Theorems · Theorem · number theory
Nat.pow_of_pow_add_prime
∀ {a n : ℕ}, 1 < a → n ≠ 0 → Nat.Prime (a ^ n + 1) → ∃ m, n = 2 ^ mPrime a ^ n + 1 implies n is a power of two (Fermat primes).
- Defined in
- Mathlib.NumberTheory.Fermat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Nat.Primestatement and proof · cited by 2,059
- LT.lt.ne'proof · cited by 1,417
- one_powproof · cited by 521
- Oddproof · cited by 364
- two_ne_zeroproof · cited by 251
- pow_mulproof · cited by 210
- pow_ne_zeroproof · cited by 208
- add_left_injproof · cited by 36
- Nat.Prime.dvd_iff_eqproof · cited by 7
- Odd.nat_add_dvd_pow_add_powproof · cited by 1
- Nat.exists_eq_two_pow_mul_oddproof · cited by 1
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