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April 24th, 2017, 12:18 AM   #1
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What is the most motivating way to introduce Wilson's Theorem?

What is the most motivating way to introduce Wilson’s Theorem? Why is Wilson’s theorem useful? With Fermat’s little Theorem we can say that working with residue 1 modulo prime p makes life easier but apart from working with a particular (p-1) factorial of a prime what other reasons are there for Wilson’s theorem to be useful?
Are there any good resources on this topic?
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April 25th, 2017, 07:52 AM   #2
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Because is the grandpa of the most simple formula that describe all the Odd Primes:

$z= (n-1)!/n$

(with n=Even it fails just in the case n=4)

...and because this $z$ is obviously connected to the Riemann's one since also here we can see trivial zeros (in case $z\in \mathbb{R}$), and non trivial ones (in case $z\in \mathbb{Q}$) so having a "Rest" (the non integer part of $z$).'s enough ?
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