Theorems · Theorem · number theory
ZMod.orderOf_one_add_mul_prime_pow
∀ {p : ℕ},
Nat.Prime p → ∀ (m : ℕ), m ≠ 0 → m + 2 ≤ p * m → ∀ (a : ℤ), ¬↑p ∣ a → ∀ (n : ℕ), orderOf (1 + ↑p ^ m * ↑a) = p ^ n- Defined in
- Mathlib.RingTheory.ZMod.UnitsCyclic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Factproof · cited by 2,726
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- mul_commproof · cited by 2,262
- Nat.Primestatement and proof · cited by 2,059
- mul_assocproof · cited by 1,667
- MulZeroClass.zero_mulproof · cited by 1,625
- pow_zeroproof · cited by 1,094
- ZModstatement and proof · cited by 1,024
- mul_addproof · cited by 413
- Int.cast_natCastproof · cited by 393
- pow_succproof · cited by 374
Cited by2
Results whose statement or proof uses this declaration.
- ZMod.orderOf_one_add_four_mulproof · cited by 1
- ZMod.orderOf_one_add_mul_primeproof · cited by 1