Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Hilbert's Tenth Problem and Mazur's Conjectures in Complementary
  Subrings of Number Fields
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th