Congruence Modulo Integer/Examples/13 equiv 3 mod 5

Example of Congruence Modulo an Integer

 * $13 \equiv 3 \pmod 5$

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

for some $k \in \Z$.

We have:
 * $13 - 3 = 10 = 2 \times 5$

Thus:
 * $13 \equiv 3 \pmod 5$