Diophantine quadruples in the sequence of shifted Tribonacci numbers (Q2803021)
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: Diophantine quadruples in the sequence of shifted Tribonacci numbers |
scientific article; zbMATH DE number 6576809
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Diophantine quadruples in the sequence of shifted Tribonacci numbers |
scientific article; zbMATH DE number 6576809 |
Statements
3 May 2016
0 references
Diophantine quadruples
0 references
Tribonacci numbers
0 references
lower bounds for nonzero linear forms in logarithms of algebraic numbers
0 references
Diophantine quadruples in the sequence of shifted Tribonacci numbers (English)
0 references
The Tribonacci sequence \(T_n\) is defined by \(T_0=0\), \(T_1=T_2=1\), and then every term is the sum of the previous three ones. The authors prove that among any four or more positive integers there are two whose product is not in \(T_n\). To prove their theorem, the authors combine certain arithmetic properties of the Tribonacci sequence and use Baker's method. The result is also related to the problem of Diophantine tuples.
0 references
