IMO Shortlist 2018 problem A6


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3. listopada 2019.
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Let m,n\geq 2 be integers. Let f(x_1,\dots, x_n) be a polynomial with real coefficients such that f(x_1,\dots, x_n)=\left\lfloor \frac{x_1+\dots + x_n}{m} \right\rfloor\text{ for every } x_1,\dots, x_n\in \{0,1,\dots, m-1\}.Prove that the total degree of f is at least n.

Izvor: https://www.imo-official.org/problems/IMO2018SL.pdf