How to briefly mention that you answered someone's question without seeming dismissive?

Question

I'm writing my first paper. I would like to mention at the end that I have answered someone's question that is related to the subject of the paper. The proof is really short and doesn't use any original techniques, so I probably will not include it. The question is, how do I mention that I solved the problem without seeming dismissive, as if the solution was not worth the ink?

Answer 1

As a rule of thumb, if it's a question raised in another paper, then cite the paper and answer it. If it was asked to you personally by another mathematician, then you can choose between not saying anything in your paper and sending an email/talking with the other person about it, or (if it is interesting enough) repeat the question in your paper, of course mentioning the person that asked it originally, and giving a complete answer.

Mentioning the question and saying that you can answer it without giving a complete argument is not an acceptable way to proceed in my opinion.