On Egyptian Fractions of Length 3

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 m1,...,mksuch that (Formula presented). Let Ak(n) be the number of solutions a to this equation. In this article, we give a formula for A2(p) and a parametrization for Egyptian fractions of length 3, which allows us to give bounds to A3(n), to fa(n) = (Formula presented), and finally to F(n) = (Formula presented).