Program for Egyption Fraction Egyptian fractions are almost always required to exclude repeated terms, since representations such as 1/5+1/5+1/5 are trivial. Any rational number has representations as an Egyptian fraction with arbitrarily many terms and with arbitrarily large denominators, although for a given fixed number of terms, there are only finitely many. Fibonacci proved that any fraction can be represented as a sum of distinct unit fractions (Hoffman 1998, p. 154). An infinite chain of unit fractions can be constructed using the identity
1/a=1/(a+1)+1/(a(a+1)).