Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partition of a Set Which Contains an Infinite Arithmetic (Respectively
  Geometric) Progression   We prove that for any partition of a set which contains an infinite
arithmetic (respectively geometric) progression into two disjoint subsets, at
least one of these subsets contains an infinite number of triplets such that
each triplet is an arithmetic (respectively geometric) progression.

12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph