Gaussian integer solutions of the Diophantine equation x⁴ + y⁴ = z³ for x‰ y
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 exis...
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| Format: | Article |
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College of Science for Women/University of Baghdad
2023
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| _version_ | 1811137820747628544 |
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| author | Ismail, Shahrina Mohd Atan, Kamel Ariffin Viscarra, Diego Sejas Kai, Siong Yow |
| author_facet | Ismail, Shahrina Mohd Atan, Kamel Ariffin Viscarra, Diego Sejas Kai, Siong Yow |
| author_sort | Ismail, Shahrina |
| collection | UPM |
| description | 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. |
| first_indexed | 2024-09-25T03:40:23Z |
| format | Article |
| id | upm.eprints-108079 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-09-25T03:40:23Z |
| publishDate | 2023 |
| publisher | College of Science for Women/University of Baghdad |
| record_format | dspace |
| spelling | upm.eprints-1080792024-09-24T07:57:00Z http://psasir.upm.edu.my/id/eprint/108079/ Gaussian integer solutions of the Diophantine equation x⁴ + y⁴ = z³ for x‰ y Ismail, Shahrina Mohd Atan, Kamel Ariffin Viscarra, Diego Sejas Kai, Siong Yow 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. College of Science for Women/University of Baghdad 2023 Article PeerReviewed 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 https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7344 10.21123/bsj.2023.7344 |
| spellingShingle | Ismail, Shahrina Mohd Atan, Kamel Ariffin Viscarra, Diego Sejas Kai, Siong Yow Gaussian integer solutions of the Diophantine equation x⁴ + y⁴ = z³ for x‰ y |
| title | Gaussian integer solutions of the Diophantine equation x⁴ + y⁴ = z³ for x‰ y |
| title_full | Gaussian integer solutions of the Diophantine equation x⁴ + y⁴ = z³ for x‰ y |
| title_fullStr | Gaussian integer solutions of the Diophantine equation x⁴ + y⁴ = z³ for x‰ y |
| title_full_unstemmed | Gaussian integer solutions of the Diophantine equation x⁴ + y⁴ = z³ for x‰ y |
| title_short | Gaussian integer solutions of the Diophantine equation x⁴ + y⁴ = z³ for x‰ y |
| title_sort | gaussian integer solutions of the diophantine equation x⁴ y⁴ z³ for x‰ y |
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