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Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

Erdős Problem 789: Is Big O Cube Root Linearithmic

By the solved variant erdos_789.variants.cube_root_linearithmic_isBigO, in order to prove erdos_789.variants.cube_root_linarithmic it suffices to show h(n)=O((nlog(n))1/3)h(n) = O((n\log(n))^{1/3}).

Mathematical statement

By the solved variant erdos_789.variants.cube_root_linearithmic_isBigO, in order to prove erdos_789.variants.cube_root_linarithmic it suffices to show h(n)=O((nlog(n))1/3)h(n) = O((n\log(n))^{1/3}).

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_789.variants.isBigO_cube_root_linearithmic

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_789.variants.isBigO_cube_root_linearithmic :    (fun n  (subsetSumThreshold n : )) =O[atTop]      fun n  (n * Real.log n) ^ ((1 : ) / 3) := 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