ABC implies there are infinitely many non-Fibonacci-Wieferich primes

研究成果: 雜誌貢獻期刊論文同行評審

1 引文 斯高帕斯(Scopus)

摘要

We define X-base Fibonacci-Wieferich primes, which generalize Wieferich primes, where X is a finite set of algebraic numbers. We show that there are infinitely many non-X-base Fibonacci-Wieferich primes, assuming the abc-conjecture of Masser-Oesterlé-Szpiro for number fields. We also provide a new conjecture concerning the rank of the free part of the abelian group generated by all elements in X and give some heuristics that support the conjecture.

原文???core.languages.en_GB???
頁(從 - 到)354-375
頁數22
期刊Journal of Number Theory
212
DOIs
出版狀態已出版 - 7月 2020

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