Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 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 exi...
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| Language: | English |
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University of Baghdad, College of Science for Women
2023-10-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7344 |
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| author | Shahrina Ismail Kamel Ariffin Mohd Atan Diego Sejas Viscarra Kai Siong Yow |
| author_facet | Shahrina Ismail Kamel Ariffin Mohd Atan Diego Sejas Viscarra Kai Siong Yow |
| author_sort | Shahrina Ismail |
| collection | DOAJ |
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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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| format | Article |
| id | doaj-art-df46b77fc5304b6aa707c08beb1c5d9e |
| institution | DOAJ |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-df46b77fc5304b6aa707c08beb1c5d9e2025-08-20T03:18:15ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862023-10-0120510.21123/bsj.2023.7344Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ yShahrina Ismail 0Kamel Ariffin Mohd Atan 1Diego Sejas Viscarra 2Kai Siong Yow3Faculty of Science and Technology, Universiti Sains Islam Malaysia, 71800, Bandar Baru Nilai, Negeri Sembilan, Malaysia.Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, 43400 UPM, Serdang, SelangorDepartamento de Ciencias Exactas, Facultad de Ingenierías y Arquitectura, Universidad Privada Boliviana, Cochabamba, Bolivia.Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia. School of Computer Science and Engineering, College of Engineering, Nanyang Technological University, 50 Nanyang Ave, Singapore 639798. 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. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7344Algebraic properties, Diophantine equation, Gaussian integer, quartic equation, nontrivial solutions, symmetrical solutions. |
| spellingShingle | Shahrina Ismail Kamel Ariffin Mohd Atan Diego Sejas Viscarra Kai Siong Yow Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y مجلة بغداد للعلوم Algebraic properties, Diophantine equation, Gaussian integer, quartic equation, nontrivial solutions, symmetrical solutions. |
| title | Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y |
| title_full | Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y |
| title_fullStr | Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y |
| title_full_unstemmed | Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y |
| title_short | Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y |
| title_sort | gaussian integer solutions of the diophantine equation x 4 y 4 z 3 for x≠ y |
| topic | Algebraic properties, Diophantine equation, Gaussian integer, quartic equation, nontrivial solutions, symmetrical solutions. |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7344 |
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