Polynomial Schur's theorem

Hong Liu, Péter Pál Pach, Csaba Sándor

We resolve the Ramsey problem for $\{x,y,z:x+y=p(z)\}$ for all polynomials $p$ over $\mathbb{Z}$. In particular, we characterise all polynomials that are $2$-Ramsey, that is, those…