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I have to determine all pairs $(a,b)$ of positive integers satisfying the condition $a^{b^2}=b^a$. So far i have found only one, namely $(1,1)$. How can i do it? Thanks for any help.

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Hints:

  1. Take logarithms
  2. $\log_b(a)\in\mathbb Q\Leftrightarrow \exists n\in\mathbb N:a=b^n$
  3. Juggle a little with the remaining expression.
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