Theorems · Theorem · number theory
ZMod.not_isCyclic_units_of_mul_coprime
∀ (m n : ℕ), Odd m → m ≠ 1 → Odd n → n ≠ 1 → m.Coprime n → ¬IsCyclic (ZMod (m * n))ˣ
- Defined in
- Mathlib.RingTheory.ZMod.UnitsCyclic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsstatement and proof · cited by 2,804
- MulEquivproof · cited by 1,142
- ZModstatement and proof · cited by 1,024
- Nat.cardproof · cited by 844
- Oddstatement and proof · cited by 364
- Nat.card_eq_fintype_cardproof · cited by 200
- IsCyclicstatement and proof · cited by 122
- MulEquiv.transproof · cited by 53
- RingEquiv.toMulEquivproof · cited by 26
- Units.mapEquivproof · cited by 16
- ZMod.card_units_eq_totientproof · cited by 15
- MulEquiv.prodUnitsproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- ZMod.isCyclic_units_iff_of_oddproof · cited by 1