An elementary solution method for the Diophantine equation \(x^2-3y^4=46\) (Q2742208)
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: An elementary solution method for the Diophantine equation \(x^2-3y^4=46\) |
scientific article; zbMATH DE number 1649790
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An elementary solution method for the Diophantine equation \(x^2-3y^4=46\) |
scientific article; zbMATH DE number 1649790 |
Statements
20 September 2001
0 references
quartic Diophantine equation
0 references
recurrent sequence method
0 references
An elementary solution method for the Diophantine equation \(x^2-3y^4=46\) (English)
0 references
\textit{N. Tzanakis} [Acta Arith. 46, 257-269 (1986; Zbl 0593.10013)] proved by the theory of quadratic fields that the equation \(x^2-3y^4=46\) has only the positive integer solutions \((x,y)=(7,1)\) and \((17,3)\). In 1989, the reviewer [Introduction to Diophantine equations (Chinese), Haerbin Gongye Daxue Chubanshe, Harbin (1989; Zbl 0849.11029)] pointed out the possibility of giving a simple elementary proof of the theorem by the recurrent sequence method. In this paper, the authors give this proof.
0 references
