Im having problems workout out

For which n are the integers mod n an integral domain?

can any1 show me how to prove this

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- Oct 23rd 2008, 07:18 AMkbartlettintegral 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 - Oct 23rd 2008, 07:35 AMJhevon
- Oct 23rd 2008, 08:36 AMThePerfectHacker
For $\displaystyle \mathbb{Z}_n$ we require that if $\displaystyle [a]_n[b]_n = [0]_n$ implies $\displaystyle [a]_n=[0]_n$ or $\displaystyle [b]_n=[0]_n$.

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

Therefore $\displaystyle n$ must be prime. - Oct 23rd 2008, 09:03 AMkbartlett
Lol im so stuipd, it was already in my lecture notes anyway.

But thanks