therefore
Sign up
Open navigation
All open problems
Source labels openChecked July 26, 2026

Erdős ProblemsNumber theory

Erdős Problem 829

Erdős Problem 829 (open).* Let A⊆NA \subseteq \mathbb{N} be the set of perfect cubes. Is it true that (1A∗1A)(n)≪(log⁡n)O(1)(1_A \ast 1_A)(n) \ll (\log n)^{O(1)}? That is, does there exist a natural number CC such that the number of representations of nn as a sum of two cub...

Number theoryAMS 11

Mathematical statement

Erdős Problem 829 (open).* Let A⊆NA \subseteq \mathbb{N} be the set of perfect cubes. Is it true that (1A∗1A)(n)≪(log⁡n)O(1)(1_A \ast 1_A)(n) \ll (\log n)^{O(1)}? That is, does there exist a natural number CC such that the number of representations of nn as a sum of two cubes is O((log⁡n)C)O((\log n)^C) as n→∞n \to \infty?

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_829

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_829 :    answer(sorry) ↔      ∃ C : ℕ, (fun n : ℕ => (sumRep cubes n : ℝ)) =O[atTop]        (fun n : ℕ => (Real.log n) ^ C) := 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 sourceformalizationerdosproblems.com/829background