# 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.
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 $$\dfrac{x_1^2}4+\dfrac{x_2^2}4=5$$.