Source labels openChecked July 26, 2026

Erdős Problem 357: Hegyvari

Let $g(n)$ be the maximal $k$ such that there exist integers $1 \le a_1, \dotsc, a_k \le n$ such that all sums of the shape $\sum_{u \le i \le v} a_i$ are distinct. It is known that $$\left(\frac 1 3 + o(1) \right)n \leq g(n) \leq \left(\frac 2 3 + o(1) \ri...

Number theory AMS 11

Mathematical statement

Let $g(n)$ be the maximal $k$ such that there exist integers $1 \le a_1, \dotsc, a_k \le n$ such that all sums of the shape $\sum_{u \le i \le v} a_i$ are distinct. It is known that $\left(\frac 1 3 + o(1) \right)n \leq g(n) \leq \left(\frac 2 3 + o(1) \right)n.$

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_357.variants.hegyvari

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_357.variants.hegyvari : ∃ (o o' : ℕ → ℝ), o =o[atTop] (1 : ℕ → ℝ) ∧    o' =o[atTop] (1 : ℕ → ℝ) ∧      ∀ᶠ n in atTop, (g n : ℝ) ∈ Set.Icc ((1 / 3 + o n) * n) ((2 / 3 + o' n)*n) := 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/357background