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#1 2007-03-07 10:44:04

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

division

Last edited by Stanley_Marsh (2007-03-07 10:46:10)


Numbers are the essence of the Universe

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#2 2007-03-07 16:15:46

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: division

Nobody?? Really urgent~


Numbers are the essence of the Universe

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#3 2007-03-07 16:54:10

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: division

I honestly haven't got a clue.  My first guess would to be this is somehow a^(p-1) and then you could apply Fermat's Little Theorem.  But that doesn't seem to help any.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#4 2007-03-07 17:17:04

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: division

I got it.

Now apply Wilson’s theorem and the result should follow.

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#5 2007-03-07 17:22:14

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: division

Excellent work, Jane.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#6 2007-03-07 18:13:40

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: division

I can only prove that

Last edited by Stanley_Marsh (2007-03-07 18:13:59)


Numbers are the essence of the Universe

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#7 2007-03-07 18:53:23

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: division

(p-1)! = -6(p-4)! = -1 (mod p)

So 6(p-4)! = 1 (mod p)


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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