Source labels openChecked July 26, 2026

Erdős Problem 319: Is Little O

Let $c(N)$ be the size of the largest $A\subseteq\{1, \dots, N\}$ such that there is a function $\delta : A \to \{-1, 1\}$ such that $\sum_{n\in A} \frac{\delta n}{n} = 0$ and $\sum_{n\in A'}\frac{\delta n}{n} \neq 0$ for all non-empty $A'\subsetneq...

Combinatorics AMS 5

Mathematical statement

Let $c(N)$ be the size of the largest $A\subseteq\{1, \dots, N\}$ such that there is a function $\delta : A \to \{-1, 1\}$ such that

\sum_{n\in A} \frac{\delta n}{n} = 0

and

\sum_{n\in A'}\frac{\delta n}{n} \neq 0

for all non-empty $A'\subsetneq A$ . Find the simplest $g(N)$ such that $c(N) = o(g(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_319.variants.isLittleO

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_319.variants.isLittleO (N : ℕ) (c : ℕ → ℝ)    (h : ∀ N, IsGreatest    { (#A : ℝ) | (A) (_ : A ⊆ Finset.Icc 1 N)      (_ : ∃ δ : ℕ → ℤˣ, ∑ n ∈ A, (δ n : ℚ) / n = 0 ∧        ∀ A' ⊂ A, A'.Nonempty → ∑ n ∈ A', (δ n : ℚ) / n ≠ 0) } (c N)) :    c =o[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/319background