11-00-WilsonsTheoremResult.tex

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\pmtitle{Wilson's theorem result}
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\begin{document}
The following is a variant of Wilson's theorem:

Let $p$ be a positive integer and $1 \leq k \leq p-1$.  Then:
\newline $p$ is prime if and only if 
$$(p-k)!(k-1)! \equiv (-1)^{k} \pmod{p}.$$

For particular $k = 1, 2, \ldots$ one gets nice results.
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