Geodesic
Non-Wieferich primes in number fields and $abc$-conjecture
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 445-453.

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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.
DOI : 10.21136/CMJ.2018.0485-16
Classification : 11A41, 11R04
Keywords: Wieferich prime; non-Wieferich prime; number field; $abc$-conjecture 
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Kotyada, Srinivas; Muthukrishnan, Subramani. Non-Wieferich primes in number fields and $abc$-conjecture. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 445-453. doi : 10.21136/CMJ.2018.0485-16. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0485-16/

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