Geodesic
Simple proofs of some generalizations of the Wilson’s theorem
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 13 (2014).

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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. 
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Górowski, Jan; Łomnicki, Adam. Simple proofs of some generalizations of the Wilson’s theorem. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 13 (2014). http://geodesic.mathdoc.fr/item/AUPCM_2014_13_a8/

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