Theorems · Theorem · commutative algebra
IsCoprime.pow_left_iff
∀ {R : Type u} [inst : CommSemiring R] {x y : R} {m : ℕ}, 0 < m → (IsCoprime (x ^ m) y ↔ IsCoprime x y)- Defined in
- Mathlib.RingTheory.Coprime.Lemmas
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- IsCoprimestatement and proof · cited by 321
- Finset.prod_constproof · cited by 154
- Finset.mem_rangeproof · cited by 140
- Finset.card_rangeproof · cited by 108
- IsCoprime.pow_leftproof · cited by 5
- IsCoprime.of_prod_leftproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- IsCoprime.pow_right_iffproof · cited by 1
- ZMod.isSquare_neg_one_of_eq_sq_add_sq_of_isCoprimeproof · cited by 1
- IsCoprime.pow_iffproof · cited by 0
- IsCyclotomicExtension.Rat.isCoprime_of_not_zeta_sub_one_dvdproof · cited by 0