985.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 985

Reference: erdosproblems.com/985

Imports (1)

FormalConjecturesUtil

Imported by 1 file

FormalConjectures/Subsets/FC100SolvedSet1.lean

theorem Erdos985.erdos_985 Is it true that, for every prime $p$, there is a prime $q \leq p$ which is a primitive root modulo $p$? sorry line 34 source
Source documentation
Is it true that, for every prime $p$, there is a prime $q \leq p$ which is a primitive root modulo $p$?

depends on sorry what this means
Statement uses: Iff, True, Nat, Nat.Prime, Ne, OfNat.ofNat, Exists, And, LT.lt, Eq, orderOf, ZMod, HSub.hSub
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
26 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_985 : answer(sorry) ↔ ∀ᵉ (p : ℕ) (hp_prime : p.Prime) (hp_nontrivial : p ≠ 2),
    ∃ q, q.Prime ∧ q < p ∧ orderOf (q : ZMod p) = p - 1 := by
…
```
theorem Erdos985.erdos_985.variants.two_three_five_primitive_root Heath-Brown proved that at least one of 2, 3, or 5 is a primitive root for infinitely many primes $p$ sorry line 45 source
Source documentation
Heath-Brown proved that at least one of 2, 3, or 5 is a primitive root for infinitely many primes $p$.

depends on sorry what this means
Statement uses: Set.Infinite, Nat, Set.ofPred, And, Nat.Prime, Or, Eq, orderOf, ZMod, OfNat.ofNat, HSub.hSub
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
28 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_985.variants.two_three_five_primitive_root :
    Set.Infinite
      {p : ℕ | p.Prime ∧
      (orderOf (2 : ZMod p) = p - 1 ∨
       orderOf (3 : ZMod p) = p - 1 ∨
       orderOf (5 : ZMod p) = p - 1)} := by
…
```