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AN ELEMENTARY PROOF IN THE THEORY OF QUADRATIC RESIDUES

  • 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.

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