id	sid	eid	entity	type
ejpam-5776	1	1	european journal	ORG
ejpam-5776	1	2	2025	DATE
ejpam-5776	1	3	18	CARDINAL
ejpam-5776	1	4	2	CARDINAL
ejpam-5776	1	5	5776	CARDINAL
ejpam-5776	1	6	1307-5543	DATE
ejpam-5776	1	7	new york	GPE
ejpam-5776	1	8	romdhini1,∗	ORG
ejpam-5776	1	9	nawawi2	DATE
ejpam-5776	1	10	faisal al-sharqi3,4	PERSON
ejpam-5776	1	11	abdurahim1	PRODUCT
ejpam-5776	1	12	ellena saufika hakim maharani1	PERSON
ejpam-5776	1	13	ifan hasnan dani1 1	PERSON
ejpam-5776	1	14	university of mataram	ORG
ejpam-5776	1	15	mataram 83125	PERSON
ejpam-5776	1	16	indonesia 2	ORG
ejpam-5776	1	17	putra malaysia	GPE
ejpam-5776	1	18	43400	CARDINAL
ejpam-5776	1	19	serdang	GPE
ejpam-5776	1	20	selangor	GPE
ejpam-5776	1	21	malaysia 3	ORG
ejpam-5776	1	22	university of anbar	ORG
ejpam-5776	1	23	ramadi	GPE
ejpam-5776	1	24	anbar	GPE
ejpam-5776	1	25	iraq	GPE
ejpam-5776	1	26	4	CARDINAL
ejpam-5776	1	27	national university of science and technology	ORG
ejpam-5776	1	28	dhi qar	GPE
ejpam-5776	1	29	iraq	GPE
ejpam-5776	5	1	2020	DATE
ejpam-5776	5	2	05c25	CARDINAL
ejpam-5776	5	3	1	CARDINAL
ejpam-5776	7	1	first	ORDINAL
ejpam-5776	9	1	wang	PERSON
ejpam-5776	10	1	1	CARDINAL
ejpam-5776	10	2	2	CARDINAL
ejpam-5776	12	1	3	CARDINAL
ejpam-5776	12	2	2020	DATE
ejpam-5776	14	1	https://doi.org/10.29020/nybg.ejpam.v18i2.5776	PERSON
ejpam-5776	14	2	m. u. romdhini	PERSON
ejpam-5776	14	3	a. nawawi	PERSON
ejpam-5776	14	4	f. al-sharqi	PERSON
ejpam-5776	14	5	a. e. s. h. maharani	PERSON
ejpam-5776	15	1	1	CARDINAL
ejpam-5776	15	2	2025	CARDINAL
ejpam-5776	17	1	j. pure	PERSON
ejpam-5776	17	2	18	CARDINAL
ejpam-5776	17	3	2	CARDINAL
ejpam-5776	17	4	2025	CARDINAL
ejpam-5776	17	5	5776 2	DATE
ejpam-5776	17	6	13	CARDINAL
ejpam-5776	18	1	4	CARDINAL
ejpam-5776	19	1	5	CARDINAL
ejpam-5776	22	1	6	CARDINAL
ejpam-5776	22	2	1978	DATE
ejpam-5776	23	1	8	CARDINAL
ejpam-5776	25	1	9	CARDINAL
ejpam-5776	25	2	10	CARDINAL
ejpam-5776	26	1	algebraic	PERSON
ejpam-5776	26	2	11	CARDINAL
ejpam-5776	26	3	12	CARDINAL
ejpam-5776	28	1	2	CARDINAL
ejpam-5776	30	1	1	CARDINAL
ejpam-5776	31	1	13	CARDINAL
ejpam-5776	32	1	z(g	PERSON
ejpam-5776	32	2	two	CARDINAL
ejpam-5776	32	3	̸=	ORG
ejpam-5776	33	1	2n	CARDINAL
ejpam-5776	33	2	n ≥ 3	DATE
ejpam-5776	35	1	∈	ORG
ejpam-5776	36	1	dxy	ORG
ejpam-5776	36	2	d(x	ORG
ejpam-5776	37	1	e(x	ORG
ejpam-5776	38	1	∈	ORG
ejpam-5776	39	1	ωd2n	ORG
ejpam-5776	39	2	2	CARDINAL
ejpam-5776	40	1	1	CARDINAL
ejpam-5776	40	2	ωd2n	ORG
ejpam-5776	41	1	dxixj	ORG
ejpam-5776	41	2	0	CARDINAL
ejpam-5776	42	1	3	CARDINAL
ejpam-5776	43	1	4	CARDINAL
ejpam-5776	44	1	xixj ∈	PERSON
ejpam-5776	44	2	0	CARDINAL
ejpam-5776	45	1	4	CARDINAL
ejpam-5776	46	1	5	CARDINAL
ejpam-5776	46	2	ωd2n	ORG
ejpam-5776	47	1	aij	ORG
ejpam-5776	47	2	aij	ORG
ejpam-5776	47	3	1	CARDINAL
ejpam-5776	50	1	xixj ∈	PERSON
ejpam-5776	50	2	0	CARDINAL
ejpam-5776	51	1	m. u. romdhini et al	PERSON
ejpam-5776	52	1	j. pure	PERSON
ejpam-5776	52	2	18	CARDINAL
ejpam-5776	52	3	2	CARDINAL
ejpam-5776	52	4	2025	CARDINAL
ejpam-5776	52	5	5776 3	DATE
ejpam-5776	52	6	13	CARDINAL
ejpam-5776	53	1	− e(ωd2n)|	PERSON
ejpam-5776	53	2	1	CARDINAL
ejpam-5776	54	1	0	CARDINAL
ejpam-5776	55	1	6	CARDINAL
ejpam-5776	60	1	14	CARDINAL
ejpam-5776	62	1	1	CARDINAL
ejpam-5776	62	2	2	DATE
ejpam-5776	65	1	ωd2n	ORG
ejpam-5776	67	1	bab = a−1	PERSON
ejpam-5776	68	1	1 ≤	MONEY
ejpam-5776	68	2	1 ≤	MONEY
ejpam-5776	70	1	1	CARDINAL
ejpam-5776	71	1	16	CARDINAL
ejpam-5776	71	2	xj	ORG
ejpam-5776	71	3	2	CARDINAL
ejpam-5776	72	1	2	CARDINAL
ejpam-5776	72	2	∈	ORG
ejpam-5776	72	3	1	CARDINAL
ejpam-5776	72	4	2	DATE
ejpam-5776	75	1	2	CARDINAL
ejpam-5776	76	1	17	CARDINAL
ejpam-5776	76	2	ωd2n	ORG
ejpam-5776	76	3	dai	ORG
ejpam-5776	76	4	aib on ωd2n	ORG
ejpam-5776	76	5	2(n− 1	ORG
ejpam-5776	77	1	17	CARDINAL
ejpam-5776	78	1	3	CARDINAL
ejpam-5776	79	1	17	CARDINAL
ejpam-5776	79	2	2	CARDINAL
ejpam-5776	79	3	∈	ORG
ejpam-5776	79	4	ω1 1	DATE
ejpam-5776	79	5	∈	ORG
ejpam-5776	80	1	2	CARDINAL
ejpam-5776	80	2	m. u. romdhini et al	PERSON
ejpam-5776	81	1	j. pure	PERSON
ejpam-5776	81	2	18	CARDINAL
ejpam-5776	81	3	2	CARDINAL
ejpam-5776	81	4	2025	CARDINAL
ejpam-5776	81	5	5776 4	DATE
ejpam-5776	81	6	13	CARDINAL
ejpam-5776	82	1	4	CARDINAL
ejpam-5776	83	1	18	CARDINAL
ejpam-5776	83	2	2	CARDINAL
ejpam-5776	83	3	2	CARDINAL
ejpam-5776	83	4	2	CARDINAL
ejpam-5776	83	5	d(j −	PERSON
ejpam-5776	83	6	2	CARDINAL
ejpam-5776	83	7	2 + bin 2	DATE
ejpam-5776	83	8	2	CARDINAL
ejpam-5776	83	9	d(j −	PERSON
ejpam-5776	83	10	2	CARDINAL
ejpam-5776	84	1	2 	PERCENT
ejpam-5776	85	1	µ+ a)n−3 (µ− b+	ORG
ejpam-5776	85	2	2d	DATE
ejpam-5776	85	3	µ+ b	ORG
ejpam-5776	85	4	2)d+	CARDINAL
ejpam-5776	85	5	3	CARDINAL
ejpam-5776	85	6	2)d)−	CARDINAL
ejpam-5776	86	1	1	CARDINAL
ejpam-5776	87	1	19	CARDINAL
ejpam-5776	88	1	1)b)−	CARDINAL
ejpam-5776	88	2	n1n2cd	PERSON
ejpam-5776	88	3	1 ≤	QUANTITY
ejpam-5776	88	4	n2 ≤ n	PRODUCT
ejpam-5776	88	5	3	CARDINAL
ejpam-5776	89	1	3.1	CARDINAL
ejpam-5776	90	1	5	CARDINAL
ejpam-5776	91	1	ωd2n	GPE
ejpam-5776	91	2	2(3n− 5	DATE
ejpam-5776	94	1	1	CARDINAL
ejpam-5776	94	2	2	CARDINAL
ejpam-5776	95	1	2n	CARDINAL
ejpam-5776	95	2	1	CARDINAL
ejpam-5776	95	3	2n	CARDINAL
ejpam-5776	95	4	1	CARDINAL
ejpam-5776	95	5	one	CARDINAL
ejpam-5776	97	1	1 ≤	QUANTITY
ejpam-5776	97	2	1	CARDINAL
ejpam-5776	97	3	2	CARDINAL
ejpam-5776	97	4	2	CARDINAL
ejpam-5776	97	5	1 ≤	QUANTITY
ejpam-5776	97	6	j = n	PERSON
ejpam-5776	98	1	2n	CARDINAL
ejpam-5776	98	2	1	CARDINAL
ejpam-5776	98	3	1	CARDINAL
ejpam-5776	98	4	1	CARDINAL
ejpam-5776	98	5	m. u. romdhini et al	PERSON
ejpam-5776	99	1	j. pure	PERSON
ejpam-5776	99	2	18	CARDINAL
ejpam-5776	99	3	2	CARDINAL
ejpam-5776	99	4	2025	CARDINAL
ejpam-5776	99	5	5776 5	DATE
ejpam-5776	99	6	13	CARDINAL
ejpam-5776	101	1	1	CARDINAL
ejpam-5776	101	2	1	CARDINAL
ejpam-5776	101	3	1	CARDINAL
ejpam-5776	102	1	0	CARDINAL
ejpam-5776	104	1	an−1b 	ORG
ejpam-5776	104	2	0 2	DATE
ejpam-5776	106	1	2 1 1	DATE
ejpam-5776	107	1	1	CARDINAL
ejpam-5776	107	2	2 0	DATE
ejpam-5776	108	1	2 1 1	DATE
ejpam-5776	109	1	1	CARDINAL
ejpam-5776	113	1	2 2	DATE
ejpam-5776	114	1	0 1 1	CARDINAL
ejpam-5776	115	1	1	CARDINAL
ejpam-5776	115	2	1 1	CARDINAL
ejpam-5776	116	1	1	CARDINAL
ejpam-5776	117	1	1	CARDINAL
ejpam-5776	117	2	1 1	DATE
ejpam-5776	118	1	1 1	CARDINAL
ejpam-5776	119	1	1	CARDINAL
ejpam-5776	123	1	1 1	DATE
ejpam-5776	124	1	1 1 1	CARDINAL
ejpam-5776	127	1	2)in−1	CARDINAL
ejpam-5776	127	2	2jn−1	CARDINAL
ejpam-5776	128	1	lemma 1	ORG
ejpam-5776	128	2	2	CARDINAL
ejpam-5776	128	3	1	CARDINAL
ejpam-5776	128	4	1	CARDINAL
ejpam-5776	128	5	2)n−2(µ+ 1)n−1	CARDINAL
ejpam-5776	128	6	3n− 5)µ+	CARDINAL
ejpam-5776	128	7	1)(n− 4	DATE
ejpam-5776	129	1	n − 2	PRODUCT
ejpam-5776	129	2	1	CARDINAL
ejpam-5776	129	3	1 2	DATE
ejpam-5776	129	4	9	CARDINAL
ejpam-5776	130	1	1 2	DATE
ejpam-5776	130	2	9	CARDINAL
ejpam-5776	133	1	1)|	CARDINAL
ejpam-5776	133	2	3n− 5± √ 5n2	CARDINAL
ejpam-5776	134	1	1 (ii	CARDINAL
ejpam-5776	134	2	2	CARDINAL
ejpam-5776	135	1	2n	CARDINAL
ejpam-5776	135	2	2)×	CARDINAL
ejpam-5776	135	3	2	CARDINAL
ejpam-5776	135	4	two	CARDINAL
ejpam-5776	136	1	1	CARDINAL
ejpam-5776	136	2	2	DATE
ejpam-5776	138	1	2	CARDINAL
ejpam-5776	138	2	2	CARDINAL
ejpam-5776	138	3	2	CARDINAL
ejpam-5776	138	4	1	CARDINAL
ejpam-5776	138	5	2	DATE
ejpam-5776	141	1	j = n	PERSON
ejpam-5776	143	1	2n	CARDINAL
ejpam-5776	143	2	2	CARDINAL
ejpam-5776	144	1	0	CARDINAL
ejpam-5776	144	2	2	CARDINAL
ejpam-5776	144	3	m. u. romdhini et al	PERSON
ejpam-5776	145	1	j. pure	PERSON
ejpam-5776	145	2	18	CARDINAL
ejpam-5776	145	3	2	CARDINAL
ejpam-5776	145	4	2025	CARDINAL
ejpam-5776	145	5	5776 6	DATE
ejpam-5776	145	6	13	CARDINAL
ejpam-5776	145	7	j = n	PERSON
ejpam-5776	145	8	1	CARDINAL
ejpam-5776	145	9	2	DATE
ejpam-5776	147	1	n2	ORG
ejpam-5776	147	2	2	CARDINAL
ejpam-5776	147	3	2	CARDINAL
ejpam-5776	147	4	j = n	PERSON
ejpam-5776	149	1	2n	CARDINAL
ejpam-5776	149	2	2	CARDINAL
ejpam-5776	149	3	1	CARDINAL
ejpam-5776	149	4	j = n	PERSON
ejpam-5776	150	1	1	CARDINAL
ejpam-5776	150	2	2	DATE
ejpam-5776	152	1	0	CARDINAL
ejpam-5776	153	1	2	CARDINAL
ejpam-5776	153	2	0	CARDINAL
ejpam-5776	158	1	0 2	DATE
ejpam-5776	159	1	2	CARDINAL
ejpam-5776	163	1	2 0	DATE
ejpam-5776	164	1	2	CARDINAL
ejpam-5776	175	1	2 2	DATE
ejpam-5776	181	1	0	CARDINAL
ejpam-5776	198	1	0 0 .	DATE
ejpam-5776	204	1	2	CARDINAL
ejpam-5776	221	1	0 0	DATE
ejpam-5776	224	1	2	CARDINAL
ejpam-5776	224	2	0	CARDINAL
ejpam-5776	225	1	4	CARDINAL
ejpam-5776	225	2	2	CARDINAL
ejpam-5776	225	3	2	CARDINAL
ejpam-5776	225	4	2	CARDINAL
ejpam-5776	225	5	2	CARDINAL
ejpam-5776	225	6	2)λ+ 4(n− 3	DATE
ejpam-5776	228	1	3(n− 2	ORG
ejpam-5776	228	2	2	CARDINAL
ejpam-5776	228	3	1	CARDINAL
ejpam-5776	228	4	2±	CARDINAL
ejpam-5776	228	5	4)|	CARDINAL
ejpam-5776	229	1	6(n− 2	DATE
ejpam-5776	230	1	3.2	CARDINAL
ejpam-5776	230	2	ωd2n	ORG
ejpam-5776	230	3	6	CARDINAL
ejpam-5776	231	1	ωd2n	GPE
ejpam-5776	232	1	1 + √	DATE
ejpam-5776	232	2	1)(10n− 1	DATE
ejpam-5776	232	3	2 + √	DATE
ejpam-5776	232	4	2)(5n− 2	DATE
ejpam-5776	234	1	m. u. romdhini et al	PERSON
ejpam-5776	235	1	j. pure	PERSON
ejpam-5776	235	2	18	CARDINAL
ejpam-5776	235	3	2	CARDINAL
ejpam-5776	235	4	2025	CARDINAL
ejpam-5776	235	5	5776 7	DATE
ejpam-5776	236	1	3	CARDINAL
ejpam-5776	236	2	3	CARDINAL
ejpam-5776	236	3	ωd2n	ORG
ejpam-5776	238	1	1 ≤	QUANTITY
ejpam-5776	238	2	1	CARDINAL
ejpam-5776	238	3	0	CARDINAL
ejpam-5776	238	4	1 ≤	QUANTITY
ejpam-5776	238	5	j = n	PERSON
ejpam-5776	239	1	2n	CARDINAL
ejpam-5776	239	2	1	CARDINAL
ejpam-5776	240	1	2 + 1	DATE
ejpam-5776	240	2	3	CARDINAL
ejpam-5776	240	3	1	CARDINAL
ejpam-5776	240	4	j = n	PERSON
ejpam-5776	240	5	1	CARDINAL
ejpam-5776	243	1	1 + 1	CARDINAL
ejpam-5776	243	2	2	CARDINAL
ejpam-5776	245	1	an−1b 	ORG
ejpam-5776	246	1	0 0	DATE
ejpam-5776	247	1	0 3 3	CARDINAL
ejpam-5776	248	1	3	CARDINAL
ejpam-5776	249	1	0 3 3	CARDINAL
ejpam-5776	250	1	3	CARDINAL
ejpam-5776	254	1	0 0	DATE
ejpam-5776	256	1	0 3 3	CARDINAL
ejpam-5776	257	1	3	CARDINAL
ejpam-5776	257	2	3 3	DATE
ejpam-5776	258	1	3	CARDINAL
ejpam-5776	259	1	2	CARDINAL
ejpam-5776	259	2	3 3	DATE
ejpam-5776	260	1	3 2	CARDINAL
ejpam-5776	261	1	2	CARDINAL
ejpam-5776	265	1	3 3	DATE
ejpam-5776	266	1	3 2 2	CARDINAL
ejpam-5776	269	1	0n−1 3j(n−1)×n 3jn×(n−1	MONEY
ejpam-5776	269	2	2jn	ORDINAL
ejpam-5776	270	1	lemma 1	ORG
ejpam-5776	270	2	2	CARDINAL
ejpam-5776	270	3	3	CARDINAL
ejpam-5776	270	4	1	CARDINAL
ejpam-5776	270	5	µn−2(µ+ 2)n−1	PERSON
ejpam-5776	270	6	1	CARDINAL
ejpam-5776	271	1	0	CARDINAL
ejpam-5776	271	2	n − 2	PRODUCT
ejpam-5776	271	3	1	CARDINAL
ejpam-5776	271	4	1± √	DATE
ejpam-5776	271	5	1)(10n− 1	DATE
ejpam-5776	273	1	1 + √	DATE
ejpam-5776	273	2	1)(10n− 1	DATE
ejpam-5776	276	1	1 ≤	QUANTITY
ejpam-5776	276	2	2	CARDINAL
ejpam-5776	276	3	0	CARDINAL
ejpam-5776	277	1	m. u. romdhini et al	PERSON
ejpam-5776	278	1	j. pure	PERSON
ejpam-5776	278	2	18	CARDINAL
ejpam-5776	278	3	2	CARDINAL
ejpam-5776	278	4	2025	CARDINAL
ejpam-5776	278	5	5776 8	DATE
ejpam-5776	278	6	1 ≤	QUANTITY
ejpam-5776	278	7	2	CARDINAL
ejpam-5776	278	8	1 ≤ j ≤	QUANTITY
ejpam-5776	279	1	2	CARDINAL
ejpam-5776	279	2	2 + 2	CARDINAL
ejpam-5776	279	3	4	CARDINAL
ejpam-5776	279	4	1 ≤	QUANTITY
ejpam-5776	279	5	2	CARDINAL
ejpam-5776	279	6	n 2	PRODUCT
ejpam-5776	280	1	2	CARDINAL
ejpam-5776	280	2	2 + n 2 +	DATE
ejpam-5776	280	3	2 + 2	CARDINAL
ejpam-5776	280	4	4	CARDINAL
ejpam-5776	281	1	n 2 −2 ≤	MONEY
ejpam-5776	282	1	2+2	CARDINAL
ejpam-5776	282	2	4	CARDINAL
ejpam-5776	282	3	2 + n 2	DATE
ejpam-5776	284	1	2 + n 2 + j	DATE
ejpam-5776	284	2	0	CARDINAL
ejpam-5776	291	1	0	CARDINAL
ejpam-5776	295	1	4 4	DATE
ejpam-5776	296	1	4	CARDINAL
ejpam-5776	305	1	0	CARDINAL
ejpam-5776	308	1	4 4	DATE
ejpam-5776	309	1	4	CARDINAL
ejpam-5776	309	2	4	CARDINAL
ejpam-5776	310	1	4 0	DATE
ejpam-5776	311	1	4 0	DATE
ejpam-5776	312	1	4	CARDINAL
ejpam-5776	321	1	4	CARDINAL
ejpam-5776	322	1	4 4	DATE
ejpam-5776	326	1	4	CARDINAL
ejpam-5776	327	1	4 0	DATE
ejpam-5776	328	1	4 0	DATE
ejpam-5776	329	1	4	CARDINAL
ejpam-5776	338	1	an−1b 4 .	PERSON
ejpam-5776	339	1	4 4	DATE
ejpam-5776	343	1	0n−2 4j(n−2)×n	ORG
ejpam-5776	343	2	2	CARDINAL
ejpam-5776	343	3	2	CARDINAL
ejpam-5776	343	4	4jn	ORDINAL
ejpam-5776	343	5	2	CARDINAL
ejpam-5776	343	6	4(j	CARDINAL
ejpam-5776	343	7	2	CARDINAL
ejpam-5776	343	8	2	CARDINAL
ejpam-5776	343	9	4jn	ORDINAL
ejpam-5776	343	10	2	CARDINAL
ejpam-5776	343	11	4(j	CARDINAL
ejpam-5776	343	12	2	CARDINAL
ejpam-5776	343	13	2	CARDINAL
ejpam-5776	344	1	4	CARDINAL
ejpam-5776	344	2	0	CARDINAL
ejpam-5776	344	3	4	CARDINAL
ejpam-5776	344	4	2	CARDINAL
ejpam-5776	345	1	0	CARDINAL
ejpam-5776	345	2	2	CARDINAL
ejpam-5776	345	3	n 2	PRODUCT
ejpam-5776	345	4	1	CARDINAL
ejpam-5776	345	5	2	CARDINAL
ejpam-5776	345	6	2± √	PRODUCT
ejpam-5776	346	1	2)(5n− 2	DATE
ejpam-5776	348	1	2	CARDINAL
ejpam-5776	348	2	2 + √	DATE
ejpam-5776	348	3	2)(5n− 2	DATE
ejpam-5776	349	1	7	CARDINAL
ejpam-5776	350	1	ωd2n	GPE
ejpam-5776	350	2	ωd2n	ORG
ejpam-5776	351	1	2	CARDINAL
ejpam-5776	351	2	1 + √	DATE
ejpam-5776	351	3	1)(10n− 1	DATE
ejpam-5776	351	4	2 + √	DATE
ejpam-5776	351	5	2)(5n− 2	DATE
ejpam-5776	352	1	m. u. romdhini et al	PERSON
ejpam-5776	353	1	j. pure	PERSON
ejpam-5776	353	2	18	CARDINAL
ejpam-5776	353	3	2	CARDINAL
ejpam-5776	353	4	2025	CARDINAL
ejpam-5776	353	5	5776 9	DATE
ejpam-5776	353	6	13	CARDINAL
ejpam-5776	355	1	6	CARDINAL
ejpam-5776	356	1	2	CARDINAL
ejpam-5776	356	2	1	CARDINAL
ejpam-5776	356	3	1)(10n− 1	DATE
ejpam-5776	356	4	∣∣∣	CARDINAL
ejpam-5776	356	5	2	CARDINAL
ejpam-5776	356	6	1 + √	DATE
ejpam-5776	356	7	1)(10n− 1	DATE
ejpam-5776	358	1	6	CARDINAL
ejpam-5776	359	1	3(n− 2	ORG
ejpam-5776	359	2	2	CARDINAL
ejpam-5776	359	3	1	CARDINAL
ejpam-5776	360	1	2)±	CARDINAL
ejpam-5776	360	2	2 √	DATE
ejpam-5776	360	3	2)(5n−	CARDINAL
ejpam-5776	360	4	2	CARDINAL
ejpam-5776	360	5	∣∣∣	CARDINAL
ejpam-5776	360	6	4	CARDINAL
ejpam-5776	360	7	2 + √	DATE
ejpam-5776	360	8	2)(5n− 2	DATE
ejpam-5776	361	1	3.3	CARDINAL
ejpam-5776	362	1	8	CARDINAL
ejpam-5776	363	1	ωd2n	GPE
ejpam-5776	365	1	1 2	CARDINAL
ejpam-5776	365	2	1	CARDINAL
ejpam-5776	365	3	1 2	DATE
ejpam-5776	366	1	1)2	CARDINAL
ejpam-5776	366	2	1 2	DATE
ejpam-5776	366	3	2 + 1 4n(n−	QUANTITY
ejpam-5776	366	4	2)(n− 1	WORK_OF_ART
ejpam-5776	369	1	theorems 2 and	ORG
ejpam-5776	369	2	3	DATE
ejpam-5776	369	3	4	CARDINAL
ejpam-5776	369	4	aij	ORG
ejpam-5776	369	5	1	CARDINAL
ejpam-5776	369	6	2	DATE
ejpam-5776	371	1	1	CARDINAL
ejpam-5776	371	2	aij	ORG
ejpam-5776	371	3	0	CARDINAL
ejpam-5776	371	4	1	CARDINAL
ejpam-5776	371	5	2	DATE
ejpam-5776	373	1	1	CARDINAL
ejpam-5776	373	2	j = n	PERSON
ejpam-5776	373	3	1	CARDINAL
ejpam-5776	375	1	1	CARDINAL
ejpam-5776	375	2	aij	ORG
ejpam-5776	375	3	1	CARDINAL
ejpam-5776	377	1	3n+1 4	DATE
ejpam-5776	377	2	j = n	PERSON
ejpam-5776	378	1	2n−1	CARDINAL
ejpam-5776	378	2	aij	ORG
ejpam-5776	378	3	1	CARDINAL
ejpam-5776	378	4	1 2	CARDINAL
ejpam-5776	378	5	aij	ORG
ejpam-5776	378	6	m. u. romdhini et al	PERSON
ejpam-5776	379	1	j. pure	PERSON
ejpam-5776	379	2	18	CARDINAL
ejpam-5776	379	3	2	CARDINAL
ejpam-5776	379	4	2025	CARDINAL
ejpam-5776	379	5	5776 10	DATE
ejpam-5776	381	1	an−1b 	ORG
ejpam-5776	382	1	0 0	DATE
ejpam-5776	384	1	3n+1 4	TIME
ejpam-5776	384	2	3n+1 4	DATE
ejpam-5776	385	1	3n+1 4	QUANTITY
ejpam-5776	387	1	3n+1 4	TIME
ejpam-5776	387	2	3n+1 4	DATE
ejpam-5776	388	1	3n+1 4	DATE
ejpam-5776	392	1	0 0	DATE
ejpam-5776	394	1	3n+1 4	TIME
ejpam-5776	394	2	3n+1 4	DATE
ejpam-5776	395	1	3n+1 4	CARDINAL
ejpam-5776	395	2	3n+1 4	DATE
ejpam-5776	396	1	3n+1	CARDINAL
ejpam-5776	396	2	1 2	DATE
ejpam-5776	397	1	1 2	CARDINAL
ejpam-5776	397	2	3n+1 4	DATE
ejpam-5776	397	3	3n+1 4	DATE
ejpam-5776	398	1	3n+1 4	CARDINAL
ejpam-5776	398	2	1 2	DATE
ejpam-5776	399	1	1 2	CARDINAL
ejpam-5776	404	1	3n+1 4	TIME
ejpam-5776	404	2	3n+1 4	DATE
ejpam-5776	405	1	3n+1 4	CARDINAL
ejpam-5776	405	2	1 2	CARDINAL
ejpam-5776	405	3	1 2	DATE
ejpam-5776	408	1	0n−1	CARDINAL
ejpam-5776	408	2	3n+1 4	DATE
ejpam-5776	408	3	3n+1 4	DATE
ejpam-5776	408	4	jn×(n−1	GPE
ejpam-5776	408	5	1 2	CARDINAL
ejpam-5776	408	6	j −	PERSON
ejpam-5776	408	7	3n+1 4	DATE
ejpam-5776	409	1	3n+1 4	DATE
ejpam-5776	409	2	jn×(n−1	GPE
ejpam-5776	409	3	µ+ n−	ORG
ejpam-5776	409	4	1 2	DATE
ejpam-5776	409	5	1 2	CARDINAL
ejpam-5776	410	1	lemma 1	ORG
ejpam-5776	410	2	3n+1 4	DATE
ejpam-5776	410	3	µ+ n−	ORG
ejpam-5776	410	4	1 2	CARDINAL
ejpam-5776	410	5	1	CARDINAL
ejpam-5776	410	6	1 2 ) µ− 1 16	DATE
ejpam-5776	410	7	1)(3n+ 1)2	CARDINAL
ejpam-5776	411	1	0	CARDINAL
ejpam-5776	411	2	2	CARDINAL
ejpam-5776	411	3	1 2	CARDINAL
ejpam-5776	411	4	1 2	CARDINAL
ejpam-5776	411	5	1	CARDINAL
ejpam-5776	411	6	1 2	DATE
ejpam-5776	411	7	1)2	CARDINAL
ejpam-5776	411	8	1 2	DATE
ejpam-5776	411	9	2 + 1 4n(n−	QUANTITY
ejpam-5776	413	1	1 2	CARDINAL
ejpam-5776	413	2	1	CARDINAL
ejpam-5776	413	3	1 2	DATE
ejpam-5776	413	4	1)2	CARDINAL
ejpam-5776	413	5	1 2	DATE
ejpam-5776	413	6	2	CARDINAL
ejpam-5776	413	7	1)(3n+ 1)2 	DATE
ejpam-5776	416	1	aij	ORG
ejpam-5776	416	2	1 ≤	QUANTITY
ejpam-5776	416	3	2	CARDINAL
ejpam-5776	416	4	aij	ORG
ejpam-5776	416	5	0	CARDINAL
ejpam-5776	416	6	1 ≤	QUANTITY
ejpam-5776	416	7	aij	ORG
ejpam-5776	416	8	1 4	DATE
ejpam-5776	416	9	2(n− 2	ORG
ejpam-5776	416	10	3n 4	DATE
ejpam-5776	416	11	1 ≤	QUANTITY
ejpam-5776	416	12	2	CARDINAL
ejpam-5776	416	13	n 2	PRODUCT
ejpam-5776	418	1	2	CARDINAL
ejpam-5776	418	2	2 + n 2 +	DATE
ejpam-5776	418	3	aij	ORG
ejpam-5776	418	4	1 4	DATE
ejpam-5776	419	1	1	CARDINAL
ejpam-5776	419	2	m. u. romdhini et al	PERSON
ejpam-5776	420	1	j. pure	PERSON
ejpam-5776	420	2	18	CARDINAL
ejpam-5776	420	3	2	CARDINAL
ejpam-5776	420	4	2025	CARDINAL
ejpam-5776	420	5	5776 11	DATE
ejpam-5776	420	6	13	CARDINAL
ejpam-5776	421	1	2	CARDINAL
ejpam-5776	421	2	2	CARDINAL
ejpam-5776	421	3	aij =	PERSON
ejpam-5776	421	4	1 4	DATE
ejpam-5776	421	5	1	CARDINAL
ejpam-5776	421	6	2 + n 2	DATE
ejpam-5776	423	1	2 + n 2 + j	DATE
ejpam-5776	423	2	aij	ORG
ejpam-5776	423	3	0	CARDINAL
ejpam-5776	429	1	0	CARDINAL
ejpam-5776	432	1	3n 4	DATE
ejpam-5776	433	1	3n	CARDINAL
ejpam-5776	434	1	3n 4	CARDINAL
ejpam-5776	443	1	0	CARDINAL
ejpam-5776	445	1	3n 4	DATE
ejpam-5776	446	1	3n	CARDINAL
ejpam-5776	447	1	3n 4	CARDINAL
ejpam-5776	447	2	3n 4	DATE
ejpam-5776	448	1	3n	CARDINAL
ejpam-5776	449	1	1 0	DATE
ejpam-5776	450	1	1	CARDINAL
ejpam-5776	459	1	3n 4	DATE
ejpam-5776	460	1	3n	CARDINAL
ejpam-5776	460	2	1	CARDINAL
ejpam-5776	463	1	1	CARDINAL
ejpam-5776	465	1	3n 4	DATE
ejpam-5776	466	1	3n	CARDINAL
ejpam-5776	467	1	1 0	DATE
ejpam-5776	468	1	1	CARDINAL
ejpam-5776	477	1	3n 4	DATE
ejpam-5776	478	1	3n	CARDINAL
ejpam-5776	478	2	1	CARDINAL
ejpam-5776	481	1	1	CARDINAL
ejpam-5776	485	1	0n−2	ORG
ejpam-5776	485	2	4 j(n−2)×n 2	DATE
ejpam-5776	485	3	4	CARDINAL
ejpam-5776	485	4	2	CARDINAL
ejpam-5776	485	5	1)(j −	DATE
ejpam-5776	485	6	2	CARDINAL
ejpam-5776	485	7	1)(j −	DATE
ejpam-5776	485	8	2	CARDINAL
ejpam-5776	485	9	4	CARDINAL
ejpam-5776	485	10	2	CARDINAL
ejpam-5776	485	11	1)(j −	DATE
ejpam-5776	485	12	2	CARDINAL
ejpam-5776	485	13	1)(j	CARDINAL
ejpam-5776	485	14	2	CARDINAL
ejpam-5776	486	1	4	CARDINAL
ejpam-5776	486	2	0	CARDINAL
ejpam-5776	486	3	3n 4	DATE
ejpam-5776	486	4	1	CARDINAL
ejpam-5776	486	5	2	CARDINAL
ejpam-5776	486	6	µ2 − (n−	ORG
ejpam-5776	486	7	2)µ−	CARDINAL
ejpam-5776	486	8	16	CARDINAL
ejpam-5776	486	9	2	CARDINAL
ejpam-5776	487	1	0	CARDINAL
ejpam-5776	487	2	2	CARDINAL
ejpam-5776	487	3	1	CARDINAL
ejpam-5776	487	4	n 2	PRODUCT
ejpam-5776	487	5	1	CARDINAL
ejpam-5776	487	6	1 2	CARDINAL
ejpam-5776	487	7	2)(n− 1)± √	DATE
ejpam-5776	489	1	ωd2n	ORG
ejpam-5776	490	1	1 2	CARDINAL
ejpam-5776	490	2	2)(n− 1	WORK_OF_ART
ejpam-5776	490	3	2	CARDINAL
ejpam-5776	491	1	9	CARDINAL
ejpam-5776	492	1	ωd2n	GPE
ejpam-5776	493	1	1	CARDINAL
ejpam-5776	493	2	1 2	DATE
ejpam-5776	493	3	1)2	CARDINAL
ejpam-5776	493	4	1 2	DATE
ejpam-5776	493	5	2 + 1 4n(n−	QUANTITY
ejpam-5776	498	1	m. u. romdhini et al	PERSON
ejpam-5776	499	1	j. pure	PERSON
ejpam-5776	499	2	18	CARDINAL
ejpam-5776	499	3	2	CARDINAL
ejpam-5776	499	4	2025	CARDINAL
ejpam-5776	499	5	5776 12	DATE
ejpam-5776	499	6	13	CARDINAL
ejpam-5776	501	1	2	CARDINAL
ejpam-5776	501	2	1	CARDINAL
ejpam-5776	501	3	∣∣∣∣12	CARDINAL
ejpam-5776	501	4	1	CARDINAL
ejpam-5776	501	5	1 2	DATE
ejpam-5776	501	6	1)2	CARDINAL
ejpam-5776	501	7	1 2	DATE
ejpam-5776	501	8	2	CARDINAL
ejpam-5776	502	1	1	CARDINAL
ejpam-5776	502	2	1 2	DATE
ejpam-5776	503	1	1)2	CARDINAL
ejpam-5776	503	2	1 2	DATE
ejpam-5776	503	3	2	CARDINAL
ejpam-5776	503	4	1)(3n+ 1)2	DATE
ejpam-5776	505	1	8	DATE
ejpam-5776	506	1	3(n− 2	ORG
ejpam-5776	506	2	2	CARDINAL
ejpam-5776	506	3	1	CARDINAL
ejpam-5776	506	4	2)(n− 1)±	DATE
ejpam-5776	507	1	√	PERSON
ejpam-5776	509	1	2	CARDINAL
ejpam-5776	510	1	2)(n− 1	DATE
ejpam-5776	513	1	2	CARDINAL
ejpam-5776	514	1	4	CARDINAL
ejpam-5776	515	1	1	CARDINAL
ejpam-5776	517	1	2	CARDINAL
ejpam-5776	519	1	3	CARDINAL
ejpam-5776	522	1	indonesia	GPE
ejpam-5776	522	2	the overseas collaborative research	ORG
ejpam-5776	523	1	1	CARDINAL
ejpam-5776	523	2	j wang	PERSON
ejpam-5776	525	1	2018	DATE
ejpam-5776	526	1	2	CARDINAL
ejpam-5776	527	1	dmax	ORG
ejpam-5776	528	1	70:221–238,	DATE
ejpam-5776	528	2	2013	DATE
ejpam-5776	529	1	m. u. romdhini et al	PERSON
ejpam-5776	530	1	j. pure	PERSON
ejpam-5776	530	2	18	CARDINAL
ejpam-5776	530	3	2	CARDINAL
ejpam-5776	530	4	2025	CARDINAL
ejpam-5776	530	5	5776 13	DATE
ejpam-5776	530	6	13	CARDINAL
ejpam-5776	530	7	3	CARDINAL
ejpam-5776	530	8	kannan	GPE
ejpam-5776	532	1	2020	DATE
ejpam-5776	533	1	4	CARDINAL
ejpam-5776	535	1	5:293	CARDINAL
ejpam-5776	535	2	304	CARDINAL
ejpam-5776	535	3	2017	DATE
ejpam-5776	536	1	5	CARDINAL
ejpam-5776	538	1	1:45–54,	DATE
ejpam-5776	538	2	2018	DATE
ejpam-5776	539	1	6	CARDINAL
ejpam-5776	541	1	math.-stat	ORG
ejpam-5776	542	1	forschungsz.	GPE
ejpam-5776	543	1	graz	GPE
ejpam-5776	543	2	1978	DATE
ejpam-5776	546	1	bulletin	PERSON
ejpam-5776	546	2	kerala mathematics association	ORG
ejpam-5776	546	3	1:129–132,	DATE
ejpam-5776	546	4	2004	DATE
ejpam-5776	547	1	8	CARDINAL
ejpam-5776	549	1	2:118–121, 2008	DATE
ejpam-5776	550	1	9	CARDINAL
ejpam-5776	550	2	al-sharqi	ORG
ejpam-5776	550	3	al-quran	PERSON
ejpam-5776	552	1	asia pacific journal of mathematics	ORG
ejpam-5776	552	2	11(9):1–9	CARDINAL
ejpam-5776	552	3	2024	DATE
ejpam-5776	553	1	10	CARDINAL
ejpam-5776	555	1	malaysian	NORP
ejpam-5776	555	2	20:65–73	CARDINAL
ejpam-5776	555	3	2024	DATE
ejpam-5776	556	1	11	CARDINAL
ejpam-5776	556	2	al-sharqi	ORG
ejpam-5776	556	3	al-quran	PERSON
ejpam-5776	557	1	22(4):93–105	CARDINAL
ejpam-5776	557	2	2023	CARDINAL
ejpam-5776	558	1	12	CARDINAL
ejpam-5776	558	2	al-sharqi	ORG
ejpam-5776	558	3	al-quran	PERSON
ejpam-5776	560	1	61(1):465–492	CARDINAL
ejpam-5776	560	2	2023	CARDINAL
ejpam-5776	561	1	13	CARDINAL
ejpam-5776	561	2	s akbari	PERSON
ejpam-5776	563	1	298(2):468–492	CARDINAL
ejpam-5776	563	2	2006	DATE
ejpam-5776	564	1	14	CARDINAL
ejpam-5776	564	2	johnson	PERSON
ejpam-5776	565	1	cambridge university press	ORG
ejpam-5776	565	2	cambridge	GPE
ejpam-5776	565	3	1985	DATE
ejpam-5776	566	1	15	CARDINAL
ejpam-5776	566	2	y shi	PERSON
ejpam-5776	568	1	new york	GPE
ejpam-5776	568	2	2012	DATE
ejpam-5776	569	1	16	CARDINAL
ejpam-5776	569	2	al-sharqi	ORG
ejpam-5776	569	3	al-quran	PERSON
ejpam-5776	571	1	european journal	ORG
ejpam-5776	571	2	17(1):212–221	CARDINAL
ejpam-5776	571	3	2024	DATE
ejpam-5776	572	1	17	CARDINAL
ejpam-5776	572	2	ali	PERSON
ejpam-5776	574	1	8(2):233–239	CARDINAL
ejpam-5776	574	2	2020	DATE
ejpam-5776	575	1	18	CARDINAL
ejpam-5776	576	1	18(3):497–508	CARDINAL
ejpam-5776	576	2	2023	CARDINAL
ejpam-5776	577	1	19	CARDINAL
ejpam-5776	577	2	s s shinde	ORG
ejpam-5776	578	1	63:161–168	CARDINAL
ejpam-5776	578	2	2017	DATE