On the problem of Pillai with Padovan numbers and powers of 3

Abstract Let { P n } n ≥0 be the sequence of Padovan numbers defined by P 0 = 0, P 1 = 1, P 2 = 1, and P n +3 = P n +1 + P n for all n ≥ 0. In this paper, we find all integers c admitting at least two representations as a difference between a Padovan number and a power of 3.