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 $D(-1)$

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Published: Sep 14, 2020
Keywords:
Diophantine m-tuple, Fibonacci number, Pellian equation
Mathematics Subject Classification:
11B39, 11D09, 11D45

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Jinseo Park
Department of Mathematics Education Catholic Kwandong University Gangneung 25601, Korea

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.



Article Details

Supporting Agencies

National Research Foundation of Korea

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