Math Is Fun Forum
Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °
You are not logged in.
- Topics: Active | Unanswered
Pages: 1
#1 2008-11-09 08:15:48
- tony123
- Member
- Registered: 2007-08-03
- Posts: 230
Let integer p and q
Let integer p and q
Prove that
Offline
#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.
Offline
#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)
Offline
Pages: 1