Arkiv för Matematik

  • Ark. Mat.
  • Volume 12, Number 1-2 (1974), 217-220.

On the least K-th power non-residue

Richard H. Hudson

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Abstract

LetCk(p) denote the group of the k-th powers (modp)p a prime with (k, p −1)>1. A new elementary result for the least k-th power non-residue is given and the result is applied to finding a new elementary bound for the maximum number of consecutuve integers in any coset of Ck(p).

Article information

Source
Ark. Mat., Volume 12, Number 1-2 (1974), 217-220.

Dates
Received: 26 May 1972
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485896203

Digital Object Identifier
doi:10.1007/BF02384758

Mathematical Reviews number (MathSciNet)
MR360435

Zentralblatt MATH identifier
0307.10001

Rights
1974 © Institut Mittag-Leffler

Citation

Hudson, Richard H. On the least K -th power non-residue. Ark. Mat. 12 (1974), no. 1-2, 217--220. doi:10.1007/BF02384758. https://projecteuclid.org/euclid.afm/1485896203


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References

  • Brauer, A., Über den kleinsten quadratischen Nichtrest, Math. Z. 33 (1931), 161–176.
  • ——, Über die Verteilung der Potenzreste, Math. Z. 35 (1932), 39–50.
  • Brauer, A. and Reynolds, T. L., On a theorem of Aubrey-Thue, Canad. J. Math. 3 (1951), 367–374.
  • Burgess, D. A., A note on the distribution of residues and non-residues, J. London Math. Soc. 38 (1963), 253–256.
  • Davenport, H. and Erdös, P., The distribution of quadratic and higher residues, Publ. Math. Debrecen 2 (1952), 252–265.
  • Hudson, R. H., On sequences of consecutive quadratic non-residues, J. Number Theory 3 (1971), 178–181.
  • ——, On the distribution of k-th power non-residues, Duke J. 39 (1972), 85–88.
  • Lehmer, D. H., Lehmer, E. and Shanks, D., Integer sequences having prescribed quadratic character. Math. Comp. 24 (1970), 433–451.
  • Nagell, T., Den minste positive nte ikke-potensrest modulo p, Norsk Mat. Tidsskr. 34 (1952), p. 13.
  • Rédei, L., Die Existenz eines Ungeraden quadratischen Nichtrestes mod p im Interval 1, $\sqrt p $ . Acta Sci. Math. (Szeged) 15 (1953), 12–19.
  • Skolem, T., Eksistens av en nte ikke-potensrest (modp) mindre enn $\sqrt p $ , Norsk Mat. Tidsskr. 33 (1951), 123–126.
  • Vinogradov, I. M., Elements of number theory, Dover Publications, Inc., 1954.
  • Western, A. E. and Miller, J. C. P., Tables of indices and primitive roots, Royal Soc. Math. Tables Vol. 9, Cambridge, 1968.