On the diophantine equation \(2^ a X^ 4+ 2^ b Y^ 4= 2^ c Z^ 4\) (Q1924893)
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scientific article; zbMATH DE number 938090
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the diophantine equation \(2^ a X^ 4+ 2^ b Y^ 4= 2^ c Z^ 4\) |
scientific article; zbMATH DE number 938090 |
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On the diophantine equation \(2^ a X^ 4+ 2^ b Y^ 4= 2^ c Z^ 4\) (English)
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22 October 1996
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Let \(a,b,c\) be nonnegative integers. In this paper it is proved that if \(X,Y,Z\) is a solution of the equation \(2^aX^4+ 2^bY^4= 2^cZ^4\) in positive and odd integers, then \[ X=Y= Z \quad \text{and} \quad a+1= b+1=c. \] Furthermore, it is proved that the equation \(X^4+ 2^m Y^2=Z^4\) has no solutions in nonzero integers \(X,Y,Z\).
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quartic diophantine equations
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