Es sei u {\displaystyle {}u} die Fundamentaleinheit von R = Z [ 2 ] {\displaystyle {}R=\mathbb {Z} [{\sqrt {2}}]} . Bestimme die multiplikative Ordnung von u {\displaystyle {}u} in R / p R {\displaystyle {}R/pR} für p = 2 , 3 , 5 , 7 , 11 {\displaystyle {}p=2,3,5,7,11} .
![{\displaystyle {}R=\mathbb {Z} [{\sqrt {2}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2aa2cdf4b23ee1d9a5e4b89ec3ada08ee4356fc3)
