Specifying functions by polinomials

Let's prove that if, F is a finite field, then every F--> F function can be defined by polynomial.

Any help would be appreciated.
Thank you!

Quote:

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Originally Posted by doug

Let's prove that if, F is a finite field, then every F--> F function can be defined by polynomial.

Any help would be appreciated.
Thank you!

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Any such function has a finite set as image, and then we can interpolate (Lagrange and stuff) this values to obtain a pol.

Tonio