Source labels openChecked July 26, 2026

Erdős Problem 1003: Icc

Erdős [Er85e] says that, presumably, for every $k \geq 1$ the equation $\phi(n) = \phi(n+1) = \cdots = \phi (n+k)$ has infinitely many solutions.

Number theory AMS 11

Mathematical statement

Erdős [Er85e] says that, presumably, for every $k \geq 1$ the equation $\phi(n) = \phi(n+1) = \cdots = \phi (n+k)$ has infinitely many solutions.

[Er85e] Erdős, P., Some problems and results in number theory. Number theory and combinatorics. Japan 1984 (Tokyo, Okayama and Kyoto, 1984) (1985), 65-87.

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_1003.variants.Icc

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_1003.variants.Icc :    answer(sorry) ↔ ∀ k ≥ 1, {n | ∀ i ∈ Set.Icc 1 k, φ n = φ (n + i)}.Infinite := 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/1003background