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A Diophantine $m$-tuple is a set $\{a_1, a_2, \dots, a_m\}$ of positive integers such that $a_ia_j+1$ is a perfect square for all $1\leq i < j \leq m$. Let $E_k$ be the elliptic curve induced by Diophantine triple $\{F_{2k}, 5F_{2k+2}, 3F_{2k}+7F_{2k+2}\}$. In this paper, we find the structure of a torsion group of $E_k$, and find all integer points on $E_k$ under assumption that rank$(E_k(\mathbb{Q}))=1$ and some further conditions.
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참고문헌 (13)
참고문헌 신청
A. Dujella / 1999 / A proof of the Hoggatt-Bergum conjecture / Proc. Amer. Math. Soc 127(7):1999~2005
A. Dujella / 2000 / A parametric family of elliptic curves / Acta Arith 94(1):87~101
A. Dujella / 2001 / Diophantine m-tuples and elliptic curves / J. Th´eor. Nombres Bordeaux 13(1):111~124
A. Dujella / 2004 / iophantine quadruples and Fibonacci numbers / Bull. Kerala Math. Assoc 1(2):133~147
A. Dujella / 1998 / A generalization of a theorem of Baker and Davenport, / Quart. J. Math. Oxford Ser (2) 49(195):291~306
A. Dujella / 2000 / A parametric family of elliptic curves / Acta Arith 94(1):87~101
A. Dujella / 2001 / Diophantine m-tuples and elliptic curves / J. Th´eor. Nombres Bordeaux 13(1):111~124
A. Dujella / 2004 / iophantine quadruples and Fibonacci numbers / Bull. Kerala Math. Assoc 1(2):133~147
A. Dujella / 1998 / A generalization of a theorem of Baker and Davenport, / Quart. J. Math. Oxford Ser (2) 49(195):291~306
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