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IMC2015, problem 10

Source: IMC2015

July 30, 2015
college contestsPolynomialsInequalityIMC2015

Problem Statement

Let nn be a positive integer, and let p(x)p(x) be a polynomial of degree nn with integer coefficients. Prove that \max_{0\le x\le1} \big|p(x)\big| > \frac1{e^n}.
Proposed by Géza Kós, Eötvös University, Budapest
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