ok im completely stumped with this with the equation
$\displaystyle n = m^3 - m$
for when n & m are integers
how to you show that n is a multiple of 6?
$\displaystyle n=m^3-m$
$\displaystyle n=m(m^2-1)$
$\displaystyle n=m(m+1)(m-1)$
$\displaystyle m(m+1)(m-1)$ 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 $\displaystyle m(m+1)(m-1)$ is a multiple of 6.
$\displaystyle n$ is a multiple of 6.