Complete Solution of Diophantine Pairs Induced by Some Fibonacci Formula

作     者：Jinseo Park Jinseo Park

作者机构：Department of Mathematics EducationCatholic Kwandong University Gangneung 25601Korea 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2023年第30卷第1期

页      面：121-132页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：supported by the National Research Foundation of Korea(NRF)gi funded by the Korea government(MSIT)(No.2019R1G1A1006396). 

主　　题：Diophantine m-tuple Fibonacci numbers Pell equation 

摘      要：A set[ai,a2,...,am)of positive integers is called a Diophantine m-tuple if aiaj+1 is a perfect square for all 1≤imax(a,b].In this paper,we find the condition for the reduction of third element c,and using this result,we prove the extendibility of Diophantine pair[F_(k)-1F_(k+1),F_(k-2)F_(k+2)],where Fn is the n-th Fibonacci number.