Theorems · Theorem · number theory
Nat.even_pow
∀ {m n : ℕ}, Even (m ^ n) ↔ Even m ∧ n ≠ 0If m and n are natural numbers, then the natural number m^n is even
if and only if m is even and n is positive.
- Defined in
- Mathlib.Algebra.Group.Nat.Even
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Evenstatement and proof · cited by 444
Cited by1
Results whose statement or proof uses this declaration.
- FiniteField.even_card_iff_char_twoproof · cited by 2