A small problem


the problem is :a^b+b^a =n   a,b,n are integers.  for each n, there are two solutions: (1,n-1）and (n-1,1)
and for some n,  there are 4 or more solutions .

then there is the question:
(1)for n has 4 solutions, can it have more solutions?
by computer it seems impossible, but how to prove it ？
(2)and for n has 4 solutions can we find the  display expression between the solutions and n？
