KCI등재
학술저널
Relation between Diophantine triple and Elliptic curve
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 33, No. 2
- : KCI등재
- 2020.05
- 227 - 236 (10 pages)
DOI : 10.14403/jcms.2020.33.2.227
A set {a1, a2, …, am} of positive integers is called Diophantine m-tuple if ai aj+1 is a perfect square for all 1 ≤ i < j ≤ m. In this paper, we find the structure of torsion group of elliptic curve Ek constructed by Diophantine triple, and find all integer points on Ek under assumption that rank(Ek(Q))=1.
1. Introduction
2. Preliminaries
3. Torsion group of the elliptic curve
4. Integer points on elliptic curve
References