Units in a ring?

Oct 2009
20
0
How would I go about figuring out how many units are in Zeta 230?
 
May 2010
13
1
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 ......
 

Drexel28

MHF Hall of Honor
Nov 2009
4,563
1,566
Berkeley, California
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 \(\displaystyle \text{card }(\mathbb{Z}/n\mathbb{Z})^{\times}=\varphi(n)\) where \(\displaystyle \varphi(n)\) is the number of things less than \(\displaystyle n\) which are relatively prime to it.
 
Oct 2009
20
0
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?