Re: Coprime Numbers

On 05.05.2008 14:09, David C. Ullrich wrote:
On Sun, 04 May 2008 17:43:22 +0200, Jannick Asmus
<jannick.news@xxxxxx> wrote:

On 04.05.2008 17:18, Chip Eastham wrote:
On May 4, 11:05 am, David C. Ullrich <dullr...@xxxxxxxxxxx> wrote:
On Sat, 03 May 2008 18:40:55 +0200, Jannick Asmus

<jannick.n...@xxxxxx> wrote:
On 03.05.2008 18:24, Maury Barbato wrote:
Hello,
let U_n be the set of all the integers that are coprime
to a positive integer n, with the multiplication modulo
n.
U_n with this operation is a group. My questions are:
1) for what value of n U_n is a cylic group?
Consider the group of units of Z/nZ for getting a necessary condition on
n such that U_n is cyclic.
HTH.
??? How could that help? Maybe I'm missing something,
Yes, definitely you are. May I ask you to carefully read the lines above - except yours of course - and *then* and only then come back.

Ok, I've done that. First, of course when the OP says that the
multiplication in U_n is "modulo n" it follows that by U_n
he must mean a set of equivalence classes. Now, is U_n
the same as the set of units in Z/Z_n?

Yes, it is - of course. But I assumed that the rewording of the claim in more obvious terms connects it closer to what the OP might know. The exercise smells so much like homework such that I hoped that such a 'hint' could have helped. But there was no reply from him till now ...

Honestly, David, my words to you were not appropriate at all. Therefore I should apologize - and I do so, David.

Best wishes,
J.
.

Relevant Pages

  • Re: please check my homework
    ... Is my bidistfunction correct? ... David ... In the above comment you should specify that n must be a positive integer, ... I'm very concerned with the problem of overflow. ...
    (comp.programming)
  • Re: how to solve this limit?
    ... so what do you think if m is a positive integer, ... David C. Ullrich wrote: ... correct by the binomial theorem, ...
    (sci.math)
  • Re: Coprime Numbers
    ... to a positive integer n, ... David C. Ullrich ... question in terms of the multiplicative group of Z/nZ. ...
    (sci.math)
  • Re: series and squares
    ... This follows from the fact that if N is a large positive integer then ... suppose that n^2 is the largest square with ... David C. Ullrich ...
    (sci.math)
  • Re: Coprime Numbers
    ... let U_n be the set of all the integers that are coprime ... to a positive integer n, with the multiplication modulo ... for what value of n U_n is a cylic group? ...
    (sci.math)