MMN-2852

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

**Z. Şiar**, Bingöl University, Department of Mathematics, Bingöl, Turkey,`zsiar@bingol.edu.tr`

**R. Keskin**, Sakarya University, Department of Mathematics, Sakarya, Turkey,`rkeskin@sakarya.edu.tr`

## Abstract

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.

Vol. 22 (2021), No. 2, pp. 951-960

DOI: 10.18514/MMN.2021.2852