Theorems · Theorem · number theory
Nat.exists_eq_two_pow_mul_odd
∀ {n : ℕ}, n ≠ 0 → ∃ k m, Odd m ∧ n = 2 ^ k * mAny nonzero natural number is the product of an odd part m and a power of
two 2 ^ k.
- Defined in
- Mathlib.Data.Nat.Factorization.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Oddstatement and proof · cited by 364
- Nat.not_even_iff_oddproof · cited by 34
- Even.two_dvdproof · cited by 15
- Nat.exists_eq_pow_mul_and_not_dvdproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Nat.pow_of_pow_add_primeproof · cited by 0