'''
Special Pythagorean triplet

Problem 9
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.
'''
a = 0
b = 0
c = 0
for n in range(1,1000):
    for m in range (1,1000):
        a = (m*m) - (n*n)
        b = 2*(m*n)
        c = (m*m)+(n*n)
        if(a+b+c==1000 and a>=0):
            print a,b,c
            print a*b*c


