Given $m,n\in\Bbb N$ with $m<n$, how many pythagorean triples $p^2+r^2=q^2$ satisfy $$m\leq p<r\leq n?$$


Is there a way to give a sharp estimate?



Sharply Estimating Pythagorean Triples
See [my preprint](http://arxiv.org/abs/1211.6509). Page 12 (this has since been published, but preprint is easiest to access).


