1. The problem statement, all variables and given/known data Prove n(n+1)(n+2) is divisible by 6 for all integers n. (WITHOUT using induction, we have yet to get to induction so I figure it would be wise to do this without it.) 2. Relevant equations The section we were given this under primarily talks about the quotient remainder theorem (n = dq+r) though I couldn't figure out how to apply this either. 3. The attempt at a solution Honestly not sure where to even begin with this one. Nothing even slightly similar has been covered as to give a slight intuition on how to begin this. I've managed to prove that it's divisible by 2 for all even and odd integers by using n = 2k and n = 2k+1 respectively. That still leaves proving it is divisible by 3 for even and odds though, which is where I get stuck doing that method.