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<p> 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), ·<sub>n</sub>), 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. </p>
</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.

Simple proofs of some generalizations of the Wilson’s theorem

Institute of Mathematics Pedagogical University Podchorazych 2, PL-30-084 Kraków Poland

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"Simple proofs of some generalizations of the Wilson\u2019s theorem"}

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...

Simple proofs of some generalizations of the Wilson’s theorem

Published Online: Dec 11, 2014

Page range: 7 - 14

Received: Jan 13, 2014

DOI: https://doi.org/10.2478/aupcsm-2014-0001

© by Jan Górowski

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.