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Complete Solution of Diophantine Pairs Induced by Some Fibonacci Formula
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A set{a1,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{Fk-1Fk+1,Fk-2Fk+2},where Fn is the n-th Fibonacci number.
Diophantine m-tupleFibonacci numbersPell equation
Jinseo Park
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Department of Mathematics Education,Catholic Kwandong University Gangneung 25601,Korea
National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)
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NSTL
万方数据
维普
