Source labels openChecked July 26, 2026

Erdős Problem 503

What is the size of the largest $A \subseteq \mathbb{R}^n$ such that every three points from $A$ determine an isosceles triangle? That is, for any three points $x$ , $y$ , $z$ from $A$ , at least two of the distances $|x - y|$ , $|y - z|$ , $|x - z|$ are equal.

Geometry AMS 51

Mathematical statement

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_503

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_503 (n : ℕ) :    IsGreatest {(A.ncard) | (A : Set (ℝ^n)) (hA : A.IsIsosceles)} answer(sorry) := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization erdosproblems.com/503background