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 x 2 ≡ a (p) solvable ? Here a is a fixed integer. If the same question is considered for congruences x n ≡ 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.


Finite Field Primary Element Residue Class Quadratic Residue Primary Complex 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Kenneth Ireland
  • Michael Rosen
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

Personalised recommendations