On perfect powers that are sums of two Fibonacci numbers

Florian Luca, Vandita Patel

Published 2017-06-30Version 1

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 $n \equiv m \pmod{2}$.