Czechoslovak Mathematical Journal, Vol. 68, No. 2, pp. 445-453, 2018
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
Affiliations: Srinivas Kotyada, Institute of Mathematical Sciences, Homi Bhabha National Institute, IV Cross Road, CIT Campus, Taramani, Chennai 600113, Tamil Nadu, India, e-mail: srini@imsc.res.in; Subramani Muthukrishnan, Chennai Mathematical Institute, H1, SIPCOT IT Park, Siruseri, Kelambakkam 603103, India, e-mail: subramani@cmi.ac.in