Polynomial Zsigmondy theorems

TL;DR

This paper extends classical primitive divisor theorems to polynomial rings, providing new analogues of well-known results using Carmichael's methods.

Contribution

It introduces polynomial analogues of Zsigmondy, Bang, Bilu-Hanrot-Voutier, and Carmichael theorems, advancing the understanding of primitive divisors in polynomial contexts.

Findings

Established polynomial versions of primitive divisor theorems

Extended classical results to polynomial rings

Used Carmichael's methods for proofs

Abstract

We find analogues of the primitive divisor results of Zsigmondy, Bang, Bilu-Hanrot-Voutier, and Carmichael in polynomial rings, following the methods of Carmichael.