id	sid	eid	entity	type
ejpam-3126	1	1	european journal	ORG
ejpam-3126	2	1	11	CARDINAL
ejpam-3126	2	2	1, 2018	DATE
ejpam-3126	2	3	35	CARDINAL
ejpam-3126	2	4	new york	GPE
ejpam-3126	2	5	pairote yiarayong1,∗	PERSON
ejpam-3126	2	6	siripitukdet1 1	ORG
ejpam-3126	2	7	naresuan university	ORG
ejpam-3126	2	8	65000	CARDINAL
ejpam-3126	2	9	thailand	GPE
ejpam-3126	3	1	φ	PERSON
ejpam-3126	5	1	∈	ORG
ejpam-3126	5	2	∈	ORG
ejpam-3126	5	3	2	CARDINAL
ejpam-3126	5	4	2	CARDINAL
ejpam-3126	5	5	almost 2	CARDINAL
ejpam-3126	5	6	ω-2	CARDINAL
ejpam-3126	6	1	2	CARDINAL
ejpam-3126	7	1	2	CARDINAL
ejpam-3126	7	2	φ	ORG
ejpam-3126	8	1	2	CARDINAL
ejpam-3126	9	1	2010	DATE
ejpam-3126	9	2	13c05	CARDINAL
ejpam-3126	9	3	13c13	CARDINAL
ejpam-3126	10	1	2	CARDINAL
ejpam-3126	10	2	φ	ORG
ejpam-3126	11	1	1	CARDINAL
ejpam-3126	11	2	2	CARDINAL
ejpam-3126	12	1	r.	NORP
ejpam-3126	13	1	∈	ORG
ejpam-3126	13	2	i.	PERSON
ejpam-3126	16	1	ϕ(i	EVENT
ejpam-3126	17	1	⊆	CARDINAL
ejpam-3126	18	1	∈	ORG
ejpam-3126	21	1	yiarayong	PERSON
ejpam-3126	21	2	manojs@nu.ac.th	ORG
ejpam-3126	21	3	m. siripitukdet	PERSON
ejpam-3126	22	1	35	CARDINAL
ejpam-3126	22	2	2018	DATE
ejpam-3126	23	1	yiarayong	PERSON
ejpam-3126	23	2	m. siripitukdet	PERSON
ejpam-3126	24	1	j. pure	PERSON
ejpam-3126	24	2	11	CARDINAL
ejpam-3126	24	3	1	CARDINAL
ejpam-3126	24	4	2018	DATE
ejpam-3126	24	5	35-50 36	PERCENT
ejpam-3126	25	1	9	CARDINAL
ejpam-3126	25	2	∈	ORG
ejpam-3126	25	3	∈	ORG
ejpam-3126	26	1	∈	ORG
ejpam-3126	26	2	∈	ORG
ejpam-3126	26	3	∈	ORG
ejpam-3126	26	4	i. badawi	PERSON
ejpam-3126	27	1	1	CARDINAL
ejpam-3126	27	2	2	CARDINAL
ejpam-3126	28	1	∈	ORG
ejpam-3126	28	2	∈	ORG
ejpam-3126	28	3	∈	ORG
ejpam-3126	28	4	i.	PERSON
ejpam-3126	28	5	r.	NORP
ejpam-3126	28	6	4	CARDINAL
ejpam-3126	28	7	3	DATE
ejpam-3126	28	8	5	DATE
ejpam-3126	28	9	6	CARDINAL
ejpam-3126	29	1	φ-prime submodule	ORG
ejpam-3126	29	2	zamani	PERSON
ejpam-3126	29	3	11	CARDINAL
ejpam-3126	30	1	φ	PERSON
ejpam-3126	30	2	s(m	ORG
ejpam-3126	31	1	φ	ORG
ejpam-3126	31	2	∈	ORG
ejpam-3126	31	3	∈	ORG
ejpam-3126	32	1	⊆	CARDINAL
ejpam-3126	33	1	φ	ORG
ejpam-3126	33	2	11	CARDINAL
ejpam-3126	33	3	∈	ORG
ejpam-3126	33	4	∈	ORG
ejpam-3126	33	5	∈	ORG
ejpam-3126	33	6	∈	ORG
ejpam-3126	33	7	2017	DATE
ejpam-3126	34	1	8	CARDINAL
ejpam-3126	35	1	∈	ORG
ejpam-3126	35	2	∈	ORG
ejpam-3126	35	3	∈	ORG
ejpam-3126	35	4	∈	ORG
ejpam-3126	36	1	10	CARDINAL
ejpam-3126	36	2	φ	ORG
ejpam-3126	36	3	φ	ORG
ejpam-3126	38	1	∈	ORG
ejpam-3126	38	2	∈	ORG
ejpam-3126	41	1	∈	ORG
ejpam-3126	42	1	10	CARDINAL
ejpam-3126	42	2	∈	ORG
ejpam-3126	42	3	∈	ORG
ejpam-3126	43	1	∈	ORG
ejpam-3126	43	2	∈	ORG
ejpam-3126	47	1	∈	ORG
ejpam-3126	47	2	∈	ORG
ejpam-3126	48	1	•	CARDINAL
ejpam-3126	49	1	φ	ORG
ejpam-3126	49	2	2	CARDINAL
ejpam-3126	50	1	•	CARDINAL
ejpam-3126	50	2	0	CARDINAL
ejpam-3126	50	3	2	CARDINAL
ejpam-3126	51	1	•	CARDINAL
ejpam-3126	53	1	yiarayong	PERSON
ejpam-3126	53	2	m. siripitukdet	PERSON
ejpam-3126	54	1	j. pure	PERSON
ejpam-3126	54	2	11	CARDINAL
ejpam-3126	54	3	1	CARDINAL
ejpam-3126	54	4	2018	DATE
ejpam-3126	54	5	35	CARDINAL
ejpam-3126	54	6	2	CARDINAL
ejpam-3126	55	1	•	CARDINAL
ejpam-3126	55	2	n ∈ s(m	ORG
ejpam-3126	56	1	φ	ORG
ejpam-3126	57	1	•	CARDINAL
ejpam-3126	59	1	•	CARDINAL
ejpam-3126	60	1	φ	ORG
ejpam-3126	61	1	section 2	LAW
ejpam-3126	62	1	∈	ORG
ejpam-3126	62	2	⊆	CARDINAL
ejpam-3126	63	1	section 3	LAW
ejpam-3126	64	1	2	CARDINAL
ejpam-3126	64	2	2	CARDINAL
ejpam-3126	64	3	φ	ORG
ejpam-3126	65	1	2	CARDINAL
ejpam-3126	66	1	2	CARDINAL
ejpam-3126	67	1	1	CARDINAL
ejpam-3126	69	1	∈	ORG
ejpam-3126	69	2	∈	ORG
ejpam-3126	69	3	1	CARDINAL
ejpam-3126	71	1	1	CARDINAL
ejpam-3126	73	1	1	CARDINAL
ejpam-3126	73	2	= z.	PERSON
ejpam-3126	73	3	12z	DATE
ejpam-3126	74	1	φ	PERSON
ejpam-3126	74	2	s(m)∪{∅	NORP
ejpam-3126	74	3	0	CARDINAL
ejpam-3126	76	1	2	CARDINAL
ejpam-3126	76	2	2	CARDINAL
ejpam-3126	76	3	3	CARDINAL
ejpam-3126	76	4	2	CARDINAL
ejpam-3126	76	5	3	CARDINAL
ejpam-3126	76	6	2	CARDINAL
ejpam-3126	76	7	6∈	DATE
ejpam-3126	76	8	integer n. therefore n	PERSON
ejpam-3126	77	1	yiarayong	PERSON
ejpam-3126	77	2	m. siripitukdet	PERSON
ejpam-3126	78	1	j. pure	PERSON
ejpam-3126	78	2	11	CARDINAL
ejpam-3126	78	3	1	CARDINAL
ejpam-3126	78	4	2018	DATE
ejpam-3126	78	5	35	CARDINAL
ejpam-3126	78	6	38	CARDINAL
ejpam-3126	78	7	1	CARDINAL
ejpam-3126	79	1	φ	PERSON
ejpam-3126	79	2	s(m	ORG
ejpam-3126	79	3	two	CARDINAL
ejpam-3126	81	1	⊆	CARDINAL
ejpam-3126	81	2	ϕ(n	PERSON
ejpam-3126	82	1	ϕ(n	PERSON
ejpam-3126	82	2	⊆	CARDINAL
ejpam-3126	84	1	1	CARDINAL
ejpam-3126	84	2	∈	ORG
ejpam-3126	84	3	∈	ORG
ejpam-3126	86	1	1	CARDINAL
ejpam-3126	87	1	⊆	CARDINAL
ejpam-3126	87	2	∈	ORG
ejpam-3126	87	3	a1a3 ∈ √	ORG
ejpam-3126	89	1	2	CARDINAL
ejpam-3126	89	2	∈	ORG
ejpam-3126	90	1	∈	ORG
ejpam-3126	90	2	6∈	CARDINAL
ejpam-3126	91	1	∈	ORG
ejpam-3126	92	1	an2 ∈	ORG
ejpam-3126	93	1	1	CARDINAL
ejpam-3126	94	1	2	CARDINAL
ejpam-3126	94	2	1	CARDINAL
ejpam-3126	96	1	ϕ(i	WORK_OF_ART
ejpam-3126	96	2	0	CARDINAL
ejpam-3126	99	1	0	CARDINAL
ejpam-3126	99	2	∈	ORG
ejpam-3126	99	3	− n	PERSON
ejpam-3126	100	1	φ	PERSON
ejpam-3126	100	2	0	CARDINAL
ejpam-3126	100	3	0	DATE
ejpam-3126	100	4	0	DATE
ejpam-3126	101	1	3	CARDINAL
ejpam-3126	101	2	4(0	CARDINAL
ejpam-3126	101	3	1	CARDINAL
ejpam-3126	101	4	1	CARDINAL
ejpam-3126	101	5	3	CARDINAL
ejpam-3126	101	6	4	CARDINAL
ejpam-3126	101	7	6∈	CARDINAL
ejpam-3126	101	8	3(0	DATE
ejpam-3126	101	9	1	CARDINAL
ejpam-3126	101	10	1	CARDINAL
ejpam-3126	101	11	6∈	CARDINAL
ejpam-3126	101	12	1	DATE
ejpam-3126	101	13	1	CARDINAL
ejpam-3126	101	14	6∈	CARDINAL
ejpam-3126	101	15	integer n.	PERSON
ejpam-3126	103	1	2	CARDINAL
ejpam-3126	104	1	φ	ORG
ejpam-3126	104	2	s(m)∪{∅	NORP
ejpam-3126	109	1	ϕ(i	WORK_OF_ART
ejpam-3126	112	1	1	CARDINAL
ejpam-3126	113	1	1	CARDINAL
ejpam-3126	113	2	4	CARDINAL
ejpam-3126	113	3	1	CARDINAL
ejpam-3126	114	1	1	CARDINAL
ejpam-3126	115	1	s(m/n	ORG
ejpam-3126	115	2	k/n	ORG
ejpam-3126	116	1	6=	CARDINAL
ejpam-3126	117	1	2010	DATE
ejpam-3126	117	2	zamani	PERSON
ejpam-3126	117	3	11	CARDINAL
ejpam-3126	117	4	φ	ORG
ejpam-3126	119	1	2	CARDINAL
ejpam-3126	120	1	φ	PERSON
ejpam-3126	120	2	s(m	ORG
ejpam-3126	120	3	two	CARDINAL
ejpam-3126	120	4	k	PERSON
ejpam-3126	120	5	k/n	ORG
ejpam-3126	121	1	yiarayong	PERSON
ejpam-3126	121	2	m. siripitukdet	PERSON
ejpam-3126	122	1	j. pure	PERSON
ejpam-3126	122	2	11	CARDINAL
ejpam-3126	122	3	1	CARDINAL
ejpam-3126	122	4	2018	DATE
ejpam-3126	122	5	35	CARDINAL
ejpam-3126	123	1	∈	ORG
ejpam-3126	123	2	∈	ORG
ejpam-3126	124	1	k/n	ORG
ejpam-3126	127	1	1	CARDINAL
ejpam-3126	127	2	∈ k	PERSON
ejpam-3126	129	1	3	CARDINAL
ejpam-3126	130	1	φ	PERSON
ejpam-3126	130	2	s(m	ORG
ejpam-3126	130	3	two	CARDINAL
ejpam-3126	131	1	n ⊆ φ(k	ORG
ejpam-3126	131	2	k/n	ORG
ejpam-3126	133	1	∈	ORG
ejpam-3126	133	2	∈ k −φ(k	PERSON
ejpam-3126	134	1	a1a2(m+n	ORG
ejpam-3126	135	1	1	CARDINAL
ejpam-3126	136	1	∈ k	PERSON
ejpam-3126	136	2	integer n.	PERSON
ejpam-3126	136	3	2	CARDINAL
ejpam-3126	136	4	3	CARDINAL
ejpam-3126	137	1	1	CARDINAL
ejpam-3126	138	1	φ	PERSON
ejpam-3126	138	2	s(m	ORG
ejpam-3126	138	3	two	CARDINAL
ejpam-3126	138	4	n ⊆ φ(k	PRODUCT
ejpam-3126	140	1	k/n	ORG
ejpam-3126	142	1	2	CARDINAL
ejpam-3126	142	2	3	DATE
ejpam-3126	142	3	zamani	PERSON
ejpam-3126	142	4	11	CARDINAL
ejpam-3126	142	5	φ	ORG
ejpam-3126	142	6	s−1	NORP
ejpam-3126	143	1	s−1	NORP
ejpam-3126	144	1	4	CARDINAL
ejpam-3126	145	1	s(m)∪{∅	NORP
ejpam-3126	146	1	s−1	NORP
ejpam-3126	148	1	∈	ORG
ejpam-3126	148	2	a1 s1 a2 s2	PERSON
ejpam-3126	149	1	∈	ORG
ejpam-3126	150	1	∈ φ(n	PERSON
ejpam-3126	150	2	a1 s1 a2 s2	PERSON
ejpam-3126	151	1	6∈ φ(n	GPE
ejpam-3126	153	1	1	CARDINAL
ejpam-3126	153	2	∈	ORG
ejpam-3126	153	3	∈	ORG
ejpam-3126	153	4	∈	ORG
ejpam-3126	154	1	an2 sm sn2	PERSON
ejpam-3126	158	1	5	CARDINAL
ejpam-3126	159	1	s(m)∪{∅	NORP
ejpam-3126	160	1	s−1	NORP
ejpam-3126	163	1	∈	ORG
ejpam-3126	164	1	1	CARDINAL
ejpam-3126	164	2	1	CARDINAL
ejpam-3126	164	3	1 ∈	CARDINAL
ejpam-3126	165	1	1	CARDINAL
ejpam-3126	165	2	∈ φ(n	PERSON
ejpam-3126	166	1	1	CARDINAL
ejpam-3126	166	2	1 6∈	CARDINAL
ejpam-3126	166	3	1	CARDINAL
ejpam-3126	167	1	yiarayong	PERSON
ejpam-3126	167	2	m. siripitukdet	PERSON
ejpam-3126	168	1	j. pure	PERSON
ejpam-3126	168	2	11	CARDINAL
ejpam-3126	168	3	1	CARDINAL
ejpam-3126	168	4	2018	DATE
ejpam-3126	168	5	35-50 40	PERCENT
ejpam-3126	169	1	s−1	NORP
ejpam-3126	170	1	s−1	NORP
ejpam-3126	170	2	1	CARDINAL
ejpam-3126	170	3	s−1	NORP
ejpam-3126	170	4	⊆	CARDINAL
ejpam-3126	172	1	4	CARDINAL
ejpam-3126	172	2	5	CARDINAL
ejpam-3126	173	1	2	CARDINAL
ejpam-3126	174	1	s(m)∪{∅	NORP
ejpam-3126	175	1	s−1	NORP
ejpam-3126	177	1	4	CARDINAL
ejpam-3126	177	2	5	DATE
ejpam-3126	179	1	6	CARDINAL
ejpam-3126	182	1	∈	ORG
ejpam-3126	182	2	⊆	CARDINAL
ejpam-3126	182	3	integer n. proof	PERSON
ejpam-3126	183	1	∈	ORG
ejpam-3126	184	1	∈	ORG
ejpam-3126	185	1	∈ φ(n	PERSON
ejpam-3126	185	2	∈	ORG
ejpam-3126	185	3	6∈ φ(n	GPE
ejpam-3126	186	1	1	CARDINAL
ejpam-3126	186	2	∈	ORG
ejpam-3126	186	3	∈	ORG
ejpam-3126	187	1	3	CARDINAL
ejpam-3126	190	1	∈	ORG
ejpam-3126	190	2	6⊆	DATE
ejpam-3126	190	3	6⊆ √	DATE
ejpam-3126	190	4	⊆	CARDINAL
ejpam-3126	190	5	integer n.	PERSON
ejpam-3126	190	6	6⊆ √	DATE
ejpam-3126	190	7	⊆	CARDINAL
ejpam-3126	190	8	integer n. proof	PERSON
ejpam-3126	191	1	6	CARDINAL
ejpam-3126	193	1	yiarayong	PERSON
ejpam-3126	193	2	m. siripitukdet	PERSON
ejpam-3126	194	1	j. pure	PERSON
ejpam-3126	194	2	11	CARDINAL
ejpam-3126	194	3	1	CARDINAL
ejpam-3126	194	4	2018	DATE
ejpam-3126	194	5	35	CARDINAL
ejpam-3126	194	6	7	CARDINAL
ejpam-3126	197	1	∈	ORG
ejpam-3126	198	1	∈	ORG
ejpam-3126	198	2	6∈ n	QUANTITY
ejpam-3126	198	3	⊆	CARDINAL
ejpam-3126	198	4	√	PERSON
ejpam-3126	200	1	∈	ORG
ejpam-3126	200	2	∈	ORG
ejpam-3126	200	3	6∈ n	QUANTITY
ejpam-3126	201	1	∈	ORG
ejpam-3126	202	1	6∈	CARDINAL
ejpam-3126	202	2	∈	ORG
ejpam-3126	203	1	1	CARDINAL
ejpam-3126	203	2	∈ n	ORG
ejpam-3126	203	3	∈	ORG
ejpam-3126	203	4	∈	ORG
ejpam-3126	203	5	√	PERSON
ejpam-3126	203	6	⊆	CARDINAL
ejpam-3126	203	7	√	PERSON
ejpam-3126	204	1	∈	ORG
ejpam-3126	204	2	⊆	CARDINAL
ejpam-3126	204	3	√	PERSON
ejpam-3126	207	1	4	CARDINAL
ejpam-3126	211	1	⊆	CARDINAL
ejpam-3126	211	2	∈	ORG
ejpam-3126	211	3	6⊆ n	DATE
ejpam-3126	212	1	⊆	CARDINAL
ejpam-3126	213	1	√	PERSON
ejpam-3126	215	1	7	CARDINAL
ejpam-3126	215	2	3	CARDINAL
ejpam-3126	216	1	2	CARDINAL
ejpam-3126	218	1	•	CARDINAL
ejpam-3126	218	2	φ	ORG
ejpam-3126	218	3	2	CARDINAL
ejpam-3126	219	1	•	CARDINAL
ejpam-3126	219	2	0	CARDINAL
ejpam-3126	219	3	2	CARDINAL
ejpam-3126	220	1	•	CARDINAL
ejpam-3126	222	1	yiarayong	PERSON
ejpam-3126	222	2	m. siripitukdet	PERSON
ejpam-3126	223	1	j. pure	PERSON
ejpam-3126	223	2	11	CARDINAL
ejpam-3126	223	3	1	CARDINAL
ejpam-3126	223	4	2018	DATE
ejpam-3126	223	5	35	CARDINAL
ejpam-3126	223	6	n ∈ s(m	ORG
ejpam-3126	224	1	φ	ORG
ejpam-3126	225	1	•	CARDINAL
ejpam-3126	227	1	•	CARDINAL
ejpam-3126	228	1	φ	ORG
ejpam-3126	229	1	2	CARDINAL
ejpam-3126	231	1	two	CARDINAL
ejpam-3126	232	1	⊆	CARDINAL
ejpam-3126	236	1	zero	CARDINAL
ejpam-3126	236	2	0	CARDINAL
ejpam-3126	237	1	2absorbing	CARDINAL
ejpam-3126	239	1	3	CARDINAL
ejpam-3126	242	1	φ	PERSON
ejpam-3126	245	1	2	CARDINAL
ejpam-3126	245	2	3)([5	CARDINAL
ejpam-3126	246	1	1	CARDINAL
ejpam-3126	246	2	2	CARDINAL
ejpam-3126	246	3	3	CARDINAL
ejpam-3126	246	4	2([5	CARDINAL
ejpam-3126	247	1	1	CARDINAL
ejpam-3126	247	2	6∈	CARDINAL
ejpam-3126	248	1	0]}×z30 and 3n([5	CARDINAL
ejpam-3126	248	2	1	CARDINAL
ejpam-3126	248	3	6∈	CARDINAL
ejpam-3126	249	1	integer n. therefore n	PERSON
ejpam-3126	250	1	2	CARDINAL
ejpam-3126	251	1	8	CARDINAL
ejpam-3126	252	1	2	CARDINAL
ejpam-3126	254	1	2	CARDINAL
ejpam-3126	256	1	2	CARDINAL
ejpam-3126	259	1	∈	ORG
ejpam-3126	259	2	∈	ORG
ejpam-3126	261	1	6∈ φ(n	GPE
ejpam-3126	262	1	1	CARDINAL
ejpam-3126	262	2	integer n.	PERSON
ejpam-3126	262	3	∈ φ(n	PERSON
ejpam-3126	264	1	9	CARDINAL
ejpam-3126	265	1	⊆	CARDINAL
ejpam-3126	265	2	6=	CARDINAL
ejpam-3126	265	3	∈	ORG
ejpam-3126	265	4	rkm	ORG
ejpam-3126	266	1	2	CARDINAL
ejpam-3126	267	1	yiarayong	PERSON
ejpam-3126	267	2	m. siripitukdet	PERSON
ejpam-3126	268	1	j. pure	PERSON
ejpam-3126	268	2	11	CARDINAL
ejpam-3126	268	3	1	CARDINAL
ejpam-3126	268	4	2018	DATE
ejpam-3126	268	5	35	CARDINAL
ejpam-3126	268	6	rkm	PERSON
ejpam-3126	268	7	2	CARDINAL
ejpam-3126	269	1	rkm	PERSON
ejpam-3126	270	1	rkm	ORG
ejpam-3126	271	1	∈	ORG
ejpam-3126	271	2	∈	ORG
ejpam-3126	271	3	∈ rkm	PERSON
ejpam-3126	272	1	6∈	DATE
ejpam-3126	272	2	∈ rkm −	PERSON
ejpam-3126	273	1	1	CARDINAL
ejpam-3126	273	2	∈	ORG
ejpam-3126	274	1	ka2	GPE
ejpam-3126	274	2	∈ rkm	PERSON
ejpam-3126	274	3	∈ rkm	PERSON
ejpam-3126	275	1	6∈	DATE
ejpam-3126	275	2	∈ rkm −	PERSON
ejpam-3126	276	1	1	CARDINAL
ejpam-3126	276	2	∈ rkm	PERSON
ejpam-3126	276	3	an2m	PERSON
ejpam-3126	276	4	∈ rkm	PERSON
ejpam-3126	276	5	integer n.	PERSON
ejpam-3126	276	6	∈	ORG
ejpam-3126	276	7	rka2	GPE
ejpam-3126	276	8	∈	ORG
ejpam-3126	277	1	∈	ORG
ejpam-3126	277	2	rkm	ORG
ejpam-3126	277	3	m)m	CARDINAL
ejpam-3126	277	4	rka2	GPE
ejpam-3126	278	1	∈ rkm	PERSON
ejpam-3126	279	1	∈ rkm	PERSON
ejpam-3126	280	1	10	CARDINAL
ejpam-3126	281	1	φ	PERSON
ejpam-3126	281	2	s(m)∪{∅	NORP
ejpam-3126	281	3	two	CARDINAL
ejpam-3126	283	1	k/n	ORG
ejpam-3126	285	1	∈	ORG
ejpam-3126	285	2	∈	ORG
ejpam-3126	286	1	6∈ φ(k	PERSON
ejpam-3126	289	1	1	CARDINAL
ejpam-3126	289	2	∈ k	PERSON
ejpam-3126	289	3	a1(m+n	PERSON
ejpam-3126	290	1	integer n. theorem	PERSON
ejpam-3126	290	2	11	CARDINAL
ejpam-3126	291	1	⊆	CARDINAL
ejpam-3126	291	2	k/n	ORG
ejpam-3126	293	1	∈	ORG
ejpam-3126	293	2	∈	ORG
ejpam-3126	294	1	6∈ φ(n	GPE
ejpam-3126	296	1	1	CARDINAL
ejpam-3126	297	1	⊆	CARDINAL
ejpam-3126	297	2	a1a2(m+n	ORG
ejpam-3126	297	3	6∈	CARDINAL
ejpam-3126	298	1	a1a2(m+n	ORG
ejpam-3126	300	1	1	CARDINAL
ejpam-3126	300	2	a1(m+n	PERSON
ejpam-3126	302	1	10	CARDINAL
ejpam-3126	302	2	11	CARDINAL
ejpam-3126	303	1	5	CARDINAL
ejpam-3126	304	1	φ	PERSON
ejpam-3126	304	2	s(m	ORG
ejpam-3126	304	3	two	CARDINAL
ejpam-3126	307	1	10	CARDINAL
ejpam-3126	307	2	11	CARDINAL
ejpam-3126	308	1	12	CARDINAL
ejpam-3126	312	1	yiarayong	PERSON
ejpam-3126	312	2	m. siripitukdet	PERSON
ejpam-3126	313	1	j. pure	PERSON
ejpam-3126	313	2	11	CARDINAL
ejpam-3126	313	3	1	CARDINAL
ejpam-3126	313	4	2018	DATE
ejpam-3126	313	5	35-50 44	PERCENT
ejpam-3126	317	1	i. let a1	PERSON
ejpam-3126	317	2	∈	ORG
ejpam-3126	317	3	∈	ORG
ejpam-3126	318	1	⊆	CARDINAL
ejpam-3126	319	1	⊆	CARDINAL
ejpam-3126	320	1	1	CARDINAL
ejpam-3126	320	2	n. ii	PERSON
ejpam-3126	322	1	2	CARDINAL
ejpam-3126	322	2	2	CARDINAL
ejpam-3126	322	3	2	CARDINAL
ejpam-3126	322	4	13	CARDINAL
ejpam-3126	323	1	two	CARDINAL
ejpam-3126	324	1	6≤	CARDINAL
ejpam-3126	324	2	2	CARDINAL
ejpam-3126	326	1	∈	ORG
ejpam-3126	326	2	∈	ORG
ejpam-3126	327	1	6∈ φ(n	GPE
ejpam-3126	328	1	1	CARDINAL
ejpam-3126	328	2	integer n.	PERSON
ejpam-3126	328	3	∈ φ(n	PERSON
ejpam-3126	329	1	⊆ φ(n	PERCENT
ejpam-3126	329	2	6⊆ φ(n	PERSON
ejpam-3126	329	3	6∈ φ(n	PERCENT
ejpam-3126	330	1	integer n. second	PERSON
ejpam-3126	331	1	⊆ φ(n	GPE
ejpam-3126	332	1	r2 ∈	PERSON
ejpam-3126	332	2	6∈	CARDINAL
ejpam-3126	333	1	an2 ∈ √	ORG
ejpam-3126	333	2	6⊆ φ(n	PERSON
ejpam-3126	334	1	r2 ∈	PERSON
ejpam-3126	334	2	∈	ORG
ejpam-3126	334	3	6∈	CARDINAL
ejpam-3126	335	1	6	CARDINAL
ejpam-3126	337	1	6=	CARDINAL
ejpam-3126	337	2	2	CARDINAL
ejpam-3126	339	1	13	CARDINAL
ejpam-3126	339	2	14	DATE
ejpam-3126	340	1	φ	ORG
ejpam-3126	340	2	s(m	ORG
ejpam-3126	340	3	two	CARDINAL
ejpam-3126	341	1	φ ≤ φ4	FAC
ejpam-3126	342	1	yiarayong	PERSON
ejpam-3126	342	2	m. siripitukdet	PERSON
ejpam-3126	343	1	j. pure	PERSON
ejpam-3126	343	2	11	CARDINAL
ejpam-3126	343	3	1	CARDINAL
ejpam-3126	343	4	2018	DATE
ejpam-3126	343	5	35	CARDINAL
ejpam-3126	344	1	2	CARDINAL
ejpam-3126	345	1	2	CARDINAL
ejpam-3126	346	1	13	CARDINAL
ejpam-3126	346	2	⊆	CARDINAL
ejpam-3126	346	3	⊆	CARDINAL
ejpam-3126	350	1	φ(n	PERSON
ejpam-3126	350	2	3	CARDINAL
ejpam-3126	350	3	15	CARDINAL
ejpam-3126	353	1	6⊆ φ(n	GPE
ejpam-3126	353	2	2	CARDINAL
ejpam-3126	354	1	6=	CARDINAL
ejpam-3126	354	2	2	CARDINAL
ejpam-3126	356	1	1.	CARDINAL
ejpam-3126	356	2	2	CARDINAL
ejpam-3126	357	1	m)m	TIME
ejpam-3126	358	1	13	CARDINAL
ejpam-3126	358	2	⊆	CARDINAL
ejpam-3126	359	1	2.	CARDINAL
ejpam-3126	359	2	2absorbing	CARDINAL
ejpam-3126	360	1	nn ⊆	ORG
ejpam-3126	360	2	1	CARDINAL
ejpam-3126	360	3	⊆	CARDINAL
ejpam-3126	362	1	16	CARDINAL
ejpam-3126	363	1	s(mi	GPE
ejpam-3126	363	2	s(mi	GPE
ejpam-3126	366	1	∈	ORG
ejpam-3126	366	2	∈	ORG
ejpam-3126	366	3	6∈√	CARDINAL
ejpam-3126	366	4	6∈	CARDINAL
ejpam-3126	366	5	2	CARDINAL
ejpam-3126	366	6	6∈	CARDINAL
ejpam-3126	366	7	∈	ORG
ejpam-3126	373	1	6∈	CARDINAL
ejpam-3126	373	2	an2	PRODUCT
ejpam-3126	373	3	6∈	CARDINAL
ejpam-3126	373	4	∈	ORG
ejpam-3126	373	5	∈	ORG
ejpam-3126	373	6	6∈	CARDINAL
ejpam-3126	374	1	m2 ∈ m2	PERSON
ejpam-3126	376	1	1	CARDINAL
ejpam-3126	378	1	∈	ORG
ejpam-3126	379	1	6∈	CARDINAL
ejpam-3126	379	2	∈	PRODUCT
ejpam-3126	381	1	∈	PRODUCT
ejpam-3126	381	2	6∈	MONEY
ejpam-3126	382	1	6∈	CARDINAL
ejpam-3126	385	1	s(mi	GPE
ejpam-3126	385	2	s(mi	GPE
ejpam-3126	386	1	yiarayong	PERSON
ejpam-3126	386	2	m. siripitukdet	PERSON
ejpam-3126	387	1	j. pure	PERSON
ejpam-3126	387	2	11	CARDINAL
ejpam-3126	387	3	1	CARDINAL
ejpam-3126	387	4	2018	DATE
ejpam-3126	387	5	35-50 46	PERCENT
ejpam-3126	389	1	∈	ORG
ejpam-3126	389	2	∈	ORG
ejpam-3126	389	3	6∈√	CARDINAL
ejpam-3126	389	4	6∈ n2	QUANTITY
ejpam-3126	389	5	an2	ORG
ejpam-3126	389	6	6∈ n2	QUANTITY
ejpam-3126	389	7	∈	ORG
ejpam-3126	391	1	16	CARDINAL
ejpam-3126	391	2	17	CARDINAL
ejpam-3126	392	1	s(mi)→	GPE
ejpam-3126	396	1	m1 ×	ORG
ejpam-3126	398	1	mi	ORG
ejpam-3126	398	2	∈	ORG
ejpam-3126	398	3	∈	ORG
ejpam-3126	398	4	∈	ORG
ejpam-3126	398	5	6∈√	CARDINAL
ejpam-3126	398	6	6∈ ni	QUANTITY
ejpam-3126	398	7	an2	PERSON
ejpam-3126	398	8	6∈ ni	QUANTITY
ejpam-3126	398	9	j ∈	PERSON
ejpam-3126	398	10	1	CARDINAL
ejpam-3126	398	11	2	DATE
ejpam-3126	400	1	∈	ORG
ejpam-3126	402	1	16	CARDINAL
ejpam-3126	405	1	2	CARDINAL
ejpam-3126	406	1	first	ORDINAL
ejpam-3126	407	1	18	CARDINAL
ejpam-3126	408	1	φ = ψ1×ψ2	ORG
ejpam-3126	409	1	m1 × m2	PRODUCT
ejpam-3126	411	1	∈	ORG
ejpam-3126	412	1	0)(m	DATE
ejpam-3126	412	2	0	CARDINAL
ejpam-3126	413	1	1	CARDINAL
ejpam-3126	413	2	∈	ORG
ejpam-3126	414	1	1	CARDINAL
ejpam-3126	415	1	s(mi	GPE
ejpam-3126	415	2	s(mi	GPE
ejpam-3126	416	1	2	CARDINAL
ejpam-3126	416	2	0}×m2 ⊆	CARDINAL
ejpam-3126	418	1	a1, b1)(a2	PRODUCT
ejpam-3126	419	1	yiarayong	PERSON
ejpam-3126	419	2	m. siripitukdet	PERSON
ejpam-3126	420	1	j. pure	PERSON
ejpam-3126	420	2	11	CARDINAL
ejpam-3126	420	3	1	CARDINAL
ejpam-3126	420	4	2018	DATE
ejpam-3126	420	5	35	CARDINAL
ejpam-3126	420	6	b1b2m2	ORG
ejpam-3126	420	7	6∈	CARDINAL
ejpam-3126	420	8	0	CARDINAL
ejpam-3126	421	1	∈	ORG
ejpam-3126	421	2	ψ1)0(n1	ORG
ejpam-3126	422	1	1	CARDINAL
ejpam-3126	422	2	∈	ORG
ejpam-3126	422	3	integer n.	PERSON
ejpam-3126	424	1	s(mi	GPE
ejpam-3126	424	2	s(mi	GPE
ejpam-3126	425	1	⊆	CARDINAL
ejpam-3126	427	1	1	CARDINAL
ejpam-3126	427	2	19	DATE
ejpam-3126	428	1	s(mi	GPE
ejpam-3126	428	2	s(mi	GPE
ejpam-3126	429	1	m1 ×	ORG
ejpam-3126	432	1	⊆	CARDINAL
ejpam-3126	436	1	nj	ORG
ejpam-3126	437	1	m1×m2×	CARDINAL
ejpam-3126	441	1	proof	PERSON
ejpam-3126	442	1	18	CARDINAL
ejpam-3126	442	2	1	CARDINAL
ejpam-3126	442	3	20	CARDINAL
ejpam-3126	443	1	s(mi	GPE
ejpam-3126	443	2	s(mi	GPE
ejpam-3126	444	1	2	CARDINAL
ejpam-3126	444	2	2	CARDINAL
ejpam-3126	446	1	2	CARDINAL
ejpam-3126	446	2	2absorbing	CARDINAL
ejpam-3126	447	1	2	CARDINAL
ejpam-3126	448	1	2	CARDINAL
ejpam-3126	449	1	6	CARDINAL
ejpam-3126	449	2	2n1	CARDINAL
ejpam-3126	449	3	0	CARDINAL
ejpam-3126	451	1	1	CARDINAL
ejpam-3126	453	1	s(mi	GPE
ejpam-3126	453	2	s(mi	GPE
ejpam-3126	454	1	2	CARDINAL
ejpam-3126	456	1	20	CARDINAL
ejpam-3126	456	2	21	DATE
ejpam-3126	459	1	nj	ORG
ejpam-3126	461	1	× ni ×mi+1 ×	PERSON
ejpam-3126	462	1	2	CARDINAL
ejpam-3126	462	2	m1 ×	ORG
ejpam-3126	464	1	proof	PERSON
ejpam-3126	465	1	20	CARDINAL
ejpam-3126	465	2	9	CARDINAL
ejpam-3126	465	3	22	DATE
ejpam-3126	466	1	s(mi	GPE
ejpam-3126	466	2	s(mi	GPE
ejpam-3126	467	1	yiarayong	PERSON
ejpam-3126	467	2	m. siripitukdet	PERSON
ejpam-3126	468	1	j. pure	PERSON
ejpam-3126	468	2	11	CARDINAL
ejpam-3126	468	3	1	CARDINAL
ejpam-3126	468	4	2018	DATE
ejpam-3126	468	5	35-50 48	PERCENT
ejpam-3126	468	6	2	CARDINAL
ejpam-3126	469	1	2	CARDINAL
ejpam-3126	470	1	6= m2	QUANTITY
ejpam-3126	471	1	1 ⇒ 2	CARDINAL
ejpam-3126	472	1	a1, b1)(a2	PRODUCT
ejpam-3126	473	1	∈	ORG
ejpam-3126	474	1	2	CARDINAL
ejpam-3126	474	2	∈	ORG
ejpam-3126	476	1	2	CARDINAL
ejpam-3126	477	1	3	CARDINAL
ejpam-3126	478	1	∈	ORG
ejpam-3126	479	1	m2 ∈ m2	PERSON
ejpam-3126	480	1	⊆	CARDINAL
ejpam-3126	480	2	1)(a2	DATE
ejpam-3126	480	3	1)(m	DATE
ejpam-3126	481	1	1	CARDINAL
ejpam-3126	481	2	∈	ORG
ejpam-3126	482	1	10	CARDINAL
ejpam-3126	483	1	s(mi	GPE
ejpam-3126	483	2	s(mi	GPE
ejpam-3126	484	1	2	CARDINAL
ejpam-3126	485	1	2	CARDINAL
ejpam-3126	486	1	6=	CARDINAL
ejpam-3126	488	1	22	CARDINAL
ejpam-3126	488	2	23	CARDINAL
ejpam-3126	491	1	2	CARDINAL
ejpam-3126	491	2	mi	ORG
ejpam-3126	491	3	m1×m2×.	GPE
ejpam-3126	493	1	2	CARDINAL
ejpam-3126	493	2	m1 ×	ORG
ejpam-3126	496	1	× ni ×mi+1 ×	PERSON
ejpam-3126	497	1	m1 ×	ORG
ejpam-3126	499	1	6=	CARDINAL
ejpam-3126	500	1	22	CARDINAL
ejpam-3126	500	2	10	CARDINAL
ejpam-3126	500	3	24	DATE
ejpam-3126	501	1	s(mi	GPE
ejpam-3126	501	2	s(mi	GPE
ejpam-3126	502	1	m1.	ORG
ejpam-3126	503	1	yiarayong	PERSON
ejpam-3126	503	2	m. siripitukdet	PERSON
ejpam-3126	504	1	j. pure	PERSON
ejpam-3126	504	2	11	CARDINAL
ejpam-3126	504	3	1	CARDINAL
ejpam-3126	504	4	2018	DATE
ejpam-3126	504	5	35	CARDINAL
ejpam-3126	506	1	11	CARDINAL
ejpam-3126	507	1	s(mi	GPE
ejpam-3126	507	2	s(mi	GPE
ejpam-3126	508	1	m1 × n2	PRODUCT
ejpam-3126	510	1	24	CARDINAL
ejpam-3126	510	2	25	DATE
ejpam-3126	511	1	s(mi	GPE
ejpam-3126	511	2	s(mi	GPE
ejpam-3126	512	1	φ	PERSON
ejpam-3126	514	1	m1 × m2 ×	PRODUCT
ejpam-3126	517	1	m1 ×	ORG
ejpam-3126	520	1	24	CARDINAL
ejpam-3126	520	2	11	CARDINAL
ejpam-3126	521	1	26	CARDINAL
ejpam-3126	522	1	s(mi)→	GPE
ejpam-3126	523	1	m1	PRODUCT
ejpam-3126	526	1	2	CARDINAL
ejpam-3126	527	1	27	CARDINAL
ejpam-3126	528	1	s(mi	GPE
ejpam-3126	528	2	s(mi	GPE
ejpam-3126	528	3	6=	CARDINAL
ejpam-3126	529	1	2	CARDINAL
ejpam-3126	531	1	m1 × m2 × m3	PRODUCT
ejpam-3126	531	2	2	CARDINAL
ejpam-3126	532	1	6=	CARDINAL
ejpam-3126	533	1	6=	CARDINAL
ejpam-3126	533	2	1	CARDINAL
ejpam-3126	533	3	2	DATE
ejpam-3126	533	4	3	CARDINAL
ejpam-3126	537	1	6= m2	QUANTITY
ejpam-3126	538	1	m3 ∈ m3	PERSON
ejpam-3126	538	2	6∈ n2	QUANTITY
ejpam-3126	538	3	6∈	CARDINAL
ejpam-3126	539	1	1	CARDINAL
ejpam-3126	539	2	0	DATE
ejpam-3126	539	3	1)(1	CARDINAL
ejpam-3126	539	4	1	CARDINAL
ejpam-3126	539	5	0)(m1,m2,m3	ORG
ejpam-3126	539	6	6∈	CARDINAL
ejpam-3126	539	7	1	CARDINAL
ejpam-3126	539	8	0	DATE
ejpam-3126	539	9	1)(1	CARDINAL
ejpam-3126	539	10	1	CARDINAL
ejpam-3126	539	11	0)(m1,m2,m3	ORG
ejpam-3126	540	1	m3 ∈	PRODUCT
ejpam-3126	542	1	0	CARDINAL
ejpam-3126	542	2	1	DATE
ejpam-3126	543	1	13	CARDINAL
ejpam-3126	543	2	0	CARDINAL
ejpam-3126	543	3	1	CARDINAL
ejpam-3126	543	4	n1× m2×n3	PERSON
ejpam-3126	543	5	2n	CARDINAL
ejpam-3126	543	6	⊆	CARDINAL
ejpam-3126	545	1	2	CARDINAL
ejpam-3126	547	1	50	CARDINAL
ejpam-3126	547	2	12	CARDINAL
ejpam-3126	548	1	s(mi	GPE
ejpam-3126	548	2	s(mi	GPE
ejpam-3126	548	3	6=	CARDINAL
ejpam-3126	549	1	2	CARDINAL
ejpam-3126	551	1	27	CARDINAL
ejpam-3126	552	1	1	CARDINAL
ejpam-3126	552	2	badawi	GPE
ejpam-3126	553	1	2absorbing	CARDINAL
ejpam-3126	554	1	turkish	NORP
ejpam-3126	554	2	40:703	CARDINAL
ejpam-3126	554	3	717	CARDINAL
ejpam-3126	554	4	2016	DATE
ejpam-3126	555	1	2	CARDINAL
ejpam-3126	555	2	anderson	PERSON
ejpam-3126	557	1	696, 2008	DATE
ejpam-3126	558	1	3	CARDINAL
ejpam-3126	558	2	anderson	PERSON
ejpam-3126	558	3	e. smith	PERSON
ejpam-3126	560	1	houston	GPE
ejpam-3126	560	2	840, 2003	DATE
ejpam-3126	561	1	4	CARDINAL
ejpam-3126	561	2	anderson	PERSON
ejpam-3126	563	1	39(5):1646	CARDINAL
ejpam-3126	563	2	1672, 2011	DATE
ejpam-3126	564	1	5	CARDINAL
ejpam-3126	565	1	2	CARDINAL
ejpam-3126	566	1	australian	NORP
ejpam-3126	566	2	75:417	PERSON
ejpam-3126	566	3	429	CARDINAL
ejpam-3126	566	4	2007	DATE
ejpam-3126	567	1	6	CARDINAL
ejpam-3126	568	1	2	CARDINAL
ejpam-3126	569	1	houston journal of mathematics	ORG
ejpam-3126	569	2	452	CARDINAL
ejpam-3126	569	3	2013	DATE
ejpam-3126	570	1	7	CARDINAL
ejpam-3126	572	1	novi sad journal of mathematics	ORG
ejpam-3126	572	2	42(1):27–35	CARDINAL
ejpam-3126	572	3	2012	DATE
ejpam-3126	573	1	8	CARDINAL
ejpam-3126	574	1	φ	PERSON
ejpam-3126	575	1	the korean mathematical society	ORG
ejpam-3126	575	2	54(4):1099	CARDINAL
ejpam-3126	575	3	1108	CARDINAL
ejpam-3126	575	4	2017	DATE
ejpam-3126	576	1	9	CARDINAL
ejpam-3126	578	1	40:1268	CARDINAL
ejpam-3126	578	2	1279	CARDINAL
ejpam-3126	578	3	2012	DATE
ejpam-3126	579	1	10	CARDINAL
ejpam-3126	581	1	acta mathematica vietnamica	PERSON
ejpam-3126	581	2	42:27 –	TIME
ejpam-3126	581	3	35	DATE
ejpam-3126	581	4	2017	DATE
ejpam-3126	582	1	11	CARDINAL
ejpam-3126	583	1	φ	ORG
ejpam-3126	584	1	glasgow mathematical journal	ORG
ejpam-3126	584	2	52(2):253	CARDINAL
ejpam-3126	584	3	259	CARDINAL
ejpam-3126	584	4	2010	DATE