On the Diophantine equation x3=dy2±q6

Abu Muriefah, Fadwa S.

doi:https://doi.org/10.1155/S0161171201006445

International Journal of Mathematics and Mathematical Sciences

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Volume 28 |Article ID 962493 | https://doi.org/10.1155/S0161171201006445

Fadwa S. Abu Muriefah, "On the Diophantine equation x3=dy2±q6", International Journal of Mathematics and Mathematical Sciences, vol. 28, Article ID 962493, 5 pages, 2001. https://doi.org/10.1155/S0161171201006445

On the Diophantine equation x3=dy2±q6

Fadwa S. Abu Muriefah¹

¹Mathematics Department, Girls College of Education, Riyadh, Saudi Arabia

Received21 Dec 2000

Abstract

Let q>3 denote an odd prime and d a positive integer without any prime factor p≡1(mod3). In this paper, we have proved that if (x,q)=1, then x3=dy2±q6 has exactly two solutions provided q≢±1(mod24).

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Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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