Question 67
Determine if there exist positive integers $a, b, m, n$ such that $a \neq b$, $m \geq 2$, $n \geq 2$, and
$$
\underbrace{a^{a^{\cdots a}}}_{m} = \underbrace{b^{b^{\cdots b}}}_{n}.
$$
$$
\underbrace{a^{a^{\cdots a}}}_{m} = \underbrace{b^{b^{\cdots b}}}_{n}.
$$