IMO 1974 LL USA39

Let n be a positive integer, n \geq2, and consider the polynomial

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IMO 1974 LL USA39

Origin: USA

Problem

Let n be a positive integer, n \geq2, and consider the polynomial equation xn −xn−2 −x + 2 = 0. For each n, determine all complex numbers x that satisfy the equation and have modulus |x| = 1.