Theorems · Theorem · number theory
Nat.prime_iff_card_units
∀ (p : ℕ) [inst : Fintype (ZMod p)ˣ], Nat.Prime p ↔ Fintype.card (ZMod p)ˣ = p - 1
- Defined in
- Mathlib.Data.Nat.Totient
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Unitsstatement and proof · cited by 2,804
- Nat.Primestatement and proof · cited by 2,059
- Fintype.cardstatement and proof · cited by 1,386
- ZModstatement and proof · cited by 1,024
- zero_tsubproof · cited by 100
- NeZero.posproof · cited by 57
- eq_zero_or_neZeroproof · cited by 36
- ZMod.card_units_eq_totientproof · cited by 15
- Nat.totient_eq_iff_primeproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- lucas_primalityproof · cited by 2
- reverse_lucas_primalityproof · cited by 1