How to (dis)prove this
(n−2)!≡1modn
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
−1=(p−1)!=(p−2)!(p−1)=−(p−2)!(modp)⟹1=(p−2)!(modp)
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