Practice (Category=FactorizationMethod(98))
Find the sum of all positive integers $n$ such that $\sqrt{n^2+85n+2017}$ is an integer.
Let integers $u$ and $v$ be two integral roots to the quadratic equation $x^2 + bx+c=0$ where $b+c=298$. If $u < v$, find the smallest possible value of $v-u$.