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China Mathematical Olympiad 1987 problem1

Source: China Mathematical Olympiad 1987 problem1

January 6, 2014
trigonometryalgebra unsolvedalgebra

Problem Statement

Let nn be a natural number. Prove that a necessary and sufficient condition for the equation zn+1−zn−1=0z^{n+1}-z^n-1=0 to have a complex root whose modulus is equal to 11 is that n+2n+2 is divisible by 66.
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