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37 lines
935 B
Python
37 lines
935 B
Python
"""
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Problem Statement:
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A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
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a^2 + b^2 = c^2
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For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
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There exists exactly one Pythagorean triplet for which a + b + c = 1000.
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Find the product abc.
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"""
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def solution(n):
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"""
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Return the product of a,b,c which are Pythagorean Triplet that satisfies
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the following:
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1. a < b < c
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2. a**2 + b**2 = c**2
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3. a + b + c = 1000
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>>> solution(1000)
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31875000
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"""
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product = -1
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d = 0
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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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"""
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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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return product
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if __name__ == "__main__":
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print(solution(int(input().strip())))
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