Only one student answered an exam question - and I strongly suspect he cheated Today we (professors + teaching assistants) proctored a midterm exam for a class of about 80 students.  There was undoubtedly a "hardest" question on the exam, since nearly the entire classroom of students asked us how to proceed with that question. To be fair, we didn't give any hints, but it was clear that one had to use a definition to be able to proceed.  

When we collected the exams, all of the exam booklets had that question unanswered -- except for one student's exam.  And this was the only student who asked to go to the bathroom.  I gave him permission to go, but I did not ask for his phone, which I now highly regret.

What can we do in this situation, in which I strongly suspect that this student went to the bathroom to look up a definition on his phone, so that he could answer the question correctly?

We still have to look at every exam to be sure that only one student got it right (the bathroom student), but if this were indeed the case, do we have any power to accuse him of cheating, or, have we missed our chance by not asking for him to leave his phone in the room?

I feel a big injustice will have been done to the rest of the honest students, if we let this one slide ...
I apologize in advance for my frankness.


  What can we do in this situation, in which I strongly suspect that this student went to the bathroom to look up a definition on his phone, so that he could answer the question correctly?


Nothing.


  have we missed our chance by not asking for him to leave his phone in the room?


You missed it, but it doesn't really matter: the student might have had a mate with a phone in the bathroom. Or not. The student might even have known the answer.


  I feel a big injustice will have been done to the rest of the honest students, if we let this one slide


In your career you quite probably have already let others slide.

I wrote in this answer that, on the basis of my (now sufficiently long) experience, if a student wants to cheat, they will. Therefore, one has to accept that, from time to time, a student cheats, and one doesn't notice or is not able to prove beyond reasonable doubt that the student cheated (and you don't want to accuse someone of cheating if you're not able to prove it, right?).

So, move on.

NB: As some have remarked in various comments, the fact that almost all students were unable to answer that question can be a major issue. In this answer, I specifically wanted to address the cheating part only, because I think that this other issue is a totally different matter, which can be also culture-dependent, and which is probably worth of a different (interesting) question.