Publication:
Perfect Triangles: Rational Points On The Curve C4 (the Unsolved Case)

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dc.contributor.authorShahrina Ismailen_US
dc.contributor.authorZainidin Eshkuvatoven_US
dc.date.accessioned2024-05-28T03:33:22Z
dc.date.available2024-05-28T03:33:22Z
dc.date.issued2020
dc.date.submitted24/6/2020
dc.description5th International Conference on Mathematical Applications in Engineering 30-31 October 2019, Putrajaya, Malaysiaen_US
dc.description.abstractFinding a perfect triangle was stated as an open problem by Guy in [6]. Numerous researches have been done in the past to find such a triangle, unfortunately, to date, no one has ever found one, nor has proved its non-existence. However, on the bright side, there are partial results which show that there exist triangles that satisfy five or even six of the seven parameters to be rational. In this paper, we perform an extensive search to investigate if we can extract any perfect triangles from the curve C4 based on the final unsolved case in [9], which will then complete the proof of existence or non-existence of perfect triangle on the curve. Multiple conjectures were tested to eliminate the possibilities of finding a perfect triangle from the last unsolved case of n ≡ 3024 (mod 6052) in [9]. Finally, a theorem was proved, which was subtle enough to eliminate this case, proving that there does not exist any perfect triangle arising from the curve C4.en_US
dc.identifier.citationShahrina Ismail and Zainidin Eshkuvatov 2020 J. Phys.: Conf. Ser. 1489 012003en_US
dc.identifier.doi10.1088/1742-6596/1489/1/012003
dc.identifier.epage5
dc.identifier.issn1742-6596
dc.identifier.issue2020
dc.identifier.spage1
dc.identifier.urihttps://iopscience.iop.org/article/10.1088/1742-6596/1489/1/012003/pdf
dc.identifier.urihttps://iopscience.iop.org/article/10.1088/1742-6596/1489/1/012003
dc.identifier.urihttps://oarep.usim.edu.my/handle/123456789/4672
dc.identifier.volume1489
dc.language.isoen_USen_US
dc.publisherInstitute of Physicsen_US
dc.relation.conference5th International Conference on Mathematical Applications in Engineeringen_US
dc.relation.ispartofJournal of Physics: Conference Seriesen_US
dc.titlePerfect Triangles: Rational Points On The Curve C4 (the Unsolved Case)en_US
dc.typeArticleen_US
dspace.entity.typePublication

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