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??? |
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頁(從 - 到) | 354-375 |
頁數 | 22 |
期刊 | Journal of Number Theory |
卷 | 212 |
DOIs | |
出版狀態 | 已出版 - 7月 2020 |