The Maximal Difference of Different Powers of an Element Modulo n - Jinyun Qi; Zhefeng Xu (Journal of Mathematics)
In this paper, we investigate the maximal difference of integer powers of an element modulo n. Let an denote the integer b with 1≤b≤n such that a≡bmod n for any integer a. Using the bounds for exponential sums, we obtain a lower bound of the function Hm1,m2n:=maxam1n−am2n:1≤a≤n,a,n=1, which gives n−Hm1,m2n=On3/4+o1.