On the Diophantine equation \(px^2+3^n=y^p\) (Q2719892)
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scientific article; zbMATH DE number 1610415
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Diophantine equation \(px^2+3^n=y^p\) |
scientific article; zbMATH DE number 1610415 |
Statements
10 October 2002
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exponential Diophantine equation
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On the Diophantine equation \(px^2+3^n=y^p\) (English)
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Let \(p\) be an odd prime with \(p>3\). In this paper the author proves that if \(p\not\equiv 7\pmod 8\), then the equation \(px^2+3^{2m}= y^p\), \(x,y,m\in \mathbb{N}\) has no solutions \((x,y,m)\) with \(\gcd (3,y)=1\); if \(p\not\equiv 5\pmod 8\), then the equation \(px^2+3^{2m+1}= y^p\), \(x,y\in \mathbb{N}\) has no solutions \((x,y,m)\) with \(\gcd (3,y)=1\).
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