TITLE: Help with math induction
QUESTION [6 upvotes]: Prove that $n(n+1)(n+2)$ is divisible by $6$ for all integers.

I'm not sure if I'm suppose to use division into cases or not. Our teacher ran out of time to go over this in class, and this is on my homework.

REPLY [2 votes]: Big Hint: $n(n+1)(n+2)-(n-1)(n)(n+1)=3(n^2+n)$