Let the sum of all integers $n$ such that $(2n^2+9/n+3)$ is an integer be $A$, what is $|A|$?
I tried expressing it to:
$k$ is an integer, $(n+3)k + 0 = 2n^2 + 9$, $n(2n-k) + 3(3-k) = 0$, from which I couldn't move on,
I also tried $(n+3)k + 0 = 2n^2 + 9$, $k = 2n$, $2n^2 - 2n^2 + 9 - 6n$. $9-6n/n+3$ is an integer, $9 - 6n = 3(3-n)$ though now I also do not know how to move on.