# Units in a ring?

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• May 28th 2010, 06:12 PM
HeadOnAPike
Units in a ring?
How would I go about figuring out how many units are in Zeta 230?
• May 28th 2010, 07:04 PM
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 ......
• May 28th 2010, 07:42 PM
Drexel28
Quote:

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.
• May 29th 2010, 03:05 AM
HeadOnAPike
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?