Ethics of not referencing StackExchange in a publication?

So I'm feeling a bit guilty. I've been working on a publication proof (my first) of an interesting theorem. The issue is I've been using StackExchange (Mathematics) to answer some similar questions when I get stuck on much smaller parts of the proof.

So the question here is, is it generally ethical to put just my name on a paper, even if I may not have come up with the lemma's using only my ideas, or is there a good way to I should reference StackExchange in a publication?

On one hand, most of the stuff I received answers for was for a learning purpose, similar to that of me asking a professor or teacher, not so much as a co-author. And although relevant to the publication, the answers I received could be very common in other proofs as well and were not directly related the lemmas themselves.

On the other hand, it was not necessarily my ideas that first assisted the lemma, but those of others through SE.

Take for example a question I asked earlier today. I wanted to see an alternate proof to an equation, so that I could use it as a new method of proving a lemma related, it as the original proof (Euler's Thereom) could not be generalized with such a method Proving $a^{(p-1)p^{k-1}} \equiv 1 \pmod {p^k}$ without Euler's Theorem. The proof I was looking for was simply done using the Binomial Theorem. Therefore the idea of using the Binomial Theorem in my proof will assist me in my own similar generalization. But even though I was just given the tool, the work will be done myself.