1058.lean`

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L4DEL: Lean4 Domain Explanation Language

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

3 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 1058

References:

erdosproblems.com/1058
[Gu04] Guy, Richard K., Unsolved problems in number theory. (2004), xviii+437.
[Lu01] Luca, Florian, On a conjecture of Erdős and Stewart. Math. Comp. (2001), 893-896.

Imports (1)

FormalConjecturesUtil

def Erdos1058.IsSolution n is a solution if n ∈ [p_{k-1}, p_k) for some k (with the convention p_0 = 1, where p_1 = 2 < p_2 < ⋯ are the primes) and the only primes dividing `n! line 40 source
Source documentation
n is a solution if n ∈ [p_{k-1}, p_k) for some k (with the convention p_0 = 1, where p_1 = 2 < p_2 < ⋯ are the primes) and the only primes dividing n! + 1 are p_k and p_{k+1}. Primes are indexed from 0 by Nat.nth Nat.Prime.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: And, LT.lt, OfNat.ofNat, Exists, LE.le, ite, Eq, Nat.nth, Nat.Prime, HSub.hSub, Dvd.dvd, HAdd.hAdd, Nat.factorial, Or
9 instances, coercions and auxiliary constants left out.
```
def IsSolution (n : ℕ) : Prop :=
…
```
theorem Erdos1058.erdos_1058 sorry line 54 source
depends on sorry what this means
Statement uses: Iff, True, Set.Finite, Nat, Set.ofPred, Erdos1058.IsSolution
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
1 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem Erdos1058.erdos_1058.variants.luca sorry line 60 source
depends on sorry what this means
Statement uses: Eq, Set, Nat, Set.ofPred, Erdos1058.IsSolution, Insert.insert, OfNat.ofNat, Singleton.singleton
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.