On the equation \(x^ n+(x+a)^ n=y^{2n}+(y+b)^{2n}\) (Q1904412)
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scientific article; zbMATH DE number 828209
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the equation \(x^ n+(x+a)^ n=y^{2n}+(y+b)^{2n}\) |
scientific article; zbMATH DE number 828209 |
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On the equation \(x^ n+(x+a)^ n=y^{2n}+(y+b)^{2n}\) (English)
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1 February 1996
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Let \(n \geq 2\). It is proved that the equation in the title with \(a,b\) odd has only finitely many nontrivial solutions in integers \(x,y\). When \(a = b = 1\), the equation admits only the trivial solutions \(x = 0\), \(y \in \{0, -1\}\) or \(x = - 1\), \(y \in \{0, -1\}\) with \(n\) even.
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higher degree diophantine equations
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