Congruence Modulo Integer/Examples/11 equiv -1 mod 12

Example of Congruence Modulo an Integer

$11 \equiv -1 \pmod {12}$

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:

$11 - \paren {-1} = 12 = 1 \times 12$

Thus:

$11 \equiv -1 \pmod {12}$

$\blacksquare$

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {4-1}$ Basic Properties of Congruences: Example $\text {4-1}$