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MathNet 2024-part-05 — 168 problems (EN–VI) Question 26

Math Olympiad Vault · MathNet 2024-part-05 — 168 problems (EN–VI)

Question 26

Find the minimum value of
$$
\frac{x_1^3 + \cdots + x_n^3}{x_1 + \cdots + x_n}
$$
where $x_1, x_2, \dots, x_n$ are distinct positive integers.