On the Diophantine equation x2 + C = yn

被引：0

作者：

Rayaguru, Sai Gopal ^{[1
]}

机构：

[1] Siksha O Anusandhan Univ, Ctr Data Sci, Bhubaneswar 751030, Odisha, India

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2024年 / 55卷 / 01期

关键词：

Diophantine equation; Integer solution; S-integers; Lucas sequence; Primitive divisors; X(2)+2(A);

D O I：

10.1007/s13226-022-00347-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we solve the Diophantine equation x(2) + C = y(n) in positive integers x, y >= 1; k, l, m >= 0 and n >= 3 with gcd (x, y) = 1, when C = 2(k)73(l)41(m) and C = 2(k)73(l)89(m).

引用

页码：69 / 77

页数：9

共 50 条

[41] ON THE DIOPHANTINE EQUATION x(2)
Cangul, Ismail Naci
Demirci, Musa
Soydan, Gokhan
Tzanakis, Nikos
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2010, 43 (02) : 209 - 225
[42] ON THE DIOPHANTINE EQUATIONS x2+2α3β19γ = yn AND x2+2α3β13γ = yn
Ghadermarzi, Amir
MATHEMATICA SLOVACA, 2019, 69 (03) : 507 - 520
[43] On the Diophantine equation NX2+2L3M = YN
Goedhart, Eva G.
Grundman, Helen G.
JOURNAL OF NUMBER THEORY, 2014, 141 : 214 - 224
[44] On the diophantine equation ax2+bm=4yn
Arif, SA
Al-Ali, AS
ACTA ARITHMETICA, 2002, 103 (04) : 343 - 346
[45] On the Diophantine equation X2 - (22m+1)Y4 =-22m
He, Bo
Togbe, Alain
Walsh, P. Gary
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2008, 73 (3-4): : 417 - 420
[46] On the Diophantine Equation cx2 + p2m=4yn
Chakraborty, K.
Hoque, A.
Srinivas, K.
RESULTS IN MATHEMATICS, 2021, 76 (02)
[47] ON THE SOLUTIONS OF THE DIOPHANTINE EQUATION (x - d)2
Koutsianas, Angelos
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2021, 64 (02) : 141 - 151
[48] A Generalised Balancing Sequence and Solutions of Diophantine Equations x2± pxy
Kameswari, P. Anuradha
Anoosha, K.
COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, 2022, 13 (01): : 253 - 263
[49] On the Diophantine equation 1/x
Yuan, Xiaodan
Luo, Jiagui
AIMS MATHEMATICS, 2017, 2 (01): : 111 - 127
[50] On the Diophantine Equation x(4)
Alvarado, Alejandra
Delorme, Jean-Joel
JOURNAL OF INTEGER SEQUENCES, 2014, 17 (11)

← 1 2 3 4 5 →