Source labels openChecked July 26, 2026

Erdős Problem 323: I

Is it true that $f_{k,k}(x) \gg_\epsilon x^{1-\epsilon}$ for all $\epsilon>0$ ?

Mathematical statement

Is it true that $f_{k,k}(x) \gg_\epsilon x^{1-\epsilon}$ for all $\epsilon>0$ ?

This would have significant applications to Waring's problem. Erdős and Graham describe this as 'unattackable by the methods at our disposal'.

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_323.parts.i

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_323.parts.i :    answer(sorry) ↔ ∀ k ≥ 1, ∀ ε > (0 : ℝ),      (fun (x : ℕ) ↦ (x : ℝ) ^ (1 - ε)) =O[atTop] (fun (x : ℕ) ↦ (f k k x : ℝ)) := 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/323background