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
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
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