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From: Archimedes Plutonium on 4 Jul 2010 17:11


Archimedes Plutonium wrote:
(snipped)
>
>
> quote of Weil's book "Number theory", 1984,
>  page 5: "Even in Euclid,
>  we fail to find a general statement about the uniqueness of the
>  factorization of an integer into primes; surely he may have been
> aware
>  of it, but all he has is a statement (Eucl.IX.14) about the l.c.m.
> of
>  any number of given primes. Finally, the proof for the existence of
>  infinitely many
>  primes (Eucl.IX.20).. "
>

Maybe Weil was just being too exaggerating. Maybe all we need for the
historical record
is for an ancient text to show a sequence such as this:

1 = 1
2 = 2
3 = 3
4 = 2x2
5 = 5
6 = 2x3
7 = 7
8 = 2x2x2
9 = 3x3
10 = 2x5
11 = 11
12 = 2x2x3
13 = 13
14 = 2x7
etc etc

So that if in Euclid's writings we see some sequence like that then we
can say Euclid was
aware of UPFAT and that it was proven in his time. And that Gauss
would only later refine
the proof.

Maybe Weil was just being overly harsh.

Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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