Theorems · Theorem · number theory
ZMod.orderOf_dvd_card_sub_one
∀ {p : ℕ} [inst : Fact (Nat.Prime p)] {a : ZMod p}, a ≠ 0 → orderOf a ∣ p - 1- Defined in
- Mathlib.FieldTheory.Finite.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- ZModstatement and proof · cited by 1,024
- orderOfstatement · cited by 324
- orderOf_dvd_of_pow_eq_oneproof · cited by 24
- ZMod.pow_card_sub_one_eq_oneproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Nat.exists_prime_gt_modEq_oneproof · cited by 1
- Nat.pow_pow_add_primeFactors_one_ltproof · cited by 1