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https://doi.org/10.3336/gm.55.1.04

Perfect powers in an alternating sum of consecutive cubes

Pranabesh Das   ORCID icon orcid.org/0000-0001-9119-5402 ; Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada
Pallab Kanti Dey ; Stat-Math Unit, Indian Statistical Institute, 7, S. J. S. Sansanwal Marg, New Delhi, Delhi - 110016, India
Bibekananda Maji   ORCID icon orcid.org/0000-0003-2155-2480 ; Department of Mathematics, Indian Institute of Technology Indore, Simrol, Indore, Madhya Pradesh - 453552, India
Sudhansu Sekhar Rout ; Institute of Mathematics and Applications, Andharua, Bhubaneswar, Odisha - 751029, India

Puni tekst: engleski, pdf (182 KB) str. 37-53 preuzimanja: 142* citiraj
APA 6th Edition
Das, P., Dey, P.K., Maji, B. i Rout, S.S. (2020). Perfect powers in an alternating sum of consecutive cubes. Glasnik matematički, 55 (1), 37-53. https://doi.org/10.3336/gm.55.1.04
MLA 8th Edition
Das, Pranabesh, et al. "Perfect powers in an alternating sum of consecutive cubes." Glasnik matematički, vol. 55, br. 1, 2020, str. 37-53. https://doi.org/10.3336/gm.55.1.04. Citirano 18.09.2021.
Chicago 17th Edition
Das, Pranabesh, Pallab Kanti Dey, Bibekananda Maji i Sudhansu Sekhar Rout. "Perfect powers in an alternating sum of consecutive cubes." Glasnik matematički 55, br. 1 (2020): 37-53. https://doi.org/10.3336/gm.55.1.04
Harvard
Das, P., et al. (2020). 'Perfect powers in an alternating sum of consecutive cubes', Glasnik matematički, 55(1), str. 37-53. https://doi.org/10.3336/gm.55.1.04
Vancouver
Das P, Dey PK, Maji B, Rout SS. Perfect powers in an alternating sum of consecutive cubes. Glasnik matematički [Internet]. 2020 [pristupljeno 18.09.2021.];55(1):37-53. https://doi.org/10.3336/gm.55.1.04
IEEE
P. Das, P.K. Dey, B. Maji i S.S. Rout, "Perfect powers in an alternating sum of consecutive cubes", Glasnik matematički, vol.55, br. 1, str. 37-53, 2020. [Online]. https://doi.org/10.3336/gm.55.1.04

Sažetak
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.

Ključne riječi
Diophantine equation; Galois representation; Frey curve; modularity; level lowering; linear forms in logarithms

Hrčak ID: 239041

URI
https://hrcak.srce.hr/239041

Posjeta: 265 *