Proof That 3|n3 - n

First let's start by expanding \(n^3 - n\):

$$ n(n^2-1) $$$$ n(n+1)(n-1) $$

If you consider any 3 consecutive numbers, one of them would be divisible by 3. This means:

$$3 | (n-1) * n * (n+1)$$

Styles

(uses cookies)