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find all polynomials 2 (IrMO 1991)

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January 17, 2014
algebrapolynomialalgebra unsolved

Problem Statement

Find all polynomials
f(x)=xn+a1xn−1+⋯+anf(x) = x^{n} + a_{1}x^{n-1} + \cdots + a_{n}
with the following properties
(a) all the coefficients a1,a2,...,ana_{1}, a_{2}, ..., a_{n} belong to the set {−1,1}\{ -1, 1 \}; and (b) all the roots of the equation f(x)=0f(x)=0 are real.
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