How to efficiently calculate all the integer solutions to $xy > c^2$ where
$0 < x < X$ and $0 < y < Y$ and $X$, $Y$, and $C$ are some positive integers.
I am looking for an algorithmic solution.
I tried brute forcing it by the following way :
- Looping from 1 to c
- Calculating when x and y both are greater than c
- Calculating when x = c and solutions for y and then vice versa
- This is the part which slows down the whole process. Calculating the possible solutions when one of them is less than c.
I am majorly interested in the number of points that are valid solutions.
I think if I rotate this rectangular hyperbola by $45o$, it would crack the problem, but this went nowhere.