Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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THE EXTENDIBILITY OF DIOPHANTINE PAIRS WITH FIBONACCI NUMBERS AND SOME CONDITIONS

  • Park, Jinseo (Department of Mathematics Education Catholic Kwandong University)
  • Received : 2021.05.08
  • Accepted : 2021.07.20
  • Published : 2021.08.15
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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. Let Fn be the nth Fibonacci number which is defined by F0 = 0, F1 = 1 and Fn+2 = Fn+1 + Fn. In this paper, we find the extendibility of Diophantine pairs {F2k, b} with some conditions.

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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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