Suppose $2013+ a^2 = b^2$, $a$ and $b$ being natural numbers, what is the minimum possible value of their product, $ab$?
I have tried algebraic manipulations such as moving $a^2$ to the other side, i.e., $2013 =b^2 - a^2$.
Now I need to find two such numbers such that their product is minimum but the square of one is surely larger than $2013$... I could not find any such solution. How can I do it?