376.lean`

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

2 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 376

Reference: erdosproblems.com/376

Imports (1)

FormalConjecturesUtil

theorem Erdos376.erdos_376 Are there infinitely many $n$ such that ${2n\choose n}$ is coprime to $105$? sorry line 34 source
Source documentation
Are there infinitely many $n$ such that ${2n\choose n}$ is coprime to $105$?

depends on sorry what this means
Statement uses: Iff, True, Set.Infinite, Nat, Set.ofPred, Erdos376.erdos_376.match_1, Nat.Coprime, Nat.centralBinom, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_376 : answer(sorry) ↔ { (n : ℕ) | n.centralBinom.Coprime 105 }.Infinite := by
…
```
theorem Erdos376.erdos_376.variants.prime Erdős, Graham, Ruzsa, and Straus [EGRS75] have shown that, for any two odd primes $p$ and $q$, there are infinite many $n$ such that ${2n\choose n}$ is coprime to $pq$ sorry line 42 source
Source documentation
Erdős, Graham, Ruzsa, and Straus [EGRS75] have shown that, for any two odd primes $p$ and $q$, there are infinite many $n$ such that ${2n\choose n}$ is coprime to $pq$.

depends on sorry what this means
Statement uses: Nat, Nat.Prime, Odd, Set.Infinite, Set.ofPred, Erdos376.erdos_376.match_1, Nat.Coprime, Nat.centralBinom, HMul.hMul
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
7 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_376.variants.prime {p q : ℕ} (h₁ : p.Prime)
    (h₂ : Odd p) (h₃ : q.Prime) (h₄ : Odd q) :
    { (n : ℕ) | n.centralBinom.Coprime (p * q) }.Infinite := by
…
```