Solution to Problem 9. Written in Python.

Problem: 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.