On perfect powers which are sum or difference of two Lucas numbers

Miskolc Mathematical Notes

article

Z. Şiar¹  R. Keskin² 

[1] Bingol University, Department of Mathematics;Sakarya University, Department of Mathematics

关键词: Fibonacci and Lucas numbers;    Exponential equations;    Linear forms in logarithms;    Baker’s method;   

DOI  :  10.18514/MMN.2021.2852

学科分类：数学（综合）

来源: Miskolci Egyetem

【 摘 要 】

In this paper, we consider the Diophantine equation L_{n}±L_{m}=kx² with k∈{1,2} and we find all solutions of this equation in nonnegative integers n,m, and x when n≡m(mod2). With the help of these solutions, we solve the equation L_{n}-L_{m}=2^{a}. In order to solve the last equation, we also use lower bounds for linear forms in logarithms and a version of the Baker-Davenport reduction method in diophantine approximation.

【 授权许可】

CC BY