Source labels openChecked July 26, 2026

Erdős Problem 242

For every $n>2$ there exist distinct integers $1 ≤ x < y < z$ such that $\frac 4 n = \frac 1 x + \frac 1 y + \frac 1 z$ .

Number theory AMS 11

Mathematical statement

For every $n>2$ there exist distinct integers $1 ≤ x < y < z$ such that $\frac 4 n = \frac 1 x + \frac 1 y + \frac 1 z$ .

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_242

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_242 (n : ℕ) (hn : 2 < n) :    ∃ x y z : ℕ, 1 ≤ x ∧ x < y ∧ y < z ∧      (4 / n : ℚ) = 1 / x + 1 / y + 1 / z := 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/242background