Integer points on the elliptic curves induced by Diophantine triples
Commun. Korean Math. Soc.
Published online March 6, 2020
Jinseo Park
Catholic Kwandong University
Abstract : A set $\{a_1, a_2, \dots, a_m\}$ of positive integers is called Diophantine $m$-tuple if $a_ia_j+1$ is a perfect square for all $1\leq i < j \leq m$. In this paper, we find the structure of torsion group of elliptic curves $E_k$ constructed by Diophantine triple $\{F_{2k}, F_{2k+2}, 4F_{2k+1}F_{2k+2}F_{2k+3}\}$, and find all integer points on the elliptic curve under assumption that rank$(E_k(\mathbb{Q}))=2$.
Keywords : Diophantine m-tuple, Fibonacci numbers, Elliptic curve
MSC numbers : 11B39, 11G05, 11D09, 11D45
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