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http://dx.doi.org/10.4134/CKMS.c190364

INTEGER POINTS ON THE ELLIPTIC CURVES INDUCED BY DIOPHANTINE TRIPLES  

Park, Jinseo (Department of Mathematical Education Catholic Kwandong University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.3, 2020 , pp. 745-757 More about this Journal
Abstract
A set {a1, a2, …, am} of positive integers is called a Diophantine m-tuple if aiaj + 1 is a perfect square for all 1 ≤ i < j ≤ m. In this paper, we find the structure of a torsion group of elliptic curves Ek constructed by a Diophantine triple {F2k, F2k+2, 4F2k+1F2k+2F2k+3}, and find all integer points on the elliptic curve under assumption that rank(Ek(ℚ)) = 2.
Keywords
Diophantine m-tuple; Fibonacci numbers; elliptic curve;
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Times Cited By KSCI : 2  (Citation Analysis)
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