Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization of Sophie Germain primes   Let $n\ge 5$ be an odd integer. It is shown that
$\{1^{\sigma(1)},\ldots,n^{\sigma(n)}\}$ is a complete residue system modulo
$n$ for some permutation $\sigma$ of $\{1,\ldots,n\}$ if and only if
$\frac{1}{2}(n-1)$ is a Sophie Germain prime. Partial results are obtained also
for the case $n$ even.

26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph