# Körper/7 Elemente/Einführung/2/Beispiel

Der Restklassenkörper ${\displaystyle {}\mathbb {Z} /(7)=\{0,1,2,3,4,5,6\}}$ hat die folgenden Verknüpfungstabellen:

${\displaystyle {}+}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$
${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$
${\displaystyle {}1}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$ ${\displaystyle {}0}$
${\displaystyle {}2}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$
${\displaystyle {}3}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$
${\displaystyle {}4}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$
${\displaystyle {}5}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$
${\displaystyle {}6}$ ${\displaystyle {}6}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$

${\displaystyle {}\cdot }$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$
${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$ ${\displaystyle {}0}$
${\displaystyle {}1}$ ${\displaystyle {}0}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$ ${\displaystyle {}4}$ ${\displaystyle {}5}$ ${\displaystyle {}6}$
${\displaystyle {}2}$ ${\displaystyle {}0}$ ${\displaystyle {}2}$ ${\displaystyle {}4}$ ${\displaystyle {}6}$ ${\displaystyle {}1}$ ${\displaystyle {}3}$ ${\displaystyle {}5}$
${\displaystyle {}3}$ ${\displaystyle {}0}$ ${\displaystyle {}3}$ ${\displaystyle {}6}$ ${\displaystyle {}2}$ ${\displaystyle {}5}$ ${\displaystyle {}1}$ ${\displaystyle {}4}$
${\displaystyle {}4}$ ${\displaystyle {}0}$ ${\displaystyle {}4}$ ${\displaystyle {}1}$ ${\displaystyle {}5}$ ${\displaystyle {}2}$ ${\displaystyle {}6}$ ${\displaystyle {}3}$
${\displaystyle {}5}$ ${\displaystyle {}0}$ ${\displaystyle {}5}$ ${\displaystyle {}3}$ ${\displaystyle {}1}$ ${\displaystyle {}6}$ ${\displaystyle {}4}$ ${\displaystyle {}2}$
${\displaystyle {}6}$ ${\displaystyle {}0}$ ${\displaystyle {}6}$ ${\displaystyle {}5}$ ${\displaystyle {}4}$ ${\displaystyle {}3}$ ${\displaystyle {}2}$ ${\displaystyle {}1}$