Relation between Diophantine triple and Elliptic curve

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

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