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

Tiebekabe, P.; Diouf, I.

doi:10.22124/jart.2021.19294.1266

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

P. Tiebekabe ¹
I. Diouf ²

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.

Keywords

Linear forms in logarithm
Diophantine equations
Fibonacci sequence
Lucas sequence
perfect powers

Volume 9, Issue 2
December 2021
Pages 131-148

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

Volume 9, Issue 2December 2021Pages 131-148

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Volume 9, Issue 2
December 2021
Pages 131-148