On the Diophantine equation \(ax^3+bx^2+cx+dy+e = xyz\) (Q5950858)
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scientific article; zbMATH DE number 1683285
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Diophantine equation \(ax^3+bx^2+cx+dy+e = xyz\) |
scientific article; zbMATH DE number 1683285 |
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On the Diophantine equation \(ax^3+bx^2+cx+dy+e = xyz\) (English)
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18 December 2001
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The author proves the following assertion. Let \(a,b,c,d\) and \(e\) be nonnegative integers; \(ade \neq 0\). Then the equation \[ ax^3+bx^2+ cx+dy+ e=xyz \] has a finite number of solutions in natural numbers \(x,y,z\). This is a generalization of a result of \textit{A. M. S. Ramasamy} and \textit{S. P. Mohanty} [J. Indian Math. Soc., New Ser. 62, 210--214 (1996; Zbl 0899.11011)].
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cubic Diophantine equation
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