First of all, I hope this problem is supposed to be here - I'm Swedish and in Sweden "calculus" & "precalculus" are rather odd terms. Anyway.. 1. The problem statement, all variables and given/known data Prove that n3 - n is divisible by 6 if n is a natural number, and divisible by 24 if n is an odd natural number. 2. Relevant equations 3. The attempt at a solution There were two problems similar to this before this one and I attempted to solve it in the way I solved those (and the way the book solved them, as well), which was to split n into its even case and odd case. Even case: n = 2k (2k)3 - 2k = 8k3 - 2k , which obviously didn't help me much. But, as I'd used earlier for previous exercises, k can either be even or odd. If k is, say, even, k = 2s 8(2s)3 - 2(2s) = 64s3 - 4s .. and I can continue on, but nothing is divisible by 6.. And I've done the same for k = 2s + 1, which also doesn't work out. And I tried the odd case I mentioned earlier (n=2k +1) and that doesn't work out and I'm so close to screaming in frustration it's not even funny.. 1. The problem statement, all variables and given/known data Show that if n is a composite number it has a divisor greater than or equal to n½. 2. Relevant equations 3. The attempt at a solution My problem is that, yes, I absolutely and completely agree with the statement due to logic, but I've not a clue where to start the proof.. I'm not asking for someone to show me the proof, but a tip as to where to start?