Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The elementary symmetric functions of a reciprocal polynomial sequence   Erd\"{o}s and Niven proved in 1946 that for any positive integers $m$ and
$d$, there are at most finitely many integers $n$ for which at least one of the
elementary symmetric functions of $1/m, 1/(m+d), ..., 1/(m+(n-1)d)$ are
integers. Recently, Wang and Hong refined this result by showing that if $n\geq
4$, then none of the elementary symmetric functions of $1/m, 1/(m+d), ...,
1/(m+(n-1)d)$ is an integer for any positive integers $m$ and $d$. Let $f$ be a
polynomial of degree at least $2$ and of nonnegative integer coefficients. In
this paper, we show that none of the elementary symmetric functions of $1/f(1),
1/f(2), ..., 1/f(n)$ is an integer except for $f(x)=x^{m}$ with $m\geq2$ being
an integer and $n=1$.

34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph