Communications of the Korean Mathematical Society (대한수학회논문집)

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INTEGER POINTS ON THE ELLIPTIC CURVES INDUCED BY DIOPHANTINE TRIPLES

  • Park, Jinseo (Department of Mathematical Education Catholic Kwandong University)
  • Received : 2019.10.15
  • Accepted : 2019.12.31
  • Published : 2020.07.31
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Abstract

A set {a1, a2, …, am} of positive integers is called a Diophantine m-tuple if aiaj + 1 is a perfect square for all 1 ≤ i < j ≤ m. In this paper, we find the structure of a torsion group of elliptic curves Ek constructed by a Diophantine triple {F2k, F2k+2, 4F2k+1F2k+2F2k+3}, and find all integer points on the elliptic curve under assumption that rank(Ek(ℚ)) = 2.

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References

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