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Abstract

Let {P n}n≥0 be the sequence of Padovan numbers defined by P0 = 0, P1 = 1, P2 = 1, and Pn+3 = Pn+1 + Pn 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.

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