A note on the Diophantine equation \(x^2 + y^6 = z^e\), \(e\geq 4\) (Q2888798)
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scientific article; zbMATH DE number 6042615
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the Diophantine equation \(x^2 + y^6 = z^e\), \(e\geq 4\) |
scientific article; zbMATH DE number 6042615 |
Statements
4 June 2012
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Diophantine equation
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A note on the Diophantine equation \(x^2 + y^6 = z^e\), \(e\geq 4\) (English)
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The title equation is considered when \(e\) is a multiple of 4 or 6. The author shows that in these cases \(x^2+y^6=z^e\) has no solutions in positive integers \(x,y,z\) such that \((x,y)=1\). The proofs are purely elementary.
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