  Let $d\in {\mathbb N}$ and $p_i$ be an integral polynomial with $p_i(0)=0$,
$1\le i\le d$. It is shown that if $S$ is piecewise syndetic in $\mathbb Z$,
then $$\{(m,n)\in{\mathbb Z}^2: m+p_1(n),\ldots,m+p_d(n)\in S\}$$ is piecewise
syndetic in ${\mathbb Z}^2$, which extends the result by Glasner and
Furstenberg for linear polynomials. Our result is obtained by showing the
density of minimal points of a dynamical system of ${\mathbb Z}^2$ action
associated with the piecewise syndetic set $S$ and the polynomials
$\{p_1,\ldots,p_d\}$.
  Moreover, it is proved that if $(X,T)$ is minimal, then for each non-empty
open subset $U$ of $X$, there is $x\in U$ with $\{n\in {\mathbb Z}:
T^{p_1(n)}x\in U, \ldots, T^{p_d(n)}x\in U\}$ piecewise syndetic.
