When is a Fraction a Unique Sum of Two Distinct Unit Fractions

Under what conditions is this true?

A unit fraction is a fraction with a numerator of one. The ancient Egyptians used sums of unit fractions as a way of expressing more general rational numbers — leading to the term Egyptian fractions.

In fact, across a wide variety of mathematics we see an interest in summing unit fractions. Many constants are expressed as the infinite sum of unit fractions, including Apery’s constant and the reciprocal Fibonacci constant. We also see unit…