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ILL 1983 Problem 72

    Prove that for all x1,x2,…,xn∈Rx_1, x_2,\ldots , x_n \in \mathbb R the following inequality holds: ∑n≥i>j≥1cos⁡2(xi−xj)≥n(n−2)4\sum_{n \geq i >j \geq 1} \cos^2(x_i - x_j ) \geq \frac{n(n-2)}{4}

    Dataset text AI-MO AoPS. Quoted with source.

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