MathDB

Cosines inequality on n variables - ILL 1983

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October 7, 2010

trigonometryinequalitiesinequalities unsolved

Problem Statement

Prove that for all

x_1, x_2,\ldots , x_n \in \mathbb R

the following inequality holds:

\sum_{n \geq i >j \geq 1} \cos^2(x_i - x_j ) \geq \frac{n(n-2)}{4}