A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,

a2 + b2 = c2
For example, 32 + 42 = 9 + 16 = 25 = 52.

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.


The key word here is Pythagorean Triplet, from Wikipedia, a Pyhtagorean Triplet consists of three positive integers, a, b, and c, such that

$$a^2 + b^2 = c^2$$

Such triplet is commonly written (a, b, c). The most comon example is (3, 4, 5)

pythagorean_triplet


WIP