323	167	10	(	(	PUNCT
ejpam-5323	167	11	−2a+4b,−4a+2c,−4a+4b	−2a+4b,−4a+2c,−4a+4b	PROPN
ejpam-5323	167	12	)	)	PUNCT
ejpam-5323	167	13	·	·	PUNCT
ejpam-5323	167	14	(	(	PUNCT
ejpam-5323	167	15	−2a,−4a,−4a	−2a,−4a,−4a	NOUN
ejpam-5323	167	16	)	)	PUNCT
ejpam-5323	167	17	=	=	SYM
ejpam-5323	168	1	36a2−	36a2−	NUM
ejpam-5323	168	2	32ab	32ab	NOUN
ejpam-5323	168	3	and	and	CCONJ
ejpam-5323	168	4	we	we	PRON
ejpam-5323	168	5	get	get	VERB
ejpam-5323	168	6	a	a	DET
ejpam-5323	168	7	contradiction	contradiction	NOUN
ejpam-5323	168	8	analogously	analogously	ADV
ejpam-5323	168	9	to	to	ADP
ejpam-5323	168	10	the	the	DET
ejpam-5323	168	11	case	case	NOUN
ejpam-5323	168	12	u⃗	u⃗	PROPN
ejpam-5323	168	13	·	·	PUNCT
ejpam-5323	168	14	v⃗.	v⃗.	CCONJ
ejpam-5323	168	15	also	also	ADV
ejpam-5323	168	16	,	,	PUNCT
ejpam-5323	168	17	it	it	PRON
ejpam-5323	168	18	can	can	AUX
ejpam-5323	168	19	be	be	AUX
ejpam-5323	168	20	proven	prove	VERB
ejpam-5323	168	21	that	that	SCONJ
ejpam-5323	168	22	the	the	DET
ejpam-5323	168	23	triangle	triangle	NOUN
ejpam-5323	168	24	△	△	PUNCT
ejpam-5323	168	25	b(p	b(p	X
ejpam-5323	168	26	)	)	PUNCT
ejpam-5323	168	27	is	be	AUX
ejpam-5323	168	28	neither	neither	DET
ejpam-5323	168	29	isosceles	isoscele	NOUN
ejpam-5323	168	30	nor	nor	CCONJ
ejpam-5323	168	31	equilateral	equilateral	ADJ
ejpam-5323	168	32	triangle	triangle	NOUN
ejpam-5323	168	33	.	.	PUNCT
ejpam-5323	169	1	proposition	proposition	NOUN
ejpam-5323	169	2	5	5	NUM
ejpam-5323	169	3	.	.	PUNCT
ejpam-5323	170	1	let	let	VERB
ejpam-5323	170	2	p	p	PRON
ejpam-5323	170	3	be	be	AUX
ejpam-5323	170	4	a	a	DET
ejpam-5323	170	5	primitive	primitive	ADJ
ejpam-5323	170	6	pythagorean	pythagorean	NOUN
ejpam-5323	170	7	triple	triple	NOUN
ejpam-5323	170	8	.	.	PUNCT
ejpam-5323	171	1	the	the	DET
ejpam-5323	171	2	triangle	triangle	NOUN
ejpam-5323	171	3	△	△	PUNCT
ejpam-5323	171	4	b(p	b(p	X
ejpam-5323	171	5	)	)	PUNCT
ejpam-5323	171	6	is	be	AUX
ejpam-5323	171	7	not	not	PART
ejpam-5323	171	8	an	an	DET
ejpam-5323	171	9	isosceles	isoscele	NOUN
ejpam-5323	171	10	triangle	triangle	NOUN
ejpam-5323	171	11	.	.	PUNCT
ejpam-5323	172	1	proof	proof	NOUN
ejpam-5323	172	2	.	.	PUNCT
ejpam-5323	173	1	let	let	VERB
ejpam-5323	173	2	p	p	NOUN
ejpam-5323	173	3	=	=	X
ejpam-5323	173	4	(	(	PUNCT
ejpam-5323	173	5	a	a	PRON
ejpam-5323	173	6	,	,	PUNCT
ejpam-5323	173	7	b	b	NOUN
ejpam-5323	173	8	,	,	PUNCT
ejpam-5323	173	9	c	c	NOUN
ejpam-5323	173	10	)	)	PUNCT
ejpam-5323	173	11	.	.	PUNCT
ejpam-5323	174	1	similarly	similarly	ADV
ejpam-5323	174	2	like	like	ADP
ejpam-5323	174	3	above	above	ADV
ejpam-5323	174	4	,	,	PUNCT
ejpam-5323	174	5	we	we	PRON
ejpam-5323	174	6	consider	consider	VERB
ejpam-5323	174	7	the	the	DET
ejpam-5323	174	8	vectors	vector	NOUN
ejpam-5323	174	9	u⃗	u⃗	PROPN
ejpam-5323	174	10	,	,	PUNCT
ejpam-5323	174	11	v⃗	v⃗	PROPN
ejpam-5323	174	12	,	,	PUNCT
ejpam-5323	174	13	w⃗	w⃗	PROPN
ejpam-5323	174	14	:	:	PUNCT
ejpam-5323	174	15	u⃗	u⃗	PROPN
ejpam-5323	174	16	=	=	PUNCT
ejpam-5323	174	17	ap⊤	ap⊤	X
ejpam-5323	174	18	−	−	PROPN
ejpam-5323	174	19	up⊤	up⊤	ADV
ejpam-5323	175	1	=	=	SYM
ejpam-5323	175	2	(	(	PUNCT
ejpam-5323	175	3	4b	4b	X
ejpam-5323	175	4	,	,	PUNCT
ejpam-5323	175	5	2b	2b	NUM
ejpam-5323	175	6	,	,	PUNCT
ejpam-5323	175	7	4b	4b	PROPN
ejpam-5323	175	8	)	)	PUNCT
ejpam-5323	175	9	,	,	PUNCT
ejpam-5323	175	10	v⃗	v⃗	PROPN
ejpam-5323	175	11	=	=	SYM
ejpam-5323	175	12	dp⊤	dp⊤	NOUN
ejpam-5323	175	13	−	−	X
ejpam-5323	175	14	up⊤	up⊤	ADV
ejpam-5323	176	1	=	=	PUNCT
ejpam-5323	177	1	(	(	PUNCT
ejpam-5323	177	2	−2a+	−2a+	PROPN
ejpam-5323	177	3	4b,−4a+	4b,−4a+	PROPN
ejpam-5323	177	4	2b,−4a+	2b,−4a+	NUM
ejpam-5323	177	5	4b	4b	PROPN
ejpam-5323	177	6	)	)	PUNCT
ejpam-5323	177	7	,	,	PUNCT
ejpam-5323	177	8	w⃗	w⃗	VERB
ejpam-5323	177	9	=	=	PUNCT
ejpam-5323	177	10	dp⊤	dp⊤	X
ejpam-5323	177	11	−ap⊤	−ap⊤	X
ejpam-5323	177	12	=	=	PUNCT
ejpam-5323	177	13	(	(	PUNCT
ejpam-5323	177	14	−2a,−4a,−4a	−2a,−4a,−4a	NOUN
ejpam-5323	177	15	)	)	PUNCT
ejpam-5323	177	16	.	.	PUNCT
ejpam-5323	178	1	it	it	PRON
ejpam-5323	178	2	remains	remain	VERB
ejpam-5323	178	3	to	to	PART
ejpam-5323	178	4	prove	prove	VERB
ejpam-5323	178	5	that	that	SCONJ
ejpam-5323	178	6	each	each	PRON
ejpam-5323	178	7	of	of	ADP
ejpam-5323	178	8	these	these	DET
ejpam-5323	178	9	vectors	vector	NOUN
ejpam-5323	178	10	has	have	VERB
ejpam-5323	178	11	a	a	DET
ejpam-5323	178	12	different	different	ADJ
ejpam-5323	178	13	norm	norm	NOUN
ejpam-5323	178	14	.	.	PUNCT
ejpam-5323	179	1	clearly	clearly	ADV
ejpam-5323	179	2	,	,	PUNCT
ejpam-5323	179	3	|u⃗|	|u⃗|	X
ejpam-5323	179	4	=	=	PUNCT
ejpam-5323	179	5	√	√	PROPN
ejpam-5323	179	6	36b2	36b2	NUM
ejpam-5323	179	7	,	,	PUNCT
ejpam-5323	180	1	l.	l.	PROPN
ejpam-5323	180	2	kőszegyová	kőszegyová	PROPN
ejpam-5323	180	3	,	,	PUNCT
ejpam-5323	180	4	e.	e.	PROPN
ejpam-5323	180	5	csókási	csókási	PROPN
ejpam-5323	180	6	,	,	PUNCT
ejpam-5323	180	7	j.	j.	PROPN
ejpam-5323	180	8	hirjak	hirjak	PROPN
ejpam-5323	180	9	/	/	SYM
ejpam-5323	180	10	eur	eur	PROPN
ejpam-5323	180	11	.	.	PUNCT
ejpam-5323	181	1	j.	j.	PROPN
ejpam-5323	181	2	pure	pure	PROPN
ejpam-5323	181	3	appl	appl	PROPN
ejpam-5323	181	4	.	.	PROPN
ejpam-5323	181	5	math	math	PROPN
ejpam-5323	181	6	,	,	PUNCT
ejpam-5323	181	7	17	17	NUM
ejpam-5323	181	8	(	(	PUNCT
ejpam-5323	181	9	3	3	NUM
ejpam-5323	181	10	)	)	PUNCT
ejpam-5323	181	11	(	(	PUNCT
ejpam-5323	181	12	2024	2024	NUM
ejpam-5323	181	13	)	)	PUNCT
ejpam-5323	181	14	,	,	PUNCT
ejpam-5323	181	15	2127	2127	NUM
ejpam-5323	181	16	-	-	SYM
ejpam-5323	181	17	2141	2141	NUM
ejpam-5323	181	18	2134	2134	NUM
ejpam-5323	181	19	|v⃗|	|v⃗|	NOUN
ejpam-5323	181	20	=	=	PUNCT
ejpam-5323	181	21	√	√	PROPN
ejpam-5323	182	1	36a2	36a2	NUM
ejpam-5323	182	2	−	−	NUM
ejpam-5323	182	3	64ab+	64ab+	NUM
ejpam-5323	183	1	36b2	36b2	NUM
ejpam-5323	183	2	,	,	PUNCT
ejpam-5323	183	3	|w⃗|	|w⃗|	NUM
ejpam-5323	183	4	=	=	SYM
ejpam-5323	183	5	√	√	PROPN
ejpam-5323	184	1	36a2	36a2	NUM
ejpam-5323	184	2	.	.	NOUN
ejpam-5323	185	1	1	1	NUM
ejpam-5323	185	2	.	.	PUNCT
ejpam-5323	185	3	)	)	PUNCT
ejpam-5323	186	1	by	by	ADP
ejpam-5323	186	2	way	way	NOUN
ejpam-5323	186	3	of	of	ADP
ejpam-5323	186	4	contradiction	contradiction	NOUN
ejpam-5323	186	5	,	,	PUNCT
ejpam-5323	186	6	let	let	VERB
ejpam-5323	186	7	us	we	PRON
ejpam-5323	186	8	assume	assume	VERB
ejpam-5323	186	9	that	that	SCONJ
ejpam-5323	186	10	|u⃗|	|u⃗|	X
ejpam-5323	186	11	=	=	SYM
ejpam-5323	186	12	|w⃗|	|w⃗|	NUM
ejpam-5323	186	13	.	.	PUNCT
ejpam-5323	187	1	then	then	ADV
ejpam-5323	187	2	√	√	VERB
ejpam-5323	188	1	36b2	36b2	NUM
ejpam-5323	188	2	=	=	NOUN
ejpam-5323	189	1	√	√	PROPN
ejpam-5323	189	2	36a2	36a2	NUM
ejpam-5323	190	1	=	=	AUX
ejpam-5323	190	2	⇒	⇒	VERB
ejpam-5323	190	3	36b2	36b2	NUM
ejpam-5323	190	4	=	=	SYM
ejpam-5323	190	5	36a2	36a2	NUM
ejpam-5323	191	1	=	=	NOUN
ejpam-5323	191	2	⇒	⇒	VERB
ejpam-5323	191	3	a	a	DET
ejpam-5323	191	4	=	=	SYM
ejpam-5323	191	5	b	b	NOUN
ejpam-5323	191	6	which	which	PRON
ejpam-5323	191	7	is	be	AUX
ejpam-5323	191	8	a	a	DET
ejpam-5323	191	9	contradiction	contradiction	NOUN
ejpam-5323	191	10	with	with	ADP
ejpam-5323	191	11	(	(	PUNCT
ejpam-5323	191	12	a	a	DET
ejpam-5323	191	13	,	,	PUNCT
ejpam-5323	191	14	b	b	NOUN
ejpam-5323	191	15	,	,	PUNCT
ejpam-5323	191	16	c	c	NOUN
ejpam-5323	191	17	)	)	PUNCT
ejpam-5323	191	18	being	be	AUX
ejpam-5323	191	19	a	a	DET
ejpam-5323	191	20	ppt	ppt	NOUN
ejpam-5323	191	21	.	.	PUNCT
ejpam-5323	192	1	2	2	NUM
ejpam-5323	192	2	.	.	PUNCT
ejpam-5323	192	3	)	)	PUNCT
ejpam-5323	193	1	if	if	SCONJ
ejpam-5323	193	2	|u⃗|	|u⃗|	NUM
ejpam-5323	193	3	=	=	SYM
ejpam-5323	193	4	|v⃗|	|v⃗|	NOUN
ejpam-5323	193	5	,	,	PUNCT
ejpam-5323	193	6	then	then	ADV
ejpam-5323	193	7	√	√	VERB
ejpam-5323	193	8	36b2	36b2	NUM
ejpam-5323	193	9	=	=	NOUN
ejpam-5323	193	10	√	√	PROPN
ejpam-5323	194	1	36a2	36a2	NUM
ejpam-5323	194	2	−	−	NUM
ejpam-5323	194	3	64ab+	64ab+	NUM
ejpam-5323	195	1	36b2	36b2	NUM
ejpam-5323	195	2	36b2	36b2	NUM
ejpam-5323	195	3	=	=	SYM
ejpam-5323	195	4	36a2	36a2	NUM
ejpam-5323	195	5	−	−	NUM
ejpam-5323	195	6	64ab+	64ab+	NUM
ejpam-5323	196	1	36b2	36b2	NUM
ejpam-5323	196	2	0	0	NUM
ejpam-5323	197	1	=	=	SYM
ejpam-5323	197	2	36a2	36a2	NUM
ejpam-5323	197	3	−	−	PROPN
ejpam-5323	197	4	64ab	64ab	NOUN
ejpam-5323	197	5	0	0	NUM
ejpam-5323	197	6	=	=	SYM
ejpam-5323	197	7	9a−	9a−	NUM
ejpam-5323	197	8	16b	16b	PROPN
ejpam-5323	197	9	.	.	PUNCT
ejpam-5323	198	1	applying	apply	VERB
ejpam-5323	198	2	euclid	euclid	PROPN
ejpam-5323	198	3	’s	’s	PART
ejpam-5323	198	4	formula	formula	NOUN
ejpam-5323	198	5	,	,	PUNCT
ejpam-5323	198	6	we	we	PRON
ejpam-5323	198	7	get	get	VERB
ejpam-5323	198	8	0	0	NUM
ejpam-5323	199	1	=	=	SYM
ejpam-5323	199	2	9(m2	9(m2	NUM
ejpam-5323	199	3	−	−	NOUN
ejpam-5323	199	4	n2)−	n2)−	ADJ
ejpam-5323	199	5	16(2mn	16(2mn	NUM
ejpam-5323	199	6	)	)	PUNCT
ejpam-5323	199	7	16(2mn	16(2mn	NUM
ejpam-5323	199	8	)	)	PUNCT
ejpam-5323	200	1	=	=	SYM
ejpam-5323	200	2	9(m2	9(m2	NUM
ejpam-5323	200	3	−	−	PROPN
ejpam-5323	200	4	n2	n2	NOUN
ejpam-5323	200	5	)	)	PUNCT
ejpam-5323	200	6	where	where	SCONJ
ejpam-5323	200	7	m	m	VERB
ejpam-5323	200	8	,	,	PUNCT
ejpam-5323	200	9	n	n	PRON
ejpam-5323	200	10	have	have	VERB
ejpam-5323	200	11	different	different	ADJ
ejpam-5323	200	12	parity	parity	NOUN
ejpam-5323	200	13	.	.	PUNCT
ejpam-5323	201	1	then	then	ADV
ejpam-5323	201	2	16(2mn	16(2mn	NUM
ejpam-5323	201	3	)	)	PUNCT
ejpam-5323	201	4	is	be	AUX
ejpam-5323	201	5	clearly	clearly	ADV
ejpam-5323	201	6	even	even	ADV
ejpam-5323	201	7	and	and	CCONJ
ejpam-5323	201	8	9(m2	9(m2	NUM
ejpam-5323	201	9	−	−	PROPN
ejpam-5323	201	10	n2	n2	NOUN
ejpam-5323	201	11	)	)	PUNCT
ejpam-5323	201	12	is	be	AUX
ejpam-5323	201	13	odd	odd	ADJ
ejpam-5323	201	14	,	,	PUNCT
ejpam-5323	201	15	which	which	PRON
ejpam-5323	201	16	is	be	AUX
ejpam-5323	201	17	a	a	DET
ejpam-5323	201	18	contradiction	contradiction	NOUN
ejpam-5323	201	19	.	.	PUNCT
ejpam-5323	202	1	3	3	X
ejpam-5323	202	2	.	.	NUM
ejpam-5323	202	3	)	)	PUNCT
ejpam-5323	202	4	finally	finally	ADV
ejpam-5323	202	5	,	,	PUNCT
ejpam-5323	202	6	let	let	VERB
ejpam-5323	202	7	|w⃗|	|w⃗|	NUM
ejpam-5323	202	8	=	=	SYM
ejpam-5323	202	9	|v⃗|	|v⃗|	PROPN
ejpam-5323	202	10	.	.	PUNCT
ejpam-5323	203	1	then	then	ADV
ejpam-5323	203	2	√	√	ADV
ejpam-5323	203	3	36a2	36a2	NUM
ejpam-5323	204	1	=	=	PUNCT
ejpam-5323	205	1	√	√	NUM
ejpam-5323	206	1	36a2	36a2	NUM
ejpam-5323	206	2	−	−	NUM
ejpam-5323	206	3	64ab+	64ab+	NUM
ejpam-5323	207	1	36b2	36b2	NUM
ejpam-5323	207	2	36a2	36a2	NUM
ejpam-5323	207	3	=	=	SYM
ejpam-5323	208	1	36a2	36a2	NUM
ejpam-5323	208	2	−	−	NUM
ejpam-5323	208	3	64ab+	64ab+	NUM
ejpam-5323	209	1	36b2	36b2	NUM
ejpam-5323	209	2	0	0	NUM
ejpam-5323	209	3	=	=	SYM
ejpam-5323	209	4	−16a+	−16a+	PROPN
ejpam-5323	209	5	9b	9b	NOUN
ejpam-5323	209	6	applying	apply	VERB
ejpam-5323	209	7	euclid	euclid	PROPN
ejpam-5323	209	8	’s	’s	PART
ejpam-5323	209	9	formula	formula	NOUN
ejpam-5323	209	10	,	,	PUNCT
ejpam-5323	209	11	we	we	PRON
ejpam-5323	209	12	get	get	VERB
ejpam-5323	209	13	0	0	NUM
ejpam-5323	210	1	=	=	SYM
ejpam-5323	210	2	−16(m2	−16(m2	ADJ
ejpam-5323	210	3	−	−	PROPN
ejpam-5323	210	4	n2	n2	NOUN
ejpam-5323	210	5	)	)	PUNCT
ejpam-5323	211	1	+	+	CCONJ
ejpam-5323	211	2	9(2mn	9(2mn	NUM
ejpam-5323	211	3	)	)	PUNCT
ejpam-5323	211	4	0	0	NUM
ejpam-5323	212	1	=	=	SYM
ejpam-5323	212	2	−8m2	−8m2	PUNCT
ejpam-5323	212	3	+	+	CCONJ
ejpam-5323	212	4	8n2	8n2	NUM
ejpam-5323	212	5	+	+	CCONJ
ejpam-5323	212	6	9mn	9mn	NOUN
ejpam-5323	212	7	.	.	PUNCT
ejpam-5323	213	1	therefore	therefore	ADV
ejpam-5323	213	2	n	n	ADV
ejpam-5323	213	3	=	=	PUNCT
ejpam-5323	213	4	−9m±	−9m±	NOUN
ejpam-5323	213	5	√	√	NUM
ejpam-5323	213	6	337	337	NUM
ejpam-5323	213	7	m	m	NUM
ejpam-5323	213	8	16	16	NUM
ejpam-5323	213	9	̸∈	̸∈	PROPN
ejpam-5323	213	10	n	n	NUM
ejpam-5323	213	11	,	,	PUNCT
ejpam-5323	213	12	which	which	PRON
ejpam-5323	213	13	is	be	AUX
ejpam-5323	213	14	a	a	DET
ejpam-5323	213	15	contradiction	contradiction	NOUN
ejpam-5323	213	16	with	with	ADP
ejpam-5323	213	17	n	n	DET
ejpam-5323	213	18	∈	∈	PROPN
ejpam-5323	213	19	n.	n.	NOUN
ejpam-5323	213	20	corollary	corollary	NOUN
ejpam-5323	213	21	4	4	NUM
ejpam-5323	213	22	.	.	PUNCT
ejpam-5323	213	23	let	let	VERB
ejpam-5323	213	24	p	p	PRON
ejpam-5323	213	25	be	be	AUX
ejpam-5323	213	26	a	a	DET
ejpam-5323	213	27	primitive	primitive	ADJ
ejpam-5323	213	28	pythagorean	pythagorean	NOUN
ejpam-5323	213	29	triple	triple	NOUN
ejpam-5323	213	30	.	.	PUNCT
ejpam-5323	214	1	the	the	DET
ejpam-5323	214	2	triangle	triangle	NOUN
ejpam-5323	214	3	△	△	PUNCT
ejpam-5323	214	4	b(p	b(p	X
ejpam-5323	214	5	)	)	PUNCT
ejpam-5323	214	6	is	be	AUX
ejpam-5323	214	7	not	not	PART
ejpam-5323	214	8	an	an	DET
ejpam-5323	214	9	equilateral	equilateral	ADJ
ejpam-5323	214	10	triangle	triangle	NOUN
ejpam-5323	214	11	.	.	PUNCT
ejpam-5323	215	1	further	far	ADV
ejpam-5323	215	2	,	,	PUNCT
ejpam-5323	215	3	we	we	PRON
ejpam-5323	215	4	study	study	VERB
ejpam-5323	215	5	the	the	DET
ejpam-5323	215	6	area	area	NOUN
ejpam-5323	215	7	,	,	PUNCT
ejpam-5323	215	8	inradius	inradius	NOUN
ejpam-5323	215	9	and	and	CCONJ
ejpam-5323	215	10	the	the	DET
ejpam-5323	215	11	radius	radius	NOUN
ejpam-5323	215	12	of	of	ADP
ejpam-5323	215	13	the	the	DET
ejpam-5323	215	14	circumcircle	circumcircle	NOUN
ejpam-5323	215	15	of	of	ADP
ejpam-5323	215	16	the	the	DET
ejpam-5323	215	17	descendant	descendant	ADJ
ejpam-5323	215	18	triangles	triangle	NOUN
ejpam-5323	215	19	in	in	ADP
ejpam-5323	215	20	berggren	berggren	PROPN
ejpam-5323	215	21	’s	’s	PART
ejpam-5323	215	22	tree	tree	NOUN
ejpam-5323	215	23	and	and	CCONJ
ejpam-5323	215	24	present	present	VERB
ejpam-5323	215	25	the	the	DET
ejpam-5323	215	26	related	related	ADJ
ejpam-5323	215	27	results	result	NOUN
ejpam-5323	215	28	.	.	PUNCT
ejpam-5323	216	1	l.	l.	PROPN
ejpam-5323	216	2	kőszegyová	kőszegyová	PROPN
ejpam-5323	216	3	,	,	PUNCT
ejpam-5323	216	4	e.	e.	PROPN
ejpam-5323	216	5	csókási	csókási	PROPN
ejpam-5323	216	6	,	,	PUNCT
ejpam-5323	216	7	j.	j.	PROPN
ejpam-5323	216	8	hirjak	hirjak	PROPN
ejpam-5323	216	9	/	/	SYM
ejpam-5323	216	10	eur	eur	PROPN
ejpam-5323	216	11	.	.	PUNCT
ejpam-5323	217	1	j.	j.	PROPN
ejpam-5323	217	2	pure	pure	PROPN
ejpam-5323	217	3	appl	appl	PROPN
ejpam-5323	217	4	.	.	PROPN
ejpam-5323	217	5	math	math	PROPN
ejpam-5323	217	6	,	,	PUNCT
ejpam-5323	217	7	17	17	NUM
ejpam-5323	217	8	(	(	PUNCT
ejpam-5323	217	9	3	3	NUM
ejpam-5323	217	10	)	)	PUNCT
ejpam-5323	217	11	(	(	PUNCT
ejpam-5323	217	12	2024	2024	NUM
ejpam-5323	217	13	)	)	PUNCT
ejpam-5323	217	14	,	,	PUNCT
ejpam-5323	217	15	2127	2127	NUM
ejpam-5323	217	16	-	-	SYM
ejpam-5323	217	17	2141	2141	NUM
ejpam-5323	217	18	2135	2135	NUM
ejpam-5323	217	19	proposition	proposition	NOUN
ejpam-5323	217	20	6	6	NUM
ejpam-5323	217	21	.	.	PUNCT
ejpam-5323	218	1	let	let	VERB
ejpam-5323	218	2	p	p	NOUN
ejpam-5323	218	3	=	=	X
ejpam-5323	218	4	(	(	PUNCT
ejpam-5323	218	5	a	a	DET
ejpam-5323	218	6	,	,	PUNCT
ejpam-5323	218	7	b	b	NOUN
ejpam-5323	218	8	,	,	PUNCT
ejpam-5323	218	9	c	c	NOUN
ejpam-5323	218	10	)	)	PUNCT
ejpam-5323	218	11	be	be	AUX
ejpam-5323	218	12	a	a	DET
ejpam-5323	218	13	primitive	primitive	ADJ
ejpam-5323	218	14	pythagorean	pythagorean	NOUN
ejpam-5323	218	15	triple	triple	NOUN
ejpam-5323	218	16	.	.	PUNCT
ejpam-5323	219	1	the	the	DET
ejpam-5323	219	2	triangle	triangle	NOUN
ejpam-5323	219	3	△	△	PUNCT
ejpam-5323	219	4	b(p	b(p	X
ejpam-5323	219	5	)	)	PUNCT
ejpam-5323	219	6	has	have	VERB
ejpam-5323	219	7	the	the	DET
ejpam-5323	219	8	area	area	NOUN
ejpam-5323	219	9	s	s	PART
ejpam-5323	219	10	=	=	SYM
ejpam-5323	219	11	2	2	NUM
ejpam-5323	219	12	√	√	NUM
ejpam-5323	219	13	17ab	17ab	NOUN
ejpam-5323	219	14	.	.	PUNCT
ejpam-5323	220	1	(	(	PUNCT
ejpam-5323	220	2	3	3	X
ejpam-5323	220	3	)	)	PUNCT
ejpam-5323	220	4	for	for	ADP
ejpam-5323	220	5	proof	proof	NOUN
ejpam-5323	220	6	,	,	PUNCT
ejpam-5323	220	7	see	see	VERB
ejpam-5323	220	8	[	[	X
ejpam-5323	220	9	9	9	NUM
ejpam-5323	220	10	]	]	PUNCT
ejpam-5323	220	11	.	.	PUNCT
ejpam-5323	221	1	corollary	corollary	ADJ
ejpam-5323	221	2	5	5	NUM
ejpam-5323	221	3	.	.	PUNCT
ejpam-5323	222	1	let	let	VERB
ejpam-5323	222	2	p	p	PRON
ejpam-5323	222	3	,	,	PUNCT
ejpam-5323	222	4	q	q	ADJ
ejpam-5323	222	5	be	be	AUX
ejpam-5323	222	6	primitive	primitive	ADJ
ejpam-5323	222	7	pythagorean	pythagorean	ADJ
ejpam-5323	222	8	triples	triple	NOUN
ejpam-5323	222	9	.	.	PUNCT
ejpam-5323	223	1	then	then	ADV
ejpam-5323	223	2	the	the	DET
ejpam-5323	223	3	triangles	triangle	NOUN
ejpam-5323	223	4	corresponding	correspond	VERB
ejpam-5323	223	5	to	to	ADP
ejpam-5323	223	6	p	p	NOUN
ejpam-5323	223	7	and	and	CCONJ
ejpam-5323	223	8	q	q	NOUN
ejpam-5323	223	9	have	have	VERB
ejpam-5323	223	10	the	the	DET
ejpam-5323	223	11	same	same	ADJ
ejpam-5323	223	12	area	area	NOUN
ejpam-5323	223	13	if	if	SCONJ
ejpam-5323	223	14	and	and	CCONJ
ejpam-5323	223	15	only	only	ADV
ejpam-5323	223	16	if	if	SCONJ
ejpam-5323	223	17	the	the	DET
ejpam-5323	223	18	triangles	triangle	NOUN
ejpam-5323	223	19	△	△	PUNCT
ejpam-5323	223	20	b(p	b(p	X
ejpam-5323	223	21	)	)	PUNCT
ejpam-5323	223	22	and	and	CCONJ
ejpam-5323	223	23	△	△	NOUN
ejpam-5323	223	24	b(q	b(q	PROPN
ejpam-5323	223	25	)	)	PUNCT
ejpam-5323	223	26	have	have	VERB
ejpam-5323	223	27	the	the	DET
ejpam-5323	223	28	same	same	ADJ
ejpam-5323	223	29	area	area	NOUN
ejpam-5323	223	30	.	.	PUNCT
ejpam-5323	224	1	it	it	PRON
ejpam-5323	224	2	would	would	AUX
ejpam-5323	224	3	be	be	AUX
ejpam-5323	224	4	interesting	interesting	ADJ
ejpam-5323	224	5	to	to	PART
ejpam-5323	224	6	know	know	VERB
ejpam-5323	224	7	whether	whether	SCONJ
ejpam-5323	224	8	there	there	PRON
ejpam-5323	224	9	even	even	ADV
ejpam-5323	224	10	exist	exist	VERB
ejpam-5323	224	11	any	any	DET
ejpam-5323	224	12	ppts	ppt	NOUN
ejpam-5323	224	13	with	with	ADP
ejpam-5323	224	14	the	the	DET
ejpam-5323	224	15	same	same	ADJ
ejpam-5323	224	16	area	area	NOUN
ejpam-5323	224	17	.	.	PUNCT
ejpam-5323	225	1	according	accord	VERB
ejpam-5323	225	2	to	to	ADP
ejpam-5323	225	3	[	[	X
ejpam-5323	225	4	13	13	NUM
ejpam-5323	225	5	]	]	PUNCT
ejpam-5323	225	6	,	,	PUNCT
ejpam-5323	225	7	the	the	DET
ejpam-5323	225	8	smallest	small	ADJ
ejpam-5323	225	9	ppts	ppt	NOUN
ejpam-5323	225	10	with	with	ADP
ejpam-5323	225	11	the	the	DET
ejpam-5323	225	12	same	same	ADJ
ejpam-5323	225	13	area	area	NOUN
ejpam-5323	225	14	are	be	AUX
ejpam-5323	225	15	(	(	PUNCT
ejpam-5323	225	16	20	20	NUM
ejpam-5323	225	17	,	,	PUNCT
ejpam-5323	225	18	21	21	NUM
ejpam-5323	225	19	,	,	PUNCT
ejpam-5323	225	20	29	29	NUM
ejpam-5323	225	21	)	)	PUNCT
ejpam-5323	225	22	and	and	CCONJ
ejpam-5323	225	23	(	(	PUNCT
ejpam-5323	225	24	12	12	NUM
ejpam-5323	225	25	,	,	PUNCT
ejpam-5323	225	26	35	35	NUM
ejpam-5323	225	27	,	,	PUNCT
ejpam-5323	225	28	37	37	NUM
ejpam-5323	225	29	)	)	PUNCT
ejpam-5323	225	30	.	.	PUNCT
ejpam-5323	226	1	both	both	PRON
ejpam-5323	226	2	of	of	ADP
ejpam-5323	226	3	them	they	PRON
ejpam-5323	226	4	have	have	VERB
ejpam-5323	226	5	the	the	DET
ejpam-5323	226	6	area	area	NOUN
ejpam-5323	226	7	210	210	NUM
ejpam-5323	226	8	.	.	PUNCT
ejpam-5323	227	1	further	far	ADV
ejpam-5323	227	2	,	,	PUNCT
ejpam-5323	227	3	the	the	DET
ejpam-5323	227	4	following	follow	VERB
ejpam-5323	227	5	theorem	theorem	NOUN
ejpam-5323	227	6	was	be	AUX
ejpam-5323	227	7	proved	prove	VERB
ejpam-5323	227	8	in	in	ADP
ejpam-5323	227	9	[	[	X
ejpam-5323	227	10	13	13	NUM
ejpam-5323	227	11	]	]	NUM
ejpam-5323	227	12	:	:	PUNCT
ejpam-5323	227	13	theorem	theorem	NOUN
ejpam-5323	227	14	3	3	NUM
ejpam-5323	227	15	.	.	X
ejpam-5323	227	16	for	for	ADP
ejpam-5323	227	17	every	every	DET
ejpam-5323	227	18	n	n	PRON
ejpam-5323	227	19	∈	∈	PROPN
ejpam-5323	227	20	n	n	CCONJ
ejpam-5323	227	21	,	,	PUNCT
ejpam-5323	227	22	there	there	PRON
ejpam-5323	227	23	exist	exist	VERB
ejpam-5323	227	24	n	n	DET
ejpam-5323	227	25	primitive	primitive	ADJ
ejpam-5323	227	26	pythagorean	pythagorean	ADJ
ejpam-5323	227	27	triples	triple	NOUN
ejpam-5323	227	28	with	with	ADP
ejpam-5323	227	29	different	different	ADJ
ejpam-5323	227	30	third	third	ADJ
ejpam-5323	227	31	components	component	NOUN
ejpam-5323	227	32	and	and	CCONJ
ejpam-5323	227	33	the	the	DET
ejpam-5323	227	34	same	same	ADJ
ejpam-5323	227	35	area	area	NOUN
ejpam-5323	227	36	.	.	PUNCT
ejpam-5323	228	1	4	4	X
ejpam-5323	228	2	.	.	X
ejpam-5323	228	3	descendants	descendant	NOUN
ejpam-5323	228	4	in	in	ADP
ejpam-5323	228	5	price	price	NOUN
ejpam-5323	228	6	’s	’s	PART
ejpam-5323	228	7	tree	tree	NOUN
ejpam-5323	228	8	another	another	DET
ejpam-5323	228	9	well	well	ADV
ejpam-5323	228	10	known	know	VERB
ejpam-5323	228	11	tree	tree	NOUN
ejpam-5323	228	12	of	of	ADP
ejpam-5323	228	13	primitive	primitive	ADJ
ejpam-5323	228	14	pythagorean	pythagorean	NOUN
ejpam-5323	228	15	triples	triple	NOUN
ejpam-5323	228	16	was	be	AUX
ejpam-5323	228	17	described	describe	VERB
ejpam-5323	228	18	by	by	ADP
ejpam-5323	228	19	price	price	NOUN
ejpam-5323	228	20	in	in	ADP
ejpam-5323	228	21	[	[	X
ejpam-5323	228	22	12	12	NUM
ejpam-5323	228	23	]	]	PUNCT
ejpam-5323	228	24	.	.	PUNCT
ejpam-5323	229	1	analogously	analogously	ADV
ejpam-5323	229	2	like	like	ADP
ejpam-5323	229	3	in	in	ADP
ejpam-5323	229	4	berggren	berggren	PROPN
ejpam-5323	229	5	’s	’s	PART
ejpam-5323	229	6	tree	tree	NOUN
ejpam-5323	229	7	,	,	PUNCT
ejpam-5323	229	8	price	price	NOUN
ejpam-5323	229	9	proved	prove	VERB
ejpam-5323	229	10	that	that	SCONJ
ejpam-5323	229	11	each	each	DET
ejpam-5323	229	12	ppt	ppt	NOUN
ejpam-5323	229	13	can	can	AUX
ejpam-5323	229	14	be	be	AUX
ejpam-5323	229	15	generated	generate	VERB
ejpam-5323	229	16	from	from	ADP
ejpam-5323	229	17	(	(	PUNCT
ejpam-5323	229	18	3	3	NUM
ejpam-5323	229	19	,	,	PUNCT
ejpam-5323	229	20	4	4	NUM
ejpam-5323	229	21	,	,	PUNCT
ejpam-5323	229	22	5	5	NUM
ejpam-5323	229	23	)	)	PUNCT
ejpam-5323	229	24	by	by	ADP
ejpam-5323	229	25	unique	unique	ADJ
ejpam-5323	229	26	three	three	NUM
ejpam-5323	229	27	-	-	ADJ
ejpam-5323	229	28	fold	fold	ADJ
ejpam-5323	229	29	ascent	ascent	NOUN
ejpam-5323	229	30	using	use	VERB
ejpam-5323	229	31	the	the	DET
ejpam-5323	229	32	three	three	NUM
ejpam-5323	229	33	matrices	matrix	NOUN
ejpam-5323	229	34	m1,m2,m3	m1,m2,m3	NOUN
ejpam-5323	229	35	:	:	PUNCT
ejpam-5323	229	36	m1	m1	PROPN
ejpam-5323	229	37	=	=	PUNCT
ejpam-5323	229	38			PROPN
ejpam-5323	229	39	2	2	NUM
ejpam-5323	229	40	1	1	NUM
ejpam-5323	229	41	−1	−1	NOUN
ejpam-5323	229	42	−2	−2	NOUN
ejpam-5323	229	43	2	2	NUM
ejpam-5323	229	44	2	2	NUM
ejpam-5323	229	45	−2	−2	NOUN
ejpam-5323	229	46	1	1	NUM
ejpam-5323	229	47	3	3	NUM
ejpam-5323	229	48			PROPN
ejpam-5323	229	49	,	,	PUNCT
ejpam-5323	229	50	m2	m2	PROPN
ejpam-5323	229	51	=	=	PUNCT
ejpam-5323	229	52	2	2	PROPN
ejpam-5323	229	53	1	1	NUM
ejpam-5323	229	54	1	1	NUM
ejpam-5323	229	55	2	2	NUM
ejpam-5323	229	56	−2	−2	NOUN
ejpam-5323	229	57	2	2	NUM
ejpam-5323	229	58	2	2	NUM
ejpam-5323	229	59	−1	−1	NOUN
ejpam-5323	229	60	3	3	NUM
ejpam-5323	229	61			PROPN
ejpam-5323	229	62	,	,	PUNCT
ejpam-5323	229	63	m3	m3	PROPN
ejpam-5323	229	64	=	=	PUNCT
ejpam-5323	229	65	2	2	ADP
ejpam-5323	229	66	−1	−1	NOUN
ejpam-5323	229	67	1	1	NUM
ejpam-5323	229	68	2	2	NUM
ejpam-5323	229	69	2	2	NUM
ejpam-5323	229	70	2	2	NUM
ejpam-5323	229	71	2	2	NUM
ejpam-5323	229	72	1	1	NUM
ejpam-5323	229	73	3	3	NUM
ejpam-5323	229	74			PROPN
ejpam-5323	229	75	.	.	PUNCT
ejpam-5323	230	1	it	it	PRON
ejpam-5323	230	2	is	be	AUX
ejpam-5323	230	3	easy	easy	ADJ
ejpam-5323	230	4	to	to	PART
ejpam-5323	230	5	show	show	VERB
ejpam-5323	230	6	that	that	SCONJ
ejpam-5323	230	7	mn	mn	PROPN
ejpam-5323	230	8	1	1	NUM
ejpam-5323	230	9	=	=	SYM
ejpam-5323	230	10			PROPN
ejpam-5323	230	11	2n	2n	NUM
ejpam-5323	230	12	−2n	−2n	NOUN
ejpam-5323	230	13	+	+	CCONJ
ejpam-5323	230	14	1	1	NUM
ejpam-5323	230	15	2n	2n	NUM
ejpam-5323	230	16	−	−	PROPN
ejpam-5323	230	17	1	1	NUM
ejpam-5323	230	18	22n	22n	NOUN
ejpam-5323	230	19	−	−	PROPN
ejpam-5323	230	20	2n	2n	NUM
ejpam-5323	230	21	2n	2n	NUM
ejpam-5323	230	22	22n	22n	NOUN
ejpam-5323	230	23	−	−	PROPN
ejpam-5323	230	24	2n	2n	NUM
ejpam-5323	230	25	22n	22n	NOUN
ejpam-5323	230	26	−	−	PROPN
ejpam-5323	230	27	2n	2n	NUM
ejpam-5323	230	28	2n	2n	NUM
ejpam-5323	230	29	−	−	PROPN
ejpam-5323	230	30	1	1	NUM
ejpam-5323	230	31	22n	22n	NOUN
ejpam-5323	230	32	−	−	NOUN
ejpam-5323	230	33	2n	2n	NUM
ejpam-5323	231	1	+	+	CCONJ
ejpam-5323	231	2	1	1	NUM
ejpam-5323	231	3			PROPN
ejpam-5323	231	4	,	,	PUNCT
ejpam-5323	231	5	mn	mn	PROPN
ejpam-5323	231	6	2	2	NUM
ejpam-5323	231	7	=	=	SYM
ejpam-5323	231	8			X
ejpam-5323	231	9	22n+2+(−1)n·2n+4	22n+2+(−1)n·2n+4	NUM
ejpam-5323	231	10	9	9	NUM
ejpam-5323	231	11	(	(	PUNCT
ejpam-5323	231	12	−1)n+1·2n+1	−1)n+1·2n+1	NOUN
ejpam-5323	232	1	3	3	NUM
ejpam-5323	232	2	22n+2+(−1)n·2n−5	22n+2+(−1)n·2n−5	NUM
ejpam-5323	232	3	9	9	NUM
ejpam-5323	232	4	22n+(−1)n·2n	22n+(−1)n·2n	NUM
ejpam-5323	232	5	3	3	NUM
ejpam-5323	232	6	(	(	PUNCT
ejpam-5323	232	7	−1)n	−1)n	X
ejpam-5323	232	8	·	·	PUNCT
ejpam-5323	232	9	2n	2n	NUM
ejpam-5323	232	10	22n+(−1)n·2n	22n+(−1)n·2n	NUM
ejpam-5323	232	11	3	3	NUM
ejpam-5323	232	12	5·22n+(−1)n·2n−4	5·22n+(−1)n·2n−4	NUM
ejpam-5323	232	13	9	9	NUM
ejpam-5323	232	14	(	(	PUNCT
ejpam-5323	232	15	−1)n·2n−1	−1)n·2n−1	PROPN
ejpam-5323	232	16	3	3	NUM
ejpam-5323	232	17	5·22n+(−1)n·2n+5	5·22n+(−1)n·2n+5	NUM
ejpam-5323	232	18	9	9	NUM
ejpam-5323	232	19			NOUN
ejpam-5323	232	20	,	,	PUNCT
ejpam-5323	232	21	mn	mn	PROPN
ejpam-5323	232	22	3	3	NUM
ejpam-5323	232	23	=	=	SYM
ejpam-5323	232	24			PROPN
ejpam-5323	232	25	2n	2n	NUM
ejpam-5323	232	26	2n	2n	NUM
ejpam-5323	232	27	−	−	ADP
ejpam-5323	232	28	1	1	NUM
ejpam-5323	232	29	−2n	−2n	PROPN
ejpam-5323	232	30	+	+	CCONJ
ejpam-5323	232	31	1	1	NUM
ejpam-5323	232	32	−22n	−22n	NOUN
ejpam-5323	232	33	+	+	CCONJ
ejpam-5323	232	34	2n	2n	NUM
ejpam-5323	232	35	2n	2n	NUM
ejpam-5323	232	36	22n	22n	NOUN
ejpam-5323	232	37	−	−	PROPN
ejpam-5323	232	38	2n	2n	NUM
ejpam-5323	232	39	−22n	−22n	X
ejpam-5323	233	1	+	+	CCONJ
ejpam-5323	233	2	2n	2n	NUM
ejpam-5323	233	3	2n	2n	NUM
ejpam-5323	233	4	−	−	PROPN
ejpam-5323	233	5	1	1	NUM
ejpam-5323	233	6	22n	22n	NOUN
ejpam-5323	233	7	−	−	NOUN
ejpam-5323	233	8	2n	2n	NUM
ejpam-5323	233	9	+	+	CCONJ
ejpam-5323	233	10	1	1	NUM
ejpam-5323	233	11			PROPN
ejpam-5323	233	12	.	.	PUNCT
ejpam-5323	234	1	theorem	theorem	VERB
ejpam-5323	234	2	4	4	NUM
ejpam-5323	234	3	.	.	PUNCT
ejpam-5323	235	1	if	if	SCONJ
ejpam-5323	235	2	(	(	PUNCT
ejpam-5323	235	3	a	a	DET
ejpam-5323	235	4	,	,	PUNCT
ejpam-5323	235	5	b	b	NOUN
ejpam-5323	235	6	,	,	PUNCT
ejpam-5323	235	7	c	c	NOUN
ejpam-5323	235	8	)	)	PUNCT
ejpam-5323	235	9	is	be	AUX
ejpam-5323	235	10	a	a	DET
ejpam-5323	235	11	primitive	primitive	ADJ
ejpam-5323	235	12	pythagorean	pythagorean	NOUN
ejpam-5323	235	13	triple	triple	NOUN
ejpam-5323	235	14	with	with	ADP
ejpam-5323	235	15	odd	odd	ADJ
ejpam-5323	235	16	a	a	PRON
ejpam-5323	235	17	,	,	PUNCT
ejpam-5323	235	18	and	and	CCONJ
ejpam-5323	235	19	m	m	PROPN
ejpam-5323	235	20	is	be	AUX
ejpam-5323	235	21	a	a	DET
ejpam-5323	235	22	matrix	matrix	NOUN
ejpam-5323	235	23	such	such	ADJ
ejpam-5323	235	24	that	that	SCONJ
ejpam-5323	235	25	m	m	PROPN
ejpam-5323	235	26	∈	∈	PROPN
ejpam-5323	235	27	{	{	PUNCT
ejpam-5323	235	28	m1,m2,m3	m1,m2,m3	NOUN
ejpam-5323	235	29	}	}	PUNCT
ejpam-5323	235	30	,	,	PUNCT
ejpam-5323	235	31	then	then	ADV
ejpam-5323	235	32	m	m	VERB
ejpam-5323	235	33	·	·	PUNCT
ejpam-5323	235	34	(	(	PUNCT
ejpam-5323	235	35	a	a	DET
ejpam-5323	235	36	,	,	PUNCT
ejpam-5323	235	37	b	b	NOUN
ejpam-5323	235	38	,	,	PUNCT
ejpam-5323	235	39	c)⊤	c)⊤	NOUN
ejpam-5323	235	40	is	be	AUX
ejpam-5323	235	41	a	a	DET
ejpam-5323	235	42	primitive	primitive	ADJ
ejpam-5323	235	43	pythagorean	pythagorean	NOUN
ejpam-5323	235	44	triple	triple	NOUN
ejpam-5323	235	45	with	with	ADP
ejpam-5323	235	46	an	an	DET
ejpam-5323	235	47	odd	odd	ADJ
ejpam-5323	235	48	first	first	ADJ
ejpam-5323	235	49	component	component	NOUN
ejpam-5323	235	50	.	.	PUNCT
ejpam-5323	236	1	l.	l.	PROPN
ejpam-5323	236	2	kőszegyová	kőszegyová	PROPN
ejpam-5323	236	3	,	,	PUNCT
ejpam-5323	236	4	e.	e.	PROPN
ejpam-5323	236	5	csókási	csókási	PROPN
ejpam-5323	236	6	,	,	PUNCT
ejpam-5323	236	7	j.	j.	PROPN
ejpam-5323	236	8	hirjak	hirjak	PROPN
ejpam-5323	236	9	/	/	SYM
ejpam-5323	236	10	eur	eur	PROPN
ejpam-5323	236	11	.	.	PUNCT
ejpam-5323	237	1	j.	j.	PROPN
ejpam-5323	237	2	pure	pure	PROPN
ejpam-5323	237	3	appl	appl	PROPN
ejpam-5323	237	4	.	.	PROPN
ejpam-5323	237	5	math	math	PROPN
ejpam-5323	237	6	,	,	PUNCT
ejpam-5323	237	7	17	17	NUM
ejpam-5323	237	8	(	(	PUNCT
ejpam-5323	237	9	3	3	NUM
ejpam-5323	237	10	)	)	PUNCT
ejpam-5323	237	11	(	(	PUNCT
ejpam-5323	237	12	2024	2024	NUM
ejpam-5323	237	13	)	)	PUNCT
ejpam-5323	237	14	,	,	PUNCT
ejpam-5323	237	15	2127	2127	NUM
ejpam-5323	237	16	-	-	SYM
ejpam-5323	237	17	2141	2141	NUM
ejpam-5323	237	18	2136	2136	NUM
ejpam-5323	237	19	(	(	PUNCT
ejpam-5323	237	20	3	3	NUM
ejpam-5323	237	21	,	,	PUNCT
ejpam-5323	237	22	4	4	NUM
ejpam-5323	237	23	,	,	PUNCT
ejpam-5323	237	24	5	5	NUM
ejpam-5323	237	25	)	)	PUNCT
ejpam-5323	237	26	(	(	PUNCT
ejpam-5323	237	27	5	5	NUM
ejpam-5323	237	28	,	,	PUNCT
ejpam-5323	237	29	12	12	NUM
ejpam-5323	237	30	,	,	PUNCT
ejpam-5323	237	31	13	13	NUM
ejpam-5323	237	32	)	)	PUNCT
ejpam-5323	237	33	(	(	PUNCT
ejpam-5323	237	34	15	15	NUM
ejpam-5323	237	35	,	,	PUNCT
ejpam-5323	237	36	8	8	NUM
ejpam-5323	237	37	,	,	PUNCT
ejpam-5323	237	38	17	17	NUM
ejpam-5323	237	39	)	)	PUNCT
ejpam-5323	237	40	(	(	PUNCT
ejpam-5323	237	41	7	7	NUM
ejpam-5323	237	42	,	,	PUNCT
ejpam-5323	237	43	24	24	NUM
ejpam-5323	237	44	,	,	PUNCT
ejpam-5323	237	45	25	25	NUM
ejpam-5323	237	46	)	)	PUNCT
ejpam-5323	237	47	(	(	PUNCT
ejpam-5323	237	48	9	9	NUM
ejpam-5323	237	49	,	,	PUNCT
ejpam-5323	237	50	40	40	NUM
ejpam-5323	237	51	,	,	PUNCT
ejpam-5323	237	52	41	41	NUM
ejpam-5323	237	53	)	)	PUNCT
ejpam-5323	237	54	(	(	PUNCT
ejpam-5323	237	55	35	35	NUM
ejpam-5323	237	56	,	,	PUNCT
ejpam-5323	237	57	12	12	NUM
ejpam-5323	237	58	,	,	PUNCT
ejpam-5323	237	59	37	37	NUM
ejpam-5323	237	60	)	)	PUNCT
ejpam-5323	237	61	(	(	PUNCT
ejpam-5323	237	62	11	11	NUM
ejpam-5323	237	63	,	,	PUNCT
ejpam-5323	237	64	60	60	NUM
ejpam-5323	237	65	,	,	PUNCT
ejpam-5323	237	66	61	61	NUM
ejpam-5323	237	67	)	)	PUNCT
ejpam-5323	237	68	(	(	PUNCT
ejpam-5323	237	69	21	21	NUM
ejpam-5323	237	70	,	,	PUNCT
ejpam-5323	237	71	20	20	NUM
ejpam-5323	237	72	,	,	PUNCT
ejpam-5323	237	73	29	29	NUM
ejpam-5323	237	74	)	)	PUNCT
ejpam-5323	237	75	(	(	PUNCT
ejpam-5323	237	76	55	55	NUM
ejpam-5323	237	77	,	,	PUNCT
ejpam-5323	237	78	48	48	NUM
ejpam-5323	237	79	,	,	PUNCT
ejpam-5323	237	80	73	73	NUM
ejpam-5323	237	81	)	)	PUNCT
ejpam-5323	237	82	(	(	PUNCT
ejpam-5323	237	83	39	39	NUM
ejpam-5323	237	84	,	,	PUNCT
ejpam-5323	237	85	80	80	NUM
ejpam-5323	237	86	,	,	PUNCT
ejpam-5323	237	87	89	89	NUM
ejpam-5323	237	88	)	)	PUNCT
ejpam-5323	237	89	(	(	PUNCT
ejpam-5323	237	90	13	13	NUM
ejpam-5323	237	91	,	,	PUNCT
ejpam-5323	237	92	84	84	NUM
ejpam-5323	237	93	,	,	PUNCT
ejpam-5323	237	94	85	85	NUM
ejpam-5323	237	95	)	)	PUNCT
ejpam-5323	237	96	(	(	PUNCT
ejpam-5323	237	97	63	63	NUM
ejpam-5323	237	98	,	,	PUNCT
ejpam-5323	237	99	16	16	NUM
ejpam-5323	237	100	,	,	PUNCT
ejpam-5323	237	101	65	65	NUM
ejpam-5323	237	102	)	)	PUNCT
ejpam-5323	237	103	(	(	PUNCT
ejpam-5323	237	104	15	15	NUM
ejpam-5323	237	105	,	,	PUNCT
ejpam-5323	237	106	112	112	NUM
ejpam-5323	237	107	,	,	PUNCT
ejpam-5323	237	108	113	113	NUM
ejpam-5323	237	109	)	)	PUNCT
ejpam-5323	237	110	m1	m1	PROPN
ejpam-5323	237	111	m2	m2	PROPN
ejpam-5323	237	112	m3	m3	PROPN
ejpam-5323	237	113	m1	m1	PROPN
ejpam-5323	237	114	m2	m2	PROPN
ejpam-5323	237	115	m3	m3	PROPN
ejpam-5323	237	116	m1	m1	PROPN
ejpam-5323	237	117	m2	m2	PROPN
ejpam-5323	237	118	m3	m3	PROPN
ejpam-5323	237	119	m1	m1	PROPN
ejpam-5323	237	120	m2	m2	PROPN
ejpam-5323	237	121	m3	m3	PROPN
ejpam-5323	237	122	figure	figure	NOUN
ejpam-5323	237	123	2	2	NUM
ejpam-5323	237	124	:	:	PUNCT
ejpam-5323	237	125	price	price	NOUN
ejpam-5323	237	126	’s	’s	PART
ejpam-5323	237	127	tree	tree	NOUN
ejpam-5323	237	128	of	of	ADP
ejpam-5323	237	129	ppts	ppt	NOUN
ejpam-5323	237	130	.	.	PUNCT
ejpam-5323	238	1	price	price	NOUN
ejpam-5323	238	2	’s	’s	PART
ejpam-5323	238	3	tree	tree	NOUN
ejpam-5323	238	4	of	of	ADP
ejpam-5323	238	5	ppt	ppt	PROPN
ejpam-5323	238	6	contains	contain	VERB
ejpam-5323	238	7	all	all	DET
ejpam-5323	238	8	ppts	ppt	NOUN
ejpam-5323	238	9	,	,	PUNCT
ejpam-5323	238	10	and	and	CCONJ
ejpam-5323	238	11	each	each	DET
ejpam-5323	238	12	ppt	ppt	NOUN
ejpam-5323	238	13	is	be	AUX
ejpam-5323	238	14	generated	generate	VERB
ejpam-5323	238	15	by	by	ADP
ejpam-5323	238	16	a	a	DET
ejpam-5323	238	17	unique	unique	ADJ
ejpam-5323	238	18	sequence	sequence	NOUN
ejpam-5323	238	19	of	of	ADP
ejpam-5323	238	20	matrix	matrix	NOUN
ejpam-5323	238	21	multiplication	multiplication	NOUN
ejpam-5323	238	22	[	[	X
ejpam-5323	238	23	12	12	NUM
ejpam-5323	238	24	]	]	PUNCT
ejpam-5323	238	25	.	.	PUNCT
ejpam-5323	239	1	the	the	DET
ejpam-5323	239	2	first	first	ADJ
ejpam-5323	239	3	levels	level	NOUN
ejpam-5323	239	4	of	of	ADP
ejpam-5323	239	5	price	price	NOUN
ejpam-5323	239	6	’s	’s	PART
ejpam-5323	239	7	tree	tree	NOUN
ejpam-5323	239	8	are	be	AUX
ejpam-5323	239	9	in	in	ADP
ejpam-5323	239	10	the	the	DET
ejpam-5323	239	11	figure	figure	NOUN
ejpam-5323	239	12	2	2	NUM
ejpam-5323	239	13	.	.	PUNCT
ejpam-5323	239	14	similar	similar	ADJ
ejpam-5323	239	15	relations	relation	NOUN
ejpam-5323	239	16	that	that	PRON
ejpam-5323	239	17	hold	hold	VERB
ejpam-5323	239	18	in	in	ADP
ejpam-5323	239	19	berggren	berggren	PROPN
ejpam-5323	239	20	’s	’s	PART
ejpam-5323	239	21	tree	tree	NOUN
ejpam-5323	239	22	of	of	ADP
ejpam-5323	239	23	ppts	ppt	NOUN
ejpam-5323	239	24	can	can	AUX
ejpam-5323	239	25	be	be	AUX
ejpam-5323	239	26	also	also	ADV
ejpam-5323	239	27	proved	prove	VERB
ejpam-5323	239	28	in	in	ADP
ejpam-5323	239	29	price	price	NOUN
ejpam-5323	239	30	’s	’s	PART
ejpam-5323	239	31	tree	tree	NOUN
ejpam-5323	239	32	.	.	PUNCT
ejpam-5323	240	1	we	we	PRON
ejpam-5323	240	2	will	will	AUX
ejpam-5323	240	3	use	use	VERB
ejpam-5323	240	4	the	the	DET
ejpam-5323	240	5	analogous	analogous	ADJ
ejpam-5323	240	6	terms	term	NOUN
ejpam-5323	240	7	and	and	CCONJ
ejpam-5323	240	8	notations	notation	NOUN
ejpam-5323	240	9	.	.	PUNCT
ejpam-5323	241	1	definition	definition	NOUN
ejpam-5323	241	2	5	5	NUM
ejpam-5323	241	3	.	.	PUNCT
ejpam-5323	242	1	let	let	VERB
ejpam-5323	242	2	r	r	PRON
ejpam-5323	242	3	be	be	AUX
ejpam-5323	242	4	a	a	DET
ejpam-5323	242	5	primitive	primitive	ADJ
ejpam-5323	242	6	pythagorean	pythagorean	NOUN
ejpam-5323	242	7	triple	triple	NOUN
ejpam-5323	242	8	.	.	PUNCT
ejpam-5323	243	1	we	we	PRON
ejpam-5323	243	2	say	say	VERB
ejpam-5323	243	3	that	that	SCONJ
ejpam-5323	243	4	r	r	NOUN
ejpam-5323	243	5	is	be	AUX
ejpam-5323	243	6	the	the	DET
ejpam-5323	243	7	parent	parent	NOUN
ejpam-5323	243	8	of	of	ADP
ejpam-5323	243	9	the	the	DET
ejpam-5323	243	10	triples	triple	NOUN
ejpam-5323	243	11	m1r	m1r	VERB
ejpam-5323	243	12	⊤,m2r	⊤,m2r	NUM
ejpam-5323	244	1	⊤,m3r	⊤,m3r	PUNCT
ejpam-5323	244	2	⊤.	⊤.	VERB
ejpam-5323	244	3	the	the	DET
ejpam-5323	244	4	triples	triple	NOUN
ejpam-5323	244	5	m1r	m1r	VERB
ejpam-5323	244	6	⊤,m2r	⊤,m2r	NUM
ejpam-5323	245	1	⊤,m3r	⊤,m3r	NUM
ejpam-5323	245	2	⊤	⊤	NOUN
ejpam-5323	245	3	are	be	AUX
ejpam-5323	245	4	called	call	VERB
ejpam-5323	245	5	the	the	DET
ejpam-5323	245	6	descendants	descendant	NOUN
ejpam-5323	245	7	of	of	ADP
ejpam-5323	245	8	r	r	NOUN
ejpam-5323	245	9	in	in	ADP
ejpam-5323	245	10	price	price	NOUN
ejpam-5323	245	11	’s	’s	PART
ejpam-5323	245	12	tree	tree	NOUN
ejpam-5323	245	13	.	.	PUNCT
ejpam-5323	246	1	proposition	proposition	NOUN
ejpam-5323	246	2	7	7	NUM
ejpam-5323	246	3	.	.	PUNCT
ejpam-5323	247	1	let	let	VERB
ejpam-5323	247	2	r	r	PRON
ejpam-5323	247	3	be	be	AUX
ejpam-5323	247	4	a	a	DET
ejpam-5323	247	5	primitive	primitive	ADJ
ejpam-5323	247	6	pythagorean	pythagorean	NOUN
ejpam-5323	247	7	triple	triple	NOUN
ejpam-5323	247	8	.	.	PUNCT
ejpam-5323	248	1	then	then	ADV
ejpam-5323	248	2	the	the	DET
ejpam-5323	248	3	points	point	NOUN
ejpam-5323	248	4	with	with	ADP
ejpam-5323	248	5	the	the	DET
ejpam-5323	248	6	coordinates	coordinate	NOUN
ejpam-5323	248	7	m1r	m1r	X
ejpam-5323	248	8	⊤,m2r	⊤,m2r	NUM
ejpam-5323	249	1	⊤,m3r	⊤,m3r	NUM
ejpam-5323	249	2	⊤	⊤	NOUN
ejpam-5323	249	3	are	be	AUX
ejpam-5323	249	4	not	not	PART
ejpam-5323	249	5	collinear	collinear	ADJ
ejpam-5323	249	6	.	.	PUNCT
ejpam-5323	250	1	proof	proof	NOUN
ejpam-5323	250	2	.	.	PUNCT
ejpam-5323	251	1	let	let	VERB
ejpam-5323	251	2	r	r	NOUN
ejpam-5323	251	3	=	=	SYM
ejpam-5323	251	4	(	(	PUNCT
ejpam-5323	251	5	a	a	PRON
ejpam-5323	251	6	,	,	PUNCT
ejpam-5323	251	7	b	b	NOUN
ejpam-5323	251	8	,	,	PUNCT
ejpam-5323	251	9	c	c	NOUN
ejpam-5323	251	10	)	)	PUNCT
ejpam-5323	251	11	.	.	PUNCT
ejpam-5323	252	1	we	we	PRON
ejpam-5323	252	2	consider	consider	VERB
ejpam-5323	252	3	the	the	DET
ejpam-5323	252	4	vectors	vector	NOUN
ejpam-5323	252	5	p⃗	p⃗	NOUN
ejpam-5323	252	6	=	=	SYM
ejpam-5323	252	7	m2r	m2r	NUM
ejpam-5323	252	8	⊤	⊤	NOUN
ejpam-5323	252	9	−	−	PROPN
ejpam-5323	252	10	m1r	m1r	PUNCT
ejpam-5323	252	11	⊤	⊤	NOUN
ejpam-5323	252	12	and	and	CCONJ
ejpam-5323	252	13	q⃗	q⃗	PROPN
ejpam-5323	252	14	=	=	SYM
ejpam-5323	252	15	m3r	m3r	NUM
ejpam-5323	252	16	⊤	⊤	PROPN
ejpam-5323	252	17	−m1r	−m1r	PROPN
ejpam-5323	252	18	⊤.	⊤.	NOUN
ejpam-5323	252	19	it	it	PRON
ejpam-5323	252	20	is	be	AUX
ejpam-5323	252	21	easy	easy	ADJ
ejpam-5323	252	22	to	to	PART
ejpam-5323	252	23	show	show	VERB
ejpam-5323	252	24	that	that	SCONJ
ejpam-5323	252	25	p⃗	p⃗	NOUN
ejpam-5323	252	26	=	=	SYM
ejpam-5323	253	1	(	(	PUNCT
ejpam-5323	253	2	m2	m2	PROPN
ejpam-5323	253	3	−m1)r	−m1)r	PROPN
ejpam-5323	253	4	⊤	⊤	PROPN
ejpam-5323	253	5	=	=	PUNCT
ejpam-5323	253	6	0	0	ADP
ejpam-5323	253	7	0	0	NUM
ejpam-5323	253	8	2	2	NUM
ejpam-5323	253	9	4	4	NUM
ejpam-5323	253	10	−4	−4	NOUN
ejpam-5323	253	11	0	0	NUM
ejpam-5323	253	12	4	4	NUM
ejpam-5323	253	13	−2	−2	NOUN
ejpam-5323	253	14	0	0	NUM
ejpam-5323	253	15			PROPN
ejpam-5323	253	16	·	·	PUNCT
ejpam-5323	253	17	a	a	NOUN
ejpam-5323	253	18	b	b	X
ejpam-5323	253	19	c	c	X
ejpam-5323	253	20			PROPN
ejpam-5323	253	21	=	=	SYM
ejpam-5323	253	22			PROPN
ejpam-5323	253	23	2c	2c	NOUN
ejpam-5323	253	24	4a−	4a−	PROPN
ejpam-5323	253	25	4b	4b	NOUN
ejpam-5323	254	1	4a−	4a−	PROPN
ejpam-5323	254	2	2b	2b	NUM
ejpam-5323	254	3			PROPN
ejpam-5323	254	4	,	,	PUNCT
ejpam-5323	254	5	q⃗	q⃗	PROPN
ejpam-5323	254	6	=	=	SYM
ejpam-5323	254	7	(	(	PUNCT
ejpam-5323	254	8	m3	m3	PROPN
ejpam-5323	254	9	−m1)r	−m1)r	PROPN
ejpam-5323	254	10	⊤	⊤	NOUN
ejpam-5323	254	11	=	=	PUNCT
ejpam-5323	254	12	0	0	ADP
ejpam-5323	254	13	−2	−2	NOUN
ejpam-5323	254	14	2	2	NUM
ejpam-5323	254	15	4	4	NUM
ejpam-5323	254	16	0	0	NUM
ejpam-5323	254	17	0	0	NUM
ejpam-5323	254	18	4	4	NUM
ejpam-5323	254	19	0	0	NUM
ejpam-5323	254	20	0	0	NUM
ejpam-5323	254	21			PROPN
ejpam-5323	254	22	·	·	PUNCT
ejpam-5323	254	23	a	a	NOUN
ejpam-5323	254	24	b	b	X
ejpam-5323	254	25	c	c	NOUN
ejpam-5323	254	26			PROPN
ejpam-5323	254	27	=	=	PUNCT
ejpam-5323	254	28	−2b+	−2b+	ADP
ejpam-5323	254	29	2c	2c	NOUN
ejpam-5323	254	30	4a	4a	NOUN
ejpam-5323	254	31	4a	4a	NOUN
ejpam-5323	254	32			PROPN
ejpam-5323	254	33	.	.	PUNCT
ejpam-5323	255	1	by	by	ADP
ejpam-5323	255	2	way	way	NOUN
ejpam-5323	255	3	of	of	ADP
ejpam-5323	255	4	contradiction	contradiction	NOUN
ejpam-5323	255	5	,	,	PUNCT
ejpam-5323	255	6	assume	assume	VERB
ejpam-5323	255	7	that	that	SCONJ
ejpam-5323	255	8	these	these	DET
ejpam-5323	255	9	vectors	vector	NOUN
ejpam-5323	255	10	are	be	AUX
ejpam-5323	255	11	linearly	linearly	ADV
ejpam-5323	255	12	dependent	dependent	ADJ
ejpam-5323	255	13	,	,	PUNCT
ejpam-5323	255	14	i.e.	i.e.	X
ejpam-5323	255	15	,	,	PUNCT
ejpam-5323	255	16	that	that	SCONJ
ejpam-5323	255	17	there	there	PRON
ejpam-5323	255	18	exists	exist	VERB
ejpam-5323	255	19	nonzero	nonzero	ADJ
ejpam-5323	255	20	real	real	ADJ
ejpam-5323	255	21	number	number	NOUN
ejpam-5323	255	22	k	k	PROPN
ejpam-5323	256	1	such	such	ADJ
ejpam-5323	256	2	that	that	PRON
ejpam-5323	256	3	(	(	PUNCT
ejpam-5323	256	4	2c	2c	NUM
ejpam-5323	256	5	,	,	PUNCT
ejpam-5323	256	6	4a	4a	NOUN
ejpam-5323	256	7	−	−	PROPN
ejpam-5323	256	8	4b	4b	PROPN
ejpam-5323	256	9	,	,	PUNCT
ejpam-5323	256	10	4a	4a	NOUN
ejpam-5323	256	11	−	−	NOUN
ejpam-5323	256	12	2b	2b	NUM
ejpam-5323	256	13	)	)	PUNCT
ejpam-5323	256	14	=	=	SYM
ejpam-5323	257	1	k(−2b	k(−2b	NUM
ejpam-5323	257	2	+	+	NUM
ejpam-5323	257	3	2c	2c	NUM
ejpam-5323	257	4	,	,	PUNCT
ejpam-5323	257	5	4a	4a	NUM
ejpam-5323	257	6	,	,	PUNCT
ejpam-5323	257	7	4a	4a	NUM
ejpam-5323	257	8	)	)	PUNCT
ejpam-5323	257	9	,	,	PUNCT
ejpam-5323	257	10	hence	hence	ADV
ejpam-5323	257	11	4a−	4a−	NUM
ejpam-5323	257	12	4b	4b	X
ejpam-5323	257	13	=	=	SYM
ejpam-5323	257	14	k(4a	k(4a	PROPN
ejpam-5323	257	15	)	)	PUNCT
ejpam-5323	257	16	and	and	CCONJ
ejpam-5323	257	17	4a−	4a−	NUM
ejpam-5323	257	18	2b	2b	NUM
ejpam-5323	257	19	=	=	SYM
ejpam-5323	257	20	k(4a	k(4a	NOUN
ejpam-5323	257	21	)	)	PUNCT
ejpam-5323	257	22	.	.	PUNCT
ejpam-5323	258	1	this	this	PRON
ejpam-5323	258	2	implies	imply	VERB
ejpam-5323	258	3	4a−	4a−	NOUN
ejpam-5323	258	4	4b	4b	X
ejpam-5323	258	5	=	=	SYM
ejpam-5323	258	6	4a−	4a−	NUM
ejpam-5323	258	7	2b	2b	X
ejpam-5323	258	8	−4b	−4b	PROPN
ejpam-5323	258	9	=	=	SYM
ejpam-5323	258	10	−2b	−2b	NUM
ejpam-5323	258	11	b	b	X
ejpam-5323	258	12	=	=	SYM
ejpam-5323	258	13	0	0	NUM
ejpam-5323	258	14	which	which	PRON
ejpam-5323	258	15	is	be	AUX
ejpam-5323	258	16	a	a	DET
ejpam-5323	258	17	contradiction	contradiction	NOUN
ejpam-5323	258	18	with	with	ADP
ejpam-5323	258	19	b	b	PROPN
ejpam-5323	258	20	∈	∈	PROPN
ejpam-5323	258	21	n.	n.	NOUN
ejpam-5323	258	22	therefore	therefore	ADV
ejpam-5323	258	23	,	,	PUNCT
ejpam-5323	258	24	p⃗	p⃗	NOUN
ejpam-5323	258	25	,	,	PUNCT
ejpam-5323	258	26	q⃗	q⃗	PROPN
ejpam-5323	258	27	are	be	AUX
ejpam-5323	258	28	linearly	linearly	ADV
ejpam-5323	258	29	independent	independent	ADJ
ejpam-5323	258	30	and	and	CCONJ
ejpam-5323	258	31	the	the	DET
ejpam-5323	258	32	points	point	NOUN
ejpam-5323	258	33	m1r	m1r	X
ejpam-5323	258	34	⊤,m2r	⊤,m2r	NUM
ejpam-5323	258	35	⊤,m3r	⊤,m3r	NUM
ejpam-5323	258	36	⊤	⊤	NOUN
ejpam-5323	258	37	are	be	AUX
ejpam-5323	258	38	not	not	PART
ejpam-5323	258	39	collinear	collinear	ADJ
ejpam-5323	258	40	.	.	PUNCT
ejpam-5323	259	1	therefore	therefore	ADV
ejpam-5323	259	2	,	,	PUNCT
ejpam-5323	259	3	the	the	DET
ejpam-5323	259	4	points	point	NOUN
ejpam-5323	259	5	m1r	m1r	X
ejpam-5323	259	6	⊤,m2r	⊤,m2r	NUM
ejpam-5323	260	1	⊤,m3r	⊤,m3r	NUM
ejpam-5323	260	2	⊤	⊤	NOUN
ejpam-5323	260	3	determine	determine	VERB
ejpam-5323	260	4	a	a	DET
ejpam-5323	260	5	plane	plane	NOUN
ejpam-5323	260	6	,	,	PUNCT
ejpam-5323	260	7	and	and	CCONJ
ejpam-5323	260	8	a	a	DET
ejpam-5323	260	9	triangle	triangle	NOUN
ejpam-5323	260	10	.	.	PUNCT
ejpam-5323	261	1	in	in	ADP
ejpam-5323	261	2	the	the	DET
ejpam-5323	261	3	following	following	NOUN
ejpam-5323	261	4	,	,	PUNCT
ejpam-5323	261	5	we	we	PRON
ejpam-5323	261	6	prove	prove	VERB
ejpam-5323	261	7	some	some	DET
ejpam-5323	261	8	properties	property	NOUN
ejpam-5323	261	9	of	of	ADP
ejpam-5323	261	10	this	this	DET
ejpam-5323	261	11	plane	plane	NOUN
ejpam-5323	261	12	(	(	PUNCT
ejpam-5323	261	13	and	and	CCONJ
ejpam-5323	261	14	this	this	DET
ejpam-5323	261	15	triangle	triangle	NOUN
ejpam-5323	261	16	)	)	PUNCT
ejpam-5323	261	17	.	.	PUNCT
ejpam-5323	262	1	l.	l.	PROPN
ejpam-5323	262	2	kőszegyová	kőszegyová	PROPN
ejpam-5323	262	3	,	,	PUNCT
ejpam-5323	262	4	e.	e.	PROPN
ejpam-5323	262	5	csókási	csókási	PROPN
ejpam-5323	262	6	,	,	PUNCT
ejpam-5323	262	7	j.	j.	PROPN
ejpam-5323	262	8	hirjak	hirjak	PROPN
ejpam-5323	262	9	/	/	SYM
ejpam-5323	262	10	eur	eur	PROPN
ejpam-5323	262	11	.	.	PUNCT
ejpam-5323	263	1	j.	j.	PROPN
ejpam-5323	263	2	pure	pure	PROPN
ejpam-5323	263	3	appl	appl	PROPN
ejpam-5323	263	4	.	.	PROPN
ejpam-5323	263	5	math	math	PROPN
ejpam-5323	263	6	,	,	PUNCT
ejpam-5323	263	7	17	17	NUM
ejpam-5323	263	8	(	(	PUNCT
ejpam-5323	263	9	3	3	NUM
ejpam-5323	263	10	)	)	PUNCT
ejpam-5323	263	11	(	(	PUNCT
ejpam-5323	263	12	2024	2024	NUM
ejpam-5323	263	13	)	)	PUNCT
ejpam-5323	263	14	,	,	PUNCT
ejpam-5323	263	15	2127	2127	NUM
ejpam-5323	263	16	-	-	SYM
ejpam-5323	263	17	2141	2141	NUM
ejpam-5323	263	18	2137	2137	NUM
ejpam-5323	263	19	definition	definition	NOUN
ejpam-5323	263	20	6	6	NUM
ejpam-5323	263	21	.	.	PUNCT
ejpam-5323	264	1	let	let	VERB
ejpam-5323	264	2	r	r	PRON
ejpam-5323	264	3	be	be	AUX
ejpam-5323	264	4	a	a	DET
ejpam-5323	264	5	primitive	primitive	ADJ
ejpam-5323	264	6	pythagorean	pythagorean	NOUN
ejpam-5323	264	7	triple	triple	NOUN
ejpam-5323	264	8	and	and	CCONJ
ejpam-5323	264	9	let	let	VERB
ejpam-5323	264	10	m1r	m1r	NOUN
ejpam-5323	264	11	⊤,m2r	⊤,m2r	X
ejpam-5323	264	12	⊤	⊤	NOUN
ejpam-5323	264	13	,	,	PUNCT
ejpam-5323	264	14	m3r	m3r	PUNCT
ejpam-5323	264	15	⊤	⊤	NOUN
ejpam-5323	264	16	be	be	VERB
ejpam-5323	264	17	its	its	PRON
ejpam-5323	264	18	descendants	descendant	NOUN
ejpam-5323	264	19	in	in	ADP
ejpam-5323	264	20	price	price	NOUN
ejpam-5323	264	21	’s	’s	PART
ejpam-5323	264	22	tree	tree	NOUN
ejpam-5323	264	23	.	.	PUNCT
ejpam-5323	265	1	the	the	DET
ejpam-5323	265	2	triangle	triangle	NOUN
ejpam-5323	265	3	with	with	ADP
ejpam-5323	265	4	vertices	vertex	NOUN
ejpam-5323	265	5	with	with	ADP
ejpam-5323	265	6	the	the	DET
ejpam-5323	265	7	coordinates	coordinate	NOUN
ejpam-5323	265	8	m1r	m1r	X
ejpam-5323	265	9	⊤,m2r	⊤,m2r	NUM
ejpam-5323	265	10	⊤,m3r	⊤,m3r	NUM
ejpam-5323	265	11	⊤	⊤	NOUN
ejpam-5323	265	12	is	be	AUX
ejpam-5323	265	13	called	call	VERB
ejpam-5323	265	14	the	the	DET
ejpam-5323	265	15	descendant	descendant	ADJ
ejpam-5323	265	16	triangle	triangle	NOUN
ejpam-5323	265	17	of	of	ADP
ejpam-5323	265	18	r	r	NOUN
ejpam-5323	265	19	in	in	ADP
ejpam-5323	265	20	price	price	NOUN
ejpam-5323	265	21	’s	’s	PART
ejpam-5323	265	22	tree	tree	NOUN
ejpam-5323	265	23	,	,	PUNCT
ejpam-5323	265	24	and	and	CCONJ
ejpam-5323	265	25	we	we	PRON
ejpam-5323	265	26	denote	denote	VERB
ejpam-5323	265	27	it	it	PRON
ejpam-5323	265	28	by	by	ADP
ejpam-5323	265	29	△	△	PROPN
ejpam-5323	265	30	p	p	X
ejpam-5323	265	31	(	(	PUNCT
ejpam-5323	265	32	r	r	NOUN
ejpam-5323	265	33	)	)	PUNCT
ejpam-5323	265	34	.	.	PUNCT
ejpam-5323	266	1	proposition	proposition	NOUN
ejpam-5323	266	2	8	8	NUM
ejpam-5323	266	3	.	.	PUNCT
ejpam-5323	267	1	let	let	VERB
ejpam-5323	267	2	r	r	NOUN
ejpam-5323	267	3	=	=	SYM
ejpam-5323	267	4	(	(	PUNCT
ejpam-5323	267	5	a	a	DET
ejpam-5323	267	6	,	,	PUNCT
ejpam-5323	267	7	b	b	NOUN
ejpam-5323	267	8	,	,	PUNCT
ejpam-5323	267	9	c	c	AUX
ejpam-5323	267	10	)	)	PUNCT
ejpam-5323	267	11	be	be	AUX
ejpam-5323	267	12	a	a	DET
ejpam-5323	267	13	primitive	primitive	ADJ
ejpam-5323	267	14	pythagorean	pythagorean	NOUN
ejpam-5323	267	15	triple	triple	NOUN
ejpam-5323	267	16	.	.	PUNCT
ejpam-5323	268	1	then	then	ADV
ejpam-5323	268	2	the	the	DET
ejpam-5323	268	3	triangle	triangle	NOUN
ejpam-5323	268	4	△	△	X
ejpam-5323	268	5	p	p	X
ejpam-5323	268	6	(	(	PUNCT
ejpam-5323	268	7	r	r	NOUN
ejpam-5323	268	8	)	)	PUNCT
ejpam-5323	268	9	belongs	belong	VERB
ejpam-5323	268	10	to	to	ADP
ejpam-5323	268	11	the	the	DET
ejpam-5323	268	12	plane	plane	NOUN
ejpam-5323	268	13	(	(	PUNCT
ejpam-5323	268	14	2a)x+	2a)x+	NUM
ejpam-5323	268	15	(	(	PUNCT
ejpam-5323	268	16	2a−	2a−	NUM
ejpam-5323	268	17	b+	b+	ADJ
ejpam-5323	268	18	c)y	c)y	X
ejpam-5323	268	19	+	+	CCONJ
ejpam-5323	268	20	(	(	PUNCT
ejpam-5323	268	21	−2a+	−2a+	PROPN
ejpam-5323	268	22	2b−	2b−	NUM
ejpam-5323	268	23	2c)z	2c)z	NUM
ejpam-5323	268	24	+	+	CCONJ
ejpam-5323	268	25	2ab−	2ab−	NOUN
ejpam-5323	268	26	2ac+	2ac+	NUM
ejpam-5323	268	27	4bc−	4bc−	NUM
ejpam-5323	268	28	4b2	4b2	NUM
ejpam-5323	268	29	=	=	SYM
ejpam-5323	268	30	0	0	NUM
ejpam-5323	268	31	.	.	PUNCT
ejpam-5323	268	32	(	(	PUNCT
ejpam-5323	268	33	4	4	X
ejpam-5323	268	34	)	)	PUNCT
ejpam-5323	268	35	proof	proof	NOUN
ejpam-5323	268	36	.	.	PUNCT
ejpam-5323	269	1	according	accord	VERB
ejpam-5323	269	2	to	to	ADP
ejpam-5323	269	3	the	the	DET
ejpam-5323	269	4	proposition	proposition	NOUN
ejpam-5323	269	5	7	7	NUM
ejpam-5323	269	6	,	,	PUNCT
ejpam-5323	269	7	the	the	DET
ejpam-5323	269	8	vertices	vertex	NOUN
ejpam-5323	269	9	m1r	m1r	X
ejpam-5323	269	10	⊤,m2r	⊤,m2r	NUM
ejpam-5323	269	11	⊤,m3r	⊤,m3r	NUM
ejpam-5323	269	12	⊤	⊤	NOUN
ejpam-5323	269	13	form	form	VERB
ejpam-5323	269	14	a	a	DET
ejpam-5323	269	15	triangle	triangle	NOUN
ejpam-5323	269	16	,	,	PUNCT
ejpam-5323	269	17	therefore	therefore	ADV
ejpam-5323	269	18	,	,	PUNCT
ejpam-5323	269	19	they	they	PRON
ejpam-5323	269	20	define	define	VERB
ejpam-5323	269	21	a	a	DET
ejpam-5323	269	22	plane	plane	NOUN
ejpam-5323	269	23	.	.	PUNCT
ejpam-5323	270	1	we	we	PRON
ejpam-5323	270	2	consider	consider	VERB
ejpam-5323	270	3	the	the	DET
ejpam-5323	270	4	vectors	vector	NOUN
ejpam-5323	270	5	p⃗	p⃗	NOUN
ejpam-5323	270	6	=	=	SYM
ejpam-5323	270	7	(	(	PUNCT
ejpam-5323	270	8	m2	m2	PROPN
ejpam-5323	270	9	−	−	PROPN
ejpam-5323	270	10	m1)r	m1)r	NOUN
ejpam-5323	270	11	⊤	⊤	NOUN
ejpam-5323	270	12	=	=	SYM
ejpam-5323	270	13	(	(	PUNCT
ejpam-5323	270	14	2c	2c	NUM
ejpam-5323	270	15	,	,	PUNCT
ejpam-5323	270	16	4a−	4a−	PROPN
ejpam-5323	270	17	4b	4b	NOUN
ejpam-5323	270	18	,	,	PUNCT
ejpam-5323	270	19	4a−	4a−	PROPN
ejpam-5323	270	20	2b	2b	NUM
ejpam-5323	270	21	)	)	PUNCT
ejpam-5323	270	22	and	and	CCONJ
ejpam-5323	270	23	q⃗	q⃗	PROPN
ejpam-5323	270	24	=	=	SYM
ejpam-5323	270	25	(	(	PUNCT
ejpam-5323	270	26	m3	m3	PROPN
ejpam-5323	270	27	−m1)r	−m1)r	PROPN
ejpam-5323	270	28	⊤	⊤	PROPN
ejpam-5323	270	29	=	=	SYM
ejpam-5323	270	30	(	(	PUNCT
ejpam-5323	270	31	−2b+2c	−2b+2c	ADJ
ejpam-5323	270	32	,	,	PUNCT
ejpam-5323	270	33	4a	4a	NUM
ejpam-5323	270	34	,	,	PUNCT
ejpam-5323	270	35	4a	4a	NUM
ejpam-5323	270	36	)	)	PUNCT
ejpam-5323	270	37	and	and	CCONJ
ejpam-5323	270	38	we	we	PRON
ejpam-5323	270	39	compute	compute	VERB
ejpam-5323	270	40	the	the	DET
ejpam-5323	270	41	normal	normal	ADJ
ejpam-5323	270	42	vector	vector	NOUN
ejpam-5323	270	43	of	of	ADP
ejpam-5323	270	44	the	the	DET
ejpam-5323	270	45	wanted	wanted	ADJ
ejpam-5323	270	46	plane	plane	NOUN
ejpam-5323	270	47	as	as	ADP
ejpam-5323	270	48	cross	cross	NOUN
ejpam-5323	270	49	product	product	NOUN
ejpam-5323	270	50	of	of	ADP
ejpam-5323	270	51	these	these	DET
ejpam-5323	270	52	vectors	vector	NOUN
ejpam-5323	270	53	:	:	PUNCT
ejpam-5323	270	54	p⃗×	p⃗×	PROPN
ejpam-5323	270	55	q⃗	q⃗	PROPN
ejpam-5323	270	56	=	=	SYM
ejpam-5323	270	57	(	(	PUNCT
ejpam-5323	270	58	−8ab,−8ab+	−8ab,−8ab+	PROPN
ejpam-5323	270	59	4b2	4b2	NUM
ejpam-5323	270	60	−	−	PROPN
ejpam-5323	270	61	4bc	4bc	NOUN
ejpam-5323	270	62	,	,	PUNCT
ejpam-5323	270	63	8ab+	8ab+	PROPN
ejpam-5323	270	64	8bc−	8bc−	NUM
ejpam-5323	270	65	8b2	8b2	NUM
ejpam-5323	270	66	)	)	PUNCT
ejpam-5323	271	1	≈	≈	PROPN
ejpam-5323	271	2	(	(	PUNCT
ejpam-5323	271	3	2a	2a	NUM
ejpam-5323	271	4	,	,	PUNCT
ejpam-5323	271	5	2a−	2a−	NUM
ejpam-5323	271	6	b+	b+	AUX
ejpam-5323	271	7	c,−2a+	c,−2a+	VERB
ejpam-5323	271	8	2b−	2b−	NUM
ejpam-5323	271	9	2c	2c	NUM
ejpam-5323	271	10	)	)	PUNCT
ejpam-5323	271	11	.	.	PUNCT
ejpam-5323	272	1	hence	hence	ADV
ejpam-5323	272	2	,	,	PUNCT
ejpam-5323	272	3	(	(	PUNCT
ejpam-5323	272	4	2a)x+(2a−	2a)x+(2a−	PROPN
ejpam-5323	272	5	b+	b+	VERB
ejpam-5323	272	6	c)y+(−2a+2b−2c)z+d	c)y+(−2a+2b−2c)z+d	PROPN
ejpam-5323	272	7	=	=	SYM
ejpam-5323	272	8	0	0	NUM
ejpam-5323	272	9	is	be	AUX
ejpam-5323	272	10	the	the	DET
ejpam-5323	272	11	equation	equation	NOUN
ejpam-5323	272	12	of	of	ADP
ejpam-5323	272	13	wanted	wanted	ADJ
ejpam-5323	272	14	plane	plane	NOUN
ejpam-5323	272	15	for	for	ADP
ejpam-5323	272	16	some	some	DET
ejpam-5323	272	17	d	d	PROPN
ejpam-5323	272	18	∈	∈	PROPN
ejpam-5323	272	19	r.	r.	PROPN
ejpam-5323	272	20	since	since	SCONJ
ejpam-5323	272	21	m1r	m1r	PROPN
ejpam-5323	272	22	⊤	⊤	PROPN
ejpam-5323	272	23	belongs	belong	VERB
ejpam-5323	272	24	to	to	ADP
ejpam-5323	272	25	this	this	DET
ejpam-5323	272	26	plane	plane	NOUN
ejpam-5323	272	27	,	,	PUNCT
ejpam-5323	272	28	we	we	PRON
ejpam-5323	272	29	get	get	VERB
ejpam-5323	272	30	(	(	PUNCT
ejpam-5323	272	31	2a)(2a+	2a)(2a+	NUM
ejpam-5323	272	32	b−	b−	NOUN
ejpam-5323	272	33	c	c	NOUN
ejpam-5323	272	34	)	)	PUNCT
ejpam-5323	273	1	+	+	CCONJ
ejpam-5323	273	2	(	(	PUNCT
ejpam-5323	273	3	2a−	2a−	NUM
ejpam-5323	273	4	b+	b+	PUNCT
ejpam-5323	273	5	c)(−2a+	c)(−2a+	NOUN
ejpam-5323	273	6	2b+	2b+	NUM
ejpam-5323	273	7	2c	2c	NUM
ejpam-5323	273	8	)	)	PUNCT
ejpam-5323	274	1	+	+	CCONJ
ejpam-5323	274	2	(	(	PUNCT
ejpam-5323	274	3	−2a+	−2a+	PROPN
ejpam-5323	274	4	2b−	2b−	NUM
ejpam-5323	274	5	2c)(−2a+	2c)(−2a+	NUM
ejpam-5323	274	6	b+	b+	X
ejpam-5323	274	7	3c	3c	NUM
ejpam-5323	274	8	)	)	PUNCT
ejpam-5323	275	1	+	+	CCONJ
ejpam-5323	275	2	d	d	NOUN
ejpam-5323	275	3	=	=	SYM
ejpam-5323	275	4	0	0	NUM
ejpam-5323	275	5	.	.	PUNCT
ejpam-5323	276	1	moreover	moreover	ADV
ejpam-5323	276	2	,	,	PUNCT
ejpam-5323	276	3	c2	c2	PROPN
ejpam-5323	276	4	=	=	PROPN
ejpam-5323	276	5	a2	a2	PROPN
ejpam-5323	276	6	+	+	CCONJ
ejpam-5323	276	7	b2	b2	NOUN
ejpam-5323	276	8	,	,	PUNCT
ejpam-5323	276	9	which	which	PRON
ejpam-5323	276	10	yields	yield	VERB
ejpam-5323	276	11	d	d	X
ejpam-5323	276	12	=	=	SYM
ejpam-5323	276	13	2ab−	2ab−	NUM
ejpam-5323	276	14	2ac+4bc−	2ac+4bc−	NUM
ejpam-5323	276	15	4b2	4b2	NOUN
ejpam-5323	276	16	.	.	PUNCT
ejpam-5323	277	1	therefore	therefore	ADV
ejpam-5323	277	2	,	,	PUNCT
ejpam-5323	277	3	△	△	X
ejpam-5323	277	4	p	p	X
ejpam-5323	277	5	(	(	PUNCT
ejpam-5323	277	6	r	r	NOUN
ejpam-5323	277	7	)	)	PUNCT
ejpam-5323	277	8	belongs	belong	VERB
ejpam-5323	277	9	to	to	ADP
ejpam-5323	277	10	the	the	DET
ejpam-5323	277	11	plane	plane	NOUN
ejpam-5323	277	12	(	(	PUNCT
ejpam-5323	277	13	2a)x+	2a)x+	NUM
ejpam-5323	277	14	(	(	PUNCT
ejpam-5323	277	15	2a−	2a−	NUM
ejpam-5323	277	16	b+	b+	ADJ
ejpam-5323	277	17	c)y	c)y	X
ejpam-5323	277	18	+	+	CCONJ
ejpam-5323	277	19	(	(	PUNCT
ejpam-5323	277	20	−2a+	−2a+	PROPN
ejpam-5323	277	21	2b−	2b−	NUM
ejpam-5323	277	22	2c)z	2c)z	NUM
ejpam-5323	277	23	+	+	CCONJ
ejpam-5323	277	24	2ab−	2ab−	NOUN
ejpam-5323	277	25	2ac+	2ac+	NUM
ejpam-5323	277	26	4bc−	4bc−	NUM
ejpam-5323	277	27	4b2	4b2	NUM
ejpam-5323	277	28	=	=	SYM
ejpam-5323	277	29	0	0	X
ejpam-5323	277	30	.	.	PUNCT
ejpam-5323	277	31	notice	notice	VERB
ejpam-5323	277	32	the	the	DET
ejpam-5323	277	33	difference	difference	NOUN
ejpam-5323	277	34	between	between	ADP
ejpam-5323	277	35	price	price	NOUN
ejpam-5323	277	36	’s	’s	PART
ejpam-5323	277	37	tree	tree	NOUN
ejpam-5323	277	38	and	and	CCONJ
ejpam-5323	277	39	berggren	berggren	PROPN
ejpam-5323	277	40	’s	’s	PART
ejpam-5323	277	41	tree	tree	NOUN
ejpam-5323	277	42	.	.	PUNCT
ejpam-5323	278	1	in	in	ADP
ejpam-5323	278	2	berggren	berggren	PROPN
ejpam-5323	278	3	’s	’s	PART
ejpam-5323	278	4	tree	tree	NOUN
ejpam-5323	278	5	,	,	PUNCT
ejpam-5323	278	6	all	all	DET
ejpam-5323	278	7	descendant	descendant	ADJ
ejpam-5323	278	8	triangles	triangle	NOUN
ejpam-5323	278	9	△	△	NOUN
ejpam-5323	278	10	b(p	b(p	X
ejpam-5323	278	11	)	)	PUNCT
ejpam-5323	278	12	belong	belong	VERB
ejpam-5323	278	13	to	to	ADP
ejpam-5323	278	14	planes	plane	NOUN
ejpam-5323	278	15	parallel	parallel	NOUN
ejpam-5323	278	16	with	with	ADP
ejpam-5323	278	17	the	the	DET
ejpam-5323	278	18	plane	plane	NOUN
ejpam-5323	278	19	2x	2x	NUM
ejpam-5323	279	1	+	+	CCONJ
ejpam-5323	279	2	2y	2y	NUM
ejpam-5323	279	3	−	−	NOUN
ejpam-5323	279	4	3z	3z	NUM
ejpam-5323	279	5	=	=	SYM
ejpam-5323	279	6	0	0	PUNCT
ejpam-5323	280	1	(	(	PUNCT
ejpam-5323	280	2	see	see	VERB
ejpam-5323	280	3	the	the	DET
ejpam-5323	280	4	proposition	proposition	NOUN
ejpam-5323	280	5	2	2	NUM
ejpam-5323	280	6	)	)	PUNCT
ejpam-5323	280	7	.	.	PUNCT
ejpam-5323	281	1	in	in	ADP
ejpam-5323	281	2	general	general	ADJ
ejpam-5323	281	3	,	,	PUNCT
ejpam-5323	281	4	the	the	DET
ejpam-5323	281	5	results	result	NOUN
ejpam-5323	281	6	in	in	ADP
ejpam-5323	281	7	berggren	berggren	PROPN
ejpam-5323	281	8	’s	’s	PART
ejpam-5323	281	9	tree	tree	NOUN
ejpam-5323	281	10	are	be	AUX
ejpam-5323	281	11	usually	usually	ADV
ejpam-5323	281	12	nicer	nice	ADJ
ejpam-5323	281	13	than	than	ADP
ejpam-5323	281	14	analogous	analogous	ADJ
ejpam-5323	281	15	results	result	NOUN
ejpam-5323	281	16	in	in	ADP
ejpam-5323	281	17	price	price	NOUN
ejpam-5323	281	18	’s	’s	PART
ejpam-5323	281	19	tree	tree	NOUN
ejpam-5323	281	20	.	.	PUNCT
ejpam-5323	282	1	also	also	ADV
ejpam-5323	282	2	,	,	PUNCT
ejpam-5323	282	3	similarly	similarly	ADV
ejpam-5323	282	4	to	to	ADP
ejpam-5323	282	5	berggren	berggren	PROPN
ejpam-5323	282	6	’s	’s	PART
ejpam-5323	282	7	tree	tree	NOUN
ejpam-5323	282	8	,	,	PUNCT
ejpam-5323	282	9	no	no	DET
ejpam-5323	282	10	plane	plane	NOUN
ejpam-5323	282	11	defined	define	VERB
ejpam-5323	282	12	by	by	ADP
ejpam-5323	282	13	a	a	DET
ejpam-5323	282	14	descendant	descendant	ADJ
ejpam-5323	282	15	triangle	triangle	NOUN
ejpam-5323	282	16	△	△	X
ejpam-5323	282	17	p	p	NOUN
ejpam-5323	282	18	(	(	PUNCT
ejpam-5323	282	19	r	r	NOUN
ejpam-5323	282	20	)	)	PUNCT
ejpam-5323	282	21	in	in	ADP
ejpam-5323	282	22	price	price	NOUN
ejpam-5323	282	23	’s	’s	PART
ejpam-5323	282	24	tree	tree	NOUN
ejpam-5323	282	25	passes	pass	VERB
ejpam-5323	282	26	through	through	ADP
ejpam-5323	282	27	the	the	DET
ejpam-5323	282	28	origin	origin	NOUN
ejpam-5323	282	29	(	(	PUNCT
ejpam-5323	282	30	0	0	NUM
ejpam-5323	282	31	,	,	PUNCT
ejpam-5323	282	32	0	0	NUM
ejpam-5323	282	33	,	,	PUNCT
ejpam-5323	282	34	0	0	NUM
ejpam-5323	282	35	)	)	PUNCT
ejpam-5323	282	36	.	.	PUNCT
ejpam-5323	283	1	proposition	proposition	NOUN
ejpam-5323	283	2	9	9	NUM
ejpam-5323	283	3	.	.	PUNCT
ejpam-5323	284	1	let	let	AUX
ejpam-5323	284	2	(	(	PUNCT
ejpam-5323	284	3	a	a	DET
ejpam-5323	284	4	,	,	PUNCT
ejpam-5323	284	5	b	b	NOUN
ejpam-5323	284	6	,	,	PUNCT
ejpam-5323	284	7	c	c	NOUN
ejpam-5323	284	8	)	)	PUNCT
ejpam-5323	284	9	be	be	AUX
ejpam-5323	284	10	a	a	DET
ejpam-5323	284	11	primitive	primitive	ADJ
ejpam-5323	284	12	pythagorean	pythagorean	NOUN
ejpam-5323	284	13	triple	triple	NOUN
ejpam-5323	284	14	.	.	PUNCT
ejpam-5323	285	1	the	the	DET
ejpam-5323	285	2	plane	plane	NOUN
ejpam-5323	285	3	(	(	PUNCT
ejpam-5323	285	4	2a)x	2a)x	NUM
ejpam-5323	285	5	+	+	CCONJ
ejpam-5323	285	6	(	(	PUNCT
ejpam-5323	285	7	2a	2a	NUM
ejpam-5323	285	8	−	−	PROPN
ejpam-5323	285	9	b	b	NOUN
ejpam-5323	285	10	+	+	CCONJ
ejpam-5323	285	11	c)y	c)y	X
ejpam-5323	285	12	+	+	CCONJ
ejpam-5323	285	13	(	(	PUNCT
ejpam-5323	285	14	−2a	−2a	X
ejpam-5323	285	15	+	+	NUM
ejpam-5323	285	16	2b	2b	NUM
ejpam-5323	285	17	−	−	PROPN
ejpam-5323	285	18	2c)z	2c)z	NUM
ejpam-5323	285	19	+	+	CCONJ
ejpam-5323	285	20	2ab	2ab	NOUN
ejpam-5323	285	21	−	−	PROPN
ejpam-5323	285	22	2ac	2ac	PROPN
ejpam-5323	286	1	+	+	CCONJ
ejpam-5323	286	2	4bc	4bc	ADJ
ejpam-5323	286	3	−	−	NOUN
ejpam-5323	286	4	4b2	4b2	NUM
ejpam-5323	286	5	=	=	SYM
ejpam-5323	286	6	0	0	PROPN
ejpam-5323	286	7	does	do	AUX
ejpam-5323	286	8	not	not	PART
ejpam-5323	286	9	pass	pass	VERB
ejpam-5323	286	10	through	through	ADP
ejpam-5323	286	11	the	the	DET
ejpam-5323	286	12	origin	origin	NOUN
ejpam-5323	286	13	(	(	PUNCT
ejpam-5323	286	14	0	0	NUM
ejpam-5323	286	15	,	,	PUNCT
ejpam-5323	286	16	0	0	NUM
ejpam-5323	286	17	,	,	PUNCT
ejpam-5323	286	18	0	0	NUM
ejpam-5323	286	19	)	)	PUNCT
ejpam-5323	286	20	.	.	PUNCT
ejpam-5323	287	1	proof	proof	NOUN
ejpam-5323	287	2	.	.	PUNCT
ejpam-5323	288	1	if	if	SCONJ
ejpam-5323	288	2	(	(	PUNCT
ejpam-5323	288	3	0	0	NUM
ejpam-5323	288	4	,	,	PUNCT
ejpam-5323	288	5	0	0	NUM
ejpam-5323	288	6	,	,	PUNCT
ejpam-5323	288	7	0	0	NUM
ejpam-5323	288	8	)	)	PUNCT
ejpam-5323	288	9	belongs	belong	VERB
ejpam-5323	288	10	to	to	ADP
ejpam-5323	288	11	this	this	DET
ejpam-5323	288	12	plane	plane	NOUN
ejpam-5323	288	13	,	,	PUNCT
ejpam-5323	288	14	then	then	ADV
ejpam-5323	288	15	2ab	2ab	NOUN
ejpam-5323	288	16	−	−	PROPN
ejpam-5323	289	1	2ac	2ac	PROPN
ejpam-5323	289	2	+	+	CCONJ
ejpam-5323	289	3	4bc	4bc	ADJ
ejpam-5323	289	4	−	−	NOUN
ejpam-5323	289	5	4b2	4b2	NUM
ejpam-5323	289	6	=	=	NOUN
ejpam-5323	289	7	0	0	NUM
ejpam-5323	289	8	.	.	PUNCT
ejpam-5323	290	1	after	after	ADP
ejpam-5323	290	2	some	some	DET
ejpam-5323	290	3	modifications	modification	NOUN
ejpam-5323	290	4	,	,	PUNCT
ejpam-5323	290	5	we	we	PRON
ejpam-5323	290	6	get	get	VERB
ejpam-5323	290	7	ab−	ab−	PRON
ejpam-5323	290	8	ac+	ac+	NOUN
ejpam-5323	290	9	2bc−	2bc−	NUM
ejpam-5323	290	10	2b2	2b2	NUM
ejpam-5323	290	11	=	=	SYM
ejpam-5323	290	12	0	0	NUM
ejpam-5323	290	13	b(a−	b(a−	PROPN
ejpam-5323	290	14	2b)−	2b)−	NUM
ejpam-5323	290	15	c(a−	c(a−	PROPN
ejpam-5323	290	16	2b	2b	NOUN
ejpam-5323	290	17	)	)	PUNCT
ejpam-5323	290	18	=	=	SYM
ejpam-5323	290	19	0	0	PUNCT
ejpam-5323	291	1	(	(	PUNCT
ejpam-5323	291	2	b−	b−	PROPN
ejpam-5323	291	3	c)(a−	c)(a−	PROPN
ejpam-5323	291	4	2b	2b	NOUN
ejpam-5323	291	5	)	)	PUNCT
ejpam-5323	292	1	=	=	SYM
ejpam-5323	292	2	0	0	NUM
ejpam-5323	292	3	which	which	PRON
ejpam-5323	292	4	holds	hold	VERB
ejpam-5323	292	5	iff	iff	PROPN
ejpam-5323	292	6	b	b	PROPN
ejpam-5323	292	7	−	−	PROPN
ejpam-5323	292	8	c	c	NOUN
ejpam-5323	292	9	=	=	SYM
ejpam-5323	292	10	0	0	NUM
ejpam-5323	292	11	or	or	CCONJ
ejpam-5323	292	12	a	a	DET
ejpam-5323	292	13	−	−	NOUN
ejpam-5323	292	14	2b	2b	NUM
ejpam-5323	292	15	=	=	SYM
ejpam-5323	292	16	0	0	X
ejpam-5323	292	17	.	.	PUNCT
ejpam-5323	293	1	however	however	ADV
ejpam-5323	293	2	,	,	PUNCT
ejpam-5323	293	3	b	b	PROPN
ejpam-5323	294	1	−	−	NOUN
ejpam-5323	294	2	c	c	NOUN
ejpam-5323	294	3	=	=	SYM
ejpam-5323	294	4	0	0	PUNCT
ejpam-5323	295	1	=	=	NOUN
ejpam-5323	295	2	⇒	⇒	X
ejpam-5323	295	3	b	b	X
ejpam-5323	295	4	=	=	SYM
ejpam-5323	295	5	c	c	PROPN
ejpam-5323	295	6	,	,	PUNCT
ejpam-5323	295	7	a	a	DET
ejpam-5323	295	8	contradiction	contradiction	NOUN
ejpam-5323	295	9	with	with	ADP
ejpam-5323	295	10	(	(	PUNCT
ejpam-5323	295	11	a	a	DET
ejpam-5323	295	12	,	,	PUNCT
ejpam-5323	295	13	b	b	NOUN
ejpam-5323	295	14	,	,	PUNCT
ejpam-5323	295	15	c	c	NOUN
ejpam-5323	295	16	)	)	PUNCT
ejpam-5323	295	17	being	be	AUX
ejpam-5323	295	18	a	a	DET
ejpam-5323	295	19	ppt	ppt	NOUN
ejpam-5323	295	20	,	,	PUNCT
ejpam-5323	295	21	and	and	CCONJ
ejpam-5323	295	22	a	a	DET
ejpam-5323	295	23	−	−	NOUN
ejpam-5323	295	24	2b	2b	NUM
ejpam-5323	295	25	=	=	SYM
ejpam-5323	295	26	0	0	PUNCT
ejpam-5323	296	1	=	=	NOUN
ejpam-5323	296	2	⇒	⇒	VERB
ejpam-5323	296	3	a	a	DET
ejpam-5323	296	4	=	=	SYM
ejpam-5323	296	5	2b	2b	NOUN
ejpam-5323	296	6	which	which	PRON
ejpam-5323	296	7	is	be	AUX
ejpam-5323	296	8	a	a	DET
ejpam-5323	296	9	contradiction	contradiction	NOUN
ejpam-5323	296	10	with	with	ADP
ejpam-5323	296	11	a	a	DET
ejpam-5323	296	12	being	be	AUX
ejpam-5323	296	13	odd	odd	ADJ
ejpam-5323	296	14	and	and	CCONJ
ejpam-5323	296	15	2b	2b	NUM
ejpam-5323	296	16	being	be	AUX
ejpam-5323	296	17	even	even	ADV
ejpam-5323	296	18	.	.	PUNCT
ejpam-5323	297	1	from	from	ADP
ejpam-5323	297	2	the	the	DET
ejpam-5323	297	3	propositions	proposition	NOUN
ejpam-5323	297	4	4	4	NUM
ejpam-5323	297	5	and	and	CCONJ
ejpam-5323	297	6	5	5	NUM
ejpam-5323	297	7	,	,	PUNCT
ejpam-5323	297	8	we	we	PRON
ejpam-5323	297	9	already	already	ADV
ejpam-5323	297	10	know	know	VERB
ejpam-5323	297	11	that	that	SCONJ
ejpam-5323	297	12	in	in	ADP
ejpam-5323	297	13	berggren	berggren	PROPN
ejpam-5323	297	14	’s	’s	PART
ejpam-5323	297	15	tree	tree	NOUN
ejpam-5323	297	16	,	,	PUNCT
ejpam-5323	297	17	the	the	DET
ejpam-5323	297	18	descendant	descendant	ADJ
ejpam-5323	297	19	triangle	triangle	NOUN
ejpam-5323	297	20	△	△	NOUN
ejpam-5323	297	21	b(p	b(p	X
ejpam-5323	297	22	)	)	PUNCT
ejpam-5323	297	23	fails	fail	VERB
ejpam-5323	297	24	to	to	PART
ejpam-5323	297	25	be	be	AUX
ejpam-5323	297	26	either	either	CCONJ
ejpam-5323	297	27	a	a	DET
ejpam-5323	297	28	right	right	ADJ
ejpam-5323	297	29	triangle	triangle	NOUN
ejpam-5323	297	30	or	or	CCONJ
ejpam-5323	297	31	an	an	DET
ejpam-5323	297	32	isosceles	isoscele	NOUN
ejpam-5323	297	33	triangle	triangle	NOUN
ejpam-5323	297	34	.	.	PUNCT
ejpam-5323	298	1	the	the	DET
ejpam-5323	298	2	following	follow	VERB
ejpam-5323	298	3	propositions	proposition	NOUN
ejpam-5323	298	4	offer	offer	VERB
ejpam-5323	298	5	the	the	DET
ejpam-5323	298	6	analogous	analogous	ADJ
ejpam-5323	298	7	results	result	NOUN
ejpam-5323	298	8	in	in	ADP
ejpam-5323	298	9	price	price	NOUN
ejpam-5323	298	10	’s	’s	PART
ejpam-5323	298	11	tree	tree	NOUN
ejpam-5323	298	12	.	.	PUNCT
ejpam-5323	299	1	l.	l.	PROPN
ejpam-5323	299	2	kőszegyová	kőszegyová	PROPN
ejpam-5323	299	3	,	,	PUNCT
ejpam-5323	299	4	e.	e.	PROPN
ejpam-5323	299	5	csókási	csókási	PROPN
ejpam-5323	299	6	,	,	PUNCT
ejpam-5323	299	7	j.	j.	PROPN
ejpam-5323	299	8	hirjak	hirjak	PROPN
ejpam-5323	299	9	/	/	SYM
ejpam-5323	299	10	eur	eur	PROPN
ejpam-5323	299	11	.	.	PUNCT
ejpam-5323	300	1	j.	j.	PROPN
ejpam-5323	300	2	pure	pure	PROPN
ejpam-5323	300	3	appl	appl	PROPN
ejpam-5323	300	4	.	.	PROPN
ejpam-5323	300	5	math	math	PROPN
ejpam-5323	300	6	,	,	PUNCT
ejpam-5323	300	7	17	17	NUM
ejpam-5323	300	8	(	(	PUNCT
ejpam-5323	300	9	3	3	NUM
ejpam-5323	300	10	)	)	PUNCT
ejpam-5323	300	11	(	(	PUNCT
ejpam-5323	300	12	2024	2024	NUM
ejpam-5323	300	13	)	)	PUNCT
ejpam-5323	300	14	,	,	PUNCT
ejpam-5323	300	15	2127	2127	NUM
ejpam-5323	300	16	-	-	SYM
ejpam-5323	300	17	2141	2141	NUM
ejpam-5323	300	18	2138	2138	NUM
ejpam-5323	300	19	proposition	proposition	NOUN
ejpam-5323	300	20	10	10	NUM
ejpam-5323	300	21	.	.	PUNCT
ejpam-5323	301	1	let	let	VERB
ejpam-5323	301	2	r	r	PRON
ejpam-5323	301	3	be	be	AUX
ejpam-5323	301	4	a	a	DET
ejpam-5323	301	5	primitive	primitive	ADJ
ejpam-5323	301	6	pythagorean	pythagorean	NOUN
ejpam-5323	301	7	triple	triple	NOUN
ejpam-5323	301	8	.	.	PUNCT
ejpam-5323	302	1	the	the	DET
ejpam-5323	302	2	triangle	triangle	NOUN
ejpam-5323	302	3	△	△	X
ejpam-5323	302	4	p	p	X
ejpam-5323	302	5	(	(	PUNCT
ejpam-5323	302	6	r	r	NOUN
ejpam-5323	302	7	)	)	PUNCT
ejpam-5323	302	8	is	be	AUX
ejpam-5323	302	9	a	a	DET
ejpam-5323	302	10	nonright	nonright	ADJ
ejpam-5323	302	11	triangle	triangle	NOUN
ejpam-5323	302	12	.	.	PUNCT
ejpam-5323	303	1	proof	proof	NOUN
ejpam-5323	303	2	.	.	PUNCT
ejpam-5323	304	1	let	let	VERB
ejpam-5323	304	2	us	we	PRON
ejpam-5323	304	3	consider	consider	VERB
ejpam-5323	304	4	the	the	DET
ejpam-5323	304	5	vectors	vector	NOUN
ejpam-5323	304	6	p⃗	p⃗	NOUN
ejpam-5323	304	7	=	=	SYM
ejpam-5323	305	1	m2r	m2r	NUM
ejpam-5323	305	2	⊤	⊤	NOUN
ejpam-5323	305	3	−m1r	−m1r	PROPN
ejpam-5323	305	4	⊤	⊤	PROPN
ejpam-5323	305	5	=	=	SYM
ejpam-5323	305	6	(	(	PUNCT
ejpam-5323	305	7	2c	2c	NUM
ejpam-5323	305	8	,	,	PUNCT
ejpam-5323	305	9	4a−	4a−	PROPN
ejpam-5323	305	10	4b	4b	NOUN
ejpam-5323	305	11	,	,	PUNCT
ejpam-5323	305	12	4a−	4a−	PROPN
ejpam-5323	305	13	2b	2b	NUM
ejpam-5323	305	14	)	)	PUNCT
ejpam-5323	305	15	,	,	PUNCT
ejpam-5323	305	16	q⃗	q⃗	PROPN
ejpam-5323	305	17	=	=	SYM
ejpam-5323	305	18	m3r	m3r	NUM
ejpam-5323	305	19	⊤	⊤	PROPN
ejpam-5323	305	20	−m1r	−m1r	PROPN
ejpam-5323	305	21	⊤	⊤	PROPN
ejpam-5323	305	22	=	=	SYM
ejpam-5323	305	23	(	(	PUNCT
ejpam-5323	305	24	−2b+	−2b+	PROPN
ejpam-5323	305	25	2c	2c	NUM
ejpam-5323	305	26	,	,	PUNCT
ejpam-5323	305	27	4a	4a	NUM
ejpam-5323	305	28	,	,	PUNCT
ejpam-5323	305	29	4a	4a	NOUN
ejpam-5323	305	30	)	)	PUNCT
ejpam-5323	305	31	,	,	PUNCT
ejpam-5323	305	32	r⃗	r⃗	ADJ
ejpam-5323	305	33	=	=	SYM
ejpam-5323	305	34	m3r	m3r	PART
ejpam-5323	305	35	⊤	⊤	PROPN
ejpam-5323	305	36	−m2r	−m2r	PUNCT
ejpam-5323	305	37	⊤	⊤	NOUN
ejpam-5323	305	38	=	=	SYM
ejpam-5323	305	39	(	(	PUNCT
ejpam-5323	305	40	−2b	−2b	PROPN
ejpam-5323	305	41	,	,	PUNCT
ejpam-5323	305	42	4b	4b	X
ejpam-5323	305	43	,	,	PUNCT
ejpam-5323	305	44	2b	2b	NUM
ejpam-5323	305	45	)	)	PUNCT
ejpam-5323	305	46	.	.	PUNCT
ejpam-5323	306	1	to	to	PART
ejpam-5323	306	2	prove	prove	VERB
ejpam-5323	306	3	that	that	SCONJ
ejpam-5323	306	4	△	△	PROPN
ejpam-5323	306	5	p	p	X
ejpam-5323	306	6	(	(	PUNCT
ejpam-5323	306	7	r	r	NOUN
ejpam-5323	306	8	)	)	PUNCT
ejpam-5323	306	9	is	be	AUX
ejpam-5323	306	10	a	a	DET
ejpam-5323	306	11	non	non	ADJ
ejpam-5323	306	12	-	-	ADJ
ejpam-5323	306	13	right	right	ADJ
ejpam-5323	306	14	triangle	triangle	NOUN
ejpam-5323	306	15	,	,	PUNCT
ejpam-5323	306	16	it	it	PRON
ejpam-5323	306	17	is	be	AUX
ejpam-5323	306	18	sufficient	sufficient	ADJ
ejpam-5323	306	19	to	to	PART
ejpam-5323	306	20	show	show	VERB
ejpam-5323	306	21	that	that	SCONJ
ejpam-5323	306	22	p⃗	p⃗	NOUN
ejpam-5323	306	23	·	·	PUNCT
ejpam-5323	306	24	q⃗	q⃗	PROPN
ejpam-5323	306	25	̸=	̸=	PROPN
ejpam-5323	306	26	0	0	NUM
ejpam-5323	306	27	,	,	PUNCT
ejpam-5323	306	28	p⃗	p⃗	NOUN
ejpam-5323	306	29	·	·	PUNCT
ejpam-5323	306	30	r⃗	r⃗	VERB
ejpam-5323	306	31	̸=	̸=	PROPN
ejpam-5323	306	32	0	0	NUM
ejpam-5323	306	33	and	and	CCONJ
ejpam-5323	306	34	q⃗	q⃗	PROPN
ejpam-5323	306	35	·	·	PUNCT
ejpam-5323	306	36	r⃗	r⃗	VERB
ejpam-5323	306	37	̸=	̸=	PROPN
ejpam-5323	306	38	0	0	NUM
ejpam-5323	306	39	.	.	PROPN
ejpam-5323	306	40	1	1	NUM
ejpam-5323	306	41	.	.	PUNCT
ejpam-5323	306	42	)	)	PUNCT
ejpam-5323	307	1	by	by	ADP
ejpam-5323	307	2	way	way	NOUN
ejpam-5323	307	3	of	of	ADP
ejpam-5323	307	4	contradiction	contradiction	NOUN
ejpam-5323	307	5	,	,	PUNCT
ejpam-5323	307	6	let	let	VERB
ejpam-5323	307	7	us	we	PRON
ejpam-5323	307	8	assume	assume	VERB
ejpam-5323	307	9	that	that	SCONJ
ejpam-5323	307	10	p⃗	p⃗	NOUN
ejpam-5323	307	11	·	·	PUNCT
ejpam-5323	307	12	q⃗	q⃗	PROPN
ejpam-5323	307	13	=	=	SYM
ejpam-5323	307	14	0	0	PROPN
ejpam-5323	307	15	.	.	PUNCT
ejpam-5323	308	1	this	this	PRON
ejpam-5323	308	2	and	and	CCONJ
ejpam-5323	308	3	a2	a2	PROPN
ejpam-5323	308	4	+	+	CCONJ
ejpam-5323	308	5	b2	b2	NOUN
ejpam-5323	308	6	=	=	SYM
ejpam-5323	308	7	c2	c2	PROPN
ejpam-5323	308	8	yield	yield	NOUN
ejpam-5323	308	9	(	(	PUNCT
ejpam-5323	308	10	2c	2c	NUM
ejpam-5323	308	11	,	,	PUNCT
ejpam-5323	308	12	4a−	4a−	PROPN
ejpam-5323	308	13	4b	4b	NOUN
ejpam-5323	308	14	,	,	PUNCT
ejpam-5323	308	15	4a−	4a−	PROPN
ejpam-5323	308	16	2b	2b	NUM
ejpam-5323	308	17	)	)	PUNCT
ejpam-5323	308	18	·	·	PUNCT
ejpam-5323	309	1	(	(	PUNCT
ejpam-5323	309	2	−2b+	−2b+	NOUN
ejpam-5323	309	3	2c	2c	NUM
ejpam-5323	309	4	,	,	PUNCT
ejpam-5323	309	5	4a	4a	NUM
ejpam-5323	309	6	,	,	PUNCT
ejpam-5323	309	7	4a	4a	NUM
ejpam-5323	309	8	)	)	PUNCT
ejpam-5323	310	1	=	=	PUNCT
ejpam-5323	311	1	16a2	16a2	NUM
ejpam-5323	311	2	−	−	NUM
ejpam-5323	311	3	8b2	8b2	NUM
ejpam-5323	312	1	+	+	NUM
ejpam-5323	312	2	4c2	4c2	NUM
ejpam-5323	312	3	−	−	NOUN
ejpam-5323	312	4	4cb	4cb	NOUN
ejpam-5323	313	1	=	=	PUNCT
ejpam-5323	313	2	0	0	NUM
ejpam-5323	314	1	20c2	20c2	NUM
ejpam-5323	314	2	−	−	PROPN
ejpam-5323	314	3	24b2	24b2	NUM
ejpam-5323	314	4	−	−	NOUN
ejpam-5323	314	5	4bc	4bc	NOUN
ejpam-5323	314	6	=	=	PUNCT
ejpam-5323	314	7	0	0	NUM
ejpam-5323	314	8	5c2	5c2	NUM
ejpam-5323	315	1	−	−	NOUN
ejpam-5323	315	2	6b2	6b2	NUM
ejpam-5323	315	3	−	−	NOUN
ejpam-5323	315	4	bc	bc	PROPN
ejpam-5323	316	1	=	=	SYM
ejpam-5323	316	2	0	0	NUM
ejpam-5323	316	3	6b2	6b2	NUM
ejpam-5323	316	4	+	+	CCONJ
ejpam-5323	316	5	bc	bc	PROPN
ejpam-5323	316	6	=	=	SYM
ejpam-5323	316	7	5c2	5c2	PROPN
ejpam-5323	316	8	.	.	PUNCT
ejpam-5323	317	1	in	in	ADP
ejpam-5323	317	2	the	the	DET
ejpam-5323	317	3	beginning	beginning	NOUN
ejpam-5323	317	4	,	,	PUNCT
ejpam-5323	317	5	we	we	PRON
ejpam-5323	317	6	set	set	VERB
ejpam-5323	317	7	the	the	DET
ejpam-5323	317	8	order	order	NOUN
ejpam-5323	317	9	of	of	ADP
ejpam-5323	317	10	the	the	DET
ejpam-5323	317	11	components	component	NOUN
ejpam-5323	317	12	of	of	ADP
ejpam-5323	317	13	(	(	PUNCT
ejpam-5323	317	14	a	a	PRON
ejpam-5323	317	15	,	,	PUNCT
ejpam-5323	317	16	b	b	NOUN
ejpam-5323	317	17	,	,	PUNCT
ejpam-5323	317	18	c	c	NOUN
ejpam-5323	317	19	)	)	PUNCT
ejpam-5323	317	20	to	to	PART
ejpam-5323	317	21	be	be	AUX
ejpam-5323	317	22	odd	odd	ADJ
ejpam-5323	317	23	,	,	PUNCT
ejpam-5323	317	24	even	even	ADV
ejpam-5323	317	25	,	,	PUNCT
ejpam-5323	317	26	odd	odd	ADJ
ejpam-5323	317	27	.	.	PUNCT
ejpam-5323	318	1	hence	hence	ADV
ejpam-5323	318	2	,	,	PUNCT
ejpam-5323	318	3	there	there	PRON
ejpam-5323	318	4	is	be	VERB
ejpam-5323	318	5	an	an	DET
ejpam-5323	318	6	even	even	ADV
ejpam-5323	318	7	natural	natural	ADJ
ejpam-5323	318	8	number	number	NOUN
ejpam-5323	318	9	on	on	ADP
ejpam-5323	318	10	the	the	DET
ejpam-5323	318	11	left	left	ADJ
ejpam-5323	318	12	side	side	NOUN
ejpam-5323	318	13	,	,	PUNCT
ejpam-5323	318	14	and	and	CCONJ
ejpam-5323	318	15	an	an	DET
ejpam-5323	318	16	odd	odd	ADJ
ejpam-5323	318	17	natural	natural	ADJ
ejpam-5323	318	18	number	number	NOUN
ejpam-5323	318	19	on	on	ADP
ejpam-5323	318	20	the	the	DET
ejpam-5323	318	21	right	right	ADJ
ejpam-5323	318	22	side	side	NOUN
ejpam-5323	318	23	,	,	PUNCT
ejpam-5323	318	24	which	which	PRON
ejpam-5323	318	25	is	be	AUX
ejpam-5323	318	26	a	a	DET
ejpam-5323	318	27	contradiction	contradiction	NOUN
ejpam-5323	318	28	.	.	PUNCT
ejpam-5323	319	1	2	2	NUM
ejpam-5323	319	2	.	.	NUM
ejpam-5323	319	3	)	)	PUNCT
ejpam-5323	319	4	analogously	analogously	ADV
ejpam-5323	319	5	,	,	PUNCT
ejpam-5323	319	6	let	let	VERB
ejpam-5323	319	7	us	we	PRON
ejpam-5323	319	8	assume	assume	VERB
ejpam-5323	319	9	that	that	SCONJ
ejpam-5323	319	10	p⃗	p⃗	NOUN
ejpam-5323	319	11	·	·	PUNCT
ejpam-5323	319	12	r⃗	r⃗	VERB
ejpam-5323	319	13	=	=	SYM
ejpam-5323	319	14	0	0	X
ejpam-5323	319	15	.	.	PUNCT
ejpam-5323	320	1	then	then	ADV
ejpam-5323	320	2	p⃗	p⃗	NOUN
ejpam-5323	320	3	·	·	PUNCT
ejpam-5323	320	4	r⃗	r⃗	ADJ
ejpam-5323	320	5	=	=	SYM
ejpam-5323	320	6	(	(	PUNCT
ejpam-5323	320	7	2c	2c	NUM
ejpam-5323	320	8	,	,	PUNCT
ejpam-5323	320	9	4a−	4a−	PROPN
ejpam-5323	320	10	4b	4b	NOUN
ejpam-5323	320	11	,	,	PUNCT
ejpam-5323	320	12	4a−	4a−	PROPN
ejpam-5323	320	13	2b	2b	NUM
ejpam-5323	320	14	)	)	PUNCT
ejpam-5323	320	15	·	·	PUNCT
ejpam-5323	320	16	(	(	PUNCT
ejpam-5323	320	17	−2b	−2b	PROPN
ejpam-5323	320	18	,	,	PUNCT
ejpam-5323	320	19	4b	4b	X
ejpam-5323	320	20	,	,	PUNCT
ejpam-5323	320	21	2b	2b	NUM
ejpam-5323	320	22	)	)	PUNCT
ejpam-5323	320	23	=	=	PUNCT
ejpam-5323	320	24	0	0	NUM
ejpam-5323	321	1	−20b2	−20b2	NOUN
ejpam-5323	321	2	+	+	NUM
ejpam-5323	321	3	24ab−	24ab−	NUM
ejpam-5323	321	4	4bc	4bc	ADJ
ejpam-5323	321	5	=	=	SYM
ejpam-5323	321	6	0	0	PUNCT
ejpam-5323	322	1	5b−	5b−	PROPN
ejpam-5323	322	2	6a+	6a+	NUM
ejpam-5323	322	3	c	c	NOUN
ejpam-5323	322	4	=	=	SYM
ejpam-5323	322	5	0	0	X
ejpam-5323	322	6	.	.	PUNCT
ejpam-5323	323	1	using	use	VERB
ejpam-5323	323	2	euclid	euclid	PROPN
ejpam-5323	323	3	’s	’s	PART
ejpam-5323	323	4	formula	formula	NOUN
ejpam-5323	323	5	,	,	PUNCT
ejpam-5323	323	6	we	we	PRON
ejpam-5323	323	7	get	get	VERB
ejpam-5323	323	8	5(2mn)−	5(2mn)−	NUM
ejpam-5323	323	9	6(m2	6(m2	NUM
ejpam-5323	323	10	−	−	NOUN
ejpam-5323	323	11	n2	n2	NOUN
ejpam-5323	323	12	)	)	PUNCT
ejpam-5323	324	1	+	+	CCONJ
ejpam-5323	324	2	(	(	PUNCT
ejpam-5323	324	3	m2	m2	PROPN
ejpam-5323	324	4	+	+	CCONJ
ejpam-5323	324	5	n2	n2	ADJ
ejpam-5323	324	6	)	)	PUNCT
ejpam-5323	324	7	=	=	SYM
ejpam-5323	324	8	0	0	NUM
ejpam-5323	325	1	10mn−	10mn−	NUM
ejpam-5323	325	2	5m2	5m2	NUM
ejpam-5323	325	3	=	=	SYM
ejpam-5323	325	4	−7n2	−7n2	PROPN
ejpam-5323	325	5	where	where	SCONJ
ejpam-5323	325	6	m	m	VERB
ejpam-5323	325	7	,	,	PUNCT
ejpam-5323	325	8	n	n	PRON
ejpam-5323	325	9	∈	∈	PROPN
ejpam-5323	325	10	n	n	AUX
ejpam-5323	325	11	have	have	VERB
ejpam-5323	325	12	different	different	ADJ
ejpam-5323	325	13	parity	parity	NOUN
ejpam-5323	325	14	.	.	PUNCT
ejpam-5323	326	1	if	if	SCONJ
ejpam-5323	326	2	m	m	NOUN
ejpam-5323	326	3	is	be	AUX
ejpam-5323	326	4	even	even	ADV
ejpam-5323	326	5	and	and	CCONJ
ejpam-5323	326	6	n	n	PRON
ejpam-5323	326	7	is	be	AUX
ejpam-5323	326	8	odd	odd	ADJ
ejpam-5323	326	9	,	,	PUNCT
ejpam-5323	326	10	then	then	ADV
ejpam-5323	326	11	the	the	DET
ejpam-5323	326	12	left	left	ADJ
ejpam-5323	326	13	side	side	NOUN
ejpam-5323	326	14	of	of	ADP
ejpam-5323	326	15	this	this	DET
ejpam-5323	326	16	equation	equation	NOUN
ejpam-5323	326	17	is	be	AUX
ejpam-5323	326	18	even	even	ADV
ejpam-5323	326	19	and	and	CCONJ
ejpam-5323	326	20	the	the	DET
ejpam-5323	326	21	right	right	ADJ
ejpam-5323	326	22	side	side	NOUN
ejpam-5323	326	23	is	be	AUX
ejpam-5323	326	24	odd	odd	ADJ
ejpam-5323	326	25	,	,	PUNCT
ejpam-5323	326	26	which	which	PRON
ejpam-5323	326	27	is	be	AUX
ejpam-5323	326	28	a	a	DET
ejpam-5323	326	29	contradiction	contradiction	NOUN
ejpam-5323	326	30	.	.	PUNCT
ejpam-5323	327	1	if	if	SCONJ
ejpam-5323	327	2	m	m	NOUN
ejpam-5323	327	3	is	be	AUX
ejpam-5323	327	4	odd	odd	ADJ
ejpam-5323	327	5	and	and	CCONJ
ejpam-5323	327	6	n	n	PRON
ejpam-5323	327	7	is	be	AUX
ejpam-5323	327	8	even	even	ADV
ejpam-5323	327	9	,	,	PUNCT
ejpam-5323	327	10	then	then	ADV
ejpam-5323	327	11	the	the	DET
ejpam-5323	327	12	left	left	ADJ
ejpam-5323	327	13	side	side	NOUN
ejpam-5323	327	14	of	of	ADP
ejpam-5323	327	15	this	this	DET
ejpam-5323	327	16	equation	equation	NOUN
ejpam-5323	327	17	is	be	AUX
ejpam-5323	327	18	odd	odd	ADJ
ejpam-5323	327	19	and	and	CCONJ
ejpam-5323	327	20	the	the	DET
ejpam-5323	327	21	right	right	ADJ
ejpam-5323	327	22	side	side	NOUN
ejpam-5323	327	23	is	be	AUX
ejpam-5323	327	24	even	even	ADV
ejpam-5323	327	25	,	,	PUNCT
ejpam-5323	327	26	also	also	ADV
ejpam-5323	327	27	a	a	DET
ejpam-5323	327	28	contradiction	contradiction	NOUN
ejpam-5323	327	29	.	.	PUNCT
ejpam-5323	328	1	hence	hence	ADV
ejpam-5323	328	2	,	,	PUNCT
ejpam-5323	328	3	p⃗	p⃗	NOUN
ejpam-5323	328	4	·	·	PUNCT
ejpam-5323	328	5	r⃗	r⃗	VERB
ejpam-5323	328	6	̸=	̸=	PROPN
ejpam-5323	328	7	0	0	NUM
ejpam-5323	328	8	.	.	PUNCT
ejpam-5323	328	9	3	3	NUM
ejpam-5323	328	10	.	.	NUM
ejpam-5323	328	11	)	)	PUNCT
ejpam-5323	329	1	finally	finally	ADV
ejpam-5323	329	2	,	,	PUNCT
ejpam-5323	329	3	we	we	PRON
ejpam-5323	329	4	assume	assume	VERB
ejpam-5323	329	5	that	that	SCONJ
ejpam-5323	329	6	q⃗	q⃗	PROPN
ejpam-5323	329	7	·	·	PUNCT
ejpam-5323	329	8	r⃗	r⃗	NOUN
ejpam-5323	329	9	=	=	SYM
ejpam-5323	329	10	0	0	X
ejpam-5323	329	11	.	.	PUNCT
ejpam-5323	330	1	then	then	ADV
ejpam-5323	330	2	q⃗	q⃗	PROPN
ejpam-5323	330	3	·	·	PUNCT
ejpam-5323	330	4	r⃗	r⃗	ADJ
ejpam-5323	330	5	=	=	SYM
ejpam-5323	330	6	(	(	PUNCT
ejpam-5323	330	7	−2b+	−2b+	PROPN
ejpam-5323	330	8	2c	2c	NUM
ejpam-5323	330	9	,	,	PUNCT
ejpam-5323	330	10	4a	4a	NUM
ejpam-5323	330	11	,	,	PUNCT
ejpam-5323	330	12	4a	4a	NOUN
ejpam-5323	330	13	)	)	PUNCT
ejpam-5323	330	14	·	·	PUNCT
ejpam-5323	330	15	(	(	PUNCT
ejpam-5323	330	16	−2b	−2b	PROPN
ejpam-5323	330	17	,	,	PUNCT
ejpam-5323	330	18	4b	4b	X
ejpam-5323	330	19	,	,	PUNCT
ejpam-5323	330	20	2b	2b	NUM
ejpam-5323	330	21	)	)	PUNCT
ejpam-5323	330	22	=	=	SYM
ejpam-5323	330	23	0	0	NUM
ejpam-5323	330	24	4b2	4b2	NUM
ejpam-5323	330	25	−	−	PROPN
ejpam-5323	330	26	4bc+	4bc+	PROPN
ejpam-5323	330	27	24ab	24ab	NOUN
ejpam-5323	331	1	=	=	SYM
ejpam-5323	331	2	0	0	NUM
ejpam-5323	331	3	b−	b−	NOUN
ejpam-5323	331	4	c+	c+	VERB
ejpam-5323	331	5	6a	6a	NOUN
ejpam-5323	331	6	=	=	SYM
ejpam-5323	331	7	0	0	X
ejpam-5323	331	8	.	.	PUNCT
ejpam-5323	331	9	using	use	VERB
ejpam-5323	331	10	euclid	euclid	PROPN
ejpam-5323	331	11	’s	’s	PART
ejpam-5323	331	12	formula	formula	NOUN
ejpam-5323	331	13	,	,	PUNCT
ejpam-5323	331	14	we	we	PRON
ejpam-5323	331	15	get	get	VERB
ejpam-5323	331	16	2mn−	2mn−	NUM
ejpam-5323	331	17	(	(	PUNCT
ejpam-5323	331	18	m2	m2	PROPN
ejpam-5323	331	19	+	+	CCONJ
ejpam-5323	331	20	n2	n2	NOUN
ejpam-5323	331	21	)	)	PUNCT
ejpam-5323	331	22	+	+	CCONJ
ejpam-5323	331	23	6(m2	6(m2	NUM
ejpam-5323	331	24	−	−	NOUN
ejpam-5323	331	25	n2	n2	NOUN
ejpam-5323	331	26	)	)	PUNCT
ejpam-5323	331	27	=	=	SYM
ejpam-5323	331	28	0	0	NUM
ejpam-5323	332	1	l.	l.	PROPN
ejpam-5323	332	2	kőszegyová	kőszegyová	PROPN
ejpam-5323	332	3	,	,	PUNCT
ejpam-5323	332	4	e.	e.	PROPN
ejpam-5323	332	5	csókási	csókási	PROPN
ejpam-5323	332	6	,	,	PUNCT
ejpam-5323	332	7	j.	j.	PROPN
ejpam-5323	332	8	hirjak	hirjak	PROPN
ejpam-5323	332	9	/	/	SYM
ejpam-5323	332	10	eur	eur	PROPN
ejpam-5323	332	11	.	.	PUNCT
ejpam-5323	333	1	j.	j.	PROPN
ejpam-5323	333	2	pure	pure	PROPN
ejpam-5323	333	3	appl	appl	PROPN
ejpam-5323	333	4	.	.	PROPN
ejpam-5323	333	5	math	math	PROPN
ejpam-5323	333	6	,	,	PUNCT
ejpam-5323	333	7	17	17	NUM
ejpam-5323	333	8	(	(	PUNCT
ejpam-5323	333	9	3	3	NUM
ejpam-5323	333	10	)	)	PUNCT
ejpam-5323	333	11	(	(	PUNCT
ejpam-5323	333	12	2024	2024	NUM
ejpam-5323	333	13	)	)	PUNCT
ejpam-5323	333	14	,	,	PUNCT
ejpam-5323	333	15	2127	2127	NUM
ejpam-5323	333	16	-	-	SYM
ejpam-5323	333	17	2141	2141	NUM
ejpam-5323	333	18	2139	2139	NUM
ejpam-5323	333	19	2mn+	2mn+	NUM
ejpam-5323	333	20	5m2	5m2	NUM
ejpam-5323	333	21	=	=	SYM
ejpam-5323	333	22	7n2	7n2	NUM
ejpam-5323	333	23	where	where	SCONJ
ejpam-5323	333	24	m	m	VERB
ejpam-5323	333	25	,	,	PUNCT
ejpam-5323	333	26	n	n	PRON
ejpam-5323	333	27	∈	∈	PROPN
ejpam-5323	333	28	n	n	AUX
ejpam-5323	333	29	have	have	VERB
ejpam-5323	333	30	different	different	ADJ
ejpam-5323	333	31	parity	parity	NOUN
ejpam-5323	333	32	.	.	PUNCT
ejpam-5323	334	1	we	we	PRON
ejpam-5323	334	2	get	get	VERB
ejpam-5323	334	3	the	the	DET
ejpam-5323	334	4	contradiction	contradiction	NOUN
ejpam-5323	334	5	analogously	analogously	ADV
ejpam-5323	334	6	to	to	ADP
ejpam-5323	334	7	the	the	DET
ejpam-5323	334	8	previous	previous	ADJ
ejpam-5323	334	9	case	case	NOUN
ejpam-5323	334	10	.	.	PUNCT
ejpam-5323	335	1	proposition	proposition	NOUN
ejpam-5323	335	2	11	11	NUM
ejpam-5323	335	3	.	.	PUNCT
ejpam-5323	336	1	let	let	VERB
ejpam-5323	336	2	r	r	PRON
ejpam-5323	336	3	be	be	AUX
ejpam-5323	336	4	a	a	DET
ejpam-5323	336	5	primitive	primitive	ADJ
ejpam-5323	336	6	pythagorean	pythagorean	NOUN
ejpam-5323	336	7	triple	triple	NOUN
ejpam-5323	336	8	.	.	PUNCT
ejpam-5323	337	1	the	the	DET
ejpam-5323	337	2	triangle	triangle	NOUN
ejpam-5323	337	3	△	△	X
ejpam-5323	337	4	p	p	X
ejpam-5323	337	5	(	(	PUNCT
ejpam-5323	337	6	r	r	NOUN
ejpam-5323	337	7	)	)	PUNCT
ejpam-5323	337	8	is	be	AUX
ejpam-5323	337	9	not	not	PART
ejpam-5323	337	10	an	an	DET
ejpam-5323	337	11	isosceles	isoscele	NOUN
ejpam-5323	337	12	triangle	triangle	NOUN
ejpam-5323	337	13	.	.	PUNCT
ejpam-5323	338	1	proof	proof	NOUN
ejpam-5323	338	2	.	.	PUNCT
ejpam-5323	339	1	let	let	VERB
ejpam-5323	339	2	r	r	NOUN
ejpam-5323	339	3	=	=	SYM
ejpam-5323	339	4	(	(	PUNCT
ejpam-5323	339	5	a	a	PRON
ejpam-5323	339	6	,	,	PUNCT
ejpam-5323	339	7	b	b	NOUN
ejpam-5323	339	8	,	,	PUNCT
ejpam-5323	339	9	c	c	NOUN
ejpam-5323	339	10	)	)	PUNCT
ejpam-5323	339	11	.	.	PUNCT
ejpam-5323	340	1	similarly	similarly	ADV
ejpam-5323	340	2	like	like	ADP
ejpam-5323	340	3	above	above	ADV
ejpam-5323	340	4	,	,	PUNCT
ejpam-5323	340	5	we	we	PRON
ejpam-5323	340	6	consider	consider	VERB
ejpam-5323	340	7	the	the	DET
ejpam-5323	340	8	vectors	vector	NOUN
ejpam-5323	340	9	p⃗	p⃗	NOUN
ejpam-5323	340	10	,	,	PUNCT
ejpam-5323	340	11	q⃗	q⃗	PROPN
ejpam-5323	340	12	,	,	PUNCT
ejpam-5323	340	13	r⃗	r⃗	NOUN
ejpam-5323	340	14	:	:	PUNCT
ejpam-5323	340	15	p⃗	p⃗	NOUN
ejpam-5323	340	16	=	=	SYM
ejpam-5323	340	17	m2r	m2r	NUM
ejpam-5323	340	18	⊤	⊤	NOUN
ejpam-5323	340	19	−m1r	−m1r	PROPN
ejpam-5323	340	20	⊤	⊤	PROPN
ejpam-5323	340	21	=	=	SYM
ejpam-5323	340	22	(	(	PUNCT
ejpam-5323	340	23	2c	2c	NUM
ejpam-5323	340	24	,	,	PUNCT
ejpam-5323	340	25	4a−	4a−	PROPN
ejpam-5323	340	26	4b	4b	NOUN
ejpam-5323	340	27	,	,	PUNCT
ejpam-5323	340	28	4a−	4a−	PROPN
ejpam-5323	340	29	2b	2b	NUM
ejpam-5323	340	30	)	)	PUNCT
ejpam-5323	340	31	,	,	PUNCT
ejpam-5323	340	32	q⃗	q⃗	PROPN
ejpam-5323	340	33	=	=	SYM
ejpam-5323	340	34	m3r	m3r	NUM
ejpam-5323	340	35	⊤	⊤	PROPN
ejpam-5323	340	36	−m1r	−m1r	PROPN
ejpam-5323	340	37	⊤	⊤	PROPN
ejpam-5323	340	38	=	=	SYM
ejpam-5323	340	39	(	(	PUNCT
ejpam-5323	340	40	−2b+	−2b+	PROPN
ejpam-5323	340	41	2c	2c	NUM
ejpam-5323	340	42	,	,	PUNCT
ejpam-5323	340	43	4a	4a	NUM
ejpam-5323	340	44	,	,	PUNCT
ejpam-5323	340	45	4a	4a	NOUN
ejpam-5323	340	46	)	)	PUNCT
ejpam-5323	340	47	,	,	PUNCT
ejpam-5323	340	48	r⃗	r⃗	ADJ
ejpam-5323	340	49	=	=	SYM
ejpam-5323	340	50	m3r	m3r	PART
ejpam-5323	340	51	⊤	⊤	PROPN
ejpam-5323	340	52	−m2r	−m2r	PUNCT
ejpam-5323	340	53	⊤	⊤	NOUN
ejpam-5323	340	54	=	=	SYM
ejpam-5323	340	55	(	(	PUNCT
ejpam-5323	340	56	−2b	−2b	PROPN
ejpam-5323	340	57	,	,	PUNCT
ejpam-5323	340	58	4b	4b	X
ejpam-5323	340	59	,	,	PUNCT
ejpam-5323	340	60	2b	2b	NUM
ejpam-5323	340	61	)	)	PUNCT
ejpam-5323	340	62	.	.	PUNCT
ejpam-5323	341	1	then	then	ADV
ejpam-5323	341	2	|p⃗|	|p⃗|	ADV
ejpam-5323	341	3	=	=	SYM
ejpam-5323	341	4	2	2	NUM
ejpam-5323	341	5	√	√	NUM
ejpam-5323	341	6	9a2	9a2	NUM
ejpam-5323	342	1	−	−	NOUN
ejpam-5323	342	2	12ab+	12ab+	NUM
ejpam-5323	342	3	6b2	6b2	NUM
ejpam-5323	343	1	|q⃗|	|q⃗|	NOUN
ejpam-5323	343	2	=	=	SYM
ejpam-5323	343	3	2	2	NUM
ejpam-5323	343	4	√	√	NUM
ejpam-5323	343	5	(	(	PUNCT
ejpam-5323	343	6	c−	c−	NOUN
ejpam-5323	343	7	b)2	b)2	ADJ
ejpam-5323	343	8	+	+	NUM
ejpam-5323	343	9	8a2	8a2	NUM
ejpam-5323	343	10	|r⃗|	|r⃗|	X
ejpam-5323	344	1	=	=	SYM
ejpam-5323	344	2	2	2	NUM
ejpam-5323	344	3	√	√	NUM
ejpam-5323	344	4	6b2	6b2	NUM
ejpam-5323	344	5	.	.	PUNCT
ejpam-5323	345	1	1	1	NUM
ejpam-5323	345	2	.	.	PUNCT
ejpam-5323	345	3	)	)	PUNCT
ejpam-5323	346	1	by	by	ADP
ejpam-5323	346	2	way	way	NOUN
ejpam-5323	346	3	of	of	ADP
ejpam-5323	346	4	contradiction	contradiction	NOUN
ejpam-5323	346	5	,	,	PUNCT
ejpam-5323	346	6	let	let	VERB
ejpam-5323	346	7	us	we	PRON
ejpam-5323	346	8	assume	assume	VERB
ejpam-5323	346	9	that	that	SCONJ
ejpam-5323	346	10	|p⃗|	|p⃗|	ADV
ejpam-5323	346	11	=	=	SYM
ejpam-5323	346	12	|q⃗|	|q⃗|	PROPN
ejpam-5323	346	13	.	.	PUNCT
ejpam-5323	346	14	this	this	DET
ejpam-5323	346	15	yields	yield	NOUN
ejpam-5323	346	16	9a2	9a2	NUM
ejpam-5323	347	1	−	−	NUM
ejpam-5323	347	2	12ab+	12ab+	NUM
ejpam-5323	347	3	6b2	6b2	NUM
ejpam-5323	347	4	=	=	SYM
ejpam-5323	347	5	c2	c2	PROPN
ejpam-5323	347	6	−	−	PROPN
ejpam-5323	347	7	2bc+	2bc+	PROPN
ejpam-5323	347	8	b2	b2	NOUN
ejpam-5323	347	9	+	+	CCONJ
ejpam-5323	347	10	8a2	8a2	NUM
ejpam-5323	347	11	9a2	9a2	NUM
ejpam-5323	348	1	−	−	NOUN
ejpam-5323	348	2	12ab+	12ab+	NUM
ejpam-5323	348	3	6b2	6b2	NUM
ejpam-5323	348	4	=	=	SYM
ejpam-5323	348	5	a2	a2	PROPN
ejpam-5323	348	6	+	+	CCONJ
ejpam-5323	348	7	b2	b2	NOUN
ejpam-5323	348	8	−	−	PROPN
ejpam-5323	348	9	2bc+	2bc+	PROPN
ejpam-5323	348	10	b2	b2	NOUN
ejpam-5323	348	11	+	+	CCONJ
ejpam-5323	348	12	8a2	8a2	NUM
ejpam-5323	348	13	bc−	bc−	NOUN
ejpam-5323	348	14	6ab+	6ab+	NUM
ejpam-5323	348	15	2b2	2b2	NUM
ejpam-5323	348	16	=	=	SYM
ejpam-5323	348	17	0	0	NUM
ejpam-5323	348	18	.	.	PUNCT
ejpam-5323	349	1	using	use	VERB
ejpam-5323	349	2	the	the	DET
ejpam-5323	349	3	euclid	euclid	PROPN
ejpam-5323	349	4	’s	’s	PART
ejpam-5323	349	5	formula	formula	NOUN
ejpam-5323	349	6	,	,	PUNCT
ejpam-5323	349	7	we	we	PRON
ejpam-5323	349	8	get	get	VERB
ejpam-5323	349	9	(	(	PUNCT
ejpam-5323	349	10	2mn)(m2	2mn)(m2	NOUN
ejpam-5323	349	11	+	+	CCONJ
ejpam-5323	349	12	n2)−	n2)−	PROPN
ejpam-5323	349	13	6(m2	6(m2	NUM
ejpam-5323	349	14	−	−	PROPN
ejpam-5323	349	15	n2)(2mn	n2)(2mn	NUM
ejpam-5323	349	16	)	)	PUNCT
ejpam-5323	350	1	+	+	CCONJ
ejpam-5323	350	2	2(2mn	2(2mn	NUM
ejpam-5323	350	3	)	)	PUNCT
ejpam-5323	351	1	=	=	SYM
ejpam-5323	351	2	0	0	NUM
ejpam-5323	352	1	m2	m2	PROPN
ejpam-5323	352	2	+	+	CCONJ
ejpam-5323	352	3	n2	n2	PROPN
ejpam-5323	352	4	−	−	PROPN
ejpam-5323	352	5	6m2	6m2	NUM
ejpam-5323	352	6	+	+	CCONJ
ejpam-5323	352	7	6n2	6n2	NUM
ejpam-5323	352	8	+	+	CCONJ
ejpam-5323	352	9	1	1	NUM
ejpam-5323	352	10	=	=	SYM
ejpam-5323	352	11	0	0	NUM
ejpam-5323	352	12	7n2	7n2	NUM
ejpam-5323	352	13	+	+	SYM
ejpam-5323	352	14	1	1	NUM
ejpam-5323	352	15	=	=	SYM
ejpam-5323	352	16	5m5	5m5	NUM
ejpam-5323	352	17	which	which	PRON
ejpam-5323	352	18	implies	imply	VERB
ejpam-5323	352	19	that	that	SCONJ
ejpam-5323	352	20	7n2	7n2	NUM
ejpam-5323	352	21	+	+	SYM
ejpam-5323	352	22	1	1	NUM
ejpam-5323	352	23	≡	≡	PROPN
ejpam-5323	352	24	0	0	NUM
ejpam-5323	352	25	(	(	PUNCT
ejpam-5323	352	26	mod	mod	NOUN
ejpam-5323	352	27	5	5	NUM
ejpam-5323	352	28	)	)	PUNCT
ejpam-5323	352	29	⇐	⇐	ADJ
ejpam-5323	352	30	⇒	⇒	NOUN
ejpam-5323	352	31	n2	n2	PROPN
ejpam-5323	352	32	≡	≡	PROPN
ejpam-5323	352	33	2	2	NUM
ejpam-5323	352	34	(	(	PUNCT
ejpam-5323	352	35	mod	mod	NOUN
ejpam-5323	352	36	5	5	NUM
ejpam-5323	352	37	)	)	PUNCT
ejpam-5323	352	38	.	.	PUNCT
ejpam-5323	353	1	however	however	ADV
ejpam-5323	353	2	,	,	PUNCT
ejpam-5323	353	3	this	this	DET
ejpam-5323	353	4	congruence	congruence	NOUN
ejpam-5323	353	5	has	have	VERB
ejpam-5323	353	6	no	no	DET
ejpam-5323	353	7	solutions	solution	NOUN
ejpam-5323	353	8	in	in	ADP
ejpam-5323	353	9	n	n	CCONJ
ejpam-5323	353	10	,	,	PUNCT
ejpam-5323	353	11	hence	hence	ADV
ejpam-5323	353	12	|p⃗|	|p⃗|	ADV
ejpam-5323	353	13	=	=	NOUN
ejpam-5323	353	14	̸	̸	NUM
ejpam-5323	353	15	|q⃗|	|q⃗|	NOUN
ejpam-5323	353	16	.	.	PROPN
ejpam-5323	353	17	2	2	NUM
ejpam-5323	353	18	.	.	PUNCT
ejpam-5323	353	19	)	)	PUNCT
ejpam-5323	354	1	further	far	ADV
ejpam-5323	354	2	,	,	PUNCT
ejpam-5323	354	3	we	we	PRON
ejpam-5323	354	4	assume	assume	VERB
ejpam-5323	354	5	that	that	SCONJ
ejpam-5323	354	6	|p⃗|	|p⃗|	ADV
ejpam-5323	354	7	=	=	SYM
ejpam-5323	354	8	|r⃗|	|r⃗|	NOUN
ejpam-5323	354	9	.	.	PUNCT
ejpam-5323	355	1	hence	hence	ADV
ejpam-5323	355	2	,	,	PUNCT
ejpam-5323	355	3	9a2	9a2	NUM
ejpam-5323	355	4	−	−	NUM
ejpam-5323	355	5	12ab+	12ab+	NUM
ejpam-5323	355	6	6b2	6b2	NUM
ejpam-5323	355	7	=	=	SYM
ejpam-5323	355	8	6b2	6b2	NUM
ejpam-5323	355	9	3a−	3a−	NUM
ejpam-5323	355	10	4b	4b	X
ejpam-5323	355	11	=	=	SYM
ejpam-5323	355	12	0	0	PROPN
ejpam-5323	355	13	3a	3a	NUM
ejpam-5323	355	14	=	=	SYM
ejpam-5323	355	15	4b	4b	X
ejpam-5323	355	16	.	.	PUNCT
ejpam-5323	356	1	however	however	ADV
ejpam-5323	356	2	,	,	PUNCT
ejpam-5323	356	3	3a	3a	PROPN
ejpam-5323	356	4	is	be	AUX
ejpam-5323	356	5	odd	odd	ADJ
ejpam-5323	356	6	and	and	CCONJ
ejpam-5323	356	7	4b	4b	PROPN
ejpam-5323	356	8	is	be	AUX
ejpam-5323	356	9	even	even	ADV
ejpam-5323	356	10	,	,	PUNCT
ejpam-5323	356	11	a	a	DET
ejpam-5323	356	12	contradiction	contradiction	NOUN
ejpam-5323	356	13	.	.	PUNCT
ejpam-5323	357	1	3	3	X
ejpam-5323	357	2	.	.	NUM
ejpam-5323	357	3	)	)	PUNCT
ejpam-5323	357	4	finally	finally	ADV
ejpam-5323	357	5	,	,	PUNCT
ejpam-5323	357	6	we	we	PRON
ejpam-5323	357	7	assume	assume	VERB
ejpam-5323	357	8	that	that	SCONJ
ejpam-5323	357	9	|q⃗|	|q⃗|	PROPN
ejpam-5323	357	10	=	=	SYM
ejpam-5323	357	11	|r⃗|	|r⃗|	PROPN
ejpam-5323	357	12	.	.	PUNCT
ejpam-5323	358	1	then	then	ADV
ejpam-5323	358	2	c2	c2	PROPN
ejpam-5323	358	3	−	−	PROPN
ejpam-5323	358	4	2bc+	2bc+	PROPN
ejpam-5323	358	5	b2	b2	NOUN
ejpam-5323	358	6	+	+	CCONJ
ejpam-5323	358	7	8a2	8a2	NUM
ejpam-5323	358	8	=	=	SYM
ejpam-5323	358	9	6b2	6b2	NUM
ejpam-5323	358	10	references	reference	NOUN
ejpam-5323	358	11	2140	2140	NUM
ejpam-5323	358	12	c2	c2	PROPN
ejpam-5323	358	13	−	−	PROPN
ejpam-5323	358	14	2bc−	2bc−	NUM
ejpam-5323	358	15	5b2	5b2	NUM
ejpam-5323	358	16	+	+	SYM
ejpam-5323	358	17	8(c2	8(c2	NUM
ejpam-5323	358	18	−	−	NOUN
ejpam-5323	358	19	b2	b2	NOUN
ejpam-5323	358	20	)	)	PUNCT
ejpam-5323	358	21	=	=	SYM
ejpam-5323	358	22	0	0	NUM
ejpam-5323	358	23	9c2	9c2	NUM
ejpam-5323	358	24	−	−	NUM
ejpam-5323	358	25	2bc−	2bc−	NUM
ejpam-5323	358	26	12b2	12b2	NUM
ejpam-5323	358	27	=	=	SYM
ejpam-5323	358	28	0	0	NUM
ejpam-5323	358	29	9c2	9c2	NUM
ejpam-5323	358	30	=	=	NOUN
ejpam-5323	358	31	b(2c+	b(2c+	NOUN
ejpam-5323	358	32	13b	13b	NOUN
ejpam-5323	358	33	)	)	PUNCT
ejpam-5323	358	34	where	where	SCONJ
ejpam-5323	358	35	c	c	PROPN
ejpam-5323	358	36	is	be	AUX
ejpam-5323	358	37	odd	odd	ADJ
ejpam-5323	358	38	and	and	CCONJ
ejpam-5323	358	39	b	b	NOUN
ejpam-5323	358	40	is	be	AUX
ejpam-5323	358	41	even	even	ADV
ejpam-5323	358	42	,	,	PUNCT
ejpam-5323	358	43	which	which	PRON
ejpam-5323	358	44	implies	imply	VERB
ejpam-5323	358	45	that	that	SCONJ
ejpam-5323	358	46	the	the	DET
ejpam-5323	358	47	left	left	ADJ
ejpam-5323	358	48	side	side	NOUN
ejpam-5323	358	49	is	be	AUX
ejpam-5323	358	50	odd	odd	ADJ
ejpam-5323	358	51	,	,	PUNCT
ejpam-5323	358	52	and	and	CCONJ
ejpam-5323	358	53	the	the	DET
ejpam-5323	358	54	right	right	ADJ
ejpam-5323	358	55	side	side	NOUN
ejpam-5323	358	56	is	be	AUX
ejpam-5323	358	57	even	even	ADV
ejpam-5323	358	58	,	,	PUNCT
ejpam-5323	358	59	a	a	DET
ejpam-5323	358	60	contradiction	contradiction	NOUN
ejpam-5323	358	61	.	.	PUNCT
ejpam-5323	359	1	therefore	therefore	ADV
ejpam-5323	359	2	,	,	PUNCT
ejpam-5323	359	3	△	△	X
ejpam-5323	359	4	p	p	X
ejpam-5323	359	5	(	(	PUNCT
ejpam-5323	359	6	r	r	NOUN
ejpam-5323	359	7	)	)	PUNCT
ejpam-5323	359	8	is	be	AUX
ejpam-5323	359	9	not	not	PART
ejpam-5323	359	10	an	an	DET
ejpam-5323	359	11	isosceles	isoscele	NOUN
ejpam-5323	359	12	triangle	triangle	NOUN
ejpam-5323	359	13	.	.	PUNCT
ejpam-5323	360	1	corollary	corollary	ADJ
ejpam-5323	360	2	6	6	NUM
ejpam-5323	360	3	.	.	PUNCT
ejpam-5323	361	1	let	let	VERB
ejpam-5323	361	2	r	r	PRON
ejpam-5323	361	3	be	be	AUX
ejpam-5323	361	4	a	a	DET
ejpam-5323	361	5	primitive	primitive	ADJ
ejpam-5323	361	6	pythagorean	pythagorean	NOUN
ejpam-5323	361	7	triple	triple	NOUN
ejpam-5323	361	8	.	.	PUNCT
ejpam-5323	362	1	the	the	DET
ejpam-5323	362	2	triangle	triangle	NOUN
ejpam-5323	362	3	△	△	X
ejpam-5323	362	4	p	p	X
ejpam-5323	362	5	(	(	PUNCT
ejpam-5323	362	6	r	r	NOUN
ejpam-5323	362	7	)	)	PUNCT
ejpam-5323	362	8	is	be	AUX
ejpam-5323	362	9	not	not	PART
ejpam-5323	362	10	an	an	DET
ejpam-5323	362	11	equilateral	equilateral	ADJ
ejpam-5323	362	12	triangle	triangle	NOUN
ejpam-5323	362	13	.	.	PUNCT
ejpam-5323	363	1	5	5	X
ejpam-5323	363	2	.	.	X
ejpam-5323	363	3	concluding	conclude	VERB
ejpam-5323	363	4	remarks	remark	NOUN
ejpam-5323	363	5	to	to	PART
ejpam-5323	363	6	consider	consider	VERB
ejpam-5323	363	7	the	the	DET
ejpam-5323	363	8	three	three	NUM
ejpam-5323	363	9	descendants	descendant	NOUN
ejpam-5323	363	10	of	of	ADP
ejpam-5323	363	11	a	a	DET
ejpam-5323	363	12	primitive	primitive	ADJ
ejpam-5323	363	13	pythagorean	pythagorean	NOUN
ejpam-5323	363	14	triple	triple	NOUN
ejpam-5323	363	15	in	in	ADP
ejpam-5323	363	16	a	a	DET
ejpam-5323	363	17	tree	tree	NOUN
ejpam-5323	363	18	of	of	ADP
ejpam-5323	363	19	primitive	primitive	ADJ
ejpam-5323	363	20	pythagorean	pythagorean	ADJ
ejpam-5323	363	21	triples	triple	NOUN
ejpam-5323	363	22	as	as	ADP
ejpam-5323	363	23	points	point	NOUN
ejpam-5323	363	24	in	in	ADP
ejpam-5323	363	25	the	the	DET
ejpam-5323	363	26	three	three	NUM
ejpam-5323	363	27	-	-	PUNCT
ejpam-5323	363	28	dimensional	dimensional	ADJ
ejpam-5323	363	29	space	space	NOUN
ejpam-5323	363	30	can	can	AUX
ejpam-5323	363	31	provide	provide	VERB
ejpam-5323	363	32	further	further	ADJ
ejpam-5323	363	33	insight	insight	NOUN
ejpam-5323	363	34	into	into	ADP
ejpam-5323	363	35	the	the	DET
ejpam-5323	363	36	structure	structure	NOUN
ejpam-5323	363	37	of	of	ADP
ejpam-5323	363	38	primitive	primitive	ADJ
ejpam-5323	363	39	pythagorean	pythagorean	ADJ
ejpam-5323	363	40	triples	triple	NOUN
ejpam-5323	363	41	.	.	PUNCT
ejpam-5323	364	1	as	as	SCONJ
ejpam-5323	364	2	these	these	DET
ejpam-5323	364	3	three	three	NUM
ejpam-5323	364	4	descendants	descendant	NOUN
ejpam-5323	364	5	form	form	VERB
ejpam-5323	364	6	a	a	DET
ejpam-5323	364	7	triangle	triangle	NOUN
ejpam-5323	364	8	in	in	ADP
ejpam-5323	364	9	either	either	CCONJ
ejpam-5323	364	10	berggren	berggren	PROPN
ejpam-5323	364	11	’s	’s	PART
ejpam-5323	364	12	or	or	CCONJ
ejpam-5323	364	13	price	price	NOUN
ejpam-5323	364	14	’s	’s	PART
ejpam-5323	364	15	tree	tree	NOUN
ejpam-5323	364	16	,	,	PUNCT
ejpam-5323	364	17	it	it	PRON
ejpam-5323	364	18	is	be	AUX
ejpam-5323	364	19	interesting	interesting	ADJ
ejpam-5323	364	20	to	to	PART
ejpam-5323	364	21	study	study	VERB
ejpam-5323	364	22	the	the	DET
ejpam-5323	364	23	properties	property	NOUN
ejpam-5323	364	24	of	of	ADP
ejpam-5323	364	25	these	these	DET
ejpam-5323	364	26	triangles	triangle	NOUN
ejpam-5323	364	27	.	.	PUNCT
ejpam-5323	365	1	this	this	DET
ejpam-5323	365	2	new	new	ADJ
ejpam-5323	365	3	approach	approach	NOUN
ejpam-5323	365	4	offers	offer	VERB
ejpam-5323	365	5	numerous	numerous	ADJ
ejpam-5323	365	6	open	open	ADJ
ejpam-5323	365	7	problems	problem	NOUN
ejpam-5323	365	8	,	,	PUNCT
ejpam-5323	365	9	which	which	PRON
ejpam-5323	365	10	we	we	PRON
ejpam-5323	365	11	would	would	AUX
ejpam-5323	365	12	like	like	VERB
ejpam-5323	365	13	to	to	PART
ejpam-5323	365	14	explore	explore	VERB
ejpam-5323	365	15	in	in	ADP
ejpam-5323	365	16	our	our	PRON
ejpam-5323	365	17	further	further	ADJ
ejpam-5323	365	18	research	research	NOUN
ejpam-5323	365	19	.	.	PUNCT
ejpam-5323	366	1	for	for	ADP
ejpam-5323	366	2	example	example	NOUN
ejpam-5323	366	3	,	,	PUNCT
ejpam-5323	366	4	we	we	PRON
ejpam-5323	366	5	proved	prove	VERB
ejpam-5323	366	6	that	that	SCONJ
ejpam-5323	366	7	the	the	DET
ejpam-5323	366	8	descendant	descendant	ADJ
ejpam-5323	366	9	triangle	triangle	NOUN
ejpam-5323	366	10	fails	fail	VERB
ejpam-5323	366	11	to	to	PART
ejpam-5323	366	12	be	be	AUX
ejpam-5323	366	13	right	right	ADJ
ejpam-5323	366	14	triangle	triangle	NOUN
ejpam-5323	366	15	in	in	ADP
ejpam-5323	366	16	both	both	DET
ejpam-5323	366	17	berggren	berggren	PROPN
ejpam-5323	366	18	’s	’s	PART
ejpam-5323	366	19	and	and	CCONJ
ejpam-5323	366	20	price	price	NOUN
ejpam-5323	366	21	’s	’s	PART
ejpam-5323	366	22	tree	tree	NOUN
ejpam-5323	366	23	.	.	PUNCT
ejpam-5323	367	1	if	if	SCONJ
ejpam-5323	367	2	it	it	PRON
ejpam-5323	367	3	always	always	ADV
ejpam-5323	367	4	fails	fail	VERB
ejpam-5323	367	5	to	to	PART
ejpam-5323	367	6	be	be	AUX
ejpam-5323	367	7	a	a	DET
ejpam-5323	367	8	right	right	ADJ
ejpam-5323	367	9	triangle	triangle	NOUN
ejpam-5323	367	10	,	,	PUNCT
ejpam-5323	367	11	could	could	AUX
ejpam-5323	367	12	it	it	PRON
ejpam-5323	367	13	always	always	ADV
ejpam-5323	367	14	be	be	AUX
ejpam-5323	367	15	acute	acute	ADJ
ejpam-5323	367	16	?	?	PUNCT
ejpam-5323	368	1	is	be	AUX
ejpam-5323	368	2	it	it	PRON
ejpam-5323	368	3	obtuse	obtuse	NOUN
ejpam-5323	368	4	in	in	ADP
ejpam-5323	368	5	some	some	DET
ejpam-5323	368	6	cases	case	NOUN
ejpam-5323	368	7	?	?	PUNCT
ejpam-5323	369	1	can	can	AUX
ejpam-5323	369	2	the	the	DET
ejpam-5323	369	3	set	set	NOUN
ejpam-5323	369	4	of	of	ADP
ejpam-5323	369	5	all	all	DET
ejpam-5323	369	6	inner	inner	ADJ
ejpam-5323	369	7	angles	angle	NOUN
ejpam-5323	369	8	be	be	AUX
ejpam-5323	369	9	somehow	somehow	ADV
ejpam-5323	369	10	described	describe	VERB
ejpam-5323	369	11	?	?	PUNCT
ejpam-5323	370	1	these	these	PRON
ejpam-5323	370	2	and	and	CCONJ
ejpam-5323	370	3	further	further	ADJ
ejpam-5323	370	4	problems	problem	NOUN
ejpam-5323	370	5	remain	remain	VERB
ejpam-5323	370	6	open	open	ADJ
ejpam-5323	370	7	and	and	CCONJ
ejpam-5323	370	8	we	we	PRON
ejpam-5323	370	9	intend	intend	VERB
ejpam-5323	370	10	to	to	PART
ejpam-5323	370	11	study	study	VERB
ejpam-5323	370	12	them	they	PRON
ejpam-5323	370	13	further	far	ADV
ejpam-5323	370	14	.	.	PUNCT
ejpam-5323	371	1	funding	fund	VERB
ejpam-5323	371	2	this	this	DET
ejpam-5323	371	3	work	work	NOUN
ejpam-5323	371	4	was	be	AUX
ejpam-5323	371	5	supported	support	VERB
ejpam-5323	371	6	by	by	ADP
ejpam-5323	371	7	european	european	PROPN
ejpam-5323	371	8	union	union	PROPN
ejpam-5323	371	9	nextgenerationeugrant	nextgenerationeugrant	NOUN
ejpam-5323	371	10	through	through	ADP
ejpam-5323	371	11	the	the	DET
ejpam-5323	371	12	project	project	NOUN
ejpam-5323	371	13	vvgs-2023	vvgs-2023	NOUN
ejpam-5323	371	14	-	-	SYM
ejpam-5323	371	15	3000	3000	NUM
ejpam-5323	371	16	.	.	PUNCT
ejpam-5323	372	1	references	reference	NOUN
ejpam-5323	372	2	[	[	X
ejpam-5323	372	3	1	1	NUM
ejpam-5323	372	4	]	]	X
ejpam-5323	372	5	r.p	r.p	PROPN
ejpam-5323	372	6	.	.	PROPN
ejpam-5323	372	7	agarwal	agarwal	PROPN
ejpam-5323	372	8	.	.	PUNCT
ejpam-5323	373	1	pythagorean	pythagorean	PROPN
ejpam-5323	373	2	triples	triple	NOUN
ejpam-5323	373	3	before	before	ADV
ejpam-5323	373	4	and	and	CCONJ
ejpam-5323	373	5	after	after	ADP
ejpam-5323	373	6	pythagoras	pythagoras	PROPN
ejpam-5323	373	7	.	.	PUNCT
ejpam-5323	374	1	computation	computation	PROPN
ejpam-5323	374	2	,	,	PUNCT
ejpam-5323	374	3	8(8):1	8(8):1	NOUN
ejpam-5323	374	4	–	–	PUNCT
ejpam-5323	374	5	36	36	NUM
ejpam-5323	374	6	,	,	PUNCT
ejpam-5323	374	7	2020	2020	NUM
ejpam-5323	374	8	.	.	PUNCT
ejpam-5323	375	1	[	[	X
ejpam-5323	375	2	2	2	NUM
ejpam-5323	375	3	]	]	PUNCT
ejpam-5323	375	4	r.	r.	PROPN
ejpam-5323	375	5	amato	amato	PROPN
ejpam-5323	375	6	.	.	PUNCT
ejpam-5323	376	1	a	a	DET
ejpam-5323	376	2	novel	novel	ADJ
ejpam-5323	376	3	approach	approach	NOUN
ejpam-5323	376	4	for	for	ADP
ejpam-5323	376	5	studying	study	VERB
ejpam-5323	376	6	pythagorean	pythagorean	PROPN
ejpam-5323	376	7	triples	triple	NOUN
ejpam-5323	376	8	suitable	suitable	ADJ
ejpam-5323	376	9	for	for	ADP
ejpam-5323	376	10	students	student	NOUN
ejpam-5323	376	11	at	at	ADP
ejpam-5323	376	12	all	all	DET
ejpam-5323	376	13	educational	educational	ADJ
ejpam-5323	376	14	levels	level	NOUN
ejpam-5323	376	15	.	.	PUNCT
ejpam-5323	377	1	eur	eur	PROPN
ejpam-5323	377	2	.	.	PUNCT
ejpam-5323	378	1	j.	j.	PROPN
ejpam-5323	378	2	pure	pure	PROPN
ejpam-5323	378	3	appl	appl	PROPN
ejpam-5323	378	4	.	.	PUNCT
ejpam-5323	378	5	math	math	PROPN
ejpam-5323	378	6	.	.	PUNCT
ejpam-5323	378	7	,	,	PUNCT
ejpam-5323	379	1	17(2):676–689	17(2):676–689	NOUN
ejpam-5323	379	2	,	,	PUNCT
ejpam-5323	379	3	2024	2024	NUM
ejpam-5323	379	4	.	.	PUNCT
ejpam-5323	380	1	[	[	X
ejpam-5323	380	2	3	3	X
ejpam-5323	380	3	]	]	X
ejpam-5323	380	4	b.k	b.k	PROPN
ejpam-5323	380	5	.	.	PROPN
ejpam-5323	380	6	gil	gil	PROPN
ejpam-5323	380	7	at	at	ADP
ejpam-5323	380	8	al	al	PROPN
ejpam-5323	380	9	.	.	PROPN
ejpam-5323	380	10	frobenius	frobenius	PROPN
ejpam-5323	380	11	numbers	number	NOUN
ejpam-5323	380	12	of	of	ADP
ejpam-5323	380	13	pythagorean	pythagorean	PROPN
ejpam-5323	380	14	triples	triple	NOUN
ejpam-5323	380	15	.	.	PUNCT
ejpam-5323	381	1	int	int	NOUN
ejpam-5323	381	2	.	.	PUNCT
ejpam-5323	382	1	j.	j.	PROPN
ejpam-5323	382	2	number	number	PROPN
ejpam-5323	382	3	theory	theory	NOUN
ejpam-5323	382	4	,	,	PUNCT
ejpam-5323	382	5	11(2):613–619	11(2):613–619	NUM
ejpam-5323	382	6	,	,	PUNCT
ejpam-5323	382	7	2015	2015	NUM
ejpam-5323	382	8	.	.	PUNCT
ejpam-5323	383	1	[	[	X
ejpam-5323	383	2	4	4	X
ejpam-5323	383	3	]	]	PUNCT
ejpam-5323	383	4	j.	j.	PROPN
ejpam-5323	383	5	austin	austin	PROPN
ejpam-5323	383	6	.	.	PUNCT
ejpam-5323	383	7	generating	generate	VERB
ejpam-5323	383	8	pythagorean	pythagorean	PROPN
ejpam-5323	383	9	triples	triple	NOUN
ejpam-5323	383	10	of	of	ADP
ejpam-5323	383	11	a	a	DET
ejpam-5323	383	12	given	give	VERB
ejpam-5323	383	13	height	height	NOUN
ejpam-5323	383	14	.	.	PUNCT
ejpam-5323	384	1	missouri	missouri	PROPN
ejpam-5323	384	2	journal	journal	PROPN
ejpam-5323	384	3	of	of	ADP
ejpam-5323	384	4	math	math	NOUN
ejpam-5323	384	5	.	.	PUNCT
ejpam-5323	385	1	sci	sci	PROPN
ejpam-5323	385	2	.	.	PROPN
ejpam-5323	385	3	,	,	PUNCT
ejpam-5323	385	4	31(2):136–145	31(2):136–145	NOUN
ejpam-5323	385	5	,	,	PUNCT
ejpam-5323	385	6	2019	2019	NUM
ejpam-5323	385	7	.	.	PUNCT
ejpam-5323	386	1	references	reference	NOUN
ejpam-5323	386	2	2141	2141	NUM
ejpam-5323	386	3	[	[	X
ejpam-5323	386	4	5	5	NUM
ejpam-5323	386	5	]	]	X
ejpam-5323	386	6	s.a	s.a	PROPN
ejpam-5323	386	7	.	.	PROPN
ejpam-5323	386	8	bhanotar	bhanotar	PROPN
ejpam-5323	386	9	and	and	CCONJ
ejpam-5323	386	10	m.k.a	m.k.a	PROPN
ejpam-5323	386	11	.	.	PUNCT
ejpam-5323	387	1	kaabar	kaabar	PROPN
ejpam-5323	387	2	.	.	PUNCT
ejpam-5323	388	1	on	on	ADP
ejpam-5323	388	2	multiple	multiple	ADJ
ejpam-5323	388	3	primitive	primitive	ADJ
ejpam-5323	388	4	pythagorean	pythagorean	ADJ
ejpam-5323	388	5	triplets	triplet	NOUN
ejpam-5323	388	6	.	.	PUNCT
ejpam-5323	389	1	palestine	palestine	PROPN
ejpam-5323	389	2	journal	journal	PROPN
ejpam-5323	389	3	of	of	ADP
ejpam-5323	389	4	mathematics	mathematic	NOUN
ejpam-5323	389	5	,	,	PUNCT
ejpam-5323	389	6	11(4):119–129	11(4):119–129	PROPN
ejpam-5323	389	7	,	,	PUNCT
ejpam-5323	389	8	2022	2022	NUM
ejpam-5323	389	9	.	.	PUNCT
ejpam-5323	390	1	[	[	X
ejpam-5323	390	2	6	6	NUM
ejpam-5323	390	3	]	]	X
ejpam-5323	390	4	r.c	r.c	PROPN
ejpam-5323	390	5	.	.	PROPN
ejpam-5323	390	6	ochien	ochien	PROPN
ejpam-5323	390	7	et	et	PROPN
ejpam-5323	390	8	al	al	PROPN
ejpam-5323	390	9	.	.	PROPN
ejpam-5323	391	1	pythagorean	pythagorean	PROPN
ejpam-5323	391	2	triples	triple	NOUN
ejpam-5323	391	3	with	with	ADP
ejpam-5323	391	4	common	common	ADJ
ejpam-5323	391	5	sides	side	NOUN
ejpam-5323	391	6	.	.	PUNCT
ejpam-5323	392	1	journal	journal	NOUN
ejpam-5323	392	2	of	of	ADP
ejpam-5323	392	3	mathematics	mathematic	NOUN
ejpam-5323	392	4	,	,	PUNCT
ejpam-5323	392	5	pages	page	NOUN
ejpam-5323	392	6	1–8	1–8	NUM
ejpam-5323	392	7	,	,	PUNCT
ejpam-5323	392	8	2019	2019	NUM
ejpam-5323	392	9	.	.	PUNCT
ejpam-5323	393	1	[	[	X
ejpam-5323	393	2	7	7	NUM
ejpam-5323	393	3	]	]	PUNCT
ejpam-5323	393	4	a.	a.	NOUN
ejpam-5323	393	5	hall	hall	PROPN
ejpam-5323	393	6	.	.	PUNCT
ejpam-5323	394	1	genealogy	genealogy	NOUN
ejpam-5323	394	2	of	of	ADP
ejpam-5323	394	3	pythagorean	pythagorean	PROPN
ejpam-5323	394	4	triads	triad	NOUN
ejpam-5323	394	5	.	.	PUNCT
ejpam-5323	395	1	the	the	DET
ejpam-5323	395	2	math	math	NOUN
ejpam-5323	395	3	.	.	PUNCT
ejpam-5323	396	1	gazette	gazette	PROPN
ejpam-5323	396	2	,	,	PUNCT
ejpam-5323	396	3	54(390):377–379	54(390):377–379	PROPN
ejpam-5323	396	4	,	,	PUNCT
ejpam-5323	396	5	1970	1970	NUM
ejpam-5323	396	6	.	.	PUNCT
ejpam-5323	397	1	[	[	X
ejpam-5323	397	2	8	8	X
ejpam-5323	397	3	]	]	PUNCT
ejpam-5323	397	4	j.	j.	PROPN
ejpam-5323	397	5	hirjak	hirjak	PROPN
ejpam-5323	397	6	.	.	PUNCT
ejpam-5323	398	1	pytagorejské	pytagorejské	NOUN
ejpam-5323	398	2	trojice	trojice	PROPN
ejpam-5323	398	3	so	so	ADV
ejpam-5323	398	4	spoločnou	spoločnou	PROPN
ejpam-5323	398	5	vlastnosťou	vlastnosťou	PROPN
ejpam-5323	398	6	.	.	PUNCT
ejpam-5323	399	1	bachelor	bachelor	PROPN
ejpam-5323	399	2	thesis	thesis	NOUN
ejpam-5323	399	3	,	,	PUNCT
ejpam-5323	399	4	p.j	p.j	PROPN
ejpam-5323	399	5	.	.	PROPN
ejpam-5323	399	6	šafárik	šafárik	PROPN
ejpam-5323	399	7	university	university	PROPN
ejpam-5323	399	8	in	in	ADP
ejpam-5323	399	9	košice	košice	PROPN
ejpam-5323	399	10	,	,	PUNCT
ejpam-5323	399	11	2022	2022	NUM
ejpam-5323	399	12	.	.	PUNCT
ejpam-5323	400	1	[	[	X
ejpam-5323	400	2	9	9	NUM
ejpam-5323	400	3	]	]	PUNCT
ejpam-5323	400	4	l.	l.	PROPN
ejpam-5323	400	5	janičková	janičková	PROPN
ejpam-5323	400	6	and	and	CCONJ
ejpam-5323	400	7	e.	e.	PROPN
ejpam-5323	400	8	csókási	csókási	PROPN
ejpam-5323	400	9	.	.	PUNCT
ejpam-5323	401	1	metric	metric	ADJ
ejpam-5323	401	2	properties	property	NOUN
ejpam-5323	401	3	in	in	ADP
ejpam-5323	401	4	berggren	berggren	PROPN
ejpam-5323	401	5	tree	tree	NOUN
ejpam-5323	401	6	of	of	ADP
ejpam-5323	401	7	primitive	primitive	ADJ
ejpam-5323	401	8	pythagorean	pythagorean	ADJ
ejpam-5323	401	9	triples	triple	NOUN
ejpam-5323	401	10	.	.	PUNCT
ejpam-5323	401	11	arxiv:2304.05230	arxiv:2304.05230	PROPN
ejpam-5323	401	12	,	,	PUNCT
ejpam-5323	401	13	2023	2023	NUM
ejpam-5323	401	14	.	.	PUNCT
ejpam-5323	402	1	[	[	X
ejpam-5323	402	2	10	10	NUM
ejpam-5323	402	3	]	]	X
ejpam-5323	402	4	e.	e.	PROPN
ejpam-5323	402	5	maor	maor	PROPN
ejpam-5323	402	6	.	.	PUNCT
ejpam-5323	403	1	the	the	DET
ejpam-5323	403	2	pythagorean	pythagorean	PROPN
ejpam-5323	403	3	theorem	theorem	PROPN
ejpam-5323	403	4	.	.	PROPN
ejpam-5323	403	5	princeton	princeton	PROPN
ejpam-5323	403	6	university	university	PROPN
ejpam-5323	403	7	press	press	NOUN
ejpam-5323	403	8	,	,	PUNCT
ejpam-5323	403	9	new	new	PROPN
ejpam-5323	403	10	jersey	jersey	PROPN
ejpam-5323	403	11	,	,	PUNCT
ejpam-5323	403	12	2007	2007	NUM
ejpam-5323	403	13	.	.	PUNCT
ejpam-5323	404	1	[	[	X
ejpam-5323	404	2	11	11	NUM
ejpam-5323	404	3	]	]	PUNCT
ejpam-5323	404	4	t.	t.	NOUN
ejpam-5323	404	5	omland	omland	PROPN
ejpam-5323	404	6	.	.	PUNCT
ejpam-5323	405	1	how	how	SCONJ
ejpam-5323	405	2	many	many	ADJ
ejpam-5323	405	3	pythagorean	pythagorean	ADJ
ejpam-5323	405	4	triples	triple	NOUN
ejpam-5323	405	5	with	with	ADP
ejpam-5323	405	6	a	a	DET
ejpam-5323	405	7	given	give	VERB
ejpam-5323	405	8	inradius	inradius	NOUN
ejpam-5323	405	9	?	?	PUNCT
ejpam-5323	405	10	.	.	PUNCT
ejpam-5323	406	1	journal	journal	NOUN
ejpam-5323	406	2	of	of	ADP
ejpam-5323	406	3	number	number	NOUN
ejpam-5323	406	4	theory	theory	NOUN
ejpam-5323	406	5	,	,	PUNCT
ejpam-5323	406	6	170:1–2	170:1–2	NOUN
ejpam-5323	406	7	,	,	PUNCT
ejpam-5323	406	8	2016	2016	NUM
ejpam-5323	406	9	.	.	PUNCT
ejpam-5323	407	1	[	[	X
ejpam-5323	407	2	12	12	NUM
ejpam-5323	407	3	]	]	X
ejpam-5323	407	4	h.l	h.l	PROPN
ejpam-5323	407	5	.	.	PROPN
ejpam-5323	407	6	pricei	pricei	PROPN
ejpam-5323	407	7	.	.	PUNCT
ejpam-5323	408	1	the	the	DET
ejpam-5323	408	2	pythagorean	pythagorean	PROPN
ejpam-5323	408	3	tree	tree	NOUN
ejpam-5323	408	4	:	:	PUNCT
ejpam-5323	408	5	a	a	DET
ejpam-5323	408	6	new	new	ADJ
ejpam-5323	408	7	species	specie	NOUN
ejpam-5323	408	8	.	.	PUNCT
ejpam-5323	409	1	arxiv:0809.4324	arxiv:0809.4324	NUM
ejpam-5323	409	2	,	,	PUNCT
ejpam-5323	409	3	2008	2008	NUM
ejpam-5323	409	4	.	.	PUNCT
ejpam-5323	410	1	[	[	X
ejpam-5323	410	2	13	13	NUM
ejpam-5323	410	3	]	]	PUNCT
ejpam-5323	410	4	w.	w.	PROPN
ejpam-5323	410	5	sierpinski	sierpinski	PROPN
ejpam-5323	410	6	.	.	PUNCT
ejpam-5323	411	1	elementary	elementary	ADJ
ejpam-5323	411	2	theory	theory	NOUN
ejpam-5323	411	3	of	of	ADP
ejpam-5323	411	4	numbers	number	NOUN
ejpam-5323	411	5	.	.	PUNCT
ejpam-5323	412	1	panstwowe	panstwowe	PROPN
ejpam-5323	412	2	wydawnictwo	wydawnictwo	PROPN
ejpam-5323	412	3	naukowe	naukowe	PROPN
ejpam-5323	412	4	,	,	PUNCT
ejpam-5323	412	5	warszawa	warszawa	PROPN
ejpam-5323	412	6	,	,	PUNCT
ejpam-5323	412	7	poland	poland	PROPN
ejpam-5323	412	8	,	,	PUNCT
ejpam-5323	412	9	1969	1969	NUM
ejpam-5323	412	10	.	.	PUNCT
ejpam-5323	413	1	[	[	X
ejpam-5323	413	2	14	14	NUM
ejpam-5323	413	3	]	]	PUNCT
ejpam-5323	413	4	a.	a.	NOUN
ejpam-5323	413	5	tripathi	tripathi	PROPN
ejpam-5323	413	6	.	.	PUNCT
ejpam-5323	414	1	on	on	ADP
ejpam-5323	414	2	pythagorean	pythagorean	PROPN
ejpam-5323	414	3	triples	triple	NOUN
ejpam-5323	414	4	containing	contain	VERB
ejpam-5323	414	5	a	a	DET
ejpam-5323	414	6	fixed	fix	VERB
ejpam-5323	414	7	integer	integer	NOUN
ejpam-5323	414	8	.	.	PUNCT
ejpam-5323	415	1	fibonacci	fibonacci	NOUN
ejpam-5323	415	2	quart	quart	PROPN
ejpam-5323	415	3	.	.	PUNCT
ejpam-5323	416	1	,	,	PUNCT
ejpam-5323	416	2	46	46	NUM
ejpam-5323	416	3	-	-	SYM
ejpam-5323	416	4	47:331–340	47:331–340	NUM
ejpam-5323	416	5	,	,	PUNCT
ejpam-5323	416	6	2008	2008	NUM
ejpam-5323	416	7	.	.	PUNCT
ejpam-5323	417	1	[	[	X
ejpam-5323	417	2	15	15	X
ejpam-5323	417	3	]	]	X
ejpam-5323	417	4	v.	v.	CCONJ
ejpam-5323	417	5	yegnanarayanan	yegnanarayanan	NOUN
ejpam-5323	417	6	and	and	CCONJ
ejpam-5323	417	7	p.yakkala	p.yakkala	NOUN
ejpam-5323	417	8	.	.	PUNCT
ejpam-5323	418	1	pythagorean	pythagorean	PROPN
ejpam-5323	418	2	triples	triple	NOUN
ejpam-5323	418	3	in	in	ADP
ejpam-5323	418	4	cryptography	cryptography	NOUN
ejpam-5323	418	5	and	and	CCONJ
ejpam-5323	418	6	associated	associated	ADJ
ejpam-5323	418	7	networks	network	NOUN
ejpam-5323	418	8	.	.	PUNCT
ejpam-5323	419	1	int	int	NOUN
ejpam-5323	419	2	.	.	PUNCT
ejpam-5323	420	1	j.	j.	PROPN
ejpam-5323	420	2	innov	innov	PROPN
ejpam-5323	420	3	.	.	PUNCT
ejpam-5323	421	1	sci	sci	PROPN
ejpam-5323	421	2	.	.	PUNCT
ejpam-5323	422	1	eng	eng	PROPN
ejpam-5323	422	2	.	.	PROPN
ejpam-5323	422	3	technol	technol	PROPN
ejpam-5323	422	4	.	.	PROPN
ejpam-5323	422	5	,	,	PUNCT
ejpam-5323	422	6	8(12):832–837	8(12):832–837	NUM
ejpam-5323	422	7	,	,	PUNCT
ejpam-5323	422	8	2019	2019	NUM
ejpam-5323	422	9	.	.	PUNCT