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


Not so. You have to find a manipulation of $p$ such that if you can find a solution / all the solutions of the manipulated $p'$ in even numbers, then you can find a solution / all the solutions of $p$. That's a very different problem.