Congruence Modulo Integer/Examples/12 equiv 0 mod 3

From ProofWiki
Jump to navigation Jump to search

Example of Congruence Modulo an Integer

$12 \equiv 0 \pmod 3$


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:

$12 - 0 = 12 = 4 \times 3$

Thus:

$12 \equiv 0 \pmod 3$

$\blacksquare$


Sources