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동문 뉴스

Problem of the week

Does there exist a (possibly \(n\)-dependent) constant \( C \) such that \[ \frac{C}{a_n} \sum_{1 \leq i < j \leq n} (a_i-a_j)^2 \leq \frac{a_1+ \dots + a_n}{n} - \sqrt[n]{a_1 \dots a_n} \leq \frac{C}{a_1} \sum_{1 \leq i < j \leq n} (a_i-a_j)^2 \] for any \( 0 < a_1 \leq a_2 \leq \dots \leq a_n \)?