Congruence Modulo Integer/Examples/17 equiv 12 mod 5
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Example of Congruence Modulo an Integer
- $17 \equiv 12 \pmod 5$
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:
- $17 - 12 = 5 = 1 \times 5$
Thus:
- $17 \equiv 12 \pmod 5$
$\blacksquare$
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {4-1}$ Basic Properties of Congruences: Example $\text {4-1}$