On the Addition of Two Cubes of Units and Nonunits mod pα

摘要

Let p ≡ 2 (mod 3) be an odd prime and α be a positive integer.In this paper,for any integer c,we obtain a formula for the number of solutions of the cubic congruence x3 + y3 ≡ c.(mod pα) with x,y units,nonunits and mixed pairs,respectively.We resolve a problem posed by Yang and Tang.