Let a, n be positive integers that are relatively prime.We say that a/n can be represented as an Egyptian fraction of length k if there exist positive integers m 1 , . . ., m k such that a n = 1be the number of solutions a to this equation.In this article, we give a formula for A 2 (p) and a parametrization for Egyptian fractions of length 3, which allows us to give bounds toand finally to F (n) = #{(a, m 1 , m 2 , m 3 ) : a n =