Using A. Weil’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(mod 4) and P0 ≡ 1 (mod 4). 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.
Published in International Journal of Mathematics and Mathematical Sciences, Volume 9, Issue 2, 1986, pages 261-266.
Buell, D.A. and Hudson, R.H. (1986). Sequences in power residue classes. International Journal of Mathematics and Mathematical Sciences, 9(2), 261-266.
Copyright © 1986 Hindawi Publishing Corporation.