We show how K. Hensel could have extended Wilson’s theorem from to the ring of integers in a number field, to find the product of all invertible elements of a finite quotient of .
On fait voir comment K. Hensel aurait pû étendre le théorème de Wilson de à l’anneau des entiers d’un corps de nombres, pour trouver le produit de tous les éléments inversibles d’un quotient fini de .
@article{JTNB_2009__21_3_517_0, author = {Dalawat, Chandan Singh}, title = {Wilson{\textquoteright}s theorem}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {517--521}, publisher = {Universit\'e Bordeaux 1}, volume = {21}, number = {3}, year = {2009}, doi = {10.5802/jtnb.686}, zbl = {1204.11166}, mrnumber = {2605531}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.686/} }
Dalawat, Chandan Singh. Wilson’s theorem. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 3, pp. 517-521. doi : 10.5802/jtnb.686. http://archive.numdam.org/articles/10.5802/jtnb.686/
[1] C. Gauss, Disquisitiones arithmeticae. Gerh. Fleischer, Lipsiae, 1801, xviii+668 pp.
[2] K. Hensel, Die multiplikative Darstellung der algebraischen Zahlen für den Bereich eines beliebigen Primteilers. J. f. d. reine und angewandte Math., 146 (1916), pp. 189–215.
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