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IMC 2005 day 2 pb 2

Source: Peter

July 26, 2005
functionalgebrapolynomialnumber theoryrelatively primeIMCcollege contests

Problem Statement

Let f:R→Rf: \mathbb{R}\to\mathbb{R} be a function such that (f(x))n(f(x))^{n} is a polynomial for every integer n≥2n\geq 2. Is ff also a polynomial?
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