Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: ABC Implies There are Infinitely Many non-Fibonacci-Wieferich Primes -
  An Application of ABC Conjecture over Number Fields   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-Oesterl\'{e}-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.

21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat