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

Abstract

For an integer $k\ge 2$, let $(F_n^{(k)}{)}_n$ be the $k-$Fibonacci sequence which starts with $0,\dots ,0,1$ ($k$ 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}.

15 pages, no figure (Submitted). arXiv admin note: text overlap with arXiv:1402.4085

Cited by in corpus (1)

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