<email@example.com> wrote in message news:firstname.lastname@example.org... 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