Generalized Fibonacci and Lucas Numbers of the form $5x^{2}$

Refik Keskin; Olcay Karaatlı

paper

Generalized Fibonacci and Lucas Numbers of the form $5 x^{2}$

arXiv:1206.4174

Abstract

Let $(U_{n} (P, Q)$ and $(V_{n} (P, Q)$ denote the generalized Fibonacci and Lucas sequence, respectively. In this study, we assume that $Q = 1.$ We determine all indices $n$ such that $U_{n} = 5 □$ and $U_{n} = 5 U_{m} □$ under some assumptions on $P .$ We show that the equation $V_{n} = 5 □$ has the solution only if $n = 1$ for the case when is odd. Moreover, we show that the equation $V_{n} = 5 V_{m} □$ has no solutions.

Generalized Fibonacci and Lucas Numbers of the form 5x2

Abstract

Generalized Fibonacci and Lucas Numbers of the form $5 x^{2}$