Given an integer N. What is the simplest Diophantine equation equivalent to the statement that integer $N\neq0$ ?

I can do one in 5 variables. Using the fact that any integer can be written as the sum of four squares.

$$N^2-(1+A^2+B^2+C^2+D^2)^2=0$$

So this can only be solved for integers $A,B,C,D,N$ when $N\neq 0$ and can be solved for all other positive and negative integers $N$.

Can it be done with fewer variables?