SOLUTION: How many pairs of integers (a,b) satisfy the equation {{{a^ab = 256}}}?

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Question 1199524: How many pairs of integers (a,b) satisfy the equation a%5Eab+=+256?
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.

256 = 2%5E8 = 4%5E4.


The solutions to the problem are


        (1)  the pair  (a,b) = (2,4),

    and

        (2)  the pair  (a,b) = (4,1).


There is no other solutions in positive integer numbers.


ANSWER.  There are two different ordered pairs (a,b) that provide the solutions to the given equation.