Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the generalization of Golomb's conjecture   Let $p$ be a sufficiently large prime number, $r$ be any given positive
integer. Suppose that $a_1,\,\dots,\,a_r$ are pairwise distinct and not zero
modulo $p$. Let $N(a_1,\,\dots,\,a_r;\,p)$ denote the number of
$\alpha_1,\,\dots,\,\alpha_r,\,\beta$, which are primitive roots modulo $p$,
such that $\alpha_1+\beta\equiv a_1,\,\dots,\,\alpha_r+\beta\equiv a_r\,({\rm
mod}\,p).$ In the first version of this paper, we proved an asymptotic formula
for $N(a_1,\,\dots,\,a_r;\,p)$ so that we could answer an open problem of
Wenpeng Zhang and Tingting Wang. But we found that our result had been included
in a paper of L. Carlitz in 1956, which is explained in the additional remark
below.

11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga