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


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