# Math Help - proof that n is a multiple of 6

1. ## proof that n is a multiple of 6

ok im completely stumped with this with the equation
$n = m^3 - m$
for when n & m are integers
how to you show that n is a multiple of 6?

2. Originally Posted by renlok
ok im completely stumped with this with the equation
$n = m^3 - m$
for when n & m are integers
how to you show that n is a multiple of 6?
$n=m^3-m$

$n=m(m^2-1)$

$n=m(m+1)(m-1)$

$m(m+1)(m-1)$ is the product of 3 consecutive integers. So one of the factors is a multiple of 3 and one of the factors is a multiple of 2.

So $m(m+1)(m-1)$ is a multiple of 6.

$n$ is a multiple of 6.