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Do you find OK to include exercises in an answer?

(Silly) Example:

Q: How can $163^{163} \pmod {37}$ be computed?

A: Apply little Fermat's Theorem. You can use Fermat-Euler's Theorem in certain conditions. Could you compute $163^{163}\pmod{24}$?

I think that it should be OK. People pay for being taught, after all, or at least, education is considered as a social service. But I have tried this in some answers with no positive or negative feedback. Perhaps, just MSE isn't the web site for doing this.

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    $\begingroup$ I don't understand what payment for being taught has to do with this. $\endgroup$ – Gerry Myerson Sep 8 '17 at 3:58
  • $\begingroup$ I think most people use MSE is for learning the general principles behind answering a question, rather than just getting the answer. If you think an exercise would help the asker with this, then go ahead. I would personally appreciate it if someone gave me some helpful examples. $\endgroup$ – Ruvi Lecamwasam Sep 8 '17 at 9:44
  • $\begingroup$ The part after Q is the question post and the part after A the answer post and you wonder if the "Could you compute..." is appropriate. Is this what your are asking? $\endgroup$ – quid Sep 8 '17 at 10:08
  • $\begingroup$ I think this is fine. Just the other day I had posted an answer where the last line was: "I leave the telescoping process to the reader. $\ddot\smile$", and while I do not know if that's what brought the (currently) 13 upvotes, it seems that leaving such exercises does not hurt, so long as you don't make it too vague and complicated for the problem. $\endgroup$ – Simply Beautiful Art Sep 8 '17 at 11:19
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    $\begingroup$ @SimplyBeautifulArt but that seems a completely different situation. You leave part of the argument needed to answer the question as "exercise." Yet the sample in OP includes in the answer part a new question that is not directly needed or even immediately useful to answer the question asked. It's use is to provide material for study going beyond what is asked. $\endgroup$ – quid Sep 8 '17 at 16:51
  • $\begingroup$ @quid Ah, I see what you mean... $\endgroup$ – Simply Beautiful Art Sep 8 '17 at 17:06
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    $\begingroup$ I have included remarks in Answers suggesting this or that as an exercise for the interested Reader, sometimes not crucial to a complete proof but sometimes an easy point that needs to be filled in to complete the proof. Also (as best I recall) I've never gotten positive or negative feedback about doing so. I don't draw the conclusion "MSE isn't the web site for doing this". Used skillfully it might be a good expository technique, and used unskillfully it might detract from an otherwise good Answer. $\endgroup$ – hardmath Sep 8 '17 at 19:12
  • $\begingroup$ I'd beg to differ. If the answer is not a full answer but a hint, though making the rest a rather simple exercise, it's ok. If the exercise is not really related to the question, it's not. The OP calls the example "silly", and I have to agree. For the original answer, you have to know only little Fermat, because $37$ is a prime. For the modulus $24$, you have to know a bit more. The irony is: You can obtain $163^{163}\equiv19\pmod{24}$ with mental calculation (using the Chinese Remainder Theorem),I wouldn't try that with the original question. $\endgroup$ – Professor Vector Sep 10 '17 at 17:23
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Many users find some success in giving more or less partial answers, including answers which are complete with the exception of small details left as implicit exercises. There are some good things and some bad things to this practice.

Many users here are students of mathematics, and one must do exercises to learn math. Being asked to finish small details reinforces some of the basic concepts behind each question. This also prevents users from simply copying down complete answers to homework questions (which some people care about, and some people don't. That's another issue).

However catering partial answers for each initial asker creates a large set of answers with less sustained appeal, and leads to massive duplication of effort. I have sometimes used some math adjacent to my research in my work and papers, but I have not taken the time to really learn it. One must set priorities on what to learn. I find it tremendously annoying when I need to understand some topic, look to MSE for examples, and only find partial or incomplete answers.

Most sites in the StackExchange network are designed to provide great, cannonical answers to questions that people come across, so that later viewers can search for the question and will know that if they find it here, then they will also have a solution.

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  • $\begingroup$ (+1) well rounded answer covering what I think to be all sides of the issue, except maybe unhappiness for the asker. $\endgroup$ – Simply Beautiful Art Sep 8 '17 at 11:21
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    $\begingroup$ I agree with the content of this answer, but I am somewhat unsure it answers the specific meta question. "Could you compute $163^{163}\pmod{24}$?" Is not a hint or rhetorical question that leads towards an answer of "How can $163^{163} \pmod {37}$ be computed?" It seems like material for further study going beyond the question actually ask. OP brings up a problem that is a conceptually harder problem than the one asked about. $\endgroup$ – quid Sep 8 '17 at 16:12

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