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project_euler/Problem 09/sol2.py

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