The same three solutions can be obtained easily with no computer. Let a
= b^x. Then b^(x*b^2)=b^(b^x) so x*b^2=b^x or finally
b=x^(1/(x-2). Clearly, b=1, b=3 and b=2 (corresponding to x=1,x=3
and x=4) work. Whether there are any other solutions remains the
question, and this seems like it may be difficult to settle.
re: computer solution (spoiler)
