Erdős Problem #1084
contact number problem
OPENdatabase updated 2025-10-17
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The maximal number of pairs of points which are distance 1 apart that a set of `n` 1-separated points in `ℝ^d` make.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · 5 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/1084.Prizenone
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1084
Attempts
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Proved exactly that $f_d(n)=\binom n2$ for $n\le d+1$, $f_d(d+2)=\binom{d+2}{2}-1$, and $f_d(d+k)=\binom{d+k}{2}-k$ for $3\le k\le d$ (with $f_d(d+3)=\binom{d+3}{2}-3$ also for $d=1,2$); the fixed-d a
PARTIAL