Let $\Phi_n: \Bbb Z_n\to \Bbb Z_n$ s. t. $\Phi_n(x)=x^n+x^{n-1}+\ldots+x+1$.

Question

Let $\Phi_n: \Bbb Z_n\to\Bbb Z_n$ s. t. $\Phi_n(x)=x^n+x^{n-1}+\ldots+x+1$. Could this function be surjective for some $n>2$? $\Bbb Z_n$ is the set of integers $\pmod n$.

Answer 1

$$\phi(1) = n+1 = 1 = \phi(0)$$

But a surjective function between finite sets is bijective