International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 6, Pages 325-331
doi:10.1155/S0161171202007573

Differences between powers of a primitive root

Marian Vâjâitu1 and Alexandru Zaharescu1,2

1Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 70700, Romania
2Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green Street, Urbana 61801, IL, USA

Received 14 May 2001

Copyright © 2002 Marian Vâjâitu and Alexandru Zaharescu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the set of differences {gx−gy(modp):1≤x,   y≤N} where p is a large prime number, g is a primitive root (modp), and p2/3<N<p.