Source labels openChecked July 26, 2026

Erdős Problem 361: Big Theta

Let $c > 0$ and $n$ be some large integer. What is the size of the largest set $A \subseteq \{1, \ldots, \lfloor c n \rfloor\}$ such that $n$ is not a sum of a subset of $A$ ? Does this depend on $n$ in an irregular way?

Number theory AMS 11

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_361.bigTheta

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_361.bigTheta    (c : ℝ) (hc : 0 < c)    (A : ℕ → ℕ)    (hA : ∀ c n, A n = ((Finset.Icc 1 ⌊c * n⌋₊).powerset.filter      (fun B ↦ n ≠ ∑ a ∈ B, a)).sup Finset.card) :    (fun n ↦ (A n : ℝ)) =Θ[atTop] (answer(sorry) : ℕ → ℝ) := 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/361background