| On the Diophantine Equation $x^3-1=2py^2$ |
| Received:August 25, 2005 Revised:May 23, 2007 |
| Key Words:
cubic Diophantine equation positive integer solution odd prime.
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| Fund Project:The National Natural Science Foundation of China (10271104); the Natural Science Foundation of Guangdong Province (011781); the Scientific Research Fund of Maoming University (203214). |
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| Abstract: |
| Let $p$ be an odd prime. This paper proves that if $p=48t^2+1$, where $t$ is a positive integer, then the equation $x^3-1=2py^2$ has no positive integer solution $(x,y)$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2007.03.030 |
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