Question 17
Determine the smallest real constant $C$ with the following property:
For any five positive real numbers $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$, not necessarily distinct, one can always find pairwise distinct indices $i, j, k, l$ such that
$$
\left|\frac{a_{i}}{a_{j}}-\frac{a_{k}}{a_{l}}\right| \leq C
$$
holds.
For any five positive real numbers $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$, not necessarily distinct, one can always find pairwise distinct indices $i, j, k, l$ such that
$$
\left|\frac{a_{i}}{a_{j}}-\frac{a_{k}}{a_{l}}\right| \leq C
$$
holds.