Novel Solutions

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slabalme81
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Joined: Tue Apr 28, 2020 7:32 pm

Novel Solutions

Post by slabalme81 »

I have recently started working my way through the Archives and was particularly interested by Problem 9, restated below for convenience.
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 $abc$.
Although it appears that the really good solutions typically make use of the factorization,
[removed by moderator]
I derived (in the forums) the factorization
[removed by moderator]
Though it presents no noticeable speed increase over the $mn$-factorization with a case as small as 1000, my solution appears to be more efficient in the specific case of identifying Pythagorean triplets by their sum. Seeing as this idea hadn't been presented previously in the forums or in the solution document, I was wondering if the solution documents are ever updated with new and improved solutions and if yes, would my above solution qualify?

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hk
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Joined: Sun Mar 26, 2006 10:34 am
Location: Haren, Netherlands

Re: Novel Solutions

Post by hk »

No, the overviews are not updated because the source files seem to be lost.
To prevent your solution to be lost foreverone of the next days I made your post in the forum permanent.
I'm going to remove the spoilers in your post.

It happens more often that later on new solutions appear in the forums.
We don't go as far as trying to update the overviews.

In this case (problem 9) the goal of the overview actually was to present the standard parametisation of pythagorean triples, not faster methods specific for the problem.
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slabalme81
Posts: 2
Joined: Tue Apr 28, 2020 7:32 pm

Re: Novel Solutions

Post by slabalme81 »

That makes sense -- thanks for the clarification!

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