Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a variant of Giuga numbers   In this paper, we characterize the odd positive integers $n$ satisfying the
congruence $\sum_{j=1} ^ {n-1} j^{\frac{n-1}{2}}\equiv 0 \pmod n$. We show that
the set of such positive integers has an asymptotic density which turns out to
be slightly larger than 3/8.

37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom