Some dynamical properties related to polynomials

Qinqi Wu

Let $d\in \mathbb{Z}$ and $p_i$ be an integral polynomial with $p_i(0)=0,1\le i\le d$. It is shown that if $S$ is thickly syndetic in $\mathbb{Z}$, then $\{(m,n)\in\mathbb{Z}^2:m+…