International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 261-266
doi:10.1155/S0161171286000315
Sequences in power residue classes
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.
Abstract
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 m≤8 the smallest prime having m consecutive quadratic residues is ≡3(mod4) and P0≡1(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, r≥2, r even.