Find the nonzero values of integer $n$ for which the quotient $\frac {13n^2+n}{2n+2}$ is an integer?
My Attempt
I assumed $(2n+2 )| (13n^2+n)$ implies existence of integer $k$ such that $$13n^2+n=k(2n+2)$$ $\implies\ 13n^2+(1-2k)n-2k=0$
$\implies\ n=\frac{(2k-1)\pm\sqrt{(1-2k)^2+104}}{26}$
But this is taking me nowhere.