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Erdős ProblemsNumber theory

Erdős Problem 349

For what values of t,α∈(0,∞)t,\alpha \in (0,\infty) is the sequence ⌊tαn⌋\lfloor t\alpha^n\rfloor complete (that is, all sufficiently large integers are the sum of distinct integers of the form ⌊tαn⌋\lfloor t\alpha^n\rfloor)?

Number theoryAMS 11

Mathematical statement

For what values of t,α∈(0,∞)t,\alpha \in (0,\infty) is the sequence ⌊tαn⌋\lfloor t\alpha^n\rfloor complete (that is, all sufficiently large integers are the sum of distinct integers of the form ⌊tαn⌋\lfloor t\alpha^n\rfloor)?

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_349

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_349 :    {(t, α) | 0 < t ∧ 0 < α ∧ IsGoodPair t α} = answer(sorry) := 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 sourceformalizationerdosproblems.com/349background