Congruence Modulo Integer/Examples/-3 equiv -5 mod 2

Example of Congruence Modulo an Integer

 * $-3 \equiv -5 \pmod 2$

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

for some $k \in \Z$.

We have:
 * $-3 - \paren {-5} = 2 = 1 \times 2$

Thus:
 * $-3 \equiv -5 \pmod 2$