id	sid	eid	entity	type
ejpam-2366	1	1	european journal	ORG
ejpam-2366	2	1	14	DATE
ejpam-2366	2	2	2	CARDINAL
ejpam-2366	2	3	2021	DATE
ejpam-2366	2	4	551	CARDINAL
ejpam-2366	2	5	1307-5543	CARDINAL
ejpam-2366	2	6	new york	GPE
ejpam-2366	2	7	φ	ORG
ejpam-2366	2	8	c. s. manjarekar2	PERSON
ejpam-2366	3	1	1	CARDINAL
ejpam-2366	3	2	st	GPE
ejpam-2366	3	3	xavier	PERSON
ejpam-2366	3	4	mumbai–400001	ORG
ejpam-2366	3	5	maharashtra	GPE
ejpam-2366	3	6	india	GPE
ejpam-2366	3	7	2	CARDINAL
ejpam-2366	3	8	maharashtra	NORP
ejpam-2366	3	9	india	GPE
ejpam-2366	4	1	φ	ORG
ejpam-2366	6	1	φ	ORG
ejpam-2366	8	1	2	CARDINAL
ejpam-2366	8	2	2020	DATE
ejpam-2366	8	3	06d10, 06e10	CARDINAL
ejpam-2366	8	4	06f99	CARDINAL
ejpam-2366	8	5	φ	ORG
ejpam-2366	8	6	1	CARDINAL
ejpam-2366	8	7	φ	ORG
ejpam-2366	8	8	φ	ORG
ejpam-2366	8	9	c. s. manjarekar	PERSON
ejpam-2366	8	10	a. v. bingi	PERSON
ejpam-2366	8	11	16	CARDINAL
ejpam-2366	9	1	φ	ORG
ejpam-2366	9	2	φ	ORG
ejpam-2366	9	3	multiplicative	NORP
ejpam-2366	9	4	φ	ORG
ejpam-2366	9	5	φ	ORG
ejpam-2366	10	1	1	CARDINAL
ejpam-2366	10	2	∈	ORG
ejpam-2366	10	3	6	CARDINAL
ejpam-2366	10	4	6 n or a	QUANTITY
ejpam-2366	11	1	10	CARDINAL
ejpam-2366	11	2	6	CARDINAL
ejpam-2366	11	3	6 n or a	QUANTITY
ejpam-2366	11	4	6 √ n	QUANTITY
ejpam-2366	12	1	c. s. manjarekar et	PERSON
ejpam-2366	13	1	al	PERSON
ejpam-2366	14	1	19	CARDINAL
ejpam-2366	14	2	20	CARDINAL
ejpam-2366	15	1	∈	ORG
ejpam-2366	15	2	6=	CARDINAL
ejpam-2366	15	3	6 n or a	QUANTITY
ejpam-2366	16	1	∈	ORG
ejpam-2366	16	2	6=	CARDINAL
ejpam-2366	16	3	6	CARDINAL
ejpam-2366	17	1	https://doi.org/10.29020/nybg.ejpam.v14i2.2366	ORG
ejpam-2366	17	2	ashok v. bingi	PERSON
ejpam-2366	17	3	csmanjrekar@yahoo.co.in	PERSON
ejpam-2366	17	4	c. s. manjarekar	PERSON
ejpam-2366	18	1	551	CARDINAL
ejpam-2366	18	2	2021	CARDINAL
ejpam-2366	19	1	a. v. bingi	PERSON
ejpam-2366	19	2	c. s. manjarekar	PERSON
ejpam-2366	20	1	j. pure	PERSON
ejpam-2366	20	2	14	CARDINAL
ejpam-2366	20	3	2	CARDINAL
ejpam-2366	20	4	2021	CARDINAL
ejpam-2366	20	5	551	CARDINAL
ejpam-2366	20	6	6 √ n	QUANTITY
ejpam-2366	21	1	φ	ORG
ejpam-2366	21	2	φ	ORG
ejpam-2366	22	1	multiplicative lattice l	ORG
ejpam-2366	22	2	1	CARDINAL
ejpam-2366	22	3	multiplicative	NORP
ejpam-2366	23	1	ae ∨	ORG
ejpam-2366	25	1	⊆	CARDINAL
ejpam-2366	25	2	6	CARDINAL
ejpam-2366	26	1	6 a1∨a2∨	QUANTITY
ejpam-2366	28	1	1	CARDINAL
ejpam-2366	30	1	∈ l	ORG
ejpam-2366	30	2	6 1	CARDINAL
ejpam-2366	30	3	1	CARDINAL
ejpam-2366	30	4	6	CARDINAL
ejpam-2366	30	5	6	CARDINAL
ejpam-2366	30	6	6	CARDINAL
ejpam-2366	30	7	6	CARDINAL
ejpam-2366	30	8	6	CARDINAL
ejpam-2366	34	1	6	CARDINAL
ejpam-2366	35	1	multiplicative	NORP
ejpam-2366	37	1	9	CARDINAL
ejpam-2366	37	2	6	CARDINAL
ejpam-2366	37	3	ab p2	ORG
ejpam-2366	37	4	6	CARDINAL
ejpam-2366	37	5	6	CARDINAL
ejpam-2366	37	6	15	CARDINAL
ejpam-2366	37	7	6	CARDINAL
ejpam-2366	37	8	ab p2	ORG
ejpam-2366	37	9	6	CARDINAL
ejpam-2366	37	10	6 √	CARDINAL
ejpam-2366	37	11	multiplicative	NORP
ejpam-2366	37	12	16	CARDINAL
ejpam-2366	38	1	5	CARDINAL
ejpam-2366	38	2	4	CARDINAL
ejpam-2366	39	1	12	CARDINAL
ejpam-2366	39	2	2	CARDINAL
ejpam-2366	39	3	6	CARDINAL
ejpam-2366	39	4	6	CARDINAL
ejpam-2366	39	5	18	CARDINAL
ejpam-2366	39	6	2	CARDINAL
ejpam-2366	39	7	6	CARDINAL
ejpam-2366	39	8	6	CARDINAL
ejpam-2366	39	9	bc	ORG
ejpam-2366	39	10	2	CARDINAL
ejpam-2366	39	11	3	CARDINAL
ejpam-2366	39	12	9	CARDINAL
ejpam-2366	40	1	multiplicative	NORP
ejpam-2366	41	1	∈	ORG
ejpam-2366	41	2	1	CARDINAL
ejpam-2366	41	3	2	CARDINAL
ejpam-2366	42	1	3	CARDINAL
ejpam-2366	42	2	4	CARDINAL
ejpam-2366	42	3	1a	CARDINAL
ejpam-2366	42	4	5	CARDINAL
ejpam-2366	42	5	0a	CARDINAL
ejpam-2366	42	6	∈	ORG
ejpam-2366	42	7	1	CARDINAL
ejpam-2366	45	1	n ∈m	ORG
ejpam-2366	45	2	6 n	QUANTITY
ejpam-2366	49	1	0	CARDINAL
ejpam-2366	50	1	a. v. bingi	PERSON
ejpam-2366	50	2	c. s. manjarekar	PERSON
ejpam-2366	51	1	j. pure	PERSON
ejpam-2366	51	2	14	CARDINAL
ejpam-2366	51	3	2	CARDINAL
ejpam-2366	51	4	2021	CARDINAL
ejpam-2366	51	5	551	CARDINAL
ejpam-2366	51	6	∈	ORG
ejpam-2366	52	1	3	CARDINAL
ejpam-2366	52	2	10	CARDINAL
ejpam-2366	53	1	∀n ∈m	PERSON
ejpam-2366	54	1	n ∈m	ORG
ejpam-2366	55	1	n ∈m	ORG
ejpam-2366	58	1	n ∈m	ORG
ejpam-2366	62	1	m∗.	DATE
ejpam-2366	64	1	∈	ORG
ejpam-2366	64	2	6	CARDINAL
ejpam-2366	74	1	17	CARDINAL
ejpam-2366	74	2	2	CARDINAL
ejpam-2366	74	3	∈	ORG
ejpam-2366	74	4	6	CARDINAL
ejpam-2366	74	5	6	CARDINAL
ejpam-2366	74	6	6	CARDINAL
ejpam-2366	74	7	6	CARDINAL
ejpam-2366	74	8	2	CARDINAL
ejpam-2366	74	9	n ∈m	ORG
ejpam-2366	74	10	6	CARDINAL
ejpam-2366	74	11	6	CARDINAL
ejpam-2366	75	1	1	CARDINAL
ejpam-2366	75	2	10	CARDINAL
ejpam-2366	75	3	14	CARDINAL
ejpam-2366	76	1	24	CARDINAL
ejpam-2366	77	1	16	CARDINAL
ejpam-2366	78	1	first	ORDINAL
ejpam-2366	78	2	φ	ORG
ejpam-2366	79	1	second	ORDINAL
ejpam-2366	80	1	φ	ORG
ejpam-2366	80	2	1	CARDINAL
ejpam-2366	80	3	φ	ORG
ejpam-2366	80	4	2	CARDINAL
ejpam-2366	80	5	φ	ORG
ejpam-2366	80	6	3	CARDINAL
ejpam-2366	80	7	4	CARDINAL
ejpam-2366	81	1	2	CARDINAL
ejpam-2366	81	2	2	CARDINAL
ejpam-2366	82	1	2	CARDINAL
ejpam-2366	82	2	5	CARDINAL
ejpam-2366	82	3	2	CARDINAL
ejpam-2366	82	4	6	CARDINAL
ejpam-2366	83	1	2	CARDINAL
ejpam-2366	84	1	φ	ORG
ejpam-2366	84	2	5	CARDINAL
ejpam-2366	85	1	φ	ORG
ejpam-2366	85	2	15-23	CARDINAL
ejpam-2366	86	1	φ	ORG
ejpam-2366	88	1	7	CARDINAL
ejpam-2366	89	1	8)	CARDINAL
ejpam-2366	90	1	a. v. bingi	PERSON
ejpam-2366	90	2	c. s. manjarekar	PERSON
ejpam-2366	91	1	j. pure	PERSON
ejpam-2366	91	2	14	CARDINAL
ejpam-2366	91	3	2	CARDINAL
ejpam-2366	91	4	2021	CARDINAL
ejpam-2366	91	5	551	CARDINAL
ejpam-2366	92	1	2.	CARDINAL
ejpam-2366	92	2	φ	ORG
ejpam-2366	92	3	a. v. bingi	PERSON
ejpam-2366	92	4	c. s. manjarekar	PERSON
ejpam-2366	92	5	8	CARDINAL
ejpam-2366	93	1	22	CARDINAL
ejpam-2366	94	1	φ	ORG
ejpam-2366	95	1	1	CARDINAL
ejpam-2366	97	1	∈	ORG
ejpam-2366	97	2	6 n or a	QUANTITY
ejpam-2366	98	1	1	CARDINAL
ejpam-2366	101	1	n ∈m	ORG
ejpam-2366	102	1	•	CARDINAL
ejpam-2366	104	1	n ∈m	ORG
ejpam-2366	104	2	2	CARDINAL
ejpam-2366	105	1	•	CARDINAL
ejpam-2366	106	1	2	CARDINAL
ejpam-2366	107	1	n ∈m	ORG
ejpam-2366	107	2	2	CARDINAL
ejpam-2366	110	1	ω	CARDINAL
ejpam-2366	111	1	6 n	QUANTITY
ejpam-2366	112	1	2	CARDINAL
ejpam-2366	113	1	two	CARDINAL
ejpam-2366	113	2	6	CARDINAL
ejpam-2366	114	1	6	CARDINAL
ejpam-2366	114	2	6	CARDINAL
ejpam-2366	114	3	6 φn+1 6	QUANTITY
ejpam-2366	114	4	6	CARDINAL
ejpam-2366	114	5	6	CARDINAL
ejpam-2366	114	6	φ	ORG
ejpam-2366	114	7	11	CARDINAL
ejpam-2366	115	1	1	CARDINAL
ejpam-2366	117	1	6	CARDINAL
ejpam-2366	117	2	6 a1	QUANTITY
ejpam-2366	118	1	6 a1	QUANTITY
ejpam-2366	118	2	6	CARDINAL
ejpam-2366	119	1	1	CARDINAL
ejpam-2366	120	1	n ∈m	ORG
ejpam-2366	122	1	1	CARDINAL
ejpam-2366	123	1	a. v. bingi	PERSON
ejpam-2366	123	2	c. s. manjarekar	PERSON
ejpam-2366	124	1	j. pure	PERSON
ejpam-2366	124	2	14	CARDINAL
ejpam-2366	124	3	2	CARDINAL
ejpam-2366	124	4	2021	CARDINAL
ejpam-2366	124	5	551	CARDINAL
ejpam-2366	125	1	3	CARDINAL
ejpam-2366	126	1	4	CARDINAL
ejpam-2366	126	2	6 n	QUANTITY
ejpam-2366	126	3	6	CARDINAL
ejpam-2366	126	4	6 n	QUANTITY
ejpam-2366	128	1	1	CARDINAL
ejpam-2366	128	2	2	CARDINAL
ejpam-2366	128	3	1	CARDINAL
ejpam-2366	129	1	∈	ORG
ejpam-2366	130	1	6	CARDINAL
ejpam-2366	130	2	6	CARDINAL
ejpam-2366	131	1	∈ l∗	GPE
ejpam-2366	131	2	6	CARDINAL
ejpam-2366	132	1	6 n	QUANTITY
ejpam-2366	133	1	6 φ(n	PERCENT
ejpam-2366	133	2	6 (φ(n	PERCENT
ejpam-2366	134	1	6	CARDINAL
ejpam-2366	135	1	1	CARDINAL
ejpam-2366	135	2	6 (φ(n	PERCENT
ejpam-2366	135	3	6	CARDINAL
ejpam-2366	137	1	2	CARDINAL
ejpam-2366	137	2	3	CARDINAL
ejpam-2366	137	3	2	CARDINAL
ejpam-2366	139	1	2	CARDINAL
ejpam-2366	141	1	k 6	ORG
ejpam-2366	141	2	k ∈ m∗.	ORG
ejpam-2366	141	3	6 k	PERSON
ejpam-2366	143	1	6	DATE
ejpam-2366	144	1	∈ m∗.	ORG
ejpam-2366	144	2	6	CARDINAL
ejpam-2366	146	1	6	CARDINAL
ejpam-2366	146	2	6 (φ(n	PERCENT
ejpam-2366	149	1	6 n	QUANTITY
ejpam-2366	149	2	6 (φ(n	PERCENT
ejpam-2366	151	1	6 n	QUANTITY
ejpam-2366	151	2	6 (φ(n	PERCENT
ejpam-2366	151	3	3.1	CARDINAL
ejpam-2366	151	4	22	CARDINAL
ejpam-2366	152	1	rn 6 n	FAC
ejpam-2366	152	2	6 n	QUANTITY
ejpam-2366	152	3	6	CARDINAL
ejpam-2366	154	1	3	CARDINAL
ejpam-2366	154	2	4	CARDINAL
ejpam-2366	154	3	3	CARDINAL
ejpam-2366	155	1	6 n	QUANTITY
ejpam-2366	155	2	3	CARDINAL
ejpam-2366	158	1	6 (φ(n	PERCENT
ejpam-2366	160	1	6 n	QUANTITY
ejpam-2366	160	2	6 n	QUANTITY
ejpam-2366	161	1	4	CARDINAL
ejpam-2366	161	2	1	CARDINAL
ejpam-2366	161	3	4	CARDINAL
ejpam-2366	163	1	x′ ∈ l∗	GPE
ejpam-2366	163	2	x′ 6	DATE
ejpam-2366	163	3	6	CARDINAL
ejpam-2366	164	1	x∨x′)(y	PERSON
ejpam-2366	164	2	6	CARDINAL
ejpam-2366	164	3	x∨x′)(y	PERSON
ejpam-2366	165	1	4	CARDINAL
ejpam-2366	165	2	6	DATE
ejpam-2366	165	3	6	CARDINAL
ejpam-2366	167	1	2	CARDINAL
ejpam-2366	167	2	1	CARDINAL
ejpam-2366	167	3	1	CARDINAL
ejpam-2366	169	1	1	CARDINAL
ejpam-2366	170	1	2	CARDINAL
ejpam-2366	170	2	∈	ORG
ejpam-2366	171	1	3	CARDINAL
ejpam-2366	172	1	4	CARDINAL
ejpam-2366	172	2	6=	CARDINAL
ejpam-2366	172	3	6 n	QUANTITY
ejpam-2366	172	4	6	CARDINAL
ejpam-2366	173	1	a. v. bingi	PERSON
ejpam-2366	173	2	c. s. manjarekar	PERSON
ejpam-2366	174	1	j. pure	PERSON
ejpam-2366	174	2	14	CARDINAL
ejpam-2366	174	3	2	CARDINAL
ejpam-2366	174	4	2021	CARDINAL
ejpam-2366	174	5	551	CARDINAL
ejpam-2366	174	6	2	CARDINAL
ejpam-2366	176	1	1	CARDINAL
ejpam-2366	177	1	2	CARDINAL
ejpam-2366	179	1	3	CARDINAL
ejpam-2366	180	1	4	CARDINAL
ejpam-2366	180	2	6 n	QUANTITY
ejpam-2366	180	3	6 n	QUANTITY
ejpam-2366	181	1	ω	CARDINAL
ejpam-2366	181	2	2	CARDINAL
ejpam-2366	182	1	2	CARDINAL
ejpam-2366	183	1	6	CARDINAL
ejpam-2366	188	1	6	CARDINAL
ejpam-2366	189	1	6 n or a	QUANTITY
ejpam-2366	190	1	3	CARDINAL
ejpam-2366	192	1	ω	CARDINAL
ejpam-2366	192	2	ω	CARDINAL
ejpam-2366	192	3	2	CARDINAL
ejpam-2366	195	1	2	CARDINAL
ejpam-2366	195	2	6	CARDINAL
ejpam-2366	195	3	6	CARDINAL
ejpam-2366	195	4	6 φn+1 6	QUANTITY
ejpam-2366	195	5	6	CARDINAL
ejpam-2366	195	6	6	CARDINAL
ejpam-2366	195	7	φ2.	GPE
ejpam-2366	196	1	3	CARDINAL
ejpam-2366	196	2	ω	CARDINAL
ejpam-2366	197	1	3	CARDINAL
ejpam-2366	199	1	ω	CARDINAL
ejpam-2366	200	1	2	CARDINAL
ejpam-2366	204	1	∈	ORG
ejpam-2366	205	1	6	CARDINAL
ejpam-2366	205	2	ω	CARDINAL
ejpam-2366	206	1	3	CARDINAL
ejpam-2366	206	2	2	CARDINAL
ejpam-2366	206	3	multiplicative	NORP
ejpam-2366	206	4	1	CARDINAL
ejpam-2366	206	5	jacobson	PERSON
ejpam-2366	206	6	∧{m ∈ l	ORG
ejpam-2366	208	1	a. v. bingi	PERSON
ejpam-2366	208	2	c. s. manjarekar	PERSON
ejpam-2366	209	1	j. pure	PERSON
ejpam-2366	209	2	14	CARDINAL
ejpam-2366	209	3	2	CARDINAL
ejpam-2366	209	4	2021	CARDINAL
ejpam-2366	209	5	551	CARDINAL
ejpam-2366	209	6	557	CARDINAL
ejpam-2366	209	7	4	CARDINAL
ejpam-2366	210	1	jacobson	PERSON
ejpam-2366	211	1	6	CARDINAL
ejpam-2366	211	2	2	CARDINAL
ejpam-2366	215	1	∈	ORG
ejpam-2366	216	1	2	CARDINAL
ejpam-2366	216	2	6 n or a	QUANTITY
ejpam-2366	217	1	6	CARDINAL
ejpam-2366	217	2	2	CARDINAL
ejpam-2366	217	3	6	CARDINAL
ejpam-2366	217	4	3.3	CARDINAL
ejpam-2366	217	5	13	CARDINAL
ejpam-2366	219	1	0	CARDINAL
ejpam-2366	219	2	6 n or a	QUANTITY
ejpam-2366	220	1	3	CARDINAL
ejpam-2366	221	1	φ(n	PERSON
ejpam-2366	223	1	1	CARDINAL
ejpam-2366	225	1	k ∈ z	PERSON
ejpam-2366	225	2	∈	ORG
ejpam-2366	225	3	= l(z24	PERSON
ejpam-2366	226	1	ki	PERSON
ejpam-2366	227	1	ki	ORG
ejpam-2366	227	2	∈	ORG
ejpam-2366	228	1	22	CARDINAL
ejpam-2366	228	2	2.5	CARDINAL
ejpam-2366	229	1	0	CARDINAL
ejpam-2366	230	1	2	CARDINAL
ejpam-2366	230	2	12	CARDINAL
ejpam-2366	230	3	6 n	QUANTITY
ejpam-2366	230	4	12	CARDINAL
ejpam-2366	230	5	2	CARDINAL
ejpam-2366	231	1	1	CARDINAL
ejpam-2366	232	1	six	CARDINAL
ejpam-2366	232	2	φ	ORG
ejpam-2366	234	1	2	CARDINAL
ejpam-2366	235	1	6=	CARDINAL
ejpam-2366	236	1	6	CARDINAL
ejpam-2366	236	2	6	CARDINAL
ejpam-2366	236	3	6=	CARDINAL
ejpam-2366	238	1	6 ba	QUANTITY
ejpam-2366	238	2	6=	CARDINAL
ejpam-2366	239	1	0	CARDINAL
ejpam-2366	240	1	6	CARDINAL
ejpam-2366	240	2	6	CARDINAL
ejpam-2366	240	3	3	CARDINAL
ejpam-2366	241	1	6=	CARDINAL
ejpam-2366	242	1	6=	DATE
ejpam-2366	246	1	5	CARDINAL
ejpam-2366	249	1	a. v. bingi	PERSON
ejpam-2366	249	2	c. s. manjarekar	PERSON
ejpam-2366	250	1	j. pure	PERSON
ejpam-2366	250	2	14	CARDINAL
ejpam-2366	250	3	2	CARDINAL
ejpam-2366	250	4	2021	CARDINAL
ejpam-2366	250	5	551	CARDINAL
ejpam-2366	252	1	6	CARDINAL
ejpam-2366	253	1	φ2.	GPE
ejpam-2366	254	1	2	CARDINAL
ejpam-2366	256	1	6 n or a	QUANTITY
ejpam-2366	258	1	6 n	QUANTITY
ejpam-2366	258	2	a∨n	ORG
ejpam-2366	258	3	6 n or a	QUANTITY
ejpam-2366	258	4	6 n or a	QUANTITY
ejpam-2366	259	1	a(a	DATE
ejpam-2366	259	2	6 φ2(n	DATE
ejpam-2366	259	3	6	CARDINAL
ejpam-2366	259	4	6	CARDINAL
ejpam-2366	259	5	lemma 2	ORG
ejpam-2366	260	1	5	CARDINAL
ejpam-2366	260	2	23	CARDINAL
ejpam-2366	260	3	ab = ac	ORG
ejpam-2366	260	4	0	CARDINAL
ejpam-2366	267	1	6	CARDINAL
ejpam-2366	268	1	φ2.	GPE
ejpam-2366	269	1	2	CARDINAL
ejpam-2366	271	1	6 n or a	QUANTITY
ejpam-2366	273	1	6 n	QUANTITY
ejpam-2366	273	2	a∨n	ORG
ejpam-2366	273	3	6 n or a	QUANTITY
ejpam-2366	273	4	6 n or a	QUANTITY
ejpam-2366	274	1	6 φ2(n	DATE
ejpam-2366	274	2	6	CARDINAL
ejpam-2366	275	1	6	DATE
ejpam-2366	275	2	2im	ORDINAL
ejpam-2366	276	1	6	CARDINAL
ejpam-2366	276	2	2	CARDINAL
ejpam-2366	276	3	0	CARDINAL
ejpam-2366	276	4	5	CARDINAL
ejpam-2366	276	5	10	CARDINAL
ejpam-2366	277	1	6	CARDINAL
ejpam-2366	277	2	1.11	CARDINAL
ejpam-2366	277	3	23	CARDINAL
ejpam-2366	278	1	2	CARDINAL
ejpam-2366	279	1	3	CARDINAL
ejpam-2366	280	1	n ∈m	ORG
ejpam-2366	280	2	2	CARDINAL
ejpam-2366	280	3	∈	ORG
ejpam-2366	280	4	6	CARDINAL
ejpam-2366	280	5	6	CARDINAL
ejpam-2366	282	1	2	CARDINAL
ejpam-2366	286	1	6	CARDINAL
ejpam-2366	287	1	φ2.	GPE
ejpam-2366	288	1	2	CARDINAL
ejpam-2366	288	2	∈	ORG
ejpam-2366	289	1	∈	ORG
ejpam-2366	290	1	6	CARDINAL
ejpam-2366	291	1	6	CARDINAL
ejpam-2366	291	2	2	CARDINAL
ejpam-2366	291	3	6	CARDINAL
ejpam-2366	292	1	2	CARDINAL
ejpam-2366	292	2	4	DATE
ejpam-2366	293	1	2	CARDINAL
ejpam-2366	293	2	n ∈ z+	ORG
ejpam-2366	294	1	∈	ORG
ejpam-2366	294	2	6	CARDINAL
ejpam-2366	295	1	6	CARDINAL
ejpam-2366	296	1	a. v. bingi	PERSON
ejpam-2366	296	2	c. s. manjarekar	PERSON
ejpam-2366	297	1	j. pure	PERSON
ejpam-2366	297	2	14	CARDINAL
ejpam-2366	297	3	2	CARDINAL
ejpam-2366	297	4	2021	CARDINAL
ejpam-2366	297	5	551	CARDINAL
ejpam-2366	297	6	577 559	CARDINAL
ejpam-2366	297	7	8	CARDINAL
ejpam-2366	298	1	2	CARDINAL
ejpam-2366	298	2	6 n. proof	QUANTITY
ejpam-2366	301	1	2	CARDINAL
ejpam-2366	301	2	2	CARDINAL
ejpam-2366	301	3	∈	ORG
ejpam-2366	303	1	6	CARDINAL
ejpam-2366	304	1	6	CARDINAL
ejpam-2366	305	1	5	CARDINAL
ejpam-2366	305	2	6	DATE
ejpam-2366	305	3	7	CARDINAL
ejpam-2366	305	4	4	CARDINAL
ejpam-2366	308	1	2	CARDINAL
ejpam-2366	309	1	0 6=	CARDINAL
ejpam-2366	310	1	9	CARDINAL
ejpam-2366	312	1	φ(n	PERSON
ejpam-2366	314	1	∈	ORG
ejpam-2366	315	1	6	CARDINAL
ejpam-2366	317	1	6 φ(n	PERCENT
ejpam-2366	317	2	6 φ(n	PERCENT
ejpam-2366	317	3	6 φ(n	PERCENT
ejpam-2366	318	1	6 n or a 6 n	QUANTITY
ejpam-2366	318	2	6 n	QUANTITY
ejpam-2366	320	1	10	CARDINAL
ejpam-2366	322	1	n φ(n	GPE
ejpam-2366	324	1	∈	ORG
ejpam-2366	325	1	6	CARDINAL
ejpam-2366	326	1	6 φ(n	PERCENT
ejpam-2366	327	1	first	ORDINAL
ejpam-2366	328	1	an0 φ(n	PERSON
ejpam-2366	329	1	6 n	QUANTITY
ejpam-2366	329	2	a(a	DATE
ejpam-2366	329	3	n0	GPE
ejpam-2366	329	4	6	CARDINAL
ejpam-2366	329	5	6 n	QUANTITY
ejpam-2366	329	6	6	CARDINAL
ejpam-2366	330	1	6 φ(n	PERCENT
ejpam-2366	331	1	a∨k0)a φ(n	PERSON
ejpam-2366	331	2	6	CARDINAL
ejpam-2366	331	3	6	CARDINAL
ejpam-2366	332	1	6 φ(n	PERCENT
ejpam-2366	333	1	n φ(n	GPE
ejpam-2366	333	2	k 6	FAC
ejpam-2366	334	1	6 n	QUANTITY
ejpam-2366	334	2	6	CARDINAL
ejpam-2366	334	3	6 n	QUANTITY
ejpam-2366	334	4	6	CARDINAL
ejpam-2366	334	5	6 n	QUANTITY
ejpam-2366	336	1	10	CARDINAL
ejpam-2366	337	1	a. v. bingi	PERSON
ejpam-2366	337	2	c. s. manjarekar	PERSON
ejpam-2366	338	1	j. pure	PERSON
ejpam-2366	338	2	14	CARDINAL
ejpam-2366	338	3	2	CARDINAL
ejpam-2366	338	4	2021	CARDINAL
ejpam-2366	338	5	551	CARDINAL
ejpam-2366	338	6	5	CARDINAL
ejpam-2366	341	1	3	CARDINAL
ejpam-2366	341	2	10	CARDINAL
ejpam-2366	342	1	2im	ORDINAL
ejpam-2366	342	2	10	CARDINAL
ejpam-2366	343	1	6	CARDINAL
ejpam-2366	348	1	ω	CARDINAL
ejpam-2366	350	1	3	CARDINAL
ejpam-2366	350	2	ω	CARDINAL
ejpam-2366	352	1	10	CARDINAL
ejpam-2366	352	2	2n 6	CARDINAL
ejpam-2366	352	3	6	DATE
ejpam-2366	352	4	2n	CARDINAL
ejpam-2366	352	5	2n	CARDINAL
ejpam-2366	354	1	3n	CARDINAL
ejpam-2366	354	2	2)n	CARDINAL
ejpam-2366	354	3	2n	CARDINAL
ejpam-2366	356	1	2n	CARDINAL
ejpam-2366	357	1	2	CARDINAL
ejpam-2366	357	2	2	CARDINAL
ejpam-2366	357	3	ω	CARDINAL
ejpam-2366	357	4	3	CARDINAL
ejpam-2366	358	1	√ φ(n	PERSON
ejpam-2366	361	1	5	CARDINAL
ejpam-2366	361	2	6√	CARDINAL
ejpam-2366	363	1	6	CARDINAL
ejpam-2366	364	1	√ φ(n	PERSON
ejpam-2366	365	1	21	CARDINAL
ejpam-2366	366	1	6 n	QUANTITY
ejpam-2366	366	2	√ φ(n	PERSON
ejpam-2366	367	1	6 √ n	FAC
ejpam-2366	367	2	√ n	PERSON
ejpam-2366	367	3	√ φ(n	PERSON
ejpam-2366	369	1	9	CARDINAL
ejpam-2366	370	1	√ φ(n	PERSON
ejpam-2366	371	1	6	DATE
ejpam-2366	374	1	φ	ORG
ejpam-2366	375	1	5	CARDINAL
ejpam-2366	377	1	n ∈m	ORG
ejpam-2366	377	2	6 n or an 6	QUANTITY
ejpam-2366	378	1	5	CARDINAL
ejpam-2366	381	1	n ∈m	ORG
ejpam-2366	382	1	•	CARDINAL
ejpam-2366	384	1	2	CARDINAL
ejpam-2366	385	1	a. v. bingi	PERSON
ejpam-2366	385	2	c. s. manjarekar	PERSON
ejpam-2366	386	1	j. pure	PERSON
ejpam-2366	386	2	14	CARDINAL
ejpam-2366	386	3	2	CARDINAL
ejpam-2366	386	4	2021	CARDINAL
ejpam-2366	386	5	551	CARDINAL
ejpam-2366	386	6	2	CARDINAL
ejpam-2366	387	1	2	CARDINAL
ejpam-2366	390	1	ω	CARDINAL
ejpam-2366	391	1	φ	ORG
ejpam-2366	391	2	φ(n	PERSON
ejpam-2366	393	1	2	CARDINAL
ejpam-2366	393	2	example 1	DATE
ejpam-2366	394	1	4	CARDINAL
ejpam-2366	395	1	4	CARDINAL
ejpam-2366	395	2	2	CARDINAL
ejpam-2366	395	3	6	CARDINAL
ejpam-2366	395	4	6 n	QUANTITY
ejpam-2366	395	5	2	CARDINAL
ejpam-2366	395	6	6	CARDINAL
ejpam-2366	395	7	8	CARDINAL
ejpam-2366	395	8	6	CARDINAL
ejpam-2366	395	9	2	CARDINAL
ejpam-2366	396	1	4	CARDINAL
ejpam-2366	396	2	1	CARDINAL
ejpam-2366	398	1	φ(n	PERSON
ejpam-2366	400	1	3	CARDINAL
ejpam-2366	400	2	example 1	DATE
ejpam-2366	401	1	0	CARDINAL
ejpam-2366	403	1	φ	ORG
ejpam-2366	404	1	φ	ORG
ejpam-2366	405	1	11	CARDINAL
ejpam-2366	406	1	∈	ORG
ejpam-2366	409	1	6 √	QUANTITY
ejpam-2366	414	1	6 n	QUANTITY
ejpam-2366	414	2	6 √ n	QUANTITY
ejpam-2366	415	1	2	CARDINAL
ejpam-2366	415	2	11	CARDINAL
ejpam-2366	416	1	10	CARDINAL
ejpam-2366	418	1	1	CARDINAL
ejpam-2366	419	1	2	CARDINAL
ejpam-2366	419	2	∈	ORG
ejpam-2366	419	3	6 √ n	QUANTITY
ejpam-2366	420	1	3	CARDINAL
ejpam-2366	421	1	a. v. bingi	PERSON
ejpam-2366	421	2	c. s. manjarekar	PERSON
ejpam-2366	422	1	j. pure	PERSON
ejpam-2366	422	2	14	CARDINAL
ejpam-2366	422	3	2	CARDINAL
ejpam-2366	422	4	2021	CARDINAL
ejpam-2366	422	5	551	CARDINAL
ejpam-2366	422	6	6=	CARDINAL
ejpam-2366	422	7	6 n	QUANTITY
ejpam-2366	422	8	6 √ n	QUANTITY
ejpam-2366	423	1	11	CARDINAL
ejpam-2366	425	1	1	CARDINAL
ejpam-2366	426	1	2	CARDINAL
ejpam-2366	428	1	3	CARDINAL
ejpam-2366	429	1	4	CARDINAL
ejpam-2366	429	2	∈	ORG
ejpam-2366	429	3	6 n	QUANTITY
ejpam-2366	430	1	ω	CARDINAL
ejpam-2366	430	2	2	CARDINAL
ejpam-2366	431	1	12	CARDINAL
ejpam-2366	432	1	6	CARDINAL
ejpam-2366	434	1	13	CARDINAL
ejpam-2366	436	1	2	CARDINAL
ejpam-2366	436	2	2	CARDINAL
ejpam-2366	437	1	13	DATE
ejpam-2366	437	2	ω	CARDINAL
ejpam-2366	438	1	12	CARDINAL
ejpam-2366	441	1	2	CARDINAL
ejpam-2366	443	1	14	DATE
ejpam-2366	444	1	jacobson	PERSON
ejpam-2366	445	1	6	CARDINAL
ejpam-2366	445	2	2	CARDINAL
ejpam-2366	447	1	φ(n	PERSON
ejpam-2366	449	1	4	CARDINAL
ejpam-2366	451	1	k ∈ z	PERSON
ejpam-2366	451	2	∈	ORG
ejpam-2366	452	1	a. v. bingi	PERSON
ejpam-2366	452	2	c. s. manjarekar	PERSON
ejpam-2366	453	1	j. pure	PERSON
ejpam-2366	453	2	14	CARDINAL
ejpam-2366	453	3	2	CARDINAL
ejpam-2366	453	4	2021	CARDINAL
ejpam-2366	453	5	551	CARDINAL
ejpam-2366	453	6	ki	PERSON
ejpam-2366	453	7	ki	ORG
ejpam-2366	453	8	∈	ORG
ejpam-2366	454	1	6	CARDINAL
ejpam-2366	455	1	6	CARDINAL
ejpam-2366	455	2	3	CARDINAL
ejpam-2366	455	3	2	CARDINAL
ejpam-2366	455	4	6 n	QUANTITY
ejpam-2366	455	5	2	CARDINAL
ejpam-2366	455	6	6	CARDINAL
ejpam-2366	455	7	1	CARDINAL
ejpam-2366	456	1	nine	CARDINAL
ejpam-2366	458	1	15	CARDINAL
ejpam-2366	461	1	15	CARDINAL
ejpam-2366	461	2	16	DATE
ejpam-2366	466	1	2	CARDINAL
ejpam-2366	467	1	6	CARDINAL
ejpam-2366	468	1	2	CARDINAL
ejpam-2366	468	2	6	CARDINAL
ejpam-2366	468	3	6 n or am 6	QUANTITY
ejpam-2366	469	1	17	CARDINAL
ejpam-2366	470	1	2	CARDINAL
ejpam-2366	472	1	2	CARDINAL
ejpam-2366	472	2	2	CARDINAL
ejpam-2366	473	1	18	CARDINAL
ejpam-2366	474	1	2	CARDINAL
ejpam-2366	476	1	2	CARDINAL
ejpam-2366	476	2	7	DATE
ejpam-2366	477	1	2	CARDINAL
ejpam-2366	477	2	n ∈ z+	ORG
ejpam-2366	478	1	∈	ORG
ejpam-2366	478	2	6	CARDINAL
ejpam-2366	478	3	6 n or am 6	QUANTITY
ejpam-2366	479	1	19	CARDINAL
ejpam-2366	480	1	2	CARDINAL
ejpam-2366	481	1	20	CARDINAL
ejpam-2366	482	1	2	CARDINAL
ejpam-2366	482	2	n. a.	PERSON
ejpam-2366	483	1	bingi	PERSON
ejpam-2366	483	2	c. s. manjarekar	PERSON
ejpam-2366	484	1	j. pure	PERSON
ejpam-2366	484	2	14	CARDINAL
ejpam-2366	484	3	2	CARDINAL
ejpam-2366	484	4	2021	CARDINAL
ejpam-2366	484	5	551	CARDINAL
ejpam-2366	484	6	16	DATE
ejpam-2366	484	7	17	DATE
ejpam-2366	484	8	18	CARDINAL
ejpam-2366	484	9	13	CARDINAL
ejpam-2366	487	1	2	CARDINAL
ejpam-2366	489	1	2	CARDINAL
ejpam-2366	490	1	0 6=	CARDINAL
ejpam-2366	491	1	2	CARDINAL
ejpam-2366	491	2	2	CARDINAL
ejpam-2366	492	1	5	CARDINAL
ejpam-2366	492	2	example 4	DATE
ejpam-2366	493	1	6	CARDINAL
ejpam-2366	494	1	6	CARDINAL
ejpam-2366	494	2	2	CARDINAL
ejpam-2366	495	1	6	CARDINAL
ejpam-2366	496	1	z8	DATE
ejpam-2366	497	1	k ∈ z	PERSON
ejpam-2366	497	2	∈	ORG
ejpam-2366	499	1	ki	PERSON
ejpam-2366	500	1	ki	ORG
ejpam-2366	500	2	∈	ORG
ejpam-2366	500	3	4	CARDINAL
ejpam-2366	501	1	4	CARDINAL
ejpam-2366	501	2	2	CARDINAL
ejpam-2366	502	1	21	DATE
ejpam-2366	504	1	φ(n	PERSON
ejpam-2366	505	1	22	CARDINAL
ejpam-2366	507	1	n φ(n	GPE
ejpam-2366	508	1	22	CARDINAL
ejpam-2366	509	1	14	CARDINAL
ejpam-2366	511	1	15	CARDINAL
ejpam-2366	513	1	16	CARDINAL
ejpam-2366	515	1	a. v. bingi	PERSON
ejpam-2366	515	2	c. s. manjarekar	PERSON
ejpam-2366	516	1	j. pure	PERSON
ejpam-2366	516	2	14	CARDINAL
ejpam-2366	516	3	2	CARDINAL
ejpam-2366	516	4	2021	CARDINAL
ejpam-2366	516	5	551	CARDINAL
ejpam-2366	516	6	17	CARDINAL
ejpam-2366	517	1	√ φ(n	PERSON
ejpam-2366	519	1	18	CARDINAL
ejpam-2366	520	1	√ φ(n	PERSON
ejpam-2366	521	1	6	DATE
ejpam-2366	523	1	23	CARDINAL
ejpam-2366	525	1	n φ(n	GPE
ejpam-2366	527	1	10	CARDINAL
ejpam-2366	528	1	2	CARDINAL
ejpam-2366	528	2	2	CARDINAL
ejpam-2366	529	1	24	CARDINAL
ejpam-2366	530	1	2	CARDINAL
ejpam-2366	531	1	25	CARDINAL
ejpam-2366	532	1	2	CARDINAL
ejpam-2366	532	2	2	CARDINAL
ejpam-2366	532	3	l. theorem 26	ORG
ejpam-2366	533	1	2	CARDINAL
ejpam-2366	534	1	2	CARDINAL
ejpam-2366	534	2	2	CARDINAL
ejpam-2366	534	3	27	DATE
ejpam-2366	536	1	2	CARDINAL
ejpam-2366	536	2	2	CARDINAL
ejpam-2366	536	3	2	CARDINAL
ejpam-2366	537	1	abc 6	ORG
ejpam-2366	537	2	6	CARDINAL
ejpam-2366	537	3	2	CARDINAL
ejpam-2366	537	4	6	CARDINAL
ejpam-2366	537	5	6	CARDINAL
ejpam-2366	538	1	5	CARDINAL
ejpam-2366	538	2	10	CARDINAL
ejpam-2366	538	3	6	CARDINAL
ejpam-2366	541	1	2	CARDINAL
ejpam-2366	541	2	2.4	CARDINAL
ejpam-2366	541	3	18	CARDINAL
ejpam-2366	541	4	√	PERSON
ejpam-2366	542	1	2	CARDINAL
ejpam-2366	542	2	φ	ORG
ejpam-2366	542	3	φ	ORG
ejpam-2366	543	1	28	CARDINAL
ejpam-2366	545	1	n φ(n	GPE
ejpam-2366	545	2	2	CARDINAL
ejpam-2366	546	1	2	CARDINAL
ejpam-2366	546	2	2	CARDINAL
ejpam-2366	547	1	theorems 10	ORG
ejpam-2366	547	2	24	DATE
ejpam-2366	547	3	26	CARDINAL
ejpam-2366	548	1	2	CARDINAL
ejpam-2366	549	1	29	CARDINAL
ejpam-2366	551	1	n φ(n	GPE
ejpam-2366	551	2	2	CARDINAL
ejpam-2366	552	1	2	CARDINAL
ejpam-2366	553	1	2	CARDINAL
ejpam-2366	553	2	l. a. v. bingi	PERSON
ejpam-2366	553	3	c. s. manjarekar	PERSON
ejpam-2366	554	1	j. pure	PERSON
ejpam-2366	554	2	14	CARDINAL
ejpam-2366	554	3	2	CARDINAL
ejpam-2366	554	4	2021	CARDINAL
ejpam-2366	554	5	551	CARDINAL
ejpam-2366	555	1	theorems 10	ORG
ejpam-2366	555	2	24	DATE
ejpam-2366	555	3	27	CARDINAL
ejpam-2366	556	1	30	CARDINAL
ejpam-2366	558	1	n φ(n	GPE
ejpam-2366	558	2	2	CARDINAL
ejpam-2366	560	1	22	CARDINAL
ejpam-2366	561	1	31	CARDINAL
ejpam-2366	564	1	n φ(n	GPE
ejpam-2366	564	2	2	CARDINAL
ejpam-2366	565	1	2	CARDINAL
ejpam-2366	566	1	30	CARDINAL
ejpam-2366	566	2	27	DATE
ejpam-2366	568	1	32	DATE
ejpam-2366	570	1	2	CARDINAL
ejpam-2366	571	1	2	CARDINAL
ejpam-2366	571	2	2	CARDINAL
ejpam-2366	572	1	theorems 5	ORG
ejpam-2366	572	2	24	DATE
ejpam-2366	572	3	26	CARDINAL
ejpam-2366	573	1	33	DATE
ejpam-2366	576	1	2	CARDINAL
ejpam-2366	577	1	2	CARDINAL
ejpam-2366	578	1	2	CARDINAL
ejpam-2366	579	1	theorems 5	ORG
ejpam-2366	579	2	24	DATE
ejpam-2366	579	3	27	CARDINAL
ejpam-2366	580	1	34	CARDINAL
ejpam-2366	583	1	2	CARDINAL
ejpam-2366	585	1	15	CARDINAL
ejpam-2366	586	1	35	DATE
ejpam-2366	590	1	2	CARDINAL
ejpam-2366	590	2	l and√ n : im	PRODUCT
ejpam-2366	590	3	2	CARDINAL
ejpam-2366	591	1	34	DATE
ejpam-2366	591	2	27	CARDINAL
ejpam-2366	592	1	a. v. bingi	PERSON
ejpam-2366	592	2	c. s. manjarekar	PERSON
ejpam-2366	593	1	j. pure	PERSON
ejpam-2366	593	2	14	CARDINAL
ejpam-2366	593	3	2	CARDINAL
ejpam-2366	593	4	2021	CARDINAL
ejpam-2366	593	5	551	CARDINAL
ejpam-2366	595	1	2	CARDINAL
ejpam-2366	596	1	2	CARDINAL
ejpam-2366	598	1	1	CARDINAL
ejpam-2366	598	2	4	CARDINAL
ejpam-2366	600	1	2.6	CARDINAL
ejpam-2366	600	2	22	CARDINAL
ejpam-2366	601	1	8	CARDINAL
ejpam-2366	606	1	7	CARDINAL
ejpam-2366	606	2	6	CARDINAL
ejpam-2366	607	1	4	CARDINAL
ejpam-2366	608	1	4	CARDINAL
ejpam-2366	609	1	36	CARDINAL
ejpam-2366	614	1	2im	ORDINAL
ejpam-2366	615	1	6 √	QUANTITY
ejpam-2366	617	1	6 √	QUANTITY
ejpam-2366	619	1	∈	ORG
ejpam-2366	619	2	6	CARDINAL
ejpam-2366	621	1	1	CARDINAL
ejpam-2366	622	1	6	CARDINAL
ejpam-2366	623	1	6	CARDINAL
ejpam-2366	623	2	2im	ORDINAL
ejpam-2366	624	1	5	CARDINAL
ejpam-2366	624	2	10	CARDINAL
ejpam-2366	624	3	6	CARDINAL
ejpam-2366	624	4	2 6	CARDINAL
ejpam-2366	625	1	2	CARDINAL
ejpam-2366	625	2	6	CARDINAL
ejpam-2366	626	1	a. v. bingi	PERSON
ejpam-2366	626	2	c. s. manjarekar	PERSON
ejpam-2366	627	1	j. pure	PERSON
ejpam-2366	627	2	14	CARDINAL
ejpam-2366	627	3	2	CARDINAL
ejpam-2366	627	4	2021	CARDINAL
ejpam-2366	627	5	551	CARDINAL
ejpam-2366	627	6	6 n	QUANTITY
ejpam-2366	627	7	an−1im 6	CARDINAL
ejpam-2366	628	1	2	CARDINAL
ejpam-2366	628	2	6 n	QUANTITY
ejpam-2366	629	1	3	CARDINAL
ejpam-2366	629	2	6 n	QUANTITY
ejpam-2366	630	1	6	CARDINAL
ejpam-2366	631	1	6	CARDINAL
ejpam-2366	632	1	6	CARDINAL
ejpam-2366	633	1	6	CARDINAL
ejpam-2366	634	1	6	CARDINAL
ejpam-2366	637	1	6 a(n	QUANTITY
ejpam-2366	638	1	6	CARDINAL
ejpam-2366	638	2	6	CARDINAL
ejpam-2366	640	1	6	DATE
ejpam-2366	643	1	8	CARDINAL
ejpam-2366	643	2	example 4	DATE
ejpam-2366	644	1	6	CARDINAL
ejpam-2366	645	1	6	CARDINAL
ejpam-2366	647	1	1	CARDINAL
ejpam-2366	648	1	37	DATE
ejpam-2366	649	1	∈	ORG
ejpam-2366	651	1	n ∈m	ORG
ejpam-2366	658	1	6=	CARDINAL
ejpam-2366	658	2	∈	ORG
ejpam-2366	659	1	6 n or a	QUANTITY
ejpam-2366	659	2	6 √ n	QUANTITY
ejpam-2366	660	1	13	CARDINAL
ejpam-2366	662	1	4	CARDINAL
ejpam-2366	668	1	∈	ORG
ejpam-2366	673	1	3	CARDINAL
ejpam-2366	673	2	38	DATE
ejpam-2366	676	1	a. v. bingi	PERSON
ejpam-2366	676	2	c. s. manjarekar	PERSON
ejpam-2366	677	1	j. pure	PERSON
ejpam-2366	677	2	14	CARDINAL
ejpam-2366	677	3	2	CARDINAL
ejpam-2366	677	4	2021	CARDINAL
ejpam-2366	677	5	551	CARDINAL
ejpam-2366	678	1	2	CARDINAL
ejpam-2366	678	2	l. 3	ORG
ejpam-2366	678	3	6	CARDINAL
ejpam-2366	678	4	∈	ORG
ejpam-2366	679	1	1	CARDINAL
ejpam-2366	679	2	2	CARDINAL
ejpam-2366	680	1	ab 6	FAC
ejpam-2366	680	2	2	CARDINAL
ejpam-2366	681	1	lemma 4	ORG
ejpam-2366	681	2	6	CARDINAL
ejpam-2366	683	1	2	CARDINAL
ejpam-2366	686	1	6 √	QUANTITY
ejpam-2366	687	1	l. 2©	ORG
ejpam-2366	687	2	3	CARDINAL
ejpam-2366	690	1	6	CARDINAL
ejpam-2366	691	1	6	CARDINAL
ejpam-2366	693	1	6	CARDINAL
ejpam-2366	693	2	1	CARDINAL
ejpam-2366	693	3	6	CARDINAL
ejpam-2366	693	4	∈	ORG
ejpam-2366	693	5	6	CARDINAL
ejpam-2366	694	1	6 n	QUANTITY
ejpam-2366	694	2	∈	ORG
ejpam-2366	695	1	6	CARDINAL
ejpam-2366	696	1	3	CARDINAL
ejpam-2366	696	2	10	CARDINAL
ejpam-2366	697	1	6	CARDINAL
ejpam-2366	697	2	6 qn 6	QUANTITY
ejpam-2366	699	1	6	CARDINAL
ejpam-2366	699	2	6 n	QUANTITY
ejpam-2366	700	1	6 √	QUANTITY
ejpam-2366	700	2	6 √ n	QUANTITY
ejpam-2366	700	3	39	CARDINAL
ejpam-2366	703	1	1	CARDINAL
ejpam-2366	704	1	2	CARDINAL
ejpam-2366	704	2	l. 3	ORG
ejpam-2366	705	1	1	CARDINAL
ejpam-2366	705	2	2	CARDINAL
ejpam-2366	705	3	1	CARDINAL
ejpam-2366	705	4	2	CARDINAL
ejpam-2366	705	5	38	CARDINAL
ejpam-2366	706	1	2	CARDINAL
ejpam-2366	706	2	1	CARDINAL
ejpam-2366	706	3	6 n	QUANTITY
ejpam-2366	707	1	6	CARDINAL
ejpam-2366	707	2	lemma 4	ORG
ejpam-2366	708	1	6	CARDINAL
ejpam-2366	709	1	6	CARDINAL
ejpam-2366	709	2	2	CARDINAL
ejpam-2366	711	1	6	DATE
ejpam-2366	711	2	6	CARDINAL
ejpam-2366	712	1	2	CARDINAL
ejpam-2366	712	2	6	CARDINAL
ejpam-2366	712	3	6 √ n	QUANTITY
ejpam-2366	712	4	6	CARDINAL
ejpam-2366	712	5	6 √ n	QUANTITY
ejpam-2366	713	1	2	CARDINAL
ejpam-2366	713	2	3	CARDINAL
ejpam-2366	714	1	3	CARDINAL
ejpam-2366	715	1	a. v. bingi	PERSON
ejpam-2366	715	2	c. s. manjarekar	PERSON
ejpam-2366	716	1	j. pure	PERSON
ejpam-2366	716	2	14	CARDINAL
ejpam-2366	716	3	2	CARDINAL
ejpam-2366	716	4	2021	CARDINAL
ejpam-2366	716	5	551	CARDINAL
ejpam-2366	716	6	3	CARDINAL
ejpam-2366	716	7	2	CARDINAL
ejpam-2366	718	1	2	CARDINAL
ejpam-2366	718	2	5	CARDINAL
ejpam-2366	718	3	10	CARDINAL
ejpam-2366	720	1	3.1	CARDINAL
ejpam-2366	720	2	17	CARDINAL
ejpam-2366	721	1	3.6	CARDINAL
ejpam-2366	721	2	17	CARDINAL
ejpam-2366	722	1	40	DATE
ejpam-2366	726	1	k =	PERSON
ejpam-2366	729	1	∈	ORG
ejpam-2366	730	1	k =	PERSON
ejpam-2366	736	1	6 p	PERCENT
ejpam-2366	736	2	6 √	QUANTITY
ejpam-2366	738	1	6 p	PERCENT
ejpam-2366	740	1	6	CARDINAL
ejpam-2366	741	1	3.6	CARDINAL
ejpam-2366	741	2	17	CARDINAL
ejpam-2366	743	1	6	CARDINAL
ejpam-2366	743	2	2	CARDINAL
ejpam-2366	744	1	6	CARDINAL
ejpam-2366	744	2	6	CARDINAL
ejpam-2366	744	3	2im	ORDINAL
ejpam-2366	745	1	5	CARDINAL
ejpam-2366	745	2	10	CARDINAL
ejpam-2366	745	3	6	CARDINAL
ejpam-2366	745	4	2	CARDINAL
ejpam-2366	747	1	6	CARDINAL
ejpam-2366	747	2	6	CARDINAL
ejpam-2366	747	3	6	CARDINAL
ejpam-2366	747	4	6	CARDINAL
ejpam-2366	747	5	6	CARDINAL
ejpam-2366	749	1	3.6	CARDINAL
ejpam-2366	749	2	17	CARDINAL
ejpam-2366	750	1	6	CARDINAL
ejpam-2366	750	2	5	CARDINAL
ejpam-2366	750	3	10	CARDINAL
ejpam-2366	751	1	39	DATE
ejpam-2366	753	1	5	CARDINAL
ejpam-2366	758	1	∈	ORG
ejpam-2366	762	1	5	CARDINAL
ejpam-2366	762	2	10	CARDINAL
ejpam-2366	763	1	5	CARDINAL
ejpam-2366	763	2	3.5	CARDINAL
ejpam-2366	763	3	22	CARDINAL
ejpam-2366	764	1	5	CARDINAL
ejpam-2366	764	2	38	CARDINAL
ejpam-2366	764	3	39	DATE
ejpam-2366	764	4	40	DATE
ejpam-2366	765	1	a. v. bingi	PERSON
ejpam-2366	765	2	c. s. manjarekar	PERSON
ejpam-2366	766	1	j. pure	PERSON
ejpam-2366	766	2	14	CARDINAL
ejpam-2366	766	3	2	CARDINAL
ejpam-2366	766	4	2021	CARDINAL
ejpam-2366	766	5	551	CARDINAL
ejpam-2366	766	6	577 571	CARDINAL
ejpam-2366	766	7	41	CARDINAL
ejpam-2366	769	1	1	CARDINAL
ejpam-2366	770	1	2	CARDINAL
ejpam-2366	770	2	l. 3	ORG
ejpam-2366	770	3	6	CARDINAL
ejpam-2366	770	4	∈	ORG
ejpam-2366	770	5	42	DATE
ejpam-2366	773	1	1	CARDINAL
ejpam-2366	774	1	2	CARDINAL
ejpam-2366	774	2	l. 3	ORG
ejpam-2366	774	3	43	DATE
ejpam-2366	778	1	k = bim	PERSON
ejpam-2366	779	1	42	DATE
ejpam-2366	780	1	19	CARDINAL
ejpam-2366	783	1	2.5	CARDINAL
ejpam-2366	783	2	22	CARDINAL
ejpam-2366	785	1	44	DATE
ejpam-2366	786	1	∈	ORG
ejpam-2366	788	1	n ∈m	ORG
ejpam-2366	791	1	n ∈m	ORG
ejpam-2366	795	1	6=	CARDINAL
ejpam-2366	795	2	∈	ORG
ejpam-2366	796	1	6 n or a	QUANTITY
ejpam-2366	797	1	3	CARDINAL
ejpam-2366	799	1	a. v. bingi	PERSON
ejpam-2366	799	2	c. s. manjarekar	PERSON
ejpam-2366	800	1	j. pure	PERSON
ejpam-2366	800	2	14	CARDINAL
ejpam-2366	800	3	2	CARDINAL
ejpam-2366	800	4	2021	CARDINAL
ejpam-2366	800	5	551	CARDINAL
ejpam-2366	800	6	45	CARDINAL
ejpam-2366	803	1	1	CARDINAL
ejpam-2366	804	1	2	CARDINAL
ejpam-2366	804	2	l. 3	ORG
ejpam-2366	804	3	6	CARDINAL
ejpam-2366	804	4	∈	ORG
ejpam-2366	805	1	1	CARDINAL
ejpam-2366	805	2	2	CARDINAL
ejpam-2366	806	1	ab 6	FAC
ejpam-2366	806	2	2	CARDINAL
ejpam-2366	807	1	lemma 4	ORG
ejpam-2366	807	2	6	CARDINAL
ejpam-2366	809	1	2	CARDINAL
ejpam-2366	812	1	6	CARDINAL
ejpam-2366	812	2	l. 2©	ORG
ejpam-2366	812	3	3	CARDINAL
ejpam-2366	815	1	6	CARDINAL
ejpam-2366	816	1	6	CARDINAL
ejpam-2366	818	1	6	CARDINAL
ejpam-2366	818	2	1	CARDINAL
ejpam-2366	818	3	6	CARDINAL
ejpam-2366	818	4	∈	ORG
ejpam-2366	818	5	6	CARDINAL
ejpam-2366	819	1	6 n	QUANTITY
ejpam-2366	819	2	∈	ORG
ejpam-2366	820	1	6	CARDINAL
ejpam-2366	821	1	3	CARDINAL
ejpam-2366	821	2	10	CARDINAL
ejpam-2366	822	1	6	CARDINAL
ejpam-2366	822	2	6 qn 6	QUANTITY
ejpam-2366	824	1	6	CARDINAL
ejpam-2366	824	2	6 n	QUANTITY
ejpam-2366	825	1	6	CARDINAL
ejpam-2366	825	2	6	CARDINAL
ejpam-2366	825	3	46	DATE
ejpam-2366	828	1	1	CARDINAL
ejpam-2366	829	1	2	CARDINAL
ejpam-2366	829	2	l. 3	ORG
ejpam-2366	830	1	1	CARDINAL
ejpam-2366	830	2	2	CARDINAL
ejpam-2366	830	3	1	CARDINAL
ejpam-2366	830	4	2	CARDINAL
ejpam-2366	830	5	45	CARDINAL
ejpam-2366	831	1	2	CARDINAL
ejpam-2366	831	2	1	CARDINAL
ejpam-2366	831	3	6 n	QUANTITY
ejpam-2366	832	1	6	CARDINAL
ejpam-2366	832	2	lemma 4	ORG
ejpam-2366	833	1	6	CARDINAL
ejpam-2366	834	1	6	CARDINAL
ejpam-2366	834	2	2	CARDINAL
ejpam-2366	836	1	6	DATE
ejpam-2366	836	2	6	CARDINAL
ejpam-2366	837	1	2	CARDINAL
ejpam-2366	837	2	6	CARDINAL
ejpam-2366	837	3	a. v. bingi	PERSON
ejpam-2366	837	4	c. s. manjarekar	PERSON
ejpam-2366	838	1	j. pure	PERSON
ejpam-2366	838	2	14	CARDINAL
ejpam-2366	838	3	2	CARDINAL
ejpam-2366	838	4	2021	CARDINAL
ejpam-2366	839	1	551	CARDINAL
ejpam-2366	839	2	6	CARDINAL
ejpam-2366	839	3	6	CARDINAL
ejpam-2366	839	4	6	CARDINAL
ejpam-2366	840	1	2	CARDINAL
ejpam-2366	840	2	3	CARDINAL
ejpam-2366	841	1	3	CARDINAL
ejpam-2366	842	1	3	CARDINAL
ejpam-2366	842	2	2	CARDINAL
ejpam-2366	844	1	2	CARDINAL
ejpam-2366	844	2	5	CARDINAL
ejpam-2366	844	3	10	CARDINAL
ejpam-2366	846	1	47	DATE
ejpam-2366	853	1	k =	PERSON
ejpam-2366	860	1	6 p	PERCENT
ejpam-2366	860	2	6	CARDINAL
ejpam-2366	861	1	6 p	PERCENT
ejpam-2366	863	1	6 p	PERCENT
ejpam-2366	864	1	6	CARDINAL
ejpam-2366	864	2	2	CARDINAL
ejpam-2366	865	1	6	CARDINAL
ejpam-2366	865	2	6	CARDINAL
ejpam-2366	865	3	2im	ORDINAL
ejpam-2366	866	1	5	CARDINAL
ejpam-2366	866	2	10	CARDINAL
ejpam-2366	866	3	6	CARDINAL
ejpam-2366	866	4	2	CARDINAL
ejpam-2366	868	1	6	CARDINAL
ejpam-2366	868	2	6	CARDINAL
ejpam-2366	868	3	6	CARDINAL
ejpam-2366	868	4	6	CARDINAL
ejpam-2366	868	5	6	CARDINAL
ejpam-2366	869	1	6	CARDINAL
ejpam-2366	870	1	46	DATE
ejpam-2366	871	1	5	CARDINAL
ejpam-2366	871	2	45	CARDINAL
ejpam-2366	871	3	46	DATE
ejpam-2366	871	4	47	DATE
ejpam-2366	872	1	48	DATE
ejpam-2366	875	1	1	CARDINAL
ejpam-2366	876	1	2	CARDINAL
ejpam-2366	876	2	l. 3	ORG
ejpam-2366	876	3	6	CARDINAL
ejpam-2366	876	4	∈	ORG
ejpam-2366	876	5	49	DATE
ejpam-2366	879	1	a. v. bingi	PERSON
ejpam-2366	879	2	c. s. manjarekar	PERSON
ejpam-2366	880	1	j. pure	PERSON
ejpam-2366	880	2	14	CARDINAL
ejpam-2366	880	3	2	CARDINAL
ejpam-2366	880	4	2021	CARDINAL
ejpam-2366	880	5	551	CARDINAL
ejpam-2366	881	1	2	CARDINAL
ejpam-2366	881	2	l. 3	ORG
ejpam-2366	881	3	49	DATE
ejpam-2366	881	4	3.8	CARDINAL
ejpam-2366	881	5	22	CARDINAL
ejpam-2366	882	1	50	CARDINAL
ejpam-2366	886	1	50	DATE
ejpam-2366	886	2	3.14	CARDINAL
ejpam-2366	886	3	22	CARDINAL
ejpam-2366	887	1	49	DATE
ejpam-2366	888	1	20	CARDINAL
ejpam-2366	891	1	16	CARDINAL
ejpam-2366	891	2	2	CARDINAL
ejpam-2366	891	3	6	CARDINAL
ejpam-2366	891	4	6	CARDINAL
ejpam-2366	891	5	6	CARDINAL
ejpam-2366	891	6	2	CARDINAL
ejpam-2366	891	7	6	CARDINAL
ejpam-2366	891	8	6	CARDINAL
ejpam-2366	891	9	6 √ q.	DATE
ejpam-2366	891	10	2	CARDINAL
ejpam-2366	891	11	multiplicative	NORP
ejpam-2366	892	1	9	DATE
ejpam-2366	893	1	2	CARDINAL
ejpam-2366	893	2	n ∈ z+	ORG
ejpam-2366	894	1	6	CARDINAL
ejpam-2366	894	2	6	CARDINAL
ejpam-2366	894	3	6	CARDINAL
ejpam-2366	894	4	10	DATE
ejpam-2366	895	1	2	CARDINAL
ejpam-2366	895	2	n ∈ z+	ORG
ejpam-2366	896	1	6	CARDINAL
ejpam-2366	896	2	6	CARDINAL
ejpam-2366	896	3	6 √ q.	DATE
ejpam-2366	896	4	l	DATE
ejpam-2366	896	5	2	CARDINAL
ejpam-2366	896	6	51	DATE
ejpam-2366	899	1	2	CARDINAL
ejpam-2366	900	1	1	CARDINAL
ejpam-2366	901	1	2	CARDINAL
ejpam-2366	901	2	l. 3	ORG
ejpam-2366	901	3	l. a. v. bingi	PERSON
ejpam-2366	901	4	c. s. manjarekar	PERSON
ejpam-2366	902	1	j. pure	PERSON
ejpam-2366	902	2	14	CARDINAL
ejpam-2366	902	3	2	CARDINAL
ejpam-2366	902	4	2021	CARDINAL
ejpam-2366	902	5	551	CARDINAL
ejpam-2366	903	1	3	CARDINAL
ejpam-2366	903	2	10	CARDINAL
ejpam-2366	904	1	1	CARDINAL
ejpam-2366	904	2	2	CARDINAL
ejpam-2366	905	1	ab 6	FAC
ejpam-2366	906	1	6	CARDINAL
ejpam-2366	906	2	l. 2	ORG
ejpam-2366	906	3	1	CARDINAL
ejpam-2366	907	1	6	CARDINAL
ejpam-2366	908	1	nim	ORG
ejpam-2366	909	1	ac 6	ORG
ejpam-2366	909	2	5	CARDINAL
ejpam-2366	909	3	10	CARDINAL
ejpam-2366	910	1	6	CARDINAL
ejpam-2366	910	2	6	CARDINAL
ejpam-2366	910	3	6	CARDINAL
ejpam-2366	910	4	6	CARDINAL
ejpam-2366	912	1	2	CARDINAL
ejpam-2366	912	2	3	CARDINAL
ejpam-2366	914	1	3	CARDINAL
ejpam-2366	915	1	3	CARDINAL
ejpam-2366	915	2	2	CARDINAL
ejpam-2366	917	1	2	CARDINAL
ejpam-2366	917	2	5	CARDINAL
ejpam-2366	917	3	10	CARDINAL
ejpam-2366	918	1	52	DATE
ejpam-2366	921	1	2	CARDINAL
ejpam-2366	922	1	1	CARDINAL
ejpam-2366	923	1	2	CARDINAL
ejpam-2366	923	2	l. 3	ORG
ejpam-2366	924	1	51	CARDINAL
ejpam-2366	925	1	2	CARDINAL
ejpam-2366	925	2	51	CARDINAL
ejpam-2366	925	3	52	DATE
ejpam-2366	926	1	21	CARDINAL
ejpam-2366	928	1	2	CARDINAL
ejpam-2366	928	2	2	CARDINAL
ejpam-2366	928	3	22	CARDINAL
ejpam-2366	930	1	2	CARDINAL
ejpam-2366	930	2	2	CARDINAL
ejpam-2366	930	3	first	ORDINAL
ejpam-2366	930	4	ph.d	ORG
ejpam-2366	931	1	2015	CARDINAL
ejpam-2366	931	2	shivaji university	ORG
ejpam-2366	931	3	kolhapur	GPE
ejpam-2366	931	4	maharashtra	GPE
ejpam-2366	931	5	india	GPE
ejpam-2366	931	6	576	CARDINAL
ejpam-2366	932	1	1	CARDINAL
ejpam-2366	932	2	al-khouja	PERSON
ejpam-2366	934	1	damascus university	ORG
ejpam-2366	934	2	19(2):9–20, 2003	DATE
ejpam-2366	935	1	2	CARDINAL
ejpam-2366	935	2	francisco alarcon	PERSON
ejpam-2366	935	3	anderson	PERSON
ejpam-2366	935	4	c jayaram	PERSON
ejpam-2366	937	1	mathematica hungarica	PERSON
ejpam-2366	937	2	30(1):1–26, 1995	DATE
ejpam-2366	938	1	3	CARDINAL
ejpam-2366	938	2	anderson	PERSON
ejpam-2366	940	1	6(2):131–145, 1976	DATE
ejpam-2366	941	1	4	CARDINAL
ejpam-2366	941	2	sachin ballal	PERSON
ejpam-2366	941	3	machchhindra gophane	PERSON
ejpam-2366	941	4	vilas kharat	ORG
ejpam-2366	943	1	southeast asian	NORP
ejpam-2366	943	2	449	CARDINAL
ejpam-2366	943	3	2016	DATE
ejpam-2366	944	1	5	CARDINAL
ejpam-2366	944	2	sachin ballal	GPE
ejpam-2366	944	3	vilas kharat	ORG
ejpam-2366	947	1	j. algebra	PERSON
ejpam-2366	947	2	8(9):439–449	CARDINAL
ejpam-2366	947	3	2014	DATE
ejpam-2366	948	1	6	CARDINAL
ejpam-2366	948	2	vilas kharat	ORG
ejpam-2366	950	1	2015:1–6	CARDINAL
ejpam-2366	950	2	2015	DATE
ejpam-2366	951	1	7	CARDINAL
ejpam-2366	951	2	kuhail	PERSON
ejpam-2366	953	1	contemporary mathematical sciences	ORG
ejpam-2366	953	2	6(17):811–824, 2011	DATE
ejpam-2366	954	1	8	CARDINAL
ejpam-2366	954	2	cs manjarekar	PERSON
ejpam-2366	957	1	9	CARDINAL
ejpam-2366	957	2	c jayaram	PERSON
ejpam-2366	959	1	40(8):2825–2840	CARDINAL
ejpam-2366	959	2	2012	DATE
ejpam-2366	960	1	10	CARDINAL
ejpam-2366	962	1	iranian	NORP
ejpam-2366	962	2	35(4):309–313, 2011	DATE
ejpam-2366	963	1	11	CARDINAL
ejpam-2366	963	2	dustin scott culhan	PERSON
ejpam-2366	965	1	university of michigan press	ORG
ejpam-2366	965	2	university of california	ORG
ejpam-2366	965	3	2005	DATE
ejpam-2366	966	1	12	CARDINAL
ejpam-2366	967	1	2	CARDINAL
ejpam-2366	967	2	2	CARDINAL
ejpam-2366	968	1	42(6):2338–2353	CARDINAL
ejpam-2366	968	2	2014	DATE
ejpam-2366	969	1	13	CARDINAL
ejpam-2366	969	2	johnson	PERSON
ejpam-2366	969	3	ja johnson	PERSON
ejpam-2366	971	1	fundamenta mathematicae	ORG
ejpam-2366	971	2	68(2):187–201	CARDINAL
ejpam-2366	971	3	1970	DATE
ejpam-2366	972	1	577	CARDINAL
ejpam-2366	972	2	14	CARDINAL
ejpam-2366	972	3	j johnson	PERSON
ejpam-2366	974	1	fundamenta mathematicae	ORG
ejpam-2366	974	2	66:347–373	CARDINAL
ejpam-2366	974	3	1970	DATE
ejpam-2366	975	1	15	CARDINAL
ejpam-2366	976	1	2013	DATE
ejpam-2366	977	1	16	CARDINAL
ejpam-2366	977	2	cs manjarekar	PERSON
ejpam-2366	977	3	av bingi	PERSON
ejpam-2366	978	1	φ	ORG
ejpam-2366	979	1	2014:1–7	CARDINAL
ejpam-2366	979	2	2014	DATE
ejpam-2366	980	1	17	CARDINAL
ejpam-2366	980	2	cs manjarekar	PERSON
ejpam-2366	980	3	av bingi	PERSON
ejpam-2366	982	1	2016	DATE
ejpam-2366	983	1	18	CARDINAL
ejpam-2366	983	2	cs manjarekar	PERSON
ejpam-2366	983	3	av bingi	PERSON
ejpam-2366	984	1	2	CARDINAL
ejpam-2366	984	2	2	CARDINAL
ejpam-2366	986	1	2:1–13	CARDINAL
ejpam-2366	986	2	2016	DATE
ejpam-2366	987	1	19	CARDINAL
ejpam-2366	987	2	cs manjarekar	PERSON
ejpam-2366	987	3	un	ORG
ejpam-2366	989	1	3(8):1–6	CARDINAL
ejpam-2366	989	2	2013	DATE
ejpam-2366	990	1	20	CARDINAL
ejpam-2366	990	2	cs manjarekar	PERSON
ejpam-2366	990	3	un	ORG
ejpam-2366	992	1	2014:1–4	CARDINAL
ejpam-2366	992	2	2014	DATE
ejpam-2366	993	1	21	CARDINAL
ejpam-2366	993	2	cs manjarekar	PERSON
ejpam-2366	995	1	studia scientifica	PERSON
ejpam-2366	995	2	hungarica	GPE
ejpam-2366	995	3	18:13	CARDINAL
ejpam-2366	995	4	19, 1983	DATE
ejpam-2366	996	1	22	CARDINAL
ejpam-2366	996	2	emel aslankarayigit	ORG
ejpam-2366	998	1	14(1):673–680	DATE
ejpam-2366	998	2	2016	DATE
ejpam-2366	999	1	23	CARDINAL
ejpam-2366	999	2	jane wells	PERSON
ejpam-2366	1001	1	fundamenta mathematicae	ORG
ejpam-2366	1001	2	3(75):235–247	ORG
ejpam-2366	1001	3	1972	DATE
ejpam-2366	1002	1	24	CARDINAL
ejpam-2366	1002	2	naser zamani	PERSON
ejpam-2366	1003	1	glasgow mathematical journal	ORG
ejpam-2366	1003	2	52(2):253–259	CARDINAL
ejpam-2366	1003	3	2010	DATE