Suppose that a mathematician such as Bugs Bunny answers one of my math questions here on MathOverflow, and then I use the idea in a research paper. How should I acknowledge such a distinguished mathematician in my paper, submitted to a reputable journal and all that?
I think it depends how important is the help you have received. If it is a crucial step in your work and without it you were not able to complete the paper, you may want to suggest the helper to be your co-author. But if it is not that important you can send him/her an email and thank him/her and let him/her know that you will acknowledge his/her help at the end of the paper.