Theorems · Theorem · number theory
Nat.exists_eq_pow_of_exponent_coprime_of_pow_eq_pow
∀ {a b m n : ℕ}, m.Coprime n → a ^ m = b ^ n → ∃ c, a = c ^ n ∧ b = c ^ m- Defined in
- Mathlib.Data.Nat.Factorization.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsuppproof · cited by 5,255
- Nat.Primeproof · cited by 2,059
- pow_zeroproof · cited by 1,094
- pow_oneproof · cited by 894
- Finsupp.supportproof · cited by 828
- zero_powproof · cited by 361
- Finsupp.prodproof · cited by 231
- Nat.factorizationproof · cited by 215
- Finsupp.mapRangeproof · cited by 91
- Nat.prime_of_mem_primeFactorsproof · cited by 29
- Nat.factorization_powproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Nat.exists_eq_pow_of_pow_eq_powproof · cited by 0