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- Title
Gaussian Integer Solutions of the Diophantine Equation x<sup>4</sup>+y<sup>4</sup>=z³ for x≠y.
- Authors
Ismail, Shahrina; Mohd Atan, Kamel Ariffin; Sejas-Viscarra, Diego; Kai Siong Yow
- Abstract
The investigation of determining solutions for the Diophantine equation x4+y4=z³ over the Gaussian integer ring for the specific case of x≠y 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.
- Subjects
GAUSSIAN integers; DIOPHANTINE equations; RINGS of integers; QUARTIC equations
- Publication
Baghdad Science Journal, 2023, Vol 20, Issue 5, p1751
- ISSN
2078-8665
- Publication type
Article
- DOI
10.21123/bsj.2023.ID