273.lean`

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

2 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 273

Reference: erdosproblems.com/273

Imports (1)

FormalConjecturesUtil

theorem Erdos273.erdos_273 Is there a covering system all of whose moduli are of the form $p-1$ for some primes $p \geq 5$? sorry line 33 source
Source documentation
Is there a covering system all of whose moduli are of the form $p-1$ for some primes $p \geq 5$?

depends on sorry what this means
Statement uses: Iff, True, Exists, StrictCoveringSystem, Int, CoveringSystem.ι, StrictCoveringSystem.toCoveringSystem, Nat, And, Nat.Prime, LE.le, OfNat.ofNat, Eq, Ideal, CoveringSystem.moduli, Ideal.span, Singleton.singleton, Set, HSub.hSub
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
18 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_273 : answer(sorry) ↔ ∃ c : StrictCoveringSystem ℤ, ∀ i, ∃ (p : ℕ), p.Prime ∧ 5 ≤ p ∧
    c.moduli i = Ideal.span {↑(p - 1)} := by
…
```
Mentions: c, StrictCoveringSystem
theorem Erdos273.erdos_273.variants.three Is there a covering system all of whose moduli are of the form $p-1$ for some primes $p \geq 3$? sorry line 41 source
Source documentation
Is there a covering system all of whose moduli are of the form $p-1$ for some primes $p \geq 3$?

depends on sorry what this means
Statement uses: Iff, True, Exists, StrictCoveringSystem, Nat, CoveringSystem.ι, StrictCoveringSystem.toCoveringSystem, And, Nat.Prime, LE.le, OfNat.ofNat, Eq, Ideal, CoveringSystem.moduli, Ideal.span, Singleton.singleton, Set, HSub.hSub
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
14 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_273.variants.three : answer(True) ↔ ∃ c : StrictCoveringSystem ℕ, ∀ i, ∃ p, p.Prime ∧ 3 ≤ p ∧
    c.moduli i = Ideal.span {↑(p - 1)} := by
…
```
Mentions: c, StrictCoveringSystem