Congruence Modulo Integer/Examples/-10 equiv 8 mod 6

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Example of Congruence Modulo an Integer

$-10 \equiv 8 \pmod 6$


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:

$-10 - 8 = -18 = \paren {-3} \times 6$

Thus:

$-10 \equiv 8 \pmod 6$

$\blacksquare$


Sources