On the Diophantine equation \(x^ 2+a^ 2=2y^ p\). (Q1890430)
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: On the Diophantine equation \(x^ 2+a^ 2=2y^ p\). |
scientific article; zbMATH DE number 2124645
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Diophantine equation \(x^ 2+a^ 2=2y^ p\). |
scientific article; zbMATH DE number 2124645 |
Statements
On the Diophantine equation \(x^ 2+a^ 2=2y^ p\). (English)
0 references
3 January 2005
0 references
The author combines lower bounds for two logarithms (in the complex case) with elementary arguments to provide an effective method to solve completely instances of the exponential Diophantine equations \(x^2+a^2=2y^p\) and \(x^2+a^2=y^p\). As examples, he solves completely the first equation for \(a\) odd, \(3\leq a \leq 305\), and the second one for \(a\) odd, \(3\leq a \leq 501\).
0 references
exponential Diophantine equations
0 references
Diophantine approximations
0 references
0 references
0.96343887
0 references
0.96086526
0 references
0.9564692
0 references
0.9538002
0 references
