Let α : Fq → Fq be a permutation and Ψ(α) be the number of collinear triples in the graph of α, where Fq denotes a finite field of q elements. When q is odd, Cooper and Solymosi once proved Ψ(α) ≥ (q − 1)∕4 and conjectured the sharp bound should be Ψ(α) ≥ (q − 1)∕2. In this note we confirm this conjecture.
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