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

作　　者：Cuifang SUN Zhi CHENG 

机构地区：[1]School of Mathematics and Computer Science, Anhui Normal University, Anhui 241003, P. R. China

出　　处：《Journal of Mathematical Research with Applications》2017年第3期274-280,共7页数学研究及应用（英文版）

基　　金：Supported by the Research Culture Fundation of Anhui Normal University(Grant No.2014xmpy11);the National Natural Science Foundation of China(Grant No.11471017)

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 x^3＋ y^3≡ c（mod p~α） with x, y units, nonunits and mixed pairs, respectively. We resolve a problem posed by Yang and Tang.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 x^3＋ y^3≡ c（mod p~α） with x, y units, nonunits and mixed pairs, respectively. We resolve a problem posed by Yang and Tang.

关 键 词：residue classes cubes of units exponential sum 

分 类 号：O156[理学—数学]