Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving $a x^p + b y^p = c z^p$ with $abc$ containing an arbitrary
  number of prime factors   In this paper we prove new cases of the asymptotic Fermat equation with
coefficients. This is done by solving remarkable $S$-units equations and
applying a method of Frey-Mazur.

32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex