Definition:Congruence (Number Theory)/Integer Multiple

Definition
Let $z \in \R$. Let $x, y \in \R$.

Then $x$ is congruent to $y$ modulo $z$ iff their difference is an integral multiple of $z$:
 * $x \equiv y \pmod z \iff \exists k \in \Z: x - y = k z$

Also see

 * Equivalence of Congruence Definitions.


 * Congruence Modulo $m$ is an Equivalence Relation