Repdigits as absolute value of difference between Lucas and Fibonacci numbers

Abstract

In this paper, we investigate the Diophantine equation |L_n₁ − F_n₂| = d(10^m − 1) / 9, where (L_n)_{n ≥ 0} and (F_n)_{n ≥ 0} are respectively Lucas and Fibonacci sequences, d ∈ {1, ..., 9} and m ≥ 1. All solutions of the aforementioned equation are provided.