International Mathematics Competition
for University Students
2015

IMC2015: Day 2, 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

  Hint    Solution