Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On perfect powers that are sums of cubes of a five term arithmetic
  progression   We prove that the equation $(x-2r)^3 + (x-r)^3 + x^3 + (x+r)^3 + (x+2r)^3=
y^p$ only has solutions which satisfy $xy=0$ for $1\leq r\leq 10^6$ and $p\geq
5$ prime.

12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin