The search for expansions of rational numbers as sums of unit fractions dates to the mathematics of ancient Egypt, in which Egyptian fraction expansions of this type were used as a notation for recording fractional quantities. The Egyptians produced tables such as the Rhind Mathematical Papyrus table of expansions of fractions of the form , most of which use either two or three terms. Egyptian fractions typically have an additional constraint, that all of the unit fractions be distinct from each other, but for the purposes of the Erdős–Straus conjecture this makes no difference: if can be expressed as a sum of three unit fractions, it can also be expressed as a sum of three distinct unit fractions by repeatedly replacing any duplicated fraction by one of the following two expansions,