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A new proof of R\'edei's theorem on the number of directions

Gabor Somlai
Dec 2022
摘要
R\'edei and Megyesi proved that the number of directions determined by a $p$element subset of $\mathbb{F}_p^2$ is either $1$ or at least $\frac{p+3}{2}$.The same result was independently obtained by Dress, Klin and Muzychuk. We givea new and short proof of this result using a Lemma proved by Kiss and theauthor. The new proof further on a result on polynomials over finite fields.
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