I've recently become aware of this result:
Theorem 1. There exists a strictly increasing function $f:\mathbb{N}\to \mathbb{N}$, such that for any finite group $G$, the following inequality holds: $$|G|\leq f(|\mathrm{Aut}(G)|)$$
I was wondering if by any chance there would exists a math olympiad problem that could be tackled using Theorem 1? That would be nice!
If not, maybe it is possible to create one? I'm not too familiar with the method to create problems, so if someone could help me, I'll appreciate it! (or even giving me an hint on how to start).
N.B : the proof of Theorem 1 actually gives such a $f$. If $h:n\mapsto \max \varphi^{-1}(\{2,\dots, n\})$ (with $\varphi$ the Euler totient function), then $f(n) = h(n)\cdot n^{2n^3+2}$ works.