A simple proof of the Zolotareff-Frobenius theorem
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- by Robert E. Dressler and Ernest E. Shult PDF
- Proc. Amer. Math. Soc. 54 (1976), 53-54 Request permission
Abstract:
We give a noncomputational, elementary group-theoretic proof of the Zolotareff-Frobenius Theorem. We use no results from the theory of quadratic residues.References
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G. Frobenius, Über das quadratische Reziprozitätsgesetz. I, S.-B. Preuss. Akad. Wiss. Berlin 1914, 335-349.
M. Lerch, Sur un Théorème arithmétique de Zolotarev, Bull. Intern. 3, Prague, 1896.
- C. Meyer, Über einige Anwendungen Dedekindscher Summen, J. Reine Angew. Math. 198 (1957), 143–203 (German). MR 104643, DOI 10.1515/crll.1957.198.143
- Marcel Riesz, Sur le lemme de Zolotareff et sur la loi de réciprocité des restes quadratiques, Math. Scand. 1 (1953), 159–169 (French). MR 57273, DOI 10.7146/math.scand.a-10376 E. Zolotareff, Nouvelle démonstration de la loi de réciprocité de Legendre, Novelles Ann. Math. (2) 11 (1872), 355-362.
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 53-54
- DOI: https://doi.org/10.1090/S0002-9939-1976-0389732-8
- MathSciNet review: 0389732