# Thread: Polynomials and Prime Fields

1. ## Polynomials and Prime Fields

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.

2. $(\mathbb{F}_p^*,\times)$ is a (cyclic) group of order $p-1.$

Therefore: $\forall a\in \mathbb{F}_p, a^p=a,$ and the polynomial function $f:\mathbb{F}_p\rightarrow\mathbb{F}_p:a\mapsto a^p-a$ is the zero function.