Let's say that I have a working Pythagorean triple generator for all integers greater or equal to 3. It generates primitive and non primitive pairs, and it's a one variable equation having to do with elements of the a term in a right triangle, not a case by case problem. I would post it here, but I would like to get credit for making it, and am afraid someone will take it. If I have something like this, would others consider it useful, and if so, what should I do with it?
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2$\begingroup$ +1 for having the drive to work it out yourself. That said, I don't think there is much new credit left to claim about Pythagorean triples. See for example Pythagorean Right-Angled Triangles for a quite extensive collection of Pythagorean calculators. $\endgroup$– dxivJul 6, 2017 at 4:29
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1$\begingroup$ Wow... that is, indeed, a rather exhaustive collection D: $\endgroup$– Eric StuckyJul 6, 2017 at 4:33
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$\begingroup$ Should I just publish what I have come up with, and see if someone has already found this? $\endgroup$– user460386Jul 6, 2017 at 6:30
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$\begingroup$ Barely related, you can generate a primitive Pythagorean triple for any given ratio $R=\frac{area}{perimeter}$ using Euclid's formula where $(m,n)=(2R+1,2R)$. $\endgroup$– poetasisJul 20, 2019 at 18:39
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The short answer: knowledge in mathematics is formally shared with the community through publications. You may be interested in this question; and this one, to a lesser extent.
Regarding credit: Unfortunately (for you), generating pythagorean triples— primitive or otherwise— is a very well-studied problem, and it's unlikely that what you have is new. [It maybe goes without saying, but for completeness: the Wikipedia page does not represent a comprehensive list of methods known for generating triples.]
At best, you may have an algorithmic improvement; that is, your method may be able to generate the first $n$ triples (ordered by norm or something) faster than other methods. But I couldn't find the state of the art on this kind of problem with a simple google result, and so you're not going to know if this is the case for your method without (1) a serious analysis of your own method, and (2) a nontrivial literature search.
[ Or, of course, you could outsource that work (e.g. to MSE), but for that you would need to provide at least a technical description of your method, and it seems like you are not willing to do this. ]
answered Jul 6, 2017 at 4:21
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$\begingroup$ FWIW: The set of pythagorean triples naturally forms a two-parameter family. But it is possible to write any two-parameter family as a one-parameter family, so this is not necessarily a guarantee of novelty. $\endgroup$ Jul 6, 2017 at 4:23