Simple proofs of some generalizations of the Wilson's 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 generated by element of order 2 of a finite abelian group. Some conditions equivalent to the cyclicity of (Phi, •n), where n>=2, is a...
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Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
2014-04-01
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| Series: | Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| Online Access: | http://studmath.up.krakow.pl/index.php/studmath/article/view/143 |
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doaj-437a83533e634b4b965b3f346dad94662020-11-24T21:44:25ZdeuWydawnictwo Naukowe Uniwersytetu PedagogicznegoAnnales Universitatis Paedagogicae Cracoviensis: Studia Mathematica 2081-545X2300-133X2014-04-01131714110Simple proofs of some generalizations of the Wilson's theoremJan GórowskiAdam ŁomnickiIn 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 (Phi, •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.http://studmath.up.krakow.pl/index.php/studmath/article/view/143 |
| collection |
DOAJ |
| language |
deu |
| format |
Article |
| sources |
DOAJ |
| author |
Jan Górowski Adam Łomnicki |
| spellingShingle |
Jan Górowski Adam Łomnicki Simple proofs of some generalizations of the Wilson's theorem Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| author_facet |
Jan Górowski Adam Łomnicki |
| author_sort |
Jan Górowski |
| title |
Simple proofs of some generalizations of the Wilson's theorem |
| title_short |
Simple proofs of some generalizations of the Wilson's theorem |
| title_full |
Simple proofs of some generalizations of the Wilson's theorem |
| title_fullStr |
Simple proofs of some generalizations of the Wilson's theorem |
| title_full_unstemmed |
Simple proofs of some generalizations of the Wilson's theorem |
| title_sort |
simple proofs of some generalizations of the wilson's theorem |
| publisher |
Wydawnictwo Naukowe Uniwersytetu Pedagogicznego |
| series |
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| issn |
2081-545X 2300-133X |
| publishDate |
2014-04-01 |
| description |
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 (Phi, •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. |
| url |
http://studmath.up.krakow.pl/index.php/studmath/article/view/143 |
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AT jangorowski simpleproofsofsomegeneralizationsofthewilsonstheorem AT adamłomnicki simpleproofsofsomegeneralizationsofthewilsonstheorem |
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1725910492678979584 |