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

Document Type : Research Paper

Authors

1 Department of Mathematics and Computer Science, University of Cheikh Anta Diop, Dakar, Senegal.

2 Department of Mathematics and Computer Science, University of Cheikh Anta Diop,, Dakar, Senegal.

10.22124/jart.2021.19294.1266

Abstract

Let $(F_n)_{n\geq 0}$ be the Fibonacci sequence given by $F_0 = 0, F_1 = 1$ and $F_{n+2} = F_{n+1}+F_n$ for $n \geq 0$. In this paper, we solve all powers of two which are sums of four Fibonacci numbers with a few exceptions that we characterize.

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