Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An analogue of Ramanujan's sum with respect to regular integers (mod
  $r$)   An integer $a$ is said to be regular (mod $r$) if there exists an integer $x$
such that $a^2x\equiv a\pmod{r}$. In this paper we introduce an analogue of
Ramanujan's sum with respect to regular integers (mod $r$) and show that this
analogue possesses properties similar to those of the usual Ramanujan's sum.

32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat