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cos

Source: Romania District Olympiad 2013,grade X(problem 4)

March 14, 2013
trigonometrymodular arithmeticinductionalgebra proposedalgebra

Problem Statement

Let n∈N∗n\in {{\mathbb{N}}^{*}}. Prove that 22ncos⁡(narccos⁡24)2\sqrt{{{2}^{n}}}\cos \left( n\arccos \frac{\sqrt{2}}{4} \right) is an odd integer.
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