Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Approach on the Seating Couples Problem   A king invites n couples to sit around a round table with 2n+1 seats. For
each couple, the king decides a prescribed distance d between 1 and n which the
two spouses have to be seated from each other (distance d means that they are
separated by exactly d-1 chairs). We will show that there is a solution for
every choice of the distances if and only if 2n+1 is a prime number, using a
theorem known as Combinatorial Nullstellensatz.

6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
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The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci