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Topic: Michael's conjecture
Replies: 16   Last Post: Aug 7, 2013 12:55 PM

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Michael Klemm

Posts: 71
Registered: 11/13/12
Re: Michael's conjecture
Posted: Aug 7, 2013 10:55 AM
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<redmond@siu.edu> wrote in message
news:45f10c37-cd9b-48a6-868b-3e1ef98baca1@googlegroups.com...
On Monday, August 5, 2013 8:57:04 PM UTC-5, 0 wrote:
> > If a composite positive integer is divisible by two or more prime
> > components, is that positive integer also divisible by the product of
> > those two prime components?


> If I recall correctly, the first proof in print of unique factorization is
> due to Gauss in his 1801 book. I think this was just one of those results
> that was so obvious that no one bothered with a proof. The later work on
> the beginnings of algebraic number theory showed that unique factorization
> could not be taken for granted.



Gauss proved the uniqueness:

16.
Theorema. Numerus compositus quicunque unico tantum modo in factores primos
resolvi potest

see
http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN235993352&DMDID=DMDLOG_0007&LOGID=LOG_0007&PHYSID=PHYS_0019

Regards
Michael




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