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Ref: https://math.stackexchange.com/q/3166216

I am sorry, I am new to Meta, so I don't exactly know the proper formatting rules here.

I am having a doubt regarding answering a question which I have referenced above. The topic of the question is "Solution of this Diophantine equation". I assume the title to be a broad overview of what's going to be in the question and most of the time I don't try to think of it as the exact question itself. Likewise in this question, the OP shows his attempt. I see the attempt and I am able to figure out the error in it. The OP then quotes the following in his question.

"Clearly, x and y are not prime numbers. Why is my solution not working? I have been able to solve similar type of equations by factorizing and then listing down the integer factors and the different cases. Why is it not working here?"

I assumed these two to be the query of the OP more or less and I answered it down. But I received criticism for it in the comment and to which I replied the reason of why it is not justified in my point of view. However, later on, the criticism comment also gathered an upvote. So, I am really confused about whether my approach is really wrong?

Edit: By solving the problem I mean: providing a solution to the problem without the user's requirement or demand mentioned in the question for it. I'd assume the premise of the problem to be what the OP asked for.

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    $\begingroup$ Always give more than what's expected .So solve the problem :) $\endgroup$ – user486983 Mar 28 at 21:56
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    $\begingroup$ But it's very possible for this to go against the intention of the OP. $\endgroup$ – Mann Mar 28 at 21:59
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    $\begingroup$ I don't think so. Alternatively you could use >! to hide the full answer and advertise OP $\endgroup$ – user486983 Mar 28 at 22:02
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    $\begingroup$ While I agree with the usage of ">!" , I still don't agree that just because "Always give more than what's expected" I should try that. Personally, I believe (so far) it's better to address the issues the OP has given. $\endgroup$ – Mann Mar 28 at 22:10
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    $\begingroup$ @Isa: please write that as an answer so that some us have the chance to downvote such misguided comment. $\endgroup$ – Martin Argerami Mar 29 at 18:30
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    $\begingroup$ :( ${}{}{}{}{}$ $\endgroup$ – user486983 Mar 29 at 19:15
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    $\begingroup$ At present, your answer has six upvotes, and no downvotes. I wouldn't worry too much about one critical comment getting one upvote. $\endgroup$ – Gerry Myerson Mar 29 at 23:03
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    $\begingroup$ I recently asked a question for which I am specifically seeking an answer conforming to stated restrictions (no induction hypothesis is used). Alternative approaches may be helpful in gaining an understanding of the problem, so I don't object to their submission. As for up-votes, down-votes and close-votes. They often have little correlation to the value or appropriateness of a question, comment or answer. Questions which I believe to be deeply insightful often get no appreciation, and "throw away, off the cuff musings" have gained me the most reputation points. $\endgroup$ – Steven Thomas Hatton Mar 31 at 18:37
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    $\begingroup$ I think the idea of letting a few negative comments and downvotes slide bears repeating. Everyone gets critical comments and downvotes on Stack Exchange - even the users with the highest reps who are experts in their fields. It's part of the human nature of the site (and the internet as a whole). Take them in stride. If you get more downvotes than upvotes on something, and/or comments seem to be explaining downvotes, then it may be time to take a second critical look at what you've posted and try to see the other perspectives. But there will always be a negative minority that you can't please. $\endgroup$ – Todd Wilcox Apr 4 at 13:53
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In a Question where the OP states a problem and then presents an incorrect solution due to misunderstanding the problem statement, it is helpful both to point out the misunderstanding and (at the risk of doing the OP's work/thinking for them) providing a correct solution (or hint).

Different contributors approach this dilemma in various ways. My own heuristic is to ask whether the OP has indeed digested the problem well enough to understand what is being asked (not necessarily enough to articulate a good approach or solution). So I'd focus on helping with the issue of where the understanding of the problem took a wrong turn. Very often it seems we learn the most from our errors of interpreting problems, or at least that such mistakes motivate us strongly to learn new material or points of view.

So the primary thing would be to help with where they went wrong, and as a secondary topic help with solving the original problem (presumably an assigned exercise in the instance linked). Untangling a student's wrong path will often require some insight beyond merely solving the problem as you would do it.

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  • $\begingroup$ It wasn't an error of understanding the problem statement but one faulty reasoning used to jump from one specific step to another. However, I do agree with your point! "Very often it seems we learn the most from our errors of interpreting problems, or at least that such mistakes motivate us strongly to learn new material or points of view." $\endgroup$ – Mann Mar 28 at 22:25
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    $\begingroup$ I was trying to be fairly generic in my response, as I think you were asking about a general policy rather than a specific-question. It seemed to me that the OP finds a solution $x=1,y=0$ and is then dismayed that $x,y$ are not primes, which to me suggests a misunderstanding of the problem. Your point of view, that it was the reasoning that had a "faulty... jump," is not wrong but worthy IMHO of more exposition to help the OP's understanding of the problem. $\endgroup$ – hardmath Mar 29 at 1:01

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