Source labels openChecked July 26, 2026

Erdős Problem 979

Let $k ≥ 2$ , and let $f_k(n)$ count the number of solutions to $n = p_1^k + \dots + p_k^k$ , where the $p_i$ are prime numbers. Is it true that $\limsup f_k(n) = \infty$ ?

Number theory AMS 11

Mathematical statement

Let $k ≥ 2$ , and let $f_k(n)$ count the number of solutions to $n = p_1^k + \dots + p_k^k$ , where the $p_i$ are prime numbers. Is it true that $\limsup f_k(n) = \infty$ ?

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_979

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_979 : answer(sorry) ↔    ∀ k ≥ 2, Filter.limsup (fun n => (solutionSet n k).encard) Filter.atTop = ⊤ := 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/979background