Project Euler Problem 9: Special Pythagorean Triplet

A Pythagorean triplet is a set of three natural numbers,
`a` < `b` < `c`, for which,
`a ^{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*.