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F 3

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May 25, 2007
trigonometryrational numbersIMO Shortlist

Problem Statement

Let α \alpha be a rational number with 0<α<1 0 < \alpha < 1 and \cos (3 \pi \alpha) \plus{} 2\cos(2 \pi \alpha) \equal{} 0. Prove that \alpha \equal{} \frac {2}{3}.
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