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## [Axiom-developer] Re: A Collection of Algebraic Identities

 From: Tito Piezas Subject: [Axiom-developer] Re: A Collection of Algebraic Identities Date: Tue, 9 Jun 2009 05:26:13 -0600

Hello Tim,

Thank you for the interest.  I just moved to Canada and I am still sorting out all my stuff.  I will get back to your questions in a few days.  :-)

-Tito

On Sun, Jun 7, 2009 at 8:59 PM, TimDaly wrote:
On Jun 4, 12:35 pm, address@hidden wrote:
> Hello all,
>
> Here's a nice identity:
>
> (p+q)^4 + (r-s)^4 = (p-q)^4 + (r+s)^4
>
> where {p,q,r,s} = {a^7+a^5-2a^3+a, 3a^2, a^6-2a^4+a^2+1, 3a^5}
>
> For similar stuff, you may be interested in "A Collection of Algebraic
> Identities":
>
>
> It's a 200+ page book I wrote and made available there.  It starts
> with the basics with 2nd powers and goes up to 8th and higher powers.
> Enjoy.
>
> - Titus

Theorem: If p^2 + (p+1)^2 = r^2, then q^2 + (q+1)^2 = (p+q+r+1)^2
where q = 3p+2r+1

q:=3p+2r+1
r:=sqrt(p^2 + (p+1)^2)
q^2 + (q+1)^2 - (p+q+r+1)^2 == (-4r -8p -4)sqrt(2p^2+2p+1)+4r^2+(8p+4)
r

which is clearly not zero. What am I missing?