Re: group theory question

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From	Phil Carmody <pc+usenet@asdf.org>
Newsgroups	sci.math
Subject	Re: group theory question
Date	Thu, 10 Oct 2024 19:17:37 +0300
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Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:

> On 09/10/2024 17:21, Phil Carmody wrote:
>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>>> Well if the conjecture fails, a counter-example suffices.  But like I
>>> said, I'm not sure what you're asking.  It should be apparent from
>>> tests that some (p,g) values work and some do not.
>>
>> Mod(3,17) is a generator, but its 2^n-th powers hit Mod(1,17) really
>> quickly.
>
> Also p=13.  Well, the powers don't hit 1, but quickly cycle with a
> period of 2.  Cycling "too soon" is the general way different primes
> fail, rather than specifically hitting 1.

Yeah, I chose 17 because it is a Fermat prime (of the form 2^n+1),
and I knew 2^n modulo EulerPhi(17)=16 would go 1, 2, 4, 8, 0, ...

> Just by inspection (mucking about in an Excel spreadsheet) it seems
> most p won't work due to 2^n [mod p-1] quickly hitting a cycle, but a
> few p DO work, so there's an interesting question as to why.
>
> Working p:  (2), 3, 5, 7, 11, 23, 59, ...
>
> (Then again I might have mucked up the spreadsheet or just misrecorded
> something, so don't take that as gospel!)

OEIS is the place to look for such sequences. It's probably something
trivial.

Phil
-- 
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Thread

group theory question Peter Fairbrother <peter@tsto.co.uk> - 2024-09-28 01:31 +0100
  Re: group theory question Peter Fairbrother <peter@tsto.co.uk> - 2024-09-28 01:53 +0100
    Re: group theory question Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-27 18:24 -0700
    Re: group theory question Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2024-09-28 04:48 +0100
      Re: group theory question Peter Fairbrother <peter@tsto.co.uk> - 2024-09-29 23:02 +0100
        Re: group theory question Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2024-09-30 02:29 +0100
          Re: group theory question Phil Carmody <pc+usenet@asdf.org> - 2024-10-09 19:21 +0300
            Re: group theory question Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2024-10-10 05:06 +0100
              Re: group theory question Phil Carmody <pc+usenet@asdf.org> - 2024-10-10 19:17 +0300
                Re: group theory question Peter Fairbrother <peter@tsto.co.uk> - 2024-11-01 00:03 +0000

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