Congruence Modulo Integer/Examples/13 equiv 3 mod 5

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Example of Congruence Modulo an Integer

$13 \equiv 3 \pmod 5$


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:

$13 - 3 = 10 = 2 \times 5$

Thus:

$13 \equiv 3 \pmod 5$

$\blacksquare$


Sources