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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.

Why did the vector cross the road?
It wanted to be normal.

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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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