Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Diophantine equation $(x+1)^{k}+(x+2)^{k}+...+(lx)^{k}=y^{n}$   Let $k,l\geq2$ be fixed integers. In this paper, firstly, we prove that all
solutions of the equation $(x+1)^{k}+(x+2)^{k}+...+(lx)^{k}=y^{n}$ in integers
$x,y,n$ with $x,y\geq1, n\geq2$ satisfy $n<C_{1}$ where $C_{1}=C_{1}(l,k)$ is
an effectively computable constant. Secondly, we prove that all solutions of
this equation in integers $x,y,n$ with $x,y\geq1, n\geq2, k\neq3$ and $l\equiv0
\pmod 2$ satisfy $\max\{x,y,n\}<C_{2}$ where $C_{2}$ is an effectively
computable constant depending only on $k$ and $l$.

12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
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
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom