[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j170289

SOME CONDITIONS ON THE FORM OF THIRD ELEMENT FROM DIOPHANTINE PAIRS AND ITS APPLICATION

Lee, June Bok (Department of Mathematical Sciences Yonsei University)
Park, Jinseo (Department of Mathematics Education Catholic Kwandong University)

Publication Information

Journal of the Korean Mathematical Society / v.55, no.2, 2018 , pp. 425-445 More about this Journal

Abstract

A set { $$a_1,\$ $;a_2,{\ldots},\;a_m$$ } of positive integers is called a Diophantine m-tuple if $a_ia_j+1$ is a perfect square for all $1{\leq}i$ < $j{\leq}m$ . In this paper, we show that the form of third element in Diophantine pairs and develop some results which are needed to prove the extendibility of the Diophantine pair {a, b} with some conditions. By using this result, we prove the extendibility of Diophantine pairs { $F_{k-2}F_{k+1},\;F_{k-1}F_{k+2}$ } and { $F_{k-2}F_{k-1},\;F_{k+1}F_{k+2}$ }, where $F_n$ is the n-th Fibonacci number.

Keywords

Diophantine m-tuple; Fibonacci numbers; Pell equation;

Citations & Related Records

Reference

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