A Pythagorean triplet is a set of three natural numbers,

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 another one that’s probably really more “math”-y
than programming-y, but I’m enjoying using my new F# hammer to solve
these, so might as well keep at it.

It seems like another nice make-a-sequence-and-then-filter-it, but just doing
1..1000 for a, b, and c, results in an awfully big sequence (a billion long).
So, a couple simple observations to make the numbers a lot smaller. The main
one is that you can just make c = 1000 - a - b, since we know that all answers
have to have that form anyway.