Solutions to $\sum_{i=1}^n 1/x_i=1$ in integers $p^a\,q^b$ with $p$ and $q$ two set primes

Abstract

We present an algorithm for computing all the solutions in not necessarily distinct integers to the decomposition of the unit into a sum of unit fractions with denominators $p^a.q^b$ where $p$ and $q$ are two distinct primes, each appearing at least once in the solution.