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Perfect powers in alternating sum of consecutive cubes

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 نشر من قبل Pranabesh Das
 تاريخ النشر 2017
  مجال البحث
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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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