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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: 133
Registered: 11/13/12
Re: Michael's conjecture
Posted: Aug 7, 2013 10:55 AM
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<> wrote in message
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:

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



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