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

[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.

[学科分类] 数学（综合）

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