On the extendibility of the Diophantine triple { 1, 5, c }

Fadwa S. Abu Muriefah and Amal Al-Rashed

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-10

Abstract:

We study the problem of extendibility of the triples of the form { 1 , 5 , c } . We prove that if c k = s k 2 + 1 , where ( s k ) is a binary recursive sequence, k is a positive integer, and the statement that all solutions of a system of simultaneous Pellian equations z 2 − c k x 2 = c k − 1 , 5 z 2 − c k y 2 = c k − 5 are given by ( x , y , z ) = ( 0 , ± 2 , ± s k ) , is valid for 2 ≤ k ≤ 31 , then it is valid for all positive integer k .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:720540

DOI: 10.1155/S0161171204305181

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