Czechoslovak Mathematical Journal, first online, pp. 1-9

Non-Wieferich primes in number fields and $abc$-conjecture

Srinivas Kotyada, Subramani Muthukrishnan

Received September 16, 2016.   First published January 19, 2018.

Abstract:  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.
Keywords:  Wieferich prime; non-Wieferich prime; number field; $abc$-conjecture
Classification MSC:  11A41, 11R04
DOI:  10.21136/CMJ.2018.0485-16

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Affiliations:   Srinivas Kotyada, Institute of Mathematical Sciences, Homi Bhabha National Institute, IV Cross Road, CIT Campus, Taramani, Chennai 600113, Tamil Nadu, India, e-mail:; Subramani Muthukrishnan, Chennai Mathematical Institute, H1, SIPCOT IT Park, Siruseri, Kelambakkam 603103, India, e-mail:

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