Problem 249. Project Euler: Problem 9, Pythagorean numbers

Created by Doug Hull

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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 = 5^2 = 25.
There exists exactly one Pythagorean triplet for which a + b + c = N (the input).
Find the product abc.
Thank you to Project Euler Problem 9.

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Last Solution submitted on Apr 28, 2025

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Aurelien Queffurust on 22 May 2012

The description should be 9 + 16 = 5^2 and not 9+16 = 2^5 ?

Ned Gulley on 22 May 2012

Thanks Aurelien! Fixed it.

Peter Wittenberg on 20 Dec 2012

This is an interesting problem. Apparently everyone (including me) had to solve it by a basic brute force method with oly very slight variations. I did manage to use my MATLAB copy to use solve from the symbolic toolbox to get the answers, but the version of MATLAB on which Cody runs doesn't have access to a license for the symbolic toolbox.

Srishti Saha on 13 Oct 2018

@ Doug Hall, I have solved all the problems in the series. However, I have not received the badge and the associated scores on completion of the series. Can you please help me with this?

Brandon on 23 May 2023

Wow, all the triangles are in the ratio of 8:15:17? Pretty huge oversight.

Christos Saragiotis on 26 Nov 2023

People have realized that all test cases are based on the primitive Pythagorean triplet (8, 15, 17) and the solutions are full of hacks. This is quite annoying as one cannot compare one's solution with other valid ones.

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Problem 249. Project Euler: Problem 9, Pythagorean numbers

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Problem 249. Project Euler: Problem 9, Pythagorean numbers

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