id	sid	eid	entity	type
ejpam-628	1	1	14_628_behboodi.dvi	CARDINAL
ejpam-628	1	2	european journal	ORG
ejpam-628	2	1	3	CARDINAL
ejpam-628	2	2	2, 2010	DATE
ejpam-628	2	3	303	CARDINAL
ejpam-628	3	1	kn	PERSON
ejpam-628	3	2	zero	CARDINAL
ejpam-628	3	3	m. behboodi1,2∗	PERSON
ejpam-628	3	4	r. beyranvand1	PERSON
ejpam-628	3	5	1	CARDINAL
ejpam-628	3	6	isfahan university of technology	ORG
ejpam-628	3	7	isfahan	GPE
ejpam-628	3	8	iran 2 school of mathematics	EVENT
ejpam-628	3	9	tehran	GPE
ejpam-628	3	10	iran	GPE
ejpam-628	4	1	z(r	DATE
ejpam-628	4	2	zero	CARDINAL
ejpam-628	4	3	r.	NORP
ejpam-628	4	4	1 ≤	QUANTITY
ejpam-628	4	5	1	CARDINAL
ejpam-628	6	1	kn	PERSON
ejpam-628	7	1	j t j	PERSON
ejpam-628	10	1	1 ≤ k ≤ 7	QUANTITY
ejpam-628	12	1	kn	PERSON
ejpam-628	12	2	n ∈ n	ORG
ejpam-628	12	3	1 ≤ ki	QUANTITY
ejpam-628	12	4	4	CARDINAL
ejpam-628	12	5	5	DATE
ejpam-628	13	1	2000	CARDINAL
ejpam-628	13	2	16b99	CARDINAL
ejpam-628	13	3	13a99	CARDINAL
ejpam-628	13	4	68r10	CARDINAL
ejpam-628	13	5	zero	CARDINAL
ejpam-628	13	6	1	CARDINAL
ejpam-628	14	1	j(r	PERSON
ejpam-628	14	2	z(r	DATE
ejpam-628	14	3	zero	CARDINAL
ejpam-628	14	4	r.	NORP
ejpam-628	16	1	zero	CARDINAL
ejpam-628	16	2	γ(r	PERSON
ejpam-628	16	3	zero	CARDINAL
ejpam-628	16	4	two	CARDINAL
ejpam-628	16	5	0	CARDINAL
ejpam-628	17	1	zero	CARDINAL
ejpam-628	19	1	1	CARDINAL
ejpam-628	19	2	γ(r	PERSON
ejpam-628	19	3	1,2,3	CARDINAL
ejpam-628	19	4	4	CARDINAL
ejpam-628	20	1	5	CARDINAL
ejpam-628	20	2	10	CARDINAL
ejpam-628	20	3	6	CARDINAL
ejpam-628	20	4	7	DATE
ejpam-628	22	1	14	CARDINAL
ejpam-628	22	2	11	CARDINAL
ejpam-628	23	1	∗corresponding	PERSON
ejpam-628	25	1	m. behboodi	PERSON
ejpam-628	25	2	r.	NORP
ejpam-628	26	1	303	CARDINAL
ejpam-628	26	2	2010	DATE
ejpam-628	27	1	m. behboodi	PERSON
ejpam-628	27	2	r. beyranvand	PERSON
ejpam-628	28	1	j. pure	PERSON
ejpam-628	28	2	3	CARDINAL
ejpam-628	28	3	2010	DATE
ejpam-628	28	4	303	CARDINAL
ejpam-628	29	1	|z(r)|= p1 k1	PRODUCT
ejpam-628	30	1	kn	PERSON
ejpam-628	31	1	1	CARDINAL
ejpam-628	33	1	1	CARDINAL
ejpam-628	33	2	section 2	LAW
ejpam-628	36	1	|z(r)|=	PRODUCT
ejpam-628	42	1	p1 k1	PRODUCT
ejpam-628	43	1	kn zero	PERSON
ejpam-628	43	2	zero	CARDINAL
ejpam-628	43	3	1 ≤	QUANTITY
ejpam-628	44	1	k ≥ 1	ORG
ejpam-628	45	1	3	CARDINAL
ejpam-628	46	1	section 3	DATE
ejpam-628	46	2	|z(r)|=	ORG
ejpam-628	46	3	1≤ k	FAC
ejpam-628	48	1	|z(r)|= p1 k1	PRODUCT
ejpam-628	49	1	kn	PERSON
ejpam-628	49	2	n ∈ n	ORG
ejpam-628	49	3	1 ≤ ki ≤ 3	QUANTITY
ejpam-628	50	1	|z(r)|=	ORG
ejpam-628	50	2	k = 4 or 5	PERSON
ejpam-628	50	3	2	CARDINAL
ejpam-628	50	4	zero	CARDINAL
ejpam-628	51	1	z(r	DATE
ejpam-628	52	1	2	CARDINAL
ejpam-628	52	2	9	CARDINAL
ejpam-628	53	1	1	CARDINAL
ejpam-628	54	1	9	CARDINAL
ejpam-628	54	2	2	CARDINAL
ejpam-628	55	1	j(r	PERSON
ejpam-628	55	2	0	CARDINAL
ejpam-628	55	3	1≤ k ≤ n	FAC
ejpam-628	55	4	j(r)∼= fq	PERSON
ejpam-628	56	1	ri	GPE
ejpam-628	56	2	1 ≤	QUANTITY
ejpam-628	56	3	zero	CARDINAL
ejpam-628	58	1	.×rs	PERSON
ejpam-628	59	1	6	CARDINAL
ejpam-628	59	2	2	CARDINAL
ejpam-628	59	3	|z(r)|=	PRODUCT
ejpam-628	63	1	1	CARDINAL
ejpam-628	63	2	8	CARDINAL
ejpam-628	64	1	m. behboodi	PERSON
ejpam-628	64	2	r. beyranvand	PERSON
ejpam-628	65	1	j. pure	PERSON
ejpam-628	65	2	3	CARDINAL
ejpam-628	65	3	2010	DATE
ejpam-628	65	4	303	CARDINAL
ejpam-628	65	5	316 305	CARDINAL
ejpam-628	65	6	2	CARDINAL
ejpam-628	68	1	s ∈ n	ORG
ejpam-628	68	2	ri	GPE
ejpam-628	71	1	1	CARDINAL
ejpam-628	72	1	|z(r)|=	PRODUCT
ejpam-628	77	1	two	CARDINAL
ejpam-628	78	1	1	CARDINAL
ejpam-628	83	1	|z(r)|=	PRODUCT
ejpam-628	85	1	1	CARDINAL
ejpam-628	91	1	ks	GPE
ejpam-628	91	2	|z(r)|=	ORG
ejpam-628	95	1	1	CARDINAL
ejpam-628	96	1	1	CARDINAL
ejpam-628	103	1	1	CARDINAL
ejpam-628	106	1	lemma 1	ORG
ejpam-628	106	2	2	CARDINAL
ejpam-628	106	3	2	CARDINAL
ejpam-628	107	1	|z(r)|=	ORG
ejpam-628	112	1	ri	GPE
ejpam-628	117	1	1	CARDINAL
ejpam-628	117	2	i=1 ti =	PERSON
ejpam-628	121	1	1)πs	CARDINAL
ejpam-628	122	1	1	CARDINAL
ejpam-628	123	1	2	CARDINAL
ejpam-628	125	1	2	CARDINAL
ejpam-628	125	2	1	CARDINAL
ejpam-628	127	1	j. moreover	PERSON
ejpam-628	127	2	2	CARDINAL
ejpam-628	127	3	1	CARDINAL
ejpam-628	127	4	q− 1	DATE
ejpam-628	128	1	m. behboodi	PERSON
ejpam-628	128	2	r. beyranvand	PERSON
ejpam-628	129	1	j. pure	PERSON
ejpam-628	129	2	3	CARDINAL
ejpam-628	129	3	2010	DATE
ejpam-628	129	4	303	CARDINAL
ejpam-628	133	1	1 ≤ i ≤ n	QUANTITY
ejpam-628	134	1	1	CARDINAL
ejpam-628	134	2	1	CARDINAL
ejpam-628	138	1	i=1(ki−ti)−	GPE
ejpam-628	138	2	∏	GPE
ejpam-628	138	3	i=1	GPE
ejpam-628	140	1	j ≤ n.	LAW
ejpam-628	140	2	ri	GPE
ejpam-628	148	1	t ≥ 1	DATE
ejpam-628	149	1	∏	CARDINAL
ejpam-628	149	2	i=1	GPE
ejpam-628	150	1	i=1 ki	PERSON
ejpam-628	152	1	i=1 ti)+s	PERSON
ejpam-628	155	1	i=1 ki−	PERSON
ejpam-628	155	2	k−	NORP
ejpam-628	155	3	2	CARDINAL
ejpam-628	156	1	k−	NORP
ejpam-628	158	1	2	CARDINAL
ejpam-628	158	2	i.	PERSON
ejpam-628	158	3	s ≥ 1	DATE
ejpam-628	158	4	1	CARDINAL
ejpam-628	160	1	s.	PERSON
ejpam-628	160	2	j = k− 2	PERSON
ejpam-628	160	3	1	CARDINAL
ejpam-628	162	1	1	CARDINAL
ejpam-628	164	1	|z(r1)|	ORG
ejpam-628	165	1	|z(r)|=	PRODUCT
ejpam-628	165	2	t ≥ 1	DATE
ejpam-628	165	3	1	CARDINAL
ejpam-628	165	4	2	CARDINAL
ejpam-628	166	1	1)(q1−	CARDINAL
ejpam-628	167	1	1	CARDINAL
ejpam-628	170	1	2	CARDINAL
ejpam-628	171	1	1	CARDINAL
ejpam-628	171	2	1	CARDINAL
ejpam-628	172	1	n ≥ 0	ORG
ejpam-628	173	1	4	CARDINAL
ejpam-628	175	1	0	CARDINAL
ejpam-628	175	2	3	CARDINAL
ejpam-628	177	1	|z(r)|=	PRODUCT
ejpam-628	179	1	one	CARDINAL
ejpam-628	179	2	lemma 1	ORG
ejpam-628	181	1	2	CARDINAL
ejpam-628	186	1	m. behboodi	PERSON
ejpam-628	186	2	r. beyranvand	PERSON
ejpam-628	187	1	j. pure	PERSON
ejpam-628	187	2	3	CARDINAL
ejpam-628	187	3	2010	DATE
ejpam-628	187	4	303	CARDINAL
ejpam-628	187	5	316 307	CARDINAL
ejpam-628	189	1	1 ≤	QUANTITY
ejpam-628	192	1	1	CARDINAL
ejpam-628	192	2	i=1 ti =	PERSON
ejpam-628	196	1	1)πs	CARDINAL
ejpam-628	197	1	1	CARDINAL
ejpam-628	200	1	3	CARDINAL
ejpam-628	200	2	p1 k1	PRODUCT
ejpam-628	201	1	zero	CARDINAL
ejpam-628	201	2	1	CARDINAL
ejpam-628	201	3	k ≥ 0	ORG
ejpam-628	202	1	32 zero	CARDINAL
ejpam-628	203	1	zero	CARDINAL
ejpam-628	204	1	k ≤ 7	ORG
ejpam-628	204	2	4	CARDINAL
ejpam-628	206	1	k ≤ 6	FAC
ejpam-628	208	1	1 ≤	QUANTITY
ejpam-628	211	1	1	CARDINAL
ejpam-628	212	1	1 ≤	QUANTITY
ejpam-628	215	1	1)(q2− 1	CARDINAL
ejpam-628	217	1	1	CARDINAL
ejpam-628	217	2	ri	GPE
ejpam-628	217	3	z2[x]/(x 2	PRODUCT
ejpam-628	222	1	2	CARDINAL
ejpam-628	228	1	i=1 ki	PERSON
ejpam-628	229	1	6− 1− 1= 4	TIME
ejpam-628	231	1	3	CARDINAL
ejpam-628	231	2	4	DATE
ejpam-628	231	3	t ≥ 1	DATE
ejpam-628	233	1	1	CARDINAL
ejpam-628	233	2	2	CARDINAL
ejpam-628	234	1	2	CARDINAL
ejpam-628	236	1	1	CARDINAL
ejpam-628	236	2	2	CARDINAL
ejpam-628	236	3	t ≥ 1	DATE
ejpam-628	237	1	2	CARDINAL
ejpam-628	238	1	+2	DATE
ejpam-628	239	1	2	CARDINAL
ejpam-628	239	2	1 or	CARDINAL
ejpam-628	239	3	1	CARDINAL
ejpam-628	239	4	m. behboodi	PERSON
ejpam-628	239	5	r. beyranvand	PERSON
ejpam-628	240	1	j. pure	PERSON
ejpam-628	240	2	3	CARDINAL
ejpam-628	240	3	2010	DATE
ejpam-628	240	4	303	CARDINAL
ejpam-628	240	5	1	CARDINAL
ejpam-628	240	6	2	CARDINAL
ejpam-628	240	7	1 i.e.	DATE
ejpam-628	240	8	|z(r1)|	ORG
ejpam-628	240	9	|z(r2)|=	ORG
ejpam-628	241	1	1	CARDINAL
ejpam-628	241	2	|r1|	PRODUCT
ejpam-628	243	1	|r1|	LAW
ejpam-628	243	2	k = 6	PERSON
ejpam-628	244	1	1	CARDINAL
ejpam-628	244	2	2	CARDINAL
ejpam-628	245	1	1	CARDINAL
ejpam-628	245	2	2	CARDINAL
ejpam-628	247	1	1)2(q1− 1	DATE
ejpam-628	249	1	p2+2p−1	ORG
ejpam-628	249	2	2p−1	CARDINAL
ejpam-628	250	1	2p− 1	DATE
ejpam-628	250	2	1	CARDINAL
ejpam-628	250	3	1	CARDINAL
ejpam-628	251	1	•	CARDINAL
ejpam-628	251	2	2	CARDINAL
ejpam-628	251	3	1 i.e.	DATE
ejpam-628	251	4	|z(r1)|	ORG
ejpam-628	252	1	k ≥ 5	ORG
ejpam-628	253	1	t ≥ 3	DATE
ejpam-628	253	2	2	CARDINAL
ejpam-628	253	3	1)(q	CARDINAL
ejpam-628	253	4	some 1≤	CARDINAL
ejpam-628	255	1	t ≤ 2	DATE
ejpam-628	256	1	1	CARDINAL
ejpam-628	257	1	2	CARDINAL
ejpam-628	257	2	2	CARDINAL
ejpam-628	257	3	1)2(q1− 1)(q2− 1	DATE
ejpam-628	258	1	3	CARDINAL
ejpam-628	258	2	k ≥ 5	DATE
ejpam-628	258	3	1)(q2− 1	DATE
ejpam-628	262	1	1	CARDINAL
ejpam-628	263	1	one	CARDINAL
ejpam-628	263	2	3	CARDINAL
ejpam-628	263	3	k1p+ 1)(k2p+	ORG
ejpam-628	264	1	1)2k1k2	DATE
ejpam-628	264	2	pk−4−	DATE
ejpam-628	264	3	k1k2	NORP
ejpam-628	264	4	1=	ORDINAL
ejpam-628	265	1	5	CARDINAL
ejpam-628	267	1	6	CARDINAL
ejpam-628	268	1	k1k2	NORP
ejpam-628	268	2	1=	ORDINAL
ejpam-628	269	1	4	CARDINAL
ejpam-628	269	2	4	CARDINAL
ejpam-628	269	3	2−	TIME
ejpam-628	270	1	1=	ORDINAL
ejpam-628	271	1	5	CARDINAL
ejpam-628	271	2	5	CARDINAL
ejpam-628	272	1	6= 1	DATE
ejpam-628	273	1	1	CARDINAL
ejpam-628	273	2	0	CARDINAL
ejpam-628	275	1	k1k2	NORP
ejpam-628	275	2	1	CARDINAL
ejpam-628	275	3	1	CARDINAL
ejpam-628	276	1	1	CARDINAL
ejpam-628	276	2	1)2(q1	CARDINAL
ejpam-628	277	1	1	CARDINAL
ejpam-628	277	2	1	CARDINAL
ejpam-628	277	3	− p2 +	PERSON
ejpam-628	278	1	1	CARDINAL
ejpam-628	279	1	2p− 1	DATE
ejpam-628	279	2	1	CARDINAL
ejpam-628	279	3	1	CARDINAL
ejpam-628	279	4	2p−1)a	CARDINAL
ejpam-628	279	5	integer a.	PERSON
ejpam-628	280	1	2ax	PRODUCT
ejpam-628	282	1	2a	CARDINAL
ejpam-628	283	1	1	CARDINAL
ejpam-628	283	2	1	CARDINAL
ejpam-628	283	3	0	CARDINAL
ejpam-628	284	1	1	CARDINAL
ejpam-628	285	1	m. behboodi	PERSON
ejpam-628	285	2	r. beyranvand	PERSON
ejpam-628	286	1	j. pure	PERSON
ejpam-628	286	2	3	CARDINAL
ejpam-628	286	3	2010	DATE
ejpam-628	286	4	303	CARDINAL
ejpam-628	286	5	2	CARDINAL
ejpam-628	286	6	5	CARDINAL
ejpam-628	286	7	4	CARDINAL
ejpam-628	286	8	2 zero	CARDINAL
ejpam-628	287	1	2	CARDINAL
ejpam-628	287	2	687	CARDINAL
ejpam-628	287	3	ri	GPE
ejpam-628	287	4	z2[x]/(x 2	PRODUCT
ejpam-628	288	1	1	CARDINAL
ejpam-628	290	1	2	CARDINAL
ejpam-628	293	1	1	CARDINAL
ejpam-628	295	1	1	CARDINAL
ejpam-628	295	2	2	CARDINAL
ejpam-628	295	3	687	CARDINAL
ejpam-628	295	4	zp2	DATE
ejpam-628	295	5	2	CARDINAL
ejpam-628	296	1	4	CARDINAL
ejpam-628	298	1	2	CARDINAL
ejpam-628	300	1	1	CARDINAL
ejpam-628	301	1	5	CARDINAL
ejpam-628	301	2	zero	CARDINAL
ejpam-628	302	1	= m2	PERSON
ejpam-628	302	2	1	CARDINAL
ejpam-628	302	3	4	CARDINAL
ejpam-628	302	4	two	CARDINAL
ejpam-628	303	1	1	CARDINAL
ejpam-628	303	2	only two	CARDINAL
ejpam-628	304	1	second	ORDINAL
ejpam-628	304	2	4	CARDINAL
ejpam-628	304	3	9	CARDINAL
ejpam-628	306	1	f∗p	GPE
ejpam-628	306	2	σ0	GPE
ejpam-628	306	3	0	CARDINAL
ejpam-628	307	1	f∗p	ORG
ejpam-628	307	2	1	CARDINAL
ejpam-628	308	1	2	CARDINAL
ejpam-628	310	1	3	CARDINAL
ejpam-628	311	1	∈ σ0	PERCENT
ejpam-628	311	2	2	CARDINAL
ejpam-628	311	3	the galois ring gr(p4	ORG
ejpam-628	312	1	t ≥ 2	DATE
ejpam-628	314	1	1	CARDINAL
ejpam-628	317	1	1	CARDINAL
ejpam-628	318	1	2	CARDINAL
ejpam-628	318	2	3	CARDINAL
ejpam-628	319	1	∈ σ0	PERCENT
ejpam-628	319	2	2	CARDINAL
ejpam-628	319	3	9	CARDINAL
ejpam-628	319	4	12	CARDINAL
ejpam-628	319	5	the galois ring gr(p4	ORG
ejpam-628	321	1	2	CARDINAL
ejpam-628	323	1	qt−	PERSON
ejpam-628	325	1	abelian	NORP
ejpam-628	328	1	∑ k=1 wi	PERSON
ejpam-628	328	2	wi	ORG
ejpam-628	328	3	∈	ORG
ejpam-628	328	4	wi	ORG
ejpam-628	328	5	1≤	DATE
ejpam-628	332	1	two	CARDINAL
ejpam-628	332	2	m. behboodi	PERSON
ejpam-628	332	3	r. beyranvand	PERSON
ejpam-628	333	1	j. pure	PERSON
ejpam-628	333	2	3	CARDINAL
ejpam-628	333	3	2010	DATE
ejpam-628	333	4	303	CARDINAL
ejpam-628	334	1	1	CARDINAL
ejpam-628	334	2	∑n k=1 wi	PERSON
ejpam-628	334	3	wi	ORG
ejpam-628	334	4	∈	ORG
ejpam-628	334	5	j ≤ n.	PERSON
ejpam-628	337	1	aia j =	PERSON
ejpam-628	338	1	∑ k=1 wi	PERSON
ejpam-628	338	2	1	CARDINAL
ejpam-628	341	1	3	CARDINAL
ejpam-628	342	1	|z(r)|=	PRODUCT
ejpam-628	343	1	zp2× fq	PERSON
ejpam-628	343	2	2)× fq	QUANTITY
ejpam-628	347	1	1	CARDINAL
ejpam-628	347	2	4	CARDINAL
ejpam-628	347	3	x3	GPE
ejpam-628	347	4	zp2[x]/(x2	CARDINAL
ejpam-628	347	5	∈	ORG
ejpam-628	348	1	∈	ORG
ejpam-628	348	2	2	CARDINAL
ejpam-628	348	3	2	CARDINAL
ejpam-628	348	4	2	CARDINAL
ejpam-628	348	5	2	CARDINAL
ejpam-628	348	6	2x	CARDINAL
ejpam-628	348	7	2	CARDINAL
ejpam-628	348	8	zp2[x	GPE
ejpam-628	348	9	z)2	PERSON
ejpam-628	348	10	cp2	PERSON
ejpam-628	348	11	∈ σ0	PERCENT
ejpam-628	348	12	2	CARDINAL
ejpam-628	348	13	z4[x]/(x	ORG
ejpam-628	348	14	zp4	PERSON
ejpam-628	348	15	〈1	PERSON
ejpam-628	348	16	0	CARDINAL
ejpam-628	348	17	2	CARDINAL
ejpam-628	348	18	j〉	PERSON
ejpam-628	348	19	〈1	PERSON
ejpam-628	348	20	0	CARDINAL
ejpam-628	348	21	j〉	PERSON
ejpam-628	348	22	〈1	PERSON
ejpam-628	348	23	0	CARDINAL
ejpam-628	348	24	2	CARDINAL
ejpam-628	348	25	j〉	PERSON
ejpam-628	348	26	〈1	PERSON
ejpam-628	348	27	2	CARDINAL
ejpam-628	348	28	2	CARDINAL
ejpam-628	348	29	0	CARDINAL
ejpam-628	353	1	〈1	PERSON
ejpam-628	353	2	2	CARDINAL
ejpam-628	353	3	2	CARDINAL
ejpam-628	353	4	0	CARDINAL
ejpam-628	355	1	〈1	PERSON
ejpam-628	355	2	2	CARDINAL
ejpam-628	355	3	2	CARDINAL
ejpam-628	357	1	〈1	PERSON
ejpam-628	357	2	2	CARDINAL
ejpam-628	357	3	2	CARDINAL
ejpam-628	358	1	2	CARDINAL
ejpam-628	358	2	〈1	PERSON
ejpam-628	358	3	4.1= 2x1	CARDINAL
ejpam-628	359	1	0	CARDINAL
ejpam-628	359	2	2	CARDINAL
ejpam-628	359	3	0	CARDINAL
ejpam-628	359	4	2	CARDINAL
ejpam-628	359	5	0	CARDINAL
ejpam-628	361	1	2	CARDINAL
ejpam-628	361	2	〈1	PERSON
ejpam-628	361	3	2.1	CARDINAL
ejpam-628	361	4	0	CARDINAL
ejpam-628	363	1	2	CARDINAL
ejpam-628	363	2	2	CARDINAL
ejpam-628	368	1	1	CARDINAL
ejpam-628	369	1	9	CARDINAL
ejpam-628	369	2	12	CARDINAL
ejpam-628	370	1	2	CARDINAL
ejpam-628	372	1	2	CARDINAL
ejpam-628	373	1	2)× fq	QUANTITY
ejpam-628	374	1	1	CARDINAL
ejpam-628	378	1	1	CARDINAL
ejpam-628	380	1	1	CARDINAL
ejpam-628	380	2	2	CARDINAL
ejpam-628	381	1	p kn n	PERSON
ejpam-628	381	2	ki ≤ 3	LAW
ejpam-628	382	1	5	CARDINAL
ejpam-628	383	1	1	CARDINAL
ejpam-628	383	2	2	CARDINAL
ejpam-628	384	1	p kn n	PERSON
ejpam-628	384	2	n ≥ 1	DATE
ejpam-628	384	3	1 ≤ ki	QUANTITY
ejpam-628	386	1	0≤ s ≤	FAC
ejpam-628	390	1	m. behboodi	PERSON
ejpam-628	390	2	r. beyranvand	PERSON
ejpam-628	391	1	j. pure	PERSON
ejpam-628	391	2	3	CARDINAL
ejpam-628	391	3	2010	DATE
ejpam-628	391	4	303	CARDINAL
ejpam-628	391	5	316 311	CARDINAL
ejpam-628	391	6	ri	GPE
ejpam-628	391	7	j j	PERSON
ejpam-628	391	8	1 ≤ j ≤ n	QUANTITY
ejpam-628	391	9	1 ≤	QUANTITY
ejpam-628	392	1	k j. consequently	PERSON
ejpam-628	392	2	ri	GPE
ejpam-628	392	3	1	CARDINAL
ejpam-628	392	4	2	CARDINAL
ejpam-628	392	5	3	CARDINAL
ejpam-628	399	1	0	CARDINAL
ejpam-628	400	1	1	CARDINAL
ejpam-628	400	2	k ≥ 1	ORG
ejpam-628	401	1	|z(ri)|= p	ORG
ejpam-628	402	1	j ≤ k j	FAC
ejpam-628	402	2	1≤	FAC
ejpam-628	402	3	j ≤ n and	LAW
ejpam-628	402	4	1 ≤	QUANTITY
ejpam-628	404	1	1,2	CARDINAL
ejpam-628	404	2	3	CARDINAL
ejpam-628	405	1	1	CARDINAL
ejpam-628	405	2	2	CARDINAL
ejpam-628	405	3	3	CARDINAL
ejpam-628	405	4	|z(r)|=	PRODUCT
ejpam-628	410	1	qt−(q1−1)(q2−1	PERSON
ejpam-628	414	1	zp2	DATE
ejpam-628	414	2	2	CARDINAL
ejpam-628	414	3	p3 = pq1q2 .	ORG
ejpam-628	416	1	q− 1	DATE
ejpam-628	416	2	2	CARDINAL
ejpam-628	417	1	4	CARDINAL
ejpam-628	418	1	|z(r1)|	ORG
ejpam-628	418	2	t ≥ 1	DATE
ejpam-628	420	1	•	CARDINAL
ejpam-628	420	2	1	CARDINAL
ejpam-628	424	1	1	CARDINAL
ejpam-628	425	1	•	CARDINAL
ejpam-628	425	2	2	CARDINAL
ejpam-628	425	3	|z(r1)|	ORG
ejpam-628	426	1	1	CARDINAL
ejpam-628	426	2	zp2	DATE
ejpam-628	426	3	2	CARDINAL
ejpam-628	426	4	p3 = pq1q2 .	ORG
ejpam-628	427	1	1)(q1−	CARDINAL
ejpam-628	428	1	1	CARDINAL
ejpam-628	429	1	•	CARDINAL
ejpam-628	429	2	3	CARDINAL
ejpam-628	429	3	|z(r1)|	ORG
ejpam-628	430	1	1	CARDINAL
ejpam-628	430	2	|r1|	PRODUCT
ejpam-628	431	1	t ≥ 1	DATE
ejpam-628	431	2	2	CARDINAL
ejpam-628	431	3	3	CARDINAL
ejpam-628	431	4	zp3	CARDINAL
ejpam-628	431	5	∈ σ0 2	MONEY
ejpam-628	431	6	q− 1	DATE
ejpam-628	431	7	2	CARDINAL
ejpam-628	436	1	1	CARDINAL
ejpam-628	437	1	zp2	DATE
ejpam-628	437	2	2	CARDINAL
ejpam-628	439	1	1)(q1− 1)(q2− 1	DATE
ejpam-628	441	1	1	CARDINAL
ejpam-628	441	2	m. behboodi	PERSON
ejpam-628	441	3	r. beyranvand	PERSON
ejpam-628	442	1	j. pure	PERSON
ejpam-628	442	2	3	CARDINAL
ejpam-628	442	3	2010	DATE
ejpam-628	442	4	303	CARDINAL
ejpam-628	442	5	316 312	CARDINAL
ejpam-628	443	1	3	CARDINAL
ejpam-628	443	2	x2− ǫp	GPE
ejpam-628	444	1	∈ σ0 2	MONEY
ejpam-628	444	2	p3 = pq1q2	ORG
ejpam-628	445	1	1)(q1−	CARDINAL
ejpam-628	446	1	1	CARDINAL
ejpam-628	446	2	+ q− 1	DATE
ejpam-628	446	3	q− 1	DATE
ejpam-628	446	4	3	CARDINAL
ejpam-628	448	1	4	CARDINAL
ejpam-628	449	1	|z(r1)|	ORG
ejpam-628	449	2	t ≥ 1	DATE
ejpam-628	451	1	•	CARDINAL
ejpam-628	451	2	1	CARDINAL
ejpam-628	454	1	1)(q2− 1	DATE
ejpam-628	455	1	1	CARDINAL
ejpam-628	455	2	•	CARDINAL
ejpam-628	457	1	2	CARDINAL
ejpam-628	457	2	|z(r1)|	ORG
ejpam-628	458	1	1	CARDINAL
ejpam-628	458	2	zp2	DATE
ejpam-628	458	3	2	CARDINAL
ejpam-628	459	1	1)(q1−	CARDINAL
ejpam-628	460	1	1	CARDINAL
ejpam-628	461	1	•	CARDINAL
ejpam-628	461	2	3	CARDINAL
ejpam-628	461	3	|z(r1)|	ORG
ejpam-628	462	1	1	CARDINAL
ejpam-628	463	1	2	CARDINAL
ejpam-628	463	2	zp3	PRODUCT
ejpam-628	463	3	3	CARDINAL
ejpam-628	463	4	x2− ǫp	GPE
ejpam-628	464	1	∈ σ0 2	MONEY
ejpam-628	464	2	p3 = pq1q2	ORG
ejpam-628	465	1	1)(q1−	CARDINAL
ejpam-628	466	1	1	CARDINAL
ejpam-628	467	1	1	CARDINAL
ejpam-628	467	2	2	CARDINAL
ejpam-628	468	1	1	CARDINAL
ejpam-628	469	1	+ q− 1	DATE
ejpam-628	470	1	9	CARDINAL
ejpam-628	470	2	12	CARDINAL
ejpam-628	471	1	•	CARDINAL
ejpam-628	471	2	4	CARDINAL
ejpam-628	471	3	|z(r1)|	ORG
ejpam-628	472	1	1	CARDINAL
ejpam-628	473	1	|r1|	LAW
ejpam-628	473	2	t ≥ 1	DATE
ejpam-628	474	1	2	CARDINAL
ejpam-628	474	2	1	CARDINAL
ejpam-628	477	1	1	CARDINAL
ejpam-628	478	1	|z(r1)|	ORG
ejpam-628	478	2	3	CARDINAL
ejpam-628	479	1	zero	CARDINAL
ejpam-628	480	1	6	CARDINAL
ejpam-628	483	1	1 ≤	QUANTITY
ejpam-628	486	1	1	CARDINAL
ejpam-628	487	1	1 ≤	QUANTITY
ejpam-628	487	2	|z(r1)|	ORG
ejpam-628	488	1	6	DATE
ejpam-628	490	1	1)(q2− 1	CARDINAL
ejpam-628	492	1	1	CARDINAL
ejpam-628	492	2	m. behboodi	PERSON
ejpam-628	492	3	r. beyranvand	PERSON
ejpam-628	493	1	j. pure	PERSON
ejpam-628	493	2	3	CARDINAL
ejpam-628	493	3	2010	DATE
ejpam-628	493	4	303	CARDINAL
ejpam-628	494	1	1 ≤	QUANTITY
ejpam-628	494	2	ri	GPE
ejpam-628	494	3	zp2	DATE
ejpam-628	494	4	2	CARDINAL
ejpam-628	495	1	1)2(q1− 1)(q2− 1	DATE
ejpam-628	496	1	1	CARDINAL
ejpam-628	496	2	z2[x]/(x 2	PRODUCT
ejpam-628	496	3	z4[x]/(2x	ORG
ejpam-628	496	4	2ǫ	CARDINAL
ejpam-628	496	5	∈ σ0	PERCENT
ejpam-628	496	6	2	CARDINAL
ejpam-628	500	1	2	CARDINAL
ejpam-628	503	1	|z(ri)|= pti	GPE
ejpam-628	506	1	i=1 ki	PERSON
ejpam-628	507	1	1≤	CARDINAL
ejpam-628	507	2	1− 1= 5	DATE
ejpam-628	509	1	1 or	CARDINAL
ejpam-628	509	2	2	CARDINAL
ejpam-628	509	3	4	CARDINAL
ejpam-628	509	4	3	CARDINAL
ejpam-628	510	1	4	CARDINAL
ejpam-628	511	1	3	CARDINAL
ejpam-628	512	1	2	CARDINAL
ejpam-628	513	1	1,2,3	CARDINAL
ejpam-628	513	2	1	CARDINAL
ejpam-628	513	3	1	CARDINAL
ejpam-628	515	1	2	CARDINAL
ejpam-628	515	2	1)(q2− 1	DATE
ejpam-628	517	1	1	CARDINAL
ejpam-628	519	1	1)3(q1	CARDINAL
ejpam-628	519	2	1)(q2− 1	DATE
ejpam-628	520	1	1	CARDINAL
ejpam-628	521	1	2	CARDINAL
ejpam-628	522	1	1	CARDINAL
ejpam-628	523	1	1)3(q1	CARDINAL
ejpam-628	523	2	1	CARDINAL
ejpam-628	525	1	s ≤ 2	ORG
ejpam-628	525	2	1	CARDINAL
ejpam-628	527	1	2	CARDINAL
ejpam-628	528	1	1,2,3	CARDINAL
ejpam-628	528	2	4	CARDINAL
ejpam-628	530	1	1)×	CARDINAL
ejpam-628	531	1	1	CARDINAL
ejpam-628	531	2	|r1|	PRODUCT
ejpam-628	531	3	|z(r1)|	ORG
ejpam-628	533	1	2	CARDINAL
ejpam-628	535	1	•	CARDINAL
ejpam-628	535	2	1	CARDINAL
ejpam-628	535	3	3	CARDINAL
ejpam-628	535	4	3	CARDINAL
ejpam-628	535	5	3	CARDINAL
ejpam-628	537	1	5	CARDINAL
ejpam-628	538	1	4	CARDINAL
ejpam-628	538	2	2	CARDINAL
ejpam-628	538	3	2	CARDINAL
ejpam-628	538	4	t ≥ 2	DATE
ejpam-628	539	1	1	CARDINAL
ejpam-628	539	2	4	CARDINAL
ejpam-628	539	3	1	CARDINAL
ejpam-628	542	1	m. behboodi	PERSON
ejpam-628	542	2	r. beyranvand	PERSON
ejpam-628	543	1	j. pure	PERSON
ejpam-628	543	2	3	CARDINAL
ejpam-628	543	3	2010	DATE
ejpam-628	543	4	303	CARDINAL
ejpam-628	543	5	2	CARDINAL
ejpam-628	543	6	2 i.e.	DATE
ejpam-628	543	7	|z(r1)|	ORG
ejpam-628	544	1	1	CARDINAL
ejpam-628	544	2	3 ≤ k1	QUANTITY
ejpam-628	545	1	4	CARDINAL
ejpam-628	545	2	4	CARDINAL
ejpam-628	546	1	3	CARDINAL
ejpam-628	546	2	2	CARDINAL
ejpam-628	546	3	t ≥ 2	DATE
ejpam-628	547	1	1	CARDINAL
ejpam-628	547	2	3−	CARDINAL
ejpam-628	547	3	1	CARDINAL
ejpam-628	548	1	q1− 1	PERSON
ejpam-628	550	1	•	CARDINAL
ejpam-628	550	2	3	CARDINAL
ejpam-628	550	3	2	CARDINAL
ejpam-628	550	4	1	CARDINAL
ejpam-628	550	5	1	CARDINAL
ejpam-628	550	6	2	CARDINAL
ejpam-628	550	7	2	CARDINAL
ejpam-628	550	8	1	CARDINAL
ejpam-628	550	9	lemma 1	ORG
ejpam-628	550	10	|r1|	PRODUCT
ejpam-628	551	1	1	CARDINAL
ejpam-628	551	2	6=	CARDINAL
ejpam-628	552	1	|r1|	LAW
ejpam-628	552	2	2	CARDINAL
ejpam-628	552	3	2	CARDINAL
ejpam-628	553	1	1)2(q1− 1)(q2− 1	DATE
ejpam-628	554	1	1	CARDINAL
ejpam-628	555	1	6	CARDINAL
ejpam-628	557	1	1	CARDINAL
ejpam-628	558	1	1	CARDINAL
ejpam-628	559	1	2	CARDINAL
ejpam-628	560	1	t ≤ 2	DATE
ejpam-628	561	1	1	CARDINAL
ejpam-628	561	2	1 i.e.	CARDINAL
ejpam-628	561	3	r2 ×	ORG
ejpam-628	563	1	6	CARDINAL
ejpam-628	563	2	1)2(q1− 1	DATE
ejpam-628	564	1	7	CARDINAL
ejpam-628	565	1	integer k	PERSON
ejpam-628	565	2	7	CARDINAL
ejpam-628	566	1	k − 1, i.e.	ORG
ejpam-628	566	2	k − 1	PERSON
ejpam-628	567	1	x2 −	ORG
ejpam-628	567	2	2kx	ORDINAL
ejpam-628	569	1	2k	CARDINAL
ejpam-628	570	1	1	CARDINAL
ejpam-628	571	1	1	CARDINAL
ejpam-628	572	1	2k	CARDINAL
ejpam-628	573	1	1	CARDINAL
ejpam-628	574	1	2	CARDINAL
ejpam-628	574	2	5	CARDINAL
ejpam-628	574	3	8	CARDINAL
ejpam-628	574	4	4	CARDINAL
ejpam-628	575	1	4	CARDINAL
ejpam-628	575	2	2	CARDINAL
ejpam-628	575	3	z4[x]/(2x	ORG
ejpam-628	575	4	2ǫ	CARDINAL
ejpam-628	575	5	∈ σ0	PERCENT
ejpam-628	575	6	2	CARDINAL
ejpam-628	576	1	r2	ORG
ejpam-628	576	2	z2[x]/(x 2	PRODUCT
ejpam-628	577	1	2	CARDINAL
ejpam-628	577	2	2 i.e.	DATE
ejpam-628	577	3	r2 ×	ORG
ejpam-628	579	1	6	CARDINAL
ejpam-628	579	2	1)2(q1− 1)(q2− 1	DATE
ejpam-628	581	1	q1− 1	ORG
ejpam-628	581	2	1	CARDINAL
ejpam-628	581	3	1 or	CARDINAL
ejpam-628	581	4	2	DATE
ejpam-628	583	1	1	CARDINAL
ejpam-628	584	1	one	CARDINAL
ejpam-628	584	2	6	CARDINAL
ejpam-628	585	1	k1p+ 1)(k2p+ 1)−	ORG
ejpam-628	585	2	1)2k1k2	DATE
ejpam-628	586	1	k1k2	NORP
ejpam-628	586	2	1=	ORDINAL
ejpam-628	587	1	8)	CARDINAL
ejpam-628	587	2	315	CARDINAL
ejpam-628	587	3	8)	CARDINAL
ejpam-628	587	4	2−	TIME
ejpam-628	588	1	1=	ORDINAL
ejpam-628	589	1	9	CARDINAL
ejpam-628	589	2	9	CARDINAL
ejpam-628	590	1	6= 1	DATE
ejpam-628	591	1	1	CARDINAL
ejpam-628	591	2	0	CARDINAL
ejpam-628	592	1	k1k2	NORP
ejpam-628	592	2	1	CARDINAL
ejpam-628	592	3	1	CARDINAL
ejpam-628	593	1	•	CARDINAL
ejpam-628	593	2	4	CARDINAL
ejpam-628	593	3	1 i.e.	DATE
ejpam-628	593	4	|z(r1)|	ORG
ejpam-628	596	1	1)(q1	CARDINAL
ejpam-628	598	1	1	CARDINAL
ejpam-628	599	1	2	CARDINAL
ejpam-628	599	2	zp2	DATE
ejpam-628	599	3	2	CARDINAL
ejpam-628	600	1	p1 k1	PRODUCT
ejpam-628	601	1	kn zero	PERSON
ejpam-628	601	2	1	CARDINAL
ejpam-628	602	1	1	CARDINAL
ejpam-628	602	2	2	CARDINAL
ejpam-628	602	3	p1 k1	PRODUCT
ejpam-628	603	1	kn zero	PERSON
ejpam-628	603	2	1 ≤ ki ≤ 5	QUANTITY
ejpam-628	603	3	|z(r)|=	PRODUCT
ejpam-628	603	4	|z(r)|=	ORG
ejpam-628	604	1	|z(r)|=	PRODUCT
ejpam-628	604	2	1	CARDINAL
ejpam-628	605	1	3	CARDINAL
ejpam-628	606	1	9	CARDINAL
ejpam-628	606	2	12	CARDINAL
ejpam-628	607	1	|z(r)|=	ORG
ejpam-628	607	2	1	CARDINAL
ejpam-628	608	1	9	CARDINAL
ejpam-628	608	2	12	CARDINAL
ejpam-628	609	1	iut	ORG
ejpam-628	609	2	ceama	GPE
ejpam-628	610	1	first	ORDINAL
ejpam-628	610	2	87160026	DATE
ejpam-628	611	1	1	CARDINAL
ejpam-628	611	2	anderson	PERSON
ejpam-628	611	3	a. farzier	PERSON
ejpam-628	611	4	a. lauve	PERSON
ejpam-628	611	5	livingston	PERSON
ejpam-628	611	6	zero	CARDINAL
ejpam-628	611	7	ii	ORG
ejpam-628	612	1	202	CARDINAL
ejpam-628	612	2	2001	DATE
ejpam-628	612	3	61-72	DATE
ejpam-628	612	4	marcel dekker	PERSON
ejpam-628	612	5	new york	GPE
ejpam-628	613	1	2	CARDINAL
ejpam-628	613	2	williams	PERSON
ejpam-628	613	3	i.	PERSON
ejpam-628	613	4	j. algebra	PERSON
ejpam-628	613	5	231	CARDINAL
ejpam-628	613	6	677	CARDINAL
ejpam-628	614	1	3	CARDINAL
ejpam-628	614	2	williams	PERSON
ejpam-628	615	1	j. algebra	PERSON
ejpam-628	615	2	231	CARDINAL
ejpam-628	615	3	691	CARDINAL
ejpam-628	616	1	4	CARDINAL
ejpam-628	616	2	zero	CARDINAL
ejpam-628	617	1	ann	PERSON
ejpam-628	618	1	181	CARDINAL
ejpam-628	618	2	1	CARDINAL
ejpam-628	618	3	1969	DATE
ejpam-628	619	1	5	CARDINAL
ejpam-628	619	2	n. ganesan	PERSON
ejpam-628	619	3	zero	CARDINAL
ejpam-628	620	1	ann	PERSON
ejpam-628	621	1	157 (1964	DATE
ejpam-628	622	1	215ű218	CARDINAL
ejpam-628	623	1	6	CARDINAL
ejpam-628	623	2	r. gilmer	PERSON
ejpam-628	623	3	zero	CARDINAL
ejpam-628	624	1	american	NORP
ejpam-628	624	2	monthly	DATE
ejpam-628	624	3	93	CARDINAL
ejpam-628	624	4	5	CARDINAL
ejpam-628	624	5	1986	DATE
ejpam-628	624	6	382	CARDINAL
ejpam-628	624	7	316	CARDINAL
ejpam-628	625	1	7	CARDINAL
ejpam-628	625	2	k. koh	PERSON
ejpam-628	625	3	zero	CARDINAL
ejpam-628	626	1	ann	PERSON
ejpam-628	627	1	171	CARDINAL
ejpam-628	627	2	1967	DATE
ejpam-628	627	3	79-80	DATE
ejpam-628	628	1	8	CARDINAL
ejpam-628	628	2	mcdonald	ORG
ejpam-628	628	3	marcell dekker	PERSON
ejpam-628	628	4	new york	GPE
ejpam-628	628	5	1974	DATE
ejpam-628	629	1	9	CARDINAL
ejpam-628	629	2	r. raghavendran	PERSON
ejpam-628	630	1	21	CARDINAL
ejpam-628	630	2	1969	DATE
ejpam-628	630	3	195	CARDINAL
ejpam-628	631	1	10	CARDINAL
ejpam-628	631	2	redmond	GPE
ejpam-628	631	3	zero	CARDINAL
ejpam-628	632	1	31	CARDINAL
ejpam-628	632	2	2003	DATE
ejpam-628	632	3	4425-4443	ORG
ejpam-628	633	1	11	CARDINAL
ejpam-628	633	2	redmond	GPE
ejpam-628	633	3	zero	CARDINAL
ejpam-628	635	1	307	CARDINAL
ejpam-628	635	2	2007	DATE