Solvability of both Diophantine equations kX^2+2lXY-2kY^2=±1 and X^2-mY^2=-2
Abstract
In this research, we investigate solving both of Diophantine equations in the title of research in . If is a prime number, then both of Diophantine equations are solvability if and only if one of them is solvability, and we find conditions to make one of equations solvability if and only if the other is solvability, and use the solution of one to find the solution of other. Besides of determine conditions to solvability of the Pell’s equation and one case of generalizations Pell’s equation, and we find relation of main solution of Pell’s equation and other case of generalization Pell’s equation. Adding of them we prove some results about solution of Pell’s equation, where is an odd number.
Downloads
Published
How to Cite
Issue
Section
License
![Creative Commons License](http://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
The authors retain the copyright and grant the right to publish in the magazine for the first time with the transfer of the commercial right to the Tishreen University Journal -Basic Sciences Series
Under a CC BY- NC-SA 04 license that allows others to share the work with of the work's authorship and initial publication in this journal. Authors can use a copy of their articles in their scientific activity, and on their scientific websites, provided that the place of publication is indicted in Tishreen University Journal -Basic Sciences Series . The Readers have the right to send, print and subscribe to the initial version of the article, and the title of Tishreen University Journal -Basic Sciences Series Publisher
journal uses a CC BY-NC-SA license which mean
You are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material
- The licensor cannot revoke these freedoms as long as you follow the license terms.
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- NonCommercial — You may not use the material for commercial purposes.
- ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.