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Note on Burde's Rational Biquadratic Reciprocity Law

Published online by Cambridge University Press:  20 November 2018

Kenneth S. Williams
Kenneth S. Williams*
Affiliation:
Carleton University Ottawa, Canada
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A short proof is given of a biquadratic reciprocity law proved by Burde in 1969.

Let p and q be primes ≡1 (mod 4) such that (p | q) = (q | p) = 1. Then there are integers a, b, c, d with

Set

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 145 - 146
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Bachmann, P., Die Lehre von der Kreisteilung, Leipzig (1872), equation (9), p. 169.Google Scholar
2. Burde, K., Ein rationales biquadratisches Reziprozitätsgesetz, Jour, reine angew. Math., 235 (1969), 175-184.Google Scholar
3. Dörrie, H., Das quadratische Reciprocitätsgesetz in quadratischen Zahlkörper mit der Classenzahl 1, Gott. Diss., 1898.Google Scholar
4. Lehmer, E., Criteria for cubic and quartic residuacity, Mathematika 5 (1958), 20-29.Google Scholar
5. Lehmer, E., On the quadratic character of some quadratic surds, Jour, reine angew. Math., 250 (1971), 42-48.Google Scholar