Lucas non-Wieferich primes in arithmetic progressions and the abc conjecture - Anitha K.; Fathima I. Mumtaj; Vijayalakshmi A. R. (Open Mathematics, 2023)
We prove the lower bound for the number of Lucas non-Wieferich primes in arithmetic progressions. More precisely, for any given integer k≥2k\ge 2, there are ≫logx\gg \hspace{0.25em}\log x Lucas non-Wieferich primes p≤xp\le x such that p≡±1(modk)p\equiv ± 1\hspace{0.25em}\left({\rm{mod}}\hspace{0.33em}k), assuming the abcabc conjecture for number fields.