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

2021/01/13 by Anitha, K., Fathima, I. Mumtaj, Vijayalakshmi, A R
#11A41 #11B25 (Primary) #11B39 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2101.04901

Abstract

We prove the lower bound for the number of Lucas non-Wieferich primes in arithmetic progressions. More precisely, for any given integer k≥ 2 there are ≫ log x Lucas non-Wieferich primes p≤ x such that p≡±1\pmodk, assuming the abc conjecture for number fields. Further, we discuss some applications of Lucas sequences in Cryptography.

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