Wilson's theorem
Abstract
We show that there are four possibilities for the product of all elements in the multiplicative group of a quotient of the ring of integers in a number field, and give precise conditions for each of the possibilities to occur. This generalisation of Wilson's theorem turns out to have been first discovered by M. Laššák (2000), but our proof is simpler and more direct.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.3879
 Bibcode:
 2007arXiv0711.3879S
 Keywords:

 Mathematics  Number Theory;
 Mathematics  History and Overview
 EPrint:
 Journal de Th{\'e}orie des nombres de Bordeaux 21 (2009) 3, 517521