Source labels openChecked July 26, 2026

Erdős Problem 14: I

Let $A ⊆ \mathbb{N}$ . Let $B ⊆ \mathbb{N}$ be the set of integers which are representable in exactly one way as the sum of two elements from $A$ . Is it true that for all $\epsilon > 0$ and large $N$ , $|{1,\ldots,N} \setminus B| \gg_\epsilon N^{1/2 - \epsi...

Number theory AMS 11

Mathematical statement

Let $A ⊆ \mathbb{N}$ . Let $B ⊆ \mathbb{N}$ be the set of integers which are representable in exactly one way as the sum of two elements from $A$ . Is it true that for all $\epsilon > 0$ and large $N$ , $|\{1,\ldots,N\} \setminus B| \gg_\epsilon N^{1/2 - \epsilon}$ ?

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_14.parts.i

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_14.parts.i :    answer(sorry) ↔ ∀ A, ∀ ε > 0, nonUniqueSumCount A ≫ almostSquareRoot ε := by sorry /--Is it possible that $|\{1,\ldots,N\} \setminus B| = o(N^\frac{1}{2})$?-/@[category research open, AMS 11]theorem erdos_14.parts.ii :    answer(sorry) ↔ ∃ (A : Set ℕ), IsLittleO atTop (nonUniqueSumCount A) squareRoot := 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/14background