1. ## Divisibility by 9

Prove that, for any positive integer $n$

$n(n-1)(n-2) - 6 \begin{bmatrix} \frac{n}{3} \end{bmatrix}$

is divisible by 9.

$\begin{bmatrix} x \end{bmatrix}$ denotes the integer part of $x$.

2. Originally Posted by CuriosityCabinet
Prove that, for any positive integer $n$

$n(n-1)(n-2) - 6 \begin{bmatrix} \frac{n}{3} \end{bmatrix}$

is divisible by 9.

$\begin{bmatrix} x \end{bmatrix}$ denotes the integer part of $x$.