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On solutions of $\sum_{i=1}^n 1/x_i = 1$ in integers of the form $2^a k^b$ (2402.09515v3)

Published 14 Feb 2024 in math.NT and math.CO

Abstract: We give an algorithm that produces all solutions of the equation $\sum_{i=1}n 1/x_i = 1$ in integers of the form $2a kb$, where $k$ is a fixed positive integer that is not a power of $2$, $a$ is an element of ${0,1,2}$ 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 $(k,n)$ for which this equation has a nontrivial solution in integers of this form.

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