Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: There are infinitely many rational Diophantine sextuples with square
  denominators
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph