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Non-Wieferich primes in number fields and abc-conjecture

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Abstract

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

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Authors and Affiliations

  1. Institute of Mathematical Sciences, Homi Bhabha National Institute, IV Cross Road, CIT Campus, Taramani, Chennai, 600113, Tamil Nadu, India

    Srinivas Kotyada

  2. Chennai Mathematical Institute, H1, SIPCOT IT Park, Siruseri, Kelambakkam, 603103, India

    Subramani Muthukrishnan

Authors
  1. Srinivas Kotyada
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  2. Subramani Muthukrishnan
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Correspondence to Srinivas Kotyada.

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Kotyada, S., Muthukrishnan, S. Non-Wieferich primes in number fields and abc-conjecture. Czech Math J 68, 445–453 (2018). https://doi.org/10.21136/CMJ.2018.0485-16

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  • DOI: https://doi.org/10.21136/CMJ.2018.0485-16

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