On perfect powers that are sum of two balancing numbers

被引：0

作者：

Bhoi, Pritam Kumar ^{[1
]}

Rout, Sudhansu Sekhar ^{[2
]}

Panda, Gopal Krishna ^{[1
]}

机构：

[1] Natl Inst Technol, Dept Math, Rourkela 769008, India

[2] Natl Inst Technol, Dept Math, Kozhikode 673601, India

来源：

PERIODICA MATHEMATICA HUNGARICA | 2024年 / 88卷 / 01期

关键词：

Diophantine equation; Linear recurrence sequence; Perfect power; Balancing number; DIOPHANTINE EQUATIONS; FIBONACCI;

D O I：

10.1007/s10998-023-00540-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let B-k denote the k-th term of balancing sequence. In this paper we find all positive integer solutions of the Diophantine equation B-n + B-m = x(q) in variables (m, n, x, q) under the assumption n equivalent to m (mod 2). Furthermore, we study the Diophantine equation B-n(3) +/- B-m(3) = x(q) with positive integer q >= 3 and gcd(B-n, B-m) = 1.

引用

页码：93 / 101

页数：9

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