Repdigits base b as products of two Lucas numbers

Abstract

Let (L_n ) be the sequence of Lucas numbers defined by L ₀ = 2, L ₁ = 1, and L_n = L _n−1 + L _n−2 for n ≥ 2. Let 0 ≤ m ≤ n and b = 2, 3, 4, 5, 6, 7, 8, 9. In this study, we show that if L_mL_n is a repdigit in the base b and has at least two digits, then