Generalized Fibonacci and Lucas numbers of the form 5x(2)

Abstract

Let (U-n(P, Q) and (V-n(P, Q) denote the generalized Fibonacci and Lucas sequences, respectively. In this study, we assume that Q = 1. We determine all indices n such that U-n = 5 square and U-n = 5U(m)square under some assumptions on P. We show that the equation Vn = 5 square has a solution only if n = 1 for the case when P is odd. Moreover, we show that the equation V-n = 5V(m)square has no solutions.