Hi guys, please help me. I have done a whole weekend of Number Theory for my midterm next week, my head is aching so bad.

I have this last question from my homework,

Find all positive integers a and b such that a^b = b^a . Prove your answer.

My prof said you can use calculus, think f(x) = x^(1/x), find max and min. And you can also use Fundamental Theory of Arithmetic. This may be very easy for some of you, but I really have no clue right now. Please help me? Thank you!