826.lean`

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L4DEL: Lean4 Domain Explanation Language

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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 826

Reference: erdosproblems.com/826

Imports (1)

FormalConjecturesUtil

theorem Erdos826.erdos_826 Are there infinitely many $n$ such that, for all $k\geq 1$ $$ \tau(n + k) \ll k? $$ sorry line 39 source
Source documentation
Are there infinitely many $n$ such that, for all $k\geq 1$ $$ \tau(n + k) \ll k? $$

depends on sorry what this means
Statement uses: Iff, True, Exists, Real, And, GT.gt, OfNat.ofNat, Set.Infinite, Nat, Set.ofPred, GE.ge, LE.le, ArithmeticFunction, ArithmeticFunction.sigma, HAdd.hAdd, HMul.hMul
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
32 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_826 : answer(sorry) ↔
    ∃ C > (0 : ℝ), { n | ∀ k ≥ 1, σ 0 (n + k) ≤ C * k }.Infinite := by
…
```