Sums of four or more values of \(\mu x^2 + \nu x\) for integers \(x\). (Q572126)
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scientific article; zbMATH DE number 2555807
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sums of four or more values of \(\mu x^2 + \nu x\) for integers \(x\). |
scientific article; zbMATH DE number 2555807 |
Statements
Sums of four or more values of \(\mu x^2 + \nu x\) for integers \(x\). (English)
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1931
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Beweis des Satzes: Es sei \(0 < \nu < \mu\), \(s \geqq 4\), \(f(x) = \mu x^2 + \nu x\) und \(T\) die Tabelle der Werte \(f(x_1) + f(x_2) + \cdots + f(x_s)\) für ganzzahlige \(x\). Dann ist der größte Sprung zwischen aufeinander folgenden Werten von \(T\) gleich \[ \begin{matrix} \quad & \l \\ \mu - \nu & \text{ für } \;\;s\mu \geqq (s + 2) \nu, \\ (s+1)\nu - (s - 1)\mu & \text{ für } \;\;s\mu \leqq (s + 2) \nu. \end{matrix} \]
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