Proof of an arithmetical theorem (Q1532931)
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scientific article; zbMATH DE number 2689448
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Proof of an arithmetical theorem |
scientific article; zbMATH DE number 2689448 |
Statements
Proof of an arithmetical theorem (English)
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1890
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Es handelt sich um folgenden Satz des Herrn Gegenbauer. Das Product \[ m(m+1k)(m+2k)\cdots(m+(n-1)k)k^{n-r}, \] wo \[ n=\sum^r_{r=1}a_{r,1}a_{r,2}\dots a_{r,s}, \] ist stets durch \[ P=\prod^r_{\kappa=1}\prod^s_{\nu=1}{(a_{\kappa,\nu}!)}^{a_{\kappa,\nu+1}\cdots a_{\kappa,s}} \] teilbar. Alle Symbole bedeuten ganze Zahlen. Specialisirungen.
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factorials
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