The Maximal Difference of Different Powers of an Element Modulo n

Jinyun Qi, Zhefeng Xu and Ali Jaballah

Journal of Mathematics, 2021, vol. 2021, 1-5

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8002211

DOI: 10.1155/2021/8002211

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