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I've got a quite simple question, but I don't get it:

Say we've got a finite field [tex]\mathbb{F}_q[/tex] and a polynomial [tex]f \in \mathbb{F}_q[X][/tex]. Let [tex]v[/tex] denote the number of distinct values of [tex]f[/tex].

Then, i hope, it should be possible to proof, that [tex]\deg f \geq 1 \Rightarrow v \geq \frac{q}{\deg f}[/tex].

I'd appreciate any suggestions.

Greetings,

korollar