On perfect powers that are sums of two Fibonacci numbers

2017/06/30 by Luca, Florian, Patel, Vandita · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1706.10294

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 ≥ 2. We find all solutions under the assumption n ≡ m \pmod2.

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