The Maximal Difference of Different Powers of an Element Modulo n

The Maximal Difference of Different Powers of an Element Modulo n

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−...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of mathematics (Hidawi) 2021, Vol.2021, p.1-5
Hauptverfasser: Qi, Jinyun, Xu, Zhefeng
Format: Artikel
Sprache:eng
Schlagworte:
Inequality
Integers
Lower bounds
Mathematical functions
Mathematics
Theorems
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2021/8002211