# International Mathematics Competition for University Students 2020

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IMC 2020
Problem 4. A polynomial $\displaystyle p$ with real coefficients satisfies the equation $\displaystyle p(x+1)-p(x)=x^{100}$ for all $\displaystyle x\in\mathbb{R}$. Prove that $\displaystyle p(1-t)\geqslant p(t)$ for $\displaystyle 0\leqslant t\leqslant 1/2$.