#!/usr/bin/env python

"""
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.
"""

import math

for i in xrange(0,1001):
  for j in xrange(0,1001):
    a,b=j,i
    c=math.sqrt(a**2 + b**2)
    if a < b < c and a + b + c == 1000:
      print a*b*c
      break
    
add solution to problem 9