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Lucas non-Wieferich primes in arithmetic progressions and the abc conjecture

Publication Type : Journal

Publisher : De Gruyter

Source : Open Mathematics

Url : https://www.degruyter.com/document/doi/10.1515/math-2022-0563/html

Campus : Chennai

School : School of Engineering

Year : 2023

Abstract : We prove the lower bound for the number of Lucas non-Wieferich primes in arithmetic progressions. More precisely, for any given integer k≥2k≥2 , there are ≫logx≫logx Lucas non-Wieferich primes p≤xp≤x such that p≡±1(modk)p≡±1(modk) , assuming the abcabc conjecture for number fields.

Cite this Research Publication : Anitha, K., Fathima, I. Mumtaj and Vijayalakshmi, A. R. (2023). Lucas Non-Wieferich primes in arithmetic progressions and the abc conjecture, Open Mathematics, vol. 21, no. 1, pp. 20220563. https://doi.org/10.1515/math-2022-0563

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