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arXiv · 1312.5943

A diophantine equation for sums of consecutive like powers

Simon Felten·Stefan Müller-Stach
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Abstract

We show that the diophantine equation $n^\ell+(n+1)^\ell + ...+ (n+k)^\ell=(n+k+1)^\ell+ ...+ (n+2k)^\ell$ has no solutions in positive integers $k,n \ge 1$ for all $\ell \ge 3$.

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Simon Felten, Stefan Müller-Stach. 2015-03-02. A diophantine equation for sums of consecutive like powers. https://arxiv.org/abs/1312.5943

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