How to (dis)prove this
$ (n-2)! \equiv 1 \mod n$
If n is said to be a prime number. I guess we'll have to use FERMAT’S LITTLE THEOREM, and I just don't know where to start from. Thanks in advance
Answer
If $\;n=p\;$ is a prime, then by Wilson's theorem
$$\color{red}{-1}=(p-1)!=(p-2)!(p-1)=\color{red}{-(p-2)!\pmod p}\implies 1= (p-2)!\pmod p$$
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