Perfect powers in an alternating sum of consecutive cubes
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 = zp, where p is prime and x,d,z are integers with 1 ≤ d ≤ 50.
Das, Pranabesh; Dey, Pallab Kanti; Maji, Bibekananda; and Rout, Sudhansu Sekhar, "Perfect powers in an alternating sum of consecutive cubes" (2020). Journal Articles. 255.