Publication: Gaussian Integer Solutions Of The Diophantine Equation 𝒙𝟒 + 𝒚𝟒 = 𝒛𝟑 For 𝒙 ≠ 𝒚
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Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
College of Science for Women/ University of Baghda
Abstract
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.
Description
Vol. 20 No. 5
Keywords
Algebraicproperties, Diophantineequation, Gaussianinteger,quartic equation, nontrivial solutions, symmetrical solutions.
Citation
Ismail , S., Atan , K. A. M., Viscarra , D. S., & Yow, K. S. (2023). Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y. Baghdad Science Journal, 20(5), 1751. https://doi.org/10.21123/bsj.2023.7344