id	sid	eid	entity	type
ejpam-6492	1	1	european journal	ORG
ejpam-6492	1	2	2025	DATE
ejpam-6492	1	3	18	CARDINAL
ejpam-6492	1	4	3	CARDINAL
ejpam-6492	1	5	6492	CARDINAL
ejpam-6492	1	6	1307-5543	DATE
ejpam-6492	1	7	new york	GPE
ejpam-6492	1	8	koshy bahar demirtürk1,∗	PERSON
ejpam-6492	1	9	izmir bakırçay university	ORG
ejpam-6492	1	10	izmir	PERSON
ejpam-6492	3	1	koshy	PERSON
ejpam-6492	5	1	2020	DATE
ejpam-6492	5	2	15b33	CARDINAL
ejpam-6492	5	3	11b39	CARDINAL
ejpam-6492	5	4	11b75	CARDINAL
ejpam-6492	5	5	11z05	CARDINAL
ejpam-6492	5	6	generalized fibonacci quaternions	ORG
ejpam-6492	5	7	1	CARDINAL
ejpam-6492	12	1	1	CARDINAL
ejpam-6492	12	2	sharma explores	PERSON
ejpam-6492	14	1	https://doi.org/10.29020/nybg.ejpam.v18i3.6492	PERSON
ejpam-6492	15	1	1	CARDINAL
ejpam-6492	15	2	2025	CARDINAL
ejpam-6492	17	1	j. pure	PERSON
ejpam-6492	17	2	18	CARDINAL
ejpam-6492	17	3	3	CARDINAL
ejpam-6492	17	4	2025	CARDINAL
ejpam-6492	17	5	6492 2	DATE
ejpam-6492	17	6	22	DATE
ejpam-6492	17	7	2	CARDINAL
ejpam-6492	20	1	4	CARDINAL
ejpam-6492	22	1	5	CARDINAL
ejpam-6492	25	1	6	CARDINAL
ejpam-6492	27	1	7	CARDINAL
ejpam-6492	31	1	lucas quaternions	PERSON
ejpam-6492	32	1	kesim	PERSON
ejpam-6492	32	2	the generalized fibonacci	ORG
ejpam-6492	32	3	lucas quaternions	PERSON
ejpam-6492	32	4	11	CARDINAL
ejpam-6492	33	1	kome et al	PERSON
ejpam-6492	33	2	lucas quaternions	PERSON
ejpam-6492	33	3	12	CARDINAL
ejpam-6492	34	1	k-order fibonacci	ORG
ejpam-6492	34	2	lucas quaternions	PERSON
ejpam-6492	34	3	13	CARDINAL
ejpam-6492	35	1	kızılateş et al	PERSON
ejpam-6492	36	1	14	CARDINAL
ejpam-6492	37	1	15	CARDINAL
ejpam-6492	37	2	fibonacci-narayana quaternions	ORG
ejpam-6492	39	1	lucas quaternions	PERSON
ejpam-6492	41	1	j. pure	PERSON
ejpam-6492	41	2	18	CARDINAL
ejpam-6492	41	3	3	CARDINAL
ejpam-6492	41	4	2025	CARDINAL
ejpam-6492	41	5	6492 3	DATE
ejpam-6492	41	6	22	CARDINAL
ejpam-6492	46	1	third	ORDINAL
ejpam-6492	47	1	koshy	PERSON
ejpam-6492	48	1	2	CARDINAL
ejpam-6492	48	2	1	CARDINAL
ejpam-6492	49	1	n ≥ 3	DATE
ejpam-6492	49	2	1	CARDINAL
ejpam-6492	51	1	2p	CARDINAL
ejpam-6492	51	2	3p	CARDINAL
ejpam-6492	51	3	5p + 3q	CARDINAL
ejpam-6492	51	4	8p	CARDINAL
ejpam-6492	51	5	13p	CARDINAL
ejpam-6492	53	1	horadam	GPE
ejpam-6492	53	2	16	CARDINAL
ejpam-6492	53	3	17	CARDINAL
ejpam-6492	54	1	1	CARDINAL
ejpam-6492	54	2	n ≥ 2	DATE
ejpam-6492	54	3	1	CARDINAL
ejpam-6492	55	1	0	CARDINAL
ejpam-6492	55	2	1	CARDINAL
ejpam-6492	56	1	1	CARDINAL
ejpam-6492	57	1	2	CARDINAL
ejpam-6492	57	2	1	CARDINAL
ejpam-6492	57	3	2	CARDINAL
ejpam-6492	57	4	1	CARDINAL
ejpam-6492	57	5	ln−1 + ln−2	ORG
ejpam-6492	57	6	n ≥ 2	ORG
ejpam-6492	57	7	18	CARDINAL
ejpam-6492	57	8	19	CARDINAL
ejpam-6492	58	1	20	CARDINAL
ejpam-6492	59	1	r(a	PERSON
ejpam-6492	61	1	j. pure	PERSON
ejpam-6492	61	2	18	CARDINAL
ejpam-6492	61	3	3	CARDINAL
ejpam-6492	61	4	2025	CARDINAL
ejpam-6492	61	5	6492 4	DATE
ejpam-6492	61	6	22	CARDINAL
ejpam-6492	61	7	1	CARDINAL
ejpam-6492	61	8	20	CARDINAL
ejpam-6492	61	9	first	ORDINAL
ejpam-6492	61	10	r(1	ORG
ejpam-6492	61	11	1	CARDINAL
ejpam-6492	61	12	1	CARDINAL
ejpam-6492	61	13	0	CARDINAL
ejpam-6492	61	14	1	DATE
ejpam-6492	61	15	1	CARDINAL
ejpam-6492	61	16	2	DATE
ejpam-6492	61	17	3	DATE
ejpam-6492	61	18	5	DATE
ejpam-6492	61	19	8	DATE
ejpam-6492	61	20	13	DATE
ejpam-6492	61	21	21	DATE
ejpam-6492	61	22	34	DATE
ejpam-6492	61	23	55	DATE
ejpam-6492	62	1	r(1	ORG
ejpam-6492	62	2	1	CARDINAL
ejpam-6492	62	3	2	CARDINAL
ejpam-6492	62	4	2	CARDINAL
ejpam-6492	62	5	1	DATE
ejpam-6492	62	6	3	DATE
ejpam-6492	62	7	4	DATE
ejpam-6492	62	8	7	DATE
ejpam-6492	62	9	11	DATE
ejpam-6492	62	10	18	DATE
ejpam-6492	62	11	29	DATE
ejpam-6492	62	12	47	DATE
ejpam-6492	62	13	76	DATE
ejpam-6492	63	1	r(2	NORP
ejpam-6492	63	2	1	CARDINAL
ejpam-6492	63	3	1	CARDINAL
ejpam-6492	63	4	0	CARDINAL
ejpam-6492	63	5	1	DATE
ejpam-6492	63	6	2	DATE
ejpam-6492	63	7	5	DATE
ejpam-6492	63	8	12	DATE
ejpam-6492	63	9	29	DATE
ejpam-6492	63	10	70	DATE
ejpam-6492	63	11	169	CARDINAL
ejpam-6492	64	1	pell-lucas numbers	PERSON
ejpam-6492	64	2	r(2	NORP
ejpam-6492	64	3	1	CARDINAL
ejpam-6492	64	4	2	CARDINAL
ejpam-6492	64	5	2	CARDINAL
ejpam-6492	64	6	2	DATE
ejpam-6492	64	7	6	DATE
ejpam-6492	64	8	14	DATE
ejpam-6492	64	9	34	DATE
ejpam-6492	64	10	82	DATE
ejpam-6492	65	1	−1	DATE
ejpam-6492	65	2	1	CARDINAL
ejpam-6492	65	3	0	CARDINAL
ejpam-6492	65	4	1	DATE
ejpam-6492	65	5	2	DATE
ejpam-6492	65	6	3	DATE
ejpam-6492	65	7	4	DATE
ejpam-6492	65	8	5	DATE
ejpam-6492	65	9	6	DATE
ejpam-6492	66	1	r(2	NORP
ejpam-6492	66	2	−1	DATE
ejpam-6492	66	3	2	CARDINAL
ejpam-6492	66	4	2	CARDINAL
ejpam-6492	66	5	2	DATE
ejpam-6492	66	6	2	DATE
ejpam-6492	66	7	2	DATE
ejpam-6492	66	8	2	DATE
ejpam-6492	66	9	2	DATE
ejpam-6492	66	10	2	DATE
ejpam-6492	67	1	1	CARDINAL
ejpam-6492	67	2	0	CARDINAL
ejpam-6492	67	3	1	DATE
ejpam-6492	67	4	3	DATE
ejpam-6492	67	5	7	DATE
ejpam-6492	67	6	15	DATE
ejpam-6492	67	7	31	DATE
ejpam-6492	68	1	2	CARDINAL
ejpam-6492	68	2	2	CARDINAL
ejpam-6492	68	3	3	DATE
ejpam-6492	68	4	5	DATE
ejpam-6492	68	5	9	DATE
ejpam-6492	68	6	16	DATE
ejpam-6492	68	7	33	DATE
ejpam-6492	69	1	r(1	ORG
ejpam-6492	69	2	−1	DATE
ejpam-6492	69	3	1	CARDINAL
ejpam-6492	69	4	0	CARDINAL
ejpam-6492	69	5	1	DATE
ejpam-6492	69	6	1	CARDINAL
ejpam-6492	69	7	0	DATE
ejpam-6492	69	8	−1	DATE
ejpam-6492	69	9	−1	DATE
ejpam-6492	69	10	0	CARDINAL
ejpam-6492	69	11	1	CARDINAL
ejpam-6492	70	1	r(1	ORG
ejpam-6492	70	2	−1	DATE
ejpam-6492	70	3	2	CARDINAL
ejpam-6492	70	4	2	CARDINAL
ejpam-6492	70	5	1	DATE
ejpam-6492	70	6	−2	ORG
ejpam-6492	70	7	−1	DATE
ejpam-6492	70	8	1	CARDINAL
ejpam-6492	70	9	2	DATE
ejpam-6492	70	10	1	CARDINAL
ejpam-6492	71	1	r(3	ORG
ejpam-6492	71	2	−1	DATE
ejpam-6492	71	3	1	CARDINAL
ejpam-6492	71	4	0	CARDINAL
ejpam-6492	71	5	1	DATE
ejpam-6492	71	6	3	DATE
ejpam-6492	71	7	8	DATE
ejpam-6492	71	8	21	DATE
ejpam-6492	71	9	55	DATE
ejpam-6492	72	1	−1	DATE
ejpam-6492	72	2	2	CARDINAL
ejpam-6492	72	3	2	CARDINAL
ejpam-6492	72	4	3	DATE
ejpam-6492	72	5	7	DATE
ejpam-6492	72	6	18	DATE
ejpam-6492	72	7	47	DATE
ejpam-6492	73	1	koshy	PERSON
ejpam-6492	73	2	19	CARDINAL
ejpam-6492	76	1	2	CARDINAL
ejpam-6492	77	1	16	CARDINAL
ejpam-6492	77	2	17	CARDINAL
ejpam-6492	77	3	∈	ORG
ejpam-6492	78	1	un	ORG
ejpam-6492	78	2	un	ORG
ejpam-6492	78	3	1	CARDINAL
ejpam-6492	78	4	un	ORG
ejpam-6492	80	1	3	CARDINAL
ejpam-6492	81	1	16	CARDINAL
ejpam-6492	81	2	17	CARDINAL
ejpam-6492	82	1	2	CARDINAL
ejpam-6492	86	1	+ 4q	CARDINAL
ejpam-6492	86	2	0	CARDINAL
ejpam-6492	86	3	+ √	DATE
ejpam-6492	87	1	− √ ∆ 2	ORG
ejpam-6492	88	1	+ q.	PERSON
ejpam-6492	88	2	+ qun−1	DATE
ejpam-6492	88	3	2	CARDINAL
ejpam-6492	89	1	j. pure	PERSON
ejpam-6492	89	2	18	CARDINAL
ejpam-6492	89	3	3	CARDINAL
ejpam-6492	89	4	2025	CARDINAL
ejpam-6492	89	5	6492 5	DATE
ejpam-6492	89	6	22	CARDINAL
ejpam-6492	90	1	+ qun−1	DATE
ejpam-6492	91	1	3	CARDINAL
ejpam-6492	92	1	+ qvn−1	PERSON
ejpam-6492	92	2	4	CARDINAL
ejpam-6492	94	1	qvn−1	GPE
ejpam-6492	95	1	5	CARDINAL
ejpam-6492	95	2	un	ORG
ejpam-6492	98	1	6	CARDINAL
ejpam-6492	99	1	20	CARDINAL
ejpam-6492	100	1	two	CARDINAL
ejpam-6492	100	2	1	CARDINAL
ejpam-6492	102	1	+ 3pq	DATE
ejpam-6492	103	1	22	CARDINAL
ejpam-6492	103	2	the generalized fibonacci	ORG
ejpam-6492	103	3	v−n	NORP
ejpam-6492	105	1	1680	CARDINAL
ejpam-6492	105	2	2	CARDINAL
ejpam-6492	105	3	1879	DATE
ejpam-6492	105	4	d’ocagne	GPE
ejpam-6492	106	1	1882	DATE
ejpam-6492	107	1	koshy	PERSON
ejpam-6492	107	2	first	ORDINAL
ejpam-6492	108	1	b. demirtürk	PERSON
ejpam-6492	109	1	j. pure	PERSON
ejpam-6492	109	2	18	CARDINAL
ejpam-6492	109	3	3	CARDINAL
ejpam-6492	109	4	2025	CARDINAL
ejpam-6492	109	5	6492 6	DATE
ejpam-6492	109	6	22	DATE
ejpam-6492	109	7	4	CARDINAL
ejpam-6492	110	1	1	CARDINAL
ejpam-6492	114	1	7	CARDINAL
ejpam-6492	114	2	23	CARDINAL
ejpam-6492	115	1	7	CARDINAL
ejpam-6492	116	1	7	CARDINAL
ejpam-6492	117	1	catalan	NORP
ejpam-6492	117	2	fn−2	ORG
ejpam-6492	117	3	−1	DATE
ejpam-6492	118	1	24	CARDINAL
ejpam-6492	119	1	25	CARDINAL
ejpam-6492	119	2	3	CARDINAL
ejpam-6492	119	3	−1)nfn	PRODUCT
ejpam-6492	121	1	fa	ORG
ejpam-6492	122	1	al	ORG
ejpam-6492	123	1	american	NORP
ejpam-6492	123	2	monthly	DATE
ejpam-6492	123	3	26	CARDINAL
ejpam-6492	124	1	vajda	DATE
ejpam-6492	125	1	21	CARDINAL
ejpam-6492	125	2	177	CARDINAL
ejpam-6492	126	1	20a	ORDINAL
ejpam-6492	128	1	horadam	PERSON
ejpam-6492	129	1	n+s	ORG
ejpam-6492	130	1	9	CARDINAL
ejpam-6492	130	2	16	CARDINAL
ejpam-6492	131	1	25	CARDINAL
ejpam-6492	131	2	fn+b	PERSON
ejpam-6492	132	1	fc	NORP
ejpam-6492	133	1	catalan	GPE
ejpam-6492	133	2	d’ocagne	GPE
ejpam-6492	133	3	7	CARDINAL
ejpam-6492	133	4	8)	CARDINAL
ejpam-6492	133	5	9	CARDINAL
ejpam-6492	133	6	koshy	PERSON
ejpam-6492	134	1	19	CARDINAL
ejpam-6492	134	2	koshy	PERSON
ejpam-6492	135	1	6	CARDINAL
ejpam-6492	136	1	1	CARDINAL
ejpam-6492	137	1	un−1un+1 − u2 n = −(−q)n−1	ORG
ejpam-6492	138	1	b. demirtürk,	PERSON
ejpam-6492	139	1	j. pure	PERSON
ejpam-6492	139	2	18	CARDINAL
ejpam-6492	139	3	3	CARDINAL
ejpam-6492	139	4	2025	CARDINAL
ejpam-6492	139	5	6492 7	DATE
ejpam-6492	139	6	22	CARDINAL
ejpam-6492	141	1	un−1un+1 − u2 n	PERSON
ejpam-6492	141	2	αn−1 − βn−1)(αn+1	ORG
ejpam-6492	145	1	−αn+1βn−1 −	PERSON
ejpam-6492	145	2	2αβ	ORDINAL
ejpam-6492	146	1	2	CARDINAL
ejpam-6492	146	2	vn−1vn+1 −	FAC
ejpam-6492	146	3	2 n	QUANTITY
ejpam-6492	147	1	vn−1vn+1 −	FAC
ejpam-6492	147	2	2 n	QUANTITY
ejpam-6492	147	3	αn−1 + βn−1)(αn+1	ORG
ejpam-6492	151	1	2αnβn	CARDINAL
ejpam-6492	151	2	2αβ	ORDINAL
ejpam-6492	152	1	3	CARDINAL
ejpam-6492	153	1	catalan	NORP
ejpam-6492	153	2	∈	ORG
ejpam-6492	153	3	un−run+r − u2 n	PERSON
ejpam-6492	155	1	un−run+r − u2 n	PERSON
ejpam-6492	155	2	αn−r	CARDINAL
ejpam-6492	158	1	αn−rβn+r + 2αnβn	QUANTITY
ejpam-6492	158	2	α2r +	GPE
ejpam-6492	158	3	2αrβr	CARDINAL
ejpam-6492	159	1	2	CARDINAL
ejpam-6492	161	1	j. pure	PERSON
ejpam-6492	161	2	18	CARDINAL
ejpam-6492	161	3	3	CARDINAL
ejpam-6492	161	4	2025	CARDINAL
ejpam-6492	161	5	6492 8	DATE
ejpam-6492	161	6	22	CARDINAL
ejpam-6492	161	7	4	CARDINAL
ejpam-6492	162	1	vn−rvn+r	ORG
ejpam-6492	162	2	2 n	QUANTITY
ejpam-6492	162	3	−q)n−r∆u2	PERSON
ejpam-6492	164	1	2 n	QUANTITY
ejpam-6492	164	2	αn−r + βn−r)(αn+r + βn+r	ORG
ejpam-6492	168	1	2αnβn	CARDINAL
ejpam-6492	168	2	2αrβr	CARDINAL
ejpam-6492	170	1	2	CARDINAL
ejpam-6492	170	2	−q)n−r∆u2	PERSON
ejpam-6492	171	1	1	CARDINAL
ejpam-6492	172	1	∈	ORG
ejpam-6492	172	2	2 n	QUANTITY
ejpam-6492	172	3	− u2 n	PERSON
ejpam-6492	174	1	3	CARDINAL
ejpam-6492	174	2	4	CARDINAL
ejpam-6492	175	1	27	CARDINAL
ejpam-6492	175	2	1 0	CARDINAL
ejpam-6492	175	3	qun un qun−1	PERSON
ejpam-6492	175	4	2	CARDINAL
ejpam-6492	175	5	vm+n −	PERSON
ejpam-6492	175	6	−q)nvm−n	PRODUCT
ejpam-6492	180	1	5	CARDINAL
ejpam-6492	180	2	∈	ORG
ejpam-6492	180	3	b. demirtürk,	PERSON
ejpam-6492	181	1	j. pure	PERSON
ejpam-6492	181	2	18	CARDINAL
ejpam-6492	181	3	3	CARDINAL
ejpam-6492	181	4	2025	CARDINAL
ejpam-6492	181	5	6492 9	DATE
ejpam-6492	181	6	22	CARDINAL
ejpam-6492	182	1	αn+r − βn+r	PERSON
ejpam-6492	182	2	2	CARDINAL
ejpam-6492	182	3	αn−r	CARDINAL
ejpam-6492	182	4	2	CARDINAL
ejpam-6492	182	5	2	CARDINAL
ejpam-6492	182	6	αβ)n+r	ORG
ejpam-6492	182	7	− 2 (	ORG
ejpam-6492	182	8	2	CARDINAL
ejpam-6492	183	1	− 2 (	ORG
ejpam-6492	183	2	α2r − β2r	GPE
ejpam-6492	189	1	6	CARDINAL
ejpam-6492	190	1	∈	ORG
ejpam-6492	190	2	2	CARDINAL
ejpam-6492	190	3	2	CARDINAL
ejpam-6492	192	1	2	CARDINAL
ejpam-6492	192	2	2	CARDINAL
ejpam-6492	192	3	2	CARDINAL
ejpam-6492	194	1	+ 2	DATE
ejpam-6492	194	2	+ 2	DATE
ejpam-6492	194	3	α2r − β2r	GPE
ejpam-6492	202	1	5	CARDINAL
ejpam-6492	202	2	6	CARDINAL
ejpam-6492	202	3	2	CARDINAL
ejpam-6492	203	1	∈	ORG
ejpam-6492	203	2	2	CARDINAL
ejpam-6492	203	3	2	CARDINAL
ejpam-6492	206	1	j. pure	PERSON
ejpam-6492	206	2	18	CARDINAL
ejpam-6492	206	3	3	CARDINAL
ejpam-6492	206	4	2025	CARDINAL
ejpam-6492	206	5	6492 10	DATE
ejpam-6492	206	6	generalized fibonacci	ORG
ejpam-6492	206	7	four	CARDINAL
ejpam-6492	206	8	william rowan hamilton	PERSON
ejpam-6492	206	9	the 19th century	DATE
ejpam-6492	206	10	three	CARDINAL
ejpam-6492	206	11	28	CARDINAL
ejpam-6492	209	1	5	CARDINAL
ejpam-6492	210	1	∈	ORG
ejpam-6492	210	2	−1	DATE
ejpam-6492	210	3	j2	ORG
ejpam-6492	210	4	−1	DATE
ejpam-6492	210	5	−1	DATE
ejpam-6492	210	6	= k = −ki	PERSON
ejpam-6492	214	1	28	CARDINAL
ejpam-6492	215	1	1	CARDINAL
ejpam-6492	215	2	j	PERSON
ejpam-6492	216	1	6	CARDINAL
ejpam-6492	217	1	two quaternions	QUANTITY
ejpam-6492	218	1	+	CARDINAL
ejpam-6492	225	1	+ j(a1b3 + a3b1	PERSON
ejpam-6492	231	1	n(q	PERSON
ejpam-6492	232	1	= √ a2 +	PERSON
ejpam-6492	232	2	29–31	CARDINAL
ejpam-6492	234	1	j. pure	PERSON
ejpam-6492	234	2	18	CARDINAL
ejpam-6492	234	3	3	CARDINAL
ejpam-6492	234	4	2025	CARDINAL
ejpam-6492	234	5	6492 11	DATE
ejpam-6492	234	6	22	CARDINAL
ejpam-6492	234	7	horadam	DATE
ejpam-6492	234	8	32	CARDINAL
ejpam-6492	234	9	lucas quaternions	PERSON
ejpam-6492	234	10	kn =	PERSON
ejpam-6492	236	1	lucas quaternions	PERSON
ejpam-6492	237	1	7	CARDINAL
ejpam-6492	238	1	un	ORG
ejpam-6492	241	1	generalized lucas quaternions	FAC
ejpam-6492	241	2	28	CARDINAL
ejpam-6492	241	3	29	DATE
ejpam-6492	241	4	31	DATE
ejpam-6492	241	5	33	CARDINAL
ejpam-6492	242	1	lucas quaternions	PERSON
ejpam-6492	242	2	7	CARDINAL
ejpam-6492	242	3	7	CARDINAL
ejpam-6492	243	1	33	CARDINAL
ejpam-6492	243	2	1 +	DATE
ejpam-6492	244	1	1 + βi +	CARDINAL
ejpam-6492	244	2	lucas quaternions	PERSON
ejpam-6492	244	3	− βnβ̂	PERSON
ejpam-6492	247	1	6	CARDINAL
ejpam-6492	259	1	− βnβ̂	PERSON
ejpam-6492	262	1	6	CARDINAL
ejpam-6492	263	1	kn	PERSON
ejpam-6492	264	1	αn+3 +	CARDINAL
ejpam-6492	266	1	j. pure	PERSON
ejpam-6492	266	2	18	CARDINAL
ejpam-6492	266	3	3	CARDINAL
ejpam-6492	266	4	2025	CARDINAL
ejpam-6492	266	5	6492 12	DATE
ejpam-6492	266	6	22	CARDINAL
ejpam-6492	266	7	lucas quaternions	PERSON
ejpam-6492	266	8	31	CARDINAL
ejpam-6492	266	9	k−n	GPE
ejpam-6492	266	10	q−1 = u−1+u0i+u1j+u2k = 1 q +0i+j+pk	PERSON
ejpam-6492	266	11	k−1	GPE
ejpam-6492	267	1	+2i+pj+(p2	PRODUCT
ejpam-6492	268	1	34	CARDINAL
ejpam-6492	268	2	lucas quaternions	PERSON
ejpam-6492	269	1	kn	PERSON
ejpam-6492	269	2	lucas quaternions	PERSON
ejpam-6492	270	1	qn −	PERSON
ejpam-6492	270	2	ln+3	GPE
ejpam-6492	271	1	2q2n−1	CARDINAL
ejpam-6492	272	1	3l2n+2	CARDINAL
ejpam-6492	272	2	qnkn	PERSON
ejpam-6492	272	3	2q2n − 3l2n+3	DATE
ejpam-6492	273	1	3k	CARDINAL
ejpam-6492	274	1	6fnqn−1	CARDINAL
ejpam-6492	275	1	3k	CARDINAL
ejpam-6492	278	1	2k	CARDINAL
ejpam-6492	278	2	4q2n−2	CARDINAL
ejpam-6492	279	1	6l2n+1	CARDINAL
ejpam-6492	279	2	6fn+1qn−1	CARDINAL
ejpam-6492	279	3	9f2n+3 + 2(−1)nq−2	CARDINAL
ejpam-6492	279	4	qn+r	PERSON
ejpam-6492	281	1	2	CARDINAL
ejpam-6492	281	2	3r	CARDINAL
ejpam-6492	281	3	qn−rln−r	GPE
ejpam-6492	281	4	q2n−2r +	DATE
ejpam-6492	281	5	qn+rln+r	ORG
ejpam-6492	281	6	− qn−rln−r	PERSON
ejpam-6492	282	1	lucas quaternions	PERSON
ejpam-6492	282	2	first	ORDINAL
ejpam-6492	283	1	1	CARDINAL
ejpam-6492	284	1	1 +	DATE
ejpam-6492	285	1	1 + βi +	CARDINAL
ejpam-6492	285	2	1	CARDINAL
ejpam-6492	286	1	α̂β̂	DATE
ejpam-6492	286	2	10	CARDINAL
ejpam-6492	287	1	− qb √	PERSON
ejpam-6492	287	2	11	CARDINAL
ejpam-6492	288	1	j. pure	PERSON
ejpam-6492	288	2	18	CARDINAL
ejpam-6492	288	3	3	CARDINAL
ejpam-6492	288	4	2025	CARDINAL
ejpam-6492	288	5	6492 13	DATE
ejpam-6492	288	6	22	CARDINAL
ejpam-6492	289	1	α̂β̂	DATE
ejpam-6492	289	2	1 +	DATE
ejpam-6492	292	1	1	CARDINAL
ejpam-6492	294	1	− qb √	PERSON
ejpam-6492	294	2	2	CARDINAL
ejpam-6492	295	1	1 +	DATE
ejpam-6492	296	1	1 + βi +	CARDINAL
ejpam-6492	296	2	− aur	PERSON
ejpam-6492	296	3	12	CARDINAL
ejpam-6492	296	4	− q∆bur	PERSON
ejpam-6492	296	5	13	CARDINAL
ejpam-6492	296	6	1	CARDINAL
ejpam-6492	296	7	k. proof	PERSON
ejpam-6492	297	1	10	CARDINAL
ejpam-6492	297	2	11	CARDINAL
ejpam-6492	298	1	− qb √ ∆)αr	ORG
ejpam-6492	298	2	− aur	PERSON
ejpam-6492	298	3	12	CARDINAL
ejpam-6492	299	1	10	CARDINAL
ejpam-6492	299	2	11	CARDINAL
ejpam-6492	301	1	− q∆bur	PERSON
ejpam-6492	301	2	13	CARDINAL
ejpam-6492	302	1	3	CARDINAL
ejpam-6492	303	1	1 +	DATE
ejpam-6492	304	1	1 + βi +	CARDINAL
ejpam-6492	306	1	14	CARDINAL
ejpam-6492	306	2	15	CARDINAL
ejpam-6492	306	3	∈	ORG
ejpam-6492	309	1	α̂βr − β̂αr	ORG
ejpam-6492	309	2	αβ)r	CARDINAL
ejpam-6492	312	1	lucas quaternions	PERSON
ejpam-6492	312	2	8	CARDINAL
ejpam-6492	312	3	9	CARDINAL
ejpam-6492	313	1	j. pure	PERSON
ejpam-6492	313	2	18	CARDINAL
ejpam-6492	313	3	3	CARDINAL
ejpam-6492	313	4	2025	CARDINAL
ejpam-6492	313	5	6492 14	DATE
ejpam-6492	313	6	22	CARDINAL
ejpam-6492	313	7	8	DATE
ejpam-6492	314	1	∈	ORG
ejpam-6492	314	2	qn−rqn+r − q2 n	PERSON
ejpam-6492	314	3	1	CARDINAL
ejpam-6492	314	4	k. proof	PERSON
ejpam-6492	315	1	12	CARDINAL
ejpam-6492	315	2	qn−rqn+r − q2 n	PERSON
ejpam-6492	316	1	α̂αn+r	CARDINAL
ejpam-6492	319	1	2	CARDINAL
ejpam-6492	319	2	− β̂α̂αn+rβn−r	PERSON
ejpam-6492	321	1	+ 2α̂β̂αnβn	PERSON
ejpam-6492	321	2	αβ)n	ORG
ejpam-6492	325	1	α̂β̂βr − β̂α̂βr	ORG
ejpam-6492	328	1	αβ)n−rur	ORG
ejpam-6492	328	2	− aur	PERSON
ejpam-6492	331	1	9	CARDINAL
ejpam-6492	332	1	∈	ORG
ejpam-6492	332	2	kn−rkn+r − k2 n	FAC
ejpam-6492	332	3	1	CARDINAL
ejpam-6492	332	4	k. proof	PERSON
ejpam-6492	333	1	14	CARDINAL
ejpam-6492	335	1	− β̂α̂αn+rβn−r	PERSON
ejpam-6492	337	1	8	CARDINAL
ejpam-6492	337	2	9	CARDINAL
ejpam-6492	337	3	3	CARDINAL
ejpam-6492	338	1	j. pure	PERSON
ejpam-6492	338	2	18	CARDINAL
ejpam-6492	338	3	3	CARDINAL
ejpam-6492	338	4	2025	CARDINAL
ejpam-6492	338	5	6492 15	DATE
ejpam-6492	338	6	22	CARDINAL
ejpam-6492	338	7	3	CARDINAL
ejpam-6492	339	1	∈	ORG
ejpam-6492	339	2	kn−rkn+r − k2 n	FAC
ejpam-6492	339	3	− q2 n	PERSON
ejpam-6492	340	1	10	CARDINAL
ejpam-6492	341	1	∈	ORG
ejpam-6492	345	1	α̂αn+r	CARDINAL
ejpam-6492	347	1	2	CARDINAL
ejpam-6492	347	2	2	CARDINAL
ejpam-6492	347	3	αβ)n+r	ORG
ejpam-6492	347	4	α̂β̂ +	DATE
ejpam-6492	347	5	+ β̂β̂β2n−2r	PERCENT
ejpam-6492	347	6	α̂β̂ +	DATE
ejpam-6492	348	1	αβ)n+r	ORG
ejpam-6492	348	2	α̂β̂ +	DATE
ejpam-6492	349	1	+ β̂β̂β2n−2r	PERCENT
ejpam-6492	349	2	α̂β̂ +	DATE
ejpam-6492	353	1	2α̂	CARDINAL
ejpam-6492	353	2	2β̂	CARDINAL
ejpam-6492	353	3	1	CARDINAL
ejpam-6492	355	1	2	CARDINAL
ejpam-6492	359	1	2	CARDINAL
ejpam-6492	373	1	j. pure	PERSON
ejpam-6492	373	2	18	CARDINAL
ejpam-6492	373	3	3	CARDINAL
ejpam-6492	373	4	2025	CARDINAL
ejpam-6492	373	5	6492 16	DATE
ejpam-6492	373	6	22	CARDINAL
ejpam-6492	373	7	11	DATE
ejpam-6492	374	1	∈	ORG
ejpam-6492	377	1	α̂αn+r	ORG
ejpam-6492	377	2	2	CARDINAL
ejpam-6492	377	3	2	CARDINAL
ejpam-6492	377	4	αβ)n+r	ORG
ejpam-6492	377	5	α̂β̂ +	DATE
ejpam-6492	378	1	+ β̂β̂β2n−2r	PERCENT
ejpam-6492	378	2	α̂β̂ +	DATE
ejpam-6492	379	1	α̂α̂α2n+2r+β̂β̂β2n+2r−α̂α̂α2nβ2r−β̂β̂α2rβ2n	CARDINAL
ejpam-6492	380	1	− α2r	PERSON
ejpam-6492	383	1	2α̂	CARDINAL
ejpam-6492	384	1	2β̂	CARDINAL
ejpam-6492	384	2	1	CARDINAL
ejpam-6492	385	1	2	CARDINAL
ejpam-6492	392	1	2	CARDINAL
ejpam-6492	401	1	10	CARDINAL
ejpam-6492	401	2	11	CARDINAL
ejpam-6492	401	3	4	CARDINAL
ejpam-6492	401	4	4	CARDINAL
ejpam-6492	402	1	∈	ORG
ejpam-6492	403	1	12	CARDINAL
ejpam-6492	404	1	∈	ORG
ejpam-6492	404	2	4	CARDINAL
ejpam-6492	404	3	1	CARDINAL
ejpam-6492	404	4	k. b. demirtürk	PERSON
ejpam-6492	405	1	j. pure	PERSON
ejpam-6492	405	2	18	CARDINAL
ejpam-6492	405	3	3	CARDINAL
ejpam-6492	405	4	2025	CARDINAL
ejpam-6492	405	5	6492 17	DATE
ejpam-6492	405	6	22	CARDINAL
ejpam-6492	406	1	2	CARDINAL
ejpam-6492	408	1	2	CARDINAL
ejpam-6492	408	2	α̂α̂α2n + β̂β̂β2n +	DATE
ejpam-6492	408	3	αβ)n	ORG
ejpam-6492	408	4	α̂β̂ +	DATE
ejpam-6492	409	1	αβ)n	ORG
ejpam-6492	409	2	α̂β̂ +	DATE
ejpam-6492	409	3	α̂α̂α2n + β̂β̂β2n +	DATE
ejpam-6492	409	4	αβ)n	ORG
ejpam-6492	409	5	α̂β̂ +	DATE
ejpam-6492	410	1	αβ)n	ORG
ejpam-6492	410	2	α̂β̂ +	DATE
ejpam-6492	411	1	2	CARDINAL
ejpam-6492	411	2	αβ)n	ORG
ejpam-6492	411	3	2a	CARDINAL
ejpam-6492	411	4	4	CARDINAL
ejpam-6492	411	5	a. theorem 13	PERSON
ejpam-6492	414	1	1	CARDINAL
ejpam-6492	414	2	k. proof	PERSON
ejpam-6492	414	3	k2mk2n−∆q2 m+n	PERSON
ejpam-6492	415	1	+ β̂β2	PERCENT
ejpam-6492	415	2	α̂αm+n	DATE
ejpam-6492	416	1	2	CARDINAL
ejpam-6492	418	1	αβ)m+n ( α̂β̂ + β̂α̂	ORG
ejpam-6492	419	1	α̂β̂	DATE
ejpam-6492	419	2	α2mβ2n	CARDINAL
ejpam-6492	420	1	αm+nβ2nα̂β̂	CARDINAL
ejpam-6492	420	2	βm−n	ORG
ejpam-6492	421	1	βm−n	ORG
ejpam-6492	421	2	αm−n +	CARDINAL
ejpam-6492	421	3	βm−n	ORG
ejpam-6492	421	4	αm+nβ2nα̂β̂	CARDINAL
ejpam-6492	422	1	αβ)2n	PERSON
ejpam-6492	422	2	αm−n +	CARDINAL
ejpam-6492	422	3	βm−n	ORG
ejpam-6492	422	4	αβ)2n	PERSON
ejpam-6492	422	5	αm−n +	CARDINAL
ejpam-6492	422	6	βm−n	ORG
ejpam-6492	423	1	αm−n	CARDINAL
ejpam-6492	424	1	− bq √	PERSON
ejpam-6492	425	1	αβ)2n	PERSON
ejpam-6492	425	2	αm−n +	CARDINAL
ejpam-6492	425	3	βm−n	ORG
ejpam-6492	426	1	αm−n	CARDINAL
ejpam-6492	426	2	βm−n	ORG
ejpam-6492	428	1	14	DATE
ejpam-6492	430	1	1	CARDINAL
ejpam-6492	430	2	k. proof	PERSON
ejpam-6492	432	1	+ β̂β2	PERCENT
ejpam-6492	432	2	2	CARDINAL
ejpam-6492	433	1	αβ)m+n ( α̂β̂ + β̂α̂	ORG
ejpam-6492	434	1	α2mβ2n	CARDINAL
ejpam-6492	436	1	j. pure	PERSON
ejpam-6492	436	2	18	CARDINAL
ejpam-6492	436	3	3	CARDINAL
ejpam-6492	436	4	2025	CARDINAL
ejpam-6492	436	5	6492 18	DATE
ejpam-6492	436	6	22	CARDINAL
ejpam-6492	436	7	αm+nβ2nα̂β̂	CARDINAL
ejpam-6492	436	8	αm−n	CARDINAL
ejpam-6492	436	9	βm−n	ORG
ejpam-6492	437	1	βm−n	ORG
ejpam-6492	437	2	αm−n	CARDINAL
ejpam-6492	437	3	βm−n	ORG
ejpam-6492	437	4	αm+nβ2nα̂β̂	CARDINAL
ejpam-6492	438	1	αβ)2n	PERSON
ejpam-6492	438	2	αm−n	CARDINAL
ejpam-6492	438	3	βm−n	ORG
ejpam-6492	438	4	αβ)2n	PERSON
ejpam-6492	438	5	αm−n	CARDINAL
ejpam-6492	438	6	βm−n	ORG
ejpam-6492	439	1	αm−n	CARDINAL
ejpam-6492	440	1	βm−n	ORG
ejpam-6492	440	2	− bq √	PERSON
ejpam-6492	441	1	αβ)2n	PERSON
ejpam-6492	441	2	αm−n	CARDINAL
ejpam-6492	441	3	βm−n	ORG
ejpam-6492	441	4	αm−n	CARDINAL
ejpam-6492	441	5	βm−n	ORG
ejpam-6492	442	1	αm−n +	CARDINAL
ejpam-6492	442	2	βm−n	ORG
ejpam-6492	445	1	15	CARDINAL
ejpam-6492	445	2	15	CARDINAL
ejpam-6492	448	1	1	CARDINAL
ejpam-6492	448	2	k. proof	PERSON
ejpam-6492	450	1	− βn+hβ̂	PERSON
ejpam-6492	458	1	α2n+h+k	CARDINAL
ejpam-6492	460	1	α2n+h+k	ORDINAL
ejpam-6492	460	2	−αnβn+h+kα̂β̂	CARDINAL
ejpam-6492	461	1	βh+k	ORG
ejpam-6492	463	1	−βkα̂β̂	ORG
ejpam-6492	466	1	αkβ̂α̂	CARDINAL
ejpam-6492	468	1	j. pure	PERSON
ejpam-6492	468	2	18	CARDINAL
ejpam-6492	468	3	3	CARDINAL
ejpam-6492	468	4	2025	CARDINAL
ejpam-6492	468	5	6492 19	DATE
ejpam-6492	468	6	22	CARDINAL
ejpam-6492	468	7	αβ)n	ORG
ejpam-6492	469	1	a	PERSON
ejpam-6492	470	1	generalized lucas quaternions	ORG
ejpam-6492	470	2	16	CARDINAL
ejpam-6492	471	1	16	CARDINAL
ejpam-6492	472	1	kn+hkn+k	ORG
ejpam-6492	472	2	− knkn+k+h	PERSON
ejpam-6492	472	3	1	CARDINAL
ejpam-6492	477	1	α2n+h+kα̂α̂ + αn+hβn+kα̂β̂ + αn+kβn+hβ̂α̂	QUANTITY
ejpam-6492	480	1	αn+hβn+kα̂β̂ + αn+kβn+hβ̂α̂	QUANTITY
ejpam-6492	481	1	αnβn+h+kα̂β̂	CARDINAL
ejpam-6492	481	2	α̂β̂	DATE
ejpam-6492	481	3	βh+k	ORG
ejpam-6492	485	1	αβ)n	ORG
ejpam-6492	485	2	− β̂α̂αk	PERSON
ejpam-6492	485	3	αβ)n	ORG
ejpam-6492	488	1	αβ)n	ORG
ejpam-6492	490	1	αβ)n	ORG
ejpam-6492	490	2	√	PERSON
ejpam-6492	492	1	15	CARDINAL
ejpam-6492	492	2	16	CARDINAL
ejpam-6492	492	3	5	CARDINAL
ejpam-6492	492	4	5	CARDINAL
ejpam-6492	493	1	kn+hkn+k	ORG
ejpam-6492	496	1	j. pure	PERSON
ejpam-6492	496	2	18	CARDINAL
ejpam-6492	496	3	3	CARDINAL
ejpam-6492	496	4	2025	CARDINAL
ejpam-6492	496	5	6492 20	DATE
ejpam-6492	497	1	catalan	GPE
ejpam-6492	497	2	d’ocagne	GPE
ejpam-6492	500	1	generalized quaternions	PERSON
ejpam-6492	501	1	three	CARDINAL
ejpam-6492	503	1	1	CARDINAL
ejpam-6492	503	2	s. sharma	PERSON
ejpam-6492	503	3	a. tomar	PERSON
ejpam-6492	503	4	s. k. padaliya	PERSON
ejpam-6492	505	1	191	CARDINAL
ejpam-6492	505	2	2025	DATE
ejpam-6492	506	1	2	CARDINAL
ejpam-6492	506	2	s. h. larsen	PERSON
ejpam-6492	508	1	13(10):1949	CARDINAL
ejpam-6492	508	2	2021	CARDINAL
ejpam-6492	509	1	3	CARDINAL
ejpam-6492	511	1	arxiv preprint arxiv:1801.01369	ORG
ejpam-6492	511	2	2017	DATE
ejpam-6492	512	1	4	CARDINAL
ejpam-6492	512	2	s. sinha	PERSON
ejpam-6492	514	1	international journal of engineering science invention	ORG
ejpam-6492	514	2	6:7–14	CARDINAL
ejpam-6492	514	3	2017	DATE
ejpam-6492	515	1	5	CARDINAL
ejpam-6492	515	2	h. tran-ngoc	PERSON
ejpam-6492	515	3	t. le-xuan	ORG
ejpam-6492	515	4	s. khatir	PERSON
ejpam-6492	515	5	g. de roeck	PERSON
ejpam-6492	515	6	t. bui-tien	PERSON
ejpam-6492	515	7	m. abdel wahab	PERSON
ejpam-6492	517	1	2023	CARDINAL
ejpam-6492	518	1	6	CARDINAL
ejpam-6492	520	1	the journal of academic science	ORG
ejpam-6492	520	2	1(1):51–66	CARDINAL
ejpam-6492	520	3	2024	DATE
ejpam-6492	521	1	7	CARDINAL
ejpam-6492	521	2	w. n. goetzmann	PERSON
ejpam-6492	523	1	10352	DATE
ejpam-6492	523	2	national bureau of economic research	ORG
ejpam-6492	523	3	2004	DATE
ejpam-6492	524	1	8	CARDINAL
ejpam-6492	524	2	s. halici	PERSON
ejpam-6492	525	1	fibonacci quaternions	FAC
ejpam-6492	526	1	clifford algebras	PERSON
ejpam-6492	526	2	22:321	CARDINAL
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ejpam-6492	607	1	quarterly	DATE
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