Ratios of sums of two Fibonacci numbers equal to powers of 2

Jhon J. Bravo, Maribel Díaz, Florian Luca

Abstract


In this paper, we find all solutions to the Diophantine equation $F_n+F_m=2^a(F_r+F_s)$, where $\{F_k\}_{k\ge 0}$ is the Fibonacci sequence. This paper continues and extends a previous work which investigated the powers of 2 which are sums of two Fibonacci numbers.

Keywords


Fibonacci number, Zeckendorf representation, linear form in logarithms, reduction method

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ISSN: 1331-0623 (Print), 1848-8013 (Online)