Citation
Yow, Kai Siong and Sapar, Siti Hasana and Pham, Hoa
(2024)
Further results on the Diophantine equation x^2+16·7^b = y^n when n is even.
Songklanakarin Journal of Science and Technology, 46 (3).
pp. 294-301.
ISSN 0125-3395
Abstract
This work extends the results for the Diophantine equation x^2+16∙7^b = y^n for n=2r, where x, y, b, r ∈ Z^+. Earlier results classified the generators of solutions, which are the pair of integers (x, y^r), into several categories and presented the general formula that determines the values of x and y^r for the respective category. The lower bound for the number of non-negative integral solutions associated with each b is also provided. We now extend the results and prove the necessary and sufficient conditions required to obtain integral solutions x and y to the equation, by considering various scenarios based on the parity of b. We also determine the values of n in which integral solutions exist.
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Additional Metadata
| Item Type: | Article |
|---|---|
| Divisions: | Faculty of Science |
| Publisher: | Prince of Songkla University |
| Keywords: | Diophantine equation; Polynomial; Generator; Integral solution |
| Depositing User: | Ms. Nuraida Ibrahim |
| Date Deposited: | 28 Jul 2025 07:02 |
| Last Modified: | 28 Jul 2025 07:02 |
| URI: | http://psasir.upm.edu.my/id/eprint/118877 |
| Statistic Details: | View Download Statistic |
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