Erdős Problem 1004
For any fixed c > 0, if x is sufficiently large then there exists n ≤ x such that the values of φ(n+k) are all distinct for 1 ≤ k ≤ (log x)^c. This is an open problem.
Mathematical statement
For any fixed c > 0, if x is sufficiently large then there exists n ≤ x such that the values of φ(n+k) are all distinct for 1 ≤ k ≤ (log x)^c. This is an open problem.
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_1004
theorem erdos_1004 : answer(sorry) ↔ ∀ c > (0 : ℝ), ∀ᶠ x in atTop, ∃ n ≤ x, IsDistinctTotientRun n ⌊(Real.log (x : ℝ)) ^ c⌋₊ := 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