From the Project Euler

*Problem 9:
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.*

**checked**