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## Homework Statement

For all natural numbers n, prove whether the following is true or false:

n

^{3}-n is always divisible by 6.

From SQA Advanced Higher Mathematics 2006 Exam Paper

## Homework Equations

I can choose from the following types of proof:

Direct proof

Proof by contradiction

Proof by contrapositive

Proof by induction

## 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?