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
S.Akhtar Arif
and Fadwa S. Abu Muriefah
Department of Mathematics, Girls College of Education, Al-Riyadh, Saudi Arabia
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.