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I believe we already have a couple of questions that are, while understandable at the high-school or even lower level, have no accepted answer in even research-level Maths.

I'm not referring to in-debate answers (such as "is 0 a natural number?"). I'm talking about problems that have not yet been solved.

Imagine if the question "Are there any integer solutions to a^n + b^n = c^n, where n > 2?" were asked fifty years ago. It's a simple question, but at the time there were no actual answers that the Mathematics community could give, besides, "We don't know."

(Note that, if someone actually were to ask Fermat's Last Theorem, it'd be quite suspicious and probably a trolling attempt. I'm speaking of questions that are not as well-known yet still pose trouble for research-level mathematics today)

Should the answer be "We don't know, and here's why. But we might one day find out." ? (With a decently typed out "why")

Also, what is the duty of the asker to choose an answer to accept? If the best answer is the answer in the form above, should it be accepted? Or should the question be left unresolved?

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I think the only answer is something of the form you've stated--"we don't know, and [here's] why."

I don't think the asker has a duty to accept an answer in any situation, really. But I'd probably be less likely to accept an answer of that form, since it's more likely to admit a substantially different response at some future point.

We might also refer some of these questions to MathOverflow, where there are more professional mathematicians who might be familiar with the current state of such research. Plenty of people have had success asking understandable-but-unsolved questions on there, as long as the question is well-enough posed that potential answerers are inspired to think before declaring that the question is too simple to be research-level.

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We could also add some related results. Let's say that someone asks for Goldbach's conjecture; we could say that the problem is old, the conjecture has been double-checked for numbers up to 10^17, and that every sufficiently large number may be expressed either as the sum of tho primes or as the sum of a prime and a semiprime.
In this way the person who asked it has at least an idea of what happens.

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