Problem 9 : Special Pythagorean triplet

Problem Statement

A Pythagorean triplet is a set of three natural numbers, \(a < b < c\), for which,

For example, \(32 + 42 = 9 + 16 = 25 = 52\).

There exists exactly one Pythagorean triplet for which

Find the product \(abc\).

Solution

for a in range(1,1000):
    for b in range(a+1,1000):
        c=1000-a-b
        if (a*a+b*b)==c*c:
            print (a*b*c) 

Output

31875000