MathDB
Composition of Polynomials

Source: Miklos Schweitzer 2015 Problem 5

November 20, 2015
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Problem Statement

Let f(x)=xn+xn−1+⋯+x+1f(x) = x^n+x^{n-1}+\dots+x+1 for an integer n≥1.n\ge 1. For which nn are there polynomials g,hg, h with real coefficients and degrees smaller than nn such that f(x)=g(h(x)).f(x) = g(h(x)).
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