Divisibility by 6
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Theorem
An integer $N$ expressed in decimal notation is divisible by $6$ if and only if
- $N$ is even
and:
- $N$ is divisible by $3$.
Proof
We have that:
- $6 \divides N \iff 2 \divides N \land 3 \divides N$
The result follows by definition of even integer.
$\blacksquare$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): divisible
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): divisible