The extensibility of Diophantine pairs {k-1, k+1}

JOURNAL OF NUMBER THEORY

卷:128

Article

Fujita, Yasutsugu

关键词: Simultaneous Pell equations;    Diophantine tuples;   

DOI  :  10.1016/j.jnt.2007.03.013

来源: Elsevier

【 摘 要 】

A set of m distinct positive integers {a(1), ... , a(m)} is called a Diophantine m-tuple if a(i)a(j) + 1 is a square for each 1 <= i < j <= m. In this paper, we show that for each integer k >= 2 the Diophantine pair {k - 1, k + 1} cannot be extended to a Diophantine quintuple. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

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