Pell and Pell-Lucas numbers as difference of two repdigits

Abstract

Let $\{P_n{\}}_{n\ge 0}$ be the sequence of Pell numbers defined by $P_0=0$, $P_1=1$ and $P_{n+2}=2P_{n+1}+P_n$ for all $n\ge 0$ and let $\{Q_n{\}}_{n\ge 0}$ be its companion sequence, the Pell-Lucas numbers defined by $Q_0=Q_1=2$ and $Q_{n+2}=2Q_{n+1}+Q_n$ for all $n\ge 0$ . In this paper, we find all Pell and Pell-Lucas numbers which can be written as difference of two repdigits. It is shown that the largest Pell and Pell-Lucas numbers which can be written as difference of two repdigits are $$P_6=70=77-7and{Q}_7=478=555-77.$$

to appear in Afrika Matematika