Index Divisibility in Dynamical Sequences and Cyclic Orbits Modulo $p$

Annie S. Chen, T. Alden Gassert, Katherine E. Stange

Let $\varphi (x)=x^d+c$ be an integral polynomial of degree at least 2, and consider the sequence $({\varphi }^n(0){)}_{n=0}^{\infty }$, which is the orbit of $0$ under iteration by $\varphi$. Let $D_{d,…