Theorems · Theorem · number theory
Int.ModEq.pow_card_sub_one_eq_one
∀ {p : ℕ}, Nat.Prime p → ∀ {n : ℤ}, IsCoprime n ↑p → n ^ (p - 1) ≡ 1 [ZMOD ↑p]Fermat's Little Theorem: for all a : ℤ coprime to p, we have
a ^ (p - 1) ≡ 1 [ZMOD p].
- Defined in
- Mathlib.FieldTheory.Finite.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Factproof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- ZModproof · cited by 1,024
- Int.cast_oneproof · cited by 371
- IsCoprimestatement and proof · cited by 321
- Int.ModEqstatement · cited by 147
- Int.cast_powproof · cited by 59
- Nat.prime_iff_prime_intproof · cited by 27
- IsCoprime.symmproof · cited by 22
- CharP.intCast_eq_zero_iffproof · cited by 7
- ZMod.pow_card_sub_one_eq_oneproof · cited by 5
- Prime.coprime_iff_not_dvdproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Nat.ModEq.pow_card_sub_one_eq_oneproof · cited by 1
- Int.ModEq.pow_eq_powproof · cited by 0
- Int.prime_dvd_pow_sub_oneproof · cited by 0