On solutions of ∑i=1n1/xi = 1 in integers of the form 2akb

We give an algorithm that produces all solutions of the equation [Formula: see text] in integers of the form [Formula: see text], where k is a fixed positive integer that is not a power of 2, a is an element of [Formula: see text] that can vary from term to term, and b 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.