1052.lean`

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

9 declarations, 3 contain sorry, 0 declared as axioms

Erdős Problem 1052

Reference: erdosproblems.com/1052

Imports (1)

FormalConjecturesUtil

Imported by 1 file

FormalConjectures/Subsets/FC100SolvedSet1.lean

def Erdos1052.properUnitaryDivisors A proper unitary divisor of $n$ is a divisor $d$ of $n$ such that $d$ is coprime to $n/d$, and $d < n$ line 32 source
Source documentation
A proper unitary divisor of $n$ is a divisor $d$ of $n$ such that $d$ is coprime to $n/d$, and $d < n$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Finset
Proof uses: Finset.filter, And, Dvd.dvd, Nat.Coprime, HDiv.hDiv, Finset.Ico, OfNat.ofNat
9 instances, coercions and auxiliary constants left out.
```
def properUnitaryDivisors (n : ℕ) : Finset ℕ :=
…
```
def Erdos1052.IsUnitaryPerfect A number $n > 0$ is a unitary perfect number if it is the sum of its proper unitary divisors line 36 source
Source documentation
A number $n > 0$ is a unitary perfect number if it is the sum of its proper unitary divisors.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: And, Eq, Finset.sum, Erdos1052.properUnitaryDivisors, LT.lt, OfNat.ofNat
3 instances, coercions and auxiliary constants left out.
```
def IsUnitaryPerfect (n : ℕ) : Prop :=
…
```
theorem Erdos1052.erdos_1052 Are there only finitely many unitary perfect numbers? sorry line 42 source
Source documentation
Are there only finitely many unitary perfect numbers?

depends on sorry what this means
Statement uses: Iff, True, Set.Finite, Nat, Set.ofPred, Erdos1052.IsUnitaryPerfect
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 erdos_1052 :
    answer(sorry) ↔ {n | IsUnitaryPerfect n}.Finite := by
…
```
Mentions: Erdos1052.IsUnitaryPerfect
theorem Erdos1052.even_of_isUnitaryPerfect All unitary perfect numbers are even sorry line 52 source
Source documentation
All unitary perfect numbers are even.
Formal proof linked here provided by AlphaProof.

depends on sorry what this means
Statement uses: Nat, Erdos1052.IsUnitaryPerfect, Even
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem even_of_isUnitaryPerfect (n : ℕ) (hn : IsUnitaryPerfect n) : Even n := by
…
```
Mentions: Erdos1052.IsUnitaryPerfect
theorem Erdos1052.isUnitaryPerfect_6 line 56 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Erdos1052.IsUnitaryPerfect, OfNat.ofNat, Nat
Proof uses: Eq.mpr, Eq, Finset.sum, Finset.filter, And, Dvd.dvd, Nat.Coprime, HDiv.hDiv, Finset.Ico, id, Eq.trans, LT.lt, True, congrArg, eq_true, Mathlib.Meta.NormNum.isNat_lt_true, Mathlib.Meta.NormNum.isNat_ofNat, Eq.refl, Bool, Bool.false and 1 more
21 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
theorem Erdos1052.isUnitaryPerfect_60 line 61 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Erdos1052.IsUnitaryPerfect, OfNat.ofNat, Nat
Proof uses: Eq.mpr, Eq, Finset.sum, Finset.filter, And, Dvd.dvd, Nat.Coprime, HDiv.hDiv, Finset.Ico, id, Eq.trans, LT.lt, True, congrArg, eq_true, Mathlib.Meta.NormNum.isNat_lt_true, Mathlib.Meta.NormNum.isNat_ofNat, Eq.refl, Bool, Bool.false and 1 more
21 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
theorem Erdos1052.isUnitaryPerfect_90 line 66 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Erdos1052.IsUnitaryPerfect, OfNat.ofNat, Nat
Proof uses: Eq.mpr, Eq, Finset.sum, Finset.filter, And, Dvd.dvd, Nat.Coprime, HDiv.hDiv, Finset.Ico, id, Eq.trans, LT.lt, True, congrArg, eq_true, Mathlib.Meta.NormNum.isNat_lt_true, Mathlib.Meta.NormNum.isNat_ofNat, Eq.refl, Bool, Bool.false and 1 more
21 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
theorem Erdos1052.isUnitaryPerfect_87360 line 71 source
depends on sorry what this means
Statement uses: Erdos1052.IsUnitaryPerfect, 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.
theorem Erdos1052.isUnitaryPerfect_146361946186458562560000 sorry line 78 source
depends on sorry what this means
Statement uses: Erdos1052.IsUnitaryPerfect, 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.