Theorems · Theorem · number theory
Nat.coprime_fermatNumber_fermatNumber
∀ {m n : ℕ}, m ≠ n → m.fermatNumber.Coprime n.fermatNumberGoldbach's theorem : no two distinct Fermat numbers share a common factor greater than one. From a letter to Euler, see page 37 in [juskevic2022].
- 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Dvd.dvd.transproof · cited by 148
- Finset.mem_rangeproof · cited by 140
- Nat.prime_twoproof · cited by 55
- Finset.dvd_prod_of_memproof · cited by 23
- Nat.fermatNumberstatement and proof · cited by 21
- Nat.dvd_primeproof · cited by 18
- Odd.not_two_dvd_natproof · cited by 4
- Nat.fermatNumber_eq_prod_add_twoproof · cited by 1
- Nat.odd_fermatNumberproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.pairwise_coprime_fermatNumberproof · cited by 0