$k$-Pell-Lucas numbers as Product of Two Repdigits

Abstract

For any integer $k\ge 2$, let $\{Q_n^{(k)}{\}}_{n\ge -(k-2)}$ denote the $k$-generalized Pell-Lucas sequence which starts with $0,\dots ,2,2$($k$ terms) where each next term is the sum of the $k$ preceding terms. In this paper, we find all the $k$-generalized Pell-Lucas numbers that are the product of two repdigits. This generalizes a result of Erduvan and Keskin \cite{Erduvan1} regarding repdigits of Pell-Lucas numbers.

15 pages