On the Diophantine equations \(x^2\pm y^4=z^3\) (Q2748322)
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 equations \(x^2\pm y^4=z^3\) |
scientific article; zbMATH DE number 1659205
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Diophantine equations \(x^2\pm y^4=z^3\) |
scientific article; zbMATH DE number 1659205 |
Statements
7 January 2004
0 references
quartic Diophantine equation
0 references
0.96701366
0 references
On the Diophantine equations \(x^2\pm y^4=z^3\) (English)
0 references
The authors consider the positive integer solutions \((x,y,z)\) of the equation \(x^2\pm y^4= z^3\) with \(\text{gcd}(x,y)= 1\). They conjecture that the equations \(x^2+ y^8= z^3\) and \(x^3+ y^8= z^2\) have only the positive integer solutions \((x,y,z)= (1549034,33,15613)\) and \((x,y,z)= (2,1,3)\), \((96222,43,30042907)\) with \(\text{gcd}(x,y)= 1\), respectively.
0 references
