Claims

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1983_01_01_pomerance: A five-point configuration credited to Pomerance in Erdős's 1983 lecture: a unit equilateral triangle, its circumcenter and a point on the unit circle about one vertex, with distances of multiplicities 4, 3, 2 and 1.

1987_01_01_palasti: Palásti (Studia Sci. Math. Hungar. 1987) gives seven points in the plane in general position determining six distinct distances, the i-th occurring i times, answering the instance n = 7 yes.

1989_01_01_palasti: Palásti (Discrete Math. 1989) gives six points, no three on a line, no four on a circle, no point equidistant from three others and no equilateral triangle, whose five distances occur 1 to 5 times; yes for n = 6.

1989_09_01_palasti: Palásti (Period. Math. Hungar. 1989) gives examples on the triangular lattice for every n from 3 to 8, the eight-point example new, answering the instance n = 8 yes.

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