[FOM] Only one proof

[Timothy Y. Chow]

Vaughan Pratt <pratt at cs.stanford.edu> wrote:
> But what about the Fundamental Theorem of Arithmetic?  All proofs I'm 
> aware of seem to boil down to one version or another of Euclid's GCD 
> algorithm.  Is there a different proof?

There's a proof, sometimes called the "Hasse-Lindemann-Zermelo" proof, 
that proceeds directly by induction without reference to GCDs.  See 
http://math.uga.edu/~pete/factorization.pdf for more info.

Tim