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Claim. There are five points in the plane, no three on a line and no four on a circle, all ten of whose pairwise distances are integers. This is the result of H. Harborth, Antwort auf eine Frage von P. Erdős nach fünf Punkten mit ganzzahligen Abständen, Elem. Math. 26 (1971), 112–113, the note that answered Erdős's question for five points; Erdős's 1983 lecture (Math. Chronicle 12 (1983), 35–54, p. 43) records that Harborth settled the case $n=5$ and that the general case, even $n=6$, was then open. In the notation of Problem 213, the answer is yes for $n=5$.

Covers. The instances $n=4$ and $n=5$, answered yes: any subset of such a set keeps all three properties, so the five points also answer $n=4$. Not covered: every $n\ge6$. The seven points of [[problems/distance_problems/E0213/claims/2007_09_29_kreisel_kurz|Kreisel and Kurz]] later answer every $n\le7$ and supersede this construction.

Depends on. Nothing in this wiki.

Acceptance. Refereed: Elemente der Mathematik 26 (1971), 112–113; the link above is the EuDML record of the paper. The site's remarks credit the five-point construction to Harborth, but the site labels the problem OPEN, so that credit is commentary on an open problem and no reviewed evidence is listed.