Source labels openChecked July 26, 2026

Erdős Problem 52

Let $A$ be a finite set of integers. Is it true that for every $\epsilon>0$ $\max( \lvert A+A\rvert,\lvert AA\rvert)\gg_\epsilon \lvert A\rvert^{2-\epsilon}?$

Number theory AMS 11

Mathematical statement

Let $A$ be a finite set of integers. Is it true that for every $\epsilon>0$ $\max( \lvert A+A\rvert,\lvert AA\rvert)\gg_\epsilon \lvert A\rvert^{2-\epsilon}?$

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_52

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_52 : answer(sorry) ↔ ∀ (ε : ℝ), 0 < ε → ε < 1 → ∃ (C : ℝ), 0 < C ∧ ∀ (A : Finset ℤ),    (max (A + A).card (A * A).card : ℝ) ≥ C * (A.card : ℝ) ^ (2 - ε) := 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/52background