Cubic and Biquadratic Reciprocity

  • Kenneth Ireland
  • Michael Rosen
Part of the Graduate Texts in Mathematics book series (GTM, volume 84)

Abstract

In Chapter 5 we saw that the law of quadratic reciprocity provided the answer to the question. For which primes p is the congruence x2 ≡ a (p) solvable? Here a is a fixed integer. If the same question is considered for congruences xn ≡ a (p), n a fixed positive integer, we are led into the realm of the higher reciprocity laws. When n = 3 and 4 we speak of cubic and biquadratic reciprocity.

Keywords

Primary Element Residue Class Regular Polygon Quadratic Residue Residue Character 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1982

Authors and Affiliations

  • Kenneth Ireland
    • 1
  • Michael Rosen
    • 2
  1. 1.Department of MathematicsUniversity of New BrunswickFrederictonCanada
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA

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