Research Article

Repdigits base b as products of two Lucas numbers

Published in: Quaestiones Mathematicae
Volume 44 , issue 10 , 2021 , pages: 1283–1293

DOI: 10.2989/16073606.2020.1787539

Author(s): Fatih Erduvan , Turkey , Refik Keskin , Turkey , Zafer Şiar , Turkey

Keywords: 11B39 , 11J86 , 11D61 , 11B39 , 11J86 , 11D61

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

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