Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An inverse problem in number theory and geometric group theory   This paper describes a new link between combinatorial number theory and
geometry. The main result states that A is a finite set of relatively prime
positive integers if and only if A = (K-K) \cap N, where K is a compact set of
real numbers such that for every real number x there exists y in K with x
\equiv y mod 1. In one direction, given a finite set A of relatively prime
positive integers, the proof constructs an appropriate compact set K such that
A = (K-K) \cap N. In the other direction, a strong form of a fundamental
theorem in geometric group theory is applied to prove that (K-K)\cap N is a
finite set of relatively prime positive integers if K satisfies the appropriate
geometrical conditions. Some related results and open problems are also
discussed.

37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys