Question 9
Determine all integers $a\gt 0$ for which there exist positive integers $n, s, m_{1}, \cdots, m_{n}, k_{1}, \cdots, k_{s}$ such that
$$
\left(a^{m_{1}}-1\right) \cdots\left(a^{m_{n}}-1\right)=\left(a^{k_{1}}+1\right) \cdots\left(a^{k_{s}}+1\right)
$$
$$
\left(a^{m_{1}}-1\right) \cdots\left(a^{m_{n}}-1\right)=\left(a^{k_{1}}+1\right) \cdots\left(a^{k_{s}}+1\right)
$$