由斐波那契公式导出的丢番图对的完全解

Pub Date : 2022-03-20 DOI:10.1142/s100538672300010x

Jinseok Park

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引用次数: 0

摘要

如果[公式:见文本]是所有[公式:见文本]的完全平方，则一个正整数集[公式:见文本]称为丢番图[公式:见文本]-元组。设[公式:见文]为[公式:见文]的丢番图三元。本文给出了三元约简的条件[公式:见文]，并利用这一结果证明了丢番图对[公式:见文]的可拓性，其中[公式:见文]是[公式:见文]-斐波那契数。

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Complete Solution of Diophantine Pairs Induced by Some Fibonacci Formula

A set [Formula: see text] of positive integers is called a Diophantine [Formula: see text]-tuple if [Formula: see text] is a perfect square for all [Formula: see text]. Let [Formula: see text] be the Diophantine triple with [Formula: see text]. In this paper, we find the condition for the reduction of third element [Formula: see text], and using this result, we prove the extendibility of Diophantine pair [Formula: see text], where [Formula: see text] is the [Formula: see text]-th Fibonacci number.

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