Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the addition of squares of units modulo n   Let $\mathbb{Z}_n$ be the ring of residue classes modulo $n$, and let
$\mathbb{Z}_n^{\ast}$ be the group of its units. 90 years ago, Brauer obtained
a formula for the number of representations of $c\in \mathbb{Z}_n$ as the sum
of $k$ units. Recently, Yang and Tang in [Q. Yang, M. Tang, On the addition of
squares of units and nonunits modulo $n$, J. Number Theory., 155 (2015) 1--12]
gave a formula for the number of solutions of the equation $x_1^2+x_2^2=c$ with
$x_{1},x_{2}\in \mathbb{Z}_n^{\ast}$. In this paper, we generalize this result.
We find an explicit formula for the number of solutions of the equation
$x^2_{1}+\cdots+x^2_{k}=c$ with $x_{1},\ldots,x_{k}\in \mathbb{Z}_n^{\ast}$.

33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc