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| From | Phil Carmody <pc+usenet@asdf.org> |
|---|---|
| Newsgroups | sci.math |
| Subject | Re: group theory question |
| Date | 2024-10-10 19:17 +0300 |
| Organization | A noiseless patient Spider |
| Message-ID | <87msjcdja6.fsf@fatphil.org> (permalink) |
| References | (2 earlier) <LYqdnWNq1-4T4Wr7nZ2dnZfqnPSdnZ2d@brightview.co.uk> <vdciqe$1sq8f$2@dont-email.me> <prKcnWxvi4lBY2T7nZ2dnZfqn_qdnZ2d@brightview.co.uk> <87r08pdz75.fsf@fatphil.org> <kYScnXqbeOwyz5r6nZ2dnZfqnPednZ2d@brightview.co.uk> |
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 -- We are no longer hunters and nomads. No longer awed and frightened, as we have gained some understanding of the world in which we live. As such, we can cast aside childish remnants from the dawn of our civilization. -- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/
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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
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