Problem 9 : Special Pythagorean triplet

Problem Statement

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

a2+b2=c2

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

There exists exactly one Pythagorean triplet for which

a+b+c=1000

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