On some Diophantine equations (Q2857836)
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scientific article; zbMATH DE number 6229032
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some Diophantine equations |
scientific article; zbMATH DE number 6229032 |
Statements
19 November 2013
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method of Euler and Lagrange
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higher degree Diophantine equations
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On some Diophantine equations (English)
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The author shows how to construct some sets of solutions to the equations \(ax^2 \pm my^2 = z^n\). Depending on the parity of \(n\) and on the \(\pm\) sign in the equation, he factorizes the LHS in the algebra of double numbers or in the complex numbers and requires each factor to be an \(n\)-th power. Comparison of coefficients of basis elements gives the formulas for \(x\) and \(y\).
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