Source labels openChecked July 26, 2026

Erdős Problem 394: Hall Conjecture

Erdős and Hall conjecture that the sum is $o(x^2/(\log x)^c)$ for any $c<\log 2$ .

Number theory AMS 11

Mathematical statement

Erdős and Hall conjecture that the sum is $o(x^2/(\log x)^c)$ for any $c<\log 2$ .

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_394.variants.hall_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_394.variants.hall_conjecture :    ∀ c < Real.log 2, (fun x ↦ ∑ n ∈ Icc 1 ⌊x⌋₊,    (t 2 n : ℝ)) =o[atTop]    (fun x ↦ x ^ 2 / (Real.log x) ^ 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 sourceformalization erdosproblems.com/394background