On the Diophantine equation \((x+y+z)^3 = nxyz\) (Q1851533)
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scientific article; zbMATH DE number 1851307
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Diophantine equation \((x+y+z)^3 = nxyz\) |
scientific article; zbMATH DE number 1851307 |
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On the Diophantine equation \((x+y+z)^3 = nxyz\) (English)
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8 January 2003
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In this paper the following assertion is proved. Let \(n\in\{8k-1,16k-4,32k-16,64k,2^{2m+1}(2k-1)+27\}\), where \(k\) and \(m\) are positive integers. Then the equation \((x+y+z)^3 = nxyz\) does not have solutions in positive integers \(x\), \(y\) and \(z\).
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cubic Diophantine equation
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