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.
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页码：93 / 101
页数：9
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