id	sid	eid	entity	type
ejpam-6781	1	1	european journal	ORG
ejpam-6781	1	2	2025	DATE
ejpam-6781	1	3	18	CARDINAL
ejpam-6781	1	4	4	CARDINAL
ejpam-6781	1	5	6781	CARDINAL
ejpam-6781	1	6	1307-5543	DATE
ejpam-6781	1	7	new york	GPE
ejpam-6781	1	8	jitman1	GPE
ejpam-6781	1	9	mohd	PERSON
ejpam-6781	1	10	mohammad2	PERSON
ejpam-6781	1	11	silpakorn university	ORG
ejpam-6781	1	12	nakhon pathom	ORG
ejpam-6781	1	13	thailand 2 centre	FAC
ejpam-6781	1	14	malaysia	GPE
ejpam-6781	1	15	al-sultan abdullah	PERSON
ejpam-6781	1	16	lebuh persiaran	PERSON
ejpam-6781	1	17	tan khalil yaakob	PERSON
ejpam-6781	1	18	kuantan	GPE
ejpam-6781	1	19	pahang	GPE
ejpam-6781	1	20	malaysia 3	ORG
ejpam-6781	1	21	thaksin university	ORG
ejpam-6781	1	22	phattalung	GPE
ejpam-6781	1	23	thailand	GPE
ejpam-6781	2	1	eisenstein	PERSON
ejpam-6781	2	2	gcd(a	GPE
ejpam-6781	3	1	1	CARDINAL
ejpam-6781	6	1	2020	DATE
ejpam-6781	6	2	11d09	CARDINAL
ejpam-6781	6	3	20k25	CARDINAL
ejpam-6781	6	4	eisenstein	PERSON
ejpam-6781	6	5	eisenstein integers	PERSON
ejpam-6781	6	6	abelian	NORP
ejpam-6781	6	7	1	CARDINAL
ejpam-6781	7	1	centuries	DATE
ejpam-6781	10	1	algebraic structures	PERSON
ejpam-6781	11	1	1	CARDINAL
ejpam-6781	11	2	w. sierpinski	PERSON
ejpam-6781	14	1	s. jitman	PERSON
ejpam-6781	14	2	mohadsham@umpsa.edu.my	PERSON
ejpam-6781	14	3	ekkasit@tsu.ac.th	ORG
ejpam-6781	14	4	e. sangwisut	PERSON
ejpam-6781	15	1	1	CARDINAL
ejpam-6781	15	2	2025	CARDINAL
ejpam-6781	16	1	s. jitman	PERSON
ejpam-6781	16	2	m. mohammad	PERSON
ejpam-6781	16	3	e. sangwisut	PERSON
ejpam-6781	17	1	j. pure	PERSON
ejpam-6781	17	2	18	CARDINAL
ejpam-6781	17	3	4	CARDINAL
ejpam-6781	17	4	2025	CARDINAL
ejpam-6781	17	5	6781 2	DATE
ejpam-6781	17	6	16	CARDINAL
ejpam-6781	17	7	2	CARDINAL
ejpam-6781	17	8	l. shedd	PERSON
ejpam-6781	17	9	64	CARDINAL
ejpam-6781	17	10	2	CARDINAL
ejpam-6781	17	11	576	CARDINAL
ejpam-6781	17	12	450	CARDINAL
ejpam-6781	17	13	045	CARDINAL
ejpam-6781	17	14	5	CARDINAL
ejpam-6781	17	15	13	CARDINAL
ejpam-6781	17	16	17	CARDINAL
ejpam-6781	17	17	29	CARDINAL
ejpam-6781	17	18	37	DATE
ejpam-6781	17	19	41	CARDINAL
ejpam-6781	17	20	53	DATE
ejpam-6781	17	21	twenty-two years later	DATE
ejpam-6781	17	22	e. j. eckert	PERSON
ejpam-6781	17	23	3	CARDINAL
ejpam-6781	18	1	eckert	PERSON
ejpam-6781	20	1	4	CARDINAL
ejpam-6781	20	2	5	CARDINAL
ejpam-6781	21	1	5	CARDINAL
ejpam-6781	22	1	eisenstein	PERSON
ejpam-6781	22	2	60-degree	QUANTITY
ejpam-6781	23	1	60	CARDINAL
ejpam-6781	24	1	6	CARDINAL
ejpam-6781	25	1	7	CARDINAL
ejpam-6781	25	2	8	CARDINAL
ejpam-6781	25	3	9	CARDINAL
ejpam-6781	25	4	120-degree	QUANTITY
ejpam-6781	25	5	60-degree	QUANTITY
ejpam-6781	26	1	eisenstein	PERSON
ejpam-6781	26	2	10	CARDINAL
ejpam-6781	27	1	eisenstein	PERSON
ejpam-6781	28	1	one	CARDINAL
ejpam-6781	28	2	ω	ORDINAL
ejpam-6781	28	3	3	CARDINAL
ejpam-6781	28	4	second	ORDINAL
ejpam-6781	30	1	section 2	LAW
ejpam-6781	30	2	eisenstein	PERSON
ejpam-6781	31	1	section 3	LAW
ejpam-6781	31	2	ω	ORDINAL
ejpam-6781	31	3	eisenstein	PERSON
ejpam-6781	31	4	ω	ORDINAL
ejpam-6781	32	1	ω	ORDINAL
ejpam-6781	32	2	section 4	DATE
ejpam-6781	32	3	eisenstein	PERSON
ejpam-6781	32	4	section 5	DATE
ejpam-6781	33	1	2	CARDINAL
ejpam-6781	33	2	eisenstein	PERSON
ejpam-6781	33	3	eisenstein	PERSON
ejpam-6781	33	4	60	CARDINAL
ejpam-6781	34	1	10	CARDINAL
ejpam-6781	35	1	eisenstein	PERSON
ejpam-6781	36	1	eisenstein	PERSON
ejpam-6781	37	1	1	CARDINAL
ejpam-6781	37	2	eisenstein	PERSON
ejpam-6781	38	1	1	CARDINAL
ejpam-6781	39	1	2ab	ORDINAL
ejpam-6781	40	1	2	CARDINAL
ejpam-6781	40	2	s. jitman	PERSON
ejpam-6781	40	3	m. mohammad	PERSON
ejpam-6781	40	4	e. sangwisut	PERSON
ejpam-6781	41	1	j. pure	PERSON
ejpam-6781	41	2	18	CARDINAL
ejpam-6781	41	3	4	CARDINAL
ejpam-6781	41	4	2025	CARDINAL
ejpam-6781	41	5	6781 3	DATE
ejpam-6781	41	6	60	CARDINAL
ejpam-6781	41	7	2	CARDINAL
ejpam-6781	41	8	1	CARDINAL
ejpam-6781	41	9	1	CARDINAL
ejpam-6781	42	1	60	CARDINAL
ejpam-6781	42	2	1	CARDINAL
ejpam-6781	42	3	60	CARDINAL
ejpam-6781	43	1	•	CARDINAL
ejpam-6781	43	2	3	CARDINAL
ejpam-6781	43	3	8	DATE
ejpam-6781	43	4	7	DATE
ejpam-6781	43	5	5	CARDINAL
ejpam-6781	43	6	8	DATE
ejpam-6781	43	7	eisenstein	PERSON
ejpam-6781	44	1	•	CARDINAL
ejpam-6781	44	2	eisenstein	PERSON
ejpam-6781	44	3	6	CARDINAL
ejpam-6781	44	4	16	DATE
ejpam-6781	44	5	14	DATE
ejpam-6781	44	6	10	CARDINAL
ejpam-6781	44	7	16	DATE
ejpam-6781	44	8	14	DATE
ejpam-6781	46	1	eisenstein	PERSON
ejpam-6781	48	1	1	CARDINAL
ejpam-6781	48	2	10	CARDINAL
ejpam-6781	50	1	2	CARDINAL
ejpam-6781	51	1	60	CARDINAL
ejpam-6781	51	2	60	CARDINAL
ejpam-6781	51	3	2	CARDINAL
ejpam-6781	51	4	eisenstein	PERSON
ejpam-6781	52	1	2	CARDINAL
ejpam-6781	52	2	10	CARDINAL
ejpam-6781	52	3	1	CARDINAL
ejpam-6781	53	1	2	CARDINAL
ejpam-6781	53	2	3	CARDINAL
ejpam-6781	54	1	6k + 1	DATE
ejpam-6781	54	2	s. jitman	PERSON
ejpam-6781	54	3	m. mohammad	PERSON
ejpam-6781	54	4	e. sangwisut	PERSON
ejpam-6781	55	1	j. pure	PERSON
ejpam-6781	55	2	18	CARDINAL
ejpam-6781	55	3	4	CARDINAL
ejpam-6781	55	4	2025	CARDINAL
ejpam-6781	55	5	6781 4	DATE
ejpam-6781	55	6	16	CARDINAL
ejpam-6781	55	7	2	CARDINAL
ejpam-6781	55	8	eisenstein	PERSON
ejpam-6781	56	1	eisenstein	PERSON
ejpam-6781	57	1	60	CARDINAL
ejpam-6781	57	2	2	CARDINAL
ejpam-6781	57	3	6k	CARDINAL
ejpam-6781	58	1	integer k.	PERSON
ejpam-6781	61	1	1	CARDINAL
ejpam-6781	61	2	6	CARDINAL
ejpam-6781	62	1	3	CARDINAL
ejpam-6781	63	1	eisenstein	PERSON
ejpam-6781	63	2	ω	ORDINAL
ejpam-6781	63	3	eisenstein	PERSON
ejpam-6781	63	4	3	CARDINAL
ejpam-6781	64	1	eisenstein integers	PERSON
ejpam-6781	64	2	ω	CARDINAL
ejpam-6781	65	1	eisenstein	PERSON
ejpam-6781	66	1	eisenstein	PERSON
ejpam-6781	66	2	ω	CARDINAL
ejpam-6781	66	3	2πi	ORDINAL
ejpam-6781	66	4	3	CARDINAL
ejpam-6781	66	5	−1+ √ 3i 2	DATE
ejpam-6781	67	1	ω	ORG
ejpam-6781	67	2	ω	ORG
ejpam-6781	68	1	+ 1	DATE
ejpam-6781	68	2	ω	ORG
ejpam-6781	68	3	ω	CARDINAL
ejpam-6781	69	1	1	CARDINAL
ejpam-6781	69	2	ω	ORDINAL
ejpam-6781	69	3	ω	GPE
ejpam-6781	69	4	ω	CARDINAL
ejpam-6781	69	5	1	CARDINAL
ejpam-6781	69	6	−1	DATE
ejpam-6781	70	1	eisenstein	PERSON
ejpam-6781	71	1	z[ω	GPE
ejpam-6781	71	2	1	CARDINAL
ejpam-6781	71	3	ω	LOC
ejpam-6781	71	4	6	CARDINAL
ejpam-6781	75	1	two	CARDINAL
ejpam-6781	75	2	z′	PERSON
ejpam-6781	76	1	two	CARDINAL
ejpam-6781	76	2	eisenstein integers	PERSON
ejpam-6781	76	3	z′	PERSON
ejpam-6781	76	4	z′	PERSON
ejpam-6781	76	5	∈	ORG
ejpam-6781	77	1	one	CARDINAL
ejpam-6781	78	1	eisenstein integers	PERSON
ejpam-6781	78	2	11–13	CARDINAL
ejpam-6781	78	3	14	CARDINAL
ejpam-6781	82	1	∣∣∣u	ORG
ejpam-6781	82	2	∈	ORG
ejpam-6781	82	3	u2 −	PERSON
ejpam-6781	82	4	1	CARDINAL
ejpam-6781	83	1	s. jitman	PERSON
ejpam-6781	83	2	m. mohammad	PERSON
ejpam-6781	83	3	e. sangwisut	PERSON
ejpam-6781	84	1	j. pure	PERSON
ejpam-6781	84	2	18	CARDINAL
ejpam-6781	84	3	4	CARDINAL
ejpam-6781	84	4	2025	CARDINAL
ejpam-6781	84	5	6781 5	DATE
ejpam-6781	84	6	16	CARDINAL
ejpam-6781	84	7	abelian	NORP
ejpam-6781	84	8	1	CARDINAL
ejpam-6781	84	9	n(ζ−1	ORG
ejpam-6781	84	10	n(ζ)−1	ORG
ejpam-6781	85	1	g(q	PERSON
ejpam-6781	85	2	g(q	PERSON
ejpam-6781	86	1	∣∣∣u	ORG
ejpam-6781	86	2	∈	ORG
ejpam-6781	86	3	u2 −	PERSON
ejpam-6781	87	1	1	CARDINAL
ejpam-6781	88	1	3	CARDINAL
ejpam-6781	88	2	g(q	PERSON
ejpam-6781	88	3	ω	ORDINAL
ejpam-6781	88	4	g(q	PERSON
ejpam-6781	88	5	ω	CARDINAL
ejpam-6781	89	1	g(q	PERSON
ejpam-6781	91	1	1	CARDINAL
ejpam-6781	92	1	g(q	PERSON
ejpam-6781	94	1	1	CARDINAL
ejpam-6781	94	2	1 + 0	DATE
ejpam-6781	94	3	g(q	PERSON
ejpam-6781	94	4	u2 + v2ω	PERSON
ejpam-6781	94	5	∈ g(q	PERSON
ejpam-6781	94	6	2−u2v2+v22	CARDINAL
ejpam-6781	96	1	u2 2−u2v2+v22	PERSON
ejpam-6781	97	1	g(q	PERSON
ejpam-6781	98	1	eisenstein	PERSON
ejpam-6781	98	2	eisenstein integer	PERSON
ejpam-6781	99	1	2a	CARDINAL
ejpam-6781	102	1	2a−	CARDINAL
ejpam-6781	102	2	2c	CARDINAL
ejpam-6781	102	3	3 2c	CARDINAL
ejpam-6781	103	1	ω	CARDINAL
ejpam-6781	103	2	g(q	PERSON
ejpam-6781	104	1	ω	CARDINAL
ejpam-6781	104	2	ω	ORDINAL
ejpam-6781	104	3	g(q	PERSON
ejpam-6781	104	4	3	CARDINAL
ejpam-6781	105	1	second	ORDINAL
ejpam-6781	106	1	0	CARDINAL
ejpam-6781	106	2	half	CARDINAL
ejpam-6781	107	1	3 2a−	CARDINAL
ejpam-6781	107	2	2a	CARDINAL
ejpam-6781	107	3	√ 3	DATE
ejpam-6781	107	4	2a	CARDINAL
ejpam-6781	107	5	second	ORDINAL
ejpam-6781	108	1	second	ORDINAL
ejpam-6781	112	1	s. jitman	PERSON
ejpam-6781	112	2	m. mohammad	PERSON
ejpam-6781	112	3	e. sangwisut	PERSON
ejpam-6781	113	1	j. pure	PERSON
ejpam-6781	113	2	18	CARDINAL
ejpam-6781	113	3	4	CARDINAL
ejpam-6781	113	4	2025	CARDINAL
ejpam-6781	113	5	6781 6	DATE
ejpam-6781	113	6	16	CARDINAL
ejpam-6781	113	7	3	CARDINAL
ejpam-6781	113	8	eisenstein	PERSON
ejpam-6781	113	9	ω	ORDINAL
ejpam-6781	114	1	18	CARDINAL
ejpam-6781	115	1	105	CARDINAL
ejpam-6781	115	2	210	CARDINAL
ejpam-6781	116	1	90	CARDINAL
ejpam-6781	117	1	90	CARDINAL
ejpam-6781	117	2	240	CARDINAL
ejpam-6781	117	3	210	CARDINAL
ejpam-6781	117	4	30	CARDINAL
ejpam-6781	117	5	3, 8	DATE
ejpam-6781	117	6	7	CARDINAL
ejpam-6781	118	1	−ω)ζ	ORG
ejpam-6781	118	2	4	CARDINAL
ejpam-6781	118	3	six	CARDINAL
ejpam-6781	118	4	g(q	PERSON
ejpam-6781	118	5	4	CARDINAL
ejpam-6781	119	1	60	CARDINAL
ejpam-6781	119	2	4	CARDINAL
ejpam-6781	119	3	g(q	PERSON
ejpam-6781	120	1	s. jitman	PERSON
ejpam-6781	120	2	m. mohammad	PERSON
ejpam-6781	120	3	e. sangwisut	PERSON
ejpam-6781	121	1	j. pure	PERSON
ejpam-6781	121	2	18	CARDINAL
ejpam-6781	121	3	4	CARDINAL
ejpam-6781	121	4	2025	CARDINAL
ejpam-6781	121	5	6781 7	DATE
ejpam-6781	121	6	16	CARDINAL
ejpam-6781	122	1	second	ORDINAL
ejpam-6781	123	1	f(ζ	ORG
ejpam-6781	124	1	1 ≤ i ≤ 6	QUANTITY
ejpam-6781	125	1	f(ζ	ORG
ejpam-6781	125	2	second	ORDINAL
ejpam-6781	126	1	second	ORDINAL
ejpam-6781	126	2	eisenstein	PERSON
ejpam-6781	127	1	5	CARDINAL
ejpam-6781	127	2	first	ORDINAL
ejpam-6781	127	3	second	ORDINAL
ejpam-6781	127	4	eisenstein	PERSON
ejpam-6781	127	5	g(q	PERSON
ejpam-6781	128	1	2	CARDINAL
ejpam-6781	129	1	eisenstein	PERSON
ejpam-6781	131	1	5	CARDINAL
ejpam-6781	131	2	g(q	PERSON
ejpam-6781	131	3	∖ u → et	ORG
ejpam-6781	131	4	6	CARDINAL
ejpam-6781	132	1	g(q	PERSON
ejpam-6781	133	1	∈	ORG
ejpam-6781	133	2	zm	ORG
ejpam-6781	133	3	1−2	CARDINAL
ejpam-6781	133	4	1−m+m2 + 1−m2 1−m+m2ω	DATE
ejpam-6781	134	1	1−2	CARDINAL
ejpam-6781	134	2	1−m+m2	CARDINAL
ejpam-6781	134	3	1−m2 1−m+m2	CARDINAL
ejpam-6781	134	4	∈	ORG
ejpam-6781	134	5	1−2	CARDINAL
ejpam-6781	134	6	2	CARDINAL
ejpam-6781	134	7	1−2	CARDINAL
ejpam-6781	134	8	1−m+m2	CARDINAL
ejpam-6781	134	9	1−m2 1−m+m2	CARDINAL
ejpam-6781	135	1	1−m2 1−m+m2	CARDINAL
ejpam-6781	135	2	2	CARDINAL
ejpam-6781	135	3	1	CARDINAL
ejpam-6781	136	1	zm ∈ g(q	ORG
ejpam-6781	136	2	∈	ORG
ejpam-6781	136	3	zm ̸=	ORG
ejpam-6781	136	4	̸= n ∈	ORG
ejpam-6781	136	5	g(q	PERSON
ejpam-6781	136	6	ω	CARDINAL
ejpam-6781	137	1	g(q	PERSON
ejpam-6781	138	1	1	CARDINAL
ejpam-6781	138	2	3 7 + 8 7ω	DATE
ejpam-6781	138	3	g(q	PERSON
ejpam-6781	138	4	second	ORDINAL
ejpam-6781	139	1	•	CARDINAL
ejpam-6781	139	2	eisenstein	PERSON
ejpam-6781	140	1	third	ORDINAL
ejpam-6781	141	1	4	CARDINAL
ejpam-6781	141	2	abelian	NORP
ejpam-6781	141	3	3	CARDINAL
ejpam-6781	141	4	g(q	PERSON
ejpam-6781	142	1	s. jitman	PERSON
ejpam-6781	142	2	m. mohammad	PERSON
ejpam-6781	142	3	e. sangwisut	PERSON
ejpam-6781	143	1	j. pure	PERSON
ejpam-6781	143	2	18	CARDINAL
ejpam-6781	143	3	4	CARDINAL
ejpam-6781	143	4	2025	CARDINAL
ejpam-6781	143	5	6781 8	DATE
ejpam-6781	145	1	323	CARDINAL
ejpam-6781	145	2	323	CARDINAL
ejpam-6781	145	3	360	CARDINAL
ejpam-6781	145	4	343	CARDINAL
ejpam-6781	145	5	49 + 16 49ω	DATE
ejpam-6781	145	6	16	CARDINAL
ejpam-6781	145	7	55	DATE
ejpam-6781	145	8	49	DATE
ejpam-6781	146	1	7	CARDINAL
ejpam-6781	146	2	8 7ω	DATE
ejpam-6781	146	3	5	CARDINAL
ejpam-6781	146	4	8	DATE
ejpam-6781	146	5	7	CARDINAL
ejpam-6781	146	6	3	CARDINAL
ejpam-6781	146	7	8	DATE
ejpam-6781	146	8	7	DATE
ejpam-6781	146	9	2 −55	PERCENT
ejpam-6781	146	10	49	DATE
ejpam-6781	146	11	16 49ω	DATE
ejpam-6781	146	12	39	CARDINAL
ejpam-6781	146	13	55	DATE
ejpam-6781	146	14	49	DATE
ejpam-6781	146	15	3	CARDINAL
ejpam-6781	146	16	37 343	CARDINAL
ejpam-6781	146	17	37	CARDINAL
ejpam-6781	146	18	360	CARDINAL
ejpam-6781	146	19	343	CARDINAL
ejpam-6781	146	20	1	CARDINAL
ejpam-6781	146	21	3 7 + 8 7 ω	DATE
ejpam-6781	146	22	g(q	PERSON
ejpam-6781	146	23	eisenstein	PERSON
ejpam-6781	148	1	1	CARDINAL
ejpam-6781	148	2	2	DATE
ejpam-6781	148	3	3	CARDINAL
ejpam-6781	148	4	3	CARDINAL
ejpam-6781	149	1	3	CARDINAL
ejpam-6781	149	2	7	CARDINAL
ejpam-6781	149	3	13	DATE
ejpam-6781	149	4	19	DATE
ejpam-6781	149	5	31	DATE
ejpam-6781	150	1	2	CARDINAL
ejpam-6781	150	2	5	DATE
ejpam-6781	150	3	11	DATE
ejpam-6781	150	4	17	DATE
ejpam-6781	151	1	3	CARDINAL
ejpam-6781	152	1	6	CARDINAL
ejpam-6781	152	2	1	CARDINAL
ejpam-6781	152	3	15	CARDINAL
ejpam-6781	153	1	11	CARDINAL
ejpam-6781	153	2	12	CARDINAL
ejpam-6781	159	1	7	CARDINAL
ejpam-6781	159	2	1	CARDINAL
ejpam-6781	159	3	g(q	PERSON
ejpam-6781	161	1	1	CARDINAL
ejpam-6781	161	2	7	CARDINAL
ejpam-6781	162	1	7	CARDINAL
ejpam-6781	162	2	1 + 3ω	CARDINAL
ejpam-6781	163	1	1 + 3ω	CARDINAL
ejpam-6781	165	1	1 + 3ω	CARDINAL
ejpam-6781	165	2	1 + 3ω	CARDINAL
ejpam-6781	166	1	1 + 3ω	CARDINAL
ejpam-6781	167	1	g(q	PERSON
ejpam-6781	168	1	13	CARDINAL
ejpam-6781	168	2	13	CARDINAL
ejpam-6781	168	3	1 + 4ω)(1 + 4ω	DATE
ejpam-6781	168	4	1 + 4ω	DATE
ejpam-6781	168	5	1 + 4ω	DATE
ejpam-6781	169	1	1 + 4ω	DATE
ejpam-6781	170	1	1	CARDINAL
ejpam-6781	170	2	ω	GPE
ejpam-6781	170	3	−1,−ω,−ω2	NORP
ejpam-6781	171	1	z[ω	GPE
ejpam-6781	172	1	z[ω	GPE
ejpam-6781	172	2	14	CARDINAL
ejpam-6781	172	3	12	CARDINAL
ejpam-6781	172	4	110	CARDINAL
ejpam-6781	173	1	6	CARDINAL
ejpam-6781	173	2	three	CARDINAL
ejpam-6781	174	1	•	CARDINAL
ejpam-6781	174	2	z[ω	GPE
ejpam-6781	176	1	p. s. jitman	PERSON
ejpam-6781	176	2	m. mohammad	PERSON
ejpam-6781	176	3	e. sangwisut	PERSON
ejpam-6781	177	1	j. pure	PERSON
ejpam-6781	177	2	18	CARDINAL
ejpam-6781	177	3	4	CARDINAL
ejpam-6781	177	4	2025	CARDINAL
ejpam-6781	177	5	6781 9	DATE
ejpam-6781	177	6	16 •	CARDINAL
ejpam-6781	177	7	∈	PRODUCT
ejpam-6781	178	1	z[ω	GPE
ejpam-6781	180	1	•	CARDINAL
ejpam-6781	180	2	3	CARDINAL
ejpam-6781	180	3	3	CARDINAL
ejpam-6781	180	4	1 + 2ω)(1 + 2ω	QUANTITY
ejpam-6781	182	1	1 + 2ω	CARDINAL
ejpam-6781	182	2	1 + 2ω	CARDINAL
ejpam-6781	182	3	z[ω	GPE
ejpam-6781	183	1	n(1 + 2ω	PRODUCT
ejpam-6781	184	1	√ 3	DATE
ejpam-6781	186	1	z′	PERSON
ejpam-6781	186	2	z′	PERSON
ejpam-6781	187	1	z[ω	GPE
ejpam-6781	187	2	z.	PERSON
ejpam-6781	187	3	4	CARDINAL
ejpam-6781	188	1	6	CARDINAL
ejpam-6781	193	1	z[ω	GPE
ejpam-6781	195	1	1 + 2ω	CARDINAL
ejpam-6781	197	1	i=1 qeii	GPE
ejpam-6781	197	2	9	CARDINAL
ejpam-6781	197	3	k ≥ 0	ORG
ejpam-6781	198	1	one	CARDINAL
ejpam-6781	199	1	g(q	PERSON
ejpam-6781	201	1	∈	ORG
ejpam-6781	201	2	⊆	CARDINAL
ejpam-6781	202	1	9	CARDINAL
ejpam-6781	203	1	i=1 qeii	GPE
ejpam-6781	203	2	10	CARDINAL
ejpam-6781	203	3	k ≥ 0	ORG
ejpam-6781	203	4	∈	PRODUCT
ejpam-6781	203	5	∖	ORG
ejpam-6781	203	6	0	CARDINAL
ejpam-6781	204	1	g(q	PERSON
ejpam-6781	205	1	s. jitman	PERSON
ejpam-6781	205	2	m. mohammad	PERSON
ejpam-6781	205	3	e. sangwisut	PERSON
ejpam-6781	206	1	j. pure	PERSON
ejpam-6781	206	2	18	CARDINAL
ejpam-6781	206	3	4	CARDINAL
ejpam-6781	206	4	2025	CARDINAL
ejpam-6781	206	5	6781 10	DATE
ejpam-6781	206	6	16	CARDINAL
ejpam-6781	206	7	3	CARDINAL
ejpam-6781	207	1	abelian	NORP
ejpam-6781	207	2	g(q	PERSON
ejpam-6781	207	3	g(q	PERSON
ejpam-6781	208	1	1	CARDINAL
ejpam-6781	208	2	ω	GPE
ejpam-6781	208	3	abelian	NORP
ejpam-6781	208	4	1	CARDINAL
ejpam-6781	211	1	10	CARDINAL
ejpam-6781	214	1	i=1 q̃j	GPE
ejpam-6781	215	1	1 + 2ω)t	DATE
ejpam-6781	215	2	11	CARDINAL
ejpam-6781	216	1	∈	ORG
ejpam-6781	217	1	∈	ORG
ejpam-6781	217	2	q̃1	ORG
ejpam-6781	218	1	∈	ORG
ejpam-6781	220	1	dr	PERSON
ejpam-6781	223	1	ω	CARDINAL
ejpam-6781	223	2	ω	ORDINAL
ejpam-6781	224	1	1	CARDINAL
ejpam-6781	224	2	1	CARDINAL
ejpam-6781	225	1	i=1 q̃j	GPE
ejpam-6781	226	1	i=1 n	PERSON
ejpam-6781	227	1	√ 3	DATE
ejpam-6781	228	1	i=1 n	PERSON
ejpam-6781	229	1	√ 3	DATE
ejpam-6781	231	1	1	CARDINAL
ejpam-6781	231	2	ci = −di	PERSON
ejpam-6781	231	3	zero	CARDINAL
ejpam-6781	232	1	11	CARDINAL
ejpam-6781	233	1	−ci	PERSON
ejpam-6781	237	1	7	CARDINAL
ejpam-6781	239	1	∈	ORG
ejpam-6781	239	2	⊕ f.	PERSON
ejpam-6781	240	1	s. jitman	PERSON
ejpam-6781	240	2	m. mohammad	PERSON
ejpam-6781	240	3	e. sangwisut	PERSON
ejpam-6781	241	1	j. pure	PERSON
ejpam-6781	241	2	18	CARDINAL
ejpam-6781	241	3	4	CARDINAL
ejpam-6781	241	4	2025	CARDINAL
ejpam-6781	241	5	6781 11	DATE
ejpam-6781	241	6	16 5	CARDINAL
ejpam-6781	241	7	eisenstein	PERSON
ejpam-6781	241	8	eisenstein	PERSON
ejpam-6781	243	1	eisenstein	PERSON
ejpam-6781	244	1	eisenstein	PERSON
ejpam-6781	245	1	1	CARDINAL
ejpam-6781	246	1	integer k	PERSON
ejpam-6781	249	1	nk	ORG
ejpam-6781	252	1	i=1 ζϵi·ni pi	PERSON
ejpam-6781	253	1	1	CARDINAL
ejpam-6781	258	1	i=1 ζ	PERSON
ejpam-6781	259	1	7	CARDINAL
ejpam-6781	259	2	i=1 ζϵi·ni	PERSON
ejpam-6781	259	3	i=1	PERSON
ejpam-6781	263	1	1	CARDINAL
ejpam-6781	264	1	k.	PERSON
ejpam-6781	265	1	i=1 pni	PERSON
ejpam-6781	266	1	i=1	PERSON
ejpam-6781	268	1	i=1	PERSON
ejpam-6781	268	2	i=1 q	PERSON
ejpam-6781	268	3	i=1	GPE
ejpam-6781	268	4	2ni	ORDINAL
ejpam-6781	268	5	1	CARDINAL
ejpam-6781	268	6	−1	DATE
ejpam-6781	270	1	i=1	GPE
ejpam-6781	270	2	2ni	ORDINAL
ejpam-6781	272	1	i=1 p ni	PERSON
ejpam-6781	273	1	∈	ORG
ejpam-6781	273	2	second	ORDINAL
ejpam-6781	275	1	eisenstein	PERSON
ejpam-6781	278	1	pia ′	WORK_OF_ART
ejpam-6781	278	2	pib ′	ORG
ejpam-6781	278	3	a′	ORG
ejpam-6781	279	1	a′	ORG
ejpam-6781	279	2	z.	PERSON
ejpam-6781	280	1	∏k	DATE
ejpam-6781	280	2	i=1	PERSON
ejpam-6781	280	3	2ni	TIME
ejpam-6781	280	4	s. jitman	PERSON
ejpam-6781	280	5	m. mohammad	PERSON
ejpam-6781	280	6	e. sangwisut	PERSON
ejpam-6781	281	1	j. pure	PERSON
ejpam-6781	281	2	18	CARDINAL
ejpam-6781	281	3	4	CARDINAL
ejpam-6781	281	4	2025	CARDINAL
ejpam-6781	281	5	6781 12	DATE
ejpam-6781	281	6	z.	PERSON
ejpam-6781	284	1	eisenstein	PERSON
ejpam-6781	285	1	eisenstein	PERSON
ejpam-6781	286	1	1	CARDINAL
ejpam-6781	286	2	1	CARDINAL
ejpam-6781	291	1	nk	ORG
ejpam-6781	292	1	1	CARDINAL
ejpam-6781	292	2	1	CARDINAL
ejpam-6781	293	1	k	PERSON
ejpam-6781	293	2	i=1 ζ	PERSON
ejpam-6781	295	1	7	CARDINAL
ejpam-6781	298	1	1	CARDINAL
ejpam-6781	298	2	g(q	PERSON
ejpam-6781	298	3	∖ u → et	ORG
ejpam-6781	298	4	5	CARDINAL
ejpam-6781	299	1	g(q	PERSON
ejpam-6781	300	1	ω	GPE
ejpam-6781	300	2	g(q	PERSON
ejpam-6781	301	1	g(q	PERSON
ejpam-6781	302	1	3	CARDINAL
ejpam-6781	302	2	g(q	PERSON
ejpam-6781	302	3	g(q	PERSON
ejpam-6781	302	4	∖	PERSON
ejpam-6781	302	5	= u ⊕	PERSON
ejpam-6781	302	6	1	CARDINAL
ejpam-6781	303	1	u ⊕	LOC
ejpam-6781	303	2	∈	ORG
ejpam-6781	304	1	1	CARDINAL
ejpam-6781	304	2	⊕	PERSON
ejpam-6781	304	3	1	CARDINAL
ejpam-6781	305	1	g(q	PERSON
ejpam-6781	306	1	u ⊕	PERSON
ejpam-6781	306	2	1}))/ω	CARDINAL
ejpam-6781	306	3	1	CARDINAL
ejpam-6781	307	1	one	CARDINAL
ejpam-6781	307	2	one	CARDINAL
ejpam-6781	307	3	1	CARDINAL
ejpam-6781	313	1	i=1 ζϵi·ni pi	PERSON
ejpam-6781	316	1	s. jitman	PERSON
ejpam-6781	316	2	m. mohammad	PERSON
ejpam-6781	316	3	e. sangwisut	PERSON
ejpam-6781	317	1	j. pure	PERSON
ejpam-6781	317	2	18	CARDINAL
ejpam-6781	317	3	4	CARDINAL
ejpam-6781	317	4	2025	CARDINAL
ejpam-6781	317	5	6781 13	DATE
ejpam-6781	317	6	16	CARDINAL
ejpam-6781	317	7	⊆	MONEY
ejpam-6781	317	8	∖	CARDINAL
ejpam-6781	317	9	1	CARDINAL
ejpam-6781	317	10	1	CARDINAL
ejpam-6781	319	1	2	CARDINAL
ejpam-6781	319	2	2	CARDINAL
ejpam-6781	321	1	1	CARDINAL
ejpam-6781	321	2	4	CARDINAL
ejpam-6781	322	1	1	CARDINAL
ejpam-6781	322	2	1	CARDINAL
ejpam-6781	323	1	k	PERSON
ejpam-6781	323	2	2k	CARDINAL
ejpam-6781	323	3	hypotenuse c. (ii	PERSON
ejpam-6781	323	4	hypotenuse c. proof	PERSON
ejpam-6781	324	1	first	ORDINAL
ejpam-6781	324	2	one	CARDINAL
ejpam-6781	324	3	one	CARDINAL
ejpam-6781	324	4	1	CARDINAL
ejpam-6781	324	5	4	CARDINAL
ejpam-6781	325	1	i=1 ζϵi·ni pi	PERSON
ejpam-6781	327	1	2k	CARDINAL
ejpam-6781	328	1	second	ORDINAL
ejpam-6781	328	2	2	CARDINAL
ejpam-6781	328	3	4	CARDINAL
ejpam-6781	329	1	4	CARDINAL
ejpam-6781	329	2	1	CARDINAL
ejpam-6781	330	1	2	CARDINAL
ejpam-6781	330	2	49	CARDINAL
ejpam-6781	331	1	72	CARDINAL
ejpam-6781	331	2	7	CARDINAL
ejpam-6781	332	1	1	CARDINAL
ejpam-6781	332	2	1+3ω	CARDINAL
ejpam-6781	333	1	7	CARDINAL
ejpam-6781	333	2	3 7ω	DATE
ejpam-6781	334	1	1+3ω	CARDINAL
ejpam-6781	335	1	7 + 3 7ω	PERCENT
ejpam-6781	337	1	4	CARDINAL
ejpam-6781	337	2	two	CARDINAL
ejpam-6781	337	3	1	CARDINAL
ejpam-6781	337	4	7	CARDINAL
ejpam-6781	337	5	3	CARDINAL
ejpam-6781	337	6	2	CARDINAL
ejpam-6781	337	7	55	CARDINAL
ejpam-6781	338	1	sixth	ORDINAL
ejpam-6781	339	1	second	ORDINAL
ejpam-6781	339	2	16 49 + 55 49ω	DATE
ejpam-6781	340	1	eisenstein	PERSON
ejpam-6781	340	2	16 49 + 55 49ω	DATE
ejpam-6781	341	1	16	CARDINAL
ejpam-6781	341	2	55	DATE
ejpam-6781	341	3	49	DATE
ejpam-6781	343	1	7 + 3 7 ω	DATE
ejpam-6781	343	2	2	CARDINAL
ejpam-6781	343	3	16 49	CARDINAL
ejpam-6781	343	4	39	CARDINAL
ejpam-6781	344	1	fifth	ORDINAL
ejpam-6781	345	1	second	ORDINAL
ejpam-6781	345	2	39 49 + 55 49ω	DATE
ejpam-6781	346	1	eisenstein	PERSON
ejpam-6781	346	2	39	CARDINAL
ejpam-6781	347	1	39	CARDINAL
ejpam-6781	347	2	55	DATE
ejpam-6781	347	3	49	DATE
ejpam-6781	348	1	et49	CARDINAL
ejpam-6781	348	2	16	CARDINAL
ejpam-6781	348	3	55	DATE
ejpam-6781	348	4	49	DATE
ejpam-6781	348	5	39	CARDINAL
ejpam-6781	348	6	55	DATE
ejpam-6781	348	7	49	DATE
ejpam-6781	349	1	s. jitman	PERSON
ejpam-6781	349	2	m. mohammad	PERSON
ejpam-6781	349	3	e. sangwisut	PERSON
ejpam-6781	350	1	j. pure	PERSON
ejpam-6781	350	2	18	CARDINAL
ejpam-6781	350	3	4	CARDINAL
ejpam-6781	350	4	2025	CARDINAL
ejpam-6781	350	5	6781 14	DATE
ejpam-6781	350	6	16	CARDINAL
ejpam-6781	351	1	91	CARDINAL
ejpam-6781	352	1	7	CARDINAL
ejpam-6781	352	2	13	DATE
ejpam-6781	352	3	7	CARDINAL
ejpam-6781	352	4	13	CARDINAL
ejpam-6781	353	1	1	CARDINAL
ejpam-6781	354	1	1 + 4ω	DATE
ejpam-6781	355	1	ζϵ17 ζϵ213	PERSON
ejpam-6781	355	2	±	CARDINAL
ejpam-6781	355	3	ζ7ζ13, ζ−1 7	DATE
ejpam-6781	356	1	13 , ζ−1 7 ζ−1 13	PERCENT
ejpam-6781	357	1	4	CARDINAL
ejpam-6781	357	2	four	CARDINAL
ejpam-6781	357	3	1	CARDINAL
ejpam-6781	357	4	1	CARDINAL
ejpam-6781	357	5	1	CARDINAL
ejpam-6781	357	6	1 + 3ω	CARDINAL
ejpam-6781	359	1	96	CARDINAL
ejpam-6781	360	1	sixth	ORDINAL
ejpam-6781	361	1	second	ORDINAL
ejpam-6781	361	2	11 91 + 96 91ω	DATE
ejpam-6781	362	1	eisenstein	PERSON
ejpam-6781	362	2	11 91 + 96 91ω	DATE
ejpam-6781	363	1	11	CARDINAL
ejpam-6781	363	2	96	DATE
ejpam-6781	363	3	91	CARDINAL
ejpam-6781	364	1	2	CARDINAL
ejpam-6781	364	2	−1	DATE
ejpam-6781	364	3	1	CARDINAL
ejpam-6781	364	4	1 + 3ω	CARDINAL
ejpam-6781	365	1	99	CARDINAL
ejpam-6781	366	1	sixth	ORDINAL
ejpam-6781	367	1	second	ORDINAL
ejpam-6781	367	2	80 91 + 99 91ω	DATE
ejpam-6781	368	1	eisenstein	PERSON
ejpam-6781	368	2	80 91 + 99 91ω	DATE
ejpam-6781	369	1	80, 99	DATE
ejpam-6781	369	2	91	CARDINAL
ejpam-6781	370	1	3	CARDINAL
ejpam-6781	370	2	1	CARDINAL
ejpam-6781	370	3	−1	DATE
ejpam-6781	371	1	1 + 3ω	CARDINAL
ejpam-6781	372	1	80 91	CARDINAL
ejpam-6781	372	2	19 91	DATE
ejpam-6781	373	1	fifth	ORDINAL
ejpam-6781	374	1	second	ORDINAL
ejpam-6781	374	2	19 91 + 99 91ω	DATE
ejpam-6781	375	1	eisenstein	PERSON
ejpam-6781	375	2	19 91 + 99 91ω	DATE
ejpam-6781	376	1	19, 99	DATE
ejpam-6781	376	2	91	CARDINAL
ejpam-6781	377	1	4	CARDINAL
ejpam-6781	377	2	−1	DATE
ejpam-6781	377	3	−1	DATE
ejpam-6781	378	1	1 + 3ω	CARDINAL
ejpam-6781	379	1	11 91	CARDINAL
ejpam-6781	380	1	fifth	ORDINAL
ejpam-6781	381	1	second	ORDINAL
ejpam-6781	381	2	85 91 + 96 91ω	DATE
ejpam-6781	382	1	eisenstein	PERSON
ejpam-6781	382	2	85 91 + 96 91ω	DATE
ejpam-6781	382	3	85, 96	DATE
ejpam-6781	382	4	91	CARDINAL
ejpam-6781	383	1	et49	CARDINAL
ejpam-6781	383	2	11, 96	DATE
ejpam-6781	383	3	91	DATE
ejpam-6781	383	4	85	CARDINAL
ejpam-6781	383	5	96	DATE
ejpam-6781	383	6	91	DATE
ejpam-6781	383	7	80	CARDINAL
ejpam-6781	383	8	99	DATE
ejpam-6781	383	9	91	DATE
ejpam-6781	383	10	19	CARDINAL
ejpam-6781	383	11	99	DATE
ejpam-6781	383	12	91	CARDINAL
ejpam-6781	384	1	6	CARDINAL
ejpam-6781	384	2	eisenstein	PERSON
ejpam-6781	384	3	60	CARDINAL
ejpam-6781	385	1	ω	ORDINAL
ejpam-6781	386	1	eisenstein integers	PERSON
ejpam-6781	386	2	ω	ORDINAL
ejpam-6781	386	3	two	CARDINAL
ejpam-6781	386	4	six	CARDINAL
ejpam-6781	386	5	one	CARDINAL
ejpam-6781	386	6	three	CARDINAL
ejpam-6781	387	1	ω	ORDINAL
ejpam-6781	387	2	s. jitman	PERSON
ejpam-6781	387	3	m. mohammad	PERSON
ejpam-6781	387	4	e. sangwisut	PERSON
ejpam-6781	388	1	j. pure	PERSON
ejpam-6781	388	2	18	CARDINAL
ejpam-6781	388	3	4	CARDINAL
ejpam-6781	388	4	2025	CARDINAL
ejpam-6781	388	5	6781 15	DATE
ejpam-6781	388	6	16	CARDINAL
ejpam-6781	389	1	second	ORDINAL
ejpam-6781	392	1	eisenstein	PERSON
ejpam-6781	392	2	one	CARDINAL
ejpam-6781	392	3	three	CARDINAL
ejpam-6781	393	1	two	CARDINAL
ejpam-6781	395	1	second	ORDINAL
ejpam-6781	395	2	16	CARDINAL
ejpam-6781	395	3	17	CARDINAL
ejpam-6781	396	1	s. jitmam	PERSON
ejpam-6781	396	2	the national research council of thailand	ORG
ejpam-6781	396	3	silpakorn university	ORG
ejpam-6781	396	4	1	CARDINAL
ejpam-6781	398	1	dover	GPE
ejpam-6781	398	2	mineola	GPE
ejpam-6781	398	3	ny	GPE
ejpam-6781	398	4	2011	DATE
ejpam-6781	399	1	2	CARDINAL
ejpam-6781	399	2	charles l. shedd	PERSON
ejpam-6781	400	1	hypotenuse	ORG
ejpam-6781	400	2	64	CARDINAL
ejpam-6781	401	1	scripta mathematica	PERSON
ejpam-6781	401	2	15:131–132, 1949	DATE
ejpam-6781	402	1	3	CARDINAL
ejpam-6781	402	2	e. eckert	PERSON
ejpam-6781	404	1	57:22–27	CARDINAL
ejpam-6781	404	2	1984	DATE
ejpam-6781	405	1	4	CARDINAL
ejpam-6781	405	2	lin tan	PERSON
ejpam-6781	407	1	69(3):163–171, 1996	ORG
ejpam-6781	408	1	5	CARDINAL
ejpam-6781	408	2	amnon yekutieli	PERSON
ejpam-6781	409	1	abelian	NORP
ejpam-6781	410	1	american	NORP
ejpam-6781	410	2	monthly	DATE
ejpam-6781	410	3	130(4):321–334	DATE
ejpam-6781	410	4	2023	CARDINAL
ejpam-6781	411	1	6	CARDINAL
ejpam-6781	412	1	87.23	CARDINAL
ejpam-6781	412	2	60	CARDINAL
ejpam-6781	413	1	87(508):148–153	GPE
ejpam-6781	413	2	2003	DATE
ejpam-6781	414	1	7	CARDINAL
ejpam-6781	414	2	john gilder	PERSON
ejpam-6781	415	1	60	CARDINAL
ejpam-6781	416	1	66:261–266	CARDINAL
ejpam-6781	416	2	1982	DATE
ejpam-6781	417	1	8	CARDINAL
ejpam-6781	418	1	120	CARDINAL
ejpam-6781	418	2	60	CARDINAL
ejpam-6781	419	1	90:299–305, 2006	DATE
ejpam-6781	420	1	9	CARDINAL
ejpam-6781	421	1	120	CARDINAL
ejpam-6781	422	1	67(442):251–255	CARDINAL
ejpam-6781	422	2	1983	DATE
ejpam-6781	423	1	10	CARDINAL
ejpam-6781	423	2	russell a. gordon.	PERSON
ejpam-6781	424	1	eisenstein	PERSON
ejpam-6781	425	1	85:12–25	CARDINAL
ejpam-6781	425	2	2012	DATE
ejpam-6781	426	1	11	CARDINAL
ejpam-6781	426	2	j. h. conway	ORG
ejpam-6781	426	3	r.	NORP
ejpam-6781	428	1	new york	GPE
ejpam-6781	428	2	ny	GPE
ejpam-6781	428	3	2012	DATE
ejpam-6781	429	1	s. jitman	PERSON
ejpam-6781	429	2	m. mohammad	PERSON
ejpam-6781	429	3	e. sangwisut	PERSON
ejpam-6781	430	1	j. pure	PERSON
ejpam-6781	430	2	18	CARDINAL
ejpam-6781	430	3	4	CARDINAL
ejpam-6781	430	4	2025	CARDINAL
ejpam-6781	430	5	6781 16	DATE
ejpam-6781	431	1	12	CARDINAL
ejpam-6781	431	2	k. ireland	PERSON
ejpam-6781	431	3	m. rosen	PERSON
ejpam-6781	433	1	new york	GPE
ejpam-6781	433	2	ny	GPE
ejpam-6781	433	3	2 edition	QUANTITY
ejpam-6781	433	4	1990	DATE
ejpam-6781	434	1	13	CARDINAL
ejpam-6781	434	2	r. takloo	PERSON
ejpam-6781	437	1	2018	DATE
ejpam-6781	438	1	14	CARDINAL
ejpam-6781	438	2	brian d. sittinger	PERSON
ejpam-6781	439	1	eisenstein	PERSON
ejpam-6781	440	1	american	NORP
ejpam-6781	440	2	monthly	DATE
ejpam-6781	440	3	2017	DATE
ejpam-6781	441	1	15	CARDINAL
ejpam-6781	441	2	kamal	PERSON
ejpam-6781	442	1	±	CARDINAL
ejpam-6781	442	2	ab±	ORG
ejpam-6781	443	1	166:208–218	DATE
ejpam-6781	443	2	2016	DATE
ejpam-6781	444	1	16	CARDINAL
ejpam-6781	444	2	d. s. kim	PERSON
ejpam-6781	444	3	t. kim.	PERSON
ejpam-6781	445	1	degenerate euler	PERSON
ejpam-6781	446	1	russian	NORP
ejpam-6781	446	2	32(31):682	CARDINAL
ejpam-6781	446	3	690	CARDINAL
ejpam-6781	446	4	2024	DATE
ejpam-6781	447	1	17	CARDINAL
ejpam-6781	447	2	t. kim	PERSON
ejpam-6781	447	3	d. s. kim.	PERSON
ejpam-6781	449	1	russian	NORP
ejpam-6781	449	2	32(2):288–296	DATE
ejpam-6781	449	3	2025	DATE