Prime numbers #
This file deals with the factors of natural numbers.
Important declarations #
Nat.factors n
: the prime factorization ofn
Nat.factors_unique
: uniqueness of the prime factorisation
theorem
Nat.replicate_subperm_factors_iff
{a : ℕ}
{b : ℕ}
{n : ℕ}
(ha : a.Prime)
(hb : b ≠ 0)
:
(List.replicate n a).Subperm b.factors ↔ a ^ n ∣ b
theorem
Nat.coprime_factors_disjoint
{a : ℕ}
{b : ℕ}
(hab : a.Coprime b)
:
a.factors.Disjoint b.factors
The sets of factors of coprime a
and b
are disjoint