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Topic: a^n = a mod 6
Replies: 8   Last Post: Jan 18, 2014 6:36 AM

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 William Elliot Posts: 2,637 Registered: 1/8/12
Re: a^n = a mod 6
Posted: Jan 16, 2014 11:49 PM

On Thu, 16 Jan 2014, quasi wrote:

> sharma wrote:
> >
> >For odd prime n, and any a, a^n = a mod 6. I thought this
> >was interesting. Is this common knowledge?

>
> An easy exercise.
>
> However primality has nothing to do with it -- it works for
> any odd positive integer n.
>
> More precisely:
>
> If a is an integer and n is an odd positive integer then
> a^n = a mod 6.

a (mod 6) n
0 1 2 3 4 5 1
0 1 4 3 4 1 2
0 1 2 3 4 5 3
0 1 4 3 4 1 4
0 1 2 3 4 5 5
...

> quasi

Date Subject Author
1/16/14 sharma.kunapalli@gmail.com
1/16/14 Brian Q. Hutchings
1/16/14 quasi
1/16/14 William Elliot
1/16/14 magidin@math.berkeley.edu
1/17/14 Port563
1/17/14 Wizard-Of-Oz
1/17/14 Port563
1/18/14 Wizard-Of-Oz