Products of Three $k-$Generalized Lucas Numbers as Repdigits

Abstract

Let $k\ge 2$ and let $(L_n^{(k)}{)}_{n\ge 2-k}$ be the $k-$generalized Lucas sequence with certain initial $k$ terms and each term afterward is the sum of the $k$ preceding terms. In this paper, we find all repdigits which are products of arbitrary three terms of $k-$generalized Lucas sequences. Thus, we find all non negative integer solutions of Diophantine equation $L_n^{(k)}{L}_m^{(k)}{L}_l^{(k)}=a\left(\frac{10^d-1}{9}\right)$ where $n\ge m\ge l\ge 0$ and $1\le a\le 9.$