I recently asked this question: "Find the number of ordered pairs of integers $(x,y)$ such that $x^2+y^2-xy=37$" on the Math SE. My question got closed as a duplicate of this question: "Find the number of ordered pairs of positive integers (x,y) that satisfy $x^{2} - xy + y^{2} = 49$".

Although the question looks similar, in the second question the constant is 49 which is a perfect square. The answers to that question make use of the fact that 49 is a perfect square.But in my question the constant is 37 which is not a perfect square, so the same methods used in the second question cannot be used to solve my question. So I want my question to be reopened.

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    $\begingroup$ The fact that $49$ is a square is incidental. The point is that, in both cases, it is easy to reduce the problem to a simple finite search. $\endgroup$ – lulu Jun 25 at 16:08
  • $\begingroup$ @lulu But I've clearly written in the above post that the answers make use of the fact that 49 is a perfect square. I can't adapt the solution to my question because of that property. $\endgroup$ – Sujal Motagi Jun 25 at 16:10
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    $\begingroup$ Of course you can. Actually, the fact that $49$ is a perfect square makes that case a little harder since you can't rule out the case $x=y$ immediately (indeed, there is such a solution). In your case, you can immediately rule that out. $\endgroup$ – lulu Jun 25 at 16:11
  • $\begingroup$ @lulu But in that answer they factored $49-y^2=(7+y)(7-y)$, how do I deal with that? $\endgroup$ – Sujal Motagi Jun 25 at 16:16
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    $\begingroup$ The second posted solution to the duplicate does not use that trick. Or use one of the simplifications that you were handed in the comments to your question. $\endgroup$ – lulu Jun 25 at 16:20
  • $\begingroup$ Btw, requesting questions to be reopened can be done in the CURED chatroom as well as the thread here on meta ...(as I recently learnt) $\endgroup$ – sai-kartik Jun 28 at 3:39
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    $\begingroup$ @sai-kartik But there are so many questions on Meta asking why their questions got closed. I don't know why mine was marked off topic. $\endgroup$ – Sujal Motagi Jun 28 at 8:31
  • $\begingroup$ You can always take your question to the CURED chatroom. It was probably built to collect all this questions and decide on them collectively. Rest assured that there are plenty of users who are regularly active in that room. ( If I was wrong about this, someone please correct me) $\endgroup$ – sai-kartik Jun 28 at 9:07

Although I was not one of those voting to close as duplicate, I will usually prefer that action to closing for lack of context.

Your Math.SE post says, "I've never solved diophantine equations of degree 2 so I didn't know how to approach this problem." This in your words justifies adding nothing of your attempts to solve the problem and leaves it to your Readers to guess at what level you approached it. Although it may seem to you that providing context for your interest in the problem is unimportant, it is helpful to those willing to make an effort to help you learn this subject.

For this reason I am often inclined to point out an existing Question whose solution can be used, perhaps mutatis mutandi, to solve the new "no context" Question. In this case I can concur with that action. Perhaps if your difficulty with or misunderstanding of the problem were more clearly presented, it would have encouraged a more specific response.

Note that context is often best presented in terms of where the problem was encountered or what makes the problem important enough to research, rather than just what effort was made or approach taken to solve the problem. Any of these kinds of context help willing Readers to appreciate what "gap" needs to be filled for a student to progress. (And we are all students!)

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  • $\begingroup$ The thing is I didn't have any approach to write it in the first place. I was totally blank when I saw the problem. That's why I haven't provided any info about my attempts. $\endgroup$ – Sujal Motagi Jun 25 at 17:51
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    $\begingroup$ @SujalMotagi: I accept that you perceived the problem just as you describe. However even in the absence of "attempts," there is context to be added. Where did you encounter this problem? What makes it interesting to you? Did you search the Math.SE corpus and read about similar diophantine quadratic problems before posting? Your own thinking is more important to the mission of learning than you seem to believe. $\endgroup$ – hardmath Jun 25 at 17:54
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    $\begingroup$ @SujalMotagi I am less concerned about past effort than about students following the directions we give. Have you taken some graph paper and drawn the ellipse $x^2 - xy + y^2 = 37$ by hand? From the inequalities in my answer, it is enough to have both $x,y$ between $-8$ and $8.$ Printable graph paper is available at printablepaper.net/category/graph For the alternative $x^2 - xy + y^2 = 49$ it is enough to have space for $x,y$ between $-9$ and $9$ Just do it. $\endgroup$ – Will Jagy Jun 25 at 19:09
  • $\begingroup$ @WillJagy Yes I have got a satisfactory answer. $\endgroup$ – Sujal Motagi Jun 26 at 7:47

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