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Re: Michael's conjecture
Posted:
Aug 7, 2013 10:55 AM


<redmond@siu.edu> wrote in message news:45f10c37cd9b48a6868b3e1ef98baca1@googlegroups.com... On Monday, August 5, 2013 8:57:04 PM UTC5, 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.unigoettingen.de/dms/load/img/?PPN=PPN235993352&DMDID=DMDLOG_0007&LOGID=LOG_0007&PHYSID=PHYS_0019
Regards Michael



