Lucas non-Wieferich primes in arithmetic progressions and the abc conjecture
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 \pm 1\hspace{0.25em}\left({\rm{mod}}\hspace{0.3...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-03-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0563 |
| _version_ | 1797848628395507712 |
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| author | Anitha K. Fathima I. Mumtaj Vijayalakshmi A. R. |
| author_facet | Anitha K. Fathima I. Mumtaj Vijayalakshmi A. R. |
| author_sort | Anitha K. |
| collection | DOAJ |
| description | 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 \pm 1\hspace{0.25em}\left({\rm{mod}}\hspace{0.33em}k), assuming the abcabc conjecture for number fields. |
| first_indexed | 2024-04-09T18:31:38Z |
| format | Article |
| id | doaj.art-1e63184a600b4782a1a189b030fa5c2e |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-04-09T18:31:38Z |
| publishDate | 2023-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-1e63184a600b4782a1a189b030fa5c2e2023-04-11T17:07:17ZengDe GruyterOpen Mathematics2391-54552023-03-0121129330210.1515/math-2022-0563Lucas non-Wieferich primes in arithmetic progressions and the abc conjectureAnitha K.0Fathima I. Mumtaj1Vijayalakshmi A. R.2Department of Mathematics, SRM IST Ramapuram, Chennai 600089, IndiaDepartment of Mathematics, Sri Venkateswara College of Engineering, Affiliated to Anna University, Sriperumbudur, Chennai 602117, IndiaDepartment of Mathematics, Sri Venkateswara College of Engineering, Sriperumbudur, Chennai 602117, IndiaWe 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 \pm 1\hspace{0.25em}\left({\rm{mod}}\hspace{0.33em}k), assuming the abcabc conjecture for number fields.https://doi.org/10.1515/math-2022-0563abc conjecturearithmetic progressionslucas sequenceslucas non-wieferich primeswieferich primes11b2511b3911a4111n13 |
| spellingShingle | Anitha K. Fathima I. Mumtaj Vijayalakshmi A. R. Lucas non-Wieferich primes in arithmetic progressions and the abc conjecture Open Mathematics abc conjecture arithmetic progressions lucas sequences lucas non-wieferich primes wieferich primes 11b25 11b39 11a41 11n13 |
| title | Lucas non-Wieferich primes in arithmetic progressions and the abc conjecture |
| title_full | Lucas non-Wieferich primes in arithmetic progressions and the abc conjecture |
| title_fullStr | Lucas non-Wieferich primes in arithmetic progressions and the abc conjecture |
| title_full_unstemmed | Lucas non-Wieferich primes in arithmetic progressions and the abc conjecture |
| title_short | Lucas non-Wieferich primes in arithmetic progressions and the abc conjecture |
| title_sort | lucas non wieferich primes in arithmetic progressions and the abc conjecture |
| topic | abc conjecture arithmetic progressions lucas sequences lucas non-wieferich primes wieferich primes 11b25 11b39 11a41 11n13 |
| url | https://doi.org/10.1515/math-2022-0563 |
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