Sequences in power residue classes

Duncan A. Buell and Richard H. Hudson

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-6

Abstract:

Using A. Well's estimates the authors have given bounds for the largest prime P 0 such that all primes p > P 0 have sequences of quadratic residues of length m . For m ≤ 8 the smallest prime having m consecutive quadratic residues is ≡ 3 ( mod 4 ) and P 0 ≡ 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 r t h power residues, r ≥ 2 , r even.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:516483

DOI: 10.1155/S0161171286000315

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