Question

What numbers A and B make this equation true:
(AA)^B = ABBA
Awarding Medal

Answer 1

What have you tried? We can make a few quick changes to the equation:

\[ (AA)^B = (A^2)^B = A^{2B}\] \[ ABBA = (AB)^2\]

This makes both sides easier to work with, and we can immediately spot some solutions.

Are we solving over integers?

Answer 2

If this is over the integers, it seems reasonably easy to limit the possible values of B to a small set, which we can try in turn. They each give a few results, except for B = 1, which is clearly valid for any A.

But I have to go, and you don't seem like you want my help. So you can do the rest :-)