Non-Wieferich primes in number fields and ABC conjecture

Abstract

Let $K/\mathbb{Q}$ be an algebraic number field of class number one and ${\mathcal{O}}_K$ be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in ${\mathcal{O}}_K$ under the assumption of the \textit{abc} conjecture for number fields.

8 pages, minor revisions done, to appear in Czechoslovak Mathematical Journal