Re: number theory : the conjecture

On Wed, 08 Aug 2007 18:46:59 EDT, tommy1729 <tommy1729@xxxxxxxxx>
wrote:

let A be a multivariable polynomial with 3 or more
variables , coefficients 1 or -1.

the variables are explicit powers in the polynomials.
in other words A is a powersum ( so no 'ab + 1' for
examp)

A = 0

this is never true for integer values of the variables
IF
the average of powers > 2 times the amount of
variables.


tommy1729

.. for distinct integer imput values of course ...

You need more restrictions to avoid trivial counterexamples.

For example, the diophantine equation

w^9 + x^9 + y^9 + z^9 = 0

has the trivial solution

w=s
x=-s
y=t
z=-t

where s,t are arbitrary integers.

To fix it, perhaps require that no proper subsum is 0.

quasi
.

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