Question 164
Find all integers $n \geqslant 3$ such that, if $a_{1}, \ldots, a_{n}$ are strictly positive reals such that $\max \left(a_{1}, \ldots, a_{n}\right) \leqslant n \cdot \min \left(a_{1}, \ldots, a_{n}\right)$, then there necessarily exist three of these reals that are the side lengths of an acute triangle, that is, a triangle whose three angles are all strictly acute.