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AN ELEMENTARY PROOF IN THE THEORY OF QUADRATIC RESIDUES

  • Kohnen, Winfried
  • Published : 2008.05.31

Abstract

We will give a short and elementary proof of the existence of infinitely many primes p such that a given positive integer a congruent 3 modulo 4 is a quadratic non-residue modulo p.

Keywords

prime;quadratic residue

References

  1. M. Ram Murty and N. Thain, Primes in certain arithmetic progressions, Preprint 2007
  2. W. Schwarz, Einfuhrung in Methoden und Ergebnisse der Primzahltheorie, Bibliographisches Institut, Mannheim-Vienna-Zurich, 1969
  3. J.-P. Serre, A Course in Arithmetic, Translated from the French. Graduate Texts in Mathematics, No. 7. Springer-Verlag, New York-Heidelberg, 1973

Cited by

  1. ON THE dTH POWER RESIDUE SYMBOL OF FUNCTION FIELDS vol.46, pp.6, 2009, https://doi.org/10.4134/BKMS.2009.46.6.1151