Theorems · Theorem · commutative algebra
Int.isCoprime_iff_gcd_eq_one
∀ {m n : ℤ}, IsCoprime m n ↔ m.gcd n = 1- Defined in
- Mathlib.RingTheory.Coprime.Lemmas
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Nat.cast_oneproof · cited by 2,501
- mul_commproof · cited by 2,262
- IsCoprimestatement and proof · cited by 321
- Int.gcdAproof · cited by 7
- Int.gcdBproof · cited by 7
- Int.gcd_eq_gcd_abproof · cited by 6
- Int.gcd_dvd_iffproof · cited by 3
Cited by16
Results whose statement or proof uses this declaration.
- Nat.isCoprime_iff_coprimeproof · cited by 6
- Int.isCoprime_iff_nat_coprimeproof · cited by 3
- Rat.mulHeight₁_eq_maxproof · cited by 2
- ZMod.eq_zero_iff_gcd_ne_oneproof · cited by 2
- ZMod.coe_int_isUnit_iff_isCoprimeproof · cited by 2
- ZMod.coe_int_mul_inv_eq_oneproof · cited by 2
- Fermat42.coprime_of_minimalproof · cited by 2
- EisensteinSeries.mem_gammaSet_oneproof · cited by 1
- Fermat42.exists_odd_minimalproof · cited by 1
- EisensteinSeries.vecMulSL_gcdproof · cited by 1
- Fermat42.not_minimalproof · cited by 1
- Int.sq_of_isCoprimeproof · cited by 0