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Keywords:
$k$-Fibonacci numbers; $k$-Lucas numbers; repdigits; linear form in logarithms; reduction method
$k$-Fibonacci numbers; $k$-Lucas numbers; repdigits; linear form in logarithms; reduction method
Summary:
For an integer $k\geq 2$, let $(F_{n}^{(k)})_{n\geq -(k-2)}$, $(L_{n}^{(k)})_{n \geq -(k-2)}$ be $k$-Fibonacci and $k$-Lucas sequences, respectively. For these sequences the first $k$ terms are $0,\ldots ,0,1$ and $0,\ldots ,0,2,1$, respectively, and each term afterwards is the sum of the preceding $k$ terms. In this paper, we determine all possibilities such that $F_{n}^{(k)} L_{m}^{(k)}$ can represent a repdigit.
References:
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