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Problem 1 of Russian Regional Olympiad 2011, grade 11

Source: Problem 1 of Russian Regional Olympiad 2011, grade 11

September 1, 2011
trigonometryalgebrapolynomialalgebra proposed

Problem Statement

Is there a real number α\alpha such that cos⁡α\cos\alpha is irrational but cos⁡2α\cos 2\alpha, cos⁡3α\cos 3\alpha, cos⁡4α\cos 4\alpha, cos⁡5α\cos 5\alpha are all rational? (Author: V. Senderov)
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