On the Diophantine equation ∑ _k=1⁵F_nk=2^a

2022/09/16 by Tiebekabe, Pagdame, Diouf, Ismaïla
#11B39 #11D61 #11J86 #FOS: Mathematics #G.4 #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2209.07871

Abstract

Let (F_n)_{n≥ 0} be the Fibonacci sequence given by F₀ = 0, F₁ = 1 and F_n+2 = F_n+1+F_n for n ≥ 0. In this paper, we have determined all the powers of 2 which are sums of five Fibonacci numbers with few exceptions that we characterize. We have also stated an open problem relating to the number of solutions of equations like those studied in this paper.

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