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- W4299592020 abstract "Let $k,lgeq2$ 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 $x,ygeq1, ngeq2$ 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 $x,ygeq1, ngeq2, kneq3$ and $lequiv0 pmod 2$ satisfy $max{x,y,n}<C_{2}$ where $C_{2}$ is an effectively computable constant depending only on $k$ and $l$." @default.
- W4299592020 created "2022-10-02" @default.
- W4299592020 creator A5055851531 @default.
- W4299592020 date "2017-01-10" @default.
- W4299592020 modified "2023-09-30" @default.
- W4299592020 title "On the Diophantine equation $(x+1)^{k}+(x+2)^{k}+...+(lx)^{k}=y^{n}$" @default.
- W4299592020 doi "https://doi.org/10.48550/arxiv.1701.02466" @default.
- W4299592020 hasPublicationYear "2017" @default.
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