Note on Burde's Rational Biquadratic Reciprocity Law
Canadian mathematical bulletin, Tome 20 (1977) no. 1, pp. 145-146

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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
Williams, Kenneth S. Note on Burde's Rational Biquadratic Reciprocity Law. Canadian mathematical bulletin, Tome 20 (1977) no. 1, pp. 145-146. doi: 10.4153/CMB-1977-026-6
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[1] 1. Bachmann, P., Die Lehre von der Kreisteilung, Leipzig (1872), equation (9), p. 169. Google Scholar

[2] 2. Burde, K., Ein rationales biquadratisches Reziprozitätsgesetz, Jour, reine angew. Math., 235 (1969), 175-184. Google Scholar

[3] 3. Dörrie, H., Das quadratische Reciprocitätsgesetz in quadratischen Zahlkörper mit der Classenzahl 1, Gott. Diss., 1898. Google Scholar

[4] 4. Lehmer, E., Criteria for cubic and quartic residuacity, Mathematika 5 (1958), 20-29. Google Scholar

[5] 5. Lehmer, E., On the quadratic character of some quadratic surds, Jour, reine angew. Math., 250 (1971), 42-48. Google Scholar

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