Question 73
An integer $a$ is called friendly if the equation
$$(m^2+n)(n^2+m)=a(m-n^3)$$
has a solution in positive integers $m,n$.
(a) Prove that $\{1,2,\dots,2013\}$ contains at least $500$ friendly integers.
(b) Determine whether $a=2$ is friendly.
$$(m^2+n)(n^2+m)=a(m-n^3)$$
has a solution in positive integers $m,n$.
(a) Prove that $\{1,2,\dots,2013\}$ contains at least $500$ friendly integers.
(b) Determine whether $a=2$ is friendly.