### International Mathematics Competition for University Students

July 27 - Aug 2 2015, Blagoevgrad, Bulgaria

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### Problem 10

10. Let $n$ be a positive integer, and let $p(x)$ be a polynomial of degree $n$ with integer coefficients. Prove that $$\max_{0\le x\le1} \big|p(x)\big| > \frac1{e^n}.$$

Proposed by Géza Kós, Eötvös University, Budapest