The Zsigmondy set for zero orbit of a rigid polynomial

Document Type : Original Article

Author

Khosro Monsef Shokri

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

10.22034/kjm.2022.261184.2086

Abstract

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.

Keywords

Zsigmondy set

Zero orbit

Primitive prime

Rigid divisibility

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