Divisor of Integer/Examples/2 divides n(n+1)

Theorem
Let $n$ be an integer.

Then:
 * $2 \divides n \paren {n + 1}$

where $\divides$ indicates divisibility.

Proof
Suppose $n$ is even.

Then $2 \divides n$ by definition.

Hence from Divisor Divides Multiple:
 * $2 \divides n \paren {n + 1}$

Suppose $n$ is odd.

Then $n + 1$ is even

Then $2 \divides n + 1$ by definition.

Hence from Divisor Divides Multiple:
 * $2 \divides n \paren {n + 1}$