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{\bf Le Anh Vinh }
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{\bf Distinct Triangle Areas in a Planar Point Set over Finite Fields}
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Let $\mathcal{P}$ be a set of $n$ points in the finite plane $\mathbbm{F}_q^2$
over the finite field $\mathbbm{F}_q$ of $q$ elements, where $q$ is an odd
prime power. For any $s \in \mathbbm{F}_q$, denote by $A (\mathcal{P}; s)$ the number of
ordered triangles whose vertices in $\mathcal{P}$ having area $s$.  We show that if the cardinality of $\mathcal{P}$ is large enough then $A (\mathcal{P}; s)$ is close to the expected number $|\mathcal{P}|^3/q$.

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