Repdigits as sums of two lucas numbers

Abstract

Let (Ln) be the Lucas sequence defined by Ln = Ln−1 +Ln−2 for n ≥ 2 with initial conditions L0 = 2 and L1 = 1. A repdigit is a nonnegative integer whose digits are all equal. In this paper, we show that if Ln + Lm is a repdigit, then Ln + Lm = 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 77, 333. © 2020, Tsing Hua University. All rights reserved.