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The number is an integer (Cosine) - [Iran Second Round 1985]

Source:

December 28, 2010
trigonometryinductionstrong inductionalgebra proposedalgebra

Problem Statement

Let α\alpha be an angle such that cos⁡α=pq\cos \alpha = \frac pq, where pp and qq are two integers. Prove that the number qncos⁡nαq^n \cos n \alpha is an integer.
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