A Diophantine equation for sums of consecutive like powers (Q2635179)
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| Language | Label | Description | Also known as |
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| English | A Diophantine equation for sums of consecutive like powers |
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A Diophantine equation for sums of consecutive like powers (English)
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11 February 2016
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Summary: We show that the Diophantine equation \[ n^\ell+(n+1)^\ell+\dots+(n+k)^\ell=(n+k+1)+\dots+(n+2k)^\ell \] has no solutions in positive integers \(k,n\geq 1\) for all \(\ell\geq 3\).
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sums of consecutive like powers
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