Source labels openChecked July 26, 2026

Bugeaud Collection of Conjectures and Open Questions: Spectrum of Sequence

Problem 10.4. Let $\xi$ be a non-zero real number and $\alpha > 1$ be a real number. The spectrum of the sequence $(\xi \alpha^n)_{n \ge 1}$ is at most countable. Posed by Mendès France [Men73].

Number theory AMS 11

Mathematical statement

Problem 10.4. Let $\xi$ be a non-zero real number and $\alpha > 1$ be a real number. The spectrum of the sequence $(\xi \alpha^n)_{n \ge 1}$ is at most countable. Posed by Mendès France [Men73].

Statement source: Books 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

spectrum_xi_alpha_pow_countable

Canonical source

Complete statement target, proof intentionally absentLean 4

lemma spectrum_xi_alpha_pow_countable (ξ : ℝ) (hξ : ξ ≠ 0) (α : ℝ) (hα : 1 < α) :    (Spectrum (fun n => ξ * α ^ n)).Countable := 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