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} .