Repdigits As Sums Of Two Lucas Numbers

Abstract

Let (L-n) be the Lucas sequence defined by L-n = Ln-1 + Ln-2 for n >= 2 with initial conditions L-0 = 2 and L-1 = 1. A repdigit is a nonnegative integer whose digits are all equal. In this paper, we show that if L-n + L-m is a repdigit, then L-n + L-m = 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 77, 333.