# Integer solutions to $xy > c^2$ where x and y are bound [closed]

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 :

1. Looping from 1 to c
2. Calculating when x and y both are greater than c
3. Calculating when x = c and solutions for y and then vice versa
4. 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.

## closed as off-topic by Alexey Ustinov, user44191, abx, Steven Landsburg, Robert IsraelSep 12 at 4:57

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• "MathOverflow is for mathematicians to ask each other questions about their research. See Math.StackExchange to ask general questions in mathematics." – Alexey Ustinov, user44191, abx, Robert Israel
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