Locally nilpotent polynomials over $\mathbb{Z}$

Sayak Sengupta

For a polynomial $u(x)$ in $\mathbb{Z}[x]$ and $r\in \mathbb{Z}$, we consider the orbit of $u(x)$ at $r$, ${\mathcal{O}}_u(r):=\{u(r),u(u(r)),\dots \}$. We ask two questions here: (i)…