ProjectEuler#9 Special Pythagorean triplet

#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 = 52.

#There exists exactly one Pythagorean triplet for which a + b + c = 1000.
#Find the product abc.

#Analysis
# loop over a and b and then check whether a**2 + b**2 == (s - a - b)**2
# From the condition a < b < c, we conclude that a<= (s-3)/3) and b < (s-a)/2)

s = 1000
for a in range(3,int((s-3)/3)+1):
    for b in range(a+1,int((s-a)/2)+1):
        c = s - a - b
        if c**2 == a**2 + b**2:
            print a,b,c
print a*b*c