Index divisibility in the orbit of 0 for integral polynomials

T. Alden Gassert, Michael T. Urbanski

Let $f(x) \in \bbz[x]$ and consider the index divisibility set $D = \{n \in \bbn : n \mid f^n(0)\}$. We present a number of properties of $D$ in the case that $(f^n(0))_{n=1}^\inft…