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arXiv · 1706.10294

On perfect powers that are sums of two Fibonacci numbers

Florian Luca·Vandita Patel
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Abstract

We study the equation $F_n + F_m = y^p$, where $F_n$ and $F_m$ are respectively the $n$-th and $m$-th Fibonacci numbers and $p \ge 2$. We find all solutions under the assumption $n \equiv m \pmod{2}$.

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Florian Luca, Vandita Patel. 2017-06-30. On perfect powers that are sums of two Fibonacci numbers. https://arxiv.org/abs/1706.10294

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