Source labels openChecked July 26, 2026

Erdős Problem 273

Is there a covering system all of whose moduli are of the form $p-1$ for some primes $p \geq 5$ ?

Combinatorics AMS 5 AMS 11

Mathematical statement

Is there a covering system all of whose moduli are of the form $p-1$ for some primes $p \geq 5$ ?

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_273

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_273 : answer(sorry) ↔ ∃ c : StrictCoveringSystem ℤ, ∀ i, ∃ (p : ℕ), p.Prime ∧ 5 ≤ p ∧    c.moduli i = Ideal.span {↑(p - 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

Pinned Formal Conjectures sourceformalization erdosproblems.com/273background