Talk:Hilbert's tenth problem

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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)