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arxiv: 1610.00488 · v2 · pith:GVA4WPJGnew · submitted 2016-10-03 · 🧮 math.NT

Non-Wieferich primes in number fields and ABC conjecture

classification 🧮 math.NT
keywords numberconjecturefieldsmathcalnon-wieferichprimesalgebraicassumption
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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.

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