Open Access
June 2019 Lucas non-Wieferich primes in arithmetic progressions
Sudhansu Sekhar Rout
Funct. Approx. Comment. Math. 60(2): 167-175 (June 2019). DOI: 10.7169/facm/1709


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 $k\geq 2$.


Download Citation

Sudhansu Sekhar Rout. "Lucas non-Wieferich primes in arithmetic progressions." Funct. Approx. Comment. Math. 60 (2) 167 - 175, June 2019.


Published: June 2019
First available in Project Euclid: 29 November 2018

zbMATH: 07068529
MathSciNet: MR3964258
Digital Object Identifier: 10.7169/facm/1709

Primary: 11A41 , 11B25 , 11B39

Keywords: $abc$ conjecture , arithmetic progressions , Lucas-Wieferich primes

Rights: Copyright © 2019 Adam Mickiewicz University

Vol.60 • No. 2 • June 2019
Back to Top