Pell or Pell-Lucas numbers as concatenations of two repdigits in base $b$

Abstract

Let $b$ be a positive integer such that $2\le b\le 10$. In this study, we find all Pell or Pell-Lucas numbers as concatenations of two repdigits in base $b$. As a corollary, it is show that the largest Pell or Pell-Lucas numbers which can be expressible as a concatenations of two repdigits in base $b$ are $P_{11}=5741$ and $Q_5=82$, respectively.

17 pages