International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 261-266

Sequences in power residue classes

Duncan A. Buell1 and Richard H. Hudson2

1Department of Computer Science, Louisiana State University, Baton Rouge 70803, LA, USA
2Department of Mathematics, University of South Carolina, Columbia 29208, SC, USA

Received 13 June 1985

Copyright © 1986 Duncan A. Buell and Richard H. Hudson. 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.


Using A. Well's estimates the authors have given bounds for the largest prime P0 such that all primes p>P0 have sequences of quadratic residues of length m. For m8 the smallest prime having m consecutive quadratic residues is 3(mod4) and P01(mod4). The reason for this phenomenon is investigated in this paper and the theory developed is used to successfully uncover analogous phenomena for rth power residues, r2, r even.