A positive integer is called congruent if it is the area of a right triangle whose side lengths are rational numbers.

For example, the right triangle with legs 20/7 and 357/5 has area 102, and the hypotenuse 2501/35 is rational, so 102 is a congruent number. This Demonstration shows representative triangles for all known congruent numbers under 1000. Finding a triangle for area is equivalent to solving the elliptic curve . Completely solving this problem is similar to solving the Birch and Swinnerton-Dyer conjecture, which is an unsolved problem with a million-dollar prize.