On the Diophantine equation x2+2k=yn - S. Akhtar Arif; Fadwa S. Abu Muriefah (International Journal of Mathematics and Mathematical Sciences)
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.