IMC 2020 · Problem 4

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