Double Exponential Lower Bound for the Number of Representations of Unity by Egyptian Fractions

摘要

Egyptian fractions appeared in the Ahmes Mathematical Papyrus (Rhind Papyrus) , one of the oldest mathematical manuscripts dating back to around 1650 B. C. The Egyptian fraction representation of a positive rational number r is a representation of the form r=1/x_1+…+1/x_n, 1≤x_1＜…x_n, where x_1,..., x_n are positive integers.