# Math Help - Basic proof

1. ## Basic proof

Show that $n(n^2 - 1)$ is divisible by 24 when n is an odd number.

What I've got so far is a lemma that the square of any odd number is of the form 8q + 1.

So I kinda have... $n(8q + 1 - 1)=8nq$

(good to see LaTeX up )

2. Originally Posted by DivideBy0
Show that $n(n^2 - 1)$ is divisible by 24 when n is an odd number.

What I've got so far is a lemma that the square of any odd number is of the form 8q + 1.

So I kinda have... $n(8q + 1 - 1)=8nq$

$n(n^2 - 1) = n(n + 1)(n - 1) = (n - 1)n(n + 1)$