Publication:
Perfect Triangles On The Curve C4

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dc.contributor.authorShahrina Binti Ismailen_US
dc.date.accessioned2024-05-28T06:11:56Z
dc.date.available2024-05-28T06:11:56Z
dc.date.issued2018
dc.descriptionVolume 109 Issue 1en_US
dc.description.abstractA Heron triangle is a triangle that has three rational sides (a,b,c) and a rational area, whereas a perfect triangle is a Heron triangle that has three rational medians (k,l,m) . Finding a perfect triangle was stated as an open problem by Richard Guy [Unsolved Problems in Number Theory (Springer, New York, 1981)]. Heron triangles with two rational medians are parametrized by the eight curves C1,…,C8 mentioned in Buchholz and Rathbun [‘An infinite set of heron triangles with two rational medians’, Amer. Math. Monthly 104(2) (1997), 106–115; ‘Heron triangles and elliptic curves’, Bull. Aust. Math.Soc. 58 (1998), 411–421] and Bácskái et al. [Symmetries of triangles with two rational medians, http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.65.6533, 2003]. In this paper, we reveal results on the curve C4 which has the property of satisfying conditions such that six of seven parameters given by three sides, two medians and area are rational. Our aim is to perform an extensive search to prove the nonexistence of a perfect triangle arising from this curve.en_US
dc.identifier.citationISMAIL, S. (2020). PERFECT TRIANGLES ON THE CURVE $C_{4}$. Journal of the Australian Mathematical Society, 109(1), 68-80. doi:10.1017/S144678871900003Xen_US
dc.identifier.doi10.1017/S144678871900003X
dc.identifier.epage80
dc.identifier.issn1446-7887
dc.identifier.issue1
dc.identifier.other2243-2
dc.identifier.spage68
dc.identifier.urihttps://www.cambridge.org/core/journals/journal-of-the-australian-mathematical-society/article/abs/perfect-triangles-on-the-curve-c4/835262913F580360432210C2A1C957AE
dc.identifier.urihttps://oarep.usim.edu.my/handle/123456789/7156
dc.identifier.volume109
dc.language.isoen_USen_US
dc.publisherCambridge University Pressen_US
dc.relation.ispartofJournal of the Australian Mathematical Societyen_US
dc.subjectelliptic curve, perfect triangle, p-adicen_US
dc.titlePerfect Triangles On The Curve C4en_US
dc.typeArticleen_US
dspace.entity.typePublication

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