Sums of Fibonacci numbers close to a power of 2

Elchin Hasanalizade

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arXiv · 2206.10356

Sums of Fibonacci numbers close to a power of 2

Elchin Hasanalizade

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Abstract

In this paper, we find all sums of two Fibonacci numbers which are close to a power of 2. As a corollary, we also determine all Lucas numbers close to a power of 2. The main tools used in this work are lower bounds for linear forms in logarithms due to Matveev and Dujella-Peth\"{o} version of the Baker-Davenport reduction method in diophantine approximation. This paper continues and extends the previous work of Chern and Cui.

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Elchin Hasanalizade. 2022-06-14. Sums of Fibonacci numbers close to a power of 2. https://arxiv.org/abs/2206.10356

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