A Generalization of Sárközy's theorem in function fields

Sárközy's theorem says that if $A \subset \mathbb{Z}$ has positive upper asymptotic density, then there are distinct $a_1, a_2 \in A$ and $n \in \mathbb{Z}$ such that $a_1-a_2 = n^2$. The same is true if $n^2$ is replaced by $F(n)$ for any polynomial $F \in \mathbb{Z}[x]$ with constant term zero. Gr