495.lean`

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

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 495

Reference: erdosproblems.com/495

Imports (1)

FormalConjecturesUtil

theorem Erdos495.erdos_495 Let $\alpha,\beta \in \mathbb{R}$ sorry line 37 source
Source documentation
Let $\alpha,\beta \in \mathbb{R}$. Is it true that$$\liminf_{n\to \infty} n \| n\alpha \| \| n\beta\| =0$$? This is also known as the Littlewood conjecture.

depends on sorry what this means
Statement uses: Iff, True, Real, Eq, Filter.liminf, Nat, HMul.hMul, distToNearestInt, Filter.atTop, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
19 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_495 : answer(sorry) ↔ ∀ α β : ℝ, liminf (fun n : ℕ ↦ (n : ℝ) * distToNearestInt (n * α)
  * distToNearestInt (n * β)) atTop = 0 := by sorry
…
```
Mentions: distToNearestInt