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, 2015

Algebra Difficulty 6.0 National Olympiad Prove it Hungary

Let $f(x,y)$ be a polynomial with two variables and integer coefficients such that $f$ is constant neither in $x$ - nor in $y$ -direction. Prove that $\max_{a,b\in[-2,2]}\big|f(a,b)\big|\ge4$ .
Based on the idea of Tamás Erdélyi, College Station, Texas
(5 pont)

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