1. The problem statement, all variables and given/known data For all natural numbers n, prove whether the following is true or false: n3-n is always divisible by 6. From SQA Advanced Higher Mathematics 2006 Exam Paper 2. Relevant equations I can choose from the following types of proof: Direct proof Proof by contradiction Proof by contrapositive Proof by induction 3. The attempt at a solution I know the statement is true, but proving it has been more difficult than I thought it would be! I tried proof by induction, but got stuck with trying to prove true for n=k+1. I then tried proving the statement true for n=2k (even number) and n=2m+1 (odd number), but again, I didn't seem to be getting anywhere. Am I along the right lines, or should I be trying something different?