International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 2, Pages 299-304
doi:10.1155/S0161171297000409
On the Diophantine equation x2+2k=yn
Department of Mathematics, Girls College of Education, Al-Riyadh, Saudi Arabia
Received 21 June 1995; Revised 29 September 1995
Copyright © 1997 S. Akhtar Arif and 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
By factorizing the equation x2+2k=yn, n≥3, k-even, in the field Q(i), various
theorems regarding the solutions of this equation in rational integers are proved. A conjecture regarding
the solutions of this equation has been put forward and proved to be true for a large class of values of k
and n.