The linear Diophantine equation with \(n\)-unknowns in \(\mathbb Q(\sqrt{5})\) (Q1125503)
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scientific article; zbMATH DE number 1375284
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The linear Diophantine equation with \(n\)-unknowns in \(\mathbb Q(\sqrt{5})\) |
scientific article; zbMATH DE number 1375284 |
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The linear Diophantine equation with \(n\)-unknowns in \(\mathbb Q(\sqrt{5})\) (English)
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1999
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The main result is the proof of the following theorem: Let \(a_i\;(3<i\leq n)\) be integers different from a unit and zero in \(\mathbb Z(\sqrt)\) such that \((a_i,a_j=1\) then the linear Diophantine equation \(a_1x_1+\dots+a_nx_n=b\) has an integer solution in the ring of integers of \(\mathbb Q(\sqrt 5)\).
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linear Diophantine equations
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quadratic fields
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continued fractions
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0.8020991086959839
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0.7476103901863098
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