Source labels openChecked July 26, 2026

Erdős Problem 50

Let $f$ be the asymptotic distribution function of $\varphi(n)/n$ , so that for each $c \in [0,1]$ , $f(c)$ is the natural density of $\{n : \varphi(n) < cn\}$ . Is it true that there is no $x$ such that the derivative $f'(x)$ exists and is positive?

Number theory AMS 11

Mathematical statement

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_50

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_50 : answer(sorry) ↔ ∀ᵉ (f : ℝ → ℝ) (hf : IsDistributionOfPhiRatio f),    ¬∃ x ∈ Icc (0 : ℝ) 1, ∃ y > 0, HasDerivWithinAt f y (Icc 0 1) x := 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/50background