On the difference between an integer and its m-th power mod n  

作　　者：XU ZheFeng 

机构地区：[1]Department of Mathematics,Northwest University

出　　处：《Science China Mathematics》2013年第8期1597-1606,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 11001218);the Research Fund for the Doctoral Program of Higher Education of China (Grant No.20106101120001)

摘　　要：For any real constants λ1, λ2 C （0, 1], let n ≥ max{[1/λ1 ], [1/λ2]}, vn ≥ 2 be integers. Suppose integers a C [1, λ1n] and b E [1, λ2n] satisfy the congruence b ≡ am （rood n）. The main purpose of this paper is to study the mean value of （a - b）2k for any fixed positive integer k and obtain some sharp asymptotic formulae.For any real constants λ1,λ2 ∈(0,1],let n max{[1/λ1],[1/λ2]},m 2 be integers.Suppose integers a ∈[1,λ1n] and b∈[1,λ2n] satisfy the congruence b ≡ a m(mod n).The main purpose of this paper is to study the mean value of(a-b) 2k for any fixed positive integer k and obtain some sharp asymptotic formulae.

关 键 词：INTEGER m-th power mod n difference incomplete interval 

分 类 号：O156[理学—数学]