id	sid	eid	entity	type
ejpam-109	1	1	european journal	ORG
ejpam-109	2	1	1	CARDINAL
ejpam-109	2	2	4, 2008	DATE
ejpam-109	2	3	3-21	DATE
ejpam-109	2	4	1307-5543	CARDINAL
ejpam-109	2	5	tokyo university of science	ORG
ejpam-109	2	6	noda	ORG
ejpam-109	2	7	chiba 278-8510	ORG
ejpam-109	2	8	japan	GPE
ejpam-109	3	1	first	ORDINAL
ejpam-109	3	2	suffix notation	ORG
ejpam-109	4	1	von staudt-clausen	PERSON
ejpam-109	4	2	kummer	PERSON
ejpam-109	5	1	11a07	CARDINAL
ejpam-109	5	2	11b68	DATE
ejpam-109	5	3	11y1	CARDINAL
ejpam-109	5	4	bernoulli	PERSON
ejpam-109	5	5	von staudt-clausen’s	PERSON
ejpam-109	5	6	kummer	PERSON
ejpam-109	5	7	1	CARDINAL
ejpam-109	6	1	taylor	PERSON
ejpam-109	8	1	2π	CARDINAL
ejpam-109	10	1	1 m+ 1 m−1 ∑ i=0 �	QUANTITY
ejpam-109	12	1	1	CARDINAL
ejpam-109	13	1	0	CARDINAL
ejpam-109	13	2	the stirling formula n	ORG
ejpam-109	13	3	2πn	ORDINAL
ejpam-109	13	4	4	CARDINAL
ejpam-109	13	5	3 ≤ m	QUANTITY
ejpam-109	13	6	1	CARDINAL
ejpam-109	14	1	2	CARDINAL
ejpam-109	14	2	n ≥ 1	DATE
ejpam-109	15	1	dm ∈ z	ORG
ejpam-109	15	2	dm	ORG
ejpam-109	15	3	0	CARDINAL
ejpam-109	15	4	∑	LOC
ejpam-109	15	5	j)m−1	GPE
ejpam-109	15	6	1.1	CARDINAL
ejpam-109	16	1	the ministry of education	ORG
ejpam-109	16	2	japan	GPE
ejpam-109	18	1	3	CARDINAL
ejpam-109	18	2	2008	DATE
ejpam-109	20	1	j. pure	PERSON
ejpam-109	20	2	1 (2008	DATE
ejpam-109	20	3	3-21	DATE
ejpam-109	20	4	4	CARDINAL
ejpam-109	21	1	1	CARDINAL
ejpam-109	22	1	14	CARDINAL
ejpam-109	23	1	1	CARDINAL
ejpam-109	25	1	dm	ORG
ejpam-109	27	1	one	CARDINAL
ejpam-109	27	2	von staudt	PERSON
ejpam-109	27	3	adams’ theorem	ORG
ejpam-109	27	4	2	CARDINAL
ejpam-109	27	5	1	CARDINAL
ejpam-109	29	1	1	CARDINAL
ejpam-109	31	1	5	CARDINAL
ejpam-109	31	2	2	CARDINAL
ejpam-109	31	3	≡ l	ORG
ejpam-109	32	1	1	CARDINAL
ejpam-109	32	2	1	CARDINAL
ejpam-109	32	3	von staudt	PERSON
ejpam-109	32	4	kummer	PERSON
ejpam-109	32	5	1	CARDINAL
ejpam-109	33	1	1	CARDINAL
ejpam-109	33	2	mod ϕ(ps	ORG
ejpam-109	33	3	1	CARDINAL
ejpam-109	33	4	1− pm−1	PRODUCT
ejpam-109	33	5	1−	ORDINAL
ejpam-109	33	6	bl l	ORG
ejpam-109	34	1	1.2	CARDINAL
ejpam-109	34	2	4.1	CARDINAL
ejpam-109	35	1	9	CARDINAL
ejpam-109	35	2	washington	GPE
ejpam-109	35	3	17	CARDINAL
ejpam-109	36	1	q(ζp	GPE
ejpam-109	38	1	first	ORDINAL
ejpam-109	38	2	kummer	PERSON
ejpam-109	38	3	fermat	ORG
ejpam-109	39	1	kummer	PERSON
ejpam-109	39	2	at least one	CARDINAL
ejpam-109	39	3	3)/2	CARDINAL
ejpam-109	39	4	bp−3	ORG
ejpam-109	41	1	jensen	PERSON
ejpam-109	42	1	10	CARDINAL
ejpam-109	42	2	1915	DATE
ejpam-109	42	3	3	CARDINAL
ejpam-109	45	1	siegel	PERSON
ejpam-109	45	2	1964	DATE
ejpam-109	45	3	1/	CARDINAL
ejpam-109	46	1	first	ORDINAL
ejpam-109	46	2	1.1	CARDINAL
ejpam-109	47	1	von studt-clausen	PERSON
ejpam-109	49	1	2	CARDINAL
ejpam-109	51	1	j. pure	PERSON
ejpam-109	51	2	1 (2008	DATE
ejpam-109	51	3	3-21	DATE
ejpam-109	51	4	5	CARDINAL
ejpam-109	51	5	dm	ORG
ejpam-109	52	1	1	CARDINAL
ejpam-109	52	2	0	CARDINAL
ejpam-109	54	1	slavutskii	ORG
ejpam-109	54	2	15	CARDINAL
ejpam-109	54	3	1845	DATE
ejpam-109	54	4	adams (	LAW
ejpam-109	54	5	1878	DATE
ejpam-109	55	1	2.1	CARDINAL
ejpam-109	56	1	2	CARDINAL
ejpam-109	57	1	1	CARDINAL
ejpam-109	61	1	bm	ORG
ejpam-109	62	1	0	CARDINAL
ejpam-109	62	2	bm	ORG
ejpam-109	63	1	bernoulli	PERSON
ejpam-109	64	1	bm ≡	ORG
ejpam-109	65	1	2≤	DATE
ejpam-109	65	2	3	CARDINAL
ejpam-109	66	1	euler	PERSON
ejpam-109	67	1	n−1 ∑	ORG
ejpam-109	68	1	t = t et − 1 (	ORG
ejpam-109	68	2	− 1	EVENT
ejpam-109	69	1	2.2	CARDINAL
ejpam-109	71	1	1m+ 2m+	TIME
ejpam-109	71	2	1)m	CARDINAL
ejpam-109	72	1	1	CARDINAL
ejpam-109	72	2	bm+1− jn j	PERSON
ejpam-109	72	3	2i + 1	QUANTITY
ejpam-109	72	4	2	CARDINAL
ejpam-109	73	1	2i	CARDINAL
ejpam-109	73	2	1	CARDINAL
ejpam-109	74	1	1 2i+ 1	CARDINAL
ejpam-109	75	1	1 x	QUANTITY
ejpam-109	76	1	1	CARDINAL
ejpam-109	76	2	2	CARDINAL
ejpam-109	77	1	2.2	CARDINAL
ejpam-109	77	2	2.3	CARDINAL
ejpam-109	78	1	dmsm(n)≡ nmn	PERSON
ejpam-109	79	1	t. agoh	PERSON
ejpam-109	80	1	j. pure	PERSON
ejpam-109	80	2	1 (2008	DATE
ejpam-109	80	3	3-21	DATE
ejpam-109	80	4	6	CARDINAL
ejpam-109	82	1	1,2	CARDINAL
ejpam-109	82	2	1	CARDINAL
ejpam-109	82	3	jn+ r j	PERSON
ejpam-109	88	1	∑ i=1	PERSON
ejpam-109	88	2	a j n �	PERSON
ejpam-109	89	1	1	CARDINAL
ejpam-109	89	2	2	DATE
ejpam-109	89	3	1,2	CARDINAL
ejpam-109	89	4	1	CARDINAL
ejpam-109	89	5	j = 1,2	LAW
ejpam-109	89	6	1	CARDINAL
ejpam-109	89	7	∑ i=1	PERSON
ejpam-109	89	8	2.1	CARDINAL
ejpam-109	90	1	1)sm(n)≡	CARDINAL
ejpam-109	90	2	∑	LOC
ejpam-109	90	3	j)m−1	GPE
ejpam-109	91	1	2.3	CARDINAL
ejpam-109	91	2	2.4	CARDINAL
ejpam-109	92	1	1	CARDINAL
ejpam-109	93	1	1	CARDINAL
ejpam-109	93	2	1	CARDINAL
ejpam-109	93	3	am− 1)nm	PERSON
ejpam-109	93	4	∑	LOC
ejpam-109	93	5	j)m−1	GPE
ejpam-109	94	1	2.5	CARDINAL
ejpam-109	95	1	2	CARDINAL
ejpam-109	96	1	1	CARDINAL
ejpam-109	97	1	1	CARDINAL
ejpam-109	97	2	pbm ∈ zp	PRODUCT
ejpam-109	97	3	pbm ≡	ORG
ejpam-109	97	4	1	CARDINAL
ejpam-109	98	1	1	CARDINAL
ejpam-109	98	2	pbm ≡	ORG
ejpam-109	98	3	1	CARDINAL
ejpam-109	99	1	2	CARDINAL
ejpam-109	99	2	bm	ORG
ejpam-109	100	1	1	CARDINAL
ejpam-109	100	2	1+ ∑ q−1|m q 6	QUANTITY
ejpam-109	100	3	1	CARDINAL
ejpam-109	101	1	j. pure	PERSON
ejpam-109	101	2	1 (2008	DATE
ejpam-109	101	3	3-21	DATE
ejpam-109	102	1	q− 1	DATE
ejpam-109	102	2	6=	CARDINAL
ejpam-109	103	1	kummer	ORG
ejpam-109	104	1	15	CARDINAL
ejpam-109	104	2	von staudt-kummer	PERSON
ejpam-109	104	3	von staudt	PERSON
ejpam-109	104	4	first	ORDINAL
ejpam-109	104	5	kummer	PERSON
ejpam-109	105	1	2.6	CARDINAL
ejpam-109	106	1	2	CARDINAL
ejpam-109	106	2	1≤ s ≤ m−1	QUANTITY
ejpam-109	108	1	1	CARDINAL
ejpam-109	111	1	1	CARDINAL
ejpam-109	111	2	1	CARDINAL
ejpam-109	115	1	resp.β	NORP
ejpam-109	116	1	1	CARDINAL
ejpam-109	116	2	0	CARDINAL
ejpam-109	116	3	1	DATE
ejpam-109	116	4	s.	PERSON
ejpam-109	118	1	1	CARDINAL
ejpam-109	118	2	ap−1	ORG
ejpam-109	118	3	γϕ(p s	ORG
ejpam-109	118	4	1	CARDINAL
ejpam-109	118	5	euler	PERSON
ejpam-109	120	1	am− 1	FAC
ejpam-109	121	1	von staudt	PERSON
ejpam-109	122	1	slavutskii	ORG
ejpam-109	122	2	4	CARDINAL
ejpam-109	122	3	15	CARDINAL
ejpam-109	123	1	1	CARDINAL
ejpam-109	124	1	e. lehmer	PERSON
ejpam-109	124	2	13	CARDINAL
ejpam-109	124	3	1939	DATE
ejpam-109	124	4	many years	DATE
ejpam-109	125	1	2.7	CARDINAL
ejpam-109	126	1	2	CARDINAL
ejpam-109	126	2	2	CARDINAL
ejpam-109	127	1	1 2	CARDINAL
ejpam-109	127	2	3m−1),q4(m	CARDINAL
ejpam-109	127	3	1 2	CARDINAL
ejpam-109	127	4	1 2	CARDINAL
ejpam-109	127	5	6m−1	CARDINAL
ejpam-109	128	1	1	CARDINAL
ejpam-109	128	2	2	CARDINAL
ejpam-109	128	3	2,3	CARDINAL
ejpam-109	128	4	4,6	CARDINAL
ejpam-109	128	5	6	CARDINAL
ejpam-109	128	6	2	CARDINAL
ejpam-109	128	7	lehmer	ORG
ejpam-109	128	8	2	CARDINAL
ejpam-109	128	9	2m−1pβm	CARDINAL
ejpam-109	128	10	1	CARDINAL
ejpam-109	128	11	2i)m	CARDINAL
ejpam-109	128	12	mod p3	ORG
ejpam-109	129	1	t. agoh	PERSON
ejpam-109	130	1	j. pure	PERSON
ejpam-109	130	2	1 (2008	DATE
ejpam-109	130	3	3-21	DATE
ejpam-109	130	4	8	CARDINAL
ejpam-109	130	5	lehmer	GPE
ejpam-109	130	6	johnson	PERSON
ejpam-109	131	1	11	CARDINAL
ejpam-109	132	1	jensen	PERSON
ejpam-109	133	1	10	CARDINAL
ejpam-109	133	2	1915	DATE
ejpam-109	133	3	2.8	CARDINAL
ejpam-109	134	1	3	CARDINAL
ejpam-109	135	1	6	CARDINAL
ejpam-109	137	1	5	CARDINAL
ejpam-109	137	2	less than 12	CARDINAL
ejpam-109	137	3	#	CARDINAL
ejpam-109	138	1	1≤ m≤	QUANTITY
ejpam-109	138	2	3)/2	CARDINAL
ejpam-109	139	1	3	CARDINAL
ejpam-109	139	2	voronoï	ORG
ejpam-109	139	3	first	ORDINAL
ejpam-109	140	1	one	CARDINAL
ejpam-109	142	1	2	CARDINAL
ejpam-109	142	2	ν =ν(m	ORG
ejpam-109	143	1	1	CARDINAL
ejpam-109	143	2	1 by convention	CARDINAL
ejpam-109	144	1	1	CARDINAL
ejpam-109	144	2	1− pm−1	PRODUCT
ejpam-109	145	1	km(n	ORG
ejpam-109	145	2	1)hm(n	CARDINAL
ejpam-109	145	3	εm(n)βm(a	PERSON
ejpam-109	146	1	1)h	CARDINAL
ejpam-109	146	2	1)bm	DATE
ejpam-109	148	1	j. pure	PERSON
ejpam-109	148	2	1 (2008	DATE
ejpam-109	148	3	3-21	DATE
ejpam-109	148	4	9	CARDINAL
ejpam-109	148	5	3.1	CARDINAL
ejpam-109	149	1	2	CARDINAL
ejpam-109	149	2	n ≥ 1	DATE
ejpam-109	150	1	w′	GPE
ejpam-109	151	1	1	CARDINAL
ejpam-109	151	2	km(n	PERSON
ejpam-109	152	1	a)≡ w−1 ∑	PERSON
ejpam-109	152	2	j)m−1	GPE
ejpam-109	152	3	j)m−1	GPE
ejpam-109	155	1	first	ORDINAL
ejpam-109	155	2	2.4	CARDINAL
ejpam-109	155	3	am− 1)nm	PERSON
ejpam-109	157	1	j)m−1	GPE
ejpam-109	158	1	1	CARDINAL
ejpam-109	158	2	w	ORG
ejpam-109	159	1	j)m−1	GPE
ejpam-109	160	1	3.1	CARDINAL
ejpam-109	160	2	j)m−1	GPE
ejpam-109	161	1	j)m−1	GPE
ejpam-109	161	2	j)m−1	GPE
ejpam-109	161	3	j)m−1	GPE
ejpam-109	161	4	− ∑ d|n d>1	ORG
ejpam-109	161	5	 	PRODUCT
ejpam-109	161	6	j)m−1	GPE
ejpam-109	161	7		PERSON
ejpam-109	161	8	3.2	CARDINAL
ejpam-109	162	1	3.1	CARDINAL
ejpam-109	162	2	w	GPE
ejpam-109	162	3	µ(d)dm−1.	GPE
ejpam-109	163	1	µ(d)dm−1βm(a)≡	GPE
ejpam-109	163	2	j)m−1	GPE
ejpam-109	165	1	m−1	PERSON
ejpam-109	165	2	1	CARDINAL
ejpam-109	165	3	3.1	CARDINAL
ejpam-109	165	4	3.2	CARDINAL
ejpam-109	165	5	1+ ∑	QUANTITY
ejpam-109	165	6	j)m−1	GPE
ejpam-109	167	1	j. pure	PERSON
ejpam-109	167	2	1 (2008	DATE
ejpam-109	167	3	3-21	DATE
ejpam-109	167	4	10	CARDINAL
ejpam-109	167	5	3.2	CARDINAL
ejpam-109	168	1	1	CARDINAL
ejpam-109	169	1	nh	LOC
ejpam-109	169	2	∑	LOC
ejpam-109	169	3	jm	PERSON
ejpam-109	171	1	3.1	CARDINAL
ejpam-109	173	1	2.5	CARDINAL
ejpam-109	173	2	0,1	CARDINAL
ejpam-109	173	3	2.2	CARDINAL
ejpam-109	174	1	µ(d)dmsm	PERSON
ejpam-109	175	1	1+ ∑	QUANTITY
ejpam-109	176	1	jm	PERSON
ejpam-109	177	1	3.3	CARDINAL
ejpam-109	178	1	ϕ(n	PERSON
ejpam-109	178	2	ϕ(n	ORG
ejpam-109	180	1	j, n	WORK_OF_ART
ejpam-109	180	2	1 and	CARDINAL
ejpam-109	180	3	ϕ(n	PERSON
ejpam-109	181	1	jm ≡ 1	ORG
ejpam-109	182	1	3.2	CARDINAL
ejpam-109	183	1	2.5	CARDINAL
ejpam-109	183	2	3.3	CARDINAL
ejpam-109	185	1	ϕ(n	PERSON
ejpam-109	185	2	xm+ ym	PERSON
ejpam-109	185	3	section 2	LAW
ejpam-109	185	4	xm ∈ zn	ORG
ejpam-109	188	1	3.2	CARDINAL
ejpam-109	188	2	2	CARDINAL
ejpam-109	188	3	≡ l	ORG
ejpam-109	189	1	≡ l	ORG
ejpam-109	189	2	3	CARDINAL
ejpam-109	189	3	nh ′m(n)≡ nh	GPE
ejpam-109	190	1	bl ∈ zn	PERSON
ejpam-109	193	1	j. pure	PERSON
ejpam-109	193	2	1 (2008	DATE
ejpam-109	193	3	3-21	DATE
ejpam-109	193	4	11	CARDINAL
ejpam-109	193	5	3.4	CARDINAL
ejpam-109	194	1	2	CARDINAL
ejpam-109	194	2	1	CARDINAL
ejpam-109	195	1	1	CARDINAL
ejpam-109	197	1	m+ 1	CARDINAL
ejpam-109	197	2	jm	ORG
ejpam-109	197	3	1	CARDINAL
ejpam-109	197	4	o	DATE
ejpam-109	197	5	∑ i=1	PERSON
ejpam-109	198	1	1	CARDINAL
ejpam-109	198	2	3	CARDINAL
ejpam-109	198	3	1	CARDINAL
ejpam-109	199	1	3.2	CARDINAL
ejpam-109	201	1	1	CARDINAL
ejpam-109	202	1	fermat	ORG
ejpam-109	203	1	1950	DATE
ejpam-109	203	2	8	CARDINAL
ejpam-109	205	1	2	CARDINAL
ejpam-109	206	1	4	CARDINAL
ejpam-109	207	1	12	CARDINAL
ejpam-109	207	2	1	CARDINAL
ejpam-109	208	1	nbn−1 ≡ n−	ORG
ejpam-109	208	2	1	CARDINAL
ejpam-109	209	1	3.5	CARDINAL
ejpam-109	210	1	2	CARDINAL
ejpam-109	211	1	nbn−1 ≡ n−	ORG
ejpam-109	211	2	1	CARDINAL
ejpam-109	213	1	1	CARDINAL
ejpam-109	213	2	561	CARDINAL
ejpam-109	213	3	3	CARDINAL
ejpam-109	213	4	11	CARDINAL
ejpam-109	213	5	17	CARDINAL
ejpam-109	215	1	p(p − 1	PRODUCT
ejpam-109	215	2	nbn−1 ≡	ORG
ejpam-109	216	1	3	CARDINAL
ejpam-109	216	2	granville	PERSON
ejpam-109	217	1	n.	ORG
ejpam-109	219	1	2	CARDINAL
ejpam-109	219	2	1	CARDINAL
ejpam-109	219	3	1	CARDINAL
ejpam-109	219	4	1	CARDINAL
ejpam-109	220	1	j. pure	PERSON
ejpam-109	220	2	1 (2008	DATE
ejpam-109	220	3	3-21	DATE
ejpam-109	220	4	12	DATE
ejpam-109	221	1	4	CARDINAL
ejpam-109	221	2	at least 12055	CARDINAL
ejpam-109	225	1	4	CARDINAL
ejpam-109	225	2	generalized von staudt-kummer congruences	PERSON
ejpam-109	225	3	von staudt-kummer congruences	PERSON
ejpam-109	225	4	2.6	CARDINAL
ejpam-109	226	1	ar	PERSON
ejpam-109	227	1	1	CARDINAL
ejpam-109	227	2	2	DATE
ejpam-109	228	1	3	CARDINAL
ejpam-109	228	2	1	CARDINAL
ejpam-109	228	3	4.1	CARDINAL
ejpam-109	229	1	1	CARDINAL
ejpam-109	229	2	2	DATE
ejpam-109	229	3	∈	ORG
ejpam-109	230	1	0(mod n	PERSON
ejpam-109	231	1	k ∏ r=1 kmr	ORG
ejpam-109	231	2	k ∑ r=1	PERSON
ejpam-109	231	3	k brϕ(n)(n	FAC
ejpam-109	233	1	mod ns	PERSON
ejpam-109	234	1	1	CARDINAL
ejpam-109	234	2	1	CARDINAL
ejpam-109	234	3	1,2	CARDINAL
ejpam-109	234	4	k ∏ r=1 hmr	ORG
ejpam-109	234	5	h brϕ(n	ORG
ejpam-109	237	1	mod ns	PERSON
ejpam-109	240	1	k l(n	ORG
ejpam-109	241	1	hl(n	PERSON
ejpam-109	241	2	r.	NORP
ejpam-109	242	1	n ≥ 3	DATE
ejpam-109	242	2	1	CARDINAL
ejpam-109	242	3	2	DATE
ejpam-109	242	4	0	CARDINAL
ejpam-109	242	5	1	DATE
ejpam-109	246	1	1≤r≤k 0≤c≤s	QUANTITY
ejpam-109	246	2	¦ ordp(mr + cbrϕ(n	PERSON
ejpam-109	246	3	1≤r≤k ¦	PERSON
ejpam-109	248	1	3.1	CARDINAL
ejpam-109	248	2	w	GPE
ejpam-109	249	1	ar jr ξ	PERSON
ejpam-109	249	2	t. agoh	PERSON
ejpam-109	250	1	j. pure	PERSON
ejpam-109	250	2	1 (2008	DATE
ejpam-109	250	3	3-21	DATE
ejpam-109	250	4	13	CARDINAL
ejpam-109	250	5	1,2	CARDINAL
ejpam-109	250	6	0,1	CARDINAL
ejpam-109	250	7	s.	PERSON
ejpam-109	250	8	kmr	PERSON
ejpam-109	250	9	k ∑ r=1	PERSON
ejpam-109	250	10	k brϕ(n)(n	FAC
ejpam-109	252	1	∑ j1=1	PERSON
ejpam-109	253	1	∑ jk=1	PERSON
ejpam-109	253	2	0≤c1,	CARDINAL
ejpam-109	254	1	∑ j1=1	PERSON
ejpam-109	255	1	∑ jk=1	PERSON
ejpam-109	255	2	mr−1 � ar jr ξ �	PERSON
ejpam-109	255	3		PRODUCT
ejpam-109	255	4	mod ns	PERSON
ejpam-109	256	1	1	CARDINAL
ejpam-109	256	2	k ∑ r=1	PERSON
ejpam-109	258	1	i=1 λi	GPE
ejpam-109	259	1	1	CARDINAL
ejpam-109	259	2	1	CARDINAL
ejpam-109	259	3	1	CARDINAL
ejpam-109	259	4	2	DATE
ejpam-109	260	1	mod ns	PERSON
ejpam-109	261	1	euler	PERSON
ejpam-109	261	2	≡ γns−1ϕ(n	ORG
ejpam-109	261	3	1	CARDINAL
ejpam-109	261	4	mod ns	PERSON
ejpam-109	264	1	acϕ(n	PERSON
ejpam-109	264	2	1	CARDINAL
ejpam-109	264	3	1	CARDINAL
ejpam-109	264	4	r.	NORP
ejpam-109	264	5	1	CARDINAL
ejpam-109	265	1	4.2	CARDINAL
ejpam-109	266	1	1	CARDINAL
ejpam-109	266	2	2	DATE
ejpam-109	266	3	1,2	CARDINAL
ejpam-109	266	4	1	CARDINAL
ejpam-109	266	5	i=1 λi ≡ 0(mod	ORG
ejpam-109	268	1	k ∏ r=1	ORG
ejpam-109	268	2	k ∑ r=1 λrβ br	PERSON
ejpam-109	271	1	j. pure	PERSON
ejpam-109	271	2	1 (2008	DATE
ejpam-109	271	3	3-21	DATE
ejpam-109	271	4	14	DATE
ejpam-109	271	5	1	CARDINAL
ejpam-109	271	6	1	CARDINAL
ejpam-109	271	7	2	DATE
ejpam-109	271	8	k ∏ r=1	ORG
ejpam-109	271	9	k ∑ r=1 λrβ br	PERSON
ejpam-109	275	1	1,2	CARDINAL
ejpam-109	281	1	n= p	ORG
ejpam-109	281	2	4.1	CARDINAL
ejpam-109	282	1	mr−1≥	DATE
ejpam-109	283	1	1−pmr−1	CARDINAL
ejpam-109	283	2	1	CARDINAL
ejpam-109	283	3	hmr	PRODUCT
ejpam-109	284	1	1,2	CARDINAL
ejpam-109	284	2	1	CARDINAL
ejpam-109	284	3	r.	NORP
ejpam-109	284	4	4.1	CARDINAL
ejpam-109	285	1	4.2	CARDINAL
ejpam-109	285	2	4.3	CARDINAL
ejpam-109	286	1	1	CARDINAL
ejpam-109	286	2	2	CARDINAL
ejpam-109	286	3	λ1,λ2 ∈ zp	PERSON
ejpam-109	288	1	1	CARDINAL
ejpam-109	291	1	1	CARDINAL
ejpam-109	294	1	1	CARDINAL
ejpam-109	294	2	4.2	CARDINAL
ejpam-109	295	1	1	CARDINAL
ejpam-109	295	2	−1	DATE
ejpam-109	295	3	2.6	CARDINAL
ejpam-109	296	1	4.4	CARDINAL
ejpam-109	297	1	2	CARDINAL
ejpam-109	297	2	1	CARDINAL
ejpam-109	297	3	3	CARDINAL
ejpam-109	298	1	m≡ l	ORG
ejpam-109	299	1	l ≥ 2	DATE
ejpam-109	299	2	km(n	ORG
ejpam-109	299	3	a)≡ kl(n	PERSON
ejpam-109	300	1	1	CARDINAL
ejpam-109	300	2	l ≥ 2	DATE
ejpam-109	301	1	t. agoh	PERSON
ejpam-109	302	1	j. pure	PERSON
ejpam-109	302	2	1 (2008	DATE
ejpam-109	302	3	3-21	DATE
ejpam-109	302	4	15	CARDINAL
ejpam-109	304	1	1	CARDINAL
ejpam-109	304	2	−1	DATE
ejpam-109	304	3	4.1	CARDINAL
ejpam-109	304	4	1	CARDINAL
ejpam-109	306	1	n ≥ 3	DATE
ejpam-109	306	2	1	CARDINAL
ejpam-109	307	1	4.5	CARDINAL
ejpam-109	308	1	2	CARDINAL
ejpam-109	312	1	1	CARDINAL
ejpam-109	312	2	1	CARDINAL
ejpam-109	312	3	λ1,λ2 ∈ zp	PERSON
ejpam-109	319	1	section 3	LAW
ejpam-109	319	2	η	PERSON
ejpam-109	320	1	ordp(dm	ORG
ejpam-109	320	2	0	CARDINAL
ejpam-109	320	3	1	DATE
ejpam-109	320	4	3.1	CARDINAL
ejpam-109	320	5	η	GPE
ejpam-109	321	1	a)≡	ORG
ejpam-109	322	1	j)m+cbϕ(n)−1	ORG
ejpam-109	323	1	a)λs−c 2 ≡ s	ORG
ejpam-109	323	2	1λ	CARDINAL
ejpam-109	324	1	j)m+cbϕ(n)−1	ORG
ejpam-109	325	1	1λ	CARDINAL
ejpam-109	325	2	j)m+cbϕ(n)−1	ORG
ejpam-109	325	3	1λ	CARDINAL
ejpam-109	325	4	j)m+cbϕ(n)−1	ORG
ejpam-109	325	5	j)m−1	GPE
ejpam-109	325	6	1λ	CARDINAL
ejpam-109	326	1	+ sλ1 bϕ(n	QUANTITY
ejpam-109	327	1	1	CARDINAL
ejpam-109	327	2	s−1−c′ 2	DATE
ejpam-109	329	1	j. pure	PERSON
ejpam-109	329	2	1 (2008	DATE
ejpam-109	329	3	3-21	DATE
ejpam-109	329	4	16	CARDINAL
ejpam-109	329	5	j)m−1	GPE
ejpam-109	330	1	+ sλ1 bϕ(n	QUANTITY
ejpam-109	330	2	j)m+bϕ(n)−1	GPE
ejpam-109	332	1	1	CARDINAL
ejpam-109	332	2	1	CARDINAL
ejpam-109	332	3	1	CARDINAL
ejpam-109	336	1	1	CARDINAL
ejpam-109	336	2	4.1	CARDINAL
ejpam-109	336	3	4.5	CARDINAL
ejpam-109	336	4	4.6	CARDINAL
ejpam-109	337	1	λ1,λ2 ∈ zp	PERSON
ejpam-109	339	1	m≥ s	PERSON
ejpam-109	340	1	1	CARDINAL
ejpam-109	343	1	1	CARDINAL
ejpam-109	346	1	m≥ s	PERSON
ejpam-109	346	2	1− pm−1 ≡	WORK_OF_ART
ejpam-109	346	3	1	CARDINAL
ejpam-109	346	4	4.5	CARDINAL
ejpam-109	347	1	generalized von staudt-kummer congruences	PERSON
ejpam-109	347	2	congruences	ORG
ejpam-109	347	3	section 3	DATE
ejpam-109	349	1	two	CARDINAL
ejpam-109	349	2	km(n	PERSON
ejpam-109	349	3	2	CARDINAL
ejpam-109	349	4	section 3	LAW
ejpam-109	349	5	z×p of zp	ORG
ejpam-109	349	6	4.1	CARDINAL
ejpam-109	349	7	18	CARDINAL
ejpam-109	350	1	von staudt-kummer congruences	PERSON
ejpam-109	350	2	16	CARDINAL
ejpam-109	351	1	5	CARDINAL
ejpam-109	351	2	lehmer	ORG
ejpam-109	351	3	lehmer	ORG
ejpam-109	351	4	2.7	CARDINAL
ejpam-109	352	1	2	CARDINAL
ejpam-109	352	2	2	CARDINAL
ejpam-109	352	3	6= 2	DATE
ejpam-109	352	4	4	CARDINAL
ejpam-109	353	1	2 n and	QUANTITY
ejpam-109	353	2	5	CARDINAL
ejpam-109	353	3	euler	PERSON
ejpam-109	353	4	2.2	CARDINAL
ejpam-109	354	1	bm+1− jn j	PERSON
ejpam-109	354	2	1	CARDINAL
ejpam-109	354	3	2	DATE
ejpam-109	354	4	m+ 1	CARDINAL
ejpam-109	356	1	j. pure	PERSON
ejpam-109	356	2	1 (2008	DATE
ejpam-109	356	3	3-21	DATE
ejpam-109	356	4	17	DATE
ejpam-109	356	5	2	CARDINAL
ejpam-109	358	1	m/2	PERSON
ejpam-109	358	2	j = m.	PERSON
ejpam-109	358	3	2i	CARDINAL
ejpam-109	358	4	4	CARDINAL
ejpam-109	358	5	0,1	CARDINAL
ejpam-109	358	6	52i−3	CARDINAL
ejpam-109	358	7	2i	CARDINAL
ejpam-109	358	8	+ 1	DATE
ejpam-109	358	9	2i	CARDINAL
ejpam-109	359	1	3	CARDINAL
ejpam-109	361	1	2	CARDINAL
ejpam-109	362	1	0	CARDINAL
ejpam-109	362	2	1	CARDINAL
ejpam-109	363	1	1 3	CARDINAL
ejpam-109	363	2	2	CARDINAL
ejpam-109	364	1	xm	ORG
ejpam-109	364	2	1	CARDINAL
ejpam-109	365	1	2	CARDINAL
ejpam-109	367	1	2.2	CARDINAL
ejpam-109	368	1	2.1	CARDINAL
ejpam-109	369	1	1	CARDINAL
ejpam-109	369	2	1	CARDINAL
ejpam-109	369	3	1)sm(n)≡	CARDINAL
ejpam-109	369	4	∑	LOC
ejpam-109	369	5	j)m−1	GPE
ejpam-109	369	6	1	CARDINAL
ejpam-109	369	7	2 n2	QUANTITY
ejpam-109	370	1	j)m−1	GPE
ejpam-109	370	2	1	CARDINAL
ejpam-109	371	1	section 2	LAW
ejpam-109	372	1	1	CARDINAL
ejpam-109	372	2	j)m−1	GPE
ejpam-109	372	3	1	CARDINAL
ejpam-109	372	4	2	CARDINAL
ejpam-109	372	5	1)βm ≡ η′−1 ∑	PERSON
ejpam-109	372	6	j)m−1	GPE
ejpam-109	372	7	1 2 η′ η′−1 ∑	TIME
ejpam-109	373	1	5.1	CARDINAL
ejpam-109	373	2	0	CARDINAL
ejpam-109	373	3	1	DATE
ejpam-109	373	4	1	CARDINAL
ejpam-109	373	5	g(a)i = ¨	ORG
ejpam-109	373	6	j ∈	PERSON
ejpam-109	373	7	j∈g(a)i jm−1	PERSON
ejpam-109	373	8	j∈g(a)i jm−2	GPE
ejpam-109	373	9	5.1	CARDINAL
ejpam-109	373	10	1)βm ≡ am−1 a−1 ∑	PRODUCT
ejpam-109	373	11	1 2	CARDINAL
ejpam-109	374	1	5.2	CARDINAL
ejpam-109	375	1	j. pure	PERSON
ejpam-109	375	2	1 (2008	DATE
ejpam-109	375	3	3-21	DATE
ejpam-109	375	4	18	CARDINAL
ejpam-109	375	5	∑ j∈g(a)a−1−i jm−1+	PERSON
ejpam-109	375	6	m−	NORP
ejpam-109	375	7	1)η′ ∑ j∈g(a)a−1−i jm−2	QUANTITY
ejpam-109	375	8	m−	NORP
ejpam-109	375	9	1)η′v	CARDINAL
ejpam-109	377	1	jm−2	DATE
ejpam-109	378	1	2.2	CARDINAL
ejpam-109	378	2	1	CARDINAL
ejpam-109	378	3	2	CARDINAL
ejpam-109	379	1	∑ i=0	PERSON
ejpam-109	381	1	lehmer	GPE
ejpam-109	381	2	2.7	CARDINAL
ejpam-109	382	1	5.1	CARDINAL
ejpam-109	383	1	2	CARDINAL
ejpam-109	384	1	2,3	CARDINAL
ejpam-109	384	2	4,6	CARDINAL
ejpam-109	384	3	2.7	CARDINAL
ejpam-109	385	1	2	CARDINAL
ejpam-109	386	1	2	CARDINAL
ejpam-109	386	2	3,4	CARDINAL
ejpam-109	386	3	6	CARDINAL
ejpam-109	386	4	5.3	CARDINAL
ejpam-109	386	5	n is ≥ 7	DATE
ejpam-109	386	6	6	CARDINAL
ejpam-109	388	1	5.3	CARDINAL
ejpam-109	388	2	2,3	CARDINAL
ejpam-109	388	3	4,6	CARDINAL
ejpam-109	388	4	6	CARDINAL
ejpam-109	388	5	5.3	CARDINAL
ejpam-109	388	6	2,3	CARDINAL
ejpam-109	390	1	6)i	DATE
ejpam-109	390	2	vi = v	PERSON
ejpam-109	390	3	6)i	CARDINAL
ejpam-109	390	4	0	CARDINAL
ejpam-109	390	5	1	DATE
ejpam-109	390	6	5	CARDINAL
ejpam-109	391	1	vi ≡	PERSON
ejpam-109	391	2	3,4	CARDINAL
ejpam-109	391	3	5	CARDINAL
ejpam-109	392	1	1	CARDINAL
ejpam-109	392	2	6	CARDINAL
ejpam-109	392	3	5.2	CARDINAL
ejpam-109	392	4	6m−	CARDINAL
ejpam-109	393	1	1 2 6m−2η′ 5	DATE
ejpam-109	393	2	6m−1(5u0+ 3u1+ u2	MONEY
ejpam-109	393	3	1 2	DATE
ejpam-109	394	1	i=0 vi ≡	PERSON
ejpam-109	394	2	2	CARDINAL
ejpam-109	395	1	v2 ≡	PERSON
ejpam-109	396	1	6m−1	CARDINAL
ejpam-109	396	2	6− 61−m)βm	CARDINAL
ejpam-109	397	1	1 3	CARDINAL
ejpam-109	397	2	mod n2	PERSON
ejpam-109	398	1	t. agoh	PERSON
ejpam-109	399	1	j. pure	PERSON
ejpam-109	399	2	1 (2008	DATE
ejpam-109	399	3	3-21	DATE
ejpam-109	399	4	19	DATE
ejpam-109	399	5	5.3	CARDINAL
ejpam-109	399	6	2	CARDINAL
ejpam-109	399	7	3	DATE
ejpam-109	399	8	2− 21−m)βm	CARDINAL
ejpam-109	399	9	1 2	QUANTITY
ejpam-109	399	10	mod n2	PERSON
ejpam-109	399	11	3− 31−m)βm	CARDINAL
ejpam-109	399	12	2(u0	CARDINAL
ejpam-109	400	1	3	CARDINAL
ejpam-109	401	1	1+ 21−m+	QUANTITY
ejpam-109	402	1	21−m)−	CARDINAL
ejpam-109	402	2	3− 31−m	DATE
ejpam-109	403	1	6− 61−m	TIME
ejpam-109	404	1	2u0	CARDINAL
ejpam-109	404	2	1 3	CARDINAL
ejpam-109	404	3	6m−1	CARDINAL
ejpam-109	404	4	m−	NORP
ejpam-109	404	5	1)6m−2η′v0	CARDINAL
ejpam-109	404	6	η′− 6	DATE
ejpam-109	404	7	j)m−1	GPE
ejpam-109	404	8	5.3	CARDINAL
ejpam-109	404	9	6	CARDINAL
ejpam-109	404	10	6	CARDINAL
ejpam-109	404	11	2	CARDINAL
ejpam-109	404	12	section 2	LAW
ejpam-109	404	13	6.1	CARDINAL
ejpam-109	406	1	1 2	CARDINAL
ejpam-109	406	2	1	CARDINAL
ejpam-109	406	3	1 2	CARDINAL
ejpam-109	407	1	1	CARDINAL
ejpam-109	407	2	1,2	CARDINAL
ejpam-109	407	3	6=	CARDINAL
ejpam-109	408	1	j.	PERSON
ejpam-109	408	2	2	CARDINAL
ejpam-109	408	3	n ′m ≡	ORG
ejpam-109	410	1	1,2	CARDINAL
ejpam-109	410	2	2mi	CARDINAL
ejpam-109	410	3	1 ≤ mi ≤ 1 2	QUANTITY
ejpam-109	410	4	3	CARDINAL
ejpam-109	411	1	1 2	CARDINAL
ejpam-109	411	2	1	CARDINAL
ejpam-109	411	3	1 2	CARDINAL
ejpam-109	411	4	1	CARDINAL
ejpam-109	411	5	chinese	NORP
ejpam-109	411	6	congruences x ≡ mi	ORG
ejpam-109	411	7	1 2	CARDINAL
ejpam-109	411	8	1	CARDINAL
ejpam-109	411	9	1	CARDINAL
ejpam-109	411	10	2	DATE
ejpam-109	411	11	0	CARDINAL
ejpam-109	411	12	1 2s	CARDINAL
ejpam-109	411	13	1	CARDINAL
ejpam-109	412	1	2α	CARDINAL
ejpam-109	412	2	1	CARDINAL
ejpam-109	413	1	2.6	CARDINAL
ejpam-109	413	2	1,2	CARDINAL
ejpam-109	414	1	at least two	CARDINAL
ejpam-109	414	2	1 2	CARDINAL
ejpam-109	414	3	1	CARDINAL
ejpam-109	414	4	1 2	CARDINAL
ejpam-109	414	5	1	CARDINAL
ejpam-109	415	1	6= 1	DATE
ejpam-109	415	2	2	CARDINAL
ejpam-109	415	3	n ′m ≡	ORG
ejpam-109	416	1	6.1	CARDINAL
ejpam-109	416	2	37	CARDINAL
ejpam-109	416	3	59	DATE
ejpam-109	416	4	131	CARDINAL
ejpam-109	416	5	three	CARDINAL
ejpam-109	417	1	37,59	CARDINAL
ejpam-109	418	1	j. pure	PERSON
ejpam-109	418	2	1 (2008	DATE
ejpam-109	418	3	3-21	DATE
ejpam-109	418	4	20 131	CARDINAL
ejpam-109	418	5	1	CARDINAL
ejpam-109	418	6	2	CARDINAL
ejpam-109	419	1	1 ≤ m ≤	QUANTITY
ejpam-109	419	2	37	CARDINAL
ejpam-109	419	3	32	DATE
ejpam-109	419	4	59,44	CARDINAL
ejpam-109	419	5	131,22	CARDINAL
ejpam-109	420	1	congruences x ≡	ORG
ejpam-109	420	2	16	CARDINAL
ejpam-109	420	3	22	CARDINAL
ejpam-109	420	4	11	CARDINAL
ejpam-109	421	1	2806	CARDINAL
ejpam-109	421	2	18	CARDINAL
ejpam-109	421	3	29	CARDINAL
ejpam-109	421	4	65	DATE
ejpam-109	421	5	2	CARDINAL
ejpam-109	421	6	2806= 5612	DATE
ejpam-109	421	7	n ′m ≡	ORG
ejpam-109	422	1	59	DATE
ejpam-109	422	2	131	CARDINAL
ejpam-109	423	1	n ≥ 3	DATE
ejpam-109	423	2	2	CARDINAL
ejpam-109	423	3	section 3	LAW
ejpam-109	424	1	≡ l	ORG
ejpam-109	425	1	1	CARDINAL
ejpam-109	425	2	hm(n)≡ hl(n	GPE
ejpam-109	425	3	4.3	CARDINAL
ejpam-109	425	4	n0 = n	ORG
ejpam-109	426	1	εm(n)/d	GPE
ejpam-109	426	2	n0	GPE
ejpam-109	426	3	n0	GPE
ejpam-109	426	4	1	CARDINAL
ejpam-109	427	1	n0	GPE
ejpam-109	427	2	n0	GPE
ejpam-109	428	1	n ′m	ORG
ejpam-109	429	1	6∈ zp	QUANTITY
ejpam-109	429	2	2.5	CARDINAL
ejpam-109	429	3	1	CARDINAL
ejpam-109	430	1	3	CARDINAL
ejpam-109	430	2	n ′m	ORG
ejpam-109	431	1	2.8	CARDINAL
ejpam-109	432	1	6.2	CARDINAL
ejpam-109	433	1	1	CARDINAL
ejpam-109	433	2	2,3	CARDINAL
ejpam-109	436	1	1	CARDINAL
ejpam-109	436	2	6	CARDINAL
ejpam-109	436	3	1	CARDINAL
ejpam-109	437	1	∏k	DATE
ejpam-109	437	2	i=1	PERSON
ejpam-109	438	1	2.5	CARDINAL
ejpam-109	438	2	d′	PERSON
ejpam-109	440	1	1	CARDINAL
ejpam-109	441	1	m1|n	DATE
ejpam-109	442	1	1	CARDINAL
ejpam-109	442	2	6 ≤	QUANTITY
ejpam-109	444	1	1	CARDINAL
ejpam-109	446	1	6.2	CARDINAL
ejpam-109	447	1	first	ORDINAL
ejpam-109	448	1	21	CARDINAL
ejpam-109	448	2	1	CARDINAL
ejpam-109	448	3	bernoulli	PERSON
ejpam-109	448	4	euler	PERSON
ejpam-109	449	1	61	CARDINAL
ejpam-109	449	2	1988	DATE
ejpam-109	449	3	1-10	CARDINAL
ejpam-109	450	1	2	CARDINAL
ejpam-109	451	1	87	CARDINAL
ejpam-109	451	2	1995	DATE
ejpam-109	451	3	501-510	CARDINAL
ejpam-109	452	1	3	CARDINAL
ejpam-109	452	2	w.r.	GPE
ejpam-109	452	3	alford	GPE
ejpam-109	452	4	a. granville	PERSON
ejpam-109	452	5	c. pomerance	PERSON
ejpam-109	452	6	ann	PERSON
ejpam-109	453	1	140	CARDINAL
ejpam-109	453	2	1994	DATE
ejpam-109	453	3	1-20	CARDINAL
ejpam-109	454	1	4	CARDINAL
ejpam-109	454	2	j.m.	GPE
ejpam-109	454	3	r. girgensohn	PERSON
ejpam-109	454	4	amer	PERSON
ejpam-109	455	1	monthly	DATE
ejpam-109	455	2	103	CARDINAL
ejpam-109	455	3	40-50	CARDINAL
ejpam-109	456	1	5	CARDINAL
ejpam-109	456	2	j. buhler	PERSON
ejpam-109	456	3	r. crandall	PERSON
ejpam-109	456	4	r. ernvall	PERSON
ejpam-109	456	5	t. metsankyla	GPE
ejpam-109	456	6	m. shokrollahi	PERSON
ejpam-109	456	7	12 million	CARDINAL
ejpam-109	456	8	j. symbolic	PERSON
ejpam-109	457	1	31(2001	CARDINAL
ejpam-109	457	2	89–96	CARDINAL
ejpam-109	458	1	6	CARDINAL
ejpam-109	459	1	amer	PERSON
ejpam-109	461	1	5	CARDINAL
ejpam-109	461	2	1954	DATE
ejpam-109	461	3	329	CARDINAL
ejpam-109	462	1	s. plouffe	PERSON
ejpam-109	462	2	2007	DATE
ejpam-109	463	1	8	CARDINAL
ejpam-109	463	2	g. giuga	PERSON
ejpam-109	463	3	su una presumibile proprietà caratteristica	PERSON
ejpam-109	463	4	dei numeri	PERSON
ejpam-109	464	1	lombardo sci	PERSON
ejpam-109	464	2	lett	PERSON
ejpam-109	467	1	sci.	PERSON
ejpam-109	468	1	nat	PERSON
ejpam-109	469	1	83	DATE
ejpam-109	469	2	1950	DATE
ejpam-109	469	3	511	CARDINAL
ejpam-109	470	1	9	CARDINAL
ejpam-109	470	2	k. iwasawa	PERSON
ejpam-109	471	1	74	CARDINAL
ejpam-109	471	2	princeton univ.	ORG
ejpam-109	472	1	princeton	GPE
ejpam-109	472	2	1972	DATE
ejpam-109	473	1	10	CARDINAL
ejpam-109	473	2	k.l. jensen	PERSON
ejpam-109	473	3	talteoretiske egenskaber	GPE
ejpam-109	473	4	de bernoulliske tal	ORG
ejpam-109	473	5	tidsskrift f. math	PERSON
ejpam-109	474	1	26	CARDINAL
ejpam-109	474	2	1915	DATE
ejpam-109	474	3	73	CARDINAL
ejpam-109	475	1	11	CARDINAL
ejpam-109	475	2	w. johnson	PERSON
ejpam-109	475	3	7 (1975	DATE
ejpam-109	475	4	251	CARDINAL
ejpam-109	476	1	12	CARDINAL
ejpam-109	476	2	kellner	PERSON
ejpam-109	476	3	2004	DATE
ejpam-109	477	1	13	CARDINAL
ejpam-109	477	2	e. lehmer	PERSON
ejpam-109	477	3	fermat	ORG
ejpam-109	477	4	wilson	GPE
ejpam-109	477	5	ann.	PERSON
ejpam-109	478	1	39	CARDINAL
ejpam-109	478	2	1938	DATE
ejpam-109	478	3	350-360	CARDINAL
ejpam-109	479	1	14	CARDINAL
ejpam-109	479	2	1	CARDINAL
ejpam-109	480	1	inst	PERSON
ejpam-109	480	2	nat	PERSON
ejpam-109	481	1	acad	ORG
ejpam-109	482	1	sci.	ORG
ejpam-109	482	2	ukraine	GPE
ejpam-109	482	3	1998	DATE
ejpam-109	482	4	71	CARDINAL
ejpam-109	483	1	15	CARDINAL
ejpam-109	484	1	slavutskii	ORG
ejpam-109	484	2	staudt	ORG
ejpam-109	485	1	sci	PERSON
ejpam-109	485	2	5 (1995	DATE
ejpam-109	485	3	70-74	DATE
ejpam-109	486	1	16	CARDINAL
ejpam-109	486	2	sun	ORG
ejpam-109	487	1	262(2003	CARDINAL
ejpam-109	487	2	253	CARDINAL
ejpam-109	488	1	17	CARDINAL
ejpam-109	488	2	washington	GPE
ejpam-109	488	3	new york	GPE
ejpam-109	488	4	1982	DATE
ejpam-109	489	1	18	CARDINAL
ejpam-109	489	2	bernoulli	ORG
ejpam-109	489	3	euler	PERSON
ejpam-109	489	4	78(1999	GPE
ejpam-109	489	5	204	CARDINAL
ejpam-109	489	6	19	CARDINAL
ejpam-109	489	7	kummer	PERSON
ejpam-109	490	1	289	CARDINAL