# Difference between revisions of "Residue class"

In modular arithmetic, a residue of an integer $a$ in modulo $n$ is the unique value of $0\leq r \leq n-1$ such that $a=kn + r$. In the context of division, a residue is simply a remainder.

A residue class is a complete set of integers that are congruent modulo $n$ for some positive integer $n$. In modulo $n$, there are exactly $n$ different residue classes, corresponding to the $n$ possible residues $\{0,1,2,3,... n-2, n-1\}$

Each residue class contains all integers in the form $kn + r$ where $r$ is the corresponding residue.