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Integer points on the elliptic curves induced by Diophantine triples

박진서
대한수학회 (The Korean Mathematical Society)|2020.07|대한수학회논문집 (Communications of the KMS)|제35권 제3호|pp. 745-757|DOI 10.4134/CKMS.c190364

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참고문헌

키워드

Fibonacci numbersDiophantine $m$-tupleelliptic curve
주제분류수학

초록

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$(E_k(\mathbb{Q}))=2$.

Abstract

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$(E_k(\mathbb{Q}))=2$.

참고문헌 (23)

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