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. 

for a in range(1, 333+1):
    for b in range(a+1, 500+1):
        c = 1000 - (a + b)
        
        if a**2 + b**2 == c**2:
            print(f"{a}^2 + {b}^2 = {c}^2")
            print(f"{a} + {b} + {c} = 1000")
            print(f"abc = {a*b*c}")
Click to reveal output 
200^2 + 375^2 = 425^2
200 + 375 + 425 = 1000
abc = 31875000

See problem 9 on projecteuler.net