Question 93
Determine the smallest real constant $C$ such that for all $a_{1}, a_{2}, a_{3}, a_{4}, a_{5} \in \mathbb{R}_{\gt 0}$, not necessarily distinct, there always exist four distinct indices $i, j, k, l$ such that:
$$
\left|\frac{a_{i}}{a_{j}}-\frac{a_{k}}{a_{l}}\right| \leq C
$$
$$
\left|\frac{a_{i}}{a_{j}}-\frac{a_{k}}{a_{l}}\right| \leq C
$$