On Integer Right Triangles With Equal Area

Introduction Right triangles with integer side lengths are one of the earliest traces of human interest in mathematics. Already in ancient Egypt the right triangle with legs a = 3 and b = 4, and with hypothenuse c = 5, was known. As it is well known, and easily checked by the reader, the formulas 8 ? ! ? : a = 2mn b = (m 2 \Gamma n 2 ) c = (m 2 + n 2 ) (1) give for any choice of nonzero integers m 6= n and an integer right triangle. (Geometrically we deal with a negative side length as if it were positive.) Such a triangle is called primitive if gcd(a; b; c) = 1. Obviously, for = 1 and m 6= n not both odd with g