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Please, visit my question.

You will see the post has 9 downvotes and one of the answers got 7 up-votes. Moreover, the answer that got 7 votes is a mere try, not a complete answer. On the other hand my complete answer (right or wrong) got no vote, or any constructive, real feedback.

Would anyone be kind enough to explain this "counter-intuitive" phenomenon? Thanks.

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    $\begingroup$ What you describe is a general phenomenon: With some frequency there are badly rated questions that have one or more highly rated answers. I have no explanation for this. But without the question there would be no great answer. So, in my opinion, at least for inspiring good answers such a question also deserves upvotes. $\endgroup$ – tj_ Aug 12 '16 at 9:00
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    $\begingroup$ I see this question, and the MO question to which it refers, have been edited in recent hours. I don't understand what you hope to gain by bumping the question here, or by editing out the only mention of motivation that had been over there -- this action goes against the advice I tried to give in my answer here, and could easily result in further downvotes. $\endgroup$ – Todd Trimble Sep 6 '16 at 1:37
  • $\begingroup$ 1. What's counterintuitive about it? 2. What is your answer you speak about? I only see one answer, and it has 8 upvotes at the moment I am writing. $\endgroup$ – Federico Poloni Sep 8 '16 at 13:25
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Unless the voters want to weigh in themselves, we can only guess.

As I see it, the question is not at all well motivated, and there is no hint why anyone might think that there are infinitely many such numbers. Indeed, as far as I know we don't have even a single such number.

Setting context or motivation should be the norm for a community of researchers who are trying to garner interest in their problems so that others will be willing to think about them. Particularly in number theory, it's very easy to cook up (possibly hard) random-looking problems, and this question does seem a little contrived to me. Maybe you could explain the real background and why you got interested?

As I see it, the reason why your answer hasn't attracted more interest is that it's a long mass of implications without much of a conceptual guideline, to a question that is of no obvious interest in the first place, and it's not well-formatted which doesn't help. In short, people don't seem to care to wade through it; people often hope to take some insight home with them after reading an answer, and they upvote answers which are recognizably insightful.

Gerhard's answer, even if incomplete, has the virtue of giving some insight or conceptual explanation in the form of heuristic. He also raises the better question (I think): are there any such $n$?

To reiterate: this is all looking into a crystal ball. In a constructive spirit, please take it as giving suggestions for asking good questions and giving good answers.

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The reversal badge is exactly about the phenomenon where a bad question gets a very good answer, namely, where a question with a score of -5 or worse receives an answer of +20 or more.

This badge has been awarded several times, and these are each more extreme instances of what is described in the question.

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