How to solve $a^{b^2} = b^a$ in positive integers

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I have this exercise:

$a,b$ are positive integers. Get all $a,b$ numbers that satisfies $a^{b^2} = b^a$

Is hard to me, but I have these advances:

$a,b$ must be both even or both odd, since $a, b$ are the base.

Besides, if $a > b$, the exponent and the exponent of $a$ is $b^2$ and the exponent of $b$ is $a$, therefore $a > b^2$

So far I have managed to develop the exercise, what can I do? How do you work with these types of mathematical problems? Thanks in advance