MathDB

11.1

Part of 2011 All-Russian Olympiad Regional Round

Problems(1)

Problem 1 of Russian Regional Olympiad 2011, grade 11

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

9/1/2011
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)
trigonometryalgebrapolynomialalgebra proposed