1. ## Remainders

Given that 1201 is prime, what is the remainder when 1200! is divided by 1201?

I know that the gcd (1200!,1201) = 1200, but I don't know if this information will be helpful or how I use it..

2. Originally Posted by kiddopop
Given that 1201 is prime, what is the remainder when 1200! is divided by 1201?

I know that the gcd (1200!,1201) = 1200

This is impossible since it's given that 1201 is prime...

, but I don't know if this information will be helpful or how I use it..

Google "Wilson's Theorem". This is all you need.

Tonio

3. Use Wilson's theorem:
(n-1)! = -1 ( mod n) where n is a prime.
So, (1201-1)! = -1 ( mod 1201),
which gives the remainder to be 1200

4. Ohhh.