| On the Exponential Diophantine Equation $x^2+(3a^2-1)^m=(4a^2-1)^n$ |
| Received:April 29, 2005 Revised:December 10, 2006 |
| Key Words:
exponential Diophantine equations Lucas sequences primitive divisors Kronecker symbol.
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| Fund Project:the Natural Science Foundation of Guangdong Province (04009801); the Important Science Research Foundation of Foshan University. |
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| Abstract: |
| We apply a new, deep theorem of Bilu, Hanrot \& Voutier and some fine results on the representation of the solutions of quadratic Diophantine equations to solve completely the exponential Diophantine equation $x^2+(3a^2-1)^m=(4a^2-1)^n$ when $3a^2-1$ is a prime or a prime power. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2007.02.003 |
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