> ----------
> From: Joseph Gallian[SMTP:jgallian@d.umn.edu]
> Sent: Tuesday, September 01, 1998 2:49 PM
> To: ABARRON@prius.jnj.com
> Cc: jgallian@d.umn.edu
> Subject: Re: FW: [HM] GCD is a Linear Combination
>
> > > From: jongsma@dordt.edu[SMTP:jongsma@dordt.edu]
> > > Sent: Monday, August 31, 1998 5:07 PM
> > > To: historia-matematica@chasque.apc.org
> > > Subject: [HM] GCD is a Linear Combination
> > >
> > > Joseph Gallian in his _Contemporary Abstract Algebra_ (4th edn, p. 5)
> > > claims
> > > that the result which asserts that the GCD of two integers is a linear
> > > combination of the numbers is Proposition 1 in book VII of Euclid's
> > > Elements.
> > > This clearly isn't the case; Propositions VII.1 and VII.2 tell how to
> > > determine
> > > whether two integers are (relatively) prime to one another and how to
> find
> > > the
> > > GCD when they are not. The so-called Euclidean Algorithm is the focus
> > > here, not the result Gallian cites.
>
>
> Thanks for the note about my misstatement.
>
> Although Propositions 1 and 2 do not state it, the alogorithm
> in Euclid allows one to write the GCD as a linear combination as I
> show on page 7 of my book. Perhaps on page 6, I should say
> something like "This result is implicit in the proof Proposition 1 in
> Book Seven ..."
>
> Joe Gallian