On Waring's problem with polynomial summands (Q2717620)
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scientific article; zbMATH DE number 1605216
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Waring's problem with polynomial summands |
scientific article; zbMATH DE number 1605216 |
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17 June 2001
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polynomial summands
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Waring problem
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On Waring's problem with polynomial summands (English)
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In this addendum for his paper [Acta Arith. 86, 245-254 (1998; Zbl 0934.11047)] the author considers even \(k\geq 6\) and shows that equality holds in his result for \(G(f_k)\) if and only if NEWLINE\[NEWLINE2\nmid f(1) \quad\text{and}\quad f(n)\equiv f(1)H(n)\pmod {2^k} \quad\forall n\in \mathbb{N},NEWLINE\]NEWLINE holds and one of \(2^{-k} f(2x)\) or \(2^{-k} (f(2x+1)- f(1))\) is constant modulo 2. The argument solely concerns the 2-adic solubility problem.
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