Waring's problem for integral quaternions (Q1782259)
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scientific article; zbMATH DE number 6939361
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Waring's problem for integral quaternions |
scientific article; zbMATH DE number 6939361 |
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Waring's problem for integral quaternions (English)
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20 September 2018
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The classical Waring's problem states that for every positive integer \(m\) it is always possible to find a positive integer \(g\) such that any positive integer can be written as the sum of \(g\) \(m\)-th powers. This paper proves that this result also holds true in the context of Lipschitz quaternions, i.e., in the set \[ \mathbb{L}=\{a+bi+cj+dk:a,b,c,d\in\mathbb{Z}\}. \]
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Waring's problem
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quaternions
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Lipschitz quaternions
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