Bounds for Diophantine quintuples. II (Q2834209)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Bounds for Diophantine quintuples. II |
scientific article; zbMATH DE number 6656740
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bounds for Diophantine quintuples. II |
scientific article; zbMATH DE number 6656740 |
Statements
25 November 2016
0 references
Diophantine \(m\)-tuples
0 references
Pell equations
0 references
linear forms in logarithms
0 references
hypergeometric method
0 references
0 references
0.9633818
0 references
0.9433864
0 references
0.91598225
0 references
0 references
0.9061106
0 references
0 references
0.8991447
0 references
0 references
Bounds for Diophantine quintuples. II (English)
0 references
A set \(\{a_1,\dots,a_n\}\) of positive integers is called a Diophantine set if \(a_ia_j+1\) is a square for all \(i\neq j\). By a nice result of Dujella it is known that there are no Diophantine sextuples, and there are only finitely many Diophantine quintuples. In fact, by a standard conjecture, Diophantine quintuples do not exist. In the paper the authors provide various relations for the terms of putative Diophantine quintuples.NEWLINENEWLINEPart I, Glas. Mat., III. Ser. 50, No. 1, 25--34 (2015; Zbl 1364.11078).
0 references
