Theorems · Theorem · number theory
pow_eq_pow_iff_of_coprime
∀ {α : Type u_1} [inst : CommGroupWithZero α] {a b : α} {m n : ℕ},
m.Coprime n → (a ^ m = b ^ n ↔ ∃ c, a = c ^ n ∧ b = c ^ m)- Defined in
- Mathlib.Data.Int.GCD
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommGroupWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Commute.allproof · cited by 119
- CommGroupWithZerostatement and proof · cited by 94
- Commute.pow_eq_pow_iff_of_coprimeproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- pow_mem_range_pow_of_coprimeproof · cited by 1