A search for c-Wieferich primes

Abstract

Let [Formula: see text] be a power of a prime number [Formula: see text], [Formula: see text] be a finite field with [Formula: see text] elements and [Formula: see text] be a subgroup of [Formula: see text] of order [Formula: see text]. We give an existence criterion and an algorithm for computing maximally [Formula: see text]-fixed c-Wieferich primes in [Formula: see text]. Using the criterion, we study how c-Wieferich primes behave in [Formula: see text] extensions.