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MathNet 2017-part-02 — 176 problems (EN–VI) Question 103

Math Olympiad Vault · MathNet 2017-part-02 — 176 problems (EN–VI)

Question 103

Find the smallest real constant $C$ such that for any positive real numbers $a_1, a_2, a_3, a_4$ and $a_5$ (not necessarily distinct), one can always choose distinct subscripts $i, j, k$ and $l$ such that $\left|\frac{a_i}{a_j} - \frac{a_k}{a_l}\right| \le C$.