On the problem of Pillai with Pell numbers, Pell–Lucas numbers and powers of 3

Abstract

Let [Formula: see text] be the sequence of Pell numbers defined by [Formula: see text], [Formula: see text] and [Formula: see text] for all [Formula: see text] and let [Formula: see text] be its companion sequence, the Pell–Lucas numbers defined by [Formula: see text] and [Formula: see text] for all [Formula: see text]. In this paper, we find all integers [Formula: see text] admitting at least two representations as a difference between a Pell number or a Pell–Lucas number and a power of [Formula: see text]