Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Diophantine equation $(x+1)^{k}+(x+2)^{k}+...+(2x)^{k}=y^n$   In this work, we give upper bounds for $n$ on the title equation. Our results
depend on assertions describing the precise exponents of $2$ and $3$ appearing
in the prime factorization of $T_{k}(x)=(x+1)^{k}+(x+2)^{k}+...+(2x)^{k}$.
Further, on combining Baker's method with the explicit solution of polynomial
exponential congruences (see e.g. BHMP), we show that for $2 \leq x \leq 13, k
\geq 1, y \geq 2$ and $n \geq 3$ the title equation has no solutions.

18
The categories of this paper are: econ
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an