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 $u$ at $r$ denoted and defined by ${\mathcal{O}}_u(r):=\{u^{(n)}(r)|n\in \mathbb{N}\}$. Her…