1107.lean`

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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 1107

References:

erdosproblems.com/1107
[He88] Heath-Brown, D. R., Ternary quadratic forms and sums of three square-full numbers. (1988)

Imports (1)

FormalConjecturesUtil

def Erdos1107.SumOfRPowerful Helper Property: $n$ is the sum of at most $r+1$ numbers, each of which is $r$-full line 37 source
Source documentation
Helper Property: $n$ is the sum of at most $r+1$ numbers, each of which is $r$-full.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Exists, List, And, LE.le, List.length, HAdd.hAdd, OfNat.ofNat, Membership.mem, Nat.Full, Eq, List.sum
7 instances, coercions and auxiliary constants left out.
```
def SumOfRPowerful (r n : ℕ) : Prop :=
…
```
theorem Erdos1107.erdos_1107 Let $r \ge 2$ sorry line 44 source
Source documentation
Let $r \ge 2$. Is every large integer the sum of at most $r + 1$ many $r$-powerful numbers?

depends on sorry what this means
Statement uses: Nat, GE.ge, OfNat.ofNat, Filter.Eventually, Erdos1107.SumOfRPowerful, Filter.atTop
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_1107 : ∀ r ≥ 2, ∀ᶠ n in atTop, SumOfRPowerful r n := by
…
```
Mentions: Erdos1107.SumOfRPowerful
theorem Erdos1107.erdos_1107.variants.two Heath-Brown [He88] proved every large integer the sum of at most three $2$-powerful numbers sorry line 51 source
Source documentation
Heath-Brown [He88] proved every large integer the sum of at most three $2$-powerful numbers.

depends on sorry what this means
Statement uses: Filter.Eventually, Nat, Erdos1107.SumOfRPowerful, OfNat.ofNat, Filter.atTop
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_1107.variants.two : ∀ᶠ n in atTop, SumOfRPowerful 2 n := by
…
```
Mentions: Erdos1107.SumOfRPowerful