Some relations for partitions into four squares (Q2736542)
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scientific article; zbMATH DE number 1644370
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some relations for partitions into four squares |
scientific article; zbMATH DE number 1644370 |
Statements
10 September 2001
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number of partitions into four squares of non-negative integers
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Some relations for partitions into four squares (English)
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Let \(P_4(n)\) denote the number of partitions of \(n\) into four squares of non-negative integers, \(n\) a non-negative integer. Here the authors prove for all \(n\), the following: NEWLINE\[NEWLINE P_4(8n)=P_4(2n),\qquad P_4(32n+28)=3P_4(8n+7),\qquad P_4(72n+69)\equiv 0\pmod 2.NEWLINE\]NEWLINENEWLINENEWLINEFor the entire collection see [Zbl 0954.00030].
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