On sums of Fibonacci numbers with few binary digits

Ingrid Vukusic; Volker Ziegler

On sums of Fibonacci numbers with few binary digits

Number Theory 2021-04-27 v1

Authors: Ingrid Vukusic , Volker Ziegler

Abstract

In this paper we completely solve the Diophantine equation $F_n+F_m=2^{a_1}+2^{a_2}+2^{a_3}+2^{a_4}+2^{a_5}$ , where $F_k$ denotes the $k$ -th Fibonacci number. In addition to complex linear forms in logarithms and the Baker-Davenport reduction method, we use $p$ -adic versions of both tools.

Keywords

fibonacci numbers diophantine equation binary digits linear forms in logarithms baker-davenport reduction p-adic

Cite

@article{arxiv.2104.12593,
  title  = {On sums of Fibonacci numbers with few binary digits},
  author = {Ingrid Vukusic and Volker Ziegler},
  journal= {arXiv preprint arXiv:2104.12593},
  year   = {2021}
}

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