International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 8, Pages 493-497
doi:10.1155/S0161171201006445
On the Diophantine equation x3=dy2±q6
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.
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).