Školjka

%V0 An integer $a$ is called friendly if the equation $(m^2+n)(n^2+m)=a(m-n)^3$ has a solution over the positive integers. a) Prove that there are at least $500$ friendly integers in the set $\{ 1,2,\ldots ,2012\}$. b) Decide whether $a=2$ is friendly.