Congruence Modulo Integer/Examples/17 equiv 12 mod 5

Example of Congruence Modulo an Integer

 * $17 \equiv 12 \pmod 5$

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

for some $k \in \Z$.

We have:
 * $17 - 12 = 5 = 1 \times 5$

Thus:
 * $17 \equiv 12 \pmod 5$