Original scientific paper

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

Jhon J. Bravo orcid.org/0000-0001-7772-9260 ; Departamento de Matemáticas, Universidad del Cauca, Popayán, Colombia
Maribel Díaz ; Departamento de Matemáticas, Universidad del Cauca, Popayán, Colombia
Florian Luca ; School of Mathematics, University of the Witwatersrand, South Africa

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

Hrčak ID:

244257

URI

https://hrcak.srce.hr/244257

Publication date:

29.9.2020.

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