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Claim. If $n$ points of $\mathbb R$ have pairwise distances that differ by at least $1$, their diameter is at least $(1+o(1))n^2$: the conjecture of Problem 670 holds for $d=1$. P. Erdős, Some unsolved problems, in Combinatorics, Geometry and Probability: A Tribute to Paul Erdős, Cambridge University Press, 1997, pp. 1--10, Problem 20, p. 6 (source card). The printed proof orders the points and sums the gaps between points a fixed number of places apart; those gaps are distinct distances, so they differ pairwise by at least $1$. Erdős adds that the conjecture is settled only on the line.

Covers. The case $d=1$ only. Every $d\ge2$ stays open, as Ho states in Remark 9 of arXiv:2604.15305.

Depends on. No page of this wiki.

Acceptance. None documented. The site labels the problem OPEN, so its remark crediting Erdős is not acceptance, and no evidence that the volume was refereed is recorded.