Solutions to ${\sum }_{i=1}^{n}1\mathrm{/}{x}_i=1$ in integers $p^a{q}^b$ with $p$ and $q$ two set primes

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 $p^a\mathrm{.}{q}^b$ where $p$ and $q$ are two distinct primes, each appearing at least once in the solution.