Non-Wieferich primes in number fields and ABC conjecture

Srinivas Kotyada; Subramani Muthukrishnan

Non-Wieferich primes in number fields and ABC conjecture

Number Theory 2017-03-13 v2

Authors: Srinivas Kotyada , Subramani Muthukrishnan

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.

Keywords

class number of quadratic fields prime number conjectures prime numbers

Cite

@article{arxiv.1610.00488,
  title  = {Non-Wieferich primes in number fields and ABC conjecture},
  author = {Srinivas Kotyada and Subramani Muthukrishnan},
  journal= {arXiv preprint arXiv:1610.00488},
  year   = {2017}
}

Comments

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

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