## RE: RE : [PrimeNumbers] variation on Wilson theorem

Expand Messages
• Another variation on Wilsonm s Theorem: Both n! and (n+1)! = -nmodn^2 iff n is prime Jon Perry perry@globalnet.co.uk
Message 1 of 5 , Apr 16, 2002
Another variation on Wilsonm's Theorem:

Both n! and (n+1)! = -nmodn^2 iff n is prime

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

-----Original Message-----
From: CRESGE - Hervé LELEU [mailto:h.leleu@...]
Sent: 16 April 2002 16:57
Subject: RE : [PrimeNumbers] variation on Wilson theorem

Does it mean that n is prime iff (a-1)!*(n-a)! = -1 (mod n) ?
where a=1 for Wilson theorem.

And also that: n is prime iff ((n-1)/2)! ^ 2 = (+/-) 1 (mod n) where
(+/-) 1 depends if (n-1)/2 is odd or even.

> -----Message d'origine-----
> De : Paul Jobling [mailto:Paul.Jobling@...]
> Envoyé : mardi 16 avril 2002 17:07
> À : 'CRESGE - Hervé LELEU'; primenumbers@yahoogroups.com
> Objet : RE: [PrimeNumbers] variation on Wilson theorem
>
>
> > Let n>2.
> > n is prime if and only if 2(n-3)! = -1 mod n
> > Is this result well-known?
>
> Wilson's theorem states that n is prime iff (n-1)! = -1 (mod
> n). This is the same as your result: you have explicitly
> multiplied n-1 and n-2 together and removed them from the
> factorial. (n-1)*(n-2) (mod n) = -1*-2 (mod n) = 2 (mod n).
>
> Regards,
>
> Paul.
>
>
> __________________________________________________
> Virus checked by MessageLabs Virus Control Centre.
>

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
The Prime Pages : http://www.primepages.org

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
Your message has been successfully submitted and would be delivered to recipients shortly.