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China Mathematical Olympiad 2024 Q2

Source: Nov 28, 2023

November 28, 2023
inequalitiesalgebraCMOChina

Problem Statement

Find the largest real number cc such that ∑i=1n∑j=1n(n−∣i−j∣)xixj≥c∑j=1nxi2\sum_{i=1}^{n}\sum_{j=1}^{n}(n-|i-j|)x_ix_j \geq c\sum_{j=1}^{n}x^2_i for any positive integer nn and any real numbers x1,x2,…,xn.x_1,x_2,\dots,x_n.
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