Complete Solution of Diophantine Pairs Induced by Some Fibonacci Formula  

作　　者：Jinseo Park 

机构地区：[1]Department of Mathematics Education,Catholic Kwandong University Gangneung 25601,Korea

出　　处：《Algebra Colloquium》2023年第1期121-132,共12页代数集刊（英文版）

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

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≤i<j≤m.Let(a,b,c)be the Diophantine triple with c>max(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.

关 键 词：Diophantine m-tuple Fibonacci numbers Pell equation 

分 类 号：O15[理学—数学]