Sequences in power residue classes
Duncan A. Buell, Richard H. Hudson · International Journal of Mathematics and Mathematical Sciences · 1986
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.