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.
@article{bwmeta1.element.doi-10_2478_aupcsm-2014-0001,
author = {Jan G\'orowski and Adam \L omnicki},
title = {Simple proofs of some generalizations of the Wilson's theorem},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
volume = {13},
year = {2014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_aupcsm-2014-0001}
}
Jan Górowski; Adam Łomnicki. Simple proofs of some generalizations of the Wilson’s theorem. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 13 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_aupcsm-2014-0001/
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