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arXiv · 2104.12593

On sums of Fibonacci numbers with few binary digits

Ingrid Vukusic·Volker Ziegler
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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.

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Ingrid Vukusic, Volker Ziegler. 2021-04-26. On sums of Fibonacci numbers with few binary digits. https://arxiv.org/abs/2104.12593

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