id	sid	eid	entity	type
ejpam-4262	1	1	european journal	ORG
ejpam-4262	2	1	15	CARDINAL
ejpam-4262	2	2	1	CARDINAL
ejpam-4262	2	3	2022	CARDINAL
ejpam-4262	2	4	328	CARDINAL
ejpam-4262	2	5	new york	GPE
ejpam-4262	2	6	thawatchai khumprapussorn department	ORG
ejpam-4262	2	7	institute of technology ladkrabang	ORG
ejpam-4262	2	8	10520	DATE
ejpam-4262	2	9	thailand	GPE
ejpam-4262	3	1	2	CARDINAL
ejpam-4262	4	1	s(m)∪{∅	NORP
ejpam-4262	5	1	∈	ORG
ejpam-4262	5	2	+ rs ∈	CARDINAL
ejpam-4262	5	3	r(m	ORG
ejpam-4262	7	1	2020	DATE
ejpam-4262	7	2	13c05	CARDINAL
ejpam-4262	7	3	16d80	DATE
ejpam-4262	7	4	16d99	CARDINAL
ejpam-4262	7	5	2	CARDINAL
ejpam-4262	7	6	1	CARDINAL
ejpam-4262	8	1	∈	ORG
ejpam-4262	8	2	∈	ORG
ejpam-4262	8	3	∈	ORG
ejpam-4262	8	4	∈	ORG
ejpam-4262	10	1	5	CARDINAL
ejpam-4262	10	2	1	CARDINAL
ejpam-4262	11	1	6	CARDINAL
ejpam-4262	11	2	2	CARDINAL
ejpam-4262	12	1	2	CARDINAL
ejpam-4262	12	2	∈	ORG
ejpam-4262	12	3	rsm ∈	ORG
ejpam-4262	13	1	rsm ∈ p\(p	ORG
ejpam-4262	14	1	4	CARDINAL
ejpam-4262	14	2	2	CARDINAL
ejpam-4262	17	1	⊆	CARDINAL
ejpam-4262	18	1	3	CARDINAL
ejpam-4262	18	2	2	CARDINAL
ejpam-4262	19	1	∈	ORG
ejpam-4262	19	2	∈	ORG
ejpam-4262	19	3	abm	LAW
ejpam-4262	19	4	∈	ORG
ejpam-4262	19	5	bm ∈ p	ORG
ejpam-4262	19	6	ab ∈	ORG
ejpam-4262	20	1	2	CARDINAL
ejpam-4262	20	2	2	CARDINAL
ejpam-4262	20	3	thawatchai.kh@kmitl.ac.th	TIME
ejpam-4262	21	1	328	CARDINAL
ejpam-4262	21	2	2022	CARDINAL
ejpam-4262	22	1	t. khumprapussorn	PERSON
ejpam-4262	23	1	j. pure	PERSON
ejpam-4262	23	2	15	CARDINAL
ejpam-4262	23	3	1	CARDINAL
ejpam-4262	23	4	2022	CARDINAL
ejpam-4262	23	5	328-334 329	QUANTITY
ejpam-4262	23	6	β(h	ORG
ejpam-4262	28	1	β(h	ORG
ejpam-4262	28	2	⊆	CARDINAL
ejpam-4262	28	3	⊆ α(h	CARDINAL
ejpam-4262	29	1	α(i	ORG
ejpam-4262	29	2	r.	NORP
ejpam-4262	29	3	α(n	ORG
ejpam-4262	29	4	β(n	CARDINAL
ejpam-4262	30	1	2	CARDINAL
ejpam-4262	30	2	∈	ORG
ejpam-4262	30	3	∈	ORG
ejpam-4262	30	4	rsm ∈ p	ORG
ejpam-4262	31	1	r(m	ORG
ejpam-4262	34	1	32	CARDINAL
ejpam-4262	34	2	n = 2pq	PRODUCT
ejpam-4262	35	1	2	CARDINAL
ejpam-4262	36	1	2	CARDINAL
ejpam-4262	36	2	∈	ORG
ejpam-4262	36	3	rsm ∈	ORG
ejpam-4262	36	4	∈	ORG
ejpam-4262	38	1	first	ORDINAL
ejpam-4262	39	1	∈	ORG
ejpam-4262	39	2	rsm ∈	ORG
ejpam-4262	39	3	∈	ORG
ejpam-4262	40	1	0	CARDINAL
ejpam-4262	41	1	section 2	LAW
ejpam-4262	41	2	section 3	LAW
ejpam-4262	42	1	2	CARDINAL
ejpam-4262	43	1	1	CARDINAL
ejpam-4262	44	1	∈	ORG
ejpam-4262	44	2	rsm ∈	ORG
ejpam-4262	44	3	∈	ORG
ejpam-4262	44	4	∈	ORG
ejpam-4262	47	1	1	CARDINAL
ejpam-4262	53	1	∈	ORG
ejpam-4262	53	2	∈	ORG
ejpam-4262	53	3	rsm ∈	ORG
ejpam-4262	54	1	rsm	PERSON
ejpam-4262	54	2	+ rs ∈	CARDINAL
ejpam-4262	54	3	∈	ORG
ejpam-4262	56	1	rsm ∈	ORG
ejpam-4262	56	2	ϕ(p	GPE
ejpam-4262	57	1	1	CARDINAL
ejpam-4262	61	1	∈	ORG
ejpam-4262	62	1	∈	ORG
ejpam-4262	63	1	+ rs ∈	CARDINAL
ejpam-4262	63	2	r(m	ORG
ejpam-4262	63	3	t. khumprapussorn	ORG
ejpam-4262	64	1	j. pure	PERSON
ejpam-4262	64	2	15	CARDINAL
ejpam-4262	64	3	1	CARDINAL
ejpam-4262	64	4	2022	CARDINAL
ejpam-4262	64	5	328-334 330	QUANTITY
ejpam-4262	66	1	∈	ORG
ejpam-4262	66	2	r(m	ORG
ejpam-4262	66	3	∈	ORG
ejpam-4262	67	1	2	CARDINAL
ejpam-4262	68	1	⊆	CARDINAL
ejpam-4262	69	1	2.1	CARDINAL
ejpam-4262	69	2	m)m	CARDINAL
ejpam-4262	72	1	∈	ORG
ejpam-4262	73	1	∈	ORG
ejpam-4262	73	2	∈	ORG
ejpam-4262	74	1	a0s ∈	PERSON
ejpam-4262	74	2	r(m	ORG
ejpam-4262	77	1	a0 ∈	ORG
ejpam-4262	77	2	⊆	CARDINAL
ejpam-4262	78	1	∈	ORG
ejpam-4262	80	1	+ rs ∈	CARDINAL
ejpam-4262	80	2	∈	ORG
ejpam-4262	81	1	2.2	CARDINAL
ejpam-4262	81	2	m)m ⊆	CARDINAL
ejpam-4262	84	1	∈	ORG
ejpam-4262	84	2	n ∈ p	ORG
ejpam-4262	85	1	rkm /∈	PERSON
ejpam-4262	85	2	r(k +	ORG
ejpam-4262	85	3	rsm /∈ ϕ(p	PERSON
ejpam-4262	87	1	k + s)(m+m	GPE
ejpam-4262	87	2	∈	ORG
ejpam-4262	88	1	k ∈	ORG
ejpam-4262	88	2	+ rs ∈	CARDINAL
ejpam-4262	88	3	r(m	ORG
ejpam-4262	91	1	r(m	ORG
ejpam-4262	92	1	+ rs ∈	CARDINAL
ejpam-4262	92	2	r(m	ORG
ejpam-4262	93	1	rkm ∈	PERSON
ejpam-4262	94	1	1	CARDINAL
ejpam-4262	94	2	ktm	PERSON
ejpam-4262	95	1	k + r)(t + s	ORG
ejpam-4262	96	1	k + r)(t + s	ORG
ejpam-4262	96	2	k +	ORG
ejpam-4262	97	1	∈	ORG
ejpam-4262	97	2	+ rs ∈	CARDINAL
ejpam-4262	97	3	r(m	ORG
ejpam-4262	98	1	ktm	PERSON
ejpam-4262	99	1	2	CARDINAL
ejpam-4262	99	2	2.2.1	CARDINAL
ejpam-4262	101	1	n+m	DATE
ejpam-4262	102	1	∈	ORG
ejpam-4262	102	2	∈	ORG
ejpam-4262	103	1	∈	ORG
ejpam-4262	103	2	∈	ORG
ejpam-4262	105	1	s(r	GPE
ejpam-4262	105	2	n+m	DATE
ejpam-4262	106	1	∈	ORG
ejpam-4262	106	2	∈	ORG
ejpam-4262	107	1	∈	ORG
ejpam-4262	107	2	∈	ORG
ejpam-4262	108	1	2.2.2	CARDINAL
ejpam-4262	114	1	∈	ORG
ejpam-4262	116	1	∈	ORG
ejpam-4262	116	2	∈	ORG
ejpam-4262	118	1	t. khumprapussorn	PERSON
ejpam-4262	119	1	j. pure	PERSON
ejpam-4262	119	2	15	CARDINAL
ejpam-4262	119	3	1	CARDINAL
ejpam-4262	119	4	2022	CARDINAL
ejpam-4262	119	5	328	CARDINAL
ejpam-4262	119	6	334 331	CARDINAL
ejpam-4262	119	7	1	CARDINAL
ejpam-4262	120	1	1	CARDINAL
ejpam-4262	121	1	0	CARDINAL
ejpam-4262	124	1	ϕ(n	ORG
ejpam-4262	124	2	⊆ φ(n	PERCENT
ejpam-4262	124	3	n ∈ s(m	ORG
ejpam-4262	136	1	⊆	CARDINAL
ejpam-4262	138	1	2	CARDINAL
ejpam-4262	140	1	0	CARDINAL
ejpam-4262	140	2	⊆	CARDINAL
ejpam-4262	143	1	∈	ORG
ejpam-4262	143	2	p × m2)\ϕ(p × m2	ORG
ejpam-4262	146	1	∈	ORG
ejpam-4262	146	2	r2)[(m1,m2	ORG
ejpam-4262	150	1	t. khumprapussorn	PERSON
ejpam-4262	151	1	j. pure	PERSON
ejpam-4262	151	2	15	CARDINAL
ejpam-4262	151	3	1	CARDINAL
ejpam-4262	151	4	2022	CARDINAL
ejpam-4262	151	5	328	CARDINAL
ejpam-4262	151	6	334 332	CARDINAL
ejpam-4262	151	7	3	CARDINAL
ejpam-4262	153	1	s(mi	GPE
ejpam-4262	153	2	s(mi	GPE
ejpam-4262	153	3	1	CARDINAL
ejpam-4262	153	4	2	CARDINAL
ejpam-4262	155	1	m1 × m2	PRODUCT
ejpam-4262	156	1	m1 × m2	PRODUCT
ejpam-4262	156	2	∈	ORG
ejpam-4262	156	3	rsm ∈	ORG
ejpam-4262	157	1	1)(s	DATE
ejpam-4262	157	2	1)(m	DATE
ejpam-4262	157	3	0	CARDINAL
ejpam-4262	157	4	rsm	ORG
ejpam-4262	158	1	1)(s	DATE
ejpam-4262	158	2	1	CARDINAL
ejpam-4262	158	3	1)(s	DATE
ejpam-4262	158	4	1	CARDINAL
ejpam-4262	158	5	1)[(m	CARDINAL
ejpam-4262	160	1	1)[(m	CARDINAL
ejpam-4262	164	1	3	CARDINAL
ejpam-4262	165	1	∈	ORG
ejpam-4262	166	1	2	CARDINAL
ejpam-4262	169	1	∈	ORG
ejpam-4262	170	1	α(ps	MONEY
ejpam-4262	170	2	ϕ(p	GPE
ejpam-4262	176	1	∈	ORG
ejpam-4262	177	1	rsm ∈	ORG
ejpam-4262	178	1	rsm ∈	ORG
ejpam-4262	178	2	∈	ORG
ejpam-4262	178	3	rsm ∈	ORG
ejpam-4262	180	1	∈	ORG
ejpam-4262	182	1	α(ps	MONEY
ejpam-4262	182	2	ϕ(p	GPE
ejpam-4262	184	1	∈	ORG
ejpam-4262	184	2	rsm ∈	ORG
ejpam-4262	187	1	∈	ORG
ejpam-4262	189	1	∈	ORG
ejpam-4262	192	1	∈	ORG
ejpam-4262	193	1	3	CARDINAL
ejpam-4262	196	1	∈	ORG
ejpam-4262	198	1	⊆	CARDINAL
ejpam-4262	198	2	α((p	PERSON
ejpam-4262	199	1	t. khumprapussorn	PERSON
ejpam-4262	200	1	j. pure	PERSON
ejpam-4262	200	2	15	CARDINAL
ejpam-4262	200	3	1	CARDINAL
ejpam-4262	200	4	2022	CARDINAL
ejpam-4262	200	5	328-334 333 proof	QUANTITY
ejpam-4262	202	1	∈	ORG
ejpam-4262	202	2	∈	ORG
ejpam-4262	204	1	∈	ORG
ejpam-4262	205	1	rsm ∈	ORG
ejpam-4262	206	1	rsm ∈	ORG
ejpam-4262	206	2	∈	ORG
ejpam-4262	207	1	rsm ∈	ORG
ejpam-4262	210	1	+ rs ∈	CARDINAL
ejpam-4262	210	2	r(m	ORG
ejpam-4262	211	1	∈	ORG
ejpam-4262	214	1	∈	ORG
ejpam-4262	217	1	⊆	CARDINAL
ejpam-4262	217	2	α((p	PERSON
ejpam-4262	219	1	∈	ORG
ejpam-4262	219	2	∈	ORG
ejpam-4262	219	3	rsm ∈	ORG
ejpam-4262	221	1	∈	ORG
ejpam-4262	222	1	∈	ORG
ejpam-4262	222	2	α((p	PERSON
ejpam-4262	224	1	+ rs ∈	CARDINAL
ejpam-4262	224	2	r(m	ORG
ejpam-4262	226	1	∈	ORG
ejpam-4262	226	2	rsm ∈ p\(p	ORG
ejpam-4262	226	3	r(m	ORG
ejpam-4262	228	1	∈	ORG
ejpam-4262	228	2	0	CARDINAL
ejpam-4262	230	1	4	CARDINAL
ejpam-4262	231	1	0	CARDINAL
ejpam-4262	237	1	∈	ORG
ejpam-4262	241	1	rsx /∈	PERSON
ejpam-4262	243	1	rsx ∈	PERSON
ejpam-4262	248	1	rsx ∈	PERSON
ejpam-4262	248	2	rsm ∈	ORG
ejpam-4262	251	1	rsx ∈	PERSON
ejpam-4262	251	2	rsm ∈	ORG
ejpam-4262	252	1	rsm ∈	ORG
ejpam-4262	253	1	rsm	ORG
ejpam-4262	254	1	∈	ORG
ejpam-4262	254	2	⊆	CARDINAL
ejpam-4262	255	1	∈	ORG
ejpam-4262	256	1	∈	ORG
ejpam-4262	256	2	0	CARDINAL
ejpam-4262	257	1	5	CARDINAL
ejpam-4262	258	1	∈	ORG
ejpam-4262	258	2	β(rm	PRODUCT
ejpam-4262	264	1	∈	ORG
ejpam-4262	264	2	∈	ORG
ejpam-4262	264	3	∈	ORG
ejpam-4262	265	1	2	CARDINAL
ejpam-4262	265	2	abm	LAW
ejpam-4262	266	1	∈	PRODUCT
ejpam-4262	267	1	334	CARDINAL
ejpam-4262	267	2	first	ORDINAL
ejpam-4262	269	1	a(m + m	FAC
ejpam-4262	271	1	∈	ORG
ejpam-4262	271	2	rbm ∈ rm	PERSON
ejpam-4262	271	3	∈	ORG
ejpam-4262	272	1	∈	ORG
ejpam-4262	273	1	∈	ORG
ejpam-4262	273	2	r(m	ORG
ejpam-4262	273	3	ab + ab ∈	ORG
ejpam-4262	273	4	a(m + m	FAC
ejpam-4262	274	1	∈	ORG
ejpam-4262	275	1	β(rm	PRODUCT
ejpam-4262	275	2	abm	LAW
ejpam-4262	275	3	m)β(m	PERSON
ejpam-4262	276	1	rbm ∈	PERSON
ejpam-4262	276	2	m)β(m	PERSON
ejpam-4262	277	1	rbm = ry	PERSON
ejpam-4262	277	2	m)β(m	PERSON
ejpam-4262	278	1	β(rm	PRODUCT
ejpam-4262	279	1	m)β(rm)+{0}r ⊆	DATE
ejpam-4262	279	2	β(rm	PRODUCT
ejpam-4262	282	1	institute of technology	ORG
ejpam-4262	282	2	no.2565-02-05-001	CARDINAL
ejpam-4262	283	1	1	CARDINAL
ejpam-4262	284	1	2	CARDINAL
ejpam-4262	284	2	2	CARDINAL
ejpam-4262	285	1	thai journal of mathematics, 9:577–584, 2011	ORG
ejpam-4262	286	1	2	CARDINAL
ejpam-4262	288	1	15:809–720	CARDINAL
ejpam-4262	288	2	2020	DATE
ejpam-4262	289	1	3	CARDINAL
ejpam-4262	290	1	2	CARDINAL
ejpam-4262	290	2	2	CARDINAL
ejpam-4262	291	1	hacet	PERSON
ejpam-4262	292	1	j. math	PERSON
ejpam-4262	293	1	48:1001–1016	CARDINAL
ejpam-4262	293	2	2019	DATE
ejpam-4262	294	1	4	CARDINAL
ejpam-4262	295	1	2	CARDINAL
ejpam-4262	296	1	1	CARDINAL
ejpam-4262	296	2	19:913–920, 2012	DATE
ejpam-4262	297	1	5	CARDINAL
ejpam-4262	298	1	2	CARDINAL
ejpam-4262	299	1	iranian	NORP
ejpam-4262	299	2	10:131–137	CARDINAL
ejpam-4262	299	3	2015	DATE
ejpam-4262	300	1	6	CARDINAL
ejpam-4262	301	1	abu-dawwas	PERSON
ejpam-4262	302	1	almost 2	CARDINAL
ejpam-4262	303	1	italian	NORP
ejpam-4262	303	2	36:923–928	CARDINAL
ejpam-4262	303	3	2016	DATE