id	sid	tid	token	lemma	pos
m-886	1	1	ijo	ijo	PROPN
m-886	1	2	international	international	PROPN
m-886	1	3	journal	journal	PROPN
m-886	1	4	of	of	ADP
m-886	1	5	mathematics	mathematics	PROPN
m-886	1	6	(	(	PUNCT
m-886	1	7	issn	issn	PROPN
m-886	1	8	:	:	PUNCT
m-886	1	9	2992	2992	NUM
m-886	1	10	-	-	SYM
m-886	1	11	4421	4421	NUM
m-886	1	12	)	)	PUNCT
m-886	1	13	dr	dr	PROPN
m-886	1	14	.	.	PROPN
m-886	1	15	n.thiruniraiselvi1	n.thiruniraiselvi1	PROPN
m-886	1	16	*	*	PROPN
m-886	1	17	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-886	1	18	volume	volume	NOUN
m-886	1	19	07	07	NUM
m-886	1	20	||	||	NOUN
m-886	1	21	issue	issue	NOUN
m-886	1	22	05||	05||	X
m-886	1	23	may	may	AUX
m-886	1	24	,	,	PUNCT
m-886	1	25	2024	2024	NUM
m-886	1	26	||	||	NOUN
m-886	1	27	techniques	technique	NOUN
m-886	1	28	to	to	PART
m-886	1	29	solve	solve	VERB
m-886	1	30	diophantine	diophantine	VERB
m-886	1	31	equation	equation	NOUN
m-886	1	32	of	of	ADP
m-886	1	33	degree	degree	NOUN
m-886	1	34	ten	ten	NUM
m-886	1	35	with	with	ADP
m-886	1	36	six	six	NUM
m-886	1	37	unknowns	unknown	NOUN
m-886	1	38	822366	822366	NUM
m-886	1	39	r)qp(800z3456yx	r)qp(800z3456yx	PROPN
m-886	1	40			PROPN
m-886	1	41	dr	dr	PROPN
m-886	1	42	.	.	PROPN
m-886	1	43	n.thiruniraiselvi1	n.thiruniraiselvi1	PROPN
m-886	1	44	*	*	PROPN
m-886	1	45	,	,	PUNCT
m-886	1	46	dr	dr	PROPN
m-886	1	47	.	.	PROPN
m-886	1	48	m.a.gopalan2	m.a.gopalan2	PROPN
m-886	1	49	1	1	NUM
m-886	1	50	assistant	assistant	NOUN
m-886	1	51	professor	professor	NOUN
m-886	1	52	,	,	PUNCT
m-886	1	53	department	department	NOUN
m-886	1	54	of	of	ADP
m-886	1	55	mathematics	mathematic	NOUN
m-886	1	56	,	,	PUNCT
m-886	1	57	school	school	NOUN
m-886	1	58	of	of	ADP
m-886	1	59	engineering	engineering	NOUN
m-886	1	60	and	and	CCONJ
m-886	1	61	technology	technology	NOUN
m-886	1	62	,	,	PUNCT
m-886	1	63	dhanalakshmi	dhanalakshmi	PROPN
m-886	1	64	srinivasan	srinivasan	PROPN
m-886	1	65	university	university	PROPN
m-886	1	66	,	,	PUNCT
m-886	1	67	samayapuram	samayapuram	PROPN
m-886	1	68	,	,	PUNCT
m-886	1	69	trichy621	trichy621	PROPN
m-886	1	70	112	112	NUM
m-886	1	71	,	,	PUNCT
m-886	1	72	tamil	tamil	PROPN
m-886	1	73	nadu	nadu	PROPN
m-886	1	74	,	,	PUNCT
m-886	1	75	india	india	PROPN
m-886	1	76	.	.	PROPN
m-886	1	77	2	2	NUM
m-886	1	78	professor	professor	NOUN
m-886	1	79	,	,	PUNCT
m-886	1	80	department	department	NOUN
m-886	1	81	of	of	ADP
m-886	1	82	mathematics	mathematic	NOUN
m-886	1	83	,	,	PUNCT
m-886	1	84	shrimati	shrimati	PROPN
m-886	1	85	indira	indira	PROPN
m-886	1	86	gandhi	gandhi	PROPN
m-886	1	87	college	college	PROPN
m-886	1	88	,	,	PUNCT
m-886	1	89	affiliated	affiliate	VERB
m-886	1	90	to	to	PART
m-886	1	91	bharathidasan	bharathidasan	VERB
m-886	1	92	university	university	NOUN
m-886	1	93	,	,	PUNCT
m-886	1	94	trichy-620	trichy-620	NOUN
m-886	1	95	002,tamil	002,tamil	NUM
m-886	1	96	nadu	nadu	PROPN
m-886	1	97	,	,	PUNCT
m-886	1	98	india	india	PROPN
m-886	1	99	.	.	PUNCT
m-886	2	1	abstract	abstract	PROPN
m-886	2	2	:	:	PUNCT
m-886	2	3	this	this	DET
m-886	2	4	paper	paper	NOUN
m-886	2	5	focuses	focus	VERB
m-886	2	6	on	on	ADP
m-886	2	7	finding	find	VERB
m-886	2	8	varieties	variety	NOUN
m-886	2	9	of	of	ADP
m-886	2	10	distinct	distinct	ADJ
m-886	2	11	integer	integer	NOUN
m-886	2	12	solutions	solution	NOUN
m-886	2	13	to	to	ADP
m-886	2	14	the	the	DET
m-886	2	15	diophantine	diophantine	NOUN
m-886	2	16	equation	equation	NOUN
m-886	2	17	of	of	ADP
m-886	2	18	degree	degree	NOUN
m-886	2	19	ten	ten	NUM
m-886	2	20	with	with	ADP
m-886	2	21	six	six	NUM
m-886	2	22	unknowns	unknown	NOUN
m-886	2	23	given	give	VERB
m-886	2	24	by	by	ADP
m-886	2	25	822366	822366	NUM
m-886	2	26	r)qp(800z3456yx	r)qp(800z3456yx	PROPN
m-886	2	27			PROPN
m-886	2	28	through	through	ADP
m-886	2	29	employing	employ	VERB
m-886	2	30	the	the	DET
m-886	2	31	substitution	substitution	NOUN
m-886	2	32	strategy	strategy	NOUN
m-886	2	33	and	and	CCONJ
m-886	2	34	method	method	NOUN
m-886	2	35	of	of	ADP
m-886	2	36	factorization	factorization	NOUN
m-886	2	37	.	.	PUNCT
m-886	3	1	a	a	DET
m-886	3	2	new	new	ADJ
m-886	3	3	representation	representation	NOUN
m-886	3	4	for	for	ADP
m-886	3	5	the	the	DET
m-886	3	6	factorization	factorization	NOUN
m-886	3	7	of	of	ADP
m-886	3	8	integer	integer	NOUN
m-886	3	9	40	40	NUM
m-886	3	10	involving	involve	VERB
m-886	3	11	sides	side	NOUN
m-886	3	12	of	of	ADP
m-886	3	13	pythagorean	pythagorean	PROPN
m-886	3	14	triangle	triangle	NOUN
m-886	3	15	has	have	AUX
m-886	3	16	been	be	AUX
m-886	3	17	introduced	introduce	VERB
m-886	3	18	.	.	PUNCT
m-886	4	1	key	key	ADJ
m-886	4	2	words	word	NOUN
m-886	4	3	:	:	PUNCT
m-886	4	4	higher	high	ADJ
m-886	4	5	degree	degree	NOUN
m-886	4	6	diophantine	diophantine	NOUN
m-886	4	7	equation	equation	NOUN
m-886	4	8	,	,	PUNCT
m-886	4	9	integer	integer	NOUN
m-886	4	10	solution	solution	NOUN
m-886	4	11	.	.	PUNCT
m-886	5	1	2020	2020	NUM
m-886	5	2	mathematics	mathematic	NOUN
m-886	5	3	subject	subject	ADJ
m-886	5	4	classification	classification	NOUN
m-886	5	5	:	:	PUNCT
m-886	5	6	11d41	11d41	X
m-886	5	7	.	.	PUNCT
m-886	6	1	introduction	introduction	NOUN
m-886	6	2	:	:	PUNCT
m-886	6	3	it	it	PRON
m-886	6	4	is	be	AUX
m-886	6	5	well	well	ADV
m-886	6	6	-	-	PUNCT
m-886	6	7	known	know	VERB
m-886	6	8	that	that	SCONJ
m-886	6	9	the	the	DET
m-886	6	10	subject	subject	NOUN
m-886	6	11	of	of	ADP
m-886	6	12	diophantine	diophantine	NOUN
m-886	6	13	equations	equation	NOUN
m-886	6	14	occupies	occupy	VERB
m-886	6	15	a	a	DET
m-886	6	16	pivotal	pivotal	ADJ
m-886	6	17	role	role	NOUN
m-886	6	18	in	in	ADP
m-886	6	19	the	the	DET
m-886	6	20	number	number	NOUN
m-886	6	21	theory	theory	NOUN
m-886	6	22	.	.	PUNCT
m-886	7	1	there	there	PRON
m-886	7	2	is	be	VERB
m-886	7	3	a	a	DET
m-886	7	4	vast	vast	ADJ
m-886	7	5	general	general	ADJ
m-886	7	6	theory	theory	NOUN
m-886	7	7	for	for	ADP
m-886	7	8	higher	high	ADJ
m-886	7	9	degree	degree	NOUN
m-886	7	10	diophantine	diophantine	NOUN
m-886	7	11	equations	equation	NOUN
m-886	7	12	in	in	ADP
m-886	7	13	many	many	ADJ
m-886	7	14	variables	variable	NOUN
m-886	7	15	and	and	CCONJ
m-886	7	16	it	it	PRON
m-886	7	17	is	be	AUX
m-886	7	18	a	a	DET
m-886	7	19	topic	topic	NOUN
m-886	7	20	for	for	ADP
m-886	7	21	research	research	NOUN
m-886	7	22	even	even	ADV
m-886	7	23	today	today	NOUN
m-886	7	24	.	.	PUNCT
m-886	8	1	while	while	SCONJ
m-886	8	2	collecting	collect	VERB
m-886	8	3	problems	problem	NOUN
m-886	8	4	on	on	ADP
m-886	8	5	diophantine	diophantine	NOUN
m-886	8	6	equations	equation	NOUN
m-886	8	7	of	of	ADP
m-886	8	8	degree	degree	NOUN
m-886	8	9	ten	ten	NUM
m-886	8	10	with	with	ADP
m-886	8	11	six	six	NUM
m-886	8	12	unknowns	unknown	NOUN
m-886	8	13	,	,	PUNCT
m-886	8	14	the	the	DET
m-886	8	15	following	follow	VERB
m-886	8	16	paper	paper	NOUN
m-886	8	17	[	[	X
m-886	8	18	1	1	X
m-886	8	19	]	]	PUNCT
m-886	8	20	has	have	AUX
m-886	8	21	been	be	AUX
m-886	8	22	noticed	notice	VERB
m-886	8	23	and	and	CCONJ
m-886	8	24	the	the	DET
m-886	8	25	authors	author	NOUN
m-886	8	26	have	have	AUX
m-886	8	27	presented	present	VERB
m-886	8	28	only	only	ADV
m-886	8	29	few	few	ADJ
m-886	8	30	sets	set	NOUN
m-886	8	31	of	of	ADP
m-886	8	32	integer	integer	NOUN
m-886	8	33	solutions	solution	NOUN
m-886	8	34	.	.	PUNCT
m-886	9	1	it	it	PRON
m-886	9	2	is	be	AUX
m-886	9	3	worth	worth	ADJ
m-886	9	4	to	to	PART
m-886	9	5	mention	mention	VERB
m-886	9	6	that	that	SCONJ
m-886	9	7	the	the	DET
m-886	9	8	equation	equation	NOUN
m-886	9	9	presented	present	VERB
m-886	9	10	in	in	ADP
m-886	9	11	[	[	X
m-886	9	12	1	1	NUM
m-886	9	13	]	]	PUNCT
m-886	9	14	has	have	VERB
m-886	9	15	many	many	ADJ
m-886	9	16	more	more	ADJ
m-886	9	17	fascinating	fascinating	ADJ
m-886	9	18	patterns	pattern	NOUN
m-886	9	19	of	of	ADP
m-886	9	20	solutions	solution	NOUN
m-886	9	21	in	in	ADP
m-886	9	22	integers	integer	NOUN
m-886	9	23	.	.	PUNCT
m-886	10	1	in	in	ADP
m-886	10	2	this	this	DET
m-886	10	3	paper	paper	NOUN
m-886	10	4	,	,	PUNCT
m-886	10	5	the	the	DET
m-886	10	6	process	process	NOUN
m-886	10	7	of	of	ADP
m-886	10	8	obtaining	obtain	VERB
m-886	10	9	some	some	DET
m-886	10	10	more	more	ADJ
m-886	10	11	choices	choice	NOUN
m-886	10	12	of	of	ADP
m-886	10	13	solutions	solution	NOUN
m-886	10	14	in	in	ADP
m-886	10	15	integers	integer	NOUN
m-886	10	16	to	to	ADP
m-886	10	17	the	the	DET
m-886	10	18	diophantine	diophantine	NOUN
m-886	10	19	equation	equation	NOUN
m-886	10	20	in	in	ADP
m-886	10	21	title	title	NOUN
m-886	10	22	is	be	AUX
m-886	10	23	illustrated	illustrate	VERB
m-886	10	24	.	.	PUNCT
m-886	11	1	substitution	substitution	NOUN
m-886	11	2	strategy	strategy	NOUN
m-886	11	3	and	and	CCONJ
m-886	11	4	factorization	factorization	NOUN
m-886	11	5	method	method	NOUN
m-886	11	6	are	be	AUX
m-886	11	7	applied	apply	VERB
m-886	11	8	successfully	successfully	ADV
m-886	11	9	to	to	PART
m-886	11	10	obtain	obtain	VERB
m-886	11	11	different	different	ADJ
m-886	11	12	choices	choice	NOUN
m-886	11	13	of	of	ADP
m-886	11	14	integer	integer	NOUN
m-886	11	15	solutions	solution	NOUN
m-886	11	16	to	to	ADP
m-886	11	17	the	the	DET
m-886	11	18	considered	consider	VERB
m-886	11	19	equation	equation	NOUN
m-886	11	20	.	.	PUNCT
m-886	12	1	it	it	PRON
m-886	12	2	is	be	AUX
m-886	12	3	to	to	PART
m-886	12	4	be	be	AUX
m-886	12	5	noted	note	VERB
m-886	12	6	that	that	SCONJ
m-886	12	7	a	a	DET
m-886	12	8	new	new	ADJ
m-886	12	9	representation	representation	NOUN
m-886	12	10	for	for	ADP
m-886	12	11	the	the	DET
m-886	12	12	factorization	factorization	NOUN
m-886	12	13	of	of	ADP
m-886	12	14	integer	integer	NOUN
m-886	12	15	40	40	NUM
m-886	12	16	involving	involve	VERB
m-886	12	17	sides	side	NOUN
m-886	12	18	of	of	ADP
m-886	12	19	pythagorean	pythagorean	PROPN
m-886	12	20	triangle	triangle	NOUN
m-886	12	21	has	have	AUX
m-886	12	22	been	be	AUX
m-886	12	23	introduced	introduce	VERB
m-886	12	24	.	.	PUNCT
m-886	13	1	ijo	ijo	PROPN
m-886	13	2	journals	journal	NOUN
m-886	13	3	volume	volume	NOUN
m-886	13	4	07	07	NUM
m-886	13	5	|	|	NOUN
m-886	13	6	issue	issue	NOUN
m-886	14	1	05	05	NUM
m-886	15	1	|	|	ADV
m-886	15	2	may	may	AUX
m-886	15	3	2024	2024	NUM
m-886	15	4	|	|	ADV
m-886	15	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-886	15	6	1	1	NUM
m-886	15	7	ijo	ijo	PROPN
m-886	15	8	international	international	ADJ
m-886	15	9	journal	journal	PROPN
m-886	15	10	of	of	ADP
m-886	15	11	mathematics	mathematics	PROPN
m-886	15	12	(	(	PUNCT
m-886	15	13	issn	issn	PROPN
m-886	15	14	:	:	PUNCT
m-886	15	15	2992	2992	NUM
m-886	15	16	-	-	SYM
m-886	15	17	4421	4421	NUM
m-886	15	18	)	)	PUNCT
m-886	16	1	dr	dr	PROPN
m-886	16	2	.	.	PROPN
m-886	16	3	n.thiruniraiselvi1	n.thiruniraiselvi1	PROPN
m-886	16	4	*	*	PROPN
m-886	16	5	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-886	16	6	volume	volume	NOUN
m-886	16	7	07	07	NUM
m-886	16	8	||	||	NOUN
m-886	16	9	issue	issue	NOUN
m-886	16	10	05||	05||	X
m-886	16	11	may	may	AUX
m-886	16	12	,	,	PUNCT
m-886	16	13	2024	2024	NUM
m-886	16	14	||	||	NOUN
m-886	16	15	method	method	NOUN
m-886	16	16	of	of	ADP
m-886	16	17	analysis	analysis	NOUN
m-886	16	18	:	:	PUNCT
m-886	16	19	the	the	DET
m-886	16	20	diophantine	diophantine	NOUN
m-886	16	21	equation	equation	NOUN
m-886	16	22	is	be	AUX
m-886	16	23	822366	822366	NUM
m-886	16	24	r)qp(800z3456yx	r)qp(800z3456yx	PROPN
m-886	16	25			PROPN
m-886	16	26	(	(	PUNCT
m-886	16	27	1	1	NUM
m-886	16	28	)	)	PUNCT
m-886	16	29	to	to	PART
m-886	16	30	start	start	VERB
m-886	16	31	with	with	ADP
m-886	16	32	,	,	PUNCT
m-886	16	33	it	it	PRON
m-886	16	34	is	be	AUX
m-886	16	35	observed	observe	VERB
m-886	16	36	by	by	ADP
m-886	16	37	inspection	inspection	NOUN
m-886	16	38	that	that	SCONJ
m-886	16	39	(	(	PUNCT
m-886	16	40	1	1	X
m-886	16	41	)	)	PUNCT
m-886	16	42	is	be	AUX
m-886	16	43	satisfied	satisfied	ADJ
m-886	16	44	by	by	ADP
m-886	16	45	the	the	DET
m-886	16	46	following	follow	VERB
m-886	16	47	sextuples	sextuple	NOUN
m-886	16	48	{	{	PUNCT
m-886	16	49	x	x	NOUN
m-886	16	50	,	,	PUNCT
m-886	16	51	y	y	PROPN
m-886	16	52	,	,	PUNCT
m-886	16	53	z	z	PROPN
m-886	16	54	,	,	PUNCT
m-886	16	55	p	p	X
m-886	16	56	,	,	PUNCT
m-886	16	57	q	q	ADJ
m-886	16	58	,	,	PUNCT
m-886	16	59	r	r	NOUN
m-886	16	60	}	}	PUNCT
m-886	16	61	=	=	NOUN
m-886	16	62	{	{	PUNCT
m-886	16	63	8u4v	8u4v	NOUN
m-886	16	64	,	,	PUNCT
m-886	16	65	4u4v,2u8v	4u4v,2u8v	NUM
m-886	16	66	,	,	PUNCT
m-886	16	67	18u4v,-6u4v	18u4v,-6u4v	NOUN
m-886	16	68	,	,	PUNCT
m-886	16	69	u2v	u2v	NOUN
m-886	16	70	}	}	PUNCT
m-886	16	71	,	,	PUNCT
m-886	16	72	{	{	PUNCT
m-886	16	73	8	8	NUM
m-886	16	74	*	*	SYM
m-886	16	75	402*(9a2	402*(9a2	NUM
m-886	16	76	+	+	NOUN
m-886	16	77	4b2)2	4b2)2	NOUN
m-886	16	78	,	,	PUNCT
m-886	16	79	4	4	NOUN
m-886	16	80	*	*	NOUN
m-886	16	81	402*(9a2	402*(9a2	NUM
m-886	16	82	+	+	NOUN
m-886	16	83	4b2	4b2	NOUN
m-886	16	84	)	)	PUNCT
m-886	16	85	2	2	NUM
m-886	16	86	,	,	PUNCT
m-886	16	87	2	2	NUM
m-886	16	88	*	*	SYM
m-886	16	89	404*(9a2	404*(9a2	NUM
m-886	16	90	+	+	NOUN
m-886	16	91	4b2)4	4b2)4	NOUN
m-886	16	92	,	,	PUNCT
m-886	16	93	18	18	NUM
m-886	16	94	*	*	SYM
m-886	16	95	402*(9a2	402*(9a2	NUM
m-886	16	96	+	+	NOUN
m-886	16	97	4b2)2	4b2)2	NOUN
m-886	16	98	,	,	PUNCT
m-886	16	99	-6	-6	NOUN
m-886	16	100	*	*	SYM
m-886	16	101	402*(9a2	402*(9a2	NOUN
m-886	16	102	+	+	NOUN
m-886	16	103	4b2)2	4b2)2	NOUN
m-886	16	104	,	,	PUNCT
m-886	16	105	40*(9a2	40*(9a2	PROPN
m-886	16	106	+	+	NOUN
m-886	16	107	4b2	4b2	NOUN
m-886	16	108	)	)	PUNCT
m-886	16	109	}	}	PUNCT
m-886	16	110	,	,	PUNCT
m-886	16	111	{	{	PUNCT
m-886	16	112	32w2,16w2,32w2,72w2,24w2,2w	32w2,16w2,32w2,72w2,24w2,2w	NOUN
m-886	16	113	}	}	PUNCT
m-886	16	114	.	.	PUNCT
m-886	17	1	however	however	ADV
m-886	17	2	there	there	PRON
m-886	17	3	are	be	VERB
m-886	17	4	often	often	ADV
m-886	17	5	fascinating	fascinating	ADJ
m-886	17	6	solution	solution	NOUN
m-886	17	7	patterns	pattern	NOUN
m-886	17	8	to	to	ADP
m-886	17	9	(	(	PUNCT
m-886	17	10	1	1	X
m-886	17	11	)	)	PUNCT
m-886	17	12	that	that	PRON
m-886	17	13	are	be	AUX
m-886	17	14	illustrated	illustrate	VERB
m-886	17	15	as	as	SCONJ
m-886	17	16	follows	follow	VERB
m-886	17	17	.	.	PUNCT
m-886	18	1	introduction	introduction	NOUN
m-886	18	2	of	of	ADP
m-886	18	3	the	the	DET
m-886	18	4	transformation	transformation	NOUN
m-886	18	5	s6t6q	s6t6q	ADP
m-886	18	6	,	,	PUNCT
m-886	18	7	s6t6p	s6t6p	NUM
m-886	18	8	,	,	PUNCT
m-886	18	9	stz	stz	NOUN
m-886	18	10	,	,	PUNCT
m-886	18	11	t2s3y	t2s3y	NUM
m-886	18	12	,	,	PUNCT
m-886	18	13	t2s3x	t2s3x	PRON
m-886	18	14			X
m-886	18	15	(	(	PUNCT
m-886	18	16	2	2	X
m-886	18	17	)	)	PUNCT
m-886	18	18	in	in	ADP
m-886	18	19	(	(	PUNCT
m-886	18	20	1	1	X
m-886	18	21	)	)	PUNCT
m-886	18	22	leads	lead	VERB
m-886	18	23	to	to	ADP
m-886	18	24	422	422	NUM
m-886	18	25	r40t4s9	r40t4s9	NOUN
m-886	18	26			NOUN
m-886	18	27	(	(	PUNCT
m-886	18	28	3	3	X
m-886	18	29	)	)	PUNCT
m-886	18	30	solving	solving	NOUN
m-886	18	31	(	(	PUNCT
m-886	18	32	3	3	NUM
m-886	18	33	)	)	PUNCT
m-886	18	34	through	through	ADP
m-886	18	35	different	different	ADJ
m-886	18	36	ways	way	NOUN
m-886	18	37	and	and	CCONJ
m-886	18	38	using	use	VERB
m-886	18	39	(	(	PUNCT
m-886	18	40	2	2	NUM
m-886	18	41	)	)	PUNCT
m-886	18	42	,	,	PUNCT
m-886	18	43	one	one	PRON
m-886	18	44	obtains	obtain	VERB
m-886	18	45	many	many	ADJ
m-886	18	46	non	non	ADJ
m-886	18	47	-	-	ADJ
m-886	18	48	zero	zero	NUM
m-886	18	49	distinct	distinct	ADJ
m-886	18	50	integer	integer	NOUN
m-886	18	51	solutions	solution	NOUN
m-886	18	52	to	to	ADP
m-886	18	53	(	(	PUNCT
m-886	18	54	1	1	NUM
m-886	18	55	)	)	PUNCT
m-886	18	56	.	.	PUNCT
m-886	19	1	pattern	pattern	NOUN
m-886	19	2	1	1	NUM
m-886	19	3	:	:	PUNCT
m-886	19	4	the	the	DET
m-886	19	5	choice	choice	NOUN
m-886	19	6	rt	rt	PROPN
m-886	19	7			NUM
m-886	19	8	(	(	PUNCT
m-886	19	9	4	4	NUM
m-886	19	10	)	)	PUNCT
m-886	19	11	in	in	ADP
m-886	19	12	leads	lead	NOUN
m-886	19	13	to	to	ADP
m-886	19	14			NOUN
m-886	19	15			NOUN
m-886	19	16			PROPN
m-886	19	17			PROPN
m-886	19	18			PROPN
m-886	19	19			NOUN
m-886	19	20			NOUN
m-886	19	21			ADJ
m-886	19	22	9	9	NUM
m-886	19	23	1r10	1r10	NUM
m-886	19	24	r4s	r4s	NOUN
m-886	19	25	2	2	NUM
m-886	19	26	22	22	NUM
m-886	19	27	(	(	PUNCT
m-886	19	28	5	5	NUM
m-886	19	29	)	)	PUNCT
m-886	19	30	let	let	VERB
m-886	19	31	19r10	19r10	NUM
m-886	19	32	22	22	NUM
m-886	19	33			ADJ
m-886	19	34			NOUN
m-886	19	35	(	(	PUNCT
m-886	19	36	6	6	NUM
m-886	19	37	)	)	PUNCT
m-886	19	38	the	the	DET
m-886	19	39	smallest	small	ADJ
m-886	19	40	positive	positive	ADJ
m-886	19	41	integers	integer	NOUN
m-886	19	42	to	to	ADP
m-886	19	43	(	(	PUNCT
m-886	19	44	6	6	NUM
m-886	19	45	)	)	PUNCT
m-886	19	46	is	be	AUX
m-886	19	47	1r,1	1r,1	NUM
m-886	19	48	00	00	NUM
m-886	20	1			NOUN
m-886	20	2	let	let	VERB
m-886	20	3	0101	0101	NUM
m-886	20	4	h	h	NOUN
m-886	20	5	,	,	PUNCT
m-886	20	6	rhr	rhr	X
m-886	20	7			DET
m-886	20	8			NOUN
m-886	20	9	(	(	PUNCT
m-886	20	10	7	7	X
m-886	20	11	)	)	PUNCT
m-886	20	12	be	be	AUX
m-886	20	13	the	the	DET
m-886	20	14	second	second	ADJ
m-886	20	15	solution	solution	NOUN
m-886	20	16	to	to	ADP
m-886	20	17	(	(	PUNCT
m-886	20	18	6	6	NUM
m-886	20	19	)	)	PUNCT
m-886	20	20	.	.	PUNCT
m-886	21	1	substituting	substitute	VERB
m-886	21	2	(	(	PUNCT
m-886	21	3	7	7	NUM
m-886	21	4	)	)	PUNCT
m-886	21	5	and	and	CCONJ
m-886	21	6	(	(	PUNCT
m-886	21	7	6	6	NUM
m-886	21	8	)	)	PUNCT
m-886	21	9	and	and	CCONJ
m-886	21	10	performing	perform	VERB
m-886	21	11	some	some	DET
m-886	21	12	algebra	algebra	NOUN
m-886	21	13	,	,	PUNCT
m-886	21	14	we	we	PRON
m-886	21	15	get	get	VERB
m-886	21	16	ijo	ijo	ADJ
m-886	21	17	journals	journal	NOUN
m-886	21	18	volume	volume	NOUN
m-886	21	19	07	07	NUM
m-886	22	1	|	|	NOUN
m-886	22	2	issue	issue	NOUN
m-886	22	3	05	05	NUM
m-886	23	1	|	|	ADV
m-886	23	2	may	may	AUX
m-886	23	3	2024	2024	NUM
m-886	23	4	|	|	ADV
m-886	23	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-886	23	6	2	2	NUM
m-886	23	7	ijo	ijo	PROPN
m-886	23	8	international	international	ADJ
m-886	23	9	journal	journal	PROPN
m-886	23	10	of	of	ADP
m-886	23	11	mathematics	mathematics	PROPN
m-886	23	12	(	(	PUNCT
m-886	23	13	issn	issn	PROPN
m-886	23	14	:	:	PUNCT
m-886	23	15	2992	2992	NUM
m-886	23	16	-	-	SYM
m-886	23	17	4421	4421	NUM
m-886	23	18	)	)	PUNCT
m-886	24	1	dr	dr	PROPN
m-886	24	2	.	.	PROPN
m-886	24	3	n.thiruniraiselvi1	n.thiruniraiselvi1	PROPN
m-886	24	4	*	*	PROPN
m-886	24	5	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-886	24	6	volume	volume	NOUN
m-886	24	7	07	07	NUM
m-886	24	8	||	||	NOUN
m-886	24	9	issue	issue	NOUN
m-886	24	10	05||	05||	X
m-886	24	11	may	may	AUX
m-886	24	12	,	,	PUNCT
m-886	24	13	2024	2024	NUM
m-886	24	14	||	||	NOUN
m-886	24	15	00	00	NUM
m-886	24	16	18r20h	18r20h	NUM
m-886	24	17			NOUN
m-886	24	18	in	in	ADP
m-886	24	19	view	view	NOUN
m-886	24	20	of	of	ADP
m-886	24	21	(	(	PUNCT
m-886	24	22	7	7	NUM
m-886	24	23	)	)	PUNCT
m-886	24	24	,	,	PUNCT
m-886	24	25	we	we	PRON
m-886	24	26	get	get	VERB
m-886	24	27	001001	001001	NUM
m-886	24	28	19r20,18r19r	19r20,18r19r	PROPN
m-886	24	29			X
m-886	24	30			NOUN
m-886	24	31	which	which	PRON
m-886	24	32	is	be	AUX
m-886	24	33	written	write	VERB
m-886	24	34	in	in	ADP
m-886	24	35	matrix	matrix	NOUN
m-886	24	36	form	form	NOUN
m-886	24	37	as	as	ADP
m-886	24	38	t	t	PROPN
m-886	24	39	00	00	PUNCT
m-886	24	40	t	t	PROPN
m-886	24	41	11	11	NUM
m-886	24	42	)	)	PUNCT
m-886	25	1	r(m),r	r(m),r	NOUN
m-886	25	2	(	(	PUNCT
m-886	25	3			PRON
m-886	25	4			ADJ
m-886	25	5	where	where	SCONJ
m-886	25	6			NOUN
m-886	25	7			VERB
m-886	25	8			PROPN
m-886	25	9			PROPN
m-886	25	10			PROPN
m-886	25	11			NOUN
m-886	25	12			NOUN
m-886	25	13	1920	1920	NUM
m-886	25	14	1819	1819	NUM
m-886	25	15	m	m	NOUN
m-886	25	16	and	and	CCONJ
m-886	25	17	t	t	PROPN
m-886	25	18	is	be	AUX
m-886	25	19	the	the	DET
m-886	25	20	transpose	transpose	NOUN
m-886	25	21	.	.	PUNCT
m-886	26	1	the	the	DET
m-886	26	2	repetition	repetition	NOUN
m-886	26	3	of	of	ADP
m-886	26	4	the	the	DET
m-886	26	5	above	above	ADJ
m-886	26	6	process	process	NOUN
m-886	26	7	leads	lead	VERB
m-886	26	8	to	to	ADP
m-886	26	9	the	the	DET
m-886	26	10	general	general	ADJ
m-886	26	11	solution	solution	NOUN
m-886	26	12	)	)	PUNCT
m-886	26	13	,	,	PUNCT
m-886	26	14	r	r	X
m-886	26	15	(	(	PUNCT
m-886	26	16	nn	nn	X
m-886	26	17			X
m-886	26	18	to	to	ADP
m-886	26	19	(	(	PUNCT
m-886	26	20	6	6	NUM
m-886	26	21	)	)	PUNCT
m-886	26	22	as	as	ADP
m-886	26	23	t	t	PROPN
m-886	26	24	00	00	PUNCT
m-886	26	25	nt	nt	PROPN
m-886	26	26	nn	nn	PROPN
m-886	26	27	)	)	PUNCT
m-886	26	28	,	,	PUNCT
m-886	26	29	r(m),r	r(m),r	PROPN
m-886	26	30	(	(	PUNCT
m-886	26	31			NUM
m-886	26	32			NOUN
m-886	26	33	let	let	VERB
m-886	26	34			NOUN
m-886	26	35	~	~	PUNCT
m-886	26	36	,	,	PUNCT
m-886	26	37	~	~	PUNCT
m-886	26	38	be	be	AUX
m-886	26	39	the	the	DET
m-886	26	40	eigen	eigen	PROPN
m-886	26	41	values	value	NOUN
m-886	26	42	of	of	ADP
m-886	26	43	the	the	DET
m-886	26	44	matrix	matrix	NOUN
m-886	26	45	m.	m.	NOUN
m-886	26	46	then	then	ADV
m-886	26	47	,	,	PUNCT
m-886	26	48	it	it	PRON
m-886	26	49	is	be	AUX
m-886	26	50	found	find	VERB
m-886	26	51	that	that	SCONJ
m-886	26	52	10619	10619	NUM
m-886	26	53	~	~	PUNCT
m-886	26	54	,	,	PUNCT
m-886	26	55	10619~	10619~	NUM
m-886	26	56			NOUN
m-886	26	57			VERB
m-886	26	58	it	it	PRON
m-886	26	59	is	be	AUX
m-886	26	60	well	well	ADV
m-886	26	61	known	know	VERB
m-886	27	1	that	that	SCONJ
m-886	27	2	)	)	PUNCT
m-886	27	3	i	i	PRON
m-886	27	4	~	~	X
m-886	27	5	m(~~	m(~~	NOUN
m-886	27	6	~	~	PUNCT
m-886	27	7	)	)	PUNCT
m-886	28	1	i	i	PRON
m-886	28	2	~	~	PUNCT
m-886	28	3	m(~~	m(~~	X
m-886	28	4	~	~	PUNCT
m-886	28	5	m	m	VERB
m-886	28	6	nn	nn	PROPN
m-886	28	7	n	n	CCONJ
m-886	28	8			PROPN
m-886	28	9			ADJ
m-886	28	10			PROPN
m-886	28	11			PROPN
m-886	28	12			NOUN
m-886	28	13			X
m-886	28	14			VERB
m-886	28	15			PROPN
m-886	28	16			PROPN
m-886	28	17			PROPN
m-886	28	18			ADV
m-886	28	19	where	where	SCONJ
m-886	28	20	i	i	PRON
m-886	28	21	is	be	AUX
m-886	28	22	the	the	DET
m-886	28	23	unit	unit	NOUN
m-886	28	24	matrix	matrix	NOUN
m-886	28	25	of	of	ADP
m-886	28	26	order	order	NOUN
m-886	28	27	2	2	NUM
m-886	28	28	.	.	PUNCT
m-886	29	1	thus	thus	ADV
m-886	29	2	,	,	PUNCT
m-886	29	3	t	t	PROPN
m-886	29	4	00nnnn	00nnnn	PUNCT
m-886	29	5	nnnn	nnnn	PROPN
m-886	29	6	t	t	PROPN
m-886	29	7	nn	nn	PROPN
m-886	29	8	)	)	PUNCT
m-886	29	9	,	,	PUNCT
m-886	29	10	r	r	NOUN
m-886	29	11	(	(	PUNCT
m-886	29	12	2	2	NUM
m-886	29	13	~~	~~	SYM
m-886	29	14	103	103	NUM
m-886	29	15	)	)	PUNCT
m-886	29	16	~~(5	~~(5	NOUN
m-886	29	17	102	102	NUM
m-886	29	18	)	)	PUNCT
m-886	29	19	~~(3	~~(3	CCONJ
m-886	29	20	2	2	NUM
m-886	29	21	~~	~~	NUM
m-886	29	22	)	)	PUNCT
m-886	29	23	,	,	PUNCT
m-886	29	24	r	r	X
m-886	29	25	(	(	PUNCT
m-886	29	26			X
m-886	29	27			NOUN
m-886	29	28			NOUN
m-886	29	29			NUM
m-886	29	30			PROPN
m-886	29	31			PROPN
m-886	30	1			PROPN
m-886	31	1			PROPN
m-886	31	2			NOUN
m-886	31	3			PROPN
m-886	31	4			NOUN
m-886	32	1			PROPN
m-886	32	2			PROPN
m-886	32	3			PROPN
m-886	33	1			PROPN
m-886	33	2			NOUN
m-886	33	3			PROPN
m-886	33	4			PROPN
m-886	33	5			PROPN
m-886	33	6	from	from	ADP
m-886	33	7	(	(	PUNCT
m-886	33	8	5	5	NUM
m-886	33	9	)	)	PUNCT
m-886	33	10	,	,	PUNCT
m-886	33	11	we	we	PRON
m-886	33	12	have	have	VERB
m-886	33	13	t	t	PROPN
m-886	33	14	00	00	PUNCT
m-886	33	15	nt	nt	PROPN
m-886	33	16	nn	nn	PROPN
m-886	33	17	)	)	PUNCT
m-886	33	18	,	,	PUNCT
m-886	33	19	r(m),r	r(m),r	PROPN
m-886	33	20	(	(	PUNCT
m-886	33	21			NUM
m-886	33	22			ADV
m-886	33	23	from	from	ADP
m-886	33	24	(	(	PUNCT
m-886	33	25	5	5	NUM
m-886	33	26	)	)	PUNCT
m-886	33	27	,	,	PUNCT
m-886	33	28	we	we	PRON
m-886	33	29	have	have	VERB
m-886	33	30	nnn	nnn	NOUN
m-886	33	31	r2s	r2s	NOUN
m-886	33	32			NOUN
m-886	33	33	in	in	ADP
m-886	33	34	view	view	NOUN
m-886	33	35	of	of	ADP
m-886	33	36	(	(	PUNCT
m-886	33	37	2	2	NUM
m-886	33	38	)	)	PUNCT
m-886	33	39	,	,	PUNCT
m-886	33	40	the	the	DET
m-886	33	41	corresponding	corresponding	ADJ
m-886	33	42	integer	integer	NOUN
m-886	33	43	solutions	solution	NOUN
m-886	33	44	to	to	ADP
m-886	33	45	(	(	PUNCT
m-886	33	46	1	1	X
m-886	33	47	)	)	PUNCT
m-886	33	48	are	be	AUX
m-886	33	49	given	give	VERB
m-886	33	50	by	by	ADP
m-886	33	51	ijo	ijo	PROPN
m-886	33	52	journals	journal	NOUN
m-886	33	53	volume	volume	NOUN
m-886	33	54	07	07	NUM
m-886	33	55	|	|	NOUN
m-886	33	56	issue	issue	NOUN
m-886	33	57	05	05	NUM
m-886	34	1	|	|	ADV
m-886	34	2	may	may	AUX
m-886	34	3	2024	2024	NUM
m-886	34	4	|	|	ADV
m-886	34	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-886	34	6	3	3	NUM
m-886	34	7	ijo	ijo	PROPN
m-886	34	8	international	international	PROPN
m-886	34	9	journal	journal	PROPN
m-886	34	10	of	of	ADP
m-886	34	11	mathematics	mathematics	PROPN
m-886	34	12	(	(	PUNCT
m-886	34	13	issn	issn	PROPN
m-886	34	14	:	:	PUNCT
m-886	34	15	2992	2992	NUM
m-886	34	16	-	-	SYM
m-886	34	17	4421	4421	NUM
m-886	34	18	)	)	PUNCT
m-886	35	1	dr	dr	PROPN
m-886	35	2	.	.	PROPN
m-886	35	3	n.thiruniraiselvi1	n.thiruniraiselvi1	PROPN
m-886	35	4	*	*	PROPN
m-886	35	5	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-886	35	6	volume	volume	NOUN
m-886	35	7	07	07	NUM
m-886	35	8	||	||	NOUN
m-886	35	9	issue	issue	NOUN
m-886	35	10	05||	05||	X
m-886	35	11	may	may	AUX
m-886	35	12	,	,	PUNCT
m-886	35	13	2024	2024	NUM
m-886	35	14	||	||	NOUN
m-886	36	1	nn	nn	PROPN
m-886	36	2	nnn	nnn	PROPN
m-886	36	3	nnn	nnn	PROPN
m-886	36	4	nn	nn	PROPN
m-886	36	5	2	2	NUM
m-886	36	6	n	n	PROPN
m-886	36	7	nnn	nnn	NOUN
m-886	36	8	nnn	nnn	PROPN
m-886	36	9	rt	rt	PROPN
m-886	36	10	)	)	PUNCT
m-886	36	11	21(r6q	21(r6q	NUM
m-886	36	12	)	)	PUNCT
m-886	36	13	21(r6p	21(r6p	NUM
m-886	37	1	r2z	r2z	PROPN
m-886	37	2	)	)	PUNCT
m-886	38	1	13(r2y	13(r2y	NUM
m-886	38	2	)	)	PUNCT
m-886	38	3	13(r2x	13(r2x	PROPN
m-886	39	1			PROPN
m-886	39	2			ADJ
m-886	39	3			ADJ
m-886	39	4			PROPN
m-886	39	5			ADJ
m-886	39	6			ADJ
m-886	39	7			NOUN
m-886	39	8			X
m-886	39	9			X
m-886	39	10			X
m-886	39	11			X
m-886	39	12	where	where	SCONJ
m-886	39	13	.	.	PUNCT
m-886	39	14	2	2	NUM
m-886	39	15	~~	~~	SYM
m-886	39	16	103	103	NUM
m-886	39	17	)	)	PUNCT
m-886	39	18	~~(5	~~(5	NUM
m-886	39	19	,	,	PUNCT
m-886	39	20	102	102	NUM
m-886	39	21	)	)	PUNCT
m-886	39	22	~~(3	~~(3	CCONJ
m-886	39	23	2	2	NUM
m-886	39	24	~~	~~	NUM
m-886	39	25	r	r	NOUN
m-886	39	26	nnnn	nnnn	PROPN
m-886	39	27	n	n	PROPN
m-886	39	28	nnnn	nnnn	PROPN
m-886	39	29	n	n	CCONJ
m-886	39	30			NOUN
m-886	39	31			X
m-886	39	32			PROPN
m-886	39	33			ADV
m-886	39	34			VERB
m-886	39	35			PROPN
m-886	39	36			PROPN
m-886	39	37			PROPN
m-886	39	38			VERB
m-886	39	39			PUNCT
m-886	39	40			NUM
m-886	39	41	pattern	pattern	NOUN
m-886	39	42	2	2	NUM
m-886	39	43	:	:	PUNCT
m-886	39	44	taking	take	VERB
m-886	39	45	kr2s	kr2s	ADJ
m-886	40	1			PROPN
m-886	40	2	(	(	PUNCT
m-886	40	3	8)	8)	NUM
m-886	40	4	in	in	ADP
m-886	40	5	(	(	PUNCT
m-886	40	6	3	3	NUM
m-886	40	7	)	)	PUNCT
m-886	40	8	,	,	PUNCT
m-886	40	9	it	it	PRON
m-886	40	10	is	be	AUX
m-886	40	11	written	write	VERB
m-886	40	12	as	as	ADP
m-886	40	13	)	)	PUNCT
m-886	40	14	k9r10(rt	k9r10(rt	PROPN
m-886	40	15	2222	2222	NUM
m-886	40	16			PROPN
m-886	40	17	(	(	PUNCT
m-886	40	18	9	9	X
m-886	40	19	)	)	PUNCT
m-886	40	20	let	let	NOUN
m-886	40	21	)	)	PUNCT
m-886	40	22	k9r10	k9r10	PROPN
m-886	40	23	(	(	PUNCT
m-886	40	24	222	222	NUM
m-886	40	25			NOUN
m-886	40	26	(	(	PUNCT
m-886	40	27	10	10	NUM
m-886	40	28	)	)	PUNCT
m-886	40	29	which	which	PRON
m-886	40	30	is	be	AUX
m-886	40	31	satisfied	satisfied	ADJ
m-886	40	32	by	by	ADP
m-886	40	33	k	k	PROPN
m-886	40	34	,	,	PUNCT
m-886	40	35	kr	kr	PROPN
m-886	40	36	00	00	NUM
m-886	40	37			NUM
m-886	40	38			NOUN
m-886	40	39	to	to	PART
m-886	40	40	obtain	obtain	VERB
m-886	40	41	the	the	DET
m-886	40	42	other	other	ADJ
m-886	40	43	solutions	solution	NOUN
m-886	40	44	to	to	ADP
m-886	40	45	(	(	PUNCT
m-886	40	46	10	10	NUM
m-886	40	47	)	)	PUNCT
m-886	40	48	,	,	PUNCT
m-886	40	49	consider	consider	VERB
m-886	40	50	the	the	DET
m-886	40	51	corresponding	correspond	VERB
m-886	40	52	pell	pell	NOUN
m-886	40	53	equation	equation	NOUN
m-886	40	54	1r10	1r10	NUM
m-886	40	55	22	22	NUM
m-886	40	56			ADP
m-886	40	57	whose	whose	DET
m-886	40	58	general	general	ADJ
m-886	40	59	solution	solution	NOUN
m-886	40	60	)	)	PUNCT
m-886	40	61	~,r	~,r	PUNCT
m-886	40	62	~	~	PUNCT
m-886	40	63	(	(	PUNCT
m-886	40	64	nn	nn	X
m-886	40	65			NOUN
m-886	40	66	is	be	AUX
m-886	40	67	given	give	VERB
m-886	40	68	by	by	ADP
m-886	40	69	nn	nn	PROPN
m-886	40	70	nn	nn	PROPN
m-886	40	71	f	f	PROPN
m-886	40	72	2	2	NUM
m-886	40	73	1~	1~	NUM
m-886	40	74	,	,	PUNCT
m-886	40	75	g	g	PROPN
m-886	40	76	102	102	NUM
m-886	40	77	1	1	NUM
m-886	40	78	r	r	NOUN
m-886	40	79	~	~	PUNCT
m-886	41	1			NUM
m-886	41	2			NUM
m-886	41	3			NOUN
m-886	41	4	(	(	PUNCT
m-886	41	5	11	11	NUM
m-886	41	6	)	)	PUNCT
m-886	41	7	applying	apply	VERB
m-886	41	8	the	the	DET
m-886	41	9	lemma	lemma	NOUN
m-886	41	10	of	of	ADP
m-886	41	11	brahmagupta	brahmagupta	NOUN
m-886	41	12	between	between	ADP
m-886	41	13	)	)	PUNCT
m-886	41	14	,	,	PUNCT
m-886	41	15	r	r	NOUN
m-886	41	16	(	(	PUNCT
m-886	41	17	00	00	NUM
m-886	41	18			NOUN
m-886	41	19	and	and	CCONJ
m-886	41	20	)	)	PUNCT
m-886	41	21	~,r	~,r	PROPN
m-886	41	22	~	~	PUNCT
m-886	41	23	(	(	PUNCT
m-886	41	24	nn	nn	X
m-886	41	25			PROPN
m-886	41	26	,	,	PUNCT
m-886	41	27	the	the	DET
m-886	41	28	general	general	ADJ
m-886	41	29	solution	solution	NOUN
m-886	41	30	)	)	PUNCT
m-886	41	31	,	,	PUNCT
m-886	41	32	r	r	X
m-886	41	33	(	(	PUNCT
m-886	41	34	1n1n	1n1n	X
m-886	41	35			ADJ
m-886	41	36			NOUN
m-886	41	37	to	to	ADP
m-886	41	38	(	(	PUNCT
m-886	41	39	10	10	NUM
m-886	41	40	)	)	PUNCT
m-886	41	41	is	be	AUX
m-886	41	42	given	give	VERB
m-886	41	43	by	by	ADP
m-886	41	44	ijo	ijo	PROPN
m-886	41	45	journals	journal	NOUN
m-886	41	46	volume	volume	NOUN
m-886	41	47	07	07	NUM
m-886	41	48	|	|	NOUN
m-886	41	49	issue	issue	NOUN
m-886	41	50	05	05	NUM
m-886	42	1	|	|	ADV
m-886	42	2	may	may	AUX
m-886	42	3	2024	2024	NUM
m-886	42	4	|	|	ADV
m-886	42	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-886	42	6	4	4	NUM
m-886	42	7	ijo	ijo	PROPN
m-886	42	8	international	international	ADJ
m-886	42	9	journal	journal	PROPN
m-886	42	10	of	of	ADP
m-886	42	11	mathematics	mathematics	PROPN
m-886	42	12	(	(	PUNCT
m-886	42	13	issn	issn	PROPN
m-886	42	14	:	:	PUNCT
m-886	42	15	2992	2992	NUM
m-886	42	16	-	-	SYM
m-886	42	17	4421	4421	NUM
m-886	42	18	)	)	PUNCT
m-886	43	1	dr	dr	PROPN
m-886	43	2	.	.	PROPN
m-886	43	3	n.thiruniraiselvi1	n.thiruniraiselvi1	PROPN
m-886	43	4	*	*	PROPN
m-886	43	5	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-886	43	6	volume	volume	NOUN
m-886	43	7	07	07	NUM
m-886	43	8	||	||	NOUN
m-886	43	9	issue	issue	NOUN
m-886	43	10	05||	05||	X
m-886	43	11	may	may	AUX
m-886	43	12	,	,	PUNCT
m-886	43	13	2024	2024	NUM
m-886	43	14	||	||	NOUN
m-886	43	15	,	,	PUNCT
m-886	43	16	g	g	PROPN
m-886	43	17	102	102	NUM
m-886	44	1	k	k	NOUN
m-886	44	2	f	f	PROPN
m-886	44	3	2	2	NUM
m-886	44	4	k	k	NOUN
m-886	44	5	r	r	NOUN
m-886	44	6	nn1n	nn1n	PROPN
m-886	44	7			PROPN
m-886	44	8	(	(	PUNCT
m-886	44	9	12	12	NUM
m-886	44	10	)	)	PUNCT
m-886	44	11	.g	.g	PROPN
m-886	45	1	10	10	NUM
m-886	45	2	k5	k5	PROPN
m-886	45	3	f	f	PROPN
m-886	45	4	2	2	NUM
m-886	45	5	k	k	NOUN
m-886	45	6	nn1n	nn1n	PROPN
m-886	45	7			NOUN
m-886	45	8			PUNCT
m-886	45	9	from	from	ADP
m-886	45	10	(	(	PUNCT
m-886	45	11	8)	8)	NUM
m-886	45	12	and	and	CCONJ
m-886	45	13	(	(	PUNCT
m-886	45	14	9	9	NUM
m-886	45	15	)	)	PUNCT
m-886	45	16	,	,	PUNCT
m-886	45	17	we	we	PRON
m-886	45	18	get	get	VERB
m-886	45	19	1n1n1n	1n1n1n	NUM
m-886	45	20	1n1n	1n1n	NUM
m-886	45	21	rt	rt	PROPN
m-886	45	22	rk2s	rk2s	PROPN
m-886	45	23			ADV
m-886	45	24			ADJ
m-886	45	25			ADJ
m-886	45	26			NUM
m-886	45	27			NOUN
m-886	45	28	in	in	ADP
m-886	45	29	view	view	NOUN
m-886	45	30	of	of	ADP
m-886	45	31	(	(	PUNCT
m-886	45	32	2	2	NUM
m-886	45	33	)	)	PUNCT
m-886	45	34	,	,	PUNCT
m-886	45	35	the	the	DET
m-886	45	36	corresponding	corresponding	ADJ
m-886	45	37	integer	integer	NOUN
m-886	45	38	solutions	solution	NOUN
m-886	45	39	to	to	ADP
m-886	45	40	(	(	PUNCT
m-886	45	41	1	1	X
m-886	45	42	)	)	PUNCT
m-886	45	43	are	be	AUX
m-886	45	44	given	give	VERB
m-886	45	45	by	by	ADP
m-886	45	46	,	,	PUNCT
m-886	45	47	)	)	PUNCT
m-886	45	48	k2)(g	k2)(g	PROPN
m-886	46	1	102	102	NUM
m-886	46	2	k	k	NOUN
m-886	46	3	f	f	PROPN
m-886	46	4	2	2	NUM
m-886	46	5	k	k	X
m-886	46	6	(	(	PUNCT
m-886	46	7	3q	3q	NUM
m-886	46	8	)	)	PUNCT
m-886	46	9	,	,	PUNCT
m-886	46	10	k2)(g	k2)(g	PROPN
m-886	46	11	102	102	NUM
m-886	47	1	k	k	NOUN
m-886	47	2	f	f	PROPN
m-886	47	3	2	2	NUM
m-886	47	4	k	k	X
m-886	47	5	(	(	PUNCT
m-886	47	6	3p	3p	NUM
m-886	47	7	)	)	PUNCT
m-886	47	8	,	,	PUNCT
m-886	47	9	g10f10()gf10	g10f10()gf10	PROPN
m-886	47	10	(	(	PUNCT
m-886	47	11	1040	1040	NUM
m-886	47	12	k	k	X
m-886	47	13	z	z	NOUN
m-886	47	14	)	)	PUNCT
m-886	47	15	,	,	PUNCT
m-886	47	16	2k6)(gf10	2k6)(gf10	NUM
m-886	47	17	(	(	PUNCT
m-886	47	18	102	102	NUM
m-886	47	19	k	k	PROPN
m-886	47	20	y	y	PROPN
m-886	47	21	)	)	PUNCT
m-886	47	22	,	,	PUNCT
m-886	47	23	2k6)(gf10	2k6)(gf10	NUM
m-886	47	24	(	(	PUNCT
m-886	47	25	102	102	NUM
m-886	47	26	k	k	NOUN
m-886	47	27	x	x	SYM
m-886	47	28	1nnn1n	1nnn1n	NUM
m-886	47	29	1nnn1n	1nnn1n	NUM
m-886	47	30	nn	nn	SYM
m-886	47	31	2	2	NUM
m-886	47	32	nn	nn	NUM
m-886	47	33	4	4	NUM
m-886	47	34	1n	1n	NUM
m-886	47	35	nn1n	nn1n	NOUN
m-886	47	36	nn1n	nn1n	NOUN
m-886	47	37			PROPN
m-886	47	38			NOUN
m-886	47	39			PUNCT
m-886	47	40			PRON
m-886	47	41			PUNCT
m-886	47	42			PROPN
m-886	47	43			PROPN
m-886	47	44			NOUN
m-886	47	45			PUNCT
m-886	47	46			VERB
m-886	47	47	jointly	jointly	ADV
m-886	47	48	with	with	ADP
m-886	47	49	(	(	PUNCT
m-886	47	50	12	12	NUM
m-886	47	51	)	)	PUNCT
m-886	47	52	,	,	PUNCT
m-886	47	53	where	where	SCONJ
m-886	47	54	.)10619()10619(g	.)10619()10619(g	NOUN
m-886	47	55	,	,	PUNCT
m-886	47	56	)	)	PUNCT
m-886	48	1	10619()10619(f	10619()10619(f	NUM
m-886	48	2	1n1n	1n1n	NOUN
m-886	48	3	n	n	CCONJ
m-886	48	4	1n1n	1n1n	NUM
m-886	48	5	n	n	CCONJ
m-886	48	6			PROPN
m-886	48	7			PROPN
m-886	48	8			PROPN
m-886	48	9			NOUN
m-886	48	10	pattern	pattern	NOUN
m-886	48	11	3	3	NUM
m-886	48	12	:	:	PUNCT
m-886	48	13	assume	assume	VERB
m-886	48	14	22	22	NUM
m-886	48	15	v9u9r	v9u9r	NUM
m-886	48	16			ADJ
m-886	48	17	(	(	PUNCT
m-886	48	18	13	13	NUM
m-886	48	19	)	)	PUNCT
m-886	48	20	consider	consider	VERB
m-886	48	21	)	)	PUNCT
m-886	48	22	i62)(i62(40	i62)(i62(40	NOUN
m-886	48	23			PRON
m-886	48	24	(	(	PUNCT
m-886	48	25	14	14	NUM
m-886	48	26	)	)	PUNCT
m-886	48	27	substituting	substitute	VERB
m-886	48	28	(	(	PUNCT
m-886	48	29	13	13	NUM
m-886	48	30	)	)	PUNCT
m-886	48	31	,	,	PUNCT
m-886	48	32	(	(	PUNCT
m-886	48	33	14	14	NUM
m-886	48	34	)	)	PUNCT
m-886	48	35	in	in	ADP
m-886	48	36	(	(	PUNCT
m-886	48	37	3	3	NUM
m-886	48	38	)	)	PUNCT
m-886	48	39	and	and	CCONJ
m-886	48	40	using	use	VERB
m-886	48	41	the	the	DET
m-886	48	42	method	method	NOUN
m-886	48	43	of	of	ADP
m-886	48	44	factorizations	factorization	NOUN
m-886	48	45	,	,	PUNCT
m-886	48	46	we	we	PRON
m-886	48	47	have	have	VERB
m-886	48	48	4)v3iu3)(i62()t2is3	4)v3iu3)(i62()t2is3	NOUN
m-886	48	49	(	(	PUNCT
m-886	48	50			NUM
m-886	48	51	equating	equate	VERB
m-886	48	52	real	real	ADJ
m-886	48	53	and	and	CCONJ
m-886	48	54	imaginary	imaginary	ADJ
m-886	48	55	parts	part	NOUN
m-886	48	56	,	,	PUNCT
m-886	48	57	we	we	PRON
m-886	48	58	have	have	VERB
m-886	48	59	ijo	ijo	NOUN
m-886	48	60	journals	journal	NOUN
m-886	48	61	volume	volume	NOUN
m-886	48	62	07	07	NUM
m-886	49	1	|	|	NOUN
m-886	49	2	issue	issue	NOUN
m-886	49	3	05	05	NUM
m-886	50	1	|	|	ADV
m-886	50	2	may	may	AUX
m-886	50	3	2024	2024	NUM
m-886	50	4	|	|	ADV
m-886	50	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-886	50	6	5	5	NUM
m-886	50	7	ijo	ijo	PROPN
m-886	50	8	international	international	ADJ
m-886	50	9	journal	journal	PROPN
m-886	50	10	of	of	ADP
m-886	50	11	mathematics	mathematics	PROPN
m-886	50	12	(	(	PUNCT
m-886	50	13	issn	issn	PROPN
m-886	50	14	:	:	PUNCT
m-886	50	15	2992	2992	NUM
m-886	50	16	-	-	SYM
m-886	50	17	4421	4421	NUM
m-886	50	18	)	)	PUNCT
m-886	51	1	dr	dr	PROPN
m-886	51	2	.	.	PROPN
m-886	51	3	n.thiruniraiselvi1	n.thiruniraiselvi1	PROPN
m-886	51	4	*	*	PROPN
m-886	51	5	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-886	51	6	volume	volume	NOUN
m-886	51	7	07	07	NUM
m-886	51	8	||	||	NOUN
m-886	51	9	issue	issue	NOUN
m-886	51	10	05||	05||	X
m-886	51	11	may	may	AUX
m-886	51	12	,	,	PUNCT
m-886	51	13	2024	2024	NUM
m-886	51	14	||	||	NOUN
m-886	51	15	)	)	PUNCT
m-886	51	16	]	]	PUNCT
m-886	51	17	vu(uv4v3vu18u3[3	vu(uv4v3vu18u3[3	X
m-886	51	18	t	t	PROPN
m-886	51	19	)	)	PUNCT
m-886	51	20	]	]	X
m-886	51	21	vu(uv24v2vu12u2[3s	vu(uv24v2vu12u2[3s	PROPN
m-886	51	22	4442244	4442244	NUM
m-886	51	23	4442243	4442243	NUM
m-886	52	1			PROPN
m-886	52	2			PROPN
m-886	52	3	in	in	ADP
m-886	52	4	view	view	NOUN
m-886	52	5	of	of	ADP
m-886	52	6	(	(	PUNCT
m-886	52	7	2	2	NUM
m-886	52	8	)	)	PUNCT
m-886	52	9	,	,	PUNCT
m-886	52	10	we	we	PRON
m-886	52	11	get	get	VERB
m-886	52	12	)	)	PUNCT
m-886	52	13	]	]	X
m-886	53	1	vu(uv28vvu6u[3	vu(uv28vvu6u[3	NUM
m-886	53	2	*	*	ADJ
m-886	53	3	6q	6q	NOUN
m-886	53	4	)	)	PUNCT
m-886	53	5	]	]	X
m-886	53	6	vu(uv20v5vu30u6[3	vu(uv20v5vu30u6[3	NOUN
m-886	53	7	*	*	SYM
m-886	53	8	6p	6p	NUM
m-886	53	9	)	)	PUNCT
m-886	53	10	]	]	SYM
m-886	53	11	vu(uv4v3vu18u3[3z	vu(uv4v3vu18u3[3z	NOUN
m-886	53	12	)	)	PUNCT
m-886	53	13	]	]	PUNCT
m-886	53	14	vu(uv32v4vu24u4[3y	vu(uv32v4vu24u4[3y	X
m-886	53	15	)	)	PUNCT
m-886	53	16	]	]	X
m-886	53	17	vu(uv16v8vu48u8[3x	vu(uv16v8vu48u8[3x	NOUN
m-886	53	18	2242247	2242247	NUM
m-886	53	19	2242247	2242247	NUM
m-886	53	20	2242247	2242247	NUM
m-886	53	21	2242244	2242244	NUM
m-886	53	22	2242243	2242243	NUM
m-886	54	1			PRON
m-886	54	2			PROPN
m-886	55	1			PROPN
m-886	55	2			X
m-886	56	1			PROPN
m-886	56	2	pattern	pattern	NOUN
m-886	56	3	4	4	NUM
m-886	56	4	:	:	PUNCT
m-886	56	5	it	it	PRON
m-886	56	6	is	be	AUX
m-886	56	7	worth	worth	ADJ
m-886	56	8	to	to	PART
m-886	56	9	mention	mention	VERB
m-886	56	10	that	that	SCONJ
m-886	56	11	the	the	DET
m-886	56	12	integer	integer	NOUN
m-886	56	13	40	40	NUM
m-886	56	14	may	may	AUX
m-886	56	15	also	also	ADV
m-886	56	16	be	be	AUX
m-886	56	17	written	write	VERB
m-886	56	18	as	as	ADP
m-886	56	19	222	222	NUM
m-886	56	20	)	)	PUNCT
m-886	56	21	(	(	PUNCT
m-886	56	22	)	)	PUNCT
m-886	56	23	]	]	PUNCT
m-886	56	24	,	,	PUNCT
m-886	56	25	(	(	PUNCT
m-886	56	26	g2i),(2)][,(g2i),(f2	g2i),(2)][,(g2i),(f2	ADP
m-886	56	27	[	[	PUNCT
m-886	56	28	40	40	NUM
m-886	56	29			NUM
m-886	56	30			PUNCT
m-886	56	31			NUM
m-886	56	32	(	(	PUNCT
m-886	56	33	15	15	NUM
m-886	56	34	)	)	PUNCT
m-886	56	35	where	where	SCONJ
m-886	56	36	)	)	PUNCT
m-886	56	37	(	(	PUNCT
m-886	56	38	)	)	PUNCT
m-886	56	39	2(3),(g;2)(3),(f	2(3),(g;2)(3),(f	NOUN
m-886	56	40	2222	2222	NUM
m-886	56	41			NOUN
m-886	56	42			PUNCT
m-886	56	43	substituting	substitute	VERB
m-886	56	44	(	(	PUNCT
m-886	56	45	13	13	NUM
m-886	56	46	)	)	PUNCT
m-886	56	47	&	&	CCONJ
m-886	56	48	(	(	PUNCT
m-886	56	49	15	15	NUM
m-886	56	50	)	)	PUNCT
m-886	56	51	in	in	ADP
m-886	56	52	(	(	PUNCT
m-886	56	53	3	3	NUM
m-886	56	54	)	)	PUNCT
m-886	56	55	and	and	CCONJ
m-886	56	56	employing	employ	VERB
m-886	56	57	the	the	DET
m-886	56	58	method	method	NOUN
m-886	56	59	of	of	ADP
m-886	56	60	factorization	factorization	NOUN
m-886	56	61	,	,	PUNCT
m-886	56	62	we	we	PRON
m-886	56	63	get	get	VERB
m-886	56	64	)	)	PUNCT
m-886	56	65	]	]	SYM
m-886	56	66	v	v	NOUN
m-886	56	67	,	,	PUNCT
m-886	56	68	u(ig)v	u(ig)v	NOUN
m-886	56	69	,	,	PUNCT
m-886	56	70	u(f)][,(g2i),(f2	u(f)][,(g2i),(f2	PROPN
m-886	56	71	[	[	PUNCT
m-886	56	72	)	)	PUNCT
m-886	56	73	(	(	PUNCT
m-886	56	74	3	3	NUM
m-886	56	75	t2is3	t2is3	NOUN
m-886	56	76	22	22	NUM
m-886	56	77	4	4	NUM
m-886	56	78			NUM
m-886	56	79			NUM
m-886	56	80			X
m-886	56	81	(	(	PUNCT
m-886	56	82	16	16	NUM
m-886	56	83	)	)	PUNCT
m-886	56	84	where	where	SCONJ
m-886	56	85	)	)	PUNCT
m-886	56	86	vu(uv4)v	vu(uv4)v	PROPN
m-886	56	87	,	,	PUNCT
m-886	56	88	u(g	u(g	PROPN
m-886	56	89	vvu6u)v	vvu6u)v	PROPN
m-886	56	90	,	,	PUNCT
m-886	56	91	u(f	u(f	PROPN
m-886	56	92	22	22	NUM
m-886	56	93	4224	4224	NUM
m-886	56	94			PROPN
m-886	56	95			PUNCT
m-886	56	96	equating	equate	VERB
m-886	56	97	the	the	DET
m-886	56	98	real	real	ADJ
m-886	56	99	and	and	CCONJ
m-886	56	100	imaginary	imaginary	ADJ
m-886	56	101	part	part	NOUN
m-886	56	102	of	of	ADP
m-886	56	103	(	(	PUNCT
m-886	56	104	16	16	NUM
m-886	56	105	)	)	PUNCT
m-886	56	106	,	,	PUNCT
m-886	56	107	one	one	NUM
m-886	56	108	obtains	obtain	VERB
m-886	56	109	)	)	PUNCT
m-886	56	110	]	]	SYM
m-886	56	111	v	v	NOUN
m-886	56	112	,	,	PUNCT
m-886	56	113	u(f),(g)v	u(f),(g)v	PROPN
m-886	56	114	,	,	PUNCT
m-886	56	115	u(g),(f	u(g),(f	NOUN
m-886	56	116	[	[	PUNCT
m-886	56	117	)	)	PUNCT
m-886	56	118	(	(	PUNCT
m-886	56	119	3	3	NUM
m-886	56	120	t	t	NOUN
m-886	56	121	)	)	PUNCT
m-886	56	122	]	]	SYM
m-886	56	123	v	v	NOUN
m-886	56	124	,	,	PUNCT
m-886	56	125	u(g),(g2)v	u(g),(g2)v	ADJ
m-886	56	126	,	,	PUNCT
m-886	56	127	u(f),(f2	u(f),(f2	NOUN
m-886	56	128	[	[	PUNCT
m-886	56	129	)	)	PUNCT
m-886	56	130	(	(	PUNCT
m-886	56	131	3	3	NUM
m-886	56	132	s	s	NOUN
m-886	56	133	22	22	NUM
m-886	56	134	4	4	NUM
m-886	56	135	22	22	NUM
m-886	56	136	3	3	NUM
m-886	56	137			ADP
m-886	56	138			NUM
m-886	57	1			NUM
m-886	58	1			NOUN
m-886	58	2			NUM
m-886	58	3			NUM
m-886	58	4	(	(	PUNCT
m-886	58	5	17	17	NUM
m-886	58	6	)	)	PUNCT
m-886	58	7	replacing	replace	VERB
m-886	58	8	u	u	NOUN
m-886	58	9	by	by	ADP
m-886	58	10	u	u	NOUN
m-886	58	11	)	)	PUNCT
m-886	58	12	(	(	PUNCT
m-886	58	13	22	22	NUM
m-886	58	14			NUM
m-886	58	15	,	,	PUNCT
m-886	58	16	v	v	NOUN
m-886	58	17	by	by	ADP
m-886	58	18	v	v	NOUN
m-886	58	19	)	)	PUNCT
m-886	58	20	(	(	PUNCT
m-886	58	21	22	22	NUM
m-886	58	22			NUM
m-886	58	23	in	in	ADP
m-886	58	24	(	(	PUNCT
m-886	58	25	16	16	NUM
m-886	58	26	)	)	PUNCT
m-886	58	27	,	,	PUNCT
m-886	58	28	we	we	PRON
m-886	58	29	have	have	VERB
m-886	58	30	)	)	PUNCT
m-886	58	31	]	]	SYM
m-886	58	32	v	v	NOUN
m-886	58	33	,	,	PUNCT
m-886	58	34	u(f),(g)v	u(f),(g)v	PROPN
m-886	58	35	,	,	PUNCT
m-886	58	36	u(g),(f[)(3	u(g),(f[)(3	PROPN
m-886	58	37	t	t	NOUN
m-886	58	38	)	)	PUNCT
m-886	58	39	]	]	SYM
m-886	58	40	v	v	NOUN
m-886	58	41	,	,	PUNCT
m-886	58	42	u(g),(g2)v	u(g),(g2)v	PROPN
m-886	58	43	,	,	PUNCT
m-886	58	44	u(f),(f2[)(3s	u(f),(f2[)(3s	PROPN
m-886	58	45	3224	3224	NUM
m-886	58	46	3223	3223	NUM
m-886	59	1			NOUN
m-886	59	2			NOUN
m-886	59	3	(	(	PUNCT
m-886	59	4	18	18	NUM
m-886	59	5	)	)	PUNCT
m-886	59	6	also	also	ADV
m-886	59	7	,	,	PUNCT
m-886	59	8	from	from	ADP
m-886	59	9	(	(	PUNCT
m-886	59	10	13	13	NUM
m-886	59	11	)	)	PUNCT
m-886	59	12	,	,	PUNCT
m-886	59	13	)	)	PUNCT
m-886	59	14	vu()(9r	vu()(9r	CCONJ
m-886	59	15	22222	22222	NUM
m-886	59	16			NOUN
m-886	59	17	(	(	PUNCT
m-886	59	18	19	19	NUM
m-886	59	19	)	)	PUNCT
m-886	59	20	from	from	ADP
m-886	59	21	(	(	PUNCT
m-886	59	22	2	2	NUM
m-886	59	23	)	)	PUNCT
m-886	59	24	and	and	CCONJ
m-886	59	25	(	(	PUNCT
m-886	59	26	18	18	NUM
m-886	59	27	)	)	PUNCT
m-886	59	28	,	,	PUNCT
m-886	59	29	it	it	PRON
m-886	59	30	is	be	AUX
m-886	59	31	seen	see	VERB
m-886	59	32	that	that	SCONJ
m-886	59	33	ijo	ijo	PROPN
m-886	59	34	journals	journal	NOUN
m-886	59	35	volume	volume	NOUN
m-886	59	36	07	07	NUM
m-886	59	37	|	|	NOUN
m-886	59	38	issue	issue	NOUN
m-886	59	39	05	05	NUM
m-886	60	1	|	|	ADV
m-886	60	2	may	may	AUX
m-886	60	3	2024	2024	NUM
m-886	60	4	|	|	ADV
m-886	60	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-886	60	6	6	6	NUM
m-886	60	7	ijo	ijo	PROPN
m-886	60	8	international	international	ADJ
m-886	60	9	journal	journal	PROPN
m-886	60	10	of	of	ADP
m-886	60	11	mathematics	mathematics	PROPN
m-886	60	12	(	(	PUNCT
m-886	60	13	issn	issn	PROPN
m-886	60	14	:	:	PUNCT
m-886	60	15	2992	2992	NUM
m-886	60	16	-	-	SYM
m-886	60	17	4421	4421	NUM
m-886	60	18	)	)	PUNCT
m-886	61	1	dr	dr	PROPN
m-886	61	2	.	.	PROPN
m-886	61	3	n.thiruniraiselvi1	n.thiruniraiselvi1	PROPN
m-886	61	4	*	*	PROPN
m-886	61	5	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-886	61	6	volume	volume	NOUN
m-886	61	7	07	07	NUM
m-886	61	8	||	||	NOUN
m-886	61	9	issue	issue	NOUN
m-886	61	10	05||	05||	X
m-886	61	11	may	may	AUX
m-886	61	12	,	,	PUNCT
m-886	61	13	2024	2024	NUM
m-886	61	14	||	||	NOUN
m-886	61	15	)	)	PUNCT
m-886	62	1	]	]	SYM
m-886	62	2	v	v	NOUN
m-886	62	3	,	,	PUNCT
m-886	62	4	u(g),(g2)v	u(g),(g2)v	ADJ
m-886	62	5	,	,	PUNCT
m-886	62	6	u(f),(f2)v	u(f),(f2)v	ADJ
m-886	62	7	,	,	PUNCT
m-886	62	8	u(f),(g3)v	u(f),(g3)v	PROPN
m-886	62	9	,	,	PUNCT
m-886	62	10	u(g),(f3[)(3	u(g),(f3[)(3	NOUN
m-886	62	11	*	*	NOUN
m-886	62	12	6q	6q	NOUN
m-886	62	13	)	)	PUNCT
m-886	62	14	]	]	SYM
m-886	62	15	v	v	NOUN
m-886	62	16	,	,	PUNCT
m-886	62	17	u(g),(g2)v	u(g),(g2)v	ADJ
m-886	62	18	,	,	PUNCT
m-886	62	19	u(f),(f2)v	u(f),(f2)v	ADJ
m-886	62	20	,	,	PUNCT
m-886	62	21	u(f),(g3)v	u(f),(g3)v	PROPN
m-886	62	22	,	,	PUNCT
m-886	62	23	u(g),(f3[)(3	u(g),(f3[)(3	NOUN
m-886	62	24	*	*	NOUN
m-886	62	25	6p	6p	NUM
m-886	62	26	)	)	PUNCT
m-886	62	27	]	]	SYM
m-886	62	28	v	v	NOUN
m-886	62	29	,	,	PUNCT
m-886	62	30	u(f),(g)v	u(f),(g)v	PROPN
m-886	62	31	,	,	PUNCT
m-886	62	32	u(g),(f)][v	u(g),(f)][v	NOUN
m-886	62	33	,	,	PUNCT
m-886	62	34	u(g),(g2)v	u(g),(g2)v	ADJ
m-886	62	35	,	,	PUNCT
m-886	62	36	u(f),(f2[)(3z	u(f),(f2[)(3z	NOUN
m-886	62	37	)	)	PUNCT
m-886	62	38	}	}	PUNCT
m-886	62	39	]	]	SYM
m-886	62	40	v	v	X
m-886	62	41	,	,	PUNCT
m-886	62	42	u(g)v	u(g)v	PROPN
m-886	62	43	,	,	PUNCT
m-886	62	44	u(f){,(g2)}v	u(f){,(g2)}v	NOUN
m-886	62	45	,	,	PUNCT
m-886	62	46	u(g)v	u(g)v	NOUN
m-886	62	47	,	,	PUNCT
m-886	62	48	u(f){,(f2[)(3y	u(f){,(f2[)(3y	NOUN
m-886	62	49	)	)	PUNCT
m-886	62	50	}	}	PUNCT
m-886	62	51	]	]	SYM
m-886	62	52	v	v	X
m-886	62	53	,	,	PUNCT
m-886	62	54	u(g)v	u(g)v	PROPN
m-886	62	55	,	,	PUNCT
m-886	62	56	u(f){,(g2)}v	u(f){,(g2)}v	NOUN
m-886	62	57	,	,	PUNCT
m-886	62	58	u(g)v	u(g)v	PROPN
m-886	62	59	,	,	PUNCT
m-886	62	60	u(f){,(f2[)(3x	u(f){,(f2[)(3x	PROPN
m-886	62	61	3223	3223	NUM
m-886	62	62	3223	3223	NUM
m-886	62	63	6227	6227	NUM
m-886	62	64	3224	3224	NUM
m-886	62	65	3224	3224	NUM
m-886	62	66			NOUN
m-886	62	67			NOUN
m-886	62	68			PUNCT
m-886	62	69			NOUN
m-886	62	70			NOUN
m-886	62	71	which	which	PRON
m-886	62	72	satisfy	satisfy	NOUN
m-886	62	73	(	(	PUNCT
m-886	62	74	1	1	NUM
m-886	62	75	)	)	PUNCT
m-886	62	76	along	along	ADP
m-886	62	77	with	with	ADP
m-886	62	78	(	(	PUNCT
m-886	62	79	19	19	NUM
m-886	62	80	)	)	PUNCT
m-886	62	81	.	.	PUNCT
m-886	63	1	pattern	pattern	NOUN
m-886	63	2	5	5	NUM
m-886	63	3	:	:	PUNCT
m-886	63	4	rewrite	rewrite	VERB
m-886	63	5	(	(	PUNCT
m-886	63	6	3	3	NUM
m-886	63	7	)	)	PUNCT
m-886	63	8	as	as	ADP
m-886	63	9	1*r40t4s9	1*r40t4s9	NUM
m-886	63	10	422	422	NUM
m-886	63	11			NOUN
m-886	63	12	(	(	PUNCT
m-886	63	13	20	20	NUM
m-886	63	14	)	)	PUNCT
m-886	63	15	assume	assume	VERB
m-886	63	16	the	the	DET
m-886	63	17	integer	integer	NOUN
m-886	63	18	1	1	NUM
m-886	63	19	on	on	ADP
m-886	63	20	the	the	DET
m-886	63	21	rhs	rhs	PROPN
m-886	63	22	of	of	ADP
m-886	63	23	(	(	PUNCT
m-886	63	24	1	1	NUM
m-886	63	25	)	)	PUNCT
m-886	63	26	as	as	ADP
m-886	63	27	)	)	PUNCT
m-886	63	28	qp	qp	PROPN
m-886	63	29	(	(	PUNCT
m-886	63	30	)	)	PUNCT
m-886	63	31	pq2iqp)(pq2iqp	pq2iqp)(pq2iqp	CCONJ
m-886	63	32	(	(	PUNCT
m-886	63	33	1	1	NUM
m-886	63	34	22	22	NUM
m-886	63	35	2222	2222	NUM
m-886	63	36			ADV
m-886	63	37			PROPN
m-886	63	38			PROPN
m-886	63	39	(	(	PUNCT
m-886	63	40	21	21	NUM
m-886	63	41	)	)	PUNCT
m-886	63	42	substituting	substituting	NOUN
m-886	63	43	(	(	PUNCT
m-886	63	44	14	14	NUM
m-886	63	45	)	)	PUNCT
m-886	63	46	,	,	PUNCT
m-886	63	47	(	(	PUNCT
m-886	63	48	21	21	NUM
m-886	63	49	)	)	PUNCT
m-886	63	50	in	in	ADP
m-886	63	51	(	(	PUNCT
m-886	63	52	20	20	NUM
m-886	63	53	)	)	PUNCT
m-886	63	54	,	,	PUNCT
m-886	63	55	we	we	PRON
m-886	63	56	have	have	VERB
m-886	63	57	)	)	PUNCT
m-886	63	58	]	]	X
m-886	63	59	q	q	X
m-886	63	60	,	,	PUNCT
m-886	63	61	p	p	X
m-886	63	62	,	,	PUNCT
m-886	63	63	v	v	NOUN
m-886	63	64	,	,	PUNCT
m-886	63	65	u(iq)q	u(iq)q	VERB
m-886	63	66	,	,	PUNCT
m-886	63	67	p	p	NOUN
m-886	63	68	,	,	PUNCT
m-886	63	69	v	v	NOUN
m-886	63	70	,	,	PUNCT
m-886	63	71	u(p	u(p	NOUN
m-886	63	72	[	[	PUNCT
m-886	63	73	)	)	PUNCT
m-886	63	74	qp	qp	PROPN
m-886	63	75	(	(	PUNCT
m-886	63	76	)	)	PUNCT
m-886	63	77	i62(3	i62(3	NOUN
m-886	63	78	)	)	PUNCT
m-886	63	79	t2is3	t2is3	NOUN
m-886	63	80	(	(	PUNCT
m-886	63	81	)	)	PUNCT
m-886	63	82	]	]	X
m-886	63	83	q	q	X
m-886	63	84	,	,	PUNCT
m-886	63	85	p(ik)q	p(ik)q	NOUN
m-886	63	86	,	,	PUNCT
m-886	63	87	p(j)][v	p(j)][v	PROPN
m-886	63	88	,	,	PUNCT
m-886	63	89	u(ig)v	u(ig)v	NOUN
m-886	63	90	,	,	PUNCT
m-886	63	91	u(f	u(f	NOUN
m-886	63	92	[	[	PUNCT
m-886	63	93	)	)	PUNCT
m-886	63	94	qp	qp	PROPN
m-886	63	95	(	(	PUNCT
m-886	63	96	)	)	PUNCT
m-886	63	97	i62(3	i62(3	NOUN
m-886	63	98	)	)	PUNCT
m-886	63	99	t2is3	t2is3	NOUN
m-886	63	100	(	(	PUNCT
m-886	63	101	)	)	PUNCT
m-886	63	102	v3is3	v3is3	NOUN
m-886	63	103	(	(	PUNCT
m-886	63	104	)	)	PUNCT
m-886	63	105	qp	qp	PROPN
m-886	63	106	(	(	PUNCT
m-886	63	107	)	)	PUNCT
m-886	63	108	pq2iqp	pq2iqp	PROPN
m-886	63	109	(	(	PUNCT
m-886	63	110	)	)	PUNCT
m-886	63	111	i62()t2is3	i62()t2is3	NOUN
m-886	63	112	(	(	PUNCT
m-886	63	113	22	22	NUM
m-886	63	114	4	4	NUM
m-886	63	115	22	22	NUM
m-886	63	116	4	4	NUM
m-886	63	117	4	4	NUM
m-886	63	118	22	22	NUM
m-886	63	119	22	22	NUM
m-886	63	120			ADV
m-886	63	121			VERB
m-886	63	122			PUNCT
m-886	63	123			PUNCT
m-886	63	124			PROPN
m-886	63	125			NOUN
m-886	63	126			PUNCT
m-886	63	127			PUNCT
m-886	63	128			ADV
m-886	63	129			PUNCT
m-886	63	130			PROPN
m-886	63	131			PROPN
m-886	63	132	where	where	SCONJ
m-886	63	133	)	)	PUNCT
m-886	63	134	q	q	NOUN
m-886	63	135	,	,	PUNCT
m-886	63	136	p(j)v	p(j)v	PROPN
m-886	63	137	,	,	PUNCT
m-886	63	138	u(g)q	u(g)q	PROPN
m-886	63	139	,	,	PUNCT
m-886	63	140	p(k)v	p(k)v	PROPN
m-886	63	141	,	,	PUNCT
m-886	63	142	u(f)q	u(f)q	PROPN
m-886	63	143	,	,	PUNCT
m-886	63	144	p	p	X
m-886	63	145	,	,	PUNCT
m-886	63	146	v	v	NOUN
m-886	63	147	,	,	PUNCT
m-886	63	148	u(q	u(q	PROPN
m-886	63	149	)	)	PUNCT
m-886	63	150	q	q	NOUN
m-886	63	151	,	,	PUNCT
m-886	63	152	p(k)v	p(k)v	PROPN
m-886	63	153	,	,	PUNCT
m-886	63	154	u(g)q	u(g)q	PROPN
m-886	63	155	,	,	PUNCT
m-886	63	156	p(j)v	p(j)v	PROPN
m-886	63	157	,	,	PUNCT
m-886	63	158	u(f)q	u(f)q	PROPN
m-886	63	159	,	,	PUNCT
m-886	63	160	p	p	X
m-886	63	161	,	,	PUNCT
m-886	63	162	v	v	NOUN
m-886	63	163	,	,	PUNCT
m-886	63	164	u(p	u(p	NOUN
m-886	63	165	)	)	PUNCT
m-886	63	166	vu(uv4)v	vu(uv4)v	NOUN
m-886	63	167	,	,	PUNCT
m-886	63	168	u(g;vvu6u)v	u(g;vvu6u)v	ADJ
m-886	63	169	,	,	PUNCT
m-886	63	170	u(f	u(f	PROPN
m-886	63	171	pq2)q	pq2)q	PROPN
m-886	63	172	,	,	PUNCT
m-886	63	173	p(k;qp)q	p(k;qp)q	NOUN
m-886	63	174	,	,	PUNCT
m-886	63	175	p(j	p(j	PROPN
m-886	63	176	224224	224224	NUM
m-886	63	177	22	22	NUM
m-886	63	178			ADJ
m-886	63	179			NOUN
m-886	63	180			NUM
m-886	63	181			NOUN
m-886	63	182	equating	equate	VERB
m-886	63	183	real	real	ADJ
m-886	63	184	and	and	CCONJ
m-886	63	185	imaginary	imaginary	ADJ
m-886	63	186	part	part	NOUN
m-886	63	187	of	of	ADP
m-886	63	188	the	the	DET
m-886	63	189	above	above	ADJ
m-886	63	190	equation	equation	NOUN
m-886	63	191	,	,	PUNCT
m-886	63	192	we	we	PRON
m-886	63	193	have	have	VERB
m-886	63	194	)	)	PUNCT
m-886	63	195	]	]	X
m-886	63	196	q	q	X
m-886	63	197	,	,	PUNCT
m-886	63	198	p	p	X
m-886	63	199	,	,	PUNCT
m-886	63	200	v	v	NOUN
m-886	63	201	,	,	PUNCT
m-886	63	202	u(q)q	u(q)q	PROPN
m-886	63	203	,	,	PUNCT
m-886	63	204	p	p	NOUN
m-886	63	205	,	,	PUNCT
m-886	63	206	v	v	NOUN
m-886	63	207	,	,	PUNCT
m-886	63	208	u(p3	u(p3	NOUN
m-886	63	209	[	[	PUNCT
m-886	63	210	)	)	PUNCT
m-886	63	211	qp	qp	NOUN
m-886	63	212	(	(	PUNCT
m-886	63	213	3	3	NUM
m-886	63	214	t	t	NOUN
m-886	63	215	)	)	PUNCT
m-886	63	216	]	]	X
m-886	64	1	q	q	X
m-886	64	2	,	,	PUNCT
m-886	64	3	p	p	X
m-886	64	4	,	,	PUNCT
m-886	64	5	v	v	NOUN
m-886	64	6	,	,	PUNCT
m-886	64	7	u(q6)q	u(q6)q	PROPN
m-886	64	8	,	,	PUNCT
m-886	64	9	p	p	NOUN
m-886	64	10	,	,	PUNCT
m-886	64	11	v	v	NOUN
m-886	64	12	,	,	PUNCT
m-886	64	13	u(p2	u(p2	ADJ
m-886	64	14	[	[	PUNCT
m-886	64	15	)	)	PUNCT
m-886	64	16	qp	qp	NOUN
m-886	64	17	(	(	PUNCT
m-886	64	18	3	3	NUM
m-886	64	19	s	s	NOUN
m-886	64	20	22	22	NUM
m-886	64	21	4	4	NUM
m-886	64	22	22	22	NUM
m-886	64	23	3	3	NUM
m-886	64	24			ADV
m-886	64	25			PUNCT
m-886	64	26			PROPN
m-886	64	27			PROPN
m-886	64	28			ADP
m-886	64	29			PROPN
m-886	64	30	ijo	ijo	PROPN
m-886	64	31	journals	journal	NOUN
m-886	64	32	volume	volume	NOUN
m-886	64	33	07	07	NUM
m-886	64	34	|	|	NOUN
m-886	64	35	issue	issue	NOUN
m-886	65	1	05	05	NUM
m-886	66	1	|	|	ADV
m-886	66	2	may	may	AUX
m-886	66	3	2024	2024	NUM
m-886	66	4	|	|	ADV
m-886	66	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-886	66	6	7	7	NUM
m-886	66	7	ijo	ijo	PROPN
m-886	66	8	international	international	ADJ
m-886	66	9	journal	journal	PROPN
m-886	66	10	of	of	ADP
m-886	66	11	mathematics	mathematics	PROPN
m-886	66	12	(	(	PUNCT
m-886	66	13	issn	issn	PROPN
m-886	66	14	:	:	PUNCT
m-886	66	15	2992	2992	NUM
m-886	66	16	-	-	SYM
m-886	66	17	4421	4421	NUM
m-886	66	18	)	)	PUNCT
m-886	66	19	dr	dr	PROPN
m-886	66	20	.	.	PROPN
m-886	66	21	n.thiruniraiselvi1	n.thiruniraiselvi1	PROPN
m-886	66	22	*	*	PROPN
m-886	66	23	https://ijojournals.com/	https://ijojournals.com/	PROPN
m-886	66	24	volume	volume	NOUN
m-886	66	25	07	07	NUM
m-886	66	26	||	||	NOUN
m-886	66	27	issue	issue	NOUN
m-886	66	28	05||	05||	X
m-886	66	29	may	may	AUX
m-886	66	30	,	,	PUNCT
m-886	66	31	2024	2024	NUM
m-886	66	32	||	||	NOUN
m-886	67	1	replacing	replace	VERB
m-886	67	2	u	u	PRON
m-886	67	3	by	by	ADP
m-886	67	4	(	(	PUNCT
m-886	67	5	p2	p2	X
m-886	67	6	+	+	SYM
m-886	67	7	q2	q2	NOUN
m-886	67	8	)	)	PUNCT
m-886	67	9	a	a	PRON
m-886	67	10	,	,	PUNCT
m-886	67	11	v	v	NOUN
m-886	67	12	by	by	ADP
m-886	67	13	(	(	PUNCT
m-886	67	14	p2	p2	X
m-886	67	15	+	+	SYM
m-886	67	16	q2	q2	NOUN
m-886	67	17	)	)	PUNCT
m-886	67	18	b	b	NOUN
m-886	67	19	in	in	ADP
m-886	67	20	the	the	DET
m-886	67	21	values	value	NOUN
m-886	67	22	of	of	ADP
m-886	67	23	s	s	PROPN
m-886	67	24	,	,	PUNCT
m-886	67	25	t	t	PROPN
m-886	67	26	and	and	CCONJ
m-886	67	27	r	r	NOUN
m-886	67	28	,	,	PUNCT
m-886	67	29	we	we	PRON
m-886	67	30	have	have	VERB
m-886	67	31	)	)	PUNCT
m-886	67	32	ba()qp(9r	ba()qp(9r	PUNCT
m-886	67	33	)	)	PUNCT
m-886	68	1	]	]	X
m-886	68	2	q	q	X
m-886	68	3	,	,	PUNCT
m-886	68	4	p	p	X
m-886	68	5	,	,	PUNCT
m-886	68	6	b	b	NOUN
m-886	68	7	,	,	PUNCT
m-886	68	8	a(q)q	a(q)q	PROPN
m-886	68	9	,	,	PUNCT
m-886	68	10	p	p	X
m-886	68	11	,	,	PUNCT
m-886	68	12	b	b	NOUN
m-886	68	13	,	,	PUNCT
m-886	68	14	a(p3[)qp(81	a(p3[)qp(81	PROPN
m-886	68	15	t	t	NOUN
m-886	68	16	)	)	PUNCT
m-886	69	1	]	]	X
m-886	69	2	q	q	X
m-886	69	3	,	,	PUNCT
m-886	69	4	p	p	X
m-886	69	5	,	,	PUNCT
m-886	69	6	b	b	PROPN
m-886	69	7	,	,	PUNCT
m-886	69	8	a(q6)q	a(q6)q	PROPN
m-886	69	9	,	,	PUNCT
m-886	69	10	p	p	X
m-886	69	11	,	,	PUNCT
m-886	69	12	b	b	NOUN
m-886	69	13	,	,	PUNCT
m-886	69	14	a(p2[)qp(27s	a(p2[)qp(27s	ADP
m-886	69	15	22222	22222	NUM
m-886	69	16	322	322	NUM
m-886	69	17	322	322	NUM
m-886	69	18			NOUN
m-886	69	19			PUNCT
m-886	69	20			PRON
m-886	69	21	conclusion	conclusion	NOUN
m-886	69	22	:	:	PUNCT
m-886	69	23	it	it	PRON
m-886	69	24	has	have	AUX
m-886	69	25	been	be	AUX
m-886	69	26	shown	show	VERB
m-886	69	27	that	that	SCONJ
m-886	69	28	higher	high	ADJ
m-886	69	29	degree	degree	NOUN
m-886	69	30	diophantine	diophantine	NOUN
m-886	69	31	equation	equation	NOUN
m-886	69	32	with	with	ADP
m-886	69	33	multiple	multiple	ADJ
m-886	69	34	variables	variable	NOUN
m-886	69	35	may	may	AUX
m-886	69	36	be	be	AUX
m-886	69	37	solved	solve	VERB
m-886	69	38	through	through	ADP
m-886	69	39	strategies	strategy	NOUN
m-886	69	40	like	like	ADP
m-886	69	41	substitution	substitution	NOUN
m-886	69	42	and	and	CCONJ
m-886	69	43	factorization	factorization	NOUN
m-886	69	44	by	by	ADP
m-886	69	45	reducing	reduce	VERB
m-886	69	46	it	it	PRON
m-886	69	47	to	to	ADP
m-886	69	48	a	a	DET
m-886	69	49	lesser	less	ADJ
m-886	69	50	degree	degree	NOUN
m-886	69	51	solvable	solvable	ADJ
m-886	69	52	diophantine	diophantine	NOUN
m-886	69	53	equation	equation	NOUN
m-886	69	54	.	.	PUNCT
m-886	70	1	one	one	PRON
m-886	70	2	may	may	AUX
m-886	70	3	search	search	VERB
m-886	70	4	for	for	ADP
m-886	70	5	other	other	ADJ
m-886	70	6	choices	choice	NOUN
m-886	70	7	of	of	ADP
m-886	70	8	higher	high	ADJ
m-886	70	9	degree	degree	NOUN
m-886	70	10	diophantine	diophantine	NOUN
m-886	70	11	equations	equation	NOUN
m-886	70	12	with	with	ADP
m-886	70	13	multiple	multiple	ADJ
m-886	70	14	variables	variable	NOUN
m-886	70	15	for	for	ADP
m-886	70	16	obtaining	obtain	VERB
m-886	70	17	their	their	PRON
m-886	70	18	respective	respective	ADJ
m-886	70	19	integer	integer	NOUN
m-886	70	20	solutions	solution	NOUN
m-886	70	21	.	.	PUNCT
m-886	71	1	references	reference	NOUN
m-886	71	2	:	:	PUNCT
m-886	72	1	[	[	X
m-886	72	2	1	1	NUM
m-886	72	3	]	]	PUNCT
m-886	72	4	j.sivasankari	j.sivasankari	ADJ
m-886	72	5	,	,	PUNCT
m-886	72	6	dr.r.anbuselvi	dr.r.anbuselvi	PROPN
m-886	72	7	,	,	PUNCT
m-886	72	8	“	"	PUNCT
m-886	72	9	integral	integral	ADJ
m-886	72	10	solutions	solution	NOUN
m-886	72	11	for	for	ADP
m-886	72	12	the	the	DET
m-886	72	13	diophantine	diophantine	NOUN
m-886	72	14	equation	equation	NOUN
m-886	72	15	of	of	ADP
m-886	72	16	higher	high	ADJ
m-886	72	17	degree	degree	NOUN
m-886	72	18	with	with	ADP
m-886	72	19	six	six	NUM
m-886	72	20	unknowns	unknown	NOUN
m-886	72	21	822366	822366	NUM
m-886	72	22	r)qp(800z3456yx	r)qp(800z3456yx	PROPN
m-886	72	23			PROPN
m-886	72	24	”	"	PUNCT
m-886	72	25	,	,	PUNCT
m-886	72	26	advances	advance	NOUN
m-886	72	27	in	in	ADP
m-886	72	28	nonlinear	nonlinear	ADJ
m-886	72	29	variational	variational	ADJ
m-886	72	30	inequalities	inequality	NOUN
m-886	72	31	,	,	PUNCT
m-886	72	32	vol	vol	NOUN
m-886	72	33	27(1	27(1	NUM
m-886	72	34	)	)	PUNCT
m-886	72	35	,	,	PUNCT
m-886	72	36	2024	2024	NUM
m-886	72	37	.	.	PUNCT
m-886	73	1	ijo	ijo	PROPN
m-886	73	2	journals	journal	NOUN
m-886	73	3	volume	volume	NOUN
m-886	73	4	07	07	NUM
m-886	73	5	|	|	NOUN
m-886	73	6	issue	issue	NOUN
m-886	74	1	05	05	NUM
m-886	75	1	|	|	ADV
m-886	75	2	may	may	AUX
m-886	75	3	2024	2024	NUM
m-886	75	4	|	|	ADV
m-886	75	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-886	75	6	8	8	NUM