Theorems · Theorem · number theory
lucas_primality_iff
∀ (p : ℕ), Nat.Prime p ↔ ∃ a, a ^ (p - 1) = 1 ∧ ∀ (q : ℕ), Nat.Prime q → q ∣ p - 1 → a ^ ((p - 1) / q) ≠ 1
A number p is prime if and only if there exists an a such that
a^(p-1) = 1 mod p and a^((p-1)/q) ≠ 1 mod p for all prime factors q of p-1.
- Defined in
- Mathlib.NumberTheory.LucasPrimality
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
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- Nat.Primestatement and proof · cited by 2,059
- ZModstatement and proof · cited by 1,024
- lucas_primalityproof · cited by 2
- reverse_lucas_primalityproof · cited by 1
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