Congruence Modulo Integer/Examples/3 equiv 18 mod 5
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Example of Congruence Modulo an Integer
- $3 \equiv 18 \pmod 5$
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:
- $3 - 18 = -15 = \paren {-3} \times 5$
Thus:
- $3 \equiv 18 \pmod 5$
$\blacksquare$
Sources
- 1964: Walter Ledermann: Introduction to the Theory of Finite Groups (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Group Concept: $\S 6$: Examples of Finite Groups: $\text{(iii)}$