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Residue Classes modulo n

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The set

$\displaystyle \{0,1,\ldots,n-1\}

forms an Abelian group with respect to the addition modulo $ n$. This group is denoted by

$\displaystyle \mathbb{Z}_n = \mathbb{Z}\,\operatorname{mod}\,n\, .

Note that the multiplication modulo $ n$ does not define a group-structure on $ \mathbb{Z}_n$ because 0 has no inverse element.
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  automatically generated 3/31/2005