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arXiv · 1705.02597

Perfect powers in alternating sum of consecutive cubes

Pranabesh Das·Pallab Kanti Dey·B. Maji·S. S. Rout
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Abstract

In this paper, we consider the problem about finding out perfect powers in an alternating sum of consecutive cubes. More precisely, we completely solve the Diophantine equation $(x+1)^3 - (x+2)^3 + \cdots - (x + 2d)^3 + (x + 2d + 1)^3 = z^p$, where $p$ is prime and $x,d,z$ are integers with $1 \leq d \leq 50$.

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Pranabesh Das, Pallab Kanti Dey, B. Maji, S. S. Rout. 2017-05-07. Perfect powers in alternating sum of consecutive cubes. https://arxiv.org/abs/1705.02597

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