MathNet 2022-part-04 — 197 problems (EN–VI) Question 163

Let $\phi_n(m) = \phi(\phi_{n-1}(m))$, where $\phi_1(m) = \phi(m)$ is the Euler totient function, and set $\omega(m)$ the smallest number $n$ such that $\phi_n(m) = 1$. If $m \lt 2^\alpha$, then prove that $\omega(m) \le \alpha$.