Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Diophantine Equation $(x+1)^k+(x+2)^k+\cdots+(\ell x)^k=y^n$
  Revisited   Let $k,\ell\geq2$ be fixed integers and $C$ be an effectively computable
constant depending only on $k$ and $\ell$. In this paper, we prove that all
solutions of the equation $(x+1)^{k}+(x+2)^{k}+...+(\ell x)^{k}=y^{n}$ in
integers $x,y,n$ with $x,y\geq1, n\geq2, k\neq3$ and $\ell\equiv 1 \pmod 2$
satisfy $\max\{x,y,n\}<C$. The case when $\ell$ is even has already been
completed by Soydan (Publ. Math. Debrecen 91 (2017), pp. 369-382).

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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con