# Thread: Prime Related Problem Again

1. ## Prime Related Problem Again

let p be an odd prime. Show that the p-3 nubers from 2 to p-2 can be paired up in such a way that the product of each pair is congruent to 1 modulo p and use this to deduce that (p-2)! congruent to 1 mod p.

I'm having trouble with the first part..

2. Try an example. Let $p=11$. What pairs would you pick from $2, 3, 4, 5, 6, 7, 8, 9\pmod{11}$?

3. 3 and 4 ?

4. Yes, that works. But the statement says that you can pair up all of those numbers. What are the others?