I'm having trouble proving the following statement:
For all primes $p$, there exists a non-constant polynomial $f(x)\in \mathbb Z_p[x]$ such that f(x) does not have a root in $\mathbb Z_p$
What I have tried so far is using the Fundamental Theorem of Algebra, which states that all polynomials $f(x)$ with $deg(f(x)) \ge 1$, there exists $x_0\in \mathbb C$ such that $f(x_0)=0$ assuming $f(z)$ has 0 roots, but that did not get me anywhere. Does anyone know of a way to solve this? Thanks!