On solutions of the Diophantine equation $F_{n_{1}}+F_{n_{2}}+F_{n_{3}}+F_{n_{4}}=2^a$

Abstract

Let (F n ) n≥0 be the Fibonacci sequence given by F 0 = 0, F 1 = 1 and F n+2 = F n+1 + F n for n ≥ 0. In this paper, we solve all powers of two which are sums of four Fibonacci numbers with a few exceptions that we characterize.