- #1

Goldenwind

- 146

- 0

## Homework Statement

Prove that n^3 - n is divisible by 6, when n is a nonnegative integer.

## 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.