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arXiv · 1206.4174

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

Refik Keskin·Olcay Karaatlı
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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\square $ and $U_{n}=5U_{m}\square $ under some assumptions on $P.$ We show that the equation $V_{n}=5\square $ has the 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.

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Refik Keskin, Olcay Karaatlı. 2012-06-19. Generalized Fibonacci and Lucas Numbers of the form $5x^{2}$. https://arxiv.org/abs/1206.4174

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