ABC Implies There are Infinitely Many non-Fibonacci-Wieferich Primes - An Application of ABC Conjecture over Number Fields
Peng, Wayne
Original · EN
In this paper, we define X-base Fibonacci-Wieferich prime which is a generalized Wieferich prime where X is a finite set of algebraic numbers. We are going to 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 free part of abelian group generated by all elements in X, and we will use the arithmetic point of view and geometric point of view to give heuristic.
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