Project Euler: #9 - Special Pythagorean triplet

Problem A Pythagorean triplet is a set of three natural numbers, a < b < c for which, $$a^2 + b^2 = c^2$$ For example, $$3^2 + 4^2 = 9 + 16 = 25 = 5^2$$ There exists exactly one Pythagorean triplet for which a + b + c = 1000.Find the product abc. Pr...