id	sid	eid	entity	type
ejpam-3182	1	1	european journal	ORG
ejpam-3182	2	1	11	CARDINAL
ejpam-3182	2	2	1, 2018	DATE
ejpam-3182	2	3	23	CARDINAL
ejpam-3182	2	4	new york	GPE
ejpam-3182	2	5	n. a. carella department	PERSON
ejpam-3182	2	6	mathematics, york college	ORG
ejpam-3182	2	7	jamaica	GPE
ejpam-3182	2	8	new york	GPE
ejpam-3182	2	9	10451	DATE
ejpam-3182	3	1	2	CARDINAL
ejpam-3182	4	1	2010	DATE
ejpam-3182	4	2	11a07, 11n05	DATE
ejpam-3182	5	1	1	CARDINAL
ejpam-3182	6	1	2	CARDINAL
ejpam-3182	6	2	riemann hypothesis	PERSON
ejpam-3182	7	1	multiplicative	ORG
ejpam-3182	7	2	2	CARDINAL
ejpam-3182	8	1	1.1	CARDINAL
ejpam-3182	8	2	2	CARDINAL
ejpam-3182	8	3	2	CARDINAL
ejpam-3182	9	1	3	CARDINAL
ejpam-3182	9	2	5	DATE
ejpam-3182	9	3	11	DATE
ejpam-3182	9	4	13	DATE
ejpam-3182	9	5	19	DATE
ejpam-3182	9	6	29	DATE
ejpam-3182	9	7	37	DATE
ejpam-3182	9	8	53	DATE
ejpam-3182	9	9	59	DATE
ejpam-3182	9	10	61	DATE
ejpam-3182	9	11	67	DATE
ejpam-3182	9	12	83	DATE
ejpam-3182	9	13	101	DATE
ejpam-3182	9	14	107	CARDINAL
ejpam-3182	9	15	107	CARDINAL
ejpam-3182	9	16	131	CARDINAL
ejpam-3182	9	17	139	DATE
ejpam-3182	10	1	1	CARDINAL
ejpam-3182	11	1	1	CARDINAL
ejpam-3182	13	1	#	CARDINAL
ejpam-3182	14	1	riemann hypothesis	PERSON
ejpam-3182	14	2	hooley	ORG
ejpam-3182	15	1	1	CARDINAL
ejpam-3182	15	2	2	CARDINAL
ejpam-3182	15	3	0	CARDINAL
ejpam-3182	15	4	7.1	CARDINAL
ejpam-3182	15	5	13	CARDINAL
ejpam-3182	16	1	10	CARDINAL
ejpam-3182	17	1	3	CARDINAL
ejpam-3182	17	2	5	DATE
ejpam-3182	17	3	32	DATE
ejpam-3182	17	4	11	DATE
ejpam-3182	17	5	3	CARDINAL
ejpam-3182	17	6	5	DATE
ejpam-3182	17	7	19	DATE
ejpam-3182	17	8	52	DATE
ejpam-3182	17	9	33	DATE
ejpam-3182	17	10	29	DATE
ejpam-3182	17	11	3	CARDINAL
ejpam-3182	17	12	11	DATE
ejpam-3182	17	13	37	DATE
ejpam-3182	17	14	45	DATE
ejpam-3182	17	15	53	DATE
ejpam-3182	17	16	55	DATE
ejpam-3182	17	17	3	CARDINAL
ejpam-3182	17	18	19	DATE
ejpam-3182	17	19	61	DATE
ejpam-3182	17	20	3	CARDINAL
ejpam-3182	17	21	n. a. carella	PERSON
ejpam-3182	18	1	23	CARDINAL
ejpam-3182	19	1	2018	DATE
ejpam-3182	20	1	n. a. carella	PERSON
ejpam-3182	21	1	j. pure	PERSON
ejpam-3182	21	2	11	CARDINAL
ejpam-3182	21	3	1	CARDINAL
ejpam-3182	21	4	2018	DATE
ejpam-3182	21	5	23	CARDINAL
ejpam-3182	21	6	2	CARDINAL
ejpam-3182	22	1	# {n	MONEY
ejpam-3182	22	2	n ∈ n : ordn(2	ORG
ejpam-3182	23	1	14	CARDINAL
ejpam-3182	23	2	10	CARDINAL
ejpam-3182	23	3	= o(x	PERSON
ejpam-3182	24	1	1.1	CARDINAL
ejpam-3182	25	1	riemann hypothesis	PERSON
ejpam-3182	25	2	2	CARDINAL
ejpam-3182	25	3	1	CARDINAL
ejpam-3182	26	1	2	CARDINAL
ejpam-3182	28	1	1− 1 p2	TIME
ejpam-3182	28	2	4	CARDINAL
ejpam-3182	28	3	0	CARDINAL
ejpam-3182	28	4	euler	PERSON
ejpam-3182	28	5	γ(s	ORG
ejpam-3182	29	1	0	CARDINAL
ejpam-3182	30	1	2p−1	CARDINAL
ejpam-3182	30	2	1	CARDINAL
ejpam-3182	30	3	0	CARDINAL
ejpam-3182	30	4	2p−1	CARDINAL
ejpam-3182	30	5	1	CARDINAL
ejpam-3182	30	6	0	CARDINAL
ejpam-3182	30	7	5	CARDINAL
ejpam-3182	30	8	2	CARDINAL
ejpam-3182	30	9	1	CARDINAL
ejpam-3182	31	1	l(x	PERSON
ejpam-3182	31	2	#{n	MONEY
ejpam-3182	32	1	25	CARDINAL
ejpam-3182	34	1	1	CARDINAL
ejpam-3182	34	2	2	CARDINAL
ejpam-3182	34	3	#	CARDINAL
ejpam-3182	37	1	1− 1 p2	TIME
ejpam-3182	37	2	6	CARDINAL
ejpam-3182	37	3	euler	PERSON
ejpam-3182	37	4	up−1	ORG
ejpam-3182	38	1	1	CARDINAL
ejpam-3182	38	2	0	CARDINAL
ejpam-3182	38	3	up−1	ORG
ejpam-3182	38	4	1	CARDINAL
ejpam-3182	38	5	0	CARDINAL
ejpam-3182	38	6	7	CARDINAL
ejpam-3182	38	7	abel-wieferich	ORG
ejpam-3182	38	8	2	CARDINAL
ejpam-3182	38	9	1	CARDINAL
ejpam-3182	39	1	1.1	CARDINAL
ejpam-3182	40	1	2	CARDINAL
ejpam-3182	41	1	1.1	CARDINAL
ejpam-3182	41	2	section 7	LAW
ejpam-3182	41	3	n. a. carella	PERSON
ejpam-3182	42	1	j. pure	PERSON
ejpam-3182	42	2	11	CARDINAL
ejpam-3182	42	3	1	CARDINAL
ejpam-3182	42	4	2018	DATE
ejpam-3182	42	5	23	CARDINAL
ejpam-3182	43	1	euler	PERSON
ejpam-3182	43	2	ϕ(n	PERSON
ejpam-3182	44	1	{k : gcd(k, n	PERSON
ejpam-3182	44	2	1	CARDINAL
ejpam-3182	45	1	ϕ(n	ORG
ejpam-3182	46	1	1	CARDINAL
ejpam-3182	46	2	2.1	CARDINAL
ejpam-3182	47	1	fermat-euler	ORG
ejpam-3182	47	2	gcd(a	GPE
ejpam-3182	47	3	1	CARDINAL
ejpam-3182	47	4	1	CARDINAL
ejpam-3182	49	1	vt t	GPE
ejpam-3182	49	2	λ(n	ORG
ejpam-3182	49	3	pv11	PRODUCT
ejpam-3182	49	4	pv22	WORK_OF_ART
ejpam-3182	52	1	0	CARDINAL
ejpam-3182	52	2	n ≥ 1	DATE
ejpam-3182	52	3	3	CARDINAL
ejpam-3182	52	4	2v−2	CARDINAL
ejpam-3182	52	5	2	CARDINAL
ejpam-3182	52	6	3	CARDINAL
ejpam-3182	53	1	9	CARDINAL
ejpam-3182	53	2	two	CARDINAL
ejpam-3182	53	3	ϕ(n	PERSON
ejpam-3182	54	1	2	CARDINAL
ejpam-3182	54	2	4	DATE
ejpam-3182	54	3	2pm	ORDINAL
ejpam-3182	54	4	1	CARDINAL
ejpam-3182	54	5	2	CARDINAL
ejpam-3182	54	6	2λ	CARDINAL
ejpam-3182	54	7	2	CARDINAL
ejpam-3182	55	1	ϕ(n	PERSON
ejpam-3182	55	2	λ(n	ORG
ejpam-3182	56	1	fermat-euler	ORG
ejpam-3182	56	2	ϕ(n	PERSON
ejpam-3182	56	3	1	CARDINAL
ejpam-3182	56	4	2.2	CARDINAL
ejpam-3182	57	1	4	CARDINAL
ejpam-3182	57	2	n ∈ n	ORG
ejpam-3182	58	1	1	CARDINAL
ejpam-3182	58	2	1	CARDINAL
ejpam-3182	58	3	gcd(a	GPE
ejpam-3182	59	1	1.	CARDINAL
ejpam-3182	59	2	1	CARDINAL
ejpam-3182	59	3	ϕ(λ(n	PRODUCT
ejpam-3182	60	1	λ(n	ORG
ejpam-3182	61	1	2	CARDINAL
ejpam-3182	61	2	congruences aλ(n	ORG
ejpam-3182	61	3	1 mod pv11	QUANTITY
ejpam-3182	61	4	1 mod pv22	QUANTITY
ejpam-3182	62	1	1	CARDINAL
ejpam-3182	62	2	10	CARDINAL
ejpam-3182	62	3	ω(n	DATE
ejpam-3182	63	1	2.1	CARDINAL
ejpam-3182	64	1	1 mod n	QUANTITY
ejpam-3182	65	1	2.3	CARDINAL
ejpam-3182	67	1	1	CARDINAL
ejpam-3182	69	1	n. n. a. carella	PERSON
ejpam-3182	70	1	j. pure	PERSON
ejpam-3182	70	2	11	CARDINAL
ejpam-3182	70	3	1	CARDINAL
ejpam-3182	70	4	2018	DATE
ejpam-3182	70	5	23	CARDINAL
ejpam-3182	71	1	1	CARDINAL
ejpam-3182	72	1	1 +	DATE
ejpam-3182	72	2	11	CARDINAL
ejpam-3182	72	3	λ(n	ORG
ejpam-3182	72	4	∈	ORG
ejpam-3182	73	1	1	CARDINAL
ejpam-3182	73	2	1	CARDINAL
ejpam-3182	73	3	mod q.	PERSON
ejpam-3182	73	4	6≡ 1 mod	QUANTITY
ejpam-3182	73	5	6≡ 1	DATE
ejpam-3182	73	6	mod q.	PERSON
ejpam-3182	73	7	modulo q.	PERSON
ejpam-3182	73	8	6≡ 1 mod n	QUANTITY
ejpam-3182	73	9	2	CARDINAL
ejpam-3182	73	10	6≡ 1 mod n ⇐⇒	QUANTITY
ejpam-3182	74	1	12	CARDINAL
ejpam-3182	75	1	6≡ 1 mod	QUANTITY
ejpam-3182	75	2	6≡ 1	DATE
ejpam-3182	75	3	mod q.	PERSON
ejpam-3182	75	4	q. 3	ORG
ejpam-3182	76	1	λ(n	ORG
ejpam-3182	77	1	1	CARDINAL
ejpam-3182	77	2	30	CARDINAL
ejpam-3182	78	1	0	CARDINAL
ejpam-3182	78	2	1	CARDINAL
ejpam-3182	78	3	modulo pk	ORG
ejpam-3182	79	1	3.1	CARDINAL
ejpam-3182	80	1	1	CARDINAL
ejpam-3182	82	1	1	CARDINAL
ejpam-3182	83	1	2k	CARDINAL
ejpam-3182	83	2	k ≤ 2	ORG
ejpam-3182	83	3	0	DATE
ejpam-3182	84	1	2k	CARDINAL
ejpam-3182	84	2	2	CARDINAL
ejpam-3182	84	3	1	CARDINAL
ejpam-3182	85	1	1	CARDINAL
ejpam-3182	85	2	2	CARDINAL
ejpam-3182	85	3	1	CARDINAL
ejpam-3182	85	4	0	CARDINAL
ejpam-3182	85	5	6=	CARDINAL
ejpam-3182	85	6	1	CARDINAL
ejpam-3182	85	7	2	CARDINAL
ejpam-3182	85	8	1	CARDINAL
ejpam-3182	86	1	13	CARDINAL
ejpam-3182	86	2	multiplicative	ORG
ejpam-3182	86	3	1	CARDINAL
ejpam-3182	87	1	6=	CARDINAL
ejpam-3182	87	2	1	CARDINAL
ejpam-3182	89	1	1	CARDINAL
ejpam-3182	90	1	0	CARDINAL
ejpam-3182	91	1	exempli gratia	PERSON
ejpam-3182	91	2	n. a. carella	PERSON
ejpam-3182	92	1	j. pure	PERSON
ejpam-3182	92	2	11	CARDINAL
ejpam-3182	92	3	1	CARDINAL
ejpam-3182	92	4	2018	DATE
ejpam-3182	92	5	23	CARDINAL
ejpam-3182	93	1	404872	DATE
ejpam-3182	93	2	1	CARDINAL
ejpam-3182	93	3	28	CARDINAL
ejpam-3182	94	1	1	CARDINAL
ejpam-3182	94	2	2	CARDINAL
ejpam-3182	95	1	1	CARDINAL
ejpam-3182	95	2	6=	CARDINAL
ejpam-3182	96	1	p(p − 1	LAW
ejpam-3182	96	2	k ≥ 2.	ORG
ejpam-3182	97	1	k ≥ 2. 4	ORG
ejpam-3182	99	1	4.1	CARDINAL
ejpam-3182	100	1	36	CARDINAL
ejpam-3182	100	2	71	CARDINAL
ejpam-3182	101	1	k ∈ n	ORG
ejpam-3182	101	2	2	CARDINAL
ejpam-3182	102	1	p≤x f(p	PERSON
ejpam-3182	103	1	14	CARDINAL
ejpam-3182	104	1	1 eγτγ(τ	CARDINAL
ejpam-3182	105	1	1 + f(p	CARDINAL
ejpam-3182	108	1	15	CARDINAL
ejpam-3182	108	2	γ(s	ORG
ejpam-3182	111	1	36	CARDINAL
ejpam-3182	112	1	12	CARDINAL
ejpam-3182	112	2	27	CARDINAL
ejpam-3182	112	3	195	CARDINAL
ejpam-3182	112	4	23	CARDINAL
ejpam-3182	112	5	70	CARDINAL
ejpam-3182	112	6	33	CARDINAL
ejpam-3182	112	7	308	CARDINAL
ejpam-3182	113	1	21	CARDINAL
ejpam-3182	113	2	25	CARDINAL
ejpam-3182	113	3	37	CARDINAL
ejpam-3182	114	1	5	CARDINAL
ejpam-3182	115	1	1	CARDINAL
ejpam-3182	115	2	∈ z.	PERSON
ejpam-3182	115	3	hooley theorem	ORG
ejpam-3182	115	4	riemann hypothesis	PERSON
ejpam-3182	116	1	0	CARDINAL
ejpam-3182	117	1	n. a. carella	PERSON
ejpam-3182	118	1	j. pure	PERSON
ejpam-3182	118	2	11	CARDINAL
ejpam-3182	118	3	1	CARDINAL
ejpam-3182	118	4	2018	DATE
ejpam-3182	118	5	23	CARDINAL
ejpam-3182	118	6	0	CARDINAL
ejpam-3182	118	7	13	CARDINAL
ejpam-3182	118	8	220	CARDINAL
ejpam-3182	119	1	25	CARDINAL
ejpam-3182	119	2	4	CARDINAL
ejpam-3182	120	1	5.1	CARDINAL
ejpam-3182	121	1	riemann hypothesis	PERSON
ejpam-3182	121	2	1	CARDINAL
ejpam-3182	122	1	0	CARDINAL
ejpam-3182	122	2	0	CARDINAL
ejpam-3182	122	3	∑ p≤x	PERSON
ejpam-3182	123	1	+o	DATE
ejpam-3182	124	1	∑ p≤x	PERSON
ejpam-3182	124	2	p∈pu	ORG
ejpam-3182	124	3	1	CARDINAL
ejpam-3182	124	4	log x− γu	PERSON
ejpam-3182	125	1	+o	DATE
ejpam-3182	129	1	1	CARDINAL
ejpam-3182	131	1	1	CARDINAL
ejpam-3182	133	1	x0	CARDINAL
ejpam-3182	133	2	16	CARDINAL
ejpam-3182	133	3	x0	ORG
ejpam-3182	133	4	0	CARDINAL
ejpam-3182	134	1	7.1	CARDINAL
ejpam-3182	134	2	1	CARDINAL
ejpam-3182	135	1	log x	PERSON
ejpam-3182	136	1	log2(x	TIME
ejpam-3182	137	1	x0	ORG
ejpam-3182	137	2	1	CARDINAL
ejpam-3182	139	1	17	CARDINAL
ejpam-3182	140	1	log log x− log	PERSON
ejpam-3182	140	2	x0 + c0	ORG
ejpam-3182	140	3	x0	ORG
ejpam-3182	141	1	+o	DATE
ejpam-3182	143	1	x0	ORG
ejpam-3182	145	1	artin-mertens	EVENT
ejpam-3182	145	2	artin-euler	ORG
ejpam-3182	146	1		GPE
ejpam-3182	146	2	− ∑ p∈pu	PERSON
ejpam-3182	146	3	1 kpk	DATE
ejpam-3182	146	4	18	CARDINAL
ejpam-3182	149	1	1	CARDINAL
ejpam-3182	149	2	euler	PERSON
ejpam-3182	149	3	γ = lim x→∞	ORG
ejpam-3182	150	1	1	CARDINAL
ejpam-3182	151	1	p≤x 1	PERSON
ejpam-3182	152	1	19	CARDINAL
ejpam-3182	152	2	n. a. carella	PERSON
ejpam-3182	153	1	j. pure	PERSON
ejpam-3182	153	2	11	CARDINAL
ejpam-3182	153	3	1	CARDINAL
ejpam-3182	153	4	2018	DATE
ejpam-3182	153	5	23	CARDINAL
ejpam-3182	154	1	18	CARDINAL
ejpam-3182	154	2	∑ k≥2	PERSON
ejpam-3182	154	3	−1	DATE
ejpam-3182	154	4	11	CARDINAL
ejpam-3182	154	5	427	CARDINAL
ejpam-3182	155	1	2	CARDINAL
ejpam-3182	158	1	∏	CARDINAL
ejpam-3182	159	1	1− 1 p(p− 1	QUANTITY
ejpam-3182	161	1	0.3739558667768911078453786	MONEY
ejpam-3182	162	1	1	CARDINAL
ejpam-3182	163	1	1	CARDINAL
ejpam-3182	163	2	0.424902273366234745796616	CARDINAL
ejpam-3182	164	1	5.2	CARDINAL
ejpam-3182	165	1	riemann hypothesis	PERSON
ejpam-3182	165	2	1	CARDINAL
ejpam-3182	166	1	p∈pu	ORG
ejpam-3182	166	2	1− 1	CARDINAL
ejpam-3182	166	3	−1	CARDINAL
ejpam-3182	168	1	∏ p≤x	PERSON
ejpam-3182	168	2	p∈pu	ORG
ejpam-3182	168	3	1 + 1	CARDINAL
ejpam-3182	169	1	∏ p∈pu	PERSON
ejpam-3182	169	2	1− p−2	PRODUCT
ejpam-3182	171	1	∏ p≤x	PERSON
ejpam-3182	171	2	p∈pu	ORG
ejpam-3182	171	3	1−	ORDINAL
ejpam-3182	171	4	1	CARDINAL
ejpam-3182	171	5	−1	DATE
ejpam-3182	172	1	+o	DATE
ejpam-3182	175	1	∑ p≤x	PERSON
ejpam-3182	175	2	p∈pu	ORG
ejpam-3182	175	3	1− 1	CARDINAL
ejpam-3182	175	4	−1	DATE
ejpam-3182	175	5	p∈pu	ORG
ejpam-3182	175	6	∑	ORG
ejpam-3182	175	7	1	CARDINAL
ejpam-3182	175	8	∑ p≤x	PERSON
ejpam-3182	175	9	p∈pu	ORG
ejpam-3182	175	10	1 kpk	DATE
ejpam-3182	176	1	20	CARDINAL
ejpam-3182	176	2	5.1	CARDINAL
ejpam-3182	177	1	first	ORDINAL
ejpam-3182	178	1	0	CARDINAL
ejpam-3182	178	2	3	CARDINAL
ejpam-3182	178	3	5	DATE
ejpam-3182	178	4	11	DATE
ejpam-3182	178	5	13	DATE
ejpam-3182	179	1	∑ k≥2	PERSON
ejpam-3182	179	2	1 k	QUANTITY
ejpam-3182	179	3	1	CARDINAL
ejpam-3182	181	1	21	CARDINAL
ejpam-3182	181	2	n. a. carella	PERSON
ejpam-3182	182	1	j. pure	PERSON
ejpam-3182	182	2	11	CARDINAL
ejpam-3182	182	3	1	CARDINAL
ejpam-3182	182	4	2018	DATE
ejpam-3182	182	5	23	CARDINAL
ejpam-3182	183	1	abel-wieferich	ORG
ejpam-3182	183	2	31	CARDINAL
ejpam-3182	183	3	333	CARDINAL
ejpam-3182	183	4	n ∈ n	ORG
ejpam-3182	183	5	22	CARDINAL
ejpam-3182	183	6	∈ z.	PERSON
ejpam-3182	183	7	abel-wieferich	PERSON
ejpam-3182	183	8	3	CARDINAL
ejpam-3182	183	9	1 + 1	CARDINAL
ejpam-3182	183	10	∏	CARDINAL
ejpam-3182	183	11	1 + 1	CARDINAL
ejpam-3182	184	1	∏ p≤x	PERSON
ejpam-3182	184	2	p∈pu	ORG
ejpam-3182	184	3	1− 1	CARDINAL
ejpam-3182	185	1	1 x	QUANTITY
ejpam-3182	185	2	23	CARDINAL
ejpam-3182	186	1	∏ p∈w	GPE
ejpam-3182	186	2	1− 1	LAW
ejpam-3182	186	3	p∈pu	ORG
ejpam-3182	186	4	1− 1	CARDINAL
ejpam-3182	187	1	1 x	QUANTITY
ejpam-3182	189	1	1	CARDINAL
ejpam-3182	189	2	w ∪w	EVENT
ejpam-3182	189	3	24	CARDINAL
ejpam-3182	189	4	1	CARDINAL
ejpam-3182	189	5	6=	CARDINAL
ejpam-3182	189	6	1	CARDINAL
ejpam-3182	189	7	25	CARDINAL
ejpam-3182	189	8	1	CARDINAL
ejpam-3182	190	1	26	CARDINAL
ejpam-3182	190	2	23	CARDINAL
ejpam-3182	191	1	∏ p∈w	GPE
ejpam-3182	191	2	1− 1	LAW
ejpam-3182	192	1	+o	DATE
ejpam-3182	192	2	1 x	QUANTITY
ejpam-3182	193	1	27	CARDINAL
ejpam-3182	193	2	2	CARDINAL
ejpam-3182	194	1	2p−1	CARDINAL
ejpam-3182	194	2	1	CARDINAL
ejpam-3182	194	3	1093	CARDINAL
ejpam-3182	194	4	3511	DATE
ejpam-3182	195	1	28	CARDINAL
ejpam-3182	195	2	∏ p∈w	GPE
ejpam-3182	195	3	1−	LANGUAGE
ejpam-3182	197	1	32	CARDINAL
ejpam-3182	198	1	n. a. carella	PERSON
ejpam-3182	199	1	j. pure	PERSON
ejpam-3182	199	2	11	CARDINAL
ejpam-3182	199	3	1	CARDINAL
ejpam-3182	199	4	2018	DATE
ejpam-3182	199	5	23-34 31 7	DATE
ejpam-3182	201	1	3	CARDINAL
ejpam-3182	202	1	7.1	CARDINAL
ejpam-3182	203	1	13	CARDINAL
ejpam-3182	204	1	n √ 1	ORG
ejpam-3182	204	2	integer	PERSON
ejpam-3182	204	3	1	CARDINAL
ejpam-3182	204	4	1	CARDINAL
ejpam-3182	206	1	29	CARDINAL
ejpam-3182	207	1	1.1	CARDINAL
ejpam-3182	207	2	riemann hypothesis	PERSON
ejpam-3182	207	3	7.1	CARDINAL
ejpam-3182	207	4	0	CARDINAL
ejpam-3182	208	1	4.1	CARDINAL
ejpam-3182	208	2	f(n	ORG
ejpam-3182	208	3	k ≥ 1	ORG
ejpam-3182	208	4	4.1	CARDINAL
ejpam-3182	209	1	1 eγτγ(τ	CARDINAL
ejpam-3182	210	1	∏	CARDINAL
ejpam-3182	212	1	1 eγα2γ	PERCENT
ejpam-3182	213	1	30	CARDINAL
ejpam-3182	213	2	1 + 1	CARDINAL
ejpam-3182	213	3	∏	CARDINAL
ejpam-3182	213	4	1 + 1	CARDINAL
ejpam-3182	214	1	30	CARDINAL
ejpam-3182	214	2	1	CARDINAL
ejpam-3182	214	3	two	CARDINAL
ejpam-3182	215	1	30	CARDINAL
ejpam-3182	215	2	2	CARDINAL
ejpam-3182	215	3	first	ORDINAL
ejpam-3182	215	4	wieferich prime powers	ORG
ejpam-3182	215	5	second	ORDINAL
ejpam-3182	215	6	3.1	CARDINAL
ejpam-3182	216	1	23	CARDINAL
ejpam-3182	216	2	section 6	LAW
ejpam-3182	216	3	5.2	CARDINAL
ejpam-3182	216	4	f(n	ORG
ejpam-3182	217	1	1 eγα2γ	PERCENT
ejpam-3182	218	1	∏ p∈w	GPE
ejpam-3182	218	2	1− 1	LAW
ejpam-3182	218	3	∏	CARDINAL
ejpam-3182	218	4	p∈pu	ORG
ejpam-3182	218	5	1− 1	CARDINAL
ejpam-3182	218	6	32	CARDINAL
ejpam-3182	219	1	1− 1 p2	TIME
ejpam-3182	219	2	31	CARDINAL
ejpam-3182	219	3	artin-euler	ORG
ejpam-3182	219	4	5.1	CARDINAL
ejpam-3182	219	5	5.2	CARDINAL
ejpam-3182	221	1	quod erat demonstrandum	PERSON
ejpam-3182	222	1	7.1	CARDINAL
ejpam-3182	223	1	hooley	ORG
ejpam-3182	223	2	v2 modulo	PERSON
ejpam-3182	223	3	2	CARDINAL
ejpam-3182	223	4	7.1	CARDINAL
ejpam-3182	223	5	1.1	CARDINAL
ejpam-3182	223	6	2	CARDINAL
ejpam-3182	224	1	3.1	CARDINAL
ejpam-3182	224	2	4.1	CARDINAL
ejpam-3182	225	1	euler	PERSON
ejpam-3182	225	2	5.1	CARDINAL
ejpam-3182	226	1	1	CARDINAL
ejpam-3182	226	2	tom m. introduction	PERSON
ejpam-3182	228	1	new york-heidelberg	GPE
ejpam-3182	228	2	1976	DATE
ejpam-3182	229	1	2	CARDINAL
ejpam-3182	229	2	david	PERSON
ejpam-3182	229	3	chantal	PERSON
ejpam-3182	231	1	amer	PERSON
ejpam-3182	232	1	j. math	PERSON
ejpam-3182	234	1	5	CARDINAL
ejpam-3182	234	2	1179-1229	CARDINAL
ejpam-3182	235	1	3	CARDINAL
ejpam-3182	235	2	roger c. baker	PERSON
ejpam-3182	235	3	paul pollack	PERSON
ejpam-3182	236	1	4	CARDINAL
ejpam-3182	236	2	r. d.	NORP
ejpam-3182	238	1	amer	PERSON
ejpam-3182	240	1	16 (1910	DATE
ejpam-3182	240	2	5	CARDINAL
ejpam-3182	240	3	232	CARDINAL
ejpam-3182	241	1	5	CARDINAL
ejpam-3182	241	2	peter j. cameron	PERSON
ejpam-3182	241	3	d. a. preece	PERSON
ejpam-3182	241	4	6	CARDINAL
ejpam-3182	241	5	joseph cohen	PERSON
ejpam-3182	241	6	ii	ORG
ejpam-3182	241	7	124	CARDINAL
ejpam-3182	241	8	2007	DATE
ejpam-3182	241	9	429	CARDINAL
ejpam-3182	242	1	7	CARDINAL
ejpam-3182	242	2	quarterly	DATE
ejpam-3182	243	1	1937,	DATE
ejpam-3182	243	2	308312	DATE
ejpam-3182	244	1	8	CARDINAL
ejpam-3182	244	2	christian	NORP
ejpam-3182	244	3	igor e. shparlinski	PERSON
ejpam-3182	245	1	9	CARDINAL
ejpam-3182	245	2	paul erdos	PERSON
ejpam-3182	245	3	harold n. shapiro	PERSON
ejpam-3182	245	4	1957	DATE
ejpam-3182	245	5	33	CARDINAL
ejpam-3182	245	6	10	CARDINAL
ejpam-3182	245	7	rajiv	PERSON
ejpam-3182	245	8	m. ram	PERSON
ejpam-3182	246	1	artin	PERSON
ejpam-3182	249	1	1984	DATE
ejpam-3182	249	2	1	CARDINAL
ejpam-3182	249	3	127	CARDINAL
ejpam-3182	250	1	11	CARDINAL
ejpam-3182	250	2	g. h.	PERSON
ejpam-3182	250	3	wright	PERSON
ejpam-3182	250	4	e. m.	PERSON
ejpam-3182	251	1	sixth	ORDINAL
ejpam-3182	252	1	d. r. heath-brown	NORP
ejpam-3182	252	2	j. h. silverman	PERSON
ejpam-3182	253	1	andrew wiles	PERSON
ejpam-3182	254	1	oxford university press	ORG
ejpam-3182	254	2	2008	DATE
ejpam-3182	255	1	12	CARDINAL
ejpam-3182	258	1	acta	PERSON
ejpam-3182	259	1	48	CARDINAL
ejpam-3182	259	2	1987	DATE
ejpam-3182	259	3	3	CARDINAL
ejpam-3182	259	4	209-260	CARDINAL
ejpam-3182	260	1	13	CARDINAL
ejpam-3182	260	2	c. hooley	PERSON
ejpam-3182	260	3	j. reine angew	PERSON
ejpam-3182	262	1	225	CARDINAL
ejpam-3182	262	2	209-220	CARDINAL
ejpam-3182	263	1	14	CARDINAL
ejpam-3182	263	2	shuguang	PERSON
ejpam-3182	263	3	carl	PERSON
ejpam-3182	264	1	2001	DATE
ejpam-3182	264	2	219	CARDINAL
ejpam-3182	264	3	8	DATE
ejpam-3182	264	4	kluwer	ORG
ejpam-3182	265	1	dordrecht	ORG
ejpam-3182	265	2	2002	DATE
ejpam-3182	266	1	15	CARDINAL
ejpam-3182	266	2	shuguang	PERSON
ejpam-3182	266	3	carl	PERSON
ejpam-3182	266	4	artin	PERSON
ejpam-3182	267	1	j. reine angew	PERSON
ejpam-3182	269	1	556	CARDINAL
ejpam-3182	269	2	2003	DATE
ejpam-3182	269	3	205	CARDINAL
ejpam-3182	270	1	16	CARDINAL
ejpam-3182	270	2	kowalski	PERSON
ejpam-3182	270	3	emmanuel.	PERSON
ejpam-3182	271	1	53	DATE
ejpam-3182	272	1	american mathematical society	ORG
ejpam-3182	272	2	ri	GPE
ejpam-3182	272	3	2004	DATE
ejpam-3182	273	1	17	CARDINAL
ejpam-3182	273	2	konyagin	GPE
ejpam-3182	273	3	sergei v.	PERSON
ejpam-3182	273	4	igor e.	PERSON
ejpam-3182	274	1	2012	DATE
ejpam-3182	274	2	1	CARDINAL
ejpam-3182	274	3	11	CARDINAL
ejpam-3182	275	1	18	CARDINAL
ejpam-3182	275	2	h. w. lenstra jr	PERSON
ejpam-3182	276	1	19	CARDINAL
ejpam-3182	276	2	h. w., jr.	PERSON
ejpam-3182	276	3	artin	PERSON
ejpam-3182	278	1	42	CARDINAL
ejpam-3182	278	2	1977	DATE
ejpam-3182	278	3	201	CARDINAL
ejpam-3182	279	1	20	CARDINAL
ejpam-3182	279	2	harald	PERSON
ejpam-3182	281	1	p. m. cohn	PERSON
ejpam-3182	281	2	second	ORDINAL
ejpam-3182	282	1	20	CARDINAL
ejpam-3182	283	1	cambridge university press	ORG
ejpam-3182	283	2	cambridge	GPE
ejpam-3182	283	3	1997	DATE
ejpam-3182	284	1	21	CARDINAL
ejpam-3182	285	1	landau	PERSON
ejpam-3182	286	1	newsl	PERSON
ejpam-3182	287	1	21 (2011	DATE
ejpam-3182	287	2	3	CARDINAL
ejpam-3182	287	3	73-81	CARDINAL
ejpam-3182	288	1	22	CARDINAL
ejpam-3182	288	2	pieter moree	PERSON
ejpam-3182	289	1	artin	PERSON
ejpam-3182	290	1	arxiv	ORG
ejpam-3182	291	1	23	CARDINAL
ejpam-3182	291	2	montgomery	GPE
ejpam-3182	291	3	hugh l.	PERSON
ejpam-3182	291	4	vaughan	ORG
ejpam-3182	291	5	robert c. multiplicative	PERSON
ejpam-3182	292	1	i.	PERSON
ejpam-3182	293	1	cambridge university press	ORG
ejpam-3182	293	2	cambridge	GPE
ejpam-3182	293	3	2007	DATE
ejpam-3182	294	1	24	CARDINAL
ejpam-3182	295	1	euclid	GPE
ejpam-3182	295	2	littlewood	ORG
ejpam-3182	297	1	berlin	GPE
ejpam-3182	297	2	2000	DATE
ejpam-3182	298	1	25	CARDINAL
ejpam-3182	298	2	francesco	PERSON
ejpam-3182	298	3	saidak	ORG
ejpam-3182	298	4	filip	ORG
ejpam-3182	298	5	igor e. square-free	PERSON
ejpam-3182	299	1	j. number	PERSON
ejpam-3182	299	2	103	CARDINAL
ejpam-3182	299	3	2003	DATE
ejpam-3182	299	4	1	CARDINAL
ejpam-3182	299	5	122	CARDINAL
ejpam-3182	300	1	34	CARDINAL
ejpam-3182	300	2	26	CARDINAL
ejpam-3182	300	3	francesco	PERSON
ejpam-3182	300	4	andrea	PERSON
ejpam-3182	301	1	multiplicative	ORG
ejpam-3182	304	1	101	DATE
ejpam-3182	304	2	2013	DATE
ejpam-3182	304	3	4	CARDINAL
ejpam-3182	304	4	319	CARDINAL
ejpam-3182	305	1	27	CARDINAL
ejpam-3182	305	2	a. g. postnikov	PERSON
ejpam-3182	305	3	68	CARDINAL
ejpam-3182	305	4	american mathematical society	ORG
ejpam-3182	305	5	ri	GPE
ejpam-3182	305	6	1988	DATE
ejpam-3182	306	1	28	CARDINAL
ejpam-3182	306	2	paszkiewicz	NORP
ejpam-3182	306	3	modp2	PRODUCT
ejpam-3182	309	1	2009	DATE
ejpam-3182	309	2	266	CARDINAL
ejpam-3182	309	3	1193-1195	CARDINAL
ejpam-3182	310	1	29	CARDINAL
ejpam-3182	310	2	hans	PERSON
ejpam-3182	312	1	j. theory nombres bordeaux	PERSON
ejpam-3182	312	2	14	DATE
ejpam-3182	312	3	2002	DATE
ejpam-3182	312	4	1	CARDINAL
ejpam-3182	312	5	287	CARDINAL
ejpam-3182	313	1	30	CARDINAL
ejpam-3182	313	2	h. e.	PERSON
ejpam-3182	315	1	second	ORDINAL
ejpam-3182	316	1	oxford	NORP
ejpam-3182	317	1	the clarendon press	ORG
ejpam-3182	317	2	oxford university press	ORG
ejpam-3182	317	3	new york	GPE
ejpam-3182	317	4	1994	DATE
ejpam-3182	318	1	31	CARDINAL
ejpam-3182	318	2	berlin	GPE
ejpam-3182	318	3	new york	GPE
ejpam-3182	318	4	1996	DATE
ejpam-3182	319	1	32	CARDINAL
ejpam-3182	319	2	peter	PERSON
ejpam-3182	320	1	artin	GPE
ejpam-3182	321	1	les xxii	ORG
ejpam-3182	321	2	journees arithmetiques	PERSON
ejpam-3182	321	3	lille	GPE
ejpam-3182	321	4	2001	DATE
ejpam-3182	322	1	j. theor	PERSON
ejpam-3182	323	1	15 (2003	DATE
ejpam-3182	323	2	1	CARDINAL
ejpam-3182	323	3	383	CARDINAL
ejpam-3182	324	1	33	CARDINAL
ejpam-3182	324	2	g. tenenbaum	PERSON
ejpam-3182	324	3	cambridge	GPE
ejpam-3182	324	4	46	DATE
ejpam-3182	324	5	cambridge university press	ORG
ejpam-3182	324	6	cambridge	GPE
ejpam-3182	324	7	1995	DATE
ejpam-3182	325	1	34	CARDINAL
ejpam-3182	325	2	stephens	PERSON
ejpam-3182	326	1	artin	PERSON
ejpam-3182	327	1	16	CARDINAL
ejpam-3182	327	2	1969	DATE
ejpam-3182	327	3	178	CARDINAL
ejpam-3182	328	1	35	CARDINAL
ejpam-3182	328	2	r. c.	PERSON
ejpam-3182	328	3	montgomery	GPE
ejpam-3182	329	1	5	CARDINAL
ejpam-3182	329	2	1973	DATE
ejpam-3182	329	3	64	CARDINAL
ejpam-3182	330	1	36	CARDINAL
ejpam-3182	330	2	e. wirsing	PERSON
ejpam-3182	330	3	das asymptotische verhalten von	PERSON
ejpam-3182	330	4	multiplikative funktionen	PRODUCT
ejpam-3182	331	1	ann	PERSON
ejpam-3182	332	1	143	CARDINAL
ejpam-3182	332	2	1961	DATE
ejpam-3182	332	3	75-102	CARDINAL
ejpam-3182	333	1	37	CARDINAL
ejpam-3182	333	2	williams	PERSON
ejpam-3182	333	3	kenneth s.	PERSON
ejpam-3182	334	1	canad	ORG
ejpam-3182	336	1	bull	PERSON
ejpam-3182	337	1	18 (1975	DATE
ejpam-3182	337	2	1	CARDINAL
ejpam-3182	337	3	123	CARDINAL