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arXiv · 2101.04901

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

K. Anitha·I. Mumtaj Fathima·A R Vijayalakshmi
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Abstract

We prove the lower bound for the number of Lucas non-Wieferich primes in arithmetic progressions. More precisely, for any given integer $k\geq 2$ there are $\gg \log x$ Lucas non-Wieferich primes $p\leq x$ such that $p\equiv\pm1\pmod{k}$, assuming the $abc$ conjecture for number fields. Further, we discuss some applications of Lucas sequences in Cryptography.

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K. Anitha, I. Mumtaj Fathima, A R Vijayalakshmi. 2021-01-13. Lucas non-Wieferich primes in arithmetic progressions and the $abc$ conjecture. https://arxiv.org/abs/2101.04901

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