- #1

chan8366

- 3

- 0

## Homework Statement

prove:6 divides (n^3-n) for all integers n.

## Homework Equations

n^3-n=(n)(n+1)(n-1)

## The Attempt at a Solution

tried to use direct proof. Then used cases that involed n=2k for some integer k and n=2k+1 for some integer k. However, i could not get it so that 6 was factored from either odd/even of n^3-n i.e. n^3-n=6m for some integer m.

Just a hint please.