Congruence Modulo Integer/Examples/11 equiv -1 mod 12
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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 $\text {4-1}$