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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

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 $k\geq 2$.

Citation

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Sudhansu Sekhar Rout. "Lucas non-Wieferich primes in arithmetic progressions." Funct. Approx. Comment. Math. 60 (2) 167 - 175, June 2019. https://doi.org/10.7169/facm/1709

Information

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

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

Subjects:
Primary: 11A41, 11B25, 11B39

Rights: Copyright © 2019 Adam Mickiewicz University

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Vol.60 • No. 2 • June 2019
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