Discrete Structures Question

[Raknarg]

I have an assignment for this class, and I've answered all the questions but one. The question asks us to prove that for all n >= 1, n(n+1)(n+2) is divisible by 6. I think I might have the idea, where in the range of n to n+2 you will always have a number divisible by 3 and divisible by 2 so they can always be factored out and turned into 6, then removed. However I'm not sure how to prove that. Can anyone help?

[Tony]

By induction.

Assume that factors 2 and 3 exist for N. Given that, show that factors 2 and 3 exist for N+1

N(N+1)(N+2) (case n)
(N+1)(N+2)(N+3) (case n+1)

+1,+2 are common. You need to show that dropping N doesn't matter, or the factor is regained with N+3