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Arif, S. Akhtar; Abu Muriefah, Fadwa S.

doi:https://doi.org/10.1155/S0161171297000409

International Journal of Mathematics and Mathematical Sciences

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Volume 20 | Article ID 610948 | https://doi.org/10.1155/S0161171297000409

On the Diophantine equation x2+2k=yn

S. Akhtar Arif¹and Fadwa S. Abu Muriefah¹

Received21 Jun 1995

Revised29 Sept 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.

Copyright

Copyright © 1997 Hindawi Publishing Corporation. 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.

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