# Congruence Modulo Integer/Examples/2 equiv -6 mod 4

## Example of Congruence Modulo an Integer

$2 \equiv -6 \pmod 4$

## Proof

By definition of congruence:

$x \equiv y \pmod n$ if and only if $x - y = k n$

for some $k \in \Z$.

We have:

$2 - \paren {-6} = 8 = 2 \times 4$

Thus:

$2 \equiv -6 \pmod 4$

$\blacksquare$