Theorems · Theorem · number theory
ZMod.eq_one_or_isUnit_sub_one
∀ {n p k : ℕ} [Fact (Nat.Prime p)], n = p ^ k → ∀ (a : ZMod n), (orderOf a).Coprime n → a = 1 ∨ IsUnit (a - 1)- Defined in
- Mathlib.FieldTheory.Finite.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 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.
Cites24
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.cast_oneproof · cited by 2,501
- Nat.Primestatement and proof · cited by 2,059
- Nat.cast_zeroproof · cited by 1,870
- IsUnitstatement and proof · cited by 1,602
- add_commproof · cited by 1,535
- eq_or_neproof · cited by 1,117
- ZModstatement and proof · cited by 1,024
- zero_subproof · cited by 335
- Fact.outproof · cited by 328
- orderOfstatement and proof · cited by 324
- Nat.ModEqproof · cited by 225
Cited by1
Results whose statement or proof uses this declaration.
- IsPGroup.smul_mul_inv_trivial_or_surjectiveproof · cited by 1