From Wikipedia: The units of the ring Z/nZ are the numbers coprime to n. They form a group under multiplication modulo n with φ(n) elements (see above). It is written as (Z/nZ)*. For example, we get (Z/nZ)* = {1,5} when n = 6, and get (Z/nZ)* = {1,3,5,7} when n = 8. In fact, it is known that (Z/nZ)* is cyclic if and only if n is 1 or 2 or 4 or p^k or 2p^k for some odd prime number p and k ≥ 1, in which case every generator of (Z/nZ)* is called a primitive root modulo n. Thus, (Z/nZ)* is cyclic for n = 6, but not for n = 8, where it is instead isomorphic to the Klein four-group. Does this mean if we have a group of units, say (Z/11Z)* (is this equal to U11...the group of units of the group Z11?) [when I say U11 and Z11, the 11 is supposed to be subscripted], then we can immediately say it is cyclic simply because 11 = 11^1, since p=11, which is an uneven prime, and k=1?
Dude wtf im high over here! Your fucking up my buzz with this shit. Aint there a math forum on this site?
Oh stop bragging that you are in Calculus. You know nobody knows wtf you are talkin about. I took Calculus at UW and ive never even heard of coprime lol
this is far from calculus. i finished Calc III last semester and am starting Abstract Algebra and Number Theories this fall, so if this were asked in september i could help more.... but writing problems on the internet is a clusterfuck and is way harder to comprehend.
dude i took abstract algebra in college (i was a math minor) and of all the math classes i took that was the one that kicked my ass. it was the only math class i really felt i did not understand at the fundamental level. quantum mechanics, physical chemistry, biophysics...they were all good, i loved them...but abstract algebra was some fucked up shit. good luck mate.
I swear I just felt a piece of my brain melt... WTF kind of answers do you expect get here? That could be the meaning of the god damn universe for all I know.
hahaha, math questions on GC, man, we come to chill here, and bullshit. personally i had trouble with the algebra in astronomy lab today...more like i couldnt comprehend any of it, and copied from the kid next to me.
This isn't even close to calculus....If you took calculus you would see that right away. I'm taking NUMBER THEORY like it says in the thread title. I just thought that with all the college kids on this site, someone's gotta be a math major. And the reason I'm asking is because I took a test today and I used the above procedure to get the answers for a question relating to it. So no, I'm not bragging, I'm asking a question...there's a big difference, mainly...everything. Bragging is arrogant...asking for help is humble. They are pretty much opposites. Also, to anyone else complaining: the thread title is very clear as to what I'm going to be asking, so I don't really know why you open it, read it, post and complain about how it's a shitty thread. Just leave it alone! However, it is the internet after all. Oh, and if two numbers are coprime, then their greatest common divisor is one. 15 and 14 are coprime since they share no common divisors other than 1.