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#1 2008-11-09 08:15:48

tony123
Member
Registered: 2007-08-03
Posts: 189

Let integer p and q

Let integer p and q

Prove that     

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#2 2008-11-09 09:27:38

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Let integer p and q

I make it p(q-1)/2.
Edit: Oh, those are floors. Ignore me then.


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#3 2008-11-09 15:37:36

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

Re: Let integer p and q

I presume you mean

tony123 wrote:

Let p and q be integers (q > 1) which are relatively prime.

Consider the integers

Since p and q are coprime, no two of them are congruent modulo q. Hence all the numbers are a permutation of 1, 2, …, q−1 (mod q). Hence if we write

we have

.

Now

Last edited by JaneFairfax (2008-11-10 01:28:44)


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