Cubic and Biquadratic Reciprocity

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


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.


Primary Element Residue Class Regular Polygon Quadratic Residue Residue Character 
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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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