Publication:
Determination of Gaussian Integer Zeroes of F(x, z) = 2x 4 − z 3

Simple item page
dc.contributor.authorShahrina Binti Ismailen_US
dc.contributor.authorAtan, K. A. M.en_US
dc.contributor.authorSejas-Viscarra, Den_US
dc.contributor.authorEshkuvatov, Z.4en_US
dc.date.accessioned2024-05-29T02:09:25Z
dc.date.available2024-05-29T02:09:25Z
dc.date.issued2022
dc.date.submitted2023-2-13
dc.descriptionMay 2022, Vol. 16, No. 2 (page 317-328)en_US
dc.description.abstractIn this paper the zeroes of the polynomial F(x, z) = 2x 4 −z 3 in Gaussian integers Z[i] are determined, a problem equivalent to finding the solutions of the Diophatine equation x 4 + y 4 = z 3 in Z[i], with a focus on the case x = y. We start by using an analytical method that examines the real and imaginary parts of the equation F(x, z) = 0. This analysis sheds light on the general algebraic behavior of the polynomial F(x, z) itself and its zeroes. This in turn allows us a deeper understanding of the different cases and conditions that give rise to trivial and non-trivial solutions to F(x, z) = 0, and those that lead to inconsistencies. This paper concludes with a general formulation of the solutions to F(x, z) = 0 in Gaussian integers. Results obtained in this work show the existence of infinitely many non-trivial zeroes for F(x, z) = 2x 4 −z 3 under the general form x = (1 + i)η 3 and c = −2η 4 for η ∈ Z[i].en_US
dc.identifier.doi10.47836/mjms.16.2.09
dc.identifier.epage328
dc.identifier.issn1823-8343
dc.identifier.issue2
dc.identifier.spage317
dc.identifier.urihttps://mjms.upm.edu.my/fullpaper/2022-May-16-2/Ismail,%20S.-317-328.pdf
dc.identifier.urihttps://oarep.usim.edu.my/handle/123456789/10462
dc.identifier.volume16
dc.language.isoenen_US
dc.publisherINSPEM, UPMen_US
dc.relation.ispartofMalaysian Journal Of Mathematical Sciencesen_US
dc.subjectGaussian integer; Diophantine equation; prime power decomposition.en_US
dc.titleDetermination of Gaussian Integer Zeroes of F(x, z) = 2x 4 − z 3en_US
dc.typeArticleen_US
dspace.entity.typePublication

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Determination of Gaussian Integer Zeroes of F(x, z) = 2x -z.pdf
Size:
1006.56 KB
Format:
Adobe Portable Document Format
Download

Collections

Scopus