Im having problems workout out
For which n are the integers mod n an integral domain?
can any1 show me how to prove this
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.