id	sid	eid	entity	type
ejpam-753	1	1	7_753_behboodi.dvi	CARDINAL
ejpam-753	1	2	european	NORP
ejpam-753	2	1	3	CARDINAL
ejpam-753	2	2	4, 2010	DATE
ejpam-753	2	3	686	CARDINAL
ejpam-753	3	1	kn	PERSON
ejpam-753	3	2	zero	CARDINAL
ejpam-753	3	3	ii m.	PERSON
ejpam-753	3	4	r. beyranvand	PERSON
ejpam-753	3	5	3 1	CARDINAL
ejpam-753	3	6	isfahan university of technology	ORG
ejpam-753	3	7	isfahan	GPE
ejpam-753	3	8	iran 2 school of mathematics	EVENT
ejpam-753	3	9	tehran	GPE
ejpam-753	3	10	iran 3	EVENT
ejpam-753	3	11	lorestan university	ORG
ejpam-753	3	12	khorramabad	GPE
ejpam-753	3	13	iran	GPE
ejpam-753	4	1	zero	CARDINAL
ejpam-753	5	1	p1 k1	PRODUCT
ejpam-753	6	1	kn zero	PERSON
ejpam-753	7	1	2000	CARDINAL
ejpam-753	7	2	16b99	CARDINAL
ejpam-753	7	3	13a99	CARDINAL
ejpam-753	7	4	68r10	CARDINAL
ejpam-753	7	5	zero	CARDINAL
ejpam-753	7	6	1	CARDINAL
ejpam-753	8	1	2	CARDINAL
ejpam-753	8	2	2	CARDINAL
ejpam-753	9	1	j(r	PERSON
ejpam-753	9	2	z(r	DATE
ejpam-753	9	3	zero	CARDINAL
ejpam-753	10	1	fq ∗	PERSON
ejpam-753	10	2	σ0	GPE
ejpam-753	10	3	σm∪{0	DATE
ejpam-753	11	1	2	CARDINAL
ejpam-753	11	2	p1 k1	PRODUCT
ejpam-753	12	1	ps ks zerodivisors	ORG
ejpam-753	12	2	1 ≤ ki ≤ 3	QUANTITY
ejpam-753	13	1	zero	CARDINAL
ejpam-753	13	2	4	CARDINAL
ejpam-753	13	3	5	CARDINAL
ejpam-753	15	1	p1 k1 p2 k2	PRODUCT
ejpam-753	17	1	ps ks zero	ORG
ejpam-753	18	1	zero	CARDINAL
ejpam-753	18	2	zero	CARDINAL
ejpam-753	21	1	m. behboodi	PERSON
ejpam-753	22	1	r.	NORP
ejpam-753	23	1	686	CARDINAL
ejpam-753	23	2	2010	DATE
ejpam-753	24	1	m. behboodi	PERSON
ejpam-753	24	2	r. beyranvand	PERSON
ejpam-753	25	1	j. pure	PERSON
ejpam-753	25	2	3	CARDINAL
ejpam-753	25	3	2010	DATE
ejpam-753	25	4	686	CARDINAL
ejpam-753	25	5	zero	CARDINAL
ejpam-753	27	1	z(r	DATE
ejpam-753	28	1	1 ≤	QUANTITY
ejpam-753	29	1	6	CARDINAL
ejpam-753	29	2	2	CARDINAL
ejpam-753	31	1	mt−(m1−n1)(m2− n2	PERSON
ejpam-753	32	1	mt − nt	FAC
ejpam-753	32	2	zero	CARDINAL
ejpam-753	33	1	7	CARDINAL
ejpam-753	34	1	two	CARDINAL
ejpam-753	35	1	1	CARDINAL
ejpam-753	36	1	8	CARDINAL
ejpam-753	36	2	2	CARDINAL
ejpam-753	37	1	1	CARDINAL
ejpam-753	37	2	2	CARDINAL
ejpam-753	37	3	|z(r)|=	ORG
ejpam-753	37	4	3	CARDINAL
ejpam-753	37	5	0	CARDINAL
ejpam-753	37	6	4	CARDINAL
ejpam-753	37	7	1≤ k ≤ n	FAC
ejpam-753	37	8	5	CARDINAL
ejpam-753	37	9	j(r)∼= fq	PERSON
ejpam-753	38	1	2	CARDINAL
ejpam-753	39	1	2	CARDINAL
ejpam-753	39	2	2	CARDINAL
ejpam-753	43	1	ri	GPE
ejpam-753	48	1	1	CARDINAL
ejpam-753	48	2	i=1 ti =	PERSON
ejpam-753	52	1	1)πs	CARDINAL
ejpam-753	53	1	1	CARDINAL
ejpam-753	54	1	1	CARDINAL
ejpam-753	54	2	1	CARDINAL
ejpam-753	54	3	1	CARDINAL
ejpam-753	59	1	2	CARDINAL
ejpam-753	60	1	j = k− 2	PERSON
ejpam-753	60	2	1	CARDINAL
ejpam-753	62	1	1	CARDINAL
ejpam-753	62	2	q− 1	DATE
ejpam-753	62	3	m. behboodi	PERSON
ejpam-753	62	4	r. beyranvand	PERSON
ejpam-753	63	1	j. pure	PERSON
ejpam-753	63	2	3	CARDINAL
ejpam-753	63	3	2010	DATE
ejpam-753	63	4	686	CARDINAL
ejpam-753	63	5	3	CARDINAL
ejpam-753	64	1	gr(p3r	ORG
ejpam-753	65	1	1≤	ORDINAL
ejpam-753	65	2	1≤ 1+	DATE
ejpam-753	65	3	1≤	CARDINAL
ejpam-753	65	4	1≤ 1+d+	DATE
ejpam-753	65	5	0	CARDINAL
ejpam-753	73	1	0	CARDINAL
ejpam-753	77	1	t	GPE
ejpam-753	82	1	⊕	GPE
ejpam-753	82	2	⊕	PERSON
ejpam-753	82	3	j v j	PERSON
ejpam-753	83	1	γkwk).(α	ORDINAL
ejpam-753	85	1	j v j	PERSON
ejpam-753	103	1	ad+k	PERSON
ejpam-753	105	1	j + pr0]]wk	LAW
ejpam-753	106	1	1 or	CARDINAL
ejpam-753	106	2	2	CARDINAL
ejpam-753	106	3	3	CARDINAL
ejpam-753	106	4	6.1	CARDINAL
ejpam-753	106	5	0	CARDINAL
ejpam-753	107	1	6=	DATE
ejpam-753	107	2	1	CARDINAL
ejpam-753	110	1	fp2 ⊕	GPE
ejpam-753	110	2	r2)(s0	ORG
ejpam-753	112	1	fp2 ⊕	GPE
ejpam-753	112	2	α0,α	ORG
ejpam-753	117	1	1	CARDINAL
ejpam-753	117	2	0	CARDINAL
ejpam-753	119	1	1	CARDINAL
ejpam-753	120	1	0 i.e.	DATE
ejpam-753	120	2	two zero	CARDINAL
ejpam-753	120	3	zero	CARDINAL
ejpam-753	121	1	1	CARDINAL
ejpam-753	121	2	1	CARDINAL
ejpam-753	123	1	rk)(s0	ORG
ejpam-753	127	1	k.	PERSON
ejpam-753	128	1	2	CARDINAL
ejpam-753	128	2	1	CARDINAL
ejpam-753	129	1	r2)(s0	ORG
ejpam-753	129	2	2	CARDINAL
ejpam-753	131	1	3	CARDINAL
ejpam-753	131	2	4.1	CARDINAL
ejpam-753	131	3	two zero	CARDINAL
ejpam-753	131	4	zero	CARDINAL
ejpam-753	132	1	r. beyranvand	PERSON
ejpam-753	133	1	j. pure	PERSON
ejpam-753	133	2	3	CARDINAL
ejpam-753	133	3	2010	DATE
ejpam-753	133	4	686-694 689	QUANTITY
ejpam-753	133	5	⊕	GPE
ejpam-753	133	6	⊕	PERSON
ejpam-753	133	7	i=1 αiui	PERSON
ejpam-753	133	8	λ∑	PERSON
ejpam-753	133	9	j v j	PERSON
ejpam-753	134	1	i=1 α′iui	PERSON
ejpam-753	135	1	λ∑	PERSON
ejpam-753	145	1	j]wk	PERSON
ejpam-753	145	2	w	ORG
ejpam-753	145	3	0	CARDINAL
ejpam-753	145	4	1 ≤	QUANTITY
ejpam-753	145	5	{vi}	PERSON
ejpam-753	145	6	w	ORG
ejpam-753	146	1	k ≤ t	FAC
ejpam-753	147	1	1	CARDINAL
ejpam-753	147	2	0	CARDINAL
ejpam-753	148	1	3	CARDINAL
ejpam-753	148	2	5.2	CARDINAL
ejpam-753	148	3	11	CARDINAL
ejpam-753	148	4	1	CARDINAL
ejpam-753	148	5	fp2 ⊕	ORG
ejpam-753	148	6	α0,α	ORG
ejpam-753	154	1	1	CARDINAL
ejpam-753	157	1	3	CARDINAL
ejpam-753	157	2	7.1	CARDINAL
ejpam-753	157	3	11	CARDINAL
ejpam-753	157	4	1	CARDINAL
ejpam-753	163	1	2	CARDINAL
ejpam-753	165	1	zp5	ORG
ejpam-753	165	2	5	CARDINAL
ejpam-753	165	3	− x3	PERSON
ejpam-753	165	4	x4 − ap	PERSON
ejpam-753	165	5	4	CARDINAL
ejpam-753	165	6	zp2[x]/(px2	GPE
ejpam-753	165	7	x3 −	GPE
ejpam-753	165	8	6= 3	DATE
ejpam-753	165	9	z9[x]/(3x2	PRODUCT
ejpam-753	165	10	3	CARDINAL
ejpam-753	165	11	− 3bx	EVENT
ejpam-753	165	12	zp2[x]/(px2	GPE
ejpam-753	165	13	x3− apx	PERSON
ejpam-753	165	14	2,	DATE
ejpam-753	165	15	zp2[x	GPE
ejpam-753	165	16	z)2	PERSON
ejpam-753	165	17	∈	ORG
ejpam-753	165	18	6= 2	DATE
ejpam-753	165	19	z8[x]/(4x	GPE
ejpam-753	165	20	1,0	CARDINAL
ejpam-753	165	21	1,1	CARDINAL
ejpam-753	165	22	∈ σ0	PERCENT
ejpam-753	165	23	2	CARDINAL
ejpam-753	165	24	6= 2	DATE
ejpam-753	165	25	z8[x]/(4x	GPE
ejpam-753	165	26	4a− 2bx	DATE
ejpam-753	165	27	1,1	CARDINAL
ejpam-753	165	28	2	CARDINAL
ejpam-753	165	29	0	CARDINAL
ejpam-753	165	30	2	CARDINAL
ejpam-753	165	31	2	CARDINAL
ejpam-753	165	32	0	CARDINAL
ejpam-753	169	1	0	CARDINAL
ejpam-753	169	2	2	CARDINAL
ejpam-753	169	3	2	CARDINAL
ejpam-753	171	1	6= 2	DATE
ejpam-753	171	2	2	CARDINAL
ejpam-753	171	3	2	CARDINAL
ejpam-753	174	1	6=	CARDINAL
ejpam-753	174	2	2	CARDINAL
ejpam-753	174	3	2.1=	CARDINAL
ejpam-753	174	4	2	CARDINAL
ejpam-753	174	5	2	CARDINAL
ejpam-753	178	1	2.1=	CARDINAL
ejpam-753	178	2	2	CARDINAL
ejpam-753	179	1	x3	GPE
ejpam-753	179	2	2	CARDINAL
ejpam-753	182	1	0	CARDINAL
ejpam-753	182	2	j〉	PERSON
ejpam-753	182	3	x3	GPE
ejpam-753	182	4	2	CARDINAL
ejpam-753	182	5	2	CARDINAL
ejpam-753	184	1	0	CARDINAL
ejpam-753	184	2	j〉	PERSON
ejpam-753	184	3	x3	GPE
ejpam-753	184	4	2	CARDINAL
ejpam-753	186	1	0	CARDINAL
ejpam-753	186	2	j〉	PERSON
ejpam-753	186	3	x3	GPE
ejpam-753	186	4	0	CARDINAL
ejpam-753	186	5	2	CARDINAL
ejpam-753	186	6	x3 2	PERSON
ejpam-753	188	1	0	CARDINAL
ejpam-753	188	2	6= 2	DATE
ejpam-753	188	3	m. behboodi	PERSON
ejpam-753	188	4	r. beyranvand	PERSON
ejpam-753	189	1	j. pure	PERSON
ejpam-753	189	2	3	CARDINAL
ejpam-753	189	3	2010	DATE
ejpam-753	189	4	686	CARDINAL
ejpam-753	189	5	x3	GPE
ejpam-753	189	6	2.1=	CARDINAL
ejpam-753	189	7	2	CARDINAL
ejpam-753	193	1	0	CARDINAL
ejpam-753	193	2	0	CARDINAL
ejpam-753	195	1	2	CARDINAL
ejpam-753	197	1	6= 2	DATE
ejpam-753	197	2	∈	ORG
ejpam-753	197	3	1	CARDINAL
ejpam-753	197	4	4.1= 4x	CARDINAL
ejpam-753	197	5	2y	CARDINAL
ejpam-753	197	6	0	CARDINAL
ejpam-753	197	7	2	CARDINAL
ejpam-753	198	1	4.1= 4x	CARDINAL
ejpam-753	198	2	2y	CARDINAL
ejpam-753	198	3	0	CARDINAL
ejpam-753	198	4	2+ 2x	DATE
ejpam-753	199	1	4.1= 4x	CARDINAL
ejpam-753	199	2	2y	CARDINAL
ejpam-753	199	3	0	CARDINAL
ejpam-753	199	4	2	CARDINAL
ejpam-753	199	5	2x	CARDINAL
ejpam-753	199	6	x3	GPE
ejpam-753	200	1	2	CARDINAL
ejpam-753	200	2	2	CARDINAL
ejpam-753	200	3	x3 2	ORG
ejpam-753	201	1	6= 2	DATE
ejpam-753	201	2	∈	ORG
ejpam-753	201	3	1,ε	CARDINAL
ejpam-753	201	4	x3	GPE
ejpam-753	201	5	2	CARDINAL
ejpam-753	201	6	1	CARDINAL
ejpam-753	201	7	2	CARDINAL
ejpam-753	201	8	x3 2	PERSON
ejpam-753	201	9	6= 2	DATE
ejpam-753	201	10	∈	ORG
ejpam-753	201	11	1,ε	CARDINAL
ejpam-753	201	12	x3	GPE
ejpam-753	201	13	2	CARDINAL
ejpam-753	202	1	2	CARDINAL
ejpam-753	202	2	1	CARDINAL
ejpam-753	202	3	x3 2	ORG
ejpam-753	203	1	6= 2	DATE
ejpam-753	203	2	∈	ORG
ejpam-753	203	3	1,ε	CARDINAL
ejpam-753	203	4	4.1= 2x	CARDINAL
ejpam-753	203	5	2	CARDINAL
ejpam-753	203	6	2	CARDINAL
ejpam-753	203	7	2	CARDINAL
ejpam-753	203	8	x3 2	ORG
ejpam-753	204	1	j〉	PERSON
ejpam-753	204	2	4.1= 2x	CARDINAL
ejpam-753	205	1	2	CARDINAL
ejpam-753	205	2	1	CARDINAL
ejpam-753	205	3	2	CARDINAL
ejpam-753	205	4	2	CARDINAL
ejpam-753	205	5	x3 2	ORG
ejpam-753	206	1	j〉	PERSON
ejpam-753	206	2	4.1= 2x	CARDINAL
ejpam-753	206	3	2	CARDINAL
ejpam-753	206	4	2	CARDINAL
ejpam-753	206	5	1	CARDINAL
ejpam-753	206	6	x3 2	ORG
ejpam-753	206	7	2	CARDINAL
ejpam-753	206	8	j〉	PERSON
ejpam-753	208	1	2	CARDINAL
ejpam-753	208	2	1	CARDINAL
ejpam-753	208	3	2	CARDINAL
ejpam-753	208	4	0	CARDINAL
ejpam-753	211	1	2	CARDINAL
ejpam-753	211	2	1	CARDINAL
ejpam-753	217	1	2	CARDINAL
ejpam-753	217	2	1	CARDINAL
ejpam-753	217	3	2	CARDINAL
ejpam-753	220	1	6= 2	DATE
ejpam-753	220	2	4.1= 2x	CARDINAL
ejpam-753	221	1	2y	CARDINAL
ejpam-753	221	2	0	CARDINAL
ejpam-753	221	3	2	CARDINAL
ejpam-753	221	4	2	CARDINAL
ejpam-753	224	1	0,1	CARDINAL
ejpam-753	224	2	6= 2	DATE
ejpam-753	224	3	4.1= 4x	CARDINAL
ejpam-753	224	4	2y	CARDINAL
ejpam-753	224	5	0	CARDINAL
ejpam-753	224	6	1,0	CARDINAL
ejpam-753	224	7	1,1	CARDINAL
ejpam-753	224	8	2	CARDINAL
ejpam-753	224	9	2	CARDINAL
ejpam-753	224	10	0	CARDINAL
ejpam-753	224	11	2	CARDINAL
ejpam-753	224	12	2	CARDINAL
ejpam-753	224	13	6= 2	DATE
ejpam-753	224	14	2	CARDINAL
ejpam-753	224	15	2	CARDINAL
ejpam-753	224	16	2	CARDINAL
ejpam-753	224	17	2	CARDINAL
ejpam-753	224	18	6= 2	DATE
ejpam-753	224	19	8.1= 2x	CARDINAL
ejpam-753	224	20	2	CARDINAL
ejpam-753	224	21	2	CARDINAL
ejpam-753	224	22	0	CARDINAL
ejpam-753	224	23	4〉	QUANTITY
ejpam-753	224	24	9	CARDINAL
ejpam-753	225	1	10	CARDINAL
ejpam-753	225	2	6	CARDINAL
ejpam-753	225	3	6=	CARDINAL
ejpam-753	225	4	2	CARDINAL
ejpam-753	225	5	2	CARDINAL
ejpam-753	226	1	5	CARDINAL
ejpam-753	226	2	9	CARDINAL
ejpam-753	227	1	1	CARDINAL
ejpam-753	229	1	1	CARDINAL
ejpam-753	229	2	2	CARDINAL
ejpam-753	230	1	2)×	CARDINAL
ejpam-753	235	1	2	CARDINAL
ejpam-753	235	2	1	CARDINAL
ejpam-753	236	1	1	CARDINAL
ejpam-753	239	1	1	CARDINAL
ejpam-753	240	1	+ q− 1	DATE
ejpam-753	240	2	3	CARDINAL
ejpam-753	240	3	x2− ǫp	GPE
ejpam-753	240	4	∈ σ0	PERCENT
ejpam-753	240	5	2	CARDINAL
ejpam-753	240	6	m. behboodi	PERSON
ejpam-753	240	7	r. beyranvand	PERSON
ejpam-753	241	1	j. pure	PERSON
ejpam-753	241	2	3	CARDINAL
ejpam-753	241	3	2010	DATE
ejpam-753	241	4	686-694 691	QUANTITY
ejpam-753	242	1	1	CARDINAL
ejpam-753	243	1	1	CARDINAL
ejpam-753	243	2	2	CARDINAL
ejpam-753	244	1	8	CARDINAL
ejpam-753	244	2	12	CARDINAL
ejpam-753	247	1	lemma 2,	ORG
ejpam-753	247	2	i=1 t	PERSON
ejpam-753	247	3	1≤ s ≤ 2	FAC
ejpam-753	249	1	1	CARDINAL
ejpam-753	249	2	1	CARDINAL
ejpam-753	250	1	1 or	CARDINAL
ejpam-753	250	2	2	CARDINAL
ejpam-753	251	1	1	CARDINAL
ejpam-753	252	1	zero	CARDINAL
ejpam-753	253	1	4	CARDINAL
ejpam-753	253	2	zp2	DATE
ejpam-753	253	3	2	CARDINAL
ejpam-753	254	1	2	CARDINAL
ejpam-753	254	2	lemma 2	ORG
ejpam-753	254	3	zero	CARDINAL
ejpam-753	255	1	+ q− 1	DATE
ejpam-753	256	1	4	CARDINAL
ejpam-753	256	2	zp3	GPE
ejpam-753	256	3	3	CARDINAL
ejpam-753	256	4	x2− ǫp	GPE
ejpam-753	256	5	∈ σ0	PERCENT
ejpam-753	256	6	2	CARDINAL
ejpam-753	256	7	2	CARDINAL
ejpam-753	256	8	2	CARDINAL
ejpam-753	257	1	1	CARDINAL
ejpam-753	258	1	ri	GPE
ejpam-753	259	1	1	CARDINAL
ejpam-753	260	1	1	CARDINAL
ejpam-753	261	1	1	CARDINAL
ejpam-753	261	2	1	CARDINAL
ejpam-753	261	3	2	CARDINAL
ejpam-753	261	4	q1− 1	ORG
ejpam-753	262	1	1	CARDINAL
ejpam-753	263	1	1	CARDINAL
ejpam-753	263	2	2	CARDINAL
ejpam-753	264	1	p kn n	PERSON
ejpam-753	264	2	n ≥ 1	DATE
ejpam-753	264	3	1 ≤ ki	QUANTITY
ejpam-753	266	1	0≤ s ≤	FAC
ejpam-753	270	1	ri	GPE
ejpam-753	270	2	j j	PERSON
ejpam-753	270	3	1 ≤ j ≤ n	QUANTITY
ejpam-753	270	4	1 ≤	QUANTITY
ejpam-753	273	1	ri	GPE
ejpam-753	273	2	2	CARDINAL
ejpam-753	273	3	5	CARDINAL
ejpam-753	273	4	1	CARDINAL
ejpam-753	279	1	lemma 2	ORG
ejpam-753	279	2	k ≥ 1	ORG
ejpam-753	279	3	0 ≤	MONEY
ejpam-753	279	4	i=1 ki	PERSON
ejpam-753	281	1	j ≤	FAC
ejpam-753	282	1	1 ≤	QUANTITY
ejpam-753	284	1	1,2,3	CARDINAL
ejpam-753	284	2	4	CARDINAL
ejpam-753	285	1	2	CARDINAL
ejpam-753	285	2	5	CARDINAL
ejpam-753	285	3	1	CARDINAL
ejpam-753	285	4	2	CARDINAL
ejpam-753	286	1	|z(r)|=	ORG
ejpam-753	290	1	1	CARDINAL
ejpam-753	290	2	z4 × z4 ×	ORG
ejpam-753	291	1	zp2	DATE
ejpam-753	291	2	2	CARDINAL
ejpam-753	293	1	1)(q1− 1)(q2− 1	DATE
ejpam-753	295	1	1	CARDINAL
ejpam-753	296	1	one	CARDINAL
ejpam-753	296	2	3	CARDINAL
ejpam-753	298	1	∈ σ0 2	MONEY
ejpam-753	299	1	1)(q1−	CARDINAL
ejpam-753	300	1	1	CARDINAL
ejpam-753	303	1	2−1)(q1−1)(q2−1	CARDINAL
ejpam-753	306	1	m. behboodi	PERSON
ejpam-753	306	2	r. beyranvand	PERSON
ejpam-753	307	1	j. pure	PERSON
ejpam-753	307	2	3	CARDINAL
ejpam-753	307	3	2010	DATE
ejpam-753	307	4	686-694 692	QUANTITY
ejpam-753	307	5	2	CARDINAL
ejpam-753	307	6	3	CARDINAL
ejpam-753	308	1	1)(q1−	CARDINAL
ejpam-753	309	1	1	CARDINAL
ejpam-753	309	2	2	CARDINAL
ejpam-753	309	3	q− 1	DATE
ejpam-753	313	1	2	CARDINAL
ejpam-753	313	2	4	CARDINAL
ejpam-753	313	3	z4 × z4 × f5	ORG
ejpam-753	313	4	2)×z4	PRODUCT
ejpam-753	314	1	z2[x]/(x 2)× z2[x]/(x	MONEY
ejpam-753	315	1	|z(r1)|	ORG
ejpam-753	315	2	t ≥ 1	DATE
ejpam-753	317	1	1	CARDINAL
ejpam-753	318	1	4	CARDINAL
ejpam-753	318	2	zp2	DATE
ejpam-753	318	3	2	CARDINAL
ejpam-753	319	1	1)(q1−	CARDINAL
ejpam-753	320	1	1	CARDINAL
ejpam-753	321	1	2	CARDINAL
ejpam-753	322	1	1	CARDINAL
ejpam-753	323	1	4	CARDINAL
ejpam-753	323	2	one	CARDINAL
ejpam-753	323	3	3	CARDINAL
ejpam-753	323	4	x2− ǫp	GPE
ejpam-753	324	1	∈ σ0 2	MONEY
ejpam-753	326	1	1)(q1	CARDINAL
ejpam-753	328	1	1	CARDINAL
ejpam-753	329	1	8	CARDINAL
ejpam-753	329	2	12	CARDINAL
ejpam-753	331	1	2	CARDINAL
ejpam-753	331	2	1)(q1− 1)(q2− 1	DATE
ejpam-753	332	1	1	CARDINAL
ejpam-753	333	1	3	CARDINAL
ejpam-753	334	1	1	CARDINAL
ejpam-753	335	1	|r1|	LAW
ejpam-753	337	1	2	CARDINAL
ejpam-753	337	2	3	CARDINAL
ejpam-753	340	1	4	CARDINAL
ejpam-753	341	1	1	CARDINAL
ejpam-753	343	1	|r1|	LAW
ejpam-753	343	2	2	CARDINAL
ejpam-753	343	3	lemma 2	ORG
ejpam-753	343	4	q− 1	DATE
ejpam-753	344	1	3	CARDINAL
ejpam-753	345	1	|z(r)|=	ORG
ejpam-753	349	1	z4×z4×f3×f3	ORG
ejpam-753	349	2	2)×z4×f3×f3	MONEY
ejpam-753	349	3	r1 × r2 ×	ORG
ejpam-753	349	4	2	MONEY
ejpam-753	349	5	3	CARDINAL
ejpam-753	349	6	z4[x]/(2x	ORG
ejpam-753	349	7	2ǫ	CARDINAL
ejpam-753	349	8	∈ σ0	PERCENT
ejpam-753	349	9	2	CARDINAL
ejpam-753	349	10	r1 × r2 × fq1 ×	ORG
ejpam-753	350	1	ri	GPE
ejpam-753	350	2	zp2	DATE
ejpam-753	350	3	2	CARDINAL
ejpam-753	353	1	zp2	DATE
ejpam-753	356	1	one	CARDINAL
ejpam-753	356	2	3	CARDINAL
ejpam-753	358	1	∈ σ0 2	MONEY
ejpam-753	364	1	2	CARDINAL
ejpam-753	364	2	1)(q1− 1)(q2− 1	DATE
ejpam-753	365	1	1	CARDINAL
ejpam-753	366	1	2	CARDINAL
ejpam-753	366	2	3	CARDINAL
ejpam-753	368	1	1)(q1	CARDINAL
ejpam-753	370	1	1	CARDINAL
ejpam-753	371	1	2	CARDINAL
ejpam-753	371	2	p3 = pq1q2 .	ORG
ejpam-753	374	1	1	CARDINAL
ejpam-753	375	1	zero	CARDINAL
ejpam-753	375	2	q− 1	DATE
ejpam-753	375	3	m. behboodi	PERSON
ejpam-753	375	4	r. beyranvand	PERSON
ejpam-753	376	1	j. pure	PERSON
ejpam-753	376	2	3	CARDINAL
ejpam-753	376	3	2010	DATE
ejpam-753	376	4	686-694 693	QUANTITY
ejpam-753	377	1	2	MONEY
ejpam-753	377	2	3	CARDINAL
ejpam-753	377	3	z4[x]/(2x	ORG
ejpam-753	377	4	2ǫ	CARDINAL
ejpam-753	377	5	∈ σ0	PERCENT
ejpam-753	377	6	2	CARDINAL
ejpam-753	378	1	2	CARDINAL
ejpam-753	378	2	4	CARDINAL
ejpam-753	378	3	two	CARDINAL
ejpam-753	379	1	1	CARDINAL
ejpam-753	380	1	|z(r1)|	ORG
ejpam-753	381	1	6	DATE
ejpam-753	383	1	1)(q2− 1	CARDINAL
ejpam-753	385	1	1	CARDINAL
ejpam-753	386	1	2	CARDINAL
ejpam-753	387	1	1 ≤	QUANTITY
ejpam-753	387	2	ri	GPE
ejpam-753	387	3	zp2	DATE
ejpam-753	387	4	2	CARDINAL
ejpam-753	388	1	1)2(q1− 1)(q2− 1	DATE
ejpam-753	389	1	1	CARDINAL
ejpam-753	390	1	2	CARDINAL
ejpam-753	390	2	1	CARDINAL
ejpam-753	390	3	2	CARDINAL
ejpam-753	392	1	zp2	DATE
ejpam-753	392	2	2	CARDINAL
ejpam-753	394	1	1)(q1	CARDINAL
ejpam-753	396	1	1	CARDINAL
ejpam-753	397	1	one	CARDINAL
ejpam-753	397	2	3	CARDINAL
ejpam-753	397	3	∈ σ0 2	MONEY
ejpam-753	401	1	qt−(p 2−1)(q1−1)(q2−1	PERSON
ejpam-753	404	1	2	CARDINAL
ejpam-753	404	2	3	CARDINAL
ejpam-753	405	1	1)(q1	CARDINAL
ejpam-753	406	1	1	CARDINAL
ejpam-753	406	2	p3 + p− 1	ORG
ejpam-753	407	1	2	CARDINAL
ejpam-753	407	2	p3 = pq1q2 .	ORG
ejpam-753	409	1	1	CARDINAL
ejpam-753	409	2	+ q− 1	DATE
ejpam-753	409	3	zero	CARDINAL
ejpam-753	410	1	2	CARDINAL
ejpam-753	410	2	2	CARDINAL
ejpam-753	411	1	qt−1	NORP
ejpam-753	412	1	2	CARDINAL
ejpam-753	413	1	1	CARDINAL
ejpam-753	413	2	2	CARDINAL
ejpam-753	414	1	3	CARDINAL
ejpam-753	414	2	2	CARDINAL
ejpam-753	414	3	4	CARDINAL
ejpam-753	415	1	4	CARDINAL
ejpam-753	415	2	2	CARDINAL
ejpam-753	415	3	1	CARDINAL
ejpam-753	416	1	5 or q1 ≥ 3	DATE
ejpam-753	416	2	3	CARDINAL
ejpam-753	417	1	27	CARDINAL
ejpam-753	417	2	5|r1||r2|q2	CARDINAL
ejpam-753	417	3	80q2	CARDINAL
ejpam-753	417	4	27	CARDINAL
ejpam-753	417	5	9|r1||r2|	CARDINAL
ejpam-753	417	6	144	CARDINAL
ejpam-753	419	1	2	CARDINAL
ejpam-753	419	2	2	CARDINAL
ejpam-753	419	3	25	CARDINAL
ejpam-753	419	4	22q1q2−	CARDINAL
ejpam-753	419	5	1)(q2− 1	DATE
ejpam-753	420	1	3	CARDINAL
ejpam-753	420	2	4	DATE
ejpam-753	420	3	25	CARDINAL
ejpam-753	420	4	3q1q2+	DATE
ejpam-753	420	5	1≥ 30	PERCENT
ejpam-753	420	6	36	DATE
ejpam-753	421	1	2	CARDINAL
ejpam-753	422	1	q1−1= 2k1	PERSON
ejpam-753	422	2	q2−1= 2k2	PERSON
ejpam-753	422	3	3	CARDINAL
ejpam-753	423	1	+ 2k2+ 1	DATE
ejpam-753	424	1	3	CARDINAL
ejpam-753	424	2	z2[x]/(x 2	PRODUCT
ejpam-753	425	1	694	CARDINAL
ejpam-753	425	2	iut	ORG
ejpam-753	425	3	ceama	GPE
ejpam-753	426	1	first	ORDINAL
ejpam-753	426	2	87160026	DATE
ejpam-753	427	1	1	CARDINAL
ejpam-753	427	2	al-khamees	PERSON
ejpam-753	427	3	two zero	CARDINAL
ejpam-753	427	4	zero	CARDINAL
ejpam-753	428	1	37	CARDINAL
ejpam-753	428	2	1981	DATE
ejpam-753	428	3	144-149	CARDINAL
ejpam-753	428	4	1981	DATE
ejpam-753	429	1	2	CARDINAL
ejpam-753	429	2	m. behboodi	PERSON
ejpam-753	429	3	r. beyranvand	PERSON
ejpam-753	430	1	kn(1 ≤ ki ≤	PERSON
ejpam-753	430	2	zero	CARDINAL
ejpam-753	431	1	j. pure	PERSON
ejpam-753	432	1	3(2	CARDINAL
ejpam-753	432	2	303	CARDINAL
ejpam-753	432	3	2010	DATE
ejpam-753	433	1	3	CARDINAL
ejpam-753	434	1	27(10	CARDINAL
ejpam-753	434	2	5049-5081	DATE
ejpam-753	435	1	1999	DATE
ejpam-753	436	1	4	CARDINAL
ejpam-753	436	2	williams	PERSON
ejpam-753	436	3	i.	PERSON
ejpam-753	436	4	j. algebra	PERSON
ejpam-753	436	5	231	CARDINAL
ejpam-753	437	1	5	CARDINAL
ejpam-753	437	2	williams	PERSON
ejpam-753	438	1	j. algebra	PERSON
ejpam-753	438	2	231	CARDINAL
ejpam-753	438	3	2000	DATE
ejpam-753	439	1	6	CARDINAL
ejpam-753	439	2	r. gilmer	PERSON
ejpam-753	439	3	zero	CARDINAL
ejpam-753	440	1	american	NORP
ejpam-753	440	2	monthly	DATE
ejpam-753	440	3	93(5	CARDINAL
ejpam-753	440	4	382-387	CARDINAL
ejpam-753	440	5	1986	DATE
ejpam-753	441	1	7	CARDINAL
ejpam-753	441	2	mcdonald	ORG
ejpam-753	441	3	marcell dekker	PERSON
ejpam-753	441	4	new york	GPE
ejpam-753	442	1	1974	DATE
ejpam-753	443	1	8	CARDINAL
ejpam-753	443	2	r. raghavendran	PERSON
ejpam-753	444	1	21	CARDINAL
ejpam-753	444	2	195	CARDINAL
ejpam-753	444	3	1969	DATE
ejpam-753	445	1	9	CARDINAL
ejpam-753	445	2	williams	PERSON
ejpam-753	446	1	38	DATE
ejpam-753	446	2	377	CARDINAL