Question 63
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.
a. Prove that there are at least 500 friendly integers in the set $\{1,2, \ldots, 2012\}$.
b. Decide whether $a=2$ is friendly.