Abstract

We give an algorithm that produces all solutions of the equation [Formula: see text] in integers of the form [Formula: see text], where [Formula: see text] is a fixed positive integer that is not a power of [Formula: see text], [Formula: see text] is an element of [Formula: see text] that can vary from term to term, and [Formula: see text] is a nonnegative integer that can vary from term to term. We also completely characterize the pairs [Formula: see text] for which this equation has a nontrivial solution in integers of this form.

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