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

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.

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.

Keywords