672.lean`

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

4 declarations, 3 contain sorry, 0 declared as axioms

Erdős Problem 672

Reference: erdosproblems.com/672

Imports (1)

FormalConjecturesUtil

def Erdos672.Erdos672With Erdős problem 672 conjectures that the below holds for any $k ≥ 4$ and $l > 1$ line 31 source
Source documentation
Erdős problem 672 conjectures that the below holds for any $k ≥ 4$ and $l > 1$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Finset, Eq, Finset.card, GT.gt, OfNat.ofNat, Nat.gcd, Set.IsAPOfLengthWith, ENat, Ne, Finset.prod, HPow.hPow
12 instances, coercions and auxiliary constants left out.
```
def Erdos672With (k l : ℕ) : Prop :=
…
```
theorem Erdos672.erdos_672 Can the product of an arithmetic progression of positive integers $n, n + d, ..., n + (k - 1)d$ of length $k ≥ 4$, with $(n, d) = 1$, be a perfect power? sorry line 42 source
Source documentation
Can the product of an arithmetic progression of positive integers $n, n + d, ..., n + (k - 1)d$ of length $k ≥ 4$, with $(n, d) = 1$, be a perfect power?
Erdős believed not, i.e. that Erdos672With k l holds for all $k ≥ 4$ and $l > 1$.

depends on sorry what this means
Statement uses: Iff, True, Exists, Nat, And, GE.ge, OfNat.ofNat, GT.gt, Not, Erdos672.Erdos672With
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_672 :
    answer(sorry) ↔ ∃ᵉ (k ≥ 4) (l > 1), ¬ Erdos672With k l := by
…
```
Mentions: Erdos672.Erdos672With
lemma Erdos672.erdos_672.variants.euler According to https://www.erdosproblems.com/672, Euler proved this sorry line 48 source
Source documentation
According to https://www.erdosproblems.com/672, Euler proved this.

depends on sorry what this means
Statement uses: Erdos672.Erdos672With, OfNat.ofNat, Nat
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.
```
lemma erdos_672.variants.euler :
    Erdos672With 4 2 := by
…
```
Mentions: Erdos672.Erdos672With
lemma Erdos672.erdos_672.variants.oblath According to https://www.erdosproblems.com/672, Obláth proved this sorry line 57 source
Source documentation
According to https://www.erdosproblems.com/672, Obláth proved this.
[Ob51] Oblath, Richard, Eine Bemerkung über Produkte aufeinander folgender Zahlen. J. Indian Math. Soc. (N.S.) (1951), 135-139.

depends on sorry what this means
Statement uses: And, Erdos672.Erdos672With, OfNat.ofNat, Nat
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.
```
lemma erdos_672.variants.oblath :
    Erdos672With 5 2 ∧ Erdos672With 3 3 ∧ Erdos672With 3 4 ∧ Erdos672With 3 5 := by
…
```
Mentions: Erdos672.Erdos672With