# Integer mod proof

1. Sep 23, 2010

### kathrynag

1. The problem statement, all variables and given/known data
Prove that either $$[a]_{n}$$$$\cap$$$$_{n}$$=empty set or $$[a]_{n}$$=$$_{n}$$.

2. Relevant equations

3. The attempt at a solution
I want to assume there is an element x in $$[a]_{n}$$$$\cap$$$$_{n}$$ and show this implies $$[a]_{n}$$=$$_{n}$$.
This tells me x is in $$[a]_{n}$$ and $$_{n}$$.
That's where I get stuck.

Last edited: Sep 23, 2010
2. Sep 23, 2010

### kathrynag

sorry, I meant to show this implies [a]=.

3. Sep 23, 2010

### Office_Shredder

Staff Emeritus
If x=a mod n then n|x-a. x=b mod n means n|x-b.

If x|x-a and n|x-b.... what can you say about a-b?

4. Sep 23, 2010

### kathrynag

x-a=x-b
x-x=a-b
0=a-b
b=a

5. Sep 23, 2010

### Office_Shredder

Staff Emeritus
x-a is probably not equal to x-b

6. Sep 23, 2010

### kathrynag

Ok then I'm not really sure where to go with a-b then.