Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The least modulus for which consecutive polynomial values are distinct   Let $d\ge4$ and $c\in(-d,d)$ be relatively prime integers. We show that for
any sufficiently large integer $n$ (in particular $n>24310$ suffices for $4\le
d\le 36$), the smallest prime $p\equiv c\pmod d$ with $p\ge(2dn-c)/(d-1)$ is
the least positive integer $m$ with $2r(d)k(dk-c)\ (k=1,\ldots,n)$ pairwise
distinct modulo $m$, where $r(d)$ is the radical of $d$. We also conjecture
that for any integer $n>4$ the least positive integer $m$ such that
$|\{k(k-1)/2\ \mbox{mod}\ m:\ k=1,\ldots,n\}|= |\{k(k-1)/2\ \mbox{mod}\ m+2:\
k=1,\ldots,n\}|=n$ is the least prime $p\ge 2n-1$ with $p+2$ also prime.

12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph