Congruence Modulo Integer/Examples/100 equiv -40 mod 20

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Example of Congruence Modulo an Integer

$100 \equiv -40 \pmod {20}$


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:

$100 - \paren {-40} = 140 = 7 \times 20$

Thus:

$100 \equiv -40 \pmod {20}$

$\blacksquare$


Sources