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arXiv · 1409.8514

Powers of two as sums of two $k-$Fibonacci numbers

Jhon J. Bravo·Carlos A. Gómez·Florian Luca
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Abstract

For an integer $k\geq 2$, let $(F_{n}^{(k)})_{n}$ be the $k-$Fibonacci sequence which starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we search for powers of 2 which are sums of two $k-$Fibonacci numbers. The main tools used in this work are lower bounds for linear forms in logarithms and a version of the Baker--Davenport reduction method in diophantine approximation. This paper continues and extends the previous work of \cite{BL2} and \cite{BL13}.

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Jhon J. Bravo, Carlos A. Gómez, Florian Luca. 2014-09-30. Powers of two as sums of two $k-$Fibonacci numbers. https://arxiv.org/abs/1409.8514

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