International Journal of Mathematics and Mathematical Sciences 
Volume 9 (1986), Issue 2, Pages 261-266
doi:10.1155/S0161171286000315

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

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.