Repdigits as sums of three balancing numbers

Abstract Let { B n } n ≥0 be the sequence of Balancing numbers defined by B 0 = 0, B 1 = 1, and B n +2 = 6 B n +1 − B n for all n ≥ 0. In this paper, we find all repdigits in base 10 which can be written as a sum of three Balancing numbers.