Number theory problem, degree 3 diophantine equation
How many positive integers are there that can be written in the form
$\frac{m^3+n^3}{m^2+n^2+m+n+1}$
where $m$ and $n$ are positive integers.
I invented this problem and was stuck with it for a long time. It is
really interesting to know if there is a solution for this problem.
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