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http://dx.doi.org/10.14403/jcms.2021.34.3.209

THE EXTENDIBILITY OF DIOPHANTINE PAIRS WITH FIBONACCI NUMBERS AND SOME CONDITIONS  

Park, Jinseo (Department of Mathematics Education Catholic Kwandong University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.34, no.3, 2021 , pp. 209-219 More about this Journal
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.
Keywords
Diophantine m-tuple; Fibonacci numbers; Pell equation;
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