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On the quadratic reciprocity law

Part of: Elementary number theory

Published online by Cambridge University Press:  09 April 2009

G. Rousseau
G. Rousseau
Affiliation:
The University Leicester, LE1 7RH, England
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Abstract

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A version of Gauss's fifth proof of the quadratic reciprocity law is given which uses only the simplest group-theoretic considerations (dispensing even with Gauss's Lemma) and makes manifest that the reciprocity law is a simple consequence of the Chinese Remainder Theorem.

MSC classification

Secondary: 11A15: Power residues, reciprocity
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 3 , December 1991 , pp. 423 - 425
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Bachmann, P., Niedere Zahlentheorie I, (Teubner, Leipzig, 1910, reprinted Chelsea, New York, 1968).Google Scholar
[2]Dirichlet, P. G. L., ‘Démonstrations nouvelles de quelques théorèmes relatifs aux nombres’, J. Reine Angew. Math. 3 (1828), 390–393.Google Scholar
[3]Gauss, C. F., Werke II, (K. Gesell. Wiss., Göttingen, 1870), 47–64.Google Scholar
[4]Schmidt, H., ‘Drei neue Beweise des Reciprocitätssatzes in der Theorie der quadratischen Reste’, J. Reine Angew. Math. 111 (1893), 107–120.CrossRefGoogle Scholar