/sci/ - Science & Math

I rember to have read somewhere that the equation a^b = b^a + 1 (a,b are positive natural numbers) has only one solution, i.e. (a,b) = (3, 2).
I also remember that this is a conjecture or maybe it was proved but the proof is really difficult.
Does someone know the name of this conjecture/theorem?
Maybe I found it while I was reading something on Erdos, I can't remember.