Theorems · Theorem · number theory
Nat.ModEq.pow_card_sub_one_eq_one
∀ {p : ℕ}, Nat.Prime p → ∀ {n : ℕ}, n.Coprime p → n ^ (p - 1) ≡ 1 [MOD p]Fermat's Little Theorem: for all n : ℕ coprime to p, we have
n ^ (p - 1) ≡ 1 [MOD p].
- Defined in
- Mathlib.FieldTheory.Finite.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.cast_oneproof · cited by 2,501
- Nat.Primestatement and proof · cited by 2,059
- Nat.ModEqstatement · cited by 225
- Int.ModEqproof · cited by 147
- Nat.cast_powproof · cited by 131
- Nat.isCoprime_iff_coprimeproof · cited by 6
- Int.natCast_modEq_iffproof · cited by 5
- Int.ModEq.pow_card_sub_one_eq_oneproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Nat.pow_card_sub_one_sub_one_mod_cardproof · cited by 0