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

Jhon J. Bravo; Maribel Díaz; Florian Luca

Vol. 25 No. 2 (2020)

Regular Articles

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

Published 2020-09-23

Jhon J. Bravo
Maribel Díaz
Florian Luca

Jhon J. Bravo
Departamento de Matematicas, Universidad del Cauca

Maribel Díaz
Universidad del Cauca

Florian Luca
University of the Witwatersrand

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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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Supplementary File(s)

3569-Bravo

Author Biography

Jhon J. Bravo

Departamento de Matematicas, Universidad del Cauca

Maribel Díaz

Departamento de Matemáticas

Florian Luca

School of Mathematics