TY - JOUR ID - 144200 TI - The Zsigmondy set for zero orbit of a rigid polynomial JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Monsef Shokri, Khosro AD - Mathematics Department, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran. Y1 - 2022 PY - 2022 VL - 8 IS - 1 SP - 115 EP - 119 KW - Zsigmondy set KW - Zero orbit KW - Primitive prime KW - Rigid divisibility DO - 10.22034/kjm.2022.261184.2086 N2 - 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. UR - https://www.kjm-math.org/article_144200.html L1 - https://www.kjm-math.org/article_144200_f1dc56eb892f4465868ddedc1b943429.pdf ER -