849.lean`

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L4DEL: Lean4 Domain Explanation Language

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Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 849

Reference: erdosproblems.com/849

Imports (1)

FormalConjecturesUtil

theorem Erdos849.erdos_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? sorry line 37 source
Source documentation
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?

depends on sorry what this means
Statement uses: Iff, True, Nat, GE.ge, OfNat.ofNat, Exists, Eq, Set.ncard, Set.ofPred, And, LE.le, HMul.hMul, Nat.choose
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
8 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_849 : answer(sorry) ↔
    ∀ t ≥ 1, ∃ a : ℕ,
      {n : ℕ | ∃ k ≥ 1, 2 * k ≤ n ∧ choose n k = a}.ncard = t := by
…
```