Pell and Pell-Lucas numbers which are concatenations of three repdigits

In this study, we focus on finding the Pell and Pell-Lucas numbers which are concatenations of three repdigits. We show that these numbers are 169, 408, 985 and 198, 478, 1154, respectively. We use a lemma that provides a large upper bound for the subscript n in the equations and Baker’s theory of lower bounds for a nonzero linear form in logarithms of algebraic numbers. In addition, continued fraction expansions of some irrational numbers were calculated to show that some inequalities have no solution.