Non-Wieferich primes in number fields and ABC conjecture

2016/10/03 by Kotyada, Srinivas, Muthukrishnan, Subramani · 1 citation
#11A41 (primary) #11R04 (secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1610.00488

Abstract

Let K/ℚ be an algebraic number field of class number one and 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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• Wieferich primes in number fields and the conjectures of Ankeny--Artin--Chowla and Mordell

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