Exponential Diophantine equations of the form \(a^x+b^y=c^z\) (Q2741807)
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scientific article; zbMATH DE number 1649511
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Exponential Diophantine equations of the form \(a^x+b^y=c^z\) |
scientific article; zbMATH DE number 1649511 |
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20 September 2001
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exponential Diophantine equations
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0.9639833
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0.94922817
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0.9466261
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Exponential Diophantine equations of the form \(a^x+b^y=c^z\) (English)
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The author proves by elementary methods that the Diophantine equations \(a^x+b^y=2^z\), where \(a,b\) are distinct primes, \(29\leq\max(a,b) \leq 97\), have no solutions \(x,y,z\) in positive integers except \(3^4+47=2^7\), \(7^2+79=2^7\), \(17+47=2^6\), \(41+23=2^6\), \(97+31=2^7\), \(3^3+37=2^6\), \(3+61=2^6\), \(11+53=2^6\), \(59+5=2^6\), \(3+29=2^5\), \(67+61=2^7\).
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