id	sid	tid	token	lemma	pos
ejpam-1844	1	1	compiles/45419980dc21a6b11049d118cdd92a9c	compiles/45419980dc21a6b11049d118cdd92a9c	NOUN
ejpam-1844	1	2	/	/	SYM
ejpam-1844	1	3	output.dvi	output.dvi	NOUN
ejpam-1844	1	4	european	european	ADJ
ejpam-1844	1	5	journal	journal	NOUN
ejpam-1844	1	6	of	of	ADP
ejpam-1844	1	7	pure	pure	ADJ
ejpam-1844	1	8	and	and	CCONJ
ejpam-1844	1	9	applied	apply	VERB
ejpam-1844	1	10	mathematics	mathematic	NOUN
ejpam-1844	1	11	vol	vol	NOUN
ejpam-1844	1	12	.	.	PROPN
ejpam-1844	2	1	6	6	NUM
ejpam-1844	2	2	,	,	PUNCT
ejpam-1844	2	3	no	no	INTJ
ejpam-1844	2	4	.	.	NOUN
ejpam-1844	2	5	3	3	NUM
ejpam-1844	2	6	,	,	PUNCT
ejpam-1844	2	7	2013	2013	NUM
ejpam-1844	2	8	,	,	PUNCT
ejpam-1844	2	9	363	363	NUM
ejpam-1844	2	10	-	-	SYM
ejpam-1844	2	11	364	364	NUM
ejpam-1844	2	12	issn	issn	PROPN
ejpam-1844	2	13	1307	1307	NUM
ejpam-1844	2	14	-	-	SYM
ejpam-1844	2	15	5543	5543	NUM
ejpam-1844	2	16	–	–	PUNCT
ejpam-1844	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1844	2	18	dickson	dickson	PROPN
ejpam-1844	2	19	’s	’s	PART
ejpam-1844	2	20	method	method	NOUN
ejpam-1844	2	21	for	for	ADP
ejpam-1844	2	22	generating	generate	VERB
ejpam-1844	2	23	pythagorean	pythagorean	PROPN
ejpam-1844	2	24	triples	triple	NOUN
ejpam-1844	2	25	revisited	revisit	VERB
ejpam-1844	2	26	josef	josef	PROPN
ejpam-1844	2	27	rukavicka	rukavicka	PROPN
ejpam-1844	2	28	department	department	PROPN
ejpam-1844	2	29	of	of	ADP
ejpam-1844	2	30	mathematics	mathematic	NOUN
ejpam-1844	2	31	,	,	PUNCT
ejpam-1844	2	32	faculty	faculty	NOUN
ejpam-1844	2	33	of	of	ADP
ejpam-1844	2	34	electrical	electrical	ADJ
ejpam-1844	2	35	engineering	engineering	NOUN
ejpam-1844	2	36	,	,	PUNCT
ejpam-1844	2	37	czech	czech	PROPN
ejpam-1844	2	38	technical	technical	PROPN
ejpam-1844	2	39	university	university	PROPN
ejpam-1844	2	40	in	in	ADP
ejpam-1844	2	41	prague	prague	PROPN
ejpam-1844	2	42	abstract	abstract	NOUN
ejpam-1844	2	43	.	.	PUNCT
ejpam-1844	3	1	the	the	DET
ejpam-1844	3	2	dickson	dickson	PROPN
ejpam-1844	3	3	’s	’s	PART
ejpam-1844	3	4	method	method	NOUN
ejpam-1844	3	5	for	for	ADP
ejpam-1844	3	6	generating	generate	VERB
ejpam-1844	3	7	pythagorean	pythagorean	NOUN
ejpam-1844	3	8	triples	triple	NOUN
ejpam-1844	3	9	states	state	VERB
ejpam-1844	3	10	that	that	SCONJ
ejpam-1844	3	11	the	the	DET
ejpam-1844	3	12	integers	integer	NOUN
ejpam-1844	3	13	a	a	PRON
ejpam-1844	3	14	=	=	SYM
ejpam-1844	3	15	r	r	NOUN
ejpam-1844	3	16	+	+	NUM
ejpam-1844	3	17	s	s	NOUN
ejpam-1844	3	18	,	,	PUNCT
ejpam-1844	3	19	b	b	X
ejpam-1844	4	1	=	=	SYM
ejpam-1844	4	2	r	r	NOUN
ejpam-1844	4	3	+	+	PROPN
ejpam-1844	4	4	t	t	PROPN
ejpam-1844	4	5	,	,	PUNCT
ejpam-1844	4	6	c	c	NOUN
ejpam-1844	4	7	=	=	SYM
ejpam-1844	4	8	r	r	NOUN
ejpam-1844	4	9	+	+	CCONJ
ejpam-1844	4	10	s+	s+	PUNCT
ejpam-1844	4	11	t	t	PROPN
ejpam-1844	4	12	form	form	VERB
ejpam-1844	4	13	a	a	DET
ejpam-1844	4	14	pythagorean	pythagorean	PROPN
ejpam-1844	4	15	triple	triple	NOUN
ejpam-1844	4	16	(	(	PUNCT
ejpam-1844	4	17	a	a	PRON
ejpam-1844	4	18	,	,	PUNCT
ejpam-1844	4	19	b	b	NOUN
ejpam-1844	4	20	,	,	PUNCT
ejpam-1844	4	21	c	c	NOUN
ejpam-1844	4	22	)	)	PUNCT
ejpam-1844	4	23	on	on	ADP
ejpam-1844	4	24	condition	condition	NOUN
ejpam-1844	4	25	that	that	SCONJ
ejpam-1844	4	26	r2	r2	NOUN
ejpam-1844	4	27	=	=	SYM
ejpam-1844	4	28	2st	2st	NOUN
ejpam-1844	4	29	,	,	PUNCT
ejpam-1844	4	30	where	where	SCONJ
ejpam-1844	4	31	r	r	NOUN
ejpam-1844	4	32	,	,	PUNCT
ejpam-1844	4	33	s	s	PART
ejpam-1844	4	34	,	,	PUNCT
ejpam-1844	4	35	t	t	PROPN
ejpam-1844	4	36	are	be	AUX
ejpam-1844	4	37	positive	positive	ADJ
ejpam-1844	4	38	integers	integer	NOUN
ejpam-1844	4	39	.	.	PUNCT
ejpam-1844	5	1	this	this	DET
ejpam-1844	5	2	paper	paper	NOUN
ejpam-1844	5	3	presents	present	VERB
ejpam-1844	5	4	a	a	DET
ejpam-1844	5	5	new	new	ADJ
ejpam-1844	5	6	simple	simple	ADJ
ejpam-1844	5	7	proof	proof	NOUN
ejpam-1844	5	8	of	of	ADP
ejpam-1844	5	9	this	this	DET
ejpam-1844	5	10	method	method	NOUN
ejpam-1844	5	11	.	.	PUNCT
ejpam-1844	6	1	2010	2010	NUM
ejpam-1844	6	2	mathematics	mathematic	NOUN
ejpam-1844	6	3	subject	subject	NOUN
ejpam-1844	6	4	classifications	classification	NOUN
ejpam-1844	6	5	:	:	PUNCT
ejpam-1844	6	6	11d45	11d45	NUM
ejpam-1844	6	7	key	key	ADJ
ejpam-1844	6	8	words	word	NOUN
ejpam-1844	6	9	and	and	CCONJ
ejpam-1844	6	10	phrases	phrase	NOUN
ejpam-1844	6	11	:	:	PUNCT
ejpam-1844	6	12	pythagorean	pythagorean	PROPN
ejpam-1844	6	13	triples	triple	NOUN
ejpam-1844	6	14	,	,	PUNCT
ejpam-1844	6	15	dickson	dickson	PROPN
ejpam-1844	6	16	’s	’s	PART
ejpam-1844	6	17	method	method	NOUN
ejpam-1844	6	18	,	,	PUNCT
ejpam-1844	6	19	diophantine	diophantine	VERB
ejpam-1844	6	20	approximation	approximation	NOUN
ejpam-1844	6	21	1	1	NUM
ejpam-1844	6	22	.	.	PUNCT
ejpam-1844	7	1	introduction	introduction	NOUN
ejpam-1844	7	2	a	a	DET
ejpam-1844	7	3	triple	triple	ADJ
ejpam-1844	7	4	(	(	PUNCT
ejpam-1844	7	5	a	a	PRON
ejpam-1844	7	6	,	,	PUNCT
ejpam-1844	7	7	b	b	NOUN
ejpam-1844	7	8	,	,	PUNCT
ejpam-1844	7	9	c	c	NOUN
ejpam-1844	7	10	)	)	PUNCT
ejpam-1844	7	11	of	of	ADP
ejpam-1844	7	12	positive	positive	ADJ
ejpam-1844	7	13	integers	integer	NOUN
ejpam-1844	7	14	is	be	AUX
ejpam-1844	7	15	called	call	VERB
ejpam-1844	7	16	a	a	DET
ejpam-1844	7	17	pythagorean	pythagorean	NOUN
ejpam-1844	7	18	triple	triple	NOUN
ejpam-1844	7	19	in	in	ADP
ejpam-1844	7	20	case	case	NOUN
ejpam-1844	7	21	that	that	SCONJ
ejpam-1844	7	22	a2	a2	PROPN
ejpam-1844	7	23	+	+	CCONJ
ejpam-1844	7	24	b2	b2	NOUN
ejpam-1844	7	25	=	=	PROPN
ejpam-1844	7	26	c2	c2	PROPN
ejpam-1844	7	27	.	.	PUNCT
ejpam-1844	8	1	there	there	PRON
ejpam-1844	8	2	are	be	VERB
ejpam-1844	8	3	several	several	ADJ
ejpam-1844	8	4	methods	method	NOUN
ejpam-1844	8	5	for	for	ADP
ejpam-1844	8	6	generating	generate	VERB
ejpam-1844	8	7	pythagorean	pythagorean	NOUN
ejpam-1844	8	8	triples	triple	NOUN
ejpam-1844	8	9	.	.	PUNCT
ejpam-1844	9	1	in	in	ADP
ejpam-1844	9	2	this	this	DET
ejpam-1844	9	3	paper	paper	NOUN
ejpam-1844	9	4	we	we	PRON
ejpam-1844	9	5	investigate	investigate	VERB
ejpam-1844	9	6	the	the	DET
ejpam-1844	9	7	dickson	dickson	PROPN
ejpam-1844	9	8	’s	’s	PART
ejpam-1844	9	9	method	method	NOUN
ejpam-1844	9	10	,	,	PUNCT
ejpam-1844	9	11	[	[	X
ejpam-1844	9	12	1	1	NUM
ejpam-1844	9	13	]	]	PUNCT
ejpam-1844	9	14	,	,	PUNCT
ejpam-1844	9	15	that	that	PRON
ejpam-1844	9	16	states	state	VERB
ejpam-1844	9	17	that	that	SCONJ
ejpam-1844	9	18	the	the	DET
ejpam-1844	9	19	integers	integer	NOUN
ejpam-1844	9	20	a	a	PRON
ejpam-1844	9	21	=	=	SYM
ejpam-1844	9	22	r	r	NOUN
ejpam-1844	9	23	+	+	NUM
ejpam-1844	9	24	s	s	NOUN
ejpam-1844	9	25	,	,	PUNCT
ejpam-1844	9	26	b	b	X
ejpam-1844	9	27	=	=	SYM
ejpam-1844	9	28	r	r	NOUN
ejpam-1844	9	29	+	+	PROPN
ejpam-1844	9	30	t	t	PROPN
ejpam-1844	9	31	,	,	PUNCT
ejpam-1844	9	32	c	c	NOUN
ejpam-1844	10	1	=	=	SYM
ejpam-1844	10	2	r	r	NOUN
ejpam-1844	10	3	+	+	CCONJ
ejpam-1844	10	4	s+	s+	PUNCT
ejpam-1844	10	5	t	t	PROPN
ejpam-1844	10	6	form	form	VERB
ejpam-1844	10	7	a	a	DET
ejpam-1844	10	8	pythagorean	pythagorean	PROPN
ejpam-1844	10	9	triple	triple	NOUN
ejpam-1844	10	10	(	(	PUNCT
ejpam-1844	10	11	a	a	PRON
ejpam-1844	10	12	,	,	PUNCT
ejpam-1844	10	13	b	b	NOUN
ejpam-1844	10	14	,	,	PUNCT
ejpam-1844	10	15	c	c	NOUN
ejpam-1844	10	16	)	)	PUNCT
ejpam-1844	10	17	on	on	ADP
ejpam-1844	10	18	condition	condition	NOUN
ejpam-1844	10	19	that	that	SCONJ
ejpam-1844	10	20	r2	r2	NOUN
ejpam-1844	10	21	=	=	SYM
ejpam-1844	10	22	2st	2st	NOUN
ejpam-1844	10	23	,	,	PUNCT
ejpam-1844	10	24	where	where	SCONJ
ejpam-1844	10	25	r	r	NOUN
ejpam-1844	10	26	,	,	PUNCT
ejpam-1844	10	27	s	s	PART
ejpam-1844	10	28	,	,	PUNCT
ejpam-1844	10	29	t	t	PROPN
ejpam-1844	10	30	are	be	AUX
ejpam-1844	10	31	positive	positive	ADJ
ejpam-1844	10	32	integers	integer	NOUN
ejpam-1844	10	33	.	.	PUNCT
ejpam-1844	11	1	the	the	DET
ejpam-1844	11	2	paper	paper	NOUN
ejpam-1844	11	3	presents	present	VERB
ejpam-1844	11	4	a	a	DET
ejpam-1844	11	5	new	new	ADJ
ejpam-1844	11	6	simple	simple	ADJ
ejpam-1844	11	7	proof	proof	NOUN
ejpam-1844	11	8	of	of	ADP
ejpam-1844	11	9	this	this	DET
ejpam-1844	11	10	method	method	NOUN
ejpam-1844	11	11	.	.	PUNCT
ejpam-1844	12	1	2	2	X
ejpam-1844	12	2	.	.	X
ejpam-1844	12	3	dickson	dickson	PROPN
ejpam-1844	12	4	’s	’s	PART
ejpam-1844	12	5	method	method	NOUN
ejpam-1844	12	6	for	for	ADP
ejpam-1844	12	7	generating	generate	VERB
ejpam-1844	12	8	pythagorean	pythagorean	NOUN
ejpam-1844	12	9	triples	triple	NOUN
ejpam-1844	12	10	theorem	theorem	VERB
ejpam-1844	12	11	1	1	NUM
ejpam-1844	12	12	.	.	PUNCT
ejpam-1844	12	13	given	give	VERB
ejpam-1844	12	14	positive	positive	ADJ
ejpam-1844	12	15	integers	integer	NOUN
ejpam-1844	12	16	k	k	NOUN
ejpam-1844	12	17	,	,	PUNCT
ejpam-1844	12	18	q	q	X
ejpam-1844	12	19	,	,	PUNCT
ejpam-1844	12	20	p	p	X
ejpam-1844	12	21	,	,	PUNCT
ejpam-1844	12	22	where	where	SCONJ
ejpam-1844	12	23	k	k	PROPN
ejpam-1844	12	24	>	>	X
ejpam-1844	12	25	q	q	PUNCT
ejpam-1844	12	26	and	and	CCONJ
ejpam-1844	12	27	let	let	VERB
ejpam-1844	12	28	c	c	NOUN
ejpam-1844	12	29	=	=	PUNCT
ejpam-1844	13	1	k	k	PROPN
ejpam-1844	14	1	+	+	CCONJ
ejpam-1844	14	2	p	p	X
ejpam-1844	14	3	,	,	PUNCT
ejpam-1844	14	4	b	b	NOUN
ejpam-1844	14	5	=	=	SYM
ejpam-1844	15	1	p	p	X
ejpam-1844	16	1	+	+	CCONJ
ejpam-1844	16	2	q	q	ADJ
ejpam-1844	16	3	,	,	PUNCT
ejpam-1844	16	4	a	a	PRON
ejpam-1844	16	5	=	=	X
ejpam-1844	16	6	k.	k.	PROPN
ejpam-1844	16	7	then	then	ADV
ejpam-1844	16	8	a2	a2	PROPN
ejpam-1844	16	9	+	+	CCONJ
ejpam-1844	16	10	b2	b2	NOUN
ejpam-1844	16	11	=	=	SYM
ejpam-1844	16	12	c2	c2	PROPN
ejpam-1844	16	13	if	if	SCONJ
ejpam-1844	16	14	and	and	CCONJ
ejpam-1844	16	15	only	only	ADV
ejpam-1844	16	16	if	if	SCONJ
ejpam-1844	16	17	q2	q2	NOUN
ejpam-1844	16	18	=	=	SYM
ejpam-1844	16	19	2p(k−	2p(k−	NUM
ejpam-1844	16	20	q	q	NOUN
ejpam-1844	16	21	)	)	PUNCT
ejpam-1844	16	22	.	.	PUNCT
ejpam-1844	17	1	proof	proof	NOUN
ejpam-1844	17	2	.	.	PUNCT
ejpam-1844	18	1	we	we	PRON
ejpam-1844	18	2	will	will	AUX
ejpam-1844	18	3	show	show	VERB
ejpam-1844	18	4	a	a	DET
ejpam-1844	18	5	bijection	bijection	NOUN
ejpam-1844	18	6	between	between	ADP
ejpam-1844	18	7	triples	triple	NOUN
ejpam-1844	18	8	(	(	PUNCT
ejpam-1844	18	9	k	k	X
ejpam-1844	18	10	,	,	PUNCT
ejpam-1844	18	11	q	q	ADJ
ejpam-1844	18	12	,	,	PUNCT
ejpam-1844	18	13	p	p	NOUN
ejpam-1844	18	14	)	)	PUNCT
ejpam-1844	18	15	and	and	CCONJ
ejpam-1844	18	16	(	(	PUNCT
ejpam-1844	18	17	a	a	PRON
ejpam-1844	18	18	,	,	PUNCT
ejpam-1844	18	19	b	b	NOUN
ejpam-1844	18	20	,	,	PUNCT
ejpam-1844	18	21	c	c	NOUN
ejpam-1844	18	22	)	)	PUNCT
ejpam-1844	18	23	.	.	PUNCT
ejpam-1844	19	1	the	the	DET
ejpam-1844	19	2	bijection	bijection	NOUN
ejpam-1844	19	3	is	be	AUX
ejpam-1844	19	4	depicted	depict	VERB
ejpam-1844	19	5	in	in	ADP
ejpam-1844	19	6	figures	figure	NOUN
ejpam-1844	19	7	1a	1a	PROPN
ejpam-1844	19	8	and	and	CCONJ
ejpam-1844	19	9	1b	1b	NUM
ejpam-1844	19	10	(	(	PUNCT
ejpam-1844	19	11	there	there	PRON
ejpam-1844	19	12	are	be	VERB
ejpam-1844	19	13	two	two	NUM
ejpam-1844	19	14	examples	example	NOUN
ejpam-1844	19	15	for	for	ADP
ejpam-1844	19	16	k	k	PROPN
ejpam-1844	19	17	=	=	SYM
ejpam-1844	19	18	8	8	NUM
ejpam-1844	19	19	,	,	PUNCT
ejpam-1844	19	20	q	q	NOUN
ejpam-1844	19	21	=	=	NOUN
ejpam-1844	19	22	4	4	NUM
ejpam-1844	19	23	,	,	PUNCT
ejpam-1844	19	24	p	p	NOUN
ejpam-1844	19	25	=	=	SYM
ejpam-1844	19	26	2	2	NUM
ejpam-1844	19	27	,	,	PUNCT
ejpam-1844	19	28	a	a	DET
ejpam-1844	19	29	=	=	X
ejpam-1844	19	30	k	k	NOUN
ejpam-1844	19	31	=	=	SYM
ejpam-1844	19	32	8	8	NUM
ejpam-1844	19	33	,	,	PUNCT
ejpam-1844	19	34	b	b	NOUN
ejpam-1844	20	1	=	=	SYM
ejpam-1844	20	2	p	p	X
ejpam-1844	20	3	+	+	NOUN
ejpam-1844	20	4	q	q	NOUN
ejpam-1844	20	5	=	=	SYM
ejpam-1844	20	6	6	6	NUM
ejpam-1844	20	7	,	,	PUNCT
ejpam-1844	20	8	c	c	NOUN
ejpam-1844	20	9	=	=	SYM
ejpam-1844	20	10	k	k	PROPN
ejpam-1844	21	1	+	+	CCONJ
ejpam-1844	21	2	p	p	X
ejpam-1844	21	3	=	=	PROPN
ejpam-1844	21	4	10	10	NUM
ejpam-1844	21	5	and	and	CCONJ
ejpam-1844	21	6	k	k	NOUN
ejpam-1844	21	7	=	=	SYM
ejpam-1844	21	8	8	8	NUM
ejpam-1844	21	9	,	,	PUNCT
ejpam-1844	21	10	p	p	NOUN
ejpam-1844	21	11	=	=	NOUN
ejpam-1844	21	12	9	9	NUM
ejpam-1844	21	13	,	,	PUNCT
ejpam-1844	21	14	q	q	NOUN
ejpam-1844	21	15	=	=	SYM
ejpam-1844	21	16	6	6	NUM
ejpam-1844	21	17	,	,	PUNCT
ejpam-1844	21	18	a	a	PRON
ejpam-1844	21	19	=	=	X
ejpam-1844	21	20	k	k	NOUN
ejpam-1844	21	21	=	=	SYM
ejpam-1844	21	22	8	8	NUM
ejpam-1844	21	23	,	,	PUNCT
ejpam-1844	21	24	b	b	NOUN
ejpam-1844	21	25	=	=	SYM
ejpam-1844	21	26	p	p	X
ejpam-1844	21	27	+	+	NOUN
ejpam-1844	21	28	q	q	NOUN
ejpam-1844	21	29	=	=	SYM
ejpam-1844	21	30	15	15	NUM
ejpam-1844	21	31	,	,	PUNCT
ejpam-1844	21	32	c	c	NOUN
ejpam-1844	21	33	=	=	PUNCT
ejpam-1844	21	34	k+	k+	NOUN
ejpam-1844	21	35	p	p	NOUN
ejpam-1844	21	36	=	=	NOUN
ejpam-1844	21	37	17	17	NUM
ejpam-1844	21	38	)	)	PUNCT
ejpam-1844	21	39	.	.	PUNCT
ejpam-1844	22	1	email	email	NOUN
ejpam-1844	22	2	addresses	address	NOUN
ejpam-1844	22	3	:	:	PUNCT
ejpam-1844	22	4	josef.rukavicka@seznam.cz	josef.rukavicka@seznam.cz	NOUN
ejpam-1844	22	5	,	,	PUNCT
ejpam-1844	22	6	rukavij@fel.cvut.cz	rukavij@fel.cvut.cz	NOUN
ejpam-1844	22	7	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1844	23	1	363	363	NUM
ejpam-1844	23	2	c	c	X
ejpam-1844	23	3	©	©	PROPN
ejpam-1844	23	4	2013	2013	NUM
ejpam-1844	23	5	ejpam	ejpam	NOUN
ejpam-1844	23	6	all	all	DET
ejpam-1844	23	7	rights	right	NOUN
ejpam-1844	23	8	reserved	reserve	VERB
ejpam-1844	23	9	.	.	PUNCT
ejpam-1844	24	1	references	reference	NOUN
ejpam-1844	24	2	364	364	NUM
ejpam-1844	24	3	(	(	PUNCT
ejpam-1844	24	4	a	a	NOUN
ejpam-1844	24	5	)	)	PUNCT
ejpam-1844	24	6	q	q	NOUN
ejpam-1844	25	1	=	=	NOUN
ejpam-1844	25	2	4	4	NUM
ejpam-1844	25	3	and	and	CCONJ
ejpam-1844	25	4	p	p	NOUN
ejpam-1844	25	5	=	=	SYM
ejpam-1844	25	6	2	2	NUM
ejpam-1844	25	7	(	(	PUNCT
ejpam-1844	25	8	b	b	NOUN
ejpam-1844	25	9	)	)	PUNCT
ejpam-1844	25	10	q	q	NOUN
ejpam-1844	26	1	=	=	PUNCT
ejpam-1844	26	2	6	6	NUM
ejpam-1844	26	3	and	and	CCONJ
ejpam-1844	26	4	p	p	NOUN
ejpam-1844	26	5	=	=	NOUN
ejpam-1844	26	6	9	9	NUM
ejpam-1844	26	7	figure	figure	NOUN
ejpam-1844	26	8	1	1	NUM
ejpam-1844	26	9	:	:	PUNCT
ejpam-1844	26	10	examples	example	NOUN
ejpam-1844	26	11	of	of	ADP
ejpam-1844	26	12	bijections	bijection	NOUN
ejpam-1844	26	13	between	between	ADP
ejpam-1844	26	14	triples	triple	NOUN
ejpam-1844	26	15	with	with	ADP
ejpam-1844	26	16	k	k	PROPN
ejpam-1844	26	17	=	=	SYM
ejpam-1844	26	18	8	8	NUM
ejpam-1844	26	19	varying	vary	VERB
ejpam-1844	26	20	q	q	NOUN
ejpam-1844	26	21	and	and	CCONJ
ejpam-1844	26	22	p.	p.	NOUN
ejpam-1844	26	23	the	the	DET
ejpam-1844	26	24	bijection	bijection	NOUN
ejpam-1844	26	25	consists	consist	VERB
ejpam-1844	26	26	in	in	ADP
ejpam-1844	26	27	transforming	transform	VERB
ejpam-1844	26	28	the	the	DET
ejpam-1844	26	29	grid	grid	NOUN
ejpam-1844	26	30	of	of	ADP
ejpam-1844	26	31	k	k	PROPN
ejpam-1844	26	32	×	×	PROPN
ejpam-1844	26	33	k	k	PROPN
ejpam-1844	26	34	squares	square	NOUN
ejpam-1844	26	35	into	into	ADP
ejpam-1844	26	36	an	an	DET
ejpam-1844	26	37	object	object	NOUN
ejpam-1844	26	38	that	that	PRON
ejpam-1844	26	39	uniquely	uniquely	ADV
ejpam-1844	26	40	determines	determine	VERB
ejpam-1844	26	41	a	a	DET
ejpam-1844	26	42	pythagorean	pythagorean	ADJ
ejpam-1844	26	43	triple	triple	NOUN
ejpam-1844	26	44	(	(	PUNCT
ejpam-1844	26	45	a	a	PRON
ejpam-1844	26	46	,	,	PUNCT
ejpam-1844	26	47	b	b	NOUN
ejpam-1844	26	48	,	,	PUNCT
ejpam-1844	26	49	c	c	NOUN
ejpam-1844	26	50	)	)	PUNCT
ejpam-1844	26	51	.	.	PUNCT
ejpam-1844	27	1	the	the	DET
ejpam-1844	27	2	crucial	crucial	ADJ
ejpam-1844	27	3	observation	observation	NOUN
ejpam-1844	27	4	is	be	AUX
ejpam-1844	27	5	that	that	SCONJ
ejpam-1844	27	6	q2	q2	NOUN
ejpam-1844	27	7	is	be	AUX
ejpam-1844	27	8	divisible	divisible	ADJ
ejpam-1844	27	9	by	by	ADP
ejpam-1844	27	10	2(k−q	2(k−q	NOUN
ejpam-1844	27	11	)	)	PUNCT
ejpam-1844	27	12	and	and	CCONJ
ejpam-1844	27	13	hence	hence	ADV
ejpam-1844	27	14	the	the	DET
ejpam-1844	27	15	squares	square	NOUN
ejpam-1844	27	16	from	from	ADP
ejpam-1844	27	17	the	the	DET
ejpam-1844	27	18	grid	grid	NOUN
ejpam-1844	27	19	of	of	ADP
ejpam-1844	27	20	q2	q2	NOUN
ejpam-1844	27	21	squares	square	NOUN
ejpam-1844	27	22	can	can	AUX
ejpam-1844	27	23	be	be	AUX
ejpam-1844	27	24	equally	equally	ADV
ejpam-1844	27	25	separated	separate	VERB
ejpam-1844	27	26	in	in	ADP
ejpam-1844	27	27	order	order	NOUN
ejpam-1844	27	28	to	to	PART
ejpam-1844	27	29	build	build	VERB
ejpam-1844	27	30	up	up	ADP
ejpam-1844	27	31	the	the	DET
ejpam-1844	27	32	l	l	NOUN
ejpam-1844	27	33	-	-	ADJ
ejpam-1844	27	34	shaped	shape	VERB
ejpam-1844	27	35	object	object	NOUN
ejpam-1844	27	36	on	on	ADP
ejpam-1844	27	37	the	the	DET
ejpam-1844	27	38	right	right	ADJ
ejpam-1844	27	39	side	side	NOUN
ejpam-1844	27	40	of	of	ADP
ejpam-1844	27	41	a	a	DET
ejpam-1844	27	42	figure	figure	NOUN
ejpam-1844	27	43	;	;	PUNCT
ejpam-1844	27	44	that	that	DET
ejpam-1844	27	45	object	object	NOUN
ejpam-1844	27	46	represents	represent	VERB
ejpam-1844	27	47	a	a	DET
ejpam-1844	27	48	pythagorean	pythagorean	ADJ
ejpam-1844	27	49	triple	triple	NOUN
ejpam-1844	27	50	(	(	PUNCT
ejpam-1844	27	51	k	k	NOUN
ejpam-1844	27	52	,	,	PUNCT
ejpam-1844	27	53	q+	q+	NOUN
ejpam-1844	27	54	p	p	X
ejpam-1844	27	55	,	,	PUNCT
ejpam-1844	27	56	k+	k+	NOUN
ejpam-1844	27	57	p	p	NOUN
ejpam-1844	27	58	)	)	PUNCT
ejpam-1844	27	59	=	=	SYM
ejpam-1844	27	60	(	(	PUNCT
ejpam-1844	27	61	a	a	PRON
ejpam-1844	27	62	,	,	PUNCT
ejpam-1844	27	63	b	b	NOUN
ejpam-1844	27	64	,	,	PUNCT
ejpam-1844	27	65	c	c	NOUN
ejpam-1844	27	66	)	)	PUNCT
ejpam-1844	27	67	.	.	PUNCT
ejpam-1844	28	1	to	to	PART
ejpam-1844	28	2	see	see	VERB
ejpam-1844	28	3	this	this	PRON
ejpam-1844	28	4	just	just	ADV
ejpam-1844	28	5	note	note	VERB
ejpam-1844	28	6	the	the	DET
ejpam-1844	28	7	l	l	ADV
ejpam-1844	28	8	-	-	PUNCT
ejpam-1844	28	9	shaped	shape	VERB
ejpam-1844	28	10	object	object	NOUN
ejpam-1844	28	11	is	be	AUX
ejpam-1844	28	12	composed	compose	VERB
ejpam-1844	28	13	of	of	ADP
ejpam-1844	28	14	k2	k2	ADJ
ejpam-1844	28	15	squares	square	NOUN
ejpam-1844	28	16	and	and	CCONJ
ejpam-1844	28	17	adding	add	VERB
ejpam-1844	28	18	(	(	PUNCT
ejpam-1844	28	19	p+	p+	VERB
ejpam-1844	28	20	q)2	q)2	PROPN
ejpam-1844	28	21	squares	square	NOUN
ejpam-1844	28	22	produces	produce	VERB
ejpam-1844	28	23	(	(	PUNCT
ejpam-1844	28	24	k+	k+	X
ejpam-1844	28	25	p)2	p)2	NOUN
ejpam-1844	28	26	squares	square	NOUN
ejpam-1844	28	27	.	.	PUNCT
ejpam-1844	29	1	on	on	ADP
ejpam-1844	29	2	the	the	DET
ejpam-1844	29	3	other	other	ADJ
ejpam-1844	29	4	hand	hand	NOUN
ejpam-1844	29	5	,	,	PUNCT
ejpam-1844	29	6	given	give	VERB
ejpam-1844	29	7	an	an	DET
ejpam-1844	29	8	l	l	NOUN
ejpam-1844	29	9	-	-	ADJ
ejpam-1844	29	10	shaped	shape	VERB
ejpam-1844	29	11	object	object	NOUN
ejpam-1844	29	12	composed	compose	VERB
ejpam-1844	29	13	of	of	ADP
ejpam-1844	29	14	k2	k2	ADJ
ejpam-1844	29	15	squares	square	NOUN
ejpam-1844	29	16	,	,	PUNCT
ejpam-1844	29	17	then	then	ADV
ejpam-1844	29	18	k	k	NOUN
ejpam-1844	29	19	,	,	PUNCT
ejpam-1844	29	20	q	q	INTJ
ejpam-1844	29	21	,	,	PUNCT
ejpam-1844	29	22	p	p	NOUN
ejpam-1844	29	23	are	be	AUX
ejpam-1844	29	24	uniquely	uniquely	ADV
ejpam-1844	29	25	determined	determine	VERB
ejpam-1844	29	26	.	.	PUNCT
ejpam-1844	30	1	also	also	ADV
ejpam-1844	30	2	note	note	VERB
ejpam-1844	30	3	that	that	SCONJ
ejpam-1844	30	4	(	(	PUNCT
ejpam-1844	30	5	b	b	X
ejpam-1844	30	6	,	,	PUNCT
ejpam-1844	30	7	a	a	DET
ejpam-1844	30	8	,	,	PUNCT
ejpam-1844	30	9	c	c	NOUN
ejpam-1844	30	10	)	)	PUNCT
ejpam-1844	30	11	and	and	CCONJ
ejpam-1844	30	12	(	(	PUNCT
ejpam-1844	30	13	a	a	DET
ejpam-1844	30	14	,	,	PUNCT
ejpam-1844	30	15	b	b	NOUN
ejpam-1844	30	16	,	,	PUNCT
ejpam-1844	30	17	c	c	NOUN
ejpam-1844	30	18	)	)	PUNCT
ejpam-1844	30	19	will	will	AUX
ejpam-1844	30	20	yield	yield	VERB
ejpam-1844	30	21	different	different	ADJ
ejpam-1844	30	22	values	value	NOUN
ejpam-1844	30	23	of	of	ADP
ejpam-1844	30	24	(	(	PUNCT
ejpam-1844	30	25	k	k	X
ejpam-1844	30	26	,	,	PUNCT
ejpam-1844	30	27	p	p	X
ejpam-1844	30	28	,	,	PUNCT
ejpam-1844	30	29	q	q	NOUN
ejpam-1844	30	30	)	)	PUNCT
ejpam-1844	30	31	.	.	PUNCT
ejpam-1844	31	1	references	reference	NOUN
ejpam-1844	31	2	[	[	X
ejpam-1844	31	3	1	1	NUM
ejpam-1844	31	4	]	]	X
ejpam-1844	31	5	l.e	l.e	PROPN
ejpam-1844	31	6	.	.	PUNCT
ejpam-1844	31	7	dickson	dickson	PROPN
ejpam-1844	31	8	.	.	PUNCT
ejpam-1844	32	1	history	history	NOUN
ejpam-1844	32	2	of	of	ADP
ejpam-1844	32	3	the	the	DET
ejpam-1844	32	4	theory	theory	NOUN
ejpam-1844	32	5	of	of	ADP
ejpam-1844	32	6	numbers	number	NOUN
ejpam-1844	32	7	,	,	PUNCT
ejpam-1844	32	8	vol	vol	NOUN
ejpam-1844	32	9	.	.	PROPN
ejpam-1844	33	1	2	2	NUM
ejpam-1844	33	2	:	:	PUNCT
ejpam-1844	33	3	diophantine	diophantine	VERB
ejpam-1844	33	4	analysis	analysis	NOUN
ejpam-1844	33	5	.	.	PUNCT
ejpam-1844	34	1	carnegie	carnegie	NOUN
ejpam-1844	34	2	institution	institution	NOUN
ejpam-1844	34	3	of	of	ADP
ejpam-1844	34	4	washington	washington	PROPN
ejpam-1844	34	5	,	,	PUNCT
ejpam-1844	34	6	publication	publication	NOUN
ejpam-1844	35	1	no	no	INTJ
ejpam-1844	35	2	.	.	PROPN
ejpam-1844	35	3	256	256	NUM
ejpam-1844	35	4	,	,	PUNCT
ejpam-1844	35	5	2:169	2:169	NUM
ejpam-1844	35	6	,	,	PUNCT
ejpam-1844	35	7	1920	1920	NUM
ejpam-1844	35	8	.	.	PUNCT