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RELATION BETWEEN DIOPHANTINE TRIPLE AND ELLIPTIC CURVE

  • Park, Jinseo (Department of Mathematics Education Catholic Kwandong University)
  • Received : 2020.02.03
  • Accepted : 2020.03.31
  • Published : 2020.05.15

Abstract

A set {a1, a2,, am} of positive integers is called Diophantine m-tuple if aiaj+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.

Keywords

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