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 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations