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positivist polynomial

Source: OBM 2017

March 20, 2023
polynomialalgebracollege contests

Problem Statement

A polynomial is called positivist if it can be written as a product of two non-constant polynomials with non-negative real coefficients. Let f(x)f(x) be a polynomial of degree greater than one such that f(xn)f(x^n) is positivist for some positive integer nn. Show that f(x)f(x) is positivist.
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