RELATION BETWEEN DIOPHANTINE TRIPLE AND ELLIPTIC CURVE

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Published: May 15, 2020
DOI: https://doi.org/10.14403/jcms.2020.33.2.227
Mathematics Subject Classification (2020):
Primary 11G05, 11D09, Secondary 11D45

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Jinseo Park
Department of Mathematics Education, Catholic Kwandong University

Abstract





A set {a1, a2, . . . , am} of positive integers is called Diophantine m-tuple if aiaj +1 is a perfect square for all 1 ≤ i < j ≤ m. In this paper, we find the structure of torsion group of elliptic curve Ek constructed by Diophantine triple, and find all integer points on Ek under assumption that rank(Ek(Q)) = 1.





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Article Details

Issue
Vol. 33 No. 2 (2020)
Section
Articles