Talk:Hilbert's tenth problem

comments

The article claims:

The equation

$p(x_{1},\ldots ,x_{k})=0$

where $p$ is a polynomial of degree $d$ is solvable in rational numbers if and only if

$(z+1)^{d}\;p\left({\frac {x_{1}}{z+1}},\ldots ,{\frac {x_{k}}{z+1}}\right)=0$

is solvable in natural numbers.

This cannot be true. x+1=0 is solvable in rational numbers, but x+z+1=0 is not solvable in natural numbers. 141.35.26.61 03:41, 21 January 2007 (UTC)

I suspect the intent was to solve the original equation over the positive rationals. But I've changed "naturals" to "integers" in the article. Ben Standeven 05:14, 7 April 2007 (UTC)

It didn't work that way either; in your version, the case z=0 caused problems. I think I've fixed it now. 141.35.26.61 12:28, 10 April 2007 (UTC)

There is no meaning for $p(a,x_{1},\ldots ,x_{k})=0$ A student that knows about polinomials may understand the article until (s)he finds such a notation with no reference to its meaning and much less its discussion of "parameters"

"...with integer coefficients such that the set of values of a for which the equation

   p(a,x_1,\ldots,x_n)=0

has solutions in natural numbers is not computable. So, not only is there no general algorithm for testing Diophantine equations for solvability, even for this one parameter family of equations, there is no algorithm ..."

For lack of refences (s)he simply gets lost.

If the article is just for those who know about it the What is the purpose of the article?