Source labels openChecked July 26, 2026

Erdős Problem 25

Let $n_1 < n_2 < \dots$ be an arbitrary sequence of integers, each with an associated residue class $a_i \pmod{n_i}$ . Let $A$ be the set of integers $n$ such that for every $i$ either $n < n_i$ or $n \not\equiv a_i \pmod{n_i}$ . Must the logarithmic density ...

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_25

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_25 : answer(sorry) ↔    ∀ (seq_n : ℕ → ℕ) (seq_a : ℕ → ℤ), (∀ i, 0 < seq_n i) → StrictMono seq_n →      ∃ d, Set.HasLogDensity        { x : ℕ | ∀ i, (x : ℤ) < seq_n i ∨ ¬((x : ℤ) ≡ seq_a i [ZMOD seq_n i]) } d := 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/25background