On the number of positive integer solutions \((x, n)\) of the generalized Ramanujan-Nagell equation \(x^2-2^r = p^n\) (Q1705826)
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 number of positive integer solutions \((x, n)\) of the generalized Ramanujan-Nagell equation \(x^2-2^r = p^n\) |
scientific article; zbMATH DE number 6851225
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of positive integer solutions \((x, n)\) of the generalized Ramanujan-Nagell equation \(x^2-2^r = p^n\) |
scientific article; zbMATH DE number 6851225 |
Statements
On the number of positive integer solutions \((x, n)\) of the generalized Ramanujan-Nagell equation \(x^2-2^r = p^n\) (English)
0 references
16 March 2018
0 references
For an odd prime \(p\) and positive integer \(r\), write \(N(2^r,p)\) for the number of positive integer solutions \((x, n)\) of the equation in the title. Improving several results from the literature, the authors prove the sharp inequality \(N(2^r, p) \leq 1\). In the proof elementary methods are combined with tools from the theory of Pell equations.
0 references
generalized Ramanujan-Nagell equation
0 references
number of solutions
0 references
upper bound estimate
0 references
0 references
0.97278273
0 references
0.9638293
0 references
0.9588615
0 references
0.9588401
0 references
