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SMO 2024 Open Round 2 Question 2

SMO · SMO 2024 Open Round 2

Question 2

Let $n$ be a fixed positive integer. Find the minimum value of
$$\frac{x_1^3+\cdots+x_n^3}{x_1+\cdots+x_n},$$
where $x_1,x_2,\ldots,x_n$ are distinct positive integers.