Find all integers $n$ such that $n^2-7n+10$ is divisible by $n-3$. Find all integers $n$ such that $n^2-7n+10$ is divisible by $n-3$.
I have been advised to find an expression containing $n^2$ that is divisible by $n-3$, but I don't see how that would help at the moment.

We have 
$$n^2 - 7n+10 = n^2 - 6n+9 -n+1 = (n-3)^2 -n+1 = (n-3)^2 - (n-3) -2.$$
Thus the expression is divisible by $n-3$ if and only if 
$-2$ is. Finding all these $n$ should not be that hard. ;)
