Perfect powers in alternating sum of consecutive cubes

2017/05/07 by Das, Pranabesh, Dey, Pallab Kanti, Maji, B. +1
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1705.02597

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 + ⋯ - (x + 2d)³ + (x + 2d + 1)³ = z^p, where p is prime and x,d,z are integers with 1 ≤ d ≤ 50.

Related

• An Elementary Approach For Sums Of Consecutive Cubes Being Prime Power Squares
• On perfect powers that are sums of cubes of a three term arithmetic progression
• Sums of two cubes as twisted perfect powers, revisited
• On perfect powers that are sums of cubes of a seven term arithmetic progression
• On perfect powers that are sums of cubes of a nine term arithmetic progression