On the Diophantine equation \(d_1x^2+4d_2=y^n\) (Q2425340)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Diophantine equation \(d_1x^2+4d_2=y^n\) |
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On the Diophantine equation \(d_1x^2+4d_2=y^n\) (English)
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29 April 2008
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The author proves that the equation \(d_1x^2+4d_2=y^n\) has no solutions in case \(d_1, d_2, x, y,n\) are positive integers satisfying \((d_1,d_2)=(x,y)=(2,y)=1\), \(d_1\), \(d_2\) squarefree, \(n>3\) odd and coprime to the class number of the field \(\mathbb{Q}(\sqrt{-d_1d_2})\). For the proof the author uses the well-known result of \textit{Y. F. Bilu, G. Hanrot} and \textit{P. M. Voutier} on primitive divisors of Lehmer sequences [J. Reine Angew. Math. 539, 75--122 (2001; Zbl 0995.11010)].
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