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Topic: help required -- ring, units, mod... etc
Replies: 9   Last Post: Mar 20, 2007 2:37 PM

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Hanford Carr

Posts: 25
Registered: 11/17/05
Re: help required -- ring, units, mod... etc
Posted: Mar 16, 2007 11:15 AM
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Maria Bertouli wrote:
>
> "Rupert" <rswarbrick@googlemail.com> wrote in message
> news:1173980327.840236.35150@l75g2000hse.googlegroups.com...

> > On Mar 15, 1:43 pm, "Maria Bertouli" <a...@spam.net> wrote:
> > > I would like to find all the positive integers n such that every unit u
> in
> > > the Integers mod n satisfies u^2=1.
> > >
> > > How can I find these?
> > >
> > > Thanks.

> >
> > Firstly, you probably should go about finding which units in integers
> > mod 5, say, have a square of one. Then try a non-prime, say 6? It
> > should become clearer after trying some examples, I think.
> >

>
> i think i've figured out it should be [u mod n]^2=1 that we are satisfying
> and not u^2 =1. but still wouldn't mind confirmation on this.
>
> so now, i know the integers mod 2, 3, 4, 6, 8, work. (i've only worked up to
> the integers mod 10)
>
> i would be interested to know if it could be proved for how many it would
> work for? i don't want an answer of course but i would like an idea of how
> to approach a method, if there is one.
>
> thanks.

snip

Use the Carmichael lambda function.
http://mathworld.wolfram.com/CarmichaelFunction.html
Find all numbers for which lambda (n) = 2.

Regards Hanford



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