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arXiv · 1409.2704

Powers of two as sum of two generalized Fibonacci numbers

Diego Marques
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Abstract

For $k\geq 2$, the $k$-generalized Fibonacci sequence $(F_n^{(k)})_{n}$ is defined by the initial values $0,0,\ldots,0,1$ ($k$ terms) and such that each term afterwards is the sum of the $k$ preceding terms. In this paper, we search for powers of two of the form $F_n^{(k)}+F_m^{(k)}$. This work is related to a recent result by Bravo and Luca concerning the case $k=2$.

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Diego Marques. 2014-09-09. Powers of two as sum of two generalized Fibonacci numbers. https://arxiv.org/abs/1409.2704

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