Re: Coprime Numbers

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?

but it seems to me that he asked when U_n is cyclic
and your advice was "consider U_n".
David C. Ullrich

Perhaps because, in another thread, the OP asks the
question in terms of the multiplicative group of Z/nZ.

Thanks, certainly this might be interpreted like that, but the OP posted
this part of the exercise first, a couple of minutes later this one on
"multiplication in Z/nZ".

Chip, thanks a lot again. Much appreciated! :-)

David C. Ullrich
.

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