Source labels openChecked July 26, 2026

Erdős Problem 849

Is it true that, for every integer $t\geq1$ , there is some integer $a$ such that ${n \choose k} = a$ with $1\leq k \le \frac{n}{2}$ has exactly $t$ solutions?

Number theory AMS 11

Mathematical statement

Is it true that, for every integer $t\geq1$ , there is some integer $a$ such that ${n \choose k} = a$ with $1\leq k \le \frac{n}{2}$ has exactly $t$ solutions?

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_849

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_849 : answer(sorry) ↔    ∀ t ≥ 1, ∃ a : ℕ,      {n : ℕ | ∃ k ≥ 1, 2 * k ≤ n ∧ choose n k = a}.ncard = t := 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/849background