825.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

2 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 825

Reference: erdosproblems.com/825

Imports (1)

FormalConjecturesUtil

theorem Erdos825.erdos_825 sorry line 42 source
depends on sorry what this means
Statement uses: Iff, True, Exists, Real, GT.gt, OfNat.ofNat, Nat, ArithmeticFunction, ArithmeticFunction.sigma, HMul.hMul, Finset, And, LE.le, Nat.properDivisors, Eq, Finset.sum, id
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 Erdos825.erdos_825.variants.necessary_cond Show that if the constant $C > 0$ is such that every integer $n$ with $\sigma(n) > Cn$ is the distinct sum of proper divisors of $n$, then we must have $C > 2$ sorry line 54 source
Source documentation
Show that if the constant $C > 0$ is such that every integer $n$ with $\sigma(n) > Cn$ is the distinct sum of proper divisors of $n$, then we must have $C > 2$.

depends on sorry what this means
Statement uses: Real, LT.lt, OfNat.ofNat, Nat, GT.gt, ArithmeticFunction, ArithmeticFunction.sigma, HMul.hMul, Exists, Finset, And, LE.le, Nat.properDivisors, Eq, Finset.sum, id
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
38 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_825.variants.necessary_cond (C : ℝ) (hC : 0 < C)
    (h : ∀ (n : ℕ) (_ : σ 1 n > C * n),
        ∃ s ⊆ n.properDivisors, n = s.sum id) :
    2 < C := by
…
```