An Infinite Two-Parameter Family of Diophantine Triples

被引：1

作者：

Cipu, Mihai ^{[1
]}

Filipin, Alan ^{[2
]}

Fujita, Yasutsugu ^{[3
]}

机构：

[1] Romanian Acad, Simion Stoilow Inst Math, Res Unit 5,POB 1-764, RO-014700 Bucharest, Romania

[2] Univ Zagreb, Fac Civil Engn, Fra Andrije Kacica Miosica 26, Zagreb 10000, Croatia

[3] Nihon Univ, Coll Ind Technol, Dept Math, 2-11-1 Shin Ei, Narashino, Chiba, Japan

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2020年 / 43卷 / 01期

关键词：

Diophantine m-tuples; Pellian equations; Linear forms in logarithms; EXTENDIBILITY;

D O I：

10.1007/s40840-018-0695-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study sets of positive integers with the property that the product of any two elements in the set increased by the unity is a square. It is shown that if the two smallest elements have the form KA(2), 4KA(4) +/- 4A for some positive integers A and K, and the third one is chosen canonically, then any such set consisting of three elements can be contained in a unique such set with four elements.

引用

页码：481 / 498

页数：18

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