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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

Received 21 June 1995; Revised 29 September 1995

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.