Another restatement of the problem is:
Given:
(p-1)! ≡ m (mod p)
where:
- p is a prime number,
- ≡ means congruent (in modular arithmetic, having the same remainder when divided by some number), and
- m is some integer between 0 and p-1 (the remainder)
What is m?
______________
This is a restatement of
Wilson's theorem. The answer (as stated three times before) is
p-1, which of course is ≡ -1 (mod p).
And a proof is available at:
http://en.wikipedia.org/wiki/Wilson's_theorem
http://modular.fas.harvard.edu/edu/Fall2001/124/lectures/lecture6/html/node1.html
- and-
http://www.utm.edu/research/primes/notes/proofs/Wilsons.html
as well as at many other sources on the net (just look up "Wilson's Theorem").
I will refrain from duplicating these proofs here.
--- SK
Edited on October 16, 2003, 4:50 pm
full solution
