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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 9:48 PM

On Jun 28, 3:33 am, Andrew Tomazos <and...@tomazos.com> wrote:
> On Jun 28, 3:30 am, Jan Burse <janbu...@fastmail.fm> wrote:
>

> > Andrew Tomazos schrieb:
>
> > >>     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.

>
> > Because of a^2+b^2 = c^2, and the class we assigned
> > to m and n. See my first post with a proof attempt.

Isn't q just the GCD of (c + a) and (c - a) ?

It's clear that b*b = (c+a) * (c-a).

It is also clear that the exponents of the prime factorization of
(b*b) must all be even.

I am not sure how you conclude from this that ((c+a)/q) and ((c-a)/q)
must be perfect squares? Can you express this step formally?
-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