The Zsigmondy set for zero orbit of a rigid polynomial

Document Type : Original Article


Mathematics Department, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.



For a monic polynomial $f$ with integer coefficients such that zero is a critical point of $f$, we consider the zero orbit, namely the sequence $(f^n(0))_{n\geq 1}$. If this orbit is an infinite sequence, then we show that the Zsigmondy set of this sequence is either empty or it has at most two elements.