id	sid	eid	entity	type
ejpam-6214	1	1	european journal	ORG
ejpam-6214	1	2	2025	DATE
ejpam-6214	1	3	18	CARDINAL
ejpam-6214	1	4	3	CARDINAL
ejpam-6214	1	5	6214	DATE
ejpam-6214	1	6	1307-5543	DATE
ejpam-6214	1	7	new york	GPE
ejpam-6214	1	8	amara chandoul1,∗	PERSON
ejpam-6214	1	9	mansour2 1	ORG
ejpam-6214	1	10	sfax	ORG
ejpam-6214	1	11	sfax university	ORG
ejpam-6214	1	12	sfax	ORG
ejpam-6214	1	13	tunisia 2 department	ORG
ejpam-6214	1	14	al-qura university	ORG
ejpam-6214	1	15	mecca 21955	ORG
ejpam-6214	1	16	saudi arabia	GPE
ejpam-6214	3	1	f(x	ORG
ejpam-6214	4	1	f(x	ORG
ejpam-6214	4	2	deg g	PERSON
ejpam-6214	6	1	deg g	PERSON
ejpam-6214	8	1	2020	DATE
ejpam-6214	8	2	11c08	CARDINAL
ejpam-6214	8	3	11r09	CARDINAL
ejpam-6214	8	4	12e05	CARDINAL
ejpam-6214	8	5	eisenstein	PERSON
ejpam-6214	8	6	1	CARDINAL
ejpam-6214	8	7	1	CARDINAL
ejpam-6214	8	8	2	CARDINAL
ejpam-6214	9	1	eisenstein	PERSON
ejpam-6214	10	1	3	CARDINAL
ejpam-6214	12	1	4	CARDINAL
ejpam-6214	15	1	a. chandoul	PERSON
ejpam-6214	15	2	samansour@uqu.edu.sa	DATE
ejpam-6214	15	3	s. mansour	PERSON
ejpam-6214	15	4	1	CARDINAL
ejpam-6214	16	1	2025	CARDINAL
ejpam-6214	17	1	a. chandoul	PERSON
ejpam-6214	17	2	s. mansour	PERSON
ejpam-6214	18	1	j. pure	PERSON
ejpam-6214	18	2	18	CARDINAL
ejpam-6214	18	3	3	CARDINAL
ejpam-6214	18	4	2025	CARDINAL
ejpam-6214	18	5	6214 2	DATE
ejpam-6214	18	6	• p	GPE
ejpam-6214	18	7	k ∈ z+	ORG
ejpam-6214	19	1	deg g	PERSON
ejpam-6214	19	2	1	CARDINAL
ejpam-6214	20	1	deg g	PERSON
ejpam-6214	20	2	1	CARDINAL
ejpam-6214	22	1	f(x	ORG
ejpam-6214	22	2	0	DATE
ejpam-6214	23	1	deg g	PERSON
ejpam-6214	25	1	deg g	PERSON
ejpam-6214	27	1	5	CARDINAL
ejpam-6214	27	2	eisenstein	PERSON
ejpam-6214	28	1	3	CARDINAL
ejpam-6214	31	1	section 2	LAW
ejpam-6214	32	1	4	CARDINAL
ejpam-6214	33	1	section 3	LAW
ejpam-6214	34	1	section 4	LAW
ejpam-6214	34	2	section 5	LAW
ejpam-6214	34	3	6	CARDINAL
ejpam-6214	35	1	7	CARDINAL
ejpam-6214	36	1	section 6	LAW
ejpam-6214	37	1	8	CARDINAL
ejpam-6214	39	1	2	CARDINAL
ejpam-6214	39	2	2.1	CARDINAL
ejpam-6214	40	1	4	CARDINAL
ejpam-6214	40	2	a. chandoul	PERSON
ejpam-6214	40	3	s. mansour	PERSON
ejpam-6214	41	1	j. pure	PERSON
ejpam-6214	41	2	18	CARDINAL
ejpam-6214	41	3	3	CARDINAL
ejpam-6214	41	4	2025	CARDINAL
ejpam-6214	41	5	6214 3	DATE
ejpam-6214	41	6	8	CARDINAL
ejpam-6214	41	7	2016	DATE
ejpam-6214	42	1	f(x	ORG
ejpam-6214	42	2	deg f < deg g	PERSON
ejpam-6214	42	3	gcd(k	ORG
ejpam-6214	42	4	deg g	PERSON
ejpam-6214	43	1	1	CARDINAL
ejpam-6214	47	1	deg g	PERSON
ejpam-6214	47	2	1	CARDINAL
ejpam-6214	48	1	deg g	PERSON
ejpam-6214	48	2	1	CARDINAL
ejpam-6214	50	1	2.2	CARDINAL
ejpam-6214	51	1	f(x	ORG
ejpam-6214	51	2	f(x	ORG
ejpam-6214	54	1	f(x	ORG
ejpam-6214	55	1	1	CARDINAL
ejpam-6214	55	2	first	ORDINAL
ejpam-6214	56	1	two	CARDINAL
ejpam-6214	56	2	only one	CARDINAL
ejpam-6214	57	1	2x	CARDINAL
ejpam-6214	57	2	2	CARDINAL
ejpam-6214	57	3	x. a. chandoul	PERSON
ejpam-6214	57	4	s. mansour	PERSON
ejpam-6214	58	1	j. pure	PERSON
ejpam-6214	58	2	18	CARDINAL
ejpam-6214	58	3	3	CARDINAL
ejpam-6214	58	4	2025	CARDINAL
ejpam-6214	58	5	6214 4	DATE
ejpam-6214	58	6	8	CARDINAL
ejpam-6214	58	7	first	ORDINAL
ejpam-6214	58	8	f̃ = f/c(f	WORK_OF_ART
ejpam-6214	59	1	f̃	PRODUCT
ejpam-6214	59	2	eisenstein	PERSON
ejpam-6214	60	1	2.3	CARDINAL
ejpam-6214	61	1	p(x	PERSON
ejpam-6214	61	2	q(x	PERSON
ejpam-6214	61	3	two	CARDINAL
ejpam-6214	63	1	r(p	PERSON
ejpam-6214	63	2	zero	CARDINAL
ejpam-6214	63	3	zero	CARDINAL
ejpam-6214	64	1	r(p	PERSON
ejpam-6214	66	1	eisenstein	PERSON
ejpam-6214	66	2	f(x	ORG
ejpam-6214	68	1	0	CARDINAL
ejpam-6214	70	1	1	CARDINAL
ejpam-6214	72	1	2.5	CARDINAL
ejpam-6214	72	2	f(x	ORG
ejpam-6214	73	1	f(x	ORG
ejpam-6214	73	2	f modulo p. if	PRODUCT
ejpam-6214	73	3	f(x	ORG
ejpam-6214	73	4	f(x	ORG
ejpam-6214	73	5	q. 2.6	PERSON
ejpam-6214	74	1	gcd(k	ORG
ejpam-6214	74	2	deg g	PERSON
ejpam-6214	76	1	2.7	CARDINAL
ejpam-6214	76	2	f(x	ORG
ejpam-6214	78	1	a. chandoul	PERSON
ejpam-6214	78	2	s. mansour	PERSON
ejpam-6214	79	1	j. pure	PERSON
ejpam-6214	79	2	18	CARDINAL
ejpam-6214	79	3	3	CARDINAL
ejpam-6214	79	4	2025	CARDINAL
ejpam-6214	79	5	6214 5	DATE
ejpam-6214	79	6	2	CARDINAL
ejpam-6214	80	1	f(x	ORG
ejpam-6214	82	1	gcd(k	ORG
ejpam-6214	82	2	deg g	PERSON
ejpam-6214	82	3	1	CARDINAL
ejpam-6214	84	1	q. proof	PERSON
ejpam-6214	85	1	eisenstein	PERSON
ejpam-6214	86	1	•	CARDINAL
ejpam-6214	86	2	res(f	ORG
ejpam-6214	87	1	f(x	ORG
ejpam-6214	90	1	•	CARDINAL
ejpam-6214	90	2	eisenstein	PERSON
ejpam-6214	90	3	k = 1	PERSON
ejpam-6214	90	4	f(0	PERSON
ejpam-6214	91	1	•	CARDINAL
ejpam-6214	91	2	deg g	PERSON
ejpam-6214	91	3	1	CARDINAL
ejpam-6214	92	1	1	CARDINAL
ejpam-6214	93	1	deg g	PERSON
ejpam-6214	94	1	1	CARDINAL
ejpam-6214	95	1	a. chandoul	PERSON
ejpam-6214	95	2	s. mansour	PERSON
ejpam-6214	96	1	j. pure	PERSON
ejpam-6214	96	2	18	CARDINAL
ejpam-6214	96	3	3	CARDINAL
ejpam-6214	96	4	2025	CARDINAL
ejpam-6214	96	5	6214 6	DATE
ejpam-6214	97	1	1	CARDINAL
ejpam-6214	97	2	gcd(k	ORG
ejpam-6214	97	3	deg g	PERSON
ejpam-6214	98	1	1	CARDINAL
ejpam-6214	98	2	f(x	ORG
ejpam-6214	101	1	+ 1	DATE
ejpam-6214	103	1	+ 1	DATE
ejpam-6214	105	1	1	CARDINAL
ejpam-6214	105	2	3	CARDINAL
ejpam-6214	105	3	1	CARDINAL
ejpam-6214	105	4	3.1	CARDINAL
ejpam-6214	107	1	2	CARDINAL
ejpam-6214	107	2	f(x	ORG
ejpam-6214	110	1	+ 1	DATE
ejpam-6214	112	1	+ 1	DATE
ejpam-6214	113	1	3.1	CARDINAL
ejpam-6214	113	2	+ 1	DATE
ejpam-6214	114	1	4.1	CARDINAL
ejpam-6214	114	2	3	CARDINAL
ejpam-6214	114	3	deg g	PERSON
ejpam-6214	117	1	+ 1	DATE
ejpam-6214	120	1	2	CARDINAL
ejpam-6214	122	1	4	CARDINAL
ejpam-6214	122	2	2	CARDINAL
ejpam-6214	123	1	+ 1	DATE
ejpam-6214	123	2	3.1	CARDINAL
ejpam-6214	124	1	5	CARDINAL
ejpam-6214	126	1	5.1	CARDINAL
ejpam-6214	127	1	algebraic number	PERSON
ejpam-6214	128	1	algebraic integers	PERSON
ejpam-6214	129	1	q(α	ORG
ejpam-6214	131	1	5.2	CARDINAL
ejpam-6214	133	1	f(x	ORG
ejpam-6214	134	1	0	CARDINAL
ejpam-6214	134	2	x.	GPE
ejpam-6214	136	1	a. chandoul	PERSON
ejpam-6214	136	2	s. mansour	PERSON
ejpam-6214	137	1	j. pure	PERSON
ejpam-6214	137	2	18	CARDINAL
ejpam-6214	137	3	3	CARDINAL
ejpam-6214	137	4	2025	CARDINAL
ejpam-6214	137	5	6214 7	DATE
ejpam-6214	139	1	deg g	PERSON
ejpam-6214	140	1	q. 5.4	PERSON
ejpam-6214	145	1	6	CARDINAL
ejpam-6214	148	1	gcd(k	ORG
ejpam-6214	148	2	deg g	PERSON
ejpam-6214	149	1	f(x	ORG
ejpam-6214	149	2	integer k	PERSON
ejpam-6214	150	1	deg g	PERSON
ejpam-6214	158	1	al-qura university	ORG
ejpam-6214	158	2	saudi arabia	GPE
ejpam-6214	158	3	25uqu4331214gssr02	CARDINAL
ejpam-6214	158	4	a. chandoul	PERSON
ejpam-6214	158	5	s. mansour	PERSON
ejpam-6214	159	1	j. pure	PERSON
ejpam-6214	159	2	18	CARDINAL
ejpam-6214	159	3	3	CARDINAL
ejpam-6214	159	4	2025	CARDINAL
ejpam-6214	159	5	6214 8	DATE
ejpam-6214	159	6	8	CARDINAL
ejpam-6214	159	7	al-qura university	ORG
ejpam-6214	159	8	saudi arabia	GPE
ejpam-6214	159	9	25uqu4331214gssr02	CARDINAL
ejpam-6214	160	1	1	CARDINAL
ejpam-6214	160	2	henri cohen	PERSON
ejpam-6214	162	1	2000	DATE
ejpam-6214	163	1	2	CARDINAL
ejpam-6214	163	2	serge lang	PERSON
ejpam-6214	165	1	third	ORDINAL
ejpam-6214	165	2	2002	DATE
ejpam-6214	166	1	3	CARDINAL
ejpam-6214	166	2	gotthold eisenstein	PERSON
ejpam-6214	169	1	und angewandte mathematik	PERSON
ejpam-6214	169	2	39:160–179	CARDINAL
ejpam-6214	169	3	1850	DATE
ejpam-6214	170	1	4	CARDINAL
ejpam-6214	171	1	two	CARDINAL
ejpam-6214	173	1	approx	PERSON
ejpam-6214	176	1	54(2):163–171	DATE
ejpam-6214	176	2	2016	DATE
ejpam-6214	177	1	5	CARDINAL
ejpam-6214	177	2	jean-pierre serre	PERSON
ejpam-6214	179	1	1973	DATE
ejpam-6214	180	1	6	CARDINAL
ejpam-6214	182	1	1999	DATE
ejpam-6214	183	1	7	CARDINAL
ejpam-6214	183	2	marc hindry	PERSON
ejpam-6214	183	3	joseph h. silverman	PERSON
ejpam-6214	185	1	2000	DATE
ejpam-6214	186	1	8	CARDINAL
ejpam-6214	186	2	andrzej schinzel	ORG
ejpam-6214	188	1	cambridge university press	ORG
ejpam-6214	188	2	2000	DATE
ejpam-6214	189	1	9	CARDINAL
ejpam-6214	189	2	michael filaseta	PERSON
ejpam-6214	191	1	mathematica hungarica	PERSON
ejpam-6214	191	2	120(1-2):137–152, 2008	DATE