A Diophantine equation in $k$-Fibonacci numbers and repdigits
Volume 152 / 2018
Colloquium Mathematicum 152 (2018), 299-315
MSC: Primary 11B39; Secondary 11J86.
DOI: 10.4064/cm7149-6-2017
Published online: 12 March 2018
Abstract
The $k$-generalized Fibonacci sequence $\{F_{n}^{(k)}\}_{n}$ starts with the $k$ values $0,\ldots ,0,1$ and each term afterwards is the sum of the $k$ preceding terms. We study which members of this sequence are sums of two repdigts, extending a result of Díaz and Luca (2011) regarding Fibonacci numbers with this property.
