On perfect powers that are sums of two Fibonacci numbers

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 $n\equiv m(\mathrm{mod}2)$.

arXiv comment6 pages