Given a Diophantine equation $p(x_1,x_2,...,x_n)$,

Can I find a reduction from $\text{dioph}(\mathbb{N}) \leq \text{dioph}(\mathbb{N}_e)$?

$\mathbb{N}_e$ is the set of even numbers.

So I have to find a manipulation of $p$ such that I only have even numbers as solution.

How can I do this? Unfortunately I have no Idea.


How about $p(x_1/2,x_2/2,...,x_n/2)$? For example, if we had $x_1^2+x_2^2=5$, we will have $\dfrac{x_1^2}4+\dfrac{x_2^2}4=5$.


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