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Determine all complex numbers x [ILL 1974]

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January 2, 2011
algebrapolynomialcomplex numbersalgebra unsolved

Problem Statement

Let nn be a positive integer, n≥2n \geq 2, and consider the polynomial equation xn−xn−2−x+2=0.x^n - x^{n-2} - x + 2 = 0. For each n,n, determine all complex numbers xx that satisfy the equation and have modulus ∣x∣=1.|x| = 1.
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