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Gaussian Integer Solutions Of The Diophantine Equation 𝒙^𝟒+𝒚^𝟒=𝒛^𝟑 For X Not Equal To Y

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dc.contributor.authorShahrina Ismailen_US
dc.contributor.authorKamel Ariffin Mohd Atanen_US
dc.contributor.authorDiego Sejas-Viscarraen_US
dc.contributor.authorKai Siong Yowen_US
dc.date.accessioned2024-05-27T14:50:03Z
dc.date.available2024-05-27T14:50:03Z
dc.date.issued2022
dc.date.submitted2023-2-9
dc.descriptionVol. 14 No. 3 (2017) Page(1-16)en_US
dc.description.abstractThe investigation of determining solutions for the Diophantine equation 𝑥𝑥4 + 𝑦𝑦4 = 𝑧𝑧3 over the Gaussian integer ring for the specific case of 𝑥𝑥 ≠ 𝑦𝑦 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.en_US
dc.identifier.doi10.21123/bsj.2022.ID
dc.identifier.epage16
dc.identifier.issn2411-7986
dc.identifier.issue3
dc.identifier.spage1
dc.identifier.urihttps://oarep.usim.edu.my/jspui/bitstream/123456789/19961/1/giwqr.pdf
dc.identifier.urihttps://oarep.usim.edu.my/handle/123456789/3838
dc.identifier.volume14
dc.language.isoenen_US
dc.publisherCollege of Science for Women/ University of Baghdaen_US
dc.relation.ispartofBaghdad Science Journalen_US
dc.subjectAlgebraic properties, Diophantine equation, Gaussian integer, quartic equationen_US
dc.titleGaussian Integer Solutions Of The Diophantine Equation 𝒙^𝟒+𝒚^𝟒=𝒛^𝟑 For X Not Equal To Yen_US
dc.typeArticleen_US
dspace.entity.typePublication

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