Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform lower bound for the least common multiple of a polynomial
  sequence   Let $n$ be a positive integer and $f(x)$ be a polynomial with nonnegative
integer coefficients. We prove that ${\rm lcm}_{\lceil n/2\rceil \le i\le n}
\{f(i)\}\ge 2^n$ except that $f(x)=x$ and $n=1, 2, 3, 4, 6$ and that $f(x)=x^s$
with $s\ge 2$ being an integer and $n=1$, where $\lceil n/2\rceil$ denotes the
smallest integer which is not less than $n/2$. This improves and extends the
lower bounds obtained by Nair in 1982, Farhi in 2007 and Oon in 2013.

10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg