Ismail, Shahrina and Mohd Atan, Kamel Ariffin and Viscarra, Diego Sejas
(2021)
Gaussian integer solutions of the Diophantine equation x4 + y4 = z3 for x 6= y / Shahrina Ismail, Kamel Ariffin Mohd Atan and Diego Sejas Viscarra.
In: e-Proceedings of the 5th International Conference on Computing, Mathematics and Statistics (iCMS 2021), 4-5 August 2021.
(Submitted)
Abstract
The investigation of determining solutions for the Diophantine equation x4 + y4 = z3 over the Gaussian integer field, for the specific case of x 6= y, is discussed. The discussion includes various preliminary results needed to build the future resolvent theory of the Diophantine equation studied. Our findings show the existence on infinitely many solutions. Since the analytical method used is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.
Metadata
Item Type: | Conference or Workshop Item (Paper) |
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Creators: | Creators Email / ID Num. Ismail, Shahrina shahrinaismail@usim.edu.my Mohd Atan, Kamel Ariffin kamelariffin48@gmail.com Viscarra, Diego Sejas diegosejas@usip.edu.bo |
Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > Mathematical statistics. Probabilities |
Divisions: | Universiti Teknologi MARA, Kedah > Sg Petani Campus |
Journal or Publication Title: | International Conference on Computing, Mathematics and Statistics (iCMS 2021) |
Event Title: | e-Proceedings of the 5th International Conference on Computing, Mathematics and Statistics (iCMS 2021) |
Event Dates: | 4-5 August 2021 |
Page Range: | pp. 19-27 |
Keywords: | Diophantine equation, Gaussian integer, algebraic properties, existence, quartic |
Date: | 2021 |
URI: | https://ir.uitm.edu.my/id/eprint/56105 |