Abstract
In this paper a remarkable simple proof of the Gauss’s generalization of the Wilson’s theorem is given. The proof is based on properties of a subgroup generated by element of order 2 of a finite abelian group. Some conditions equivalent to the cyclicity of (Φ(n), ·n), where n > 2 is an integer are presented, in particular, a condition for the existence of the unique element of order 2 in such a group.
Language: English
Page range: 7 - 14
Submitted on: Jan 13, 2014
Published on: Dec 11, 2014
Published by: Pedagogical University of Cracow
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
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© 2014 Jan Górowski, Adam Łomnicki, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.