def problem009():
    """


    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.
    """

    perimeter = 1000
    for a in range(1, perimeter + 1):
        for b in range(a + 1, perimeter + 1):
            c = perimeter - a - b
            if a * a + b * b == c * c:
                # It is now implied that b < c, because we have a > 0
                return a * b * c


if __name__ == "__main__":
    print(problem009())
