1. The problem statement, all variables and given/known data Prove that n^3 - n is divisible by 6, when n is a nonnegative integer. 3. The attempt at a solution Mathematical induction: It works for n=0 It works for n=1 (Extra step, just in case) Check if it works for the (k+1)th step. For it to work, it must be expressible as 6x, where x is some integer. In other words, to prove: (k+1)^3 - k = 6x Can someone nudge me on this? I'm either making a mistake by calling it 6x, and maybe it should be 6k or something else... ...and/or, I'm just missing the algebraic skills to change LS into RS.