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Keywords:
Wieferich prime; non-Wieferich prime; number field; $abc$-conjecture
Wieferich prime; non-Wieferich prime; number field; $abc$-conjecture
Summary:
Let $K/\mathbb {Q}$ be an algebraic number field of class number one and let $\mathcal {O}_K$ 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 $abc$-conjecture for number fields.
References:
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