id	sid	eid	entity	type
ejpam-5372	1	1	european journal	ORG
ejpam-5372	2	1	17	CARDINAL
ejpam-5372	2	2	4	CARDINAL
ejpam-5372	2	3	2024	DATE
ejpam-5372	2	4	2431-2447	CARDINAL
ejpam-5372	2	5	1307-5543	CARDINAL
ejpam-5372	2	6	new york	GPE
ejpam-5372	2	7	marc wolf1,∗	PERSON
ejpam-5372	2	8	wolf1 1	ORG
ejpam-5372	2	9	tsoftemail	ORG
ejpam-5372	2	10	france	GPE
ejpam-5372	3	1	modulo	ORG
ejpam-5372	7	1	3	CARDINAL
ejpam-5372	8	1	2020	DATE
ejpam-5372	8	2	11a07	CARDINAL
ejpam-5372	8	3	68p05	CARDINAL
ejpam-5372	8	4	11b05	CARDINAL
ejpam-5372	8	5	fermat	ORG
ejpam-5372	8	6	two	CARDINAL
ejpam-5372	8	7	1	CARDINAL
ejpam-5372	9	1	1.1	CARDINAL
ejpam-5372	10	1	lagrange	GPE
ejpam-5372	10	2	fermat	ORG
ejpam-5372	12	1	euler	PERSON
ejpam-5372	12	2	2	CARDINAL
ejpam-5372	12	3	2	CARDINAL
ejpam-5372	12	4	k ∈	ORG
ejpam-5372	13	1	φ	PERSON
ejpam-5372	14	1	one	CARDINAL
ejpam-5372	15	1	∈	ORG
ejpam-5372	15	2	2	CARDINAL
ejpam-5372	16	1	first	ORDINAL
ejpam-5372	18	1	m. wolf	PERSON
ejpam-5372	18	2	f. wolf	PERSON
ejpam-5372	18	3	2431	CARDINAL
ejpam-5372	18	4	2024	CARDINAL
ejpam-5372	19	1	m. wolf	PERSON
ejpam-5372	19	2	f. wolf	PERSON
ejpam-5372	20	1	j. pure	PERSON
ejpam-5372	20	2	17	CARDINAL
ejpam-5372	20	3	4	CARDINAL
ejpam-5372	20	4	2024	CARDINAL
ejpam-5372	20	5	2431-2447 2432	CARDINAL
ejpam-5372	22	1	2	CARDINAL
ejpam-5372	22	2	∈ n∗	ORG
ejpam-5372	22	3	1	CARDINAL
ejpam-5372	23	1	second	ORDINAL
ejpam-5372	24	1	1.2	CARDINAL
ejpam-5372	24	2	1	CARDINAL
ejpam-5372	28	1	at least one	CARDINAL
ejpam-5372	28	2	e. (ii	ORG
ejpam-5372	31	1	∈	ORG
ejpam-5372	31	2	2	CARDINAL
ejpam-5372	32	1	1	CARDINAL
ejpam-5372	32	2	∈	ORG
ejpam-5372	32	3	{ gk	PERSON
ejpam-5372	32	4	k ∈ z	PERSON
ejpam-5372	32	5	2	CARDINAL
ejpam-5372	35	1	1	CARDINAL
ejpam-5372	35	2	1	CARDINAL
ejpam-5372	35	3	2	CARDINAL
ejpam-5372	36	1	2	CARDINAL
ejpam-5372	36	2	g = hk.	ORG
ejpam-5372	37	1	1	CARDINAL
ejpam-5372	37	2	2	CARDINAL
ejpam-5372	38	1	2u	CARDINAL
ejpam-5372	39	1	hu	PERSON
ejpam-5372	40	1	2	CARDINAL
ejpam-5372	41	1	∈	ORG
ejpam-5372	41	2	2	CARDINAL
ejpam-5372	42	1	gz	PERSON
ejpam-5372	42	2	gs	ORG
ejpam-5372	42	3	gqnr	ORG
ejpam-5372	42	4	gs	ORG
ejpam-5372	44	1	1	CARDINAL
ejpam-5372	45	1	3	CARDINAL
ejpam-5372	45	2	1	CARDINAL
ejpam-5372	45	3	2	CARDINAL
ejpam-5372	46	1	2	CARDINAL
ejpam-5372	47	1	∈	ORG
ejpam-5372	47	2	2	CARDINAL
ejpam-5372	48	1	⊂	GPE
ejpam-5372	48	2	gs ⊂	ORG
ejpam-5372	50	1	second	ORDINAL
ejpam-5372	52	1	2	CARDINAL
ejpam-5372	52	2	⊂	GPE
ejpam-5372	53	1	3	CARDINAL
ejpam-5372	54	1	∈	ORG
ejpam-5372	54	2	2	CARDINAL
ejpam-5372	57	1	m. wolf	PERSON
ejpam-5372	57	2	f. wolf	PERSON
ejpam-5372	58	1	j. pure	PERSON
ejpam-5372	58	2	17	CARDINAL
ejpam-5372	58	3	4	CARDINAL
ejpam-5372	58	4	2024	CARDINAL
ejpam-5372	58	5	2431-2447 2433	CARDINAL
ejpam-5372	60	1	⋃ g∈rk	PERSON
ejpam-5372	62	1	1	CARDINAL
ejpam-5372	63	1	3	CARDINAL
ejpam-5372	64	1	rk	ORG
ejpam-5372	64	2	4	CARDINAL
ejpam-5372	65	1	∈	ORG
ejpam-5372	65	2	2	CARDINAL
ejpam-5372	65	3	2	CARDINAL
ejpam-5372	65	4	1	CARDINAL
ejpam-5372	66	1	0 ≤ k ≤ n	QUANTITY
ejpam-5372	66	2	2k	CARDINAL
ejpam-5372	66	3	1 ≤ k ≤	QUANTITY
ejpam-5372	67	1	2k−1	CARDINAL
ejpam-5372	67	2	k > n	ORG
ejpam-5372	69	1	k ∈	ORG
ejpam-5372	69	2	2k	CARDINAL
ejpam-5372	70	1	first	ORDINAL
ejpam-5372	70	2	two	CARDINAL
ejpam-5372	71	1	2k	CARDINAL
ejpam-5372	71	2	2	CARDINAL
ejpam-5372	73	1	2.1	CARDINAL
ejpam-5372	73	2	∈	ORG
ejpam-5372	73	3	2	CARDINAL
ejpam-5372	74	1	φ	ORG
ejpam-5372	75	1	1	CARDINAL
ejpam-5372	77	1	5	CARDINAL
ejpam-5372	78	1	1	CARDINAL
ejpam-5372	78	2	∏ q∈p	CARDINAL
ejpam-5372	80	1	{ gk	PERSON
ejpam-5372	80	2	1 ≤	QUANTITY
ejpam-5372	80	3	2	CARDINAL
ejpam-5372	80	4	1	CARDINAL
ejpam-5372	80	5	1	CARDINAL
ejpam-5372	80	6	∈	ORG
ejpam-5372	80	7	∈	ORG
ejpam-5372	80	8	2q	CARDINAL
ejpam-5372	80	9	⇔ ∅ ⊊	ORG
ejpam-5372	81	1	2	CARDINAL
ejpam-5372	81	2	1 and ∀q	CARDINAL
ejpam-5372	81	3	2	CARDINAL
ejpam-5372	81	4	2q	CARDINAL
ejpam-5372	82	1	m. wolf	PERSON
ejpam-5372	82	2	f. wolf	PERSON
ejpam-5372	83	1	j. pure	PERSON
ejpam-5372	83	2	17	CARDINAL
ejpam-5372	83	3	4	CARDINAL
ejpam-5372	83	4	2024	CARDINAL
ejpam-5372	83	5	2431-2447 2434	CARDINAL
ejpam-5372	83	6	second	ORDINAL
ejpam-5372	83	7	only one	CARDINAL
ejpam-5372	83	8	two	CARDINAL
ejpam-5372	85	1	∈	ORG
ejpam-5372	86	1	gk	PERSON
ejpam-5372	87	1	∈	ORG
ejpam-5372	87	2	1	CARDINAL
ejpam-5372	89	1	1	CARDINAL
ejpam-5372	90	1	∈	ORG
ejpam-5372	90	2	1	CARDINAL
ejpam-5372	91	1	1	CARDINAL
ejpam-5372	91	2	1	CARDINAL
ejpam-5372	92	1	1	CARDINAL
ejpam-5372	93	1	1	CARDINAL
ejpam-5372	95	1	∈	PRODUCT
ejpam-5372	95	2	gs	ORG
ejpam-5372	95	3	1	CARDINAL
ejpam-5372	97	1	p−1	ORG
ejpam-5372	97	2	2	CARDINAL
ejpam-5372	97	3	1	CARDINAL
ejpam-5372	97	4	4	CARDINAL
ejpam-5372	98	1	2q	CARDINAL
ejpam-5372	98	2	∈	ORG
ejpam-5372	98	3	∈	ORG
ejpam-5372	99	1	2q	CARDINAL
ejpam-5372	101	1	two	CARDINAL
ejpam-5372	101	2	one	CARDINAL
ejpam-5372	102	1	1	CARDINAL
ejpam-5372	103	1	∈	ORG
ejpam-5372	104	1	2	CARDINAL
ejpam-5372	105	1	∈	ORG
ejpam-5372	105	2	∈	ORG
ejpam-5372	105	3	2	CARDINAL
ejpam-5372	105	4	2q	CARDINAL
ejpam-5372	106	1	2	CARDINAL
ejpam-5372	106	2	2q	CARDINAL
ejpam-5372	107	1	∈	ORG
ejpam-5372	107	2	2	CARDINAL
ejpam-5372	107	3	2	CARDINAL
ejpam-5372	107	4	2	CARDINAL
ejpam-5372	107	5	−1	CARDINAL
ejpam-5372	107	6	2	CARDINAL
ejpam-5372	107	7	−1	DATE
ejpam-5372	109	1	2.2	CARDINAL
ejpam-5372	109	2	2.2.1	CARDINAL
ejpam-5372	110	1	4	CARDINAL
ejpam-5372	111	1	0 ≤	MONEY
ejpam-5372	111	2	⟨h⟩(x	CARDINAL
ejpam-5372	114	1	∈	ORG
ejpam-5372	114	2	2	CARDINAL
ejpam-5372	114	3	1	CARDINAL
ejpam-5372	114	4	2nz	ORDINAL
ejpam-5372	116	1	∈	ORG
ejpam-5372	117	1	0 ≤	MONEY
ejpam-5372	118	1	〈 g2 tz	PERSON
ejpam-5372	119	1	0	CARDINAL
ejpam-5372	119	2	∈	ORG
ejpam-5372	121	1	m. wolf	PERSON
ejpam-5372	121	2	f. wolf	PERSON
ejpam-5372	122	1	j. pure	PERSON
ejpam-5372	122	2	17	CARDINAL
ejpam-5372	122	3	4	CARDINAL
ejpam-5372	122	4	2024	CARDINAL
ejpam-5372	122	5	2431-2447 2435	CARDINAL
ejpam-5372	123	1	2n	CARDINAL
ejpam-5372	124	1	euler	PERSON
ejpam-5372	124	2	2	CARDINAL
ejpam-5372	124	3	−1	DATE
ejpam-5372	132	1	2	CARDINAL
ejpam-5372	132	2	1	CARDINAL
ejpam-5372	133	1	2	CARDINAL
ejpam-5372	134	1	⟨m⟩(z	DATE
ejpam-5372	135	1	⊂	GPE
ejpam-5372	135	2	⊂	GPE
ejpam-5372	136	1	⊂	GPE
ejpam-5372	137	1	∣∣∣	CARDINAL
ejpam-5372	138	1	2n−1	CARDINAL
ejpam-5372	139	1	mkr ≡	PERSON
ejpam-5372	140	1	1 ≤ k ≤	QUANTITY
ejpam-5372	143	1	′−kr ′	DATE
ejpam-5372	144	1	2n−1	DATE
ejpam-5372	145	1	1	CARDINAL
ejpam-5372	146	1	k = k	PERSON
ejpam-5372	149	1	∣∣∣	CARDINAL
ejpam-5372	151	1	2n−1z	CARDINAL
ejpam-5372	151	2	2	CARDINAL
ejpam-5372	154	1	⊂	GPE
ejpam-5372	156	1	∈	ORG
ejpam-5372	156	2	∈	PERSON
ejpam-5372	157	1	1	CARDINAL
ejpam-5372	157	2	2nz	ORDINAL
ejpam-5372	158	1	2	CARDINAL
ejpam-5372	158	2	≡ m2n−1zr2 n−1z ≡ r2	ORG
ejpam-5372	159	1	2nz	ORDINAL
ejpam-5372	159	2	2nz	ORDINAL
ejpam-5372	159	3	2nz	ORDINAL
ejpam-5372	160	1	5	CARDINAL
ejpam-5372	160	2	∈	ORG
ejpam-5372	161	1	8	CARDINAL
ejpam-5372	164	1	φ	ORG
ejpam-5372	164	2	1	CARDINAL
ejpam-5372	164	3	1	CARDINAL
ejpam-5372	164	4	φ	ORG
ejpam-5372	164	5	2	CARDINAL
ejpam-5372	164	6	φ	PERSON
ejpam-5372	164	7	coprime	ORG
ejpam-5372	164	8	φ	PERSON
ejpam-5372	164	9	2k	CARDINAL
ejpam-5372	165	1	2k−1	CARDINAL
ejpam-5372	166	1	3	CARDINAL
ejpam-5372	166	2	4	CARDINAL
ejpam-5372	166	3	1 i.e.	CARDINAL
ejpam-5372	166	4	2	CARDINAL
ejpam-5372	166	5	φ	PERSON
ejpam-5372	166	6	1	CARDINAL
ejpam-5372	166	7	2)φ	CARDINAL
ejpam-5372	166	8	2	CARDINAL
ejpam-5372	167	1	2	CARDINAL
ejpam-5372	168	1	1	CARDINAL
ejpam-5372	169	1	4	CARDINAL
ejpam-5372	169	2	φ	ORG
ejpam-5372	169	3	1	CARDINAL
ejpam-5372	169	4	2n)φ	DATE
ejpam-5372	170	1	2n−1φ	CARDINAL
ejpam-5372	170	2	φ	ORG
ejpam-5372	170	3	2	CARDINAL
ejpam-5372	170	4	2n−1	CARDINAL
ejpam-5372	170	5	2n−2φ	CARDINAL
ejpam-5372	171	1	9	CARDINAL
ejpam-5372	174	1	r(n)⧹r(n−1	GPE
ejpam-5372	175	1	⊂	GPE
ejpam-5372	176	1	m. wolf	PERSON
ejpam-5372	176	2	f. wolf	PERSON
ejpam-5372	177	1	j. pure	PERSON
ejpam-5372	177	2	17	CARDINAL
ejpam-5372	177	3	4	CARDINAL
ejpam-5372	177	4	2024	CARDINAL
ejpam-5372	177	5	2431-2447	CARDINAL
ejpam-5372	178	1	∈	ORG
ejpam-5372	178	2	∈	PRODUCT
ejpam-5372	178	3	1	CARDINAL
ejpam-5372	178	4	2nz	ORDINAL
ejpam-5372	179	1	∈	PERSON
ejpam-5372	180	1	∈	PRODUCT
ejpam-5372	182	1	2q	CARDINAL
ejpam-5372	182	2	p−1	ORG
ejpam-5372	182	3	n ≥ 3	DATE
ejpam-5372	182	4	2q	CARDINAL
ejpam-5372	183	1	≡ m	ORG
ejpam-5372	183	2	2q	CARDINAL
ejpam-5372	184	1	4	CARDINAL
ejpam-5372	184	2	−1	DATE
ejpam-5372	184	3	4	CARDINAL
ejpam-5372	184	4	1	CARDINAL
ejpam-5372	187	1	10	CARDINAL
ejpam-5372	189	1	first	ORDINAL
ejpam-5372	191	1	⊂	GPE
ejpam-5372	192	1	±m2	PERSON
ejpam-5372	193	1	⊂	GPE
ejpam-5372	196	1	−m2 ∈ gs	ORG
ejpam-5372	197	1	−gs	GPE
ejpam-5372	197	2	gs	ORG
ejpam-5372	198	1	−1	DATE
ejpam-5372	199	1	6	CARDINAL
ejpam-5372	199	2	∈	PRODUCT
ejpam-5372	199	3	m2 ∈ gs	PERSON
ejpam-5372	200	1	n ≥ 2	DATE
ejpam-5372	200	2	∈	ORG
ejpam-5372	202	1	1	CARDINAL
ejpam-5372	203	1	2	CARDINAL
ejpam-5372	204	1	2	CARDINAL
ejpam-5372	207	1	1	CARDINAL
ejpam-5372	207	2	2	CARDINAL
ejpam-5372	209	1	⊂	GPE
ejpam-5372	210	1	4	CARDINAL
ejpam-5372	210	2	1	CARDINAL
ejpam-5372	212	1	4	CARDINAL
ejpam-5372	212	2	1	CARDINAL
ejpam-5372	213	1	4	CARDINAL
ejpam-5372	213	2	4	CARDINAL
ejpam-5372	213	3	−1	DATE
ejpam-5372	213	4	−m2 ∈ gs	ORG
ejpam-5372	214	1	∈ gs	PERSON
ejpam-5372	214	2	/∈ gs	ORG
ejpam-5372	215	1	gs	ORG
ejpam-5372	215	2	−gs	ORG
ejpam-5372	215	3	gs	ORG
ejpam-5372	216	1	9	CARDINAL
ejpam-5372	216	2	10	CARDINAL
ejpam-5372	217	1	5	CARDINAL
ejpam-5372	218	1	∈	ORG
ejpam-5372	218	2	g′	PERSON
ejpam-5372	220	1	11	CARDINAL
ejpam-5372	221	1	g′ z	PERSON
ejpam-5372	221	2	gs	ORG
ejpam-5372	223	1	∈	ORG
ejpam-5372	224	1	k ∈ n∗	ORG
ejpam-5372	224	2	gs	PERSON
ejpam-5372	224	3	∈ gs	PERSON
ejpam-5372	224	4	•	CARDINAL
ejpam-5372	225	1	= gs	PERSON
ejpam-5372	225	2	2	CARDINAL
ejpam-5372	226	1	m. wolf	PERSON
ejpam-5372	226	2	f. wolf	PERSON
ejpam-5372	227	1	j. pure	PERSON
ejpam-5372	227	2	17	CARDINAL
ejpam-5372	227	3	4	CARDINAL
ejpam-5372	227	4	2024	CARDINAL
ejpam-5372	227	5	2431-2447	CARDINAL
ejpam-5372	229	1	−gs =	PERSON
ejpam-5372	230	1	⊔ gs	PERSON
ejpam-5372	230	2	2	CARDINAL
ejpam-5372	232	1	gs	ORG
ejpam-5372	232	2	2	CARDINAL
ejpam-5372	232	3	−gs (2	ORG
ejpam-5372	232	4	•	CARDINAL
ejpam-5372	232	5	g′	PERSON
ejpam-5372	232	6	⋃n−1 t=0 gs	PERSON
ejpam-5372	232	7	2	CARDINAL
ejpam-5372	232	8	∈	ORG
ejpam-5372	232	9	2	CARDINAL
ejpam-5372	232	10	q|p− 1	DATE
ejpam-5372	232	11	2q	CARDINAL
ejpam-5372	234	1	g′	PERSON
ejpam-5372	234	2	∈	ORG
ejpam-5372	234	3	g ∈ gz	PERSON
ejpam-5372	234	4	g ∈	PERSON
ejpam-5372	235	1	5	CARDINAL
ejpam-5372	235	2	2	CARDINAL
ejpam-5372	235	3	p−1	ORG
ejpam-5372	235	4	2	CARDINAL
ejpam-5372	235	5	−1	DATE
ejpam-5372	235	6	p−1	ORG
ejpam-5372	237	1	p−1	ORG
ejpam-5372	237	2	1	CARDINAL
ejpam-5372	237	3	7	CARDINAL
ejpam-5372	237	4	gs ⊂ g′	ORG
ejpam-5372	239	1	g′	PERSON
ejpam-5372	240	1	∈	ORG
ejpam-5372	241	1	•	CARDINAL
ejpam-5372	241	2	11	CARDINAL
ejpam-5372	241	3	two	CARDINAL
ejpam-5372	242	1	g′	PERSON
ejpam-5372	242	2	10	CARDINAL
ejpam-5372	242	3	gs	ORG
ejpam-5372	242	4	2	CARDINAL
ejpam-5372	244	1	gs	ORG
ejpam-5372	244	2	gs	ORG
ejpam-5372	244	3	2	CARDINAL
ejpam-5372	245	1	gs	ORG
ejpam-5372	245	2	2	CARDINAL
ejpam-5372	246	1	−1	DATE
ejpam-5372	246	2	7	CARDINAL
ejpam-5372	247	1	•	CARDINAL
ejpam-5372	247	2	10	CARDINAL
ejpam-5372	248	1	2	CARDINAL
ejpam-5372	248	2	gs	ORG
ejpam-5372	248	3	g′	PERSON
ejpam-5372	249	1	−gs =	PERSON
ejpam-5372	250	1	⊔ gs	PERSON
ejpam-5372	250	2	2	CARDINAL
ejpam-5372	251	1	•	CARDINAL
ejpam-5372	251	2	5	CARDINAL
ejpam-5372	251	3	gs = −gs	ORG
ejpam-5372	251	4	gs	ORG
ejpam-5372	251	5	2	CARDINAL
ejpam-5372	251	6	half	CARDINAL
ejpam-5372	251	7	gs	ORG
ejpam-5372	251	8	10	CARDINAL
ejpam-5372	251	9	gs	ORG
ejpam-5372	251	10	gs	ORG
ejpam-5372	251	11	2	CARDINAL
ejpam-5372	251	12	−gs	PERSON
ejpam-5372	251	13	2	CARDINAL
ejpam-5372	253	1	gs	ORG
ejpam-5372	253	2	2	CARDINAL
ejpam-5372	253	3	−gs (2	ORG
ejpam-5372	254	1	3	CARDINAL
ejpam-5372	255	1	gs	PERSON
ejpam-5372	255	2	2	CARDINAL
ejpam-5372	255	3	−gs (2	ORG
ejpam-5372	255	4	g ∈ gz	PERSON
ejpam-5372	255	5	k coprime	ORG
ejpam-5372	255	6	1	CARDINAL
ejpam-5372	255	7	g4k ≡ −g4	ORG
ejpam-5372	255	8	gs	ORG
ejpam-5372	255	9	2	CARDINAL
ejpam-5372	255	10	2	CARDINAL
ejpam-5372	255	11	g k−1 2 )8 ≡ −1 ≡	ORG
ejpam-5372	255	12	n ≥ 4	ORG
ejpam-5372	256	1	n ≥ 4	DATE
ejpam-5372	256	2	−1	DATE
ejpam-5372	256	3	gs	ORG
ejpam-5372	256	4	2	CARDINAL
ejpam-5372	256	5	2	CARDINAL
ejpam-5372	257	1	•	CARDINAL
ejpam-5372	257	2	gs	ORG
ejpam-5372	257	3	2	CARDINAL
ejpam-5372	257	4	2t+1	DATE
ejpam-5372	258	1	2	CARDINAL
ejpam-5372	259	1	2	CARDINAL
ejpam-5372	259	2	induction∣∣∣gs	GPE
ejpam-5372	259	3	2	CARDINAL
ejpam-5372	259	4	∣∣∣	CARDINAL
ejpam-5372	260	1	1 2	CARDINAL
ejpam-5372	260	2	1 2t+1 |gz	TIME
ejpam-5372	262	1	−gs (2n−1)	ORG
ejpam-5372	263	1	2n−1	CARDINAL
ejpam-5372	263	2	2n−1	CARDINAL
ejpam-5372	263	3	∣∣∣	CARDINAL
ejpam-5372	263	4	1 2n−1 |gz	QUANTITY
ejpam-5372	264	1	gs	ORG
ejpam-5372	264	2	2	CARDINAL
ejpam-5372	264	3	0≤t≤n−1	CARDINAL
ejpam-5372	265	1	5	CARDINAL
ejpam-5372	265	2	∈	ORG
ejpam-5372	265	3	rgs	ORG
ejpam-5372	265	4	2	CARDINAL
ejpam-5372	265	5	⊂	GPE
ejpam-5372	266	1	g′	PERSON
ejpam-5372	266	2	⋃n−1 t=0 gs	PERSON
ejpam-5372	266	3	2	CARDINAL
ejpam-5372	267	1	5	CARDINAL
ejpam-5372	267	2	g′	PERSON
ejpam-5372	267	3	∈	ORG
ejpam-5372	267	4	2	CARDINAL
ejpam-5372	267	5	q|p− 1	DATE
ejpam-5372	267	6	2q	CARDINAL
ejpam-5372	268	1	m. wolf	PERSON
ejpam-5372	268	2	f. wolf	PERSON
ejpam-5372	269	1	j. pure	PERSON
ejpam-5372	269	2	17	CARDINAL
ejpam-5372	269	3	4	CARDINAL
ejpam-5372	269	4	2024	CARDINAL
ejpam-5372	269	5	2431-2447	CARDINAL
ejpam-5372	269	6	1	CARDINAL
ejpam-5372	270	1	•	CARDINAL
ejpam-5372	270	2	∈	ORG
ejpam-5372	271	1	∈	ORG
ejpam-5372	271	2	2	CARDINAL
ejpam-5372	271	3	2q	CARDINAL
ejpam-5372	271	4	∈	ORG
ejpam-5372	271	5	∈	ORG
ejpam-5372	271	6	∈	ORG
ejpam-5372	271	7	∈	ORG
ejpam-5372	271	8	2	CARDINAL
ejpam-5372	273	1	first	ORDINAL
ejpam-5372	273	2	second	ORDINAL
ejpam-5372	273	3	5	CARDINAL
ejpam-5372	274	1	chinese	NORP
ejpam-5372	275	1	z.	PERSON
ejpam-5372	275	2	2x	CARDINAL
ejpam-5372	275	3	0	CARDINAL
ejpam-5372	276	1	2n	CARDINAL
ejpam-5372	276	2	2n−1z	CARDINAL
ejpam-5372	276	3	∈	ORG
ejpam-5372	276	4	2	CARDINAL
ejpam-5372	276	5	2q	CARDINAL
ejpam-5372	277	1	z. 2.2.2	PERSON
ejpam-5372	279	1	r(n)⧹r(n−1	GPE
ejpam-5372	281	1	2	CARDINAL
ejpam-5372	282	1	∈ gs	PERSON
ejpam-5372	283	1	∈	ORG
ejpam-5372	283	2	∀k	DATE
ejpam-5372	283	3	∈	PRODUCT
ejpam-5372	284	1	first	ORDINAL
ejpam-5372	284	2	1	CARDINAL
ejpam-5372	285	1	∈	ORG
ejpam-5372	285	2	2	CARDINAL
ejpam-5372	285	3	1	CARDINAL
ejpam-5372	285	4	2q	CARDINAL
ejpam-5372	286	1	2	CARDINAL
ejpam-5372	286	2	2q	CARDINAL
ejpam-5372	286	3	2	CARDINAL
ejpam-5372	286	4	2q	CARDINAL
ejpam-5372	287	1	6	CARDINAL
ejpam-5372	288	1	∈	ORG
ejpam-5372	288	2	1	CARDINAL
ejpam-5372	288	3	1	CARDINAL
ejpam-5372	288	4	integer k	PERSON
ejpam-5372	288	5	ak ≡ 1	ORG
ejpam-5372	290	1	12	CARDINAL
ejpam-5372	291	1	∈ gs	PERSON
ejpam-5372	292	1	1	CARDINAL
ejpam-5372	296	1	2k	CARDINAL
ejpam-5372	296	2	1	CARDINAL
ejpam-5372	298	1	modulo p	ORG
ejpam-5372	298	2	k ≡ b1 ≡	ORG
ejpam-5372	298	3	b. m. wolf	PERSON
ejpam-5372	298	4	f. wolf	PERSON
ejpam-5372	299	1	j. pure	PERSON
ejpam-5372	299	2	17	CARDINAL
ejpam-5372	299	3	4	CARDINAL
ejpam-5372	299	4	2024	CARDINAL
ejpam-5372	299	5	2431-2447 2439	CARDINAL
ejpam-5372	299	6	1	CARDINAL
ejpam-5372	302	1	pohlig-hellman algorithm	ORG
ejpam-5372	303	1	•	CARDINAL
ejpam-5372	303	2	2	CARDINAL
ejpam-5372	304	1	13	CARDINAL
ejpam-5372	305	1	z.	PERSON
ejpam-5372	305	2	1	CARDINAL
ejpam-5372	306	1	1	CARDINAL
ejpam-5372	308	1	chinese	NORP
ejpam-5372	308	2	≃ ∏ q∈dp(p−1	PERCENT
ejpam-5372	309	1	∏ q∈dp(p−1	PERCENT
ejpam-5372	309	2	∣∣(z	DATE
ejpam-5372	311	1	αq−1	PERSON
ejpam-5372	312	1	1	CARDINAL
ejpam-5372	312	2	14	CARDINAL
ejpam-5372	313	1	∈	ORG
ejpam-5372	313	2	gs	ORG
ejpam-5372	313	3	mp−2 ∈	ORG
ejpam-5372	313	4	gs	ORG
ejpam-5372	315	1	mp−2	ORG
ejpam-5372	315	2	gs	ORG
ejpam-5372	316	1	two	CARDINAL
ejpam-5372	317	1	3	CARDINAL
ejpam-5372	318	1	0	CARDINAL
ejpam-5372	318	2	1	CARDINAL
ejpam-5372	318	3	2n−tz	CARDINAL
ejpam-5372	318	4	1	CARDINAL
ejpam-5372	319	1	∈	ORG
ejpam-5372	320	1	m2an−1	NORP
ejpam-5372	320	2	1	CARDINAL
ejpam-5372	323	1	∈	ORG
ejpam-5372	324	1	2 ≤ 2	MONEY
ejpam-5372	324	2	2z	CARDINAL
ejpam-5372	324	3	1	CARDINAL
ejpam-5372	324	4	2an−1	CARDINAL
ejpam-5372	325	1	2	CARDINAL
ejpam-5372	325	2	2n−1z	CARDINAL
ejpam-5372	326	1	3	CARDINAL
ejpam-5372	328	1	2a0	CARDINAL
ejpam-5372	329	1	2p−	CARDINAL
ejpam-5372	329	2	4	CARDINAL
ejpam-5372	329	3	1 +	CARDINAL
ejpam-5372	329	4	3	CARDINAL
ejpam-5372	329	5	1	CARDINAL
ejpam-5372	330	1	gs	ORG
ejpam-5372	331	1	15	CARDINAL
ejpam-5372	332	1	1	CARDINAL
ejpam-5372	333	1	2	CARDINAL
ejpam-5372	335	1	0 ≤ x	QUANTITY
ejpam-5372	335	2	1	CARDINAL
ejpam-5372	336	1	logd2	ORG
ejpam-5372	336	2	1	CARDINAL
ejpam-5372	338	1	gs	ORG
ejpam-5372	338	2	2k	CARDINAL
ejpam-5372	338	3	k odd and l coprime	ORG
ejpam-5372	339	1	≡ 1	ORG
ejpam-5372	339	2	k0	ORG
ejpam-5372	339	3	2k0	MONEY
ejpam-5372	339	4	l0	ORG
ejpam-5372	340	1	m. wolf	PERSON
ejpam-5372	340	2	f. wolf	PERSON
ejpam-5372	341	1	j. pure	PERSON
ejpam-5372	341	2	17	CARDINAL
ejpam-5372	341	3	4	CARDINAL
ejpam-5372	341	4	2024	CARDINAL
ejpam-5372	341	5	2431-2447 2440	CARDINAL
ejpam-5372	341	6	2kx	ORDINAL
ejpam-5372	341	7	2k0	CARDINAL
ejpam-5372	341	8	2xl0	CARDINAL
ejpam-5372	342	1	k0	ORG
ejpam-5372	342	2	2 xl0	PERSON
ejpam-5372	343	1	logd2	GPE
ejpam-5372	343	2	1	CARDINAL
ejpam-5372	343	3	0 ≤ x	QUANTITY
ejpam-5372	343	4	1	CARDINAL
ejpam-5372	345	1	2	CARDINAL
ejpam-5372	348	1	1	CARDINAL
ejpam-5372	351	1	∈	ORG
ejpam-5372	351	2	1	CARDINAL
ejpam-5372	351	3	logd2	GPE
ejpam-5372	351	4	1	CARDINAL
ejpam-5372	351	5	first	ORDINAL
ejpam-5372	351	6	xam ′2a(2x−1	PERSON
ejpam-5372	352	1	0	CARDINAL
ejpam-5372	352	2	logd2	GPE
ejpam-5372	352	3	1	CARDINAL
ejpam-5372	354	1	∈	ORG
ejpam-5372	354	2	g ∈	PERSON
ejpam-5372	357	1	dirichlet	PERSON
ejpam-5372	357	2	1	CARDINAL
ejpam-5372	357	3	2	CARDINAL
ejpam-5372	358	1	2	QUANTITY
ejpam-5372	359	1	2	CARDINAL
ejpam-5372	360	1	k ∈ n	ORG
ejpam-5372	361	1	′b u	GPE
ejpam-5372	361	2	0	CARDINAL
ejpam-5372	362	1	logd2	GPE
ejpam-5372	362	2	1	CARDINAL
ejpam-5372	363	1	3	CARDINAL
ejpam-5372	364	1	∈	ORG
ejpam-5372	364	2	1	CARDINAL
ejpam-5372	364	3	logd2	GPE
ejpam-5372	364	4	1	CARDINAL
ejpam-5372	365	1	1	CARDINAL
ejpam-5372	366	1	φ	PERSON
ejpam-5372	366	2	1	CARDINAL
ejpam-5372	366	3	2n)φ	DATE
ejpam-5372	367	1	logd2	GPE
ejpam-5372	367	2	1	CARDINAL
ejpam-5372	367	3	2	CARDINAL
ejpam-5372	367	4	logd2	ORG
ejpam-5372	367	5	1	CARDINAL
ejpam-5372	368	1	2logd2(1,z	WORK_OF_ART
ejpam-5372	368	2	z. corollary 4	PERSON
ejpam-5372	369	1	logd2	GPE
ejpam-5372	369	2	1	CARDINAL
ejpam-5372	371	1	1	CARDINAL
ejpam-5372	373	1	3	CARDINAL
ejpam-5372	373	2	logd2	GPE
ejpam-5372	373	3	1	CARDINAL
ejpam-5372	373	4	φ	PERSON
ejpam-5372	374	1	logd2	GPE
ejpam-5372	374	2	1	CARDINAL
ejpam-5372	374	3	φ	PERSON
ejpam-5372	374	4	1	CARDINAL
ejpam-5372	376	1	1	CARDINAL
ejpam-5372	377	1	m. wolf	PERSON
ejpam-5372	377	2	f. wolf	PERSON
ejpam-5372	378	1	j. pure	PERSON
ejpam-5372	378	2	17	CARDINAL
ejpam-5372	378	3	4	CARDINAL
ejpam-5372	378	4	2024	CARDINAL
ejpam-5372	378	5	2431-2447	CARDINAL
ejpam-5372	378	6	16	CARDINAL
ejpam-5372	379	1	15	CARDINAL
ejpam-5372	380	1	2	CARDINAL
ejpam-5372	381	1	0	CARDINAL
ejpam-5372	381	2	logd2	GPE
ejpam-5372	381	3	1	CARDINAL
ejpam-5372	382	1	0	CARDINAL
ejpam-5372	382	2	logd2	GPE
ejpam-5372	382	3	1	CARDINAL
ejpam-5372	383	1	±g2	DATE
ejpam-5372	384	1	0	CARDINAL
ejpam-5372	384	2	logd2	GPE
ejpam-5372	384	3	1	CARDINAL
ejpam-5372	386	1	2	CARDINAL
ejpam-5372	386	2	gs	ORG
ejpam-5372	387	1	∪a	CARDINAL
ejpam-5372	387	2	2ak0	CARDINAL
ejpam-5372	388	1	2bk0	CARDINAL
ejpam-5372	388	2	2	CARDINAL
ejpam-5372	389	1	2xal0	CARDINAL
ejpam-5372	389	2	2ybl0	PRODUCT
ejpam-5372	390	1	2logd2(1,z	TIME
ejpam-5372	390	2	0	CARDINAL
ejpam-5372	391	1	one	CARDINAL
ejpam-5372	392	1	gs	PERSON
ejpam-5372	392	2	gz	PERSON
ejpam-5372	393	1	gs	ORG
ejpam-5372	394	1	±g2 xam	WORK_OF_ART
ejpam-5372	396	1	4	CARDINAL
ejpam-5372	397	1	logd2	GPE
ejpam-5372	397	2	1	CARDINAL
ejpam-5372	398	1	1	CARDINAL
ejpam-5372	398	2	1	CARDINAL
ejpam-5372	398	3	2	CARDINAL
ejpam-5372	398	4	16	CARDINAL
ejpam-5372	398	5	5	CARDINAL
ejpam-5372	399	1	3	CARDINAL
ejpam-5372	399	2	1	CARDINAL
ejpam-5372	399	3	2n−1	CARDINAL
ejpam-5372	400	1	2n−2	CARDINAL
ejpam-5372	400	2	1	CARDINAL
ejpam-5372	400	3	16	CARDINAL
ejpam-5372	401	1	257	CARDINAL
ejpam-5372	401	2	63	CARDINAL
ejpam-5372	401	3	6	CARDINAL
ejpam-5372	402	1	14	CARDINAL
ejpam-5372	402	2	2	CARDINAL
ejpam-5372	402	3	16	CARDINAL
ejpam-5372	403	1	logd2	GPE
ejpam-5372	403	2	1	CARDINAL
ejpam-5372	403	3	0	CARDINAL
ejpam-5372	404	1	k ∈	ORG
ejpam-5372	405	1	1	CARDINAL
ejpam-5372	405	2	2	CARDINAL
ejpam-5372	406	1	1	CARDINAL
ejpam-5372	406	2	1	CARDINAL
ejpam-5372	406	3	1	CARDINAL
ejpam-5372	406	4	2.2.3	CARDINAL
ejpam-5372	407	1	1	CARDINAL
ejpam-5372	408	1	16	CARDINAL
ejpam-5372	410	1	m. wolf	PERSON
ejpam-5372	410	2	f. wolf	PERSON
ejpam-5372	411	1	j. pure	PERSON
ejpam-5372	411	2	17	CARDINAL
ejpam-5372	411	3	4	CARDINAL
ejpam-5372	411	4	2024	CARDINAL
ejpam-5372	411	5	2431-2447	CARDINAL
ejpam-5372	411	6	1	CARDINAL
ejpam-5372	412	1	1	CARDINAL
ejpam-5372	415	1	2	CARDINAL
ejpam-5372	415	2	2	CARDINAL
ejpam-5372	416	1	two	CARDINAL
ejpam-5372	416	2	•	CARDINAL
ejpam-5372	416	3	∈	ORG
ejpam-5372	416	4	2	CARDINAL
ejpam-5372	416	5	φ(p	PERSON
ejpam-5372	416	6	2q	CARDINAL
ejpam-5372	417	1	11	CARDINAL
ejpam-5372	417	2	∈ g′ z	PERSON
ejpam-5372	418	1	∈	ORG
ejpam-5372	419	1	2	CARDINAL
ejpam-5372	420	1	∈	ORG
ejpam-5372	420	2	φ(p	PERSON
ejpam-5372	421	1	5	CARDINAL
ejpam-5372	421	2	∈	ORG
ejpam-5372	422	1	2	CARDINAL
ejpam-5372	423	1	0 ≤	QUANTITY
ejpam-5372	424	1	′ of r(n	ORG
ejpam-5372	424	2	≡ 1	ORG
ejpam-5372	425	1	logd2	ORG
ejpam-5372	425	2	1	CARDINAL
ejpam-5372	425	3	first	ORDINAL
ejpam-5372	425	4	11	CARDINAL
ejpam-5372	426	1	first	ORDINAL
ejpam-5372	426	2	1	CARDINAL
ejpam-5372	426	3	1	CARDINAL
ejpam-5372	429	1	u (ak	ORG
ejpam-5372	429	2	0	CARDINAL
ejpam-5372	429	3	k ∈	ORG
ejpam-5372	430	1	0,k	CARDINAL
ejpam-5372	430	2	φ	ORG
ejpam-5372	430	3	2	CARDINAL
ejpam-5372	430	4	1	CARDINAL
ejpam-5372	431	1	1	CARDINAL
ejpam-5372	431	2	atkin	PERSON
ejpam-5372	431	3	4	CARDINAL
ejpam-5372	432	1	u (ak	ORG
ejpam-5372	432	2	k ∈	ORG
ejpam-5372	433	1	0,k	CARDINAL
ejpam-5372	433	2	±m ′ak u (ak	ORG
ejpam-5372	434	1	3	CARDINAL
ejpam-5372	434	2	2	CARDINAL
ejpam-5372	434	3	ec	ORG
ejpam-5372	436	1	2n+r	CARDINAL
ejpam-5372	436	2	∈ n∗	ORG
ejpam-5372	436	3	∈	ORG
ejpam-5372	436	4	0	CARDINAL
ejpam-5372	436	5	1	CARDINAL
ejpam-5372	437	1	2	CARDINAL
ejpam-5372	438	1	ec	ORG
ejpam-5372	438	2	∏	CARDINAL
ejpam-5372	440	1	ec	ORG
ejpam-5372	440	2	1	CARDINAL
ejpam-5372	440	3	2	CARDINAL
ejpam-5372	441	1	ax2 + bx	ORG
ejpam-5372	446	1	m. wolf	PERSON
ejpam-5372	446	2	f. wolf	PERSON
ejpam-5372	447	1	j. pure	PERSON
ejpam-5372	447	2	17	CARDINAL
ejpam-5372	447	3	4	CARDINAL
ejpam-5372	447	4	2024	CARDINAL
ejpam-5372	447	5	2431-2447	CARDINAL
ejpam-5372	447	6	3.1	CARDINAL
ejpam-5372	448	1	fermat	ORG
ejpam-5372	448	2	two	CARDINAL
ejpam-5372	448	3	2	CARDINAL
ejpam-5372	450	1	ec	ORG
ejpam-5372	454	1	∈	ORG
ejpam-5372	454	2	ec	ORG
ejpam-5372	457	1	−1	DATE
ejpam-5372	461	1	∈	ORG
ejpam-5372	461	2	ec	ORG
ejpam-5372	462	1	ec	ORG
ejpam-5372	464	1	fermat	ORG
ejpam-5372	464	2	two	CARDINAL
ejpam-5372	464	3	5	CARDINAL
ejpam-5372	464	4	∈ n∗	MONEY
ejpam-5372	466	1	ac− bd)2+(ad+ bc)2	PERSON
ejpam-5372	469	1	ec	ORG
ejpam-5372	470	1	17	CARDINAL
ejpam-5372	471	1		GPE
ejpam-5372	472	1	1	CARDINAL
ejpam-5372	473	1	1	CARDINAL
ejpam-5372	473	2	2 	DATE
ejpam-5372	475	1	2	CARDINAL
ejpam-5372	475	2	n p p−1	ORG
ejpam-5372	475	3	∈	ORG
ejpam-5372	475	4	∈	ORG
ejpam-5372	476	1	∏	CARDINAL
ejpam-5372	479	1	5	CARDINAL
ejpam-5372	482	1	17	CARDINAL
ejpam-5372	483	1	p1,4	ORG
ejpam-5372	484	1	18	CARDINAL
ejpam-5372	486	1	⊂	GPE
ejpam-5372	487	1	2	CARDINAL
ejpam-5372	489	1	2ax	ORG
ejpam-5372	491	1	n p p−1	ORG
ejpam-5372	491	2	∈	ORG
ejpam-5372	491	3	m. wolf	PERSON
ejpam-5372	491	4	f. wolf	PERSON
ejpam-5372	492	1	j. pure	PERSON
ejpam-5372	492	2	17	CARDINAL
ejpam-5372	492	3	4	CARDINAL
ejpam-5372	492	4	2024	CARDINAL
ejpam-5372	492	5	2431-2447	CARDINAL
ejpam-5372	493	1	2	CARDINAL
ejpam-5372	493	2	∈	ORG
ejpam-5372	494	1	ec	ORG
ejpam-5372	494	2	∈	ORG
ejpam-5372	495	1	2	CARDINAL
ejpam-5372	496	1	⊂	GPE
ejpam-5372	496	2	2a	CARDINAL
ejpam-5372	496	3	modulo p	ORG
ejpam-5372	496	4	2	CARDINAL
ejpam-5372	497	1	6	CARDINAL
ejpam-5372	498	1	2	CARDINAL
ejpam-5372	498	2	p1,4 ∩	ORG
ejpam-5372	498	3	∈	ORG
ejpam-5372	498	4	n∗)f	ORG
ejpam-5372	500	1	1	CARDINAL
ejpam-5372	500	2	2pαfx + b)2	MONEY
ejpam-5372	503	1	qc	GPE
ejpam-5372	503	2	qc	GPE
ejpam-5372	503	3	b′	PRODUCT
ejpam-5372	505	1	17	CARDINAL
ejpam-5372	505	2	p1,4 ∩	ORG
ejpam-5372	509	1	18	CARDINAL
ejpam-5372	512	1	1	CARDINAL
ejpam-5372	512	2	y ∈ z	PERSON
ejpam-5372	512	3	= qc	PERSON
ejpam-5372	513	1	2pαf	CARDINAL
ejpam-5372	515	1	qc	GPE
ejpam-5372	515	2	qc	GPE
ejpam-5372	516	1	3	CARDINAL
ejpam-5372	518	1	two	CARDINAL
ejpam-5372	520	1	first	ORDINAL
ejpam-5372	520	2	17	CARDINAL
ejpam-5372	520	3	p1,4	ORG
ejpam-5372	525	1	y ′2 − y2.	ORG
ejpam-5372	526	1	2x +mk	QUANTITY
ejpam-5372	528	1	1	CARDINAL
ejpam-5372	528	2	1 2ln(x	CARDINAL
ejpam-5372	529	1	en+1	ORG
ejpam-5372	529	2	dp|4n+1 ( en+1	ORG
ejpam-5372	532	1	2ne	ORG
ejpam-5372	532	2	∑	ORG
ejpam-5372	532	3	1	CARDINAL
ejpam-5372	533	1	1	CARDINAL
ejpam-5372	534	1	∏	CARDINAL
ejpam-5372	536	1	0	CARDINAL
ejpam-5372	537	1	second	ORDINAL
ejpam-5372	537	2	6	CARDINAL
ejpam-5372	537	3	2	CARDINAL
ejpam-5372	538	1	∏	CARDINAL
ejpam-5372	539	1	m. wolf	PERSON
ejpam-5372	539	2	f. wolf	PERSON
ejpam-5372	540	1	j. pure	PERSON
ejpam-5372	540	2	17	CARDINAL
ejpam-5372	540	3	4	CARDINAL
ejpam-5372	540	4	2024	CARDINAL
ejpam-5372	540	5	2431-2447 2445	QUANTITY
ejpam-5372	540	6	first	ORDINAL
ejpam-5372	540	7	first	ORDINAL
ejpam-5372	541	1	bl ̸≡	GPE
ejpam-5372	549	1	dp|eq	PERSON
ejpam-5372	550	1	+ o	DATE
ejpam-5372	550	2	dp|eq	ORG
ejpam-5372	550	3	2	CARDINAL
ejpam-5372	551	1	3.2	CARDINAL
ejpam-5372	554	1	3][6	CARDINAL
ejpam-5372	555	1	daniel bernstein	PERSON
ejpam-5372	556	1	8	CARDINAL
ejpam-5372	558	1	3][6	CARDINAL
ejpam-5372	558	2	3.2	CARDINAL
ejpam-5372	560	1	19	CARDINAL
ejpam-5372	561	1	section 2	LAW
ejpam-5372	561	2	1	CARDINAL
ejpam-5372	561	3	2nz	ORDINAL
ejpam-5372	562	1	2	CARDINAL
ejpam-5372	562	2	2	CARDINAL
ejpam-5372	562	3	±m	ORG
ejpam-5372	562	4	2	CARDINAL
ejpam-5372	562	5	2	CARDINAL
ejpam-5372	565	1	2k	CARDINAL
ejpam-5372	566	1	1+(2n	CARDINAL
ejpam-5372	566	2	1	CARDINAL
ejpam-5372	566	3	1	CARDINAL
ejpam-5372	567	1	2	CARDINAL
ejpam-5372	567	2	1	CARDINAL
ejpam-5372	569	1	2n	CARDINAL
ejpam-5372	569	2	2	CARDINAL
ejpam-5372	569	3	k ≡	PERSON
ejpam-5372	569	4	1− z	WORK_OF_ART
ejpam-5372	569	5	∈	ORG
ejpam-5372	569	6	0	DATE
ejpam-5372	570	1	2	CARDINAL
ejpam-5372	570	2	m. moreover	PERSON
ejpam-5372	570	3	2	CARDINAL
ejpam-5372	571	1	7	CARDINAL
ejpam-5372	572	1	r.	NORP
ejpam-5372	572	2	2	CARDINAL
ejpam-5372	573	1	4	CARDINAL
ejpam-5372	573	2	2	CARDINAL
ejpam-5372	573	3	4 ∈ n∗	MONEY
ejpam-5372	573	4	4	CARDINAL
ejpam-5372	573	5	2	CARDINAL
ejpam-5372	573	6	2	CARDINAL
ejpam-5372	573	7	1×	CARDINAL
ejpam-5372	573	8	2	CARDINAL
ejpam-5372	573	9	2	CARDINAL
ejpam-5372	576	1	∈	ORG
ejpam-5372	576	2	±m	ORG
ejpam-5372	576	3	4	CARDINAL
ejpam-5372	578	1	19	CARDINAL
ejpam-5372	578	2	±1	PERSON
ejpam-5372	578	3	2	CARDINAL
ejpam-5372	579	1	2	CARDINAL
ejpam-5372	579	2	2	CARDINAL
ejpam-5372	579	3	euler	PERSON
ejpam-5372	579	4	∈	ORG
ejpam-5372	579	5	m. wolf	PERSON
ejpam-5372	579	6	f. wolf	PERSON
ejpam-5372	580	1	j. pure	PERSON
ejpam-5372	580	2	17	CARDINAL
ejpam-5372	580	3	4	CARDINAL
ejpam-5372	580	4	2024	CARDINAL
ejpam-5372	580	5	2431-2447 2446	CARDINAL
ejpam-5372	581	1	modulo p	ORG
ejpam-5372	581	2	ec	ORG
ejpam-5372	583	1	2	CARDINAL
ejpam-5372	587	1	n∗)n	ORG
ejpam-5372	587	2	∈	ORG
ejpam-5372	587	3	2	CARDINAL
ejpam-5372	588	1	1	CARDINAL
ejpam-5372	591	1	2 k	QUANTITY
ejpam-5372	592	1	2	CARDINAL
ejpam-5372	592	2	1	CARDINAL
ejpam-5372	593	1	4 k	QUANTITY
ejpam-5372	595	1	2	CARDINAL
ejpam-5372	595	2	∈	ORG
ejpam-5372	595	3	euler criterion g	PERSON
ejpam-5372	595	4	2	CARDINAL
ejpam-5372	595	5	−1	DATE
ejpam-5372	595	6	•	CARDINAL
ejpam-5372	595	7	1 ≤ k ≤ 2n−2	QUANTITY
ejpam-5372	596	1	2	CARDINAL
ejpam-5372	596	2	−1	DATE
ejpam-5372	597	1	xk = ∞.	PERSON
ejpam-5372	598	1	2	CARDINAL
ejpam-5372	599	1	xk ≡ ±(−ck	ORG
ejpam-5372	599	2	4	CARDINAL
ejpam-5372	599	3	∈	ORG
ejpam-5372	599	4	2	CARDINAL
ejpam-5372	599	5	gs	ORG
ejpam-5372	599	6	two	CARDINAL
ejpam-5372	605	1	2447	CARDINAL
ejpam-5372	605	2	1	CARDINAL
ejpam-5372	606	1	littlewood	ORG
ejpam-5372	606	2	n2 + a. mathematics of computation	ORG
ejpam-5372	608	1	72):pp	CARDINAL
ejpam-5372	609	1	321–332, 1960	DATE
ejpam-5372	610	1	2	CARDINAL
ejpam-5372	610	2	marc wolf	PERSON
ejpam-5372	610	3	wolf	PERSON
ejpam-5372	611	1	x2+c	PERSON
ejpam-5372	611	2	11(no.	DATE
ejpam-5372	612	1	6):pp.	CARDINAL
ejpam-5372	613	1	2023	CARDINAL
ejpam-5372	615	1	3	CARDINAL
ejpam-5372	615	2	tonelli alberto	PERSON
ejpam-5372	615	3	bemerkung	PERSON
ejpam-5372	616	1	nachrichten von der königl	PERSON
ejpam-5372	617	1	gesellschaft der	PERSON
ejpam-5372	617	2	und der georg-augustsuniversität	PERSON
ejpam-5372	618	1	1891(no.	DATE
ejpam-5372	619	1	6):pp	CARDINAL
ejpam-5372	620	1	344–346, 1891	DATE
ejpam-5372	623	1	4	CARDINAL
ejpam-5372	623	2	marc wolf	PERSON
ejpam-5372	623	3	wolf	PERSON
ejpam-5372	625	1	8(no	TIME
ejpam-5372	626	1	2):pp	CARDINAL
ejpam-5372	627	1	11–41	CARDINAL
ejpam-5372	627	2	2020	DATE
ejpam-5372	629	1	5	CARDINAL
ejpam-5372	629	2	herbert s. zuckerman ivan niven	PERSON
ejpam-5372	632	1	1994	DATE
ejpam-5372	634	1	270(no.	DATE
ejpam-5372	635	1	6):pp.	CARDINAL
ejpam-5372	635	2	540, 1994	DATE
ejpam-5372	637	1	6	CARDINAL
ejpam-5372	638	1	five	CARDINAL
ejpam-5372	639	1	second	ORDINAL
ejpam-5372	642	1	51–70, 1973	DATE
ejpam-5372	643	1	7	CARDINAL
ejpam-5372	643	2	michel cipolla	PERSON
ejpam-5372	643	3	un	ORG
ejpam-5372	643	4	la	GPE
ejpam-5372	643	5	della congruenza di secondo grado	PERSON
ejpam-5372	644	1	napoli	GPE
ejpam-5372	645	1	9	CARDINAL
ejpam-5372	646	1	154–163, 1903	DATE
ejpam-5372	647	1	8	CARDINAL
ejpam-5372	647	2	daniel j. bernstein	PERSON
ejpam-5372	649	1	2007	DATE