Complete residue system

Revision as of 19:50, 1 January 2010 by MathWise (talk | contribs) (Examples)

A Complete residue system modulo $n$ is a set of integers which satisfy the following condition: Every integer is congruent to a unique member of the set modulo $n$.

In other words, the set contains exactly one member of each residue class.

Examples

$\{1,2,3\}$, $\{4,5,6\}$, and $\{9,17,85\}$ are all Complete residue systems $\pmod{3}$

$\{k, k+1, k+2, k+3 ... k+m-1\}$ is a complete residue system $\pmod{m}$, for any integer $k$ and positive integer $m$. Basically, any consecutive string of $m$ integers forms a complete residue system $\pmod{m}$