Turkish Journal of Mathematics
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.
DOI
10.3906/mat-2011-59
Keywords
Generalized Lucas number, repdigit, linear form in logarithms, reduction method
First Page
1166
Last Page
1179
Recommended Citation
RAYAGURU, S. G, & BRAVO, J. J (2021). Repdigits as sums of two generalized Lucas numbers. Turkish Journal of Mathematics 45 (3): 1166-1179. https://doi.org/10.3906/mat-2011-59
