Congruence Modulo Integer/Examples/3 equiv 18 mod 5

Example of Congruence Modulo an Integer

 * $3 \equiv 18 \pmod 5$

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

for some $k \in \Z$.

We have:
 * $3 - 18 = -15 = \left({-3}\right) \times 5$

Thus:
 * $3 \equiv 18 \pmod 5$