From: bassam king karzeddin on
Dear All

I saw a thread here in sci.math few months back which I can't remember now where is it exactly, but fortunately I do remember the issue provides a formula of
(a^3 + b^3 + c^3), and was asking about a generalization formula of (a^n + b^n + c^n), I think the formula is :

a^3 + b^3 + c^3 =
(a + b + c)*(a^2 +b^2 +c^2 -(a*b + a*c + b*c)) + 3*a*b*c

Where the proof is not difficult.

I hoop this would be of some help



B.Karzeddin
Al-Hussein Bin Talal University
JORDAN


Message was edited by: bassam king karzeddin

From: bassam king karzeddin on
Dear All

you may make use of the following identity equations to this thread

(x+y+z)*(x^2+y^2+(x+y)*z) = (x+z)*(x^2+y^2+y*z)
+(y+z)*(x^2+y^2+x*z)

OR:

(x+y-z)*(x^2+y^2-(x+y)*z)=(x-z)*(x^2+y^2-y*z)
+(y-z)*(x^2+y^2-x*z)

Where (x, y, z) belongs to C, complex numbers

Thanking YOU

Bassam Karzeddin
AL-Hussein Bin Talal University
JORDAN
From: bassam king karzeddin on
> Not a poem - just a mirror for you to see your
> reflection, and others to see your transparency.

Thank you any way, and I will accept that from you, despite you didn't answer some question, as long as they are true....!

Regards
B.Karzeddin
From: Roman B. Binder on
> Hello Roman B. binder
> Please do fast then, because your counter example for
> cubic will put us all to rest.
>
> Good Luck
> B.Karzeddin

Hi,

I should meant only, that my parameters give that
same possibility and shape for counterexample
for the simple FLT equation x^n +y^n = z^n
as for any other properly calculated shapes:
here is Your for n=3: (x+y+z)^3 = 3(x+y)(x+z)(y+z)....(*)
but for to achieve x^3+y^3=z^3 we need proper natural
values and signs and for n=3 eq.(*) should be:
(x+y-z)^3 = 3(x+y)(z-x)(z-y)
There is nothing new in such shapes indeed,
You have still 3 different values.
My parameters gives to You possibility for
to judge only x+y = t^n or n^(nu-1) t^n .
But everybody could like whatever who likes...

Success
Ro-Bin
From: bassam king karzeddin on
Hi R.B.Binder

I know success will never happen through here or use net, because simply it is against the rules of JOURNALS

But save your time there is no counter example....

Regards
B.Karzeddin
Al Hussein bin Talal University
JORDAN