Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The sum of irreducible fractions with consecutive denominators is never
  an integer in a very weak arithmetic   Two theorems of elmentary arithmetic, one stating that the sum of the
reciprocals of any number of consecutive positive integers is never an integer,
and a generalization thereof by Trygve Nagell, are shown to be provable inside
a very weak arithmetic, Richard Kaye's $PA^-$, in which there is no induction
axiom whatsoever.

9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph