Korean J. Math.  Vol 28, No 3 (2020)  pp.539-554
DOI: https://doi.org/10.11568/kjm.2020.28.3.539

The extendibility of Diophantine pairs with property $D(-1)$

Jinseo Park

Abstract


A set $\{a_1, a_2, \cdots, a_m\}$ of $m$ distinct positive integers is called a $D(-1)$-$m$-tuple if the product of any distinct two elements in the set decreased by one is a perfect square. In this paper, we find a solution of Pellian equations which is constructed by $D(-1)$-triples and using this result, we prove the extendibility of $D(-1)$-pair with some conditions.


Keywords


Diophantine m-tuple, Fibonacci number, Pellian equation

Subject classification

11B39; 11D09; 11D45

Sponsor(s)

National Research Foundation of Korea

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References


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