# Simple proofs of some generalizations of the Wilson’s theorem

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2014)

- Volume: 13, Issue: 1, page 7-14
- ISSN: 2300-133X

## Access Full Article

top## Abstract

top## How to cite

topJan Górowski, and Adam Łomnicki. "Simple proofs of some generalizations of the Wilson’s theorem." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 13.1 (2014): 7-14. <http://eudml.org/doc/268695>.

@article{JanGórowski2014,

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.},

author = {Jan Górowski, Adam Łomnicki},

journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},

keywords = {groups; congruences},

language = {eng},

number = {1},

pages = {7-14},

title = {Simple proofs of some generalizations of the Wilson’s theorem},

url = {http://eudml.org/doc/268695},

volume = {13},

year = {2014},

}

TY - JOUR

AU - Jan Górowski

AU - Adam Łomnicki

TI - Simple proofs of some generalizations of the Wilson’s theorem

JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

PY - 2014

VL - 13

IS - 1

SP - 7

EP - 14

AB - 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.

LA - eng

KW - groups; congruences

UR - http://eudml.org/doc/268695

ER -

## References

top- [1] Lin Cong, Zhipeng Li, On Wilson’s theorem and Polignac conjecture, Math. Medley 32 (2005), 11-16. (arXiv:math/0408018v1). Cited on 7.
- [2] J.B. Cosgrave, K. Dilcher, Extensions of the Gauss-Wilson theorem, Integers 8 (2008), A39, 15pp. Cited on 7 and 13. Zbl1210.11008
- [3] M. Hassani, M. Momeni-Pour, Euler type generalization of Wilson’s theorem, arXiv:math/0605705v1 28 May, 2006. Cited on 10.
- [4] G.A. Miller, A new proof of the generalized Wilson’s theorem, Ann. of Math. (2) 4 (1903), 188-190. Cited on 7. Zbl34.0217.02

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.