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A set $\{a_1, a_2, \dots, a_m\}$ of positive integers is called a 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 a torsion group of elliptic curves $E_k$ constructed by a 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$(E_k(\mathbb{Q}))=2$.
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참고문헌 (23)
참고문헌 신청
Lj. Ba´ci´c / 2016 / The extendibility of D(4)-pairs {F2k, F2k+6} and {P2k, P2k+4} / Rad Hrvat. Akad. Znan. Umjet. Mat. Znan 20:27~35
J. H. E. Cohn / 1964 / Square Fibonacci numbers, etc / Fibonacci Quart. 2:109~113
J. E. Cremona / 1997 / Algorithms for Modular Elliptic Curves / Cambridge University Press
L. E. Dickson / 1966 / History of the Theory of Numbers. Vol. II / Chelsea Publishing Co.
A. Dujella / 1999 / A proof of the Hoggatt-Bergum conjecture / Proc. Amer. Math. Soc 127(7):1999~2005
J. H. E. Cohn / 1964 / Square Fibonacci numbers, etc / Fibonacci Quart. 2:109~113
J. E. Cremona / 1997 / Algorithms for Modular Elliptic Curves / Cambridge University Press
L. E. Dickson / 1966 / History of the Theory of Numbers. Vol. II / Chelsea Publishing Co.
A. Dujella / 1999 / A proof of the Hoggatt-Bergum conjecture / Proc. Amer. Math. Soc 127(7):1999~2005
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