# Perfect powers in alternating sum of consecutive cubes

## TL;DR

This paper completely solves a specific Diophantine equation involving alternating sums of consecutive cubes equaling perfect powers, for a range of parameters, advancing understanding of perfect powers in such sums.

## Contribution

The paper provides a complete solution to the Diophantine equation for all cases with 1 ≤ d ≤ 50, identifying all integer solutions for the given form.

## Key findings

- All solutions for the equation are determined within the specified range.
- The solutions reveal the structure of perfect powers in alternating sums of consecutive cubes.
- The results extend knowledge of exponential Diophantine equations involving cubic sums.

## 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 $1 \leq d \leq 50$.