Theorems · Theorem · number theory
ZMod.isCyclic_units_two_pow_iff
∀ (n : ℕ), IsCyclic (ZMod (2 ^ n))ˣ ↔ n ≤ 2
- Defined in
- Mathlib.RingTheory.ZMod.UnitsCyclic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Unitsstatement and proof · cited by 2,804
- ZModstatement and proof · cited by 1,024
- IsCyclicstatement and proof · cited by 122
- pow_dvd_powproof · cited by 56
- Nat.prime_twoproof · cited by 55
- ZMod.unitsMapproof · cited by 24
- isCyclic_of_surjectiveproof · cited by 14
- ZMod.unitsMap_surjectiveproof · cited by 7
- ZMod.not_isCyclic_units_eightproof · cited by 2
- ZMod.isCyclic_units_primeproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ArithmeticFunction.carmichael_two_pow_of_le_two_eq_totientproof · cited by 1
- ArithmeticFunction.carmichael_two_pow_of_ne_twoproof · cited by 1