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Minimum of sum of cosines of differences

Source: Russian TST 2014, Day 10 P3 (Group NG)

January 8, 2024
algebraminimum valuetrigonometry

Problem Statement

Let n>1n>1 be an integer and x1,x2,…,xnx_1,x_2,\ldots,x_n be nn{} arbitrary real numbers. Determine the minimum value of ∑i<j∣cos⁡(xi−xj)∣.\sum_{i<j}|\cos(x_i-x_j)|.
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