I made it divisible by 8:Code:Given that m is an odd positive integer, prove that $\displaystyle (m^2+3)(m^2+15)$ is divisible by 32 for all such values of m.

$\displaystyle ((k+2)^2+3)((k+2)^2+15)-((k^2+3)(k^2+15))

=8 (k^3+3k^2+13k+11)$

But I could not make it divisible by 32. A little help please, I feel I was very close to the solution.

My method is right, right?