Source labels openChecked July 26, 2026

Erdős Problem 325: Weaker

Writing $f_{k, 3}(x)$ for the number of integers $\leq x$ which are the sum of three $k$ th powers, is it even true that $f_{k, 3}(x) \gg_{\epsilon} x ^ (3 / k - \epsilon)$ ?

Number theory AMS 11

Mathematical statement

Writing $f_{k, 3}(x)$ for the number of integers $\leq x$ which are the sum of three $k$ th powers, is it even true that $f_{k, 3}(x) \gg_{\epsilon} x ^ (3 / k - \epsilon)$ ?

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_325.variants.weaker

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_325.variants.weaker :    answer(sorry) ↔ ∀ ε > 0, ∀ k : ℕ, 3 ≤ k → (fun x : ℕ => (x : ℝ) ^ ((3 / k : ℝ) - ε)) =O[atTop]      (fun x => (cardIsSumThreePowerBelow 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/325background