Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the powerful values of polynomials over number fields   In this paper, assuming a conjecture of Vojta on the bounded degree algebraic
numbers on a number field $k$, we determine explicit lower and upper bounds for
the cardinal number of the set of polynomials $f\in k[x]$ with degree $r\geq 2$
whose irreducible factors have multiplicity strictly less than $s$ and the
values $f(b_1),\cdots, f(b_M)$ are $s$-powerful elements in $k^*$ for a certain
positive integer $M$, where $b_i$'s belong to an arbitrary sequence of the
pairwise distinct element of $k$ that satisfy certain conditions.

8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph