A Diophantine equation in $k$-Fibonacci numbers and repdigits
Copyright policy )A Diophantine equation in $k$-Fibonacci numbers and repdigits
Summary: The \(k\)-generalized Fibonacci sequence \(\{F_{n}^{(k)}\}_{n}\) starts with the \(k\) values \(0,\dots ,0,1\) 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 \textit{S. Díaz Alvarado} and \textit{F. Luca} [Aportaciones Mat., Investig. 20, 97--108 (2011; Zbl 1287.11021)] regarding Fibonacci numbers with this property.
- Max Planck Institute for Mathematics Germany
- University of the Witwatersrand South Africa
- University of Cauca Colombia
- University of Valle Colombia
- Max Planck Society Germany
repdigits, generalized Fibonacci numbers, Fibonacci and Lucas numbers and polynomials and generalizations, lower bounds for nonzero linear forms in logarithms of algebraic numbers, Radix representation; digital problems, Linear forms in logarithms; Baker's method
repdigits, generalized Fibonacci numbers, Fibonacci and Lucas numbers and polynomials and generalizations, lower bounds for nonzero linear forms in logarithms of algebraic numbers, Radix representation; digital problems, Linear forms in logarithms; Baker's method
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