Repdigits as sums of two generalized Lucas numbers

Authors: SAI GOPAL RAYAGURU, JHON JAIRO BRAVO

Abstract: A generalization of the well-known Lucas sequence is the $k$-Lucas sequence with some fixed integer $k \geq 2$. The first $k$ terms of this sequence are $0,\ldots,0,2,1$, and each term afterwards is the sum of the preceding $k$ terms. In this paper, we determine all repdigits, which are expressible as sums of two $k$-Lucas numbers. This work generalizes a prior result of Şiar and Keskin who dealt with the above problem for the particular case of Lucas numbers and a result of Bravo and Luca who searched for repdigits that are $k$-Lucas numbers.

Keywords: Generalized Lucas number, repdigit, linear form in logarithms, reduction method

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