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DIOPHANTINE TRIPLE WITH FIBONACCI NUMBERS AND ELLIPTIC CURVE

  • Park, Jinseo (Department of Mathematics Education Catholic Kwandong University)
  • Received : 2020.07.16
  • Accepted : 2021.01.12
  • Published : 2021.07.31
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Abstract

A Diophantine m-tuple is a set {a1, a2, …, am} of positive integers such that aiaj+1 is a perfect square for all 1 ≤ i < j ≤ m. Let Ek be the elliptic curve induced by Diophantine triple {F2k, 5F2k+2, 3F2k + 7F2k+2}. In this paper, we find the structure of a torsion group of Ek, and find all integer points on Ek under assumption that rank(Ek(ℚ)) = 1 and some further conditions.

Keywords

Acknowledgement

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2019R1G1A1006396).

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