Citing Mathematical Proofs given on Math Stack Exchange
There are actually two questions on MathOverflow that ask how to cite answers found on MathOverflow. I would recommend following their advice.
One of them is a fairly old question, whose answer is somewhat outdated. Summarizing:
Even though you may not be legally obligated to show where you got your answer (for example, when MO points you to a theorem already in the literature), it is a good idea — it never hurts to be generous and honest. (And if you're copying part of an answer, not citing it would be plagiarism.)
There is a little button for each answer that says "cite" and will give you a citation. You might have to reformat this to make it fit in your journal's bibliography style.
Perhaps the person who posted it actually found it elsewhere and can provide a reference to you. Alternately, if you are willing to be publicly known here, you can find a way to exchange emails and hence give proper credit to the individual(s).
In the past, I've exchanged emails with members on this site using a mod as a go-between, but that implies that you can reach the mod via email and that the mod actually knows the other person's email. I note that the mods themselves aren't able to get people's email addresses from the site and it requires someone with higher authority. But if it is possible, the correct way is to ask a mod or administrator to give your email address to the other person, rather than to ask for theirs.
However, the rules are the same. If you use someone else's work, you need to cite them and an anonymous citation may not be enough unless they tell you on the site that you may do that. In that case, keep a record (pdf) of the exchange. The chatroom rather than the comment stream may be a better place to explore such things. (https://chat.stackexchange.com/rooms/2496/the-ivory-tower, or something similar at the math site: https://chat.stackexchange.com/?tab=site&host=math.stackexchange.com.)
But see the answers for the questions that this duplicates, also. I would, myself, worry about a citation that used an alias as author, rather than a true-name.