On the Diophantine equation $\displaystyle \sum _{k=1}^{5}F_{n_k}=2^a$

Pagdame Tiebekabe; Ismaïla Diouf

On the Diophantine equation $\displaystyle \sum _{k=1}^{5}F_{n_k}=2^a$

Number Theory 2022-09-27 v2

Authors: Pagdame Tiebekabe , Ismaïla Diouf

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 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.

Keywords

diophantine equation fibonacci numbers powers of 2 open problem

Cite

@article{arxiv.2209.07871,
  title  = {On the Diophantine equation $\displaystyle \sum _{k=1}^{5}F_{n_k}=2^a$},
  author = {Pagdame Tiebekabe and Ismaïla Diouf},
  journal= {arXiv preprint arXiv:2209.07871},
  year   = {2022}
}

Comments

This article was presented at the 20th International Conference on Fibonacci Numbers and their Applications in Bosnia at the University of Sarajevo. arXiv admin note: substantial text overlap with arXiv:2202.10127

On the Diophantine equation $\displaystyle \sum _{k=1}^{5}F_{n_k}=2^a$

Abstract

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