# Math Help - integral domain?

1. ## integral domain?

Im having problems workout out
For which n are the integers mod n an integral domain?

can any1 show me how to prove this

2. Originally Posted by kbartlett
Im having problems workout out
For which n are the integers mod n an integral domain?

can any1 show me how to prove this
ok, lets start with the basics. do you know what an integral domain is?

3. Originally Posted by kbartlett
Im having problems workout out
For which n are the integers mod n an integral domain?
For $\mathbb{Z}_n$ we require that if $[a]_n[b]_n = [0]_n$ implies $[a]_n=[0]_n$ or $[b]_n=[0]_n$.

Now if $n$ is not prime there is $1 < d < n$ so that $d|n$. Then $[d]_n [n/d]_n = [0]_n$ but neither $[d]_n,[n/d]_n$ are identity elements.

Therefore $n$ must be prime.

4. Lol im so stuipd, it was already in my lecture notes anyway.

But thanks