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Is this a known equality?

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alainv...@gmail.com

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Nov 9, 2009, 4:35:08 AM11/9/09
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Good morning,

I was working about additive splitting of integer
polynomials and fell upon this equality:
4a^4 + b^4 = {a^2+(a+b)^2}.{a^2+(a -b)^2}...


Best regards,
Alain

Don Stockbauer

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Nov 9, 2009, 4:48:45 AM11/9/09
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On Nov 9, 3:35 am, "alainvergh...@gmail.com" <alainvergh...@gmail.com>
wrote:

I was working on equations which reveal to the contemplator deep
meanings of space, time and affinity and fell upon this equation:

1 = 1

But then, that's just me.

alainv...@gmail.com

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Nov 9, 2009, 4:53:20 AM11/9/09
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Bonjour,

are sure that "1 = 1 " is an equation?

alain

Don Stockbauer

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Nov 9, 2009, 4:57:01 AM11/9/09
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On Nov 9, 3:53 am, "alainvergh...@gmail.com" <alainvergh...@gmail.com>
wrote:

Are you sure that you exist?

GJ Woeginger

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Nov 9, 2009, 5:00:59 AM11/9/09
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alainv...@gmail.com <alainv...@gmail.com> wrote:
# Good morning,
#
# I was working about additive splitting of integer
# polynomials and fell upon this equality:
# 4a^4 + b^4 = {a^2+(a+b)^2}.{a^2+(a -b)^2}...
#

This is commonly known as Sophie Germain's Identity;
see for instance

http://en.wikipedia.org/wiki/Sophie_Germain

(the paragraph on her contributions to number theory).

--Gerhard

___________________________________________________________
Gerhard J. Woeginger http://www.win.tue.nl/~gwoegi/

Don Stockbauer

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Nov 9, 2009, 5:03:14 AM11/9/09
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On Nov 9, 4:00 am, gwo...@figipc78.tu-graz.ac.at (GJ Woeginger) wrote:

Nice to get your name stuck on something.

Phil Carmody

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Nov 9, 2009, 3:53:09 PM11/9/09
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gwo...@figipc78.tu-graz.ac.at (GJ Woeginger) writes:
> alainv...@gmail.com <alainv...@gmail.com> wrote:
> # Good morning,
> #
> # I was working about additive splitting of integer
> # polynomials and fell upon this equality:
> # 4a^4 + b^4 = {a^2+(a+b)^2}.{a^2+(a -b)^2}...
>
> This is commonly known as Sophie Germain's Identity;

That I didn't know (and I really ought to have done).
To me it was just an Aurefeuillian factorisation.
I've got to admit, there's something prettier about
Sophie-Germain's rendering of it.

Phil
--
Any true emperor never needs to wear clothes. -- Devany on r.a.s.f1

Don Stockbauer

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Nov 9, 2009, 11:33:29 PM11/9/09
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On Nov 9, 2:53 pm, Phil Carmody <thefatphil_demun...@yahoo.co.uk>
wrote:
> gwo...@figipc78.tu-graz.ac.at (GJ Woeginger) writes:

> > alainvergh...@gmail.com <alainvergh...@gmail.com> wrote:
> > # Good morning,
> > #
> > # I was working about additive splitting of integer
> > # polynomials and fell upon this equality:
> > # 4a^4 + b^4 = {a^2+(a+b)^2}.{a^2+(a -b)^2}...
>
> > This is commonly known as Sophie Germain's Identity;
>
> That I didn't know (and I really ought to have done).
> To me it was just an Aurefeuillian factorisation.
> I've got to admit, there's something prettier about
> Sophie-Germain's rendering of it.
>
> Phil
> --
> Any true emperor never needs to wear clothes. -- Devany on r.a.s.f1

Except where it's cold.

Don Stockbauer

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Nov 10, 2009, 12:23:44 PM11/10/09
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1 =1 is an equation, innit, albeit a short one? Hofstadter uses
0 = 0 as an equation in his "Godel, Escher, Bach".

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