Show that if f(x) = x^p - x belongs to Fp[x], then its polynomial function f^b: Fp --> Fp is identically zero.
Note: Fp refers to a prime field.
$\displaystyle (\mathbb{F}_p^*,\times)$ is a (cyclic) group of order $\displaystyle p-1.$
Therefore: $\displaystyle \forall a\in \mathbb{F}_p, a^p=a,$ and the polynomial function $\displaystyle f:\mathbb{F}_p\rightarrow\mathbb{F}_p:a\mapsto a^p-a$ is the zero function.