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Re: help required  ring, units, mod... etc
Posted:
Mar 16, 2007 11:15 AM


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 nonprime, 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



