Re: Karzeddin's evolving conjectures ...

On Nov 22, 2007 6:40 PM "quasi" wrote:
On Thu, 22 Nov 2007 18:16:21 EST, bassam king
karzeddin
<bassam@xxxxxxxxxx> wrote:


Yes I made right this time, & I think I have the
right to stay here with the generous offer by
quasi

Of course you have the right to stay -- you don't
need my permission.

You can't find a counter example to the following
integer equation:

Z^P = X^P + Y^P + 2*N*X*Y*Z

Where:

(X, Y, Z, N) are coprime positive integers
pairwise
Z is even positive integer
P is odd prime number where P divides N*X*Y*Z,
and
P>3

But I already gave some counterexamples with P >
3.

For example, for P = 5:

p = 5, x = 1, y = 23, z = 5084, n =
n = 14523267475345

Where also P=3, implies N=1, as was proved so
easily

in "fermat's last theorem short proof"

But P = 3 doesn't imply N = 1.

The counterexample I posted for P = 3 had N > 1:

p = 3, x = 13, y = 67, z = 30296, n = 526893

Also, once you require N to to be relatively prime
to
X,Y,Z, the
conjecture no longer generalizes FLT, since for
FLT,
you need N = 0.

quasi

Once more congratulations for big work of
conterexamples for Bassam's conjectures:
but one of them is true:
k^3 = m^3 + n^3 +2nmk for natural numbers at
at least.
then my supplements of FLT as:
t^n = a^n + b^n + 2*n^u abt for at least natural
t;a;b;n and of gcd=1 and n>=5 and prime
I cant see some like this
in Your counterexamples


why would this conjecture "live" longer ?
Regards
Ro-bin
.

Relevant Pages

  • Re: Karzeddins evolving conjectures ...
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    (sci.math)
  • Re: Conjecture (FLT related): Is a^n + b^n + c^n ever a multiple of a*b*c?
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  • Re: Computability
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  • Re: -- FLTMA and the existing proof
    ... Some are redundant and should be eliminated, ... the prior counterexamples were mixed -- some were case ... It's both confusing and inappropriate to use the FLT statement as part ... of your conjecture. ...
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  • Re: -- FLTMA and the existing proof
    ... Some are redundant and should be eliminated, ... the prior counterexamples were mixed -- some were case ... It's both confusing and inappropriate to use the FLT statement as part ... of your conjecture. ...
    (sci.math)
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