Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connections between covers of $\mathbb Z$ and subset sums   In this paper we establish connections between covers of $\mathbb Z$ by
residue classes and subset sums in a field. Suppose that
$A_0=\{a_s(n_s)\}_{s=0}^k$ covers each integer at least $p$ times with the
residue class $a_0(n_0)=a_0+n_0\mathbb Z$ irredundant, where $p$ is a prime not
dividing any of $n_1,\ldots,n_k$. Let $m_1,\ldots,m_k\in\mathbb Z$ be
relatively prime to $n_1,\ldots,n_k$ respectively. For any
$c,c_1,\ldots,c_k\in\mathbb Z/p\mathbb Z$ with $c_1\cdots c_k\not=0$, we show
that the set $$\bigg\{\bigg\{\sum_{s\in I}\frac{m_s}{n_s}\bigg\}:\,
I\subseteq\{1,\ldots,k\} \ \mbox{and}\ \sum_{s\in I}c_s=c\bigg\}$$ contains an
arithmetic progression of length $n_0$ with common difference $1/n_0$, where
$\{x\}$ denotes the fractional part of a real number $x$.

27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin