How to prove (p-1) = -1 (mod p), p is a prime.

Thread starter lifom
Start date Feb 15, 2011
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Prime

Feb 15, 2011

lifom

(p-1)! = -1(mod p), where p is a prime
I have tried small values of p but I can't find any pattern. Can anyone give me some hints or directions? I don't know a detail proof. Thank you

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Feb 15, 2011

robert Ihnot

The matter turns on inverses. For every a in the system there is an a^-1, such that a*a^-1 = 1. (Generally that is an axiom of the group property.)

Feb 16, 2011

Xitami

http://primes.utm.edu/notes/proofs/Wilsons.html

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