2018-10-19 12:48:28 +00:00
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"""A Pythagorean triplet is a set of three natural numbers, for which,
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a^2+b^2=c^2
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Given N, Check if there exists any Pythagorean triplet for which a+b+c=N
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Find maximum possible value of product of a,b,c among all such Pythagorean triplets, If there is no such Pythagorean triplet print -1."""
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#!/bin/python3
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product=-1
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d=0
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2018-10-20 19:45:08 +00:00
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N = int(input())
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2018-10-19 12:48:28 +00:00
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for a in range(1,N//3):
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"""Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c """
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b=(N*N-2*a*N)//(2*N-2*a)
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c=N-a-b
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if c*c==(a*a+b*b):
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d=(a*b*c)
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if d>=product:
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product=d
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print(product)
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