Riddle 9: Special Pythagorean triplet

The Task A Pythagorean triplet is a set of three natural numbers, a < b < c, for which a^2 + b^2 = c^2. For example, 32 + 42 = 9 + 16 = 25 = 52. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc. Solutio...