Erdős Problem 689
Let n be sufficiently large. Is there some choice of congruence class a_p for all primes 2 ≤ p ≤ n such that every integer in [1,n] satisfies at least two of the congruences ≡ a_p (mod p)?
Mathematical statement
Let n be sufficiently large. Is there some choice of congruence class a_p for all primes
2 ≤ p ≤ n such that every integer in [1,n] satisfies at least two of the congruences
≡ a_p (mod p)?
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_689
theorem erdos_689 : answer(sorry) ↔ ∀ᶠ n in .atTop, ∃ a : ℕ → ℕ, ∀ m ∈ Finset.Icc 1 n, 2 ≤ (Finset.Icc 1 n |>.filter fun p => p.Prime ∧ a p ≡ m [MOD p]).card := 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