Functiones et Approximatio Commentarii Mathematici

Lucas non-Wieferich primes in arithmetic progressions

Sudhansu Sekhar Rout

Abstract

In this note, we define the Lucas Wieferich primes which are an analogue of the famous Wieferich primes. Conditionally there are infinitely many non-Wieferich primes. We prove under the assumption of the $abc$ conjecture for the number field $\mathbb{Q}(\sqrt{\Delta})$ that for fixed positive integer~$M$ there are at least $O((\log x/\log \log x)(\log \log \log x)^{M})$ many Lucas non-Wieferich primes $p \equiv 1(mod k)$ for any fixed integer $k\geq 2$.

Article information

Source
Funct. Approx. Comment. Math., Volume 60, Number 2 (2019), 167-175.

Dates
First available in Project Euclid: 29 November 2018

https://projecteuclid.org/euclid.facm/1543460427

Digital Object Identifier
doi:10.7169/facm/1709

Mathematical Reviews number (MathSciNet)
MR3964258

Zentralblatt MATH identifier
07068529

Citation

Rout, Sudhansu Sekhar. Lucas non-Wieferich primes in arithmetic progressions. Funct. Approx. Comment. Math. 60 (2019), no. 2, 167--175. doi:10.7169/facm/1709. https://projecteuclid.org/euclid.facm/1543460427

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