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`.

This is a Project Euler Problem: https://projecteuler.net/problem=9