414.lean`

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

2 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 414

Reference: erdosproblems.com/414

Imports (1)

FormalConjecturesUtil

def Erdos414.h The auxiliary function $h(n) = n + τ(n)$ (where $τ(n) counts the number of divisors of $n$) line 32 source
Source comment
The auxiliary function $h(n) = n + τ(n)$ (where $τ(n) counts the number of divisors of $n$)

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: HAdd.hAdd, Finset.card, Nat.divisors
2 instances, coercions and auxiliary constants left out.
```
def h (n : ℕ) : ℕ := n + n.divisors.card
…
```
theorem Erdos414.erdos_414 Let $h_1(n) = h(n)$ and $h_k(n) = h(h_{k-1}(n))$ sorry line 39 source
Source documentation
Let $h_1(n) = h(n)$ and $h_k(n) = h(h_{k-1}(n))$. Is it true, for any $m,n$, there exist $i$ and $j$ such that $h_i(m) = h_j(n)$?

depends on sorry what this means
Statement uses: Iff, True, Nat, GT.gt, OfNat.ofNat, Exists, Eq, Nat.iterate, Erdos414.h
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_414 : answer(sorry) ↔ ∀ᵉ  (m > 0) (n > 0), ∃ i j, h^[i] m = h^[j] n := by
…
```
Mentions: Erdos414.h