Divisibility Proof for n(n²-1)(n+2) by 12 using Factorization

[twoski]

Homework Statement

Prove that for any n ∈ Z, n(n² − 1)(n + 2) is divisible by 12 .

The Attempt at a Solution

We first assume n = k for some value k.

Next we assume k(k² − 1)(k + 2) = 12m for some value m.

I don't know where to go from here. I don't think this is supposed to be an induction proof because our professor never explained induction to us yet. Every other proof I've seen for questions like this use induction (because it's so much easier to)...

 

[tiny-tim]

hi twoski!

(try using the X² button just above the Reply box )

hint: factor (n² - 1)