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.
Generalized Lucas number, repdigit, linear form in logarithms, reduction method
RAYAGURU, SAI GOPAL and BRAVO, JHON JAIRO
"Repdigits as sums of two generalized Lucas numbers,"
Turkish Journal of Mathematics: Vol. 45:
3, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss3/6