Let K {\displaystyle {}K} be a finite field with q {\displaystyle {}q} elements. Show that every function φ : K → K {\displaystyle {}\varphi \colon K\rightarrow K} can be expressed in a unique way as a polynomial P ∈ K [ X ] {\displaystyle {}P\in K[X]} of degree < q {\displaystyle {}<q} .
![{\displaystyle {}P\in K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4692e3ffcbd66e900f8975113ff3f32f1cabc21a)
