Pythagorean triangles with legs less than \(n\) (Q1612335)

The authors obtain asymptotic estimates for the number of Pythagorean triples \((a,b,c)\) such that \(a<n\), \(b<n\). These estimates are \(4\pi^{-2} \log(1+ \sqrt{2})n+ O(\sqrt{n})\) in the case of primitive triples and \(4\pi^{-2} \log(1+ \sqrt{2})n\log n+ O(n)\) in the case of general triples.