Congruence Modulo Integer/Examples/57 not equiv 208 mod 4

Example of Non-Congruence Modulo an Integer

 * $57 \not \equiv 208 \pmod 4$

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

for some $k \in \Z$.

We have:
 * $208 - 57 = 151 = 37 \times 4 + 3$

and so $208 - 57$ is not of the form $k \times 4$ for some $k \in \Z$.

Thus:
 * $57 \not \equiv 208 \pmod 4$