# Thread: Units in a ring?

1. ## Units in a ring?

How would I go about figuring out how many units are in Zeta 230?

2. by zeta 230, do you mean the ring of intergers modulo 230? if so, the units are the invertible elements, ie 1, 3, 77, 7 , 33 ......

3. Originally Posted by Purslow
by zeta 230, do you mean the ring of intergers modulo 230? if so, the units are the invertible elements, ie 1, 3, 77, 7 , 33 ......
Why not just say it? In general $\text{card }(\mathbb{Z}/n\mathbb{Z})^{\times}=\varphi(n)$ where $\varphi(n)$ is the number of things less than $n$ which are relatively prime to it.

4. Yes, the ring of integers mod 230. How do I find out the number of units (inverses for the product) without actually going through them all?