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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A simple proof of the Zolotareff-Frobenius theorem

Authors: Robert E. Dressler and Ernest E. Shult
Journal: Proc. Amer. Math. Soc. 54 (1976), 53-54
MathSciNet review: 0389732
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Abstract | References | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] G. Frobenius, Über das quadratische Reziprozitätsgesetz. I, S.-B. Preuss. Akad. Wiss. Berlin 1914, 335-349.
  • [2] M. Lerch, Sur un Théorème arithmétique de Zolotarev, Bull. Intern. 3, Prague, 1896.
  • [3] C. Meyer, Über einige Anwendungen Dedekindscher Summen, J. Reine Angew. Math. 198 (1957), 143–203 (German). MR 0104643 (21 #3396)
  • [4] Marcel Riesz, Sur le lemme de Zolotareff et sur la loi de réciprocité des restes quadratiques, Math. Scand. 1 (1953), 159–169 (French). MR 0057273 (15,200d)
  • [5] E. Zolotareff, Nouvelle démonstration de la loi de réciprocité de Legendre, Novelles Ann. Math. (2) 11 (1872), 355-362.

Additional Information

PII: S 0002-9939(1976)0389732-8
Keywords: Zolotareff's Theorem, permutation, Jacobi symbol
Article copyright: © Copyright 1976 American Mathematical Society