Congruence Modulo Integer/Examples/12 equiv 0 mod 3

Example of Congruence Modulo an Integer

 * $12 \equiv 0 \pmod 3$

Proof
By definition of congruence:
 * $x \equiv y \pmod n$ $x - y = k n$

for some $k \in \Z$.

We have:
 * $12 - 0 = 12 = 4 \times 3$

Thus:
 * $12 \equiv 0 \pmod 3$