A search for c-Wieferich primes

Abstract

Let $q$ be a power of a prime number $p$, ${\mathbb{F}}_q$ be a finite field with $q$ elements and $\mathcal{G}$ be a subgroup of $({\mathbb{F}}_q,+)$ of order $p$. We give an existence criterion and an algorithm for computing maximally $\mathcal{G}$-fixed c-Wieferich primes in ${\mathbb{F}}_q[T]$. Using the criterion, we study how c-Wieferich primes behave in ${\mathbb{F}}_q[T]$ extensions.

18 pages, accepted for publication in International Journal of Number Theory