International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 8, Pages 493-497

On the Diophantine equation x3=dy2±q6

Fadwa S. Abu Muriefah

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

Received 21 December 2000

Copyright © 2001 Fadwa S. Abu Muriefah. 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.


Let q>3 denote an odd prime and d a positive integer without any prime factor p1(mod3). In this paper, we have proved that if (x,q)=1, then x3=dy2±q6 has exactly two solutions provided q±1(mod24).