# Problem_9.py
"""
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
pow(a, 2) + pow(b, 2) = pow(c, 2)
For example, pow(3, 2) + pow(4, 2) = 9 + 16 = 25 = pow(5, 2).
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
找出满足a + b + c = 1000的毕达哥拉斯三元数组(Pythagorean triplet)
找出三数之积
"""
import math

ans = []
for a in range(1, 1000):
    for b in range(a, 1000):
        power = pow(a, 2) + pow(b, 2)
        c = math.sqrt(power)
        if c % int(c) != 0.0:
            continue
        c = int(c)
        print(a, b, c, a+b+c)
        if a+b+c == 1000:
            ans.extend([a, b, c])
            break

print(ans)
tot = 1
for i in ans:
    tot *= i
print(tot)