Citation
Ismail, Shahrina and Mohd Atan, Kamel Ariffin and Viscarra, Diego Sejas and Kai, Siong Yow
(2023)
Gaussian integer solutions of the Diophantine equation x⁴ + y⁴ = z³ for x‰ y.
Baghdad Science Journal, 20 (5).
1751 -1762.
ISSN 2078-8665; ESSN: 2411-7986
Abstract
The investigation of determining solutions for the Diophantine equation over the Gaussian integer ring for the specific case of is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.
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Additional Metadata
| Item Type: | Article |
|---|---|
| Divisions: | Faculty of Science Institute for Mathematical Research |
| DOI Number: | https://doi.org/10.21123/bsj.2023.7344 |
| Publisher: | College of Science for Women/University of Baghdad |
| Keywords: | Algebraic properties; Diophantine equation; Gaussian integer; Quartic equation; Nontrivial solutions; Symmetrical solutions |
| Depositing User: | Ms. Zaimah Saiful Yazan |
| Date Deposited: | 24 Sep 2024 07:57 |
| Last Modified: | 24 Sep 2024 07:57 |
| Altmetrics: | http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.21123/bsj.2023.7344 |
| URI: | http://psasir.upm.edu.my/id/eprint/108079 |
| Statistic Details: | View Download Statistic |
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