The \(p\)-adic proof of Eisenstein's congruence (Q2745490)
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scientific article; zbMATH DE number 1654749
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The \(p\)-adic proof of Eisenstein's congruence |
scientific article; zbMATH DE number 1654749 |
Statements
27 February 2002
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Eisenstein's congruence
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\(p\)-adic number
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0.9160888
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0.9064787
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0.8935974
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0.8909751
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The \(p\)-adic proof of Eisenstein's congruence (English)
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Let \(p\) be an odd prime, and for \(k\) with \((k,p)=1\) let \(k^*\) satisfy \(kk^*\equiv 1\pmod p\). Then Eisenstein's congruence states that \(2^{p-1}/p\equiv 1^*+3^*+5^*+\cdots+(p-2)^* \pmod q\). This note gives a proof of the congruence.
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