677.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 677

Reference: erdosproblems.com/677

Imports (1)

FormalConjecturesUtil

lemma Erdos677.lcmInterval_eq_example1 Erdős expected very few solutions for $M(n, k) = M(m, l)$, where $m \geq n + k$ and $l > 1$ line 36 source
Source documentation
Erdős expected very few solutions for $M(n, k) = M(m, l)$, where $m \geq n + k$ and $l > 1$. The only solutions he knew were the following.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: And, Eq, Nat, Finset.lcmInterval, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl
16 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
lemma lcmInterval_eq_example1 : lcmInterval 4 3 = lcmInterval 13 2 ∧
                                lcmInterval 3 4 = lcmInterval 19 2 := by decide
…
```
theorem Erdos677.erdos_677 Denote by $M(n, k)$ the least common multiple of the finite set $\{n+1, \dotsc, n+k\}$ sorry line 44 source
Source documentation
Denote by $M(n, k)$ the least common multiple of the finite set $\{n+1, \dotsc, n+k\}$. Is it true that for all $m \geq n + k$, we get $M(m, k) \neq M(n, k)$?

depends on sorry what this means
Statement uses: Nat, GT.gt, OfNat.ofNat, GE.ge, HAdd.hAdd, Ne, Finset.lcmInterval
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
22 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_677 :
    ∀ (m n k : ℕ), k > 0 → m ≥ n + k → lcmInterval m k ≠ lcmInterval n k := by
…
```