In [16]:

    

"""
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.
"""

def findPythagoreanTriplet(x):
    """Returns Pythagorean triplet(s) for limit x."""
    
    #  There's likely a better way with multisets, might look into 
    # http://code.activestate.com/recipes/218332-generator-for-integer-partitions/ for speed.
    
    solutions = []
    for a in range(1,x+1):
        for b in range(a+1,x+1):
            for c in range(b+1,x+1):
                if((a**2 + b**2 == c**2) & (a + b + c == x)):
                    solutions.append([a, b, c])
                    print(a, b, c)
    return solutions

findPythagoreanTriplet(1000)


    

    




200 375 425






    
Out[16]:





[[200, 375, 425]]

In [17]:

    

200*375*425


    

    
Out[17]:





31875000