I've been asked to prove these 2 things :

1.

2. if then x^{2}=-1 has a solution.

I haven't manage to come by enough examples of Wilson's theorem, so I'm really in the dark here.

Any help will be much appreciated.

Thanks.

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- May 8th 2012, 02:27 PMLabanWilson's theorem proofing questions?
I've been asked to prove these 2 things :

1.

2. if then x^{2}=-1 has a solution.

I haven't manage to come by enough examples of Wilson's theorem, so I'm really in the dark here.

Any help will be much appreciated.

Thanks. - May 8th 2012, 07:18 PMwsldamRe: Wilson's theorem proofing questions?
I will prove when 'n' is an odd prime (so we can invoke Wilson's Theorem).

Let p be an odd prime. Then by Wilson's Theorem:

Since we can freely subtract p from each term in the second half of the previous equation. This gives us:

Now note that in the second half of the right hand side there are '-1's' (pardon my notation abuse). Pulling out the '-1's' we have the result.

If then . Hence, by our previous result, . Therefore has a solution. - May 8th 2012, 09:20 PMprincepsRe: Wilson's theorem proofing questions?
- May 9th 2012, 04:41 PMLabanRe: Wilson's theorem proofing questions?