Theorems · Theorem · group theory
pow_mod_orderOf
∀ {G : Type u_1} [inst : Monoid G] (x : G) (n : ℕ), x ^ (n % orderOf x) = x ^ n- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by12
Results whose statement or proof uses this declaration.
- orderOf_dvd_iff_pow_eq_oneproof · cited by 22
- exists_pow_eq_self_of_coprimeproof · cited by 3
- IsPrimitiveRoot.associated_sub_one_pow_sub_one_of_coprimeproof · cited by 3
- finEquivPowers_symm_applyproof · cited by 2
- IsOfFinOrder.mem_powers_iff_mem_range_orderOfproof · cited by 2
- sum_hom_units_eq_zeroproof · cited by 1
- Equiv.Perm.pow_mod_card_support_cycleOf_self_applyproof · cited by 1
- Equiv.Perm.pow_mod_orderOf_cycleOf_applyproof · cited by 1
- IsPrimitiveRoot.exists_pow_or_neg_mul_pow_of_isOfFinOrderproof · cited by 1
- pow_mod_natCardproof · cited by 1
- mem_powers_iff_mem_range_orderOfproof · cited by 0
- pow_mod_cardproof · cited by 0