"""
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.
"""


def find_pythag_triplet():
    """Return product(abc) where a**2 + b**2 = c**2 and a + b + c = 1000."""
    for a in range(1, 1000):
        for b in range(1, 1000):
            for c in range(1, 1000):
                if a + b + c == 1000:
                    if a**2 + b**2 == c**2:
                        return a * b * c
    return 0


print(find_pythag_triplet())
