Theorems · Theorem · number theory
Nat.prime_of_pow_sub_one_prime
∀ {a n : ℕ}, n ≠ 1 → Nat.Prime (a ^ n - 1) → a = 2 ∧ Nat.Prime nPrime a ^ n - 1 implies a = 2 and prime n.
- Defined in
- Mathlib.NumberTheory.Fermat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.leproof · cited by 2,189
- Nat.Primestatement and proof · cited by 2,059
- le_rflproof · cited by 1,558
- LT.lt.ne'proof · cited by 1,417
- one_powproof · cited by 521
- LT.lt.transproof · cited by 370
- pow_posproof · cited by 292
- pow_mulproof · cited by 210
- one_posproof · cited by 102
- Nat.Prime.posproof · cited by 83
- tsub_pos_iff_ltproof · cited by 27
- Nat.pow_right_injectiveproof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- Nat.Prime.of_mersenneproof · cited by 1