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My post has been downvoted, and I'm not sure what the appropriate action is for me to take.

On the one hand, there's contribution from other users so the post can't and shouldn't be deleted.

On the other hand, I'm not sure what I can do to improve the post - it's been flagged as a duplicate as a more elementary approach to linking a couple of more general lemmas.

Are the downvotes due to the post simply being a duplicate? It then feels like more of a punishment for past-me for not understanding the connection with the general lemmas, as well as finding them. Would editing the post to better explain how it's a duplicate be useful (while keeping the original content below it for consistency with comments and answer)?

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    $\begingroup$ FWIW, my experience over the last eight years I've been here (a moderate amount of time) is that the last few years have seen an uptick in down-votes for question flaws that in years past would have been overlooked: lack of context in otherwise interesting questions, failure to search for duplicates of otherwise interesting questions, even errors in approaches to otherwise interesting questions. You may sense a theme here. I don't agree with these down-votes, generally; I feel they should be reserved for rudeness and resistance to improvements. But others evidently feel differently. $\endgroup$
    – Brian Tung
    Oct 25 at 0:54
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    $\begingroup$ I agree with Brian's take. I'm not sure what the best general approach is, but in this particular case I would not recommend that you do anything. [I upvoted because I find the ill-placed downvotes irritating; so, this should balance them out.] $\endgroup$
    – Benjamin Dickman
    Oct 25 at 17:52
  • $\begingroup$ Suppose that someone downvotes your question because they want users to move to the duplicate post faster and see the answer there rather than see the potentially inferior (in the eyes of the voter) answer(s) to your question. Then, you can't change their opinion by changing your post, even if the only thing you did incorrectly (this may be very arguably wrong) was not find the duplicate post. I'm trying to find an intersection between "someone downvoted my post for legitimate reasons" and "I can't do anything about that", and this situation lies there. $\endgroup$
    – Sarvesh Ravichandran Iyer
    Oct 26 at 5:51

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The issue of closing a Question as a duplicate when it amounts to a special case of an earlier Question has come up before. Often the topic is broached on Meta Math.SE when there is a doubt about the correctness of such marking.

In this instance you got a good Answer and were able to learn something from that as well as the proposed duplicate. A Comment spells out the steps needed to connect the more general "Euclid's lemma" (which certainly takes liberties with Euclid's name) to the problem you asked for help with. Or at least I was able to learn something...

The policy on Math.SE takes "exact duplicate" more literally than most SE Communities I participate in. The preponderance of sites use the criterion of whether a proposed Question "can be answered" by the (good) Answers of a pre-existing Question.

To avoid a proliferation of minor variations on a problem type, the notion of abstract duplicates and a List of Generalizations of Common Questions was adopted here fairly early in the life of Math.SE. These mechanisms continue to enjoy fairly robust extensions.

A highly upvoted feature request would have provided a "hierarchy of duplicates", but this probably could only make sense for a subject as highly structured as mathematics. So we make do with the simple linking together of closed-as-duplicates.

Finally I don't think you need to do anything with your Question, and I think it and the Answer by Mike Daas are quality contributions to the site. Of course others may feel otherwise, and theirs is the privilege to vote accordingly.

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    $\begingroup$ Re: "talking liberty". It is pedagogically helpful (and not uncommon) to use the same name for theorems that (immediately) generalize from numbers to ideals (and gcds), e.g. the distributive law. As I explained in the link I gave there, the (coprime) version of Euclid's Lemma for integers immediately generalizes to coprime (i.e. comaximal) ideals, so it is conceptually advantageous to preserve use of the ubiquitous name "Euclid's Lemma". $\endgroup$
    – Bill Dubuque
    Oct 15 at 22:20

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