MMN-1505
Powers of two as sums of two $k-$Fibonacci numbers
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}.
Vol. 17 (2016), No. 1, pp. 85-100
DOI: 10.18514/MMN.2016.1505