All open problems
Source labels openChecked July 26, 2026

BooksNumber theory

Bugeaud Collection of Conjectures and Open Questions: Rapidly Increasing Sequences Dense Modulo One

Problem 10.6, intermediate-growth variant.

Mathematical statement

Problem 10.6, intermediate-growth variant.

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

problem_10_6_variant_2

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem problem_10_6_variant_2 :     m :   ,    StrictMono m     ( α : , 0 < α  α < 1  HasIntermediateGrowth α m)      ξ : , Irrational ξ       Dense (Set.range fun n => (↑(ξ * m n) : AddCircle (1 : ))) := 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