While working on my algorithm I came to this problem:
$$x_{1,2} = \frac{-b-a+y \pm \sqrt{(b + a-y)^2 - 4c}}{-2}$$ $$x_1 = \frac{c}{x_2}$$
- $a,b,c$ are positive known integers
- $y$ is positive integer
How can I find for what values of $y$, $x_{1,2}$ are positive integers? In the title I gave an example for such numbers, the solutions is $x_{1,2} = 661,727$, $y = 56$