I'm looking for an example for the Greenleaf theorem:
Let $f_1(x)=\dots=f_n(x)=0$ be polynomials in $\mathbb{Z}[x]$. For all except finitely many primes $p$, all solutions in $\mathbb{F}^n _p$ can be lifted to solutions in $\mathbb{Z}^n_p$.
I can't understand how a polynomial over $\mathbb{Z}[x]$ can have a solution in $\mathbb{F}^n _p$.