Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Formal Proof Language Example - Human-Readable?
Replies: 39   Last Post: Jun 27, 2009 11:09 PM

 Messages: [ Previous | Next ]
 Andrew Tomazos Posts: 137 Registered: 8/1/05
Re: Formal Proof Language Example - Human-Readable?
Posted: Jun 27, 2009 9:27 PM

On Jun 28, 3:26 am, Andrew Tomazos <and...@tomazos.com> wrote:
> On Jun 27, 12:36 pm, Jan Burse <janbu...@fastmail.fm> wrote:
>
>
>

> > Andrew Tomazos schrieb:
>
> > > We can assume that theorems about the nature of integer factorization
> > > have previously been established - but which ones specifically would
> > > we use to prove your above statements?

>
> > > I think it would be beneficial if we could compute q, n and m
> > > directly.

>
> > This will result in a multi set of prime
> > numbers:

>
> >     z = p1^s1 * ... * pk^sk
>
> >     pi: Some prime number
> >     si: Some multiplicity

>
> > Now we can continue working with multi sets. Lets
> > assume we have the multi sets for

>
> >     c + a = p1^s1 * ... * pk^sk = q * n * n
> >     c - a = q1^t1 * ... * qj^sj = q * m * m

>
> > Then q is the intersection of the two multi sets,
> > and the rest follows easily:

>
> >     q = intersect(c + a, c - a)
> >     n = sqrt(c + a / q)
> >     m = sqrt(c - a / q)

It's clear that q is an integer, but how do you know that (c + a / q)
and (c - a / q) are both perfect squares?  That is required if n and m
are to be integers.
-Andrew.

Date Subject Author
6/21/09 Andrew Tomazos
6/21/09 Jan Burse
6/21/09 Andrew Tomazos
6/21/09 Jan Burse
6/21/09 Andrew Tomazos
6/21/09 Jan Burse
6/21/09 Jan Burse
6/21/09 Jan Burse
6/21/09 Andrew Tomazos
6/21/09 Jan Burse
6/21/09 Andrew Tomazos
6/21/09 Jan Burse
6/21/09 Jan Burse
6/24/09 Andrew Tomazos
6/25/09 MeAmI.org
6/25/09 Jan Burse
6/26/09 Andrew Tomazos
6/27/09 Jan Burse
6/27/09 Andrew Tomazos
6/27/09 Jan Burse
6/27/09 Andrew Tomazos
6/27/09 Joshua Cranmer
6/27/09 Andrew Tomazos
6/21/09 Marshall
6/21/09 Spiros Bousbouras
6/24/09 Tim Smith
6/21/09 Charlie-Boo
6/21/09 William Elliot
6/22/09 MeAmI.org
6/22/09 MeAmI.org
6/23/09 Slawomir
6/24/09 David Bernier
6/24/09 MeAmI.org
6/24/09 MeAmI.org
6/24/09 Andrew Tomazos
6/24/09 Andrew Tomazos
6/25/09 Slawomir