239957.lean`

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

3 declarations, 1 contain sorry, 0 declared as axioms

Primitive roots of the form k² + 1

Every prime $p$ has a primitive root $0 < g < p$ of the form $k^2 + 1$, where $k$ is an integer.

Zhi-Wei Sun has offered a prize of RMB 2,000 for the first proof.

References:

A239957
Z.-W. Sun, "New observations on primitive roots modulo primes," arXiv:1405.0290 [math.NT], 2014.

Imports (1)

FormalConjecturesUtil

def OeisA239957.A The predicate that $p$ has a primitive root $0 < g < p$ of the form $k^2 + 1$, where $k$ is an integer line 37 source
Source documentation
The predicate that $p$ has a primitive root $0 < g < p$ of the form $k^2 + 1$, where $k$ is an integer.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Exists, Int, And, LT.lt, HAdd.hAdd, HPow.hPow, OfNat.ofNat, Eq, orderOf, ZMod, HSub.hSub
26 instances, coercions and auxiliary constants left out.
```
def A (p : ℕ) : Prop :=
…
```
theorem OeisA239957.a_2 line 41 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: OeisA239957.A, OfNat.ofNat, Nat
Proof uses: Exists.intro, Int, And, LT.lt, HAdd.hAdd, HPow.hPow, Eq, orderOf, ZMod, HSub.hSub, And.intro, Mathlib.Meta.NormNum.isNat_lt_true, Mathlib.Meta.NormNum.isNat_add, Eq.refl, Mathlib.Meta.NormNum.isNat_pow, Mathlib.Meta.NormNum.isNat_ofNat, Mathlib.Meta.NormNum.zero_natPow, Mathlib.Meta.NormNum.isNat_natCast, Bool, Bool.false and 13 more
50 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
theorem OeisA239957.conjecture Zhi-Wei Sun's Conjecture (A239957): Every prime $p$ has a primitive root $0 < g < p$ of the form $k^2 + 1$, where $k$ is an integer sorry line 49 source
Source documentation
Zhi-Wei Sun's Conjecture (A239957): Every prime $p$ has a primitive root $0 < g < p$ of the form $k^2 + 1$, where $k$ is an integer.

depends on sorry what this means
Statement uses: Nat, Nat.Prime, OeisA239957.A
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 conjecture (p : ℕ) (hp : p.Prime) : A p := by
…
```
Mentions: OeisA239957.A