Erdős Problem 477: Monomial

Probably there is no such $A$ for the polynomial $X^k$ for any $k \ge 2$ . This is asked in [Sek59].

Field theory and polynomials AMS 12

Mathematical statement

Probably there is no such $A$ for the polynomial $X^k$ for any $k \ge 2$ . This is asked in [Sek59].

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_477.variants.monomial

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_477.variants.monomial (k : ℕ) (hk : 2 ≤ k) :    letI f := X ^ k    ∀ A : Set ℤ, ∃ z, ¬ ∃! a ∈ A ×ˢ (f.eval '' {n | 0 < n}), z = a.1 + a.2 := 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/477background Sek59background