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Composition of polynomials has roots powers of 2

Source: St. Petersburg 2023 11.1

August 12, 2023
algebra

Problem Statement

Let f(x),g(x)f(x), g(x) be real polynomials of degrees 22 and 33, respectively. Could it happen that f(g(x))f(g(x)) has 66 distinct roots, which are powers of 22?