Gaussian integer solutions of the Diophantine equation x4 + y4 = z3 for x 6= y / Shahrina Ismail, Kamel Ariffin Mohd Atan and Diego Sejas Viscarra

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)
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
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